how to time travel quantum physics

• Table of Contents
• Random Entry
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Advanced Tools
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

Time Travel and Modern Physics

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn’t this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

1. Paradoxes Lost?

2. topology and constraints, 3. the general possibility of time travel in general relativity, 4. two toy models, 5. slightly more realistic models of time travel, 6. the possibility of time travel redux, 7. even if there are constraints, so what, 8. computational models, 9. quantum mechanics to the rescue, 10. conclusions, other internet resources, related entries.

• Supplement: Remarks and Limitations on the Toy Models

Modern physics strips away many aspects of the manifest image of time. Time as it appears in the equations of classical mechanics has no need for a distinguished present moment, for example. Relativity theory leads to even sharper contrasts. It replaces absolute simultaneity, according to which it is possible to unambiguously determine the time order of distant events, with relative simultaneity: extending an “instant of time” throughout space is not unique, but depends on the state of motion of an observer. More dramatically, in general relativity the mathematical properties of time (or better, of spacetime)—its topology and geometry—depend upon how matter is arranged rather than being fixed once and for all. So physics can be, and indeed has to be, formulated without treating time as a universal, fixed background structure. Since general relativity represents gravity through spacetime geometry, the allowed geometries must be as varied as the ways in which matter can be arranged. Alongside geometrical models used to describe the solar system, black holes, and much else, the scope of variation extends to include some exotic structures unlike anything astrophysicists have observed. In particular, there are spacetime geometries with curves that loop back on themselves: closed timelike curves (CTCs), which describe the possible trajectory of an observer who returns exactly back to their earlier state—without any funny business, such as going faster than the speed of light. These geometries satisfy the relevant physical laws, the equations of general relativity, and in that sense time travel is physically possible.

Yet circular time generates paradoxes, familiar from science fiction stories featuring time travel: [ 1 ]

• Consistency: Kurt plans to murder his own grandfather Adolph, by traveling along a CTC to an appropriate moment in the past. He is an able marksman, and waits until he has a clear shot at grandpa. Normally he would not miss. Yet if he succeeds, there is no way that he will then exist to plan and carry out the mission. Kurt pulls the trigger: what can happen?
• Underdetermination: Suppose that Kurt first travels back in order to give his earlier self a copy of How to Build a Time Machine. This is the same book that allows him to build a time machine, which he then carries with him on his journey to the past. Who wrote the book?
• Easy Knowledge: A fan of classical music enhances their computer with a circuit that exploits a CTC. This machine efficiently solves problems at a higher level of computational complexity than conventional computers, leading (among other things) to finding the smallest circuits that can generate Bach’s oeuvre—and to compose new pieces in the same style. Such easy knowledge is at odds with our understanding of our epistemic predicament. (This third paradox has not drawn as much attention.)

The first two paradoxes were once routinely taken to show that solutions with CTCs should be rejected—with charges varying from violating logic, to being “physically unreasonable”, to undermining the notion of free will. Closer analysis of the paradoxes has largely reversed this consensus. Physicists have discovered many solutions with CTCs and have explored their properties in pursuing foundational questions, such as whether physics is compatible with the idea of objective temporal passage (starting with Gödel 1949). Philosophers have also used time travel scenarios to probe questions about, among other things, causation, modality, free will, and identity (see, e.g., Earman 1972 and Lewis’s seminal 1976 paper).

We begin below with Consistency , turning to the other paradoxes in later sections. A standard, stone-walling response is to insist that the past cannot be changed, as a matter of logic, even by a time traveler (e.g., Gödel 1949, Clarke 1977, Horwich 1987). Adolph cannot both die and survive, as a matter of logic, so any scheme to alter the past must fail. In many of the best time travel fictions, the actions of a time traveler are constrained in novel and unexpected ways. Attempts to change the past fail, and they fail, often tragically, in just such a way that they set the stage for the time traveler’s self-defeating journey. The first question is whether there is an analog of the consistent story when it comes to physics in the presence of CTCs. As we will see, there is a remarkable general argument establishing the existence of consistent solutions. Yet a second question persists: why can’t time-traveling Kurt kill his own grandfather? Doesn’t the necessity of failures to change the past put unusual and unexpected constraints on time travelers, or objects that move along CTCs? The same argument shows that there are in fact no constraints imposed by the existence of CTCs, in some cases. After discussing this line of argument, we will turn to the palatability and further implications of such constraints if they are required, and then turn to the implications of quantum mechanics.

Wheeler and Feynman (1949) were the first to claim that the fact that nature is continuous could be used to argue that causal influences from later events to earlier events, as are made possible by time travel, will not lead to paradox without the need for any constraints. Maudlin (1990) showed how to make their argument precise and more general, and argued that nonetheless it was not completely general.

Imagine the following set-up. We start off having a camera with a black and white film ready to take a picture of whatever comes out of the time machine. An object, in fact a developed film, comes out of the time machine. We photograph it, and develop the film. The developed film is subsequently put in the time machine, and set to come out of the time machine at the time the picture is taken. This surely will create a paradox: the developed film will have the opposite distribution of black, white, and shades of gray, from the object that comes out of the time machine. For developed black and white films (i.e., negatives) have the opposite shades of gray from the objects they are pictures of. But since the object that comes out of the time machine is the developed film itself it we surely have a paradox.

However, it does not take much thought to realize that there is no paradox here. What will happen is that a uniformly gray picture will emerge, which produces a developed film that has exactly the same uniform shade of gray. No matter what the sensitivity of the film is, as long as the dependence of the brightness of the developed film depends in a continuous manner on the brightness of the object being photographed, there will be a shade of gray that, when photographed, will produce exactly the same shade of gray on the developed film. This is the essence of Wheeler and Feynman’s idea. Let us first be a bit more precise and then a bit more general.

For simplicity let us suppose that the film is always a uniform shade of gray (i.e., at any time the shade of gray does not vary by location on the film). The possible shades of gray of the film can then be represented by the (real) numbers from 0, representing pure black, to 1, representing pure white.

Let us now distinguish various stages in the chronological order of the life of the film. In stage \(S_1\) the film is young; it has just been placed in the camera and is ready to be exposed. It is then exposed to the object that comes out of the time machine. (That object in fact is a later stage of the film itself). By the time we come to stage \(S_2\) of the life of the film, it has been developed and is about to enter the time machine. Stage \(S_3\) occurs just after it exits the time machine and just before it is photographed. Stage \(S_4\) occurs after it has been photographed and before it starts fading away. Let us assume that the film starts out in stage \(S_1\) in some uniform shade of gray, and that the only significant change in the shade of gray of the film occurs between stages \(S_1\) and \(S_2\). During that period it acquires a shade of gray that depends on the shade of gray of the object that was photographed. In other words, the shade of gray that the film acquires at stage \(S_2\) depends on the shade of gray it has at stage \(S_3\). The influence of the shade of gray of the film at stage \(S_3\), on the shade of gray of the film at stage \(S_2\), can be represented as a mapping, or function, from the real numbers between 0 and 1 (inclusive), to the real numbers between 0 and 1 (inclusive). Let us suppose that the process of photography is such that if one imagines varying the shade of gray of an object in a smooth, continuous manner then the shade of gray of the developed picture of that object will also vary in a smooth, continuous manner. This implies that the function in question will be a continuous function. Now any continuous function from the real numbers between 0 and 1 (inclusive) to the real numbers between 0 and 1 (inclusive) must map at least one number to itself. One can quickly convince oneself of this by graphing such functions. For one will quickly see that any continuous function \(f\) from \([0,1]\) to \([0,1]\) must intersect the line \(x=y\) somewhere, and thus there must be at least one point \(x\) such that \(f(x)=x\). Such points are called fixed points of the function. Now let us think about what such a fixed point represents. It represents a shade of gray such that, when photographed, it will produce a developed film with exactly that same shade of gray. The existence of such a fixed point implies a solution to the apparent paradox.

Let us now be more general and allow color photography. One can represent each possible color of an object (of uniform color) by the proportions of blue, green and red that make up that color. (This is why television screens can produce all possible colors.) Thus one can represent all possible colors of an object by three points on three orthogonal lines \(x, y\) and \(z\), that is to say, by a point in a three-dimensional cube. This cube is also known as the “Cartesian product” of the three line segments. Now, one can also show that any continuous map from such a cube to itself must have at least one fixed point. So color photography can not be used to create time travel paradoxes either!

Even more generally, consider some system \(P\) which, as in the above example, has the following life. It starts in some state \(S_1\), it interacts with an object that comes out of a time machine (which happens to be its older self), it travels back in time, it interacts with some object (which happens to be its younger self), and finally it grows old and dies. Let us assume that the set of possible states of \(P\) can be represented by a Cartesian product of \(n\) closed intervals of the reals, i.e., let us assume that the topology of the state-space of \(P\) is isomorphic to a finite Cartesian product of closed intervals of the reals. Let us further assume that the development of \(P\) in time, and the dependence of that development on the state of objects that it interacts with, is continuous. Then, by a well-known fixed point theorem in topology (see, e.g., Hocking & Young 1961: 273), no matter what the nature of the interaction is, and no matter what the initial state of the object is, there will be at least one state \(S_3\) of the older system (as it emerges from the time travel machine) that will influence the initial state \(S_1\) of the younger system (when it encounters the older system) so that, as the younger system becomes older, it develops exactly into state \(S_3\). Thus without imposing any constraints on the initial state \(S_1\) of the system \(P\), we have shown that there will always be perfectly ordinary, non-paradoxical, solutions, in which everything that happens, happens according to the usual laws of development. Of course, there is looped causation, hence presumably also looped explanation, but what do you expect if there is looped time?

Unfortunately, for the fan of time travel, a little reflection suggests that there are systems for which the needed fixed point theorem does not hold. Imagine, for instance, that we have a dial that can only rotate in a plane. We are going to put the dial in the time machine. Indeed we have decided that if we see the later stage of the dial come out of the time machine set at angle \(x\), then we will set the dial to \(x+90\), and throw it into the time machine. Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point. And why wouldn’t some state-spaces have the topology of a circle?

However, we have so far not used another continuity assumption which is also a reasonable assumption. So far we have only made the following demand: the state the dial is in at stage \(S_2\) must be a continuous function of the state of the dial at stage \(S_3\). But, the state of the dial at stage \(S_2\) is arrived at by taking the state of the dial at stage \(S_1\), and rotating it over some angle. It is not merely the case that the effect of the interaction, namely the state of the dial at stage \(S_2\), should be a continuous function of the cause, namely the state of the dial at stage \(S_3\). It is additionally the case that path taken to get there, the way the dial is rotated between stages \(S_1\) and \(S_2\) must be a continuous function of the state at stage \(S_3\). And, rather surprisingly, it turns out that this can not be done. Let us illustrate what the problem is before going to a more general demonstration that there must be a fixed point solution in the dial case.

Forget time travel for the moment. Suppose that you and I each have a watch with a single dial neither of which is running. My watch is set at 12. You are going to announce what your watch is set at. My task is going to be to adjust my watch to yours no matter what announcement you make. And my actions should have a continuous (single valued) dependence on the time that you announce. Surprisingly, this is not possible! For instance, suppose that if you announce “12”, then I achieve that setting on my watch by doing nothing. Now imagine slowly and continuously increasing the announced times, starting at 12. By continuity, I must achieve each of those settings by rotating my dial to the right. If at some point I switch and achieve the announced goal by a rotation of my dial to the left, I will have introduced a discontinuity in my actions, a discontinuity in the actions that I take as a function of the announced angle. So I will be forced, by continuity, to achieve every announcement by rotating the dial to the right. But, this rotation to the right will have to be abruptly discontinued as the announcements grow larger and I eventually approach 12 again, since I achieved 12 by not rotating the dial at all. So, there will be a discontinuity at 12 at the latest. In general, continuity of my actions as a function of announced times can not be maintained throughout if I am to be able to replicate all possible settings. Another way to see the problem is that one can similarly reason that, as one starts with 12, and imagines continuously making the announced times earlier, one will be forced, by continuity, to achieve the announced times by rotating the dial to the left. But the conclusions drawn from the assumption of continuous increases and the assumption of continuous decreases are inconsistent. So we have an inconsistency following from the assumption of continuity and the assumption that I always manage to set my watch to your watch. So, a dial developing according to a continuous dynamics from a given initial state, can not be set up so as to react to a second dial, with which it interacts, in such a way that it is guaranteed to always end up set at the same angle as the second dial. Similarly, it can not be set up so that it is guaranteed to always end up set at 90 degrees to the setting of the second dial. All of this has nothing to do with time travel. However, the impossibility of such set ups is what prevents us from enacting the rotation by 90 degrees that would create paradox in the time travel setting.

Let us now give the positive result that with such dials there will always be fixed point solutions, as long as the dynamics is continuous. Let us call the state of the dial before it interacts with its older self the initial state of the dial. And let us call the state of the dial after it emerges from the time machine the final state of the dial. There is also an intermediate state of the dial, after it interacts with its older self and before it is put into the time machine. We can represent the initial or intermediate states of the dial, before it goes into the time machine, as an angle \(x\) in the horizontal plane and the final state of the dial, after it comes out of the time machine, as an angle \(y\) in the vertical plane. All possible \(\langle x,y\rangle\) pairs can thus be visualized as a torus with each \(x\) value picking out a vertical circular cross-section and each \(y\) picking out a point on that cross-section. See figure 1 .

Figure 1 [An extended description of figure 1 is in the supplement.]

Suppose that the dial starts at angle \(i\) which picks out vertical circle \(I\) on the torus. The initial angle \(i\) that the dial is at before it encounters its older self, and the set of all possible final angles that the dial can have when it emerges from the time machine is represented by the circle \(I\) on the torus (see figure 1 ). Given any possible angle of the emerging dial, the dial initially at angle \(i\) will develop to some other angle. One can picture this development by rotating each point on \(I\) in the horizontal direction by the relevant amount. Since the rotation has to depend continuously on the angle of the emerging dial, circle \(I\) during this development will deform into some loop \(L\) on the torus. Loop \(L\) thus represents all possible intermediate angles \(x\) that the dial is at when it is thrown into the time machine, given that it started at angle \(i\) and then encountered a dial (its older self) which was at angle \(y\) when it emerged from the time machine. We therefore have consistency if \(x=y\) for some \(x\) and \(y\) on loop \(L\). Now, let loop \(C\) be the loop which consists of all the points on the torus for which \(x=y\). Ring \(I\) intersects \(C\) at point \(\langle i,i\rangle\). Obviously any continuous deformation of \(I\) must still intersect \(C\) somewhere. So \(L\) must intersect \(C\) somewhere, say at \(\langle j,j\rangle\). But that means that no matter how the development of the dial starting at \(I\) depends on the angle of the emerging dial, there will be some angle for the emerging dial such that the dial will develop exactly into that angle (by the time it enters the time machine) under the influence of that emerging dial. This is so no matter what angle one starts with, and no matter how the development depends on the angle of the emerging dial. Thus even for a circular state-space there are no constraints needed other than continuity.

Unfortunately there are state-spaces that escape even this argument. Consider for instance a pointer that can be set to all values between 0 and 1, where 0 and 1 are not possible values. That is, suppose that we have a state-space that is isomorphic to an open set of real numbers. Now suppose that we have a machine that sets the pointer to half the value that the pointer is set at when it emerges from the time machine.

Figure 2 [An extended description of figure 2 is in the supplement.]

Suppose the pointer starts at value \(I\). As before we can represent the combination of this initial position and all possible final positions by the line \(I\). Under the influence of the pointer coming out of the time machine the pointer value will develop to a value that equals half the value of the final value that it encountered. We can represent this development as the continuous deformation of line \(I\) into line \(L\), which is indicated by the arrows in figure 2 . This development is fully continuous. Points \(\langle x,y\rangle\) on line \(I\) represent the initial position \(x=I\) of the (young) pointer, and the position \(y\) of the older pointer as it emerges from the time machine. Points \(\langle x,y\rangle\) on line \(L\) represent the position \(x\) that the younger pointer should develop into, given that it encountered the older pointer emerging from the time machine set at position \(y\). Since the pointer is designed to develop to half the value of the pointer that it encounters, the line \(L\) corresponds to \(x=1/2 y\). We have consistency if there is some point such that it develops into that point, if it encounters that point. Thus, we have consistency if there is some point \(\langle x,y\rangle\) on line \(L\) such that \(x=y\). However, there is no such point: lines \(L\) and \(C\) do not intersect. Thus there is no consistent solution, despite the fact that the dynamics is fully continuous.

Of course if 0 were a possible value, \(L\) and \(C\) would intersect at 0. This is surprising and strange: adding one point to the set of possible values of a quantity here makes the difference between paradox and peace. One might be tempted to just add the extra point to the state-space in order to avoid problems. After all, one might say, surely no measurements could ever tell us whether the set of possible values includes that exact point or not. Unfortunately there can be good theoretical reasons for supposing that some quantity has a state-space that is open: the set of all possible speeds of massive objects in special relativity surely is an open set, since it includes all speeds up to, but not including, the speed of light. Quantities that have possible values that are not bounded also lead to counter examples to the presented fixed point argument. And it is not obvious to us why one should exclude such possibilities. So the argument that no constraints are needed is not fully general.

An interesting question of course is: exactly for which state-spaces must there be such fixed points? The arguments above depend on a well-known fixed point theorem (due to Schauder) that guarantees the existence of a fixed point for compact, convex state spaces. We do not know what subsequent extensions of this result imply regarding fixed points for a wider variety of systems, or whether there are other general results along these lines. (See Kutach 2003 for more on this issue.)

A further interesting question is whether this line of argument is sufficient to resolve Consistency (see also Dowe 2007). When they apply, these results establish the existence of a solution, such as the shade of uniform gray in the first example. But physicists routinely demand more than merely the existence of a solution, namely that solutions to the equations are stable—such that “small” changes of the initial state lead to “small” changes of the resulting trajectory. (Clarifying the two senses of “small” in this statement requires further work, specifying the relevant topology.) Stability in this sense underwrites the possibility of applying equations to real systems given our inability to fix initial states with indefinite precision. (See Fletcher 2020 for further discussion.) The fixed point theorems guarantee that for an initial state \(S_1\) there is a solution, but this solution may not be “close” to the solution for a nearby initial state, \(S'\). We are not aware of any proofs that the solutions guaranteed to exist by the fixed point theorems are also stable in this sense.

Time travel has recently been discussed quite extensively in the context of general relativity. General relativity places few constraints on the global structure of space and time. This flexibility leads to a possibility first described in print by Hermann Weyl:

Every world-point is the origin of the double-cone of the active future and the passive past [i.e., the two lobes of the light cone]. Whereas in the special theory of relativity these two portions are separated by an intervening region, it is certainly possible in the present case [i.e., general relativity] for the cone of the active future to overlap with that of the passive past; so that, in principle, it is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a timelike direction at every point, to return to the neighborhood of a point which it has already once passed through. (Weyl 1918/1920 [1952: 274])

A time-like curve is simply a space-time trajectory such that the speed of light is never equaled or exceeded along this trajectory. Time-like curves represent possible trajectories of ordinary objects. In general relativity a curve that is everywhere timelike locally can nonetheless loop back on itself, forming a CTC. Weyl makes the point vividly in terms of the light cones: along such a curve, the future lobe of the light cone (the “active future”) intersects the past lobe of the light cone (the “passive past”). Traveling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited. Or, by staying close to such a CTC, one could come arbitrarily close to a point in space-time that one previously visited. General relativity, in a straightforward sense, allows time travel: there appear to be many space-times compatible with the fundamental equations of general relativity in which there are CTC’s. Space-time, for instance, could have a Minkowski metric everywhere, and yet have CTC’s everywhere by having the temporal dimension (topologically) rolled up as a circle. Or, one can have wormhole connections between different parts of space-time which allow one to enter “mouth \(A\)” of such a wormhole connection, travel through the wormhole, exit the wormhole at “mouth \(B\)” and re-enter “mouth \(A\)” again. CTCs can even arise when the spacetime is topologically \(\mathbb{R}^4\), due to the “tilting” of light cones produced by rotating matter (as in Gödel 1949’s spacetime).

General relativity thus appears to provide ample opportunity for time travel. Note that just because there are CTC’s in a space-time, this does not mean that one can get from any point in the space-time to any other point by following some future directed timelike curve—there may be insurmountable practical obstacles. In Gödel’s spacetime, it is the case that there are CTCs passing through every point in the spacetime. Yet these CTCs are not geodesics, so traversing them requires acceleration. Calculations of the minimal fuel required to travel along the appropriate curve should discourage any would-be time travelers (Malament 1984, 1985; Manchak 2011). But more generally CTCs may be confined to smaller regions; some parts of space-time can have CTC’s while other parts do not. Let us call the part of a space-time that has CTC’s the “time travel region” of that space-time, while calling the rest of that space-time the “normal region”. More precisely, the “time travel region” consists of all the space-time points \(p\) such that there exists a (non-zero length) timelike curve that starts at \(p\) and returns to \(p\). Now let us turn to examining space-times with CTC’s a bit more closely for potential problems.

In order to get a feeling for the sorts of implications that closed timelike curves can have, it may be useful to consider two simple models. In space-times with closed timelike curves the traditional initial value problem cannot be framed in the usual way. For it presupposes the existence of Cauchy surfaces, and if there are CTCs then no Cauchy surface exists. (A Cauchy surface is a spacelike surface such that every inextendable timelike curve crosses it exactly once. One normally specifies initial conditions by giving the conditions on such a surface.) Nonetheless, if the topological complexities of the manifold are appropriately localized, we can come quite close. Let us call an edgeless spacelike surface \(S\) a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that

• every point in the manifold can be connected by a timelike curve to \(S\), and
• any timelike curve which connects a point in one region to a point in the other region intersects \(S\) exactly once.

It is obvious that a quasi-Cauchy surface must entirely inhabit the normal region of the space-time; if any point \(p\) of \(S\) is in the time travel region, then any timelike curve which intersects \(p\) can be extended to a timelike curve which intersects \(S\) near \(p\) again. In extreme cases of time travel, a model may have no normal region at all (e.g., Minkowski space-time rolled up like a cylinder in a time-like direction), in which case our usual notions of temporal precedence will not apply. But temporal anomalies like wormholes (and time machines) can be sufficiently localized to permit the existence of quasi-Cauchy surfaces.

Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from \(S)\) and its future (ditto mutatis mutandis ). If the whole past of \(S\) is in the normal region of the manifold, then \(S\) is a partial Cauchy surface : every inextendable timelike curve which exists to the past of \(S\) intersects \(S\) exactly once, but (if there is time travel in the future) not every inextendable timelike curve which exists to the future of \(S\) intersects \(S\). Now we can ask a particularly clear question: consider a manifold which contains a time travel region, but also has a partial Cauchy surface \(S\), such that all of the temporal funny business is to the future of \(S\). If all you could see were \(S\) and its past, you would not know that the space-time had any time travel at all. The question is: are there any constraints on the sort of data which can be put on \(S\) and continued to a global solution of the dynamics which are different from the constraints (if any) on the data which can be put on a Cauchy surface in a simply connected manifold and continued to a global solution? If there is time travel to our future, might we we able to tell this now, because of some implied oddity in the arrangement of present things?

It is not at all surprising that there might be constraints on the data which can be put on a locally space-like surface which passes through the time travel region: after all, we never think we can freely specify what happens on a space-like surface and on another such surface to its future, but in this case the surface at issue lies to its own future. But if there were particular constraints for data on a partial Cauchy surface then we would apparently need to have to rule out some sorts of otherwise acceptable states on \(S\) if there is to be time travel to the future of \(S\). We then might be able to establish that there will be no time travel in the future by simple inspection of the present state of the universe. As we will see, there is reason to suspect that such constraints on the partial Cauchy surface are non-generic. But we are getting ahead of ourselves: first let’s consider the effect of time travel on a very simple dynamics.

The simplest possible example is the Newtonian theory of perfectly elastic collisions among equally massive particles in one spatial dimension. The space-time is two-dimensional, so we can represent it initially as the Euclidean plane, and the dynamics is completely specified by two conditions. When particles are traveling freely, their world lines are straight lines in the space-time, and when two particles collide, they exchange momenta, so the collision looks like an “\(X\)” in space-time, with each particle changing its momentum at the impact. [ 2 ] The dynamics is purely local, in that one can check that a set of world-lines constitutes a model of the dynamics by checking that the dynamics is obeyed in every arbitrarily small region. It is also trivial to generate solutions from arbitrary initial data if there are no CTCs: given the initial positions and momenta of a set of particles, one simply draws a straight line from each particle in the appropriate direction and continues it indefinitely. Once all the lines are drawn, the worldline of each particle can be traced from collision to collision. The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.

What happens if we change the topology of the space-time by hand to produce CTCs? The simplest way to do this is depicted in figure 3 : we cut and paste the space-time so it is no longer simply connected by identifying the line \(L-\) with the line \(L+\). Particles “going in” to \(L+\) from below “emerge” from \(L-\) , and particles “going in” to \(L-\) from below “emerge” from \(L+\).

Figure 3: Inserting CTCs by Cut and Paste. [An extended description of figure 3 is in the supplement.]

How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice \(S\) and continue it to a unique solution. After the change in topology, \(S\) is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on \(S\) always be continued to a global solution? Second, is that solution unique? If the answer to the first question is \(no\), then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on \(S\) even though that region lies completely to the future of \(S\). If the answer to the second question is \(no\), then we have an odd sort of indeterminism, analogous to the unwritten book: the complete physical state on \(S\) does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in \(S\)’s future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).

In this case the answer to the first question is yes and to the second is no : there are no constraints on the data which can be put on \(S\), but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from \(S\) as required by the initial data. If a line hits \(L-\) from the bottom, just continue it coming out of the top of \(L+\) in the appropriate place, and if a line hits \(L+\) from the bottom, continue it emerging from \(L-\) at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left:

Figure 4: The Minimal Solution. [An extended description of figure 4 is in the supplement.]

The particle “travels back in time” three times. It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

But the same initial state on \(S\) is also consistent with other global solutions. The new requirement imposed by the topology is just that the data going into \(L+\) from the bottom match the data coming out of \(L-\) from the top, and the data going into \(L-\) from the bottom match the data coming out of \(L+\) from the top. So we can add any number of vertical lines connecting \(L-\) and \(L+\) to a solution and still have a solution. For example, adding a few such lines to the minimal solution yields:

Figure 5: A Non-Minimal Solution. [An extended description of figure 5 is in the supplement.]

The particle now collides with itself twice: first before it reaches \(L+\) for the first time, and again shortly before it exits the CTC region. From the particle’s point of view, it is traveling to the right at a constant speed until it hits an older version of itself and comes to rest. It remains at rest until it is hit from the right by a younger version of itself, and then continues moving off, and the same process repeats later. It is clear that this is a global model of the dynamics, and that any number of distinct models could be generating by varying the number and placement of vertical lines.

Knowing the data on \(S\), then, gives us only incomplete information about how things will go for the particle. We know that the particle will enter the CTC region, and will reach \(L+\), we know that it will be the only particle in the universe, we know exactly where and with what speed it will exit the CTC region. But we cannot determine how many collisions the particle will undergo (if any), nor how long (in proper time) it will stay in the CTC region. If the particle were a clock, we could not predict what time it would indicate when exiting the region. Furthermore, the dynamics gives us no handle on what to think of the various possibilities: there are no probabilities assigned to the various distinct possible outcomes.

Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, \(S\) is no longer a Cauchy surface, so it is perhaps not surprising that data on \(S\) do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of \(L-\) must exactly match data “going in” to \(L+\), even though what comes out of \(L-\) helps to determine what goes into \(L+\). This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on \({L+}/{L-}\).

The fact that the extra freedom outweighs the extra constraint also points up one unexpected way that the supposed paradoxes of time travel may be overcome. Let’s try to set up a paradoxical situation using the little closed time loop above. If we send a single particle into the loop from the left and do nothing else, we know exactly where it will exit the right side of the time travel region. Now suppose we station someone at the other side of the region with the following charge: if the particle should come out on the right side, the person is to do something to prevent the particle from going in on the left in the first place. In fact, this is quite easy to do: if we send a particle in from the right, it seems that it can exit on the left and deflect the incoming left-hand particle.

Carrying on our reflection in this way, we further realize that if the particle comes out on the right, we might as well send it back in order to deflect itself from entering in the first place. So all we really need to do is the following: set up a perfectly reflecting particle mirror on the right-hand side of the time travel region, and launch the particle from the left so that— if nothing interferes with it —it will just barely hit \(L+\). Our paradox is now apparently complete. If, on the one hand, nothing interferes with the particle it will enter the time-travel region on the left, exit on the right, be reflected from the mirror, re-enter from the right, and come out on the left to prevent itself from ever entering. So if it enters, it gets deflected and never enters. On the other hand, if it never enters then nothing goes in on the left, so nothing comes out on the right, so nothing is reflected back, and there is nothing to deflect it from entering. So if it doesn’t enter, then there is nothing to deflect it and it enters. If it enters, then it is deflected and doesn’t enter; if it doesn’t enter then there is nothing to deflect it and it enters: paradox complete.

But at least one solution to the supposed paradox is easy to construct: just follow the recipe for constructing the minimal solution, continuing the initial trajectory of the particle (reflecting it the mirror in the obvious way) and then read of the number and trajectories of the particles from the resulting diagram. We get the result of figure 6 :

Figure 6: Resolving the “Paradox”. [An extended description of figure 6 is in the supplement.]

As we can see, the particle approaching from the left never reaches \(L+\): it is deflected first by a particle which emerges from \(L-\). But it is not deflected by itself , as the paradox suggests, it is deflected by another particle. Indeed, there are now four particles in the diagram: the original particle and three particles which are confined to closed time-like curves. It is not the leftmost particle which is reflected by the mirror, nor even the particle which deflects the leftmost particle; it is another particle altogether.

The paradox gets it traction from an incorrect presupposition. If there is only one particle in the world at \(S\) then there is only one particle which could participate in an interaction in the time travel region: the single particle would have to interact with its earlier (or later) self. But there is no telling what might come out of \(L-\): the only requirement is that whatever comes out must match what goes in at \(L+\). So if you go to the trouble of constructing a working time machine, you should be prepared for a different kind of disappointment when you attempt to go back and kill yourself: you may be prevented from entering the machine in the first place by some completely unpredictable entity which emerges from it. And once again a peculiar sort of indeterminism appears: if there are many self-consistent things which could prevent you from entering, there is no telling which is even likely to materialize. This is just like the case of the unwritten book: the book is never written, so nothing determines what fills its pages.

So when the freedom to put data on \(L-\) outweighs the constraint that the same data go into \(L+\), instead of paradox we get an embarrassment of riches: many solution consistent with the data on \(S\), or many possible books. To see a case where the constraint “outweighs” the freedom, we need to construct a very particular, and frankly artificial, dynamics and topology. Consider the space of all linear dynamics for a scalar field on a lattice. (The lattice can be though of as a simple discrete space-time.) We will depict the space-time lattice as a directed graph. There is to be a scalar field defined at every node of the graph, whose value at a given node depends linearly on the values of the field at nodes which have arrows which lead to it. Each edge of the graph can be assigned a weighting factor which determines how much the field at the input node contributes to the field at the output node. If we name the nodes by the letters a , b , c , etc., and the edges by their endpoints in the obvious way, then we can label the weighting factors by the edges they are associated with in an equally obvious way.

Suppose that the graph of the space-time lattice is acyclic , as in figure 7 . (A graph is Acyclic if one can not travel in the direction of the arrows and go in a loop.)

Figure 7: An Acyclic Lattice. [An extended description of figure 7 is in the supplement.]

It is easy to regard a set of nodes as the analog of a Cauchy surface, e.g., the set \(\{a, b, c\}\), and it is obvious if arbitrary data are put on those nodes the data will generate a unique solution in the future. [ 3 ] If the value of the field at node \(a\) is 3 and at node \(b\) is 7, then its value at node \(d\) will be \(3W_{ad}\) and its value at node \(e\) will be \(3W_{ae} + 7W_{be}\). By varying the weighting factors we can adjust the dynamics, but in an acyclic graph the future evolution of the field will always be unique.

Let us now again artificially alter the topology of the lattice to admit CTCs, so that the graph now is cyclic. One of the simplest such graphs is depicted in figure 8 : there are now paths which lead from \(z\) back to itself, e.g., \(z\) to \(y\) to \(z\).

Figure 8: Time Travel on a Lattice. [An extended description of figure 8 is in the supplement.]

Can we now put arbitrary data on \(v\) and \(w\), and continue that data to a global solution? Will the solution be unique?

In the generic case, there will be a solution and the solution will be unique. The equations for the value of the field at \(x, y\), and \(z\) are:

Solving these equations for \(z\) yields

which gives a unique value for \(z\) in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where \(1-W_{zx}W_{xz} - W_{zy}W_{yz} = 0\). If we choose weighting factors in just this way, then arbitrary data at \(v\) and \(w\) cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at \(v\) and \(w\): the field there must be zero (assuming \(W_{vx}\) and \(W_{wy}\) to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at \(v\) and \(w\) must be so chosen that \(vW_{vx}W_{xz} = -wW_{wy}W_{yz}\). In either case, the field values at \(v\) and \(w\) are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.

Our toy models suggest three things. The first is that it may be impossible to prove in complete generality that arbitrary data on a partial Cauchy surface can always be continued to a global solution: our artificial case provides an example where it cannot. The second is that such odd constraints are not likely to be generic: we had to delicately fine-tune the dynamics to get a problem. The third is that the opposite problem, namely data on a partial Cauchy surface being consistent with many different global solutions, is likely to be generic: we did not have to do any fine-tuning to get this result.

This third point leads to a peculiar sort of indeterminism, illustrated by the case of the unwritten book: the entire state on \(S\) does not determine what will happen in the future even though the local dynamics is deterministic and there are no other “edges” to space-time from which data could influence the result. What happens in the time travel region is constrained but not determined by what happens on \(S\), and the dynamics does not even supply any probabilities for the various possibilities. The example of the photographic negative discussed in section 2, then, seems likely to be unusual, for in that case there is a unique fixed point for the dynamics, and the set-up plus the dynamical laws determine the outcome. In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized. (See the supplement on

Remarks and Limitations on the Toy Models .

It is ironic that time travel should lead generically not to contradictions or to constraints (in the normal region) but to underdetermination of what happens in the time travel region by what happens everywhere else (an underdetermination tied neither to a probabilistic dynamics nor to a free edge to space-time). The traditional objection to time travel is that it leads to contradictions: there is no consistent way to complete an arbitrarily constructed story about how the time traveler intends to act. Instead, though, it appears that the more significant problem is underdetermination: the story can be consistently completed in many different ways.

Echeverria, Klinkhammer, and Thorne (1991) considered the case of 3-dimensional single hard spherical ball that can go through a single time travel wormhole so as to collide with its younger self.

Figure 9 [An extended description of figure 9 is in the supplement.]

The threat of paradox in this case arises in the following form. Consider the initial trajectory of a ball as it approaches the time travel region. For some initial trajectories, the ball does not undergo a collision before reaching mouth 1, but upon exiting mouth 2 it will collide with its earlier self. This leads to a contradiction if the collision is strong enough to knock the ball off its trajectory and deflect it from entering mouth 1. Of course, the Wheeler-Feynman strategy is to look for a “glancing blow” solution: a collision which will produce exactly the (small) deviation in trajectory of the earlier ball that produces exactly that collision. Are there always such solutions? [ 4 ]

Echeverria, Klinkhammer & Thorne found a large class of initial trajectories that have consistent “glancing blow” continuations, and found none that do not (but their search was not completely general). They did not produce a rigorous proof that every initial trajectory has a consistent continuation, but suggested that it is very plausible that every initial trajectory has a consistent continuation. That is to say, they have made it very plausible that, in the billiard ball wormhole case, the time travel structure of such a wormhole space-time does not result in constraints on states on spacelike surfaces in the non-time travel region.

In fact, as one might expect from our discussion in the previous section, they found the opposite problem from that of inconsistency: they found underdetermination. For a large class of initial trajectories there are multiple different consistent “glancing blow” continuations of that trajectory (many of which involve multiple wormhole traversals). For example, if one initially has a ball that is traveling on a trajectory aimed straight between the two mouths, then one obvious solution is that the ball passes between the two mouths and never time travels. But another solution is that the younger ball gets knocked into mouth 1 exactly so as to come out of mouth 2 and produce that collision. Echeverria et al. do not note the possibility (which we pointed out in the previous section) of the existence of additional balls in the time travel region. We conjecture (but have no proof) that for every initial trajectory of \(A\) there are some, and generically many, multiple-ball continuations.

Friedman, Morris, et al. (1990) examined the case of source-free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes. In general there appear to be no known counter examples to the claim that in “somewhat realistic” time-travel space-times with a partial Cauchy surface there are no constraints imposed on the state on such a partial Cauchy surface by the existence of CTC’s. (See, e.g., Friedman & Morris 1991; Thorne 1994; Earman 1995; Earman, Smeenk, & Wüthrich 2009; and Dowe 2007.)

How about the issue of constraints in the time travel region \(T\)? Prima facie , constraints in such a region would not appear to be surprising. But one might still expect that there should be no constraints on states on a spacelike surface, provided one keeps the surface “small enough”. In the physics literature the following question has been asked: for any point \(p\) in \(T\), and any space-like surface \(S\) that includes \(p\) is there a neighborhood \(E\) of \(p\) in \(S\) such that any solution on \(E\) can be extended to a solution on the whole space-time? With respect to this question, there are some simple models in which one has this kind of extendability of local solutions to global ones, and some simple models in which one does not have such extendability, with no clear general pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See, e.g., Yurtsever 1990; Friedman, Morris, et al. 1990; Novikov 1992; Earman 1995; and Earman, Smeenk, & Wüthrich 2009). What are we to think of all of this?

The toy models above all treat billiard balls, fields, and other objects propagating through a background spacetime with CTCs. Even if we can show that a consistent solution exists, there is a further question: what kind of matter and dynamics could generate CTCs to begin with? There are various solutions of Einstein’s equations with CTCs, but how do these exotic spacetimes relate to the models actually used in describing the world? In other words, what positive reasons might we have to take CTCs seriously as a feature of the actual universe, rather than an exotic possibility of primarily mathematical interest?

We should distinguish two different kinds of “possibility” that we might have in mind in posing such questions (following Stein 1970). First, we can consider a solution as a candidate cosmological model, describing the (large-scale gravitational degrees of freedom of the) entire universe. The case for ruling out spacetimes with CTCs as potential cosmological models strikes us as, surprisingly, fairly weak. Physicists used to simply rule out solutions with CTCs as unreasonable by fiat, due to the threat of paradoxes, which we have dismantled above. But it is also challenging to make an observational case. Observations tell us very little about global features, such as the existence of CTCs, because signals can only reach an observer from a limited region of spacetime, called the past light cone. Our past light cone—and indeed the collection of all the past light cones for possible observers in a given spacetime—can be embedded in spacetimes with quite different global features (Malament 1977, Manchak 2009). This undercuts the possibility of using observations to constrain global topology, including (among other things) ruling out the existence of CTCs.

Yet the case in favor of taking cosmological models with CTCs seriously is also not particularly strong. Some solutions used to describe black holes, which are clearly relevant in a variety of astrophysical contexts, include CTCs. But the question of whether the CTCs themselves play an essential representational role is subtle: the CTCs arise in the maximal extensions of these solutions, and can plausibly be regarded as extraneous to successful applications. Furthermore, many of the known solutions with CTCs have symmetries, raising the possibility that CTCs are not a stable or robust feature. Slight departures from symmetry may lead to a solution without CTCs, suggesting that the CTCs may be an artifact of an idealized model.

The second sense of possibility regards whether “reasonable” initial conditions can be shown to lead to, or not to lead to, the formation of CTCs. As with the toy models above, suppose that we have a partial Cauchy surface \(S\), such that all the temporal funny business lies to the future. Rather than simply assuming that there is a region with CTCs to the future, we can ask instead whether it is possible to create CTCs by manipulating matter in the initial, well-behaved region—that is, whether it is possible to build a time machine. Several physicists have pursued “chronology protection theorems” aiming to show that the dynamics of general relativity (or some other aspects of physics) rules this out, and to clarify why this is the case. The proof of such a theorem would justify neglecting solutions with CTCs as a source of insight into the nature of time in the actual world. But as of yet there are several partial results that do not fully settle the question. One further intriguing possibility is that even if general relativity by itself does protect chronology, it may not be possible to formulate a sensible theory describing matter and fields in solutions with CTCs. (See SEP entry on Time Machines; Smeenk and Wüthrich 2011 for more.)

There is a different question regarding the limitations of these toy models. The toy models and related examples show that there are consistent solutions for simple systems in the presence of CTCs. As usual we have made the analysis tractable by building toy models, selecting only a few dynamical degrees of freedom and tracking their evolution. But there is a large gap between the systems we have described and the time travel stories they evoke, with Kurt traveling along a CTC with murderous intentions. In particular, many features of the manifest image of time are tied to the thermodynamical properties of macroscopic systems. Rovelli (unpublished) considers a extremely simple system to illustrate the problem: can a clock move along a CTC? A clock consists of something in periodic motion, such as a pendulum bob, and something that counts the oscillations, such as an escapement mechanism. The escapement mechanism cannot work without friction; this requires dissipation and increasing entropy. For a clock that counts oscillations as it moves along a time-like trajectory, the entropy must be a monotonically increasing function. But that is obviously incompatible with the clock returning to precisely the same state at some future time as it completes a loop. The point generalizes, obviously, to imply that anything like a human, with memory and agency, cannot move along a CTC.

Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it. We will now examine this argument in more detail by presenting four possible responses, with counterresponses, to this argument.

Response 1. There is nothing implausible or new about such constraints. For instance, if the universe is spatially closed, there has to be enough matter to produce the needed curvature, and this puts constraints on the matter distribution on a space-like hypersurface. Thus global space-time structure can quite unproblematically constrain matter distributions on space-like hypersurfaces in it. Moreover we have no realistic idea what these constraints look like, so we hardly can be said to have evidence that they do not obtain.

Counterresponse 1. Of course there are constraining relations between the global structure of space-time and the matter in it. The Einstein equations relate curvature of the manifold to the matter distribution in it. But what is so strange and implausible about the constraints imposed by the existence of closed time-like curves is that these constraints in essence have nothing to do with the Einstein equations. When investigating such constraints one typically treats the particles and/or field in question as test particles and/or fields in a given space-time, i.e., they are assumed not to affect the metric of space-time in any way. In typical space-times without closed time-like curves this means that one has, in essence, complete freedom of matter distribution on a space-like hypersurface. (See response 2 for some more discussion of this issue). The constraints imposed by the possibility of time travel have a quite different origin and are implausible. In the ordinary case there is a causal interaction between matter and space-time that results in relations between global structure of space-time and the matter distribution in it. In the time travel case there is no such causal story to be told: there simply has to be some pre-established harmony between the global space-time structure and the matter distribution on some space-like surfaces. This is implausible.

Response 2. Constraints upon matter distributions are nothing new. For instance, Maxwell’s equations constrain electric fields \(\boldsymbol{E}\) on an initial surface to be related to the (simultaneous) charge density distribution \(\varrho\) by the equation \(\varrho = \text{div}(\boldsymbol{E})\). (If we assume that the \(E\) field is generated solely by the charge distribution, this conditions amounts to requiring that the \(E\) field at any point in space simply be the one generated by the charge distribution according to Coulomb’s inverse square law of electrostatics.) This is not implausible divine harmony. Such constraints can hold as a matter of physical law. Moreover, if we had inferred from the apparent free variation of conditions on spatial regions that there could be no such constraints we would have mistakenly inferred that \(\varrho = \text{div}(\boldsymbol{E})\) could not be a law of nature.

Counterresponse 2. The constraints imposed by the existence of closed time-like lines are of quite a different character from the constraint imposed by \(\varrho = \text{div}(\boldsymbol{E})\). The constraints imposed by \(\varrho = \text{div}(\boldsymbol{E})\) on the state on a space-like hypersurface are:

• local constraints (i.e., to check whether the constraint holds in a region you just need to see whether it holds at each point in the region),
• quite independent of the global space-time structure,
• quite independent of how the space-like surface in question is embedded in a given space-time, and
• very simply and generally stateable.

On the other hand, the consistency constraints imposed by the existence of closed time-like curves (i) are not local, (ii) are dependent on the global structure of space-time, (iii) depend on the location of the space-like surface in question in a given space-time, and (iv) appear not to be simply stateable other than as the demand that the state on that space-like surface embedded in such and such a way in a given space-time, do not lead to inconsistency. On some views of laws (e.g., David Lewis’ view) this plausibly implies that such constraints, even if they hold, could not possibly be laws. But even if one does not accept such a view of laws, one could claim that the bizarre features of such constraints imply that it is implausible that such constraints hold in our world or in any world remotely like ours.

Response 3. It would be strange if there are constraints in the non-time travel region. It is not strange if there are constraints in the time travel region. They should be explained in terms of the strange, self-interactive, character of time travel regions. In this region there are time-like trajectories from points to themselves. Thus the state at such a point, in such a region, will, in a sense, interact with itself. It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity. Normally, of course, self-interaction isn’t true instantaneous self-interaction, but consists of a feed-back mechanism that takes time. But in time travel regions something like true instantaneous self-interaction occurs. This explains why constraints on states occur in such time travel regions: the states “ ab initio ” have to be “equilibrium states”. Indeed in a way this also provides some picture of why indeterminism occurs in time travel regions: at the onset of self-interaction states can fork into different equi-possible equilibrium states.

Counterresponse 3. This is explanation by woolly analogy. It all goes to show that time travel leads to such bizarre consequences that it is unlikely that it occurs in a world remotely like ours.

Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point \(p\) are ruled out if one holds that space-time structure fixed. One might then ask

Why does the actual state near \(p\) in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near \(p\) had been slightly different?

And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of \(p\) been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface \(S\) can always be embedded into a space-time such that that state on \(S\) consistently extends to a solution on the entire space-time.

But we know the answer to that question. A well-known theorem in general relativity says the following: any initial data set on a three dimensional manifold \(S\) with positive definite metric has a unique embedding into a maximal space-time in which \(S\) is a Cauchy surface (see, e.g., Geroch & Horowitz 1979: 284 for more detail), i.e., there is a unique largest space-time which has \(S\) as a Cauchy surface and contains a consistent evolution of the initial value data on \(S\). Now since \(S\) is a Cauchy surface this space-time does not have closed time like curves. But it may have extensions (in which \(S\) is not a Cauchy surface) which include closed timelike curves, indeed it may be that any maximal extension of it would include closed timelike curves. (This appears to be the case for extensions of states on certain surfaces of Taub-NUT space-times. See Earman, Smeenk, & Wüthrich 2009). But these extensions, of course, will be consistent. So properly speaking, there are no constraints on states on space-like surfaces. Nonetheless the space-time in which these are embedded may or may not include closed time-like curves.

Counterresponse 4. This, in essence, is the stonewalling answer which we indicated in section 1. However, whether or not you call the constraints imposed by a given space-time on distributions of matter on certain space-like surfaces “genuine constraints”, whether or not they can be considered lawlike, and whether or not they need to be explained, the existence of such constraints can still be used to argue that time travel worlds are so bizarre that it is implausible that our world or any world remotely like ours is a time travel world.

Suppose that one is in a time travel world. Suppose that given the global space-time structure of this world, there are constraints imposed upon, say, the state of motion of a ball on some space-like surface when it is treated as a test particle, i.e., when it is assumed that the ball does not affect the metric properties of the space-time it is in. (There is lots of other matter that, via the Einstein equation, corresponds exactly to the curvature that there is everywhere in this time travel worlds.) Now a real ball of course does have some effect on the metric of the space-time it is in. But let us consider a ball that is so small that its effect on the metric is negligible. Presumably it will still be the case that certain states of this ball on that space-like surface are not compatible with the global time travel structure of this universe.

This means that the actual distribution of matter on such a space-like surface can be extended into a space-time with closed time-like lines, but that certain counterfactual distributions of matter on this space-like surface can not be extended into the same space-time. But note that the changes made in the matter distribution (when going from the actual to the counterfactual distribution) do not in any non-negligible way affect the metric properties of the space-time. (Recall that the changes only effect test particles.) Thus the reason why the global time travel properties of the counterfactual space-time have to be significantly different from the actual space-time is not that there are problems with metric singularities or alterations in the metric that force significant global changes when we go to the counterfactual matter distribution. The reason that the counterfactual space-time has to be different is that in the counterfactual world the ball’s initial state of motion starting on the space-like surface, could not “meet up” in a consistent way with its earlier self (could not be consistently extended) if we were to let the global structure of the counterfactual space-time be the same as that of the actual space-time. Now, it is not bizarre or implausible that there is a counterfactual dependence of manifold structure, even of its topology, on matter distributions on spacelike surfaces. For instance, certain matter distributions may lead to singularities, others may not. We may indeed in some sense have causal power over the topology of the space-time we live in. But this power normally comes via the Einstein equations. But it is bizarre to think that there could be a counterfactual dependence of global space-time structure on the arrangement of certain tiny bits of matter on some space-like surface, where changes in that arrangement by assumption do not affect the metric anywhere in space-time in any significant way . It is implausible that we live in such a world, or that a world even remotely like ours is like that.

Let us illustrate this argument in a different way by assuming that wormhole time travel imposes constraints upon the states of people prior to such time travel, where the people have so little mass/energy that they have negligible effect, via the Einstein equation, on the local metric properties of space-time. Do you think it more plausible that we live in a world where wormhole time travel occurs but it only occurs when people’s states are such that these local states happen to combine with time travel in such a way that nobody ever succeeds in killing their younger self, or do you think it more plausible that we are not in a wormhole time travel world? [ 5 ]

An alternative approach to time travel (initiated by Deutsch 1991) abstracts away from the idealized toy models described above. [ 6 ] This computational approach considers instead the evolution of bits (simple physical systems with two discrete states) through a network of interactions, which can be represented by a circuit diagram with gates corresponding to the interactions. Motivated by the possibility of CTCs, Deutsch proposed adding a new kind of channel that connects the output of a given gate back to its input —in essence, a backwards-time step. More concretely, given a gate that takes \(n\) bits as input, we can imagine taking some number \(i \lt n\) of these bits through a channel that loops back and then do double-duty as inputs. Consistency requires that the state of these \(i\) bits is the same for output and input. (We will consider an illustration of this kind of system in the next section.) Working through examples of circuit diagrams with a CTC channel leads to similar treatments of Consistency and Underdetermination as the discussion above (see, e.g., Wallace 2012: § 10.6). But the approach offers two new insights (both originally due to Deutsch): the Easy Knowledge paradox, and a particularly clear extension to time travel in quantum mechanics.

A computer equipped with a CTC channel can exploit the need to find consistent evolution to solve remarkably hard problems. (This is quite different than the first idea that comes to mind to enhance computational power: namely to just devote more time to a computation, and then send the result back on the CTC to an earlier state.) The gate in a circuit incorporating a CTC implements a function from the input bits to the output bits, under the constraint that the output and input match the i bits going through the CTC channel. This requires, in effect, finding the fixed point of the relevant function. Given the generality of the model, there are few limits on the functions that could be implemented on the CTC circuit. Nature has to solve a hard computational problem just to ensure consistent evolution. This can then be extended to other complex computational problems—leading, more precisely, to solutions of NP -complete problems in polynomial time (see Aaronson 2013: Chapter 20 for an overview and further references). The limits imposed by computational complexity are an essential part of our epistemic situation, and computers with CTCs would radically change this.

We now turn to the application of the computational approach to the quantum physics of time travel (see Deutsch 1991; Deutsch & Lockwood 1994). By contrast with the earlier discussions of constraints in classical systems, they claim to show that time travel never imposes any constraints on the pre-time travel state of quantum systems. The essence of this account is as follows. [ 7 ]

A quantum system starts in state \(S_1\), interacts with its older self, after the interaction is in state \(S_2\), time travels while developing into state \(S_3\), then interacts with its younger self, and ends in state \(S_4\) (see figure 10 ).

Figure 10 [An extended description of figure 10 is in the supplement.]

Deutsch assumes that the set of possible states of this system are the mixed states, i.e., are represented by the density matrices over the Hilbert space of that system. Deutsch then shows that for any initial state \(S_1\), any unitary interaction between the older and younger self, and any unitary development during time travel, there is a consistent solution, i.e., there is at least one pair of states \(S_2\) and \(S_3\) such that when \(S_1\) interacts with \(S_3\) it will change to state \(S_2\) and \(S_2\) will then develop into \(S_3\). The states \(S_2, S_3\) and \(S_4\) will typically be not be pure states, i.e., will be non-trivial mixed states, even if \(S_1\) is pure. In order to understand how this leads to interpretational problems let us give an example. Consider a system that has a two dimensional Hilbert space with as a basis the states \(\vc{+}\) and \(\vc{-}\). Let us suppose that when state \(\vc{+}\) of the young system encounters state \(\vc{+}\) of the older system, they interact and the young system develops into state \(\vc{-}\) and the old system remains in state \(\vc{+}\). In obvious notation:

Similarly, suppose that:

Let us furthermore assume that there is no development of the state of the system during time travel, i.e., that \(\vc{+}_2\) develops into \(\vc{+}_3\), and that \(\vc{-}_2\) develops into \(\vc{-}_3\).

Now, if the only possible states of the system were \(\vc{+}\) and \(\vc{-}\) (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state \(\vc{+}_1\) is impossible. For if \(\vc{+}_1\) interacts with \(\vc{+}_3\) then it will develop into \(\vc{-}_2\), which, during time travel, will develop into \(\vc{-}_3\), which inconsistent with the assumed state \(\vc{+}_3\). Similarly if \(\vc{+}_1\) interacts with \(\vc{-}_3\) it will develop into \(\vc{+}_2\), which will then develop into \(\vc{+}_3\) which is also inconsistent. Thus the system can not start in state \(\vc{+}_1\).

But, says Deutsch, in quantum mechanics such a system can also be in any mixture of the states \(\vc{+}\) and \(\vc{-}\). Suppose that the older system, prior to the interaction, is in a state \(S_3\) which is an equal mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\). Then the younger system during the interaction will develop into a mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), which will then develop into a mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\), which is consistent! More generally Deutsch uses a fixed point theorem to show that no matter what the unitary development during interaction is, and no matter what the unitary development during time travel is, for any state \(S_1\) there is always a state \(S_3\) (which typically is not a pure state) which causes \(S_1\) to develop into a state \(S_2\) which develops into that state \(S_3\). Thus quantum mechanics comes to the rescue: it shows in all generality that no constraints on initial states are needed!

One might wonder why Deutsch appeals to mixed states: will superpositions of states \(\vc{+}\) and \(\vc{-}\) not suffice? Unfortunately such an idea does not work. Suppose again that the initial state is \(\vc{+}_1\). One might suggest that that if state \(S_3\) is

one will obtain a consistent development. For one might think that when initial state \(\vc{+}_1\) encounters the superposition

it will develop into superposition

and that this in turn will develop into

as desired. However this is not correct. For initial state \(\vc{+}_1\) when it encounters

will develop into the entangled state

In so far as one can speak of the state of the young system after this interaction, it is in the mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), not in the superposition

So Deutsch does need his recourse to mixed states.

This clarification of why Deutsch needs his mixtures does however indicate a serious worry about the simplifications that are part of Deutsch’s account. After the interaction the old and young system will (typically) be in an entangled state. Although for purposes of a measurement on one of the two systems one can say that this system is in a mixed state, one can not represent the full state of the two systems by specifying the mixed state of each separate part, as there are correlations between observables of the two systems that are not represented by these two mixed states, but are represented in the joint entangled state. But if there really is an entangled state of the old and young systems directly after the interaction, how is one to represent the subsequent development of this entangled state? Will the state of the younger system remain entangled with the state of the older system as the younger system time travels and the older system moves on into the future? On what space-like surfaces are we to imagine this total entangled state to be? At this point it becomes clear that there is no obvious and simple way to extend elementary non-relativistic quantum mechanics to space-times with closed time-like curves: we apparently need to characterize not just the entanglement between two systems, but entanglement relative to specific spacetime descriptions.

How does Deutsch avoid these complications? Deutsch assumes a mixed state \(S_3\) of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state \(S_1\) younger system. After this interaction there is an entangled state \(S'\) of the two systems. Deutsch computes the mixed state \(S_2\) of the younger system which is implied by this entangled state \(S'\). His demand for consistency then is just that this mixed state \(S_2\) develops into the mixed state \(S_3\). Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?

If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state \(\vc{+}_3\) or in state \(\vc{-}_3\) prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state \(\vc{+}_1\) in all worlds. In some of the many worlds the older system will be in the \(\vc{+}_3\) state, let us call them A -worlds, and in some worlds, B -worlds, it will be in the \(\vc{-}_3\) state. Thus in A -worlds after interaction we will have state \(\vc{-}_2\) , and in B -worlds we will have state \(\vc{+}_2\). During time travel the \(\vc{-}_2\) state will remain the same, i.e., turn into state \(\vc{-}_3\), but the systems in question will travel from A -worlds to B -worlds. Similarly the \(\vc{+}\) \(_2\) states will travel from the B -worlds to the A -worlds, thus preserving consistency.

Now whatever one thinks of the merits of many worlds interpretations, and of this understanding of it applied to mixtures, in the end one does not obtain genuine time travel in Deutsch’s account. The systems in question travel from one time in one world to another time in another world, but no system travels to an earlier time in the same world. (This is so at least in the normal sense of the word “world”, the sense that one means when, for instance, one says “there was, and will be, only one Elvis Presley in this world.”) Thus, even if it were a reasonable view, it is not quite as interesting as it may have initially seemed. (See Wallace 2012 for a more sympathetic treatment, that explores several further implications of accepting time travel in conjunction with the many worlds interpretation.)

We close by acknowledging that Deutsch’s starting point—the claim that this computational model captures the essential features of quantum systems in a spacetime with CTCs—has been the subject of some debate. Several physicists have pursued a quite different treatment of evolution of quantum systems through CTC’s, based on considering the “post-selected” state (see Lloyd et al. 2011). Their motivations for implementing the consistency condition in terms of the post-selected state reflects a different stance towards quantum foundations. A different line of argument aims to determine whether Deutsch’s treatment holds as an appropriate limiting case of a more rigorous treatment, such as quantum field theory in curved spacetimes. For example, Verch (2020) establishes several results challenging the assumption that Deutsch’s treatment is tied to the presence of CTC’s, or that it is compatible with the entanglement structure of quantum fields.

What remains of the grandfather paradox in general relativistic time travel worlds is the fact that in some cases the states on edgeless spacelike surfaces are “overconstrained”, so that one has less than the usual freedom in specifying conditions on such a surface, given the time-travel structure, and in some cases such states are “underconstrained”, so that states on edgeless space-like surfaces do not determine what happens elsewhere in the way that they usually do, given the time travel structure. There can also be mixtures of those two types of cases. The extent to which states are overconstrained and/or underconstrained in realistic models is as yet unclear, though it would be very surprising if neither obtained. The extant literature has primarily focused on the problem of overconstraint, since that, often, either is regarded as a metaphysical obstacle to the possibility time travel, or as an epistemological obstacle to the plausibility of time travel in our world. While it is true that our world would be quite different from the way we normally think it is if states were overconstrained, underconstraint seems at least as bizarre as overconstraint. Nonetheless, neither directly rules out the possibility of time travel.

If time travel entailed contradictions then the issue would be settled. And indeed, most of the stories employing time travel in popular culture are logically incoherent: one cannot “change” the past to be different from what it was, since the past (like the present and the future) only occurs once. But if the only requirement demanded is logical coherence, then it seems all too easy. A clever author can devise a coherent time-travel scenario in which everything happens just once and in a consistent way. This is just too cheap: logical coherence is a very weak condition, and many things we take to be metaphysically impossible are logically coherent. For example, it involves no logical contradiction to suppose that water is not molecular, but if both chemistry and Kripke are right it is a metaphysical impossibility. We have been interested not in logical possibility but in physical possibility. But even so, our conditions have been relatively weak: we have asked only whether time-travel is consistent with the universal validity of certain fundamental physical laws and with the notion that the physical state on a surface prior to the time travel region be unconstrained. It is perfectly possible that the physical laws obey this condition, but still that time travel is not metaphysically possible because of the nature of time itself. Consider an analogy. Aristotle believed that water is homoiomerous and infinitely divisible: any bit of water could be subdivided, in principle, into smaller bits of water. Aristotle’s view contains no logical contradiction. It was certainly consistent with Aristotle’s conception of water that it be homoiomerous, so this was, for him, a conceptual possibility. But if chemistry is right, Aristotle was wrong both about what water is like and what is possible for it. It can’t be infinitely divided, even though no logical or conceptual analysis would reveal that.

Similarly, even if all of our consistency conditions can be met, it does not follow that time travel is physically possible, only that some specific physical considerations cannot rule it out. The only serious proof of the possibility of time travel would be a demonstration of its actuality. For if we agree that there is no actual time travel in our universe, the supposition that there might have been involves postulating a substantial difference from actuality, a difference unlike in kind from anything we could know if firsthand. It is unclear to us exactly what the content of possible would be if one were to either maintain or deny the possibility of time travel in these circumstances, unless one merely meant that the possibility is not ruled out by some delineated set of constraints. As the example of Aristotle’s theory of water shows, conceptual and logical “possibility” do not entail possibility in a full-blooded sense. What exactly such a full-blooded sense would be in case of time travel, and whether one could have reason to believe it to obtain, remain to us obscure.

• Aaronson, Scott, 2013, Quantum Computing since Democritus , Cambridge: Cambridge University Press. doi:10.1017/CBO9780511979309
• Arntzenius, Frank, 2006, “Time Travel: Double Your Fun”, Philosophy Compass , 1(6): 599–616. doi:10.1111/j.1747-9991.2006.00045.x
• Clarke, C.J.S., 1977, “Time in General Relativity” in Foundations of Space-Time Theory , Minnesota Studies in the Philosophy of Science , Vol VIII, Earman, J., Glymour, C., and Stachel, J. (eds), pp. 94–108. Minneapolis: University of Minnesota Press.
• Deutsch, David, 1991, “Quantum Mechanics near Closed Timelike Lines”, Physical Review D , 44(10): 3197–3217. doi:10.1103/PhysRevD.44.3197
• Deutsch, David and Michael Lockwood, 1994, “The Quantum Physics of Time Travel”, Scientific American , 270(3): 68–74. doi:10.1038/scientificamerican0394-68
• Dowe, Phil, 2007, “Constraints on Data in Worlds with Closed Timelike Curves”, Philosophy of Science , 74(5): 724–735. doi:10.1086/525617
• Earman, John, 1972, “Implications of Causal Propagation Outside the Null Cone”, Australasian Journal of Philosophy , 50(3): 222–237. doi:10.1080/00048407212341281
• Earman, John, 1995, Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes , New York: Oxford University Press.
• Earman, John, Christopher Smeenk, and Christian Wüthrich, 2009, “Do the Laws of Physics Forbid the Operation of Time Machines?”, Synthese , 169(1): 91–124. doi:10.1007/s11229-008-9338-2
• Echeverria, Fernando, Gunnar Klinkhammer, and Kip S. Thorne, 1991, “Billiard Balls in Wormhole Spacetimes with Closed Timelike Curves: Classical Theory”, Physical Review D , 44(4): 1077–1099. doi:10.1103/PhysRevD.44.1077
• Effingham, Nikk, 2020, Time Travel: Probability and Impossibility , Oxford: Oxford University Press. doi:10.1093/oso/9780198842507.001.0001
• Fletcher, Samuel C., 2020, “The Principle of Stability”, Philosopher’s Imprint , 20: article 3. [ Fletcher 2020 available online ]
• Friedman, John and Michael Morris, 1991, “The Cauchy Problem for the Scalar Wave Equation Is Well Defined on a Class of Spacetimes with Closed Timelike Curves”, Physical Review Letters , 66(4): 401–404. doi:10.1103/PhysRevLett.66.401
• Friedman, John, Michael S. Morris, Igor D. Novikov, Fernando Echeverria, Gunnar Klinkhammer, Kip S. Thorne, and Ulvi Yurtsever, 1990, “Cauchy Problem in Spacetimes with Closed Timelike Curves”, Physical Review D , 42(6): 1915–1930. doi:10.1103/PhysRevD.42.1915
• Geroch, Robert and Gary Horowitz, 1979, “Global Structures of Spacetimes”, in General Relativity: An Einstein Centenary Survey , Stephen Hawking and W. Israel (eds.), Cambridge/New York: Cambridge University Press, Chapter 5, pp. 212–293.
• Gödel, Kurt, 1949, “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy”, in Albert Einstein, Philosopher-Scientist , Paul Arthur Schilpp (ed.), Evanston, IL: Library of Living Philosophers, 557–562.
• Hocking, John G. and Gail S. Young, 1961, Topology , (Addison-Wesley Series in Mathematics), Reading, MA: Addison-Wesley.
• Horwich, Paul, 1987, “Time Travel”, in his Asymmetries in Time: Problems in the Philosophy of Science , , Cambridge, MA: MIT Press, 111–128.
• Kutach, Douglas N., 2003, “Time Travel and Consistency Constraints”, Philosophy of Science , 70(5): 1098–1113. doi:10.1086/377392
• Lewis, David, 1976, “The Paradoxes of Time Travel”, American Philosophical Quarterly , 13(2): 145–152.
• Lloyd, Seth, Lorenzo Maccone, Raul Garcia-Patron, Vittorio Giovannetti, and Yutaka Shikano, 2011, “Quantum Mechanics of Time Travel through Post-Selected Teleportation”, Physical Review D , 84(2): 025007. doi:10.1103/PhysRevD.84.025007
• Malament, David B., 1977, “Observationally Indistinguishable Spacetimes: Comments on Glymour’s Paper”, in Foundations of Space-Time Theories , John Earman, Clark N. Glymour, and John J. Stachel (eds.), (Minnesota Studies in the Philosophy of Science 8), Minneapolis, MN: University of Minnesota Press, 61–80.
• –––, 1984, “‘Time Travel’ in the Gödel Universe”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1984(2): 91–100. doi:10.1086/psaprocbienmeetp.1984.2.192497
• –––, 1985, “Minimal Acceleration Requirements for ‘Time Travel’, in Gödel Space‐time”, Journal of Mathematical Physics , 26(4): 774–777. doi:10.1063/1.526566
• Manchak, John Byron, 2009, “Can We Know the Global Structure of Spacetime?”, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics , 40(1): 53–56. doi:10.1016/j.shpsb.2008.07.004
• –––, 2011, “On Efficient ‘Time Travel’ in Gödel Spacetime”, General Relativity and Gravitation , 43(1): 51–60. doi:10.1007/s10714-010-1068-3
• Maudlin, Tim, 1990, “Time-Travel and Topology”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1990(1): 303–315. doi:10.1086/psaprocbienmeetp.1990.1.192712
• Novikov, I. D., 1992, “Time Machine and Self-Consistent Evolution in Problems with Self-Interaction”, Physical Review D , 45(6): 1989–1994. doi:10.1103/PhysRevD.45.1989
• Smeenk, Chris and Christian Wüthrich, 2011, “Time Travel and Time Machines”, in the Oxford Handbook on Time , Craig Callender (ed.), Oxford: Oxford University Press, 577–630..
• Stein, Howard, 1970, “On the Paradoxical Time-Structures of Gödel”, Philosophy of Science , 37(4): 589–601. doi:10.1086/288328
• Thorne, Kip S., 1994, Black Holes and Time Warps: Einstein’s Outrageous Legacy , (Commonwealth Fund Book Program), New York: W.W. Norton.
• Verch, Rainer, 2020, “The D-CTC Condition in Quantum Field Theory”, in Progress and Visions in Quantum Theory in View of Gravity , Felix Finster, Domenico Giulini, Johannes Kleiner, and Jürgen Tolksdorf (eds.), Cham: Springer International Publishing, 221–232. doi:10.1007/978-3-030-38941-3_9
• Wallace, David, 2012, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation , Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199546961.001.0001
• Wasserman, Ryan, 2018, Paradoxes of Time Travel , Oxford: Oxford University Press. doi:10.1093/oso/9780198793335.001.0001
• Weyl, Hermann, 1918/1920 [1922/1952], Raum, Zeit, Materie , Berlin: Springer; fourth edition 1920. Translated as Space—Time—Matter , Henry Leopold Brose (trans.), New York: Dutton, 1922. Reprinted 1952, New York: Dover Publications.
• Wheeler, John Archibald and Richard Phillips Feynman, 1949, “Classical Electrodynamics in Terms of Direct Interparticle Action”, Reviews of Modern Physics , 21(3): 425–433. doi:10.1103/RevModPhys.21.425
• Yurtsever, Ulvi, 1990, “Test Fields on Compact Space‐times”, Journal of Mathematical Physics , 31(12): 3064–3078. doi:10.1063/1.528960

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
• Rovelli, Carlo, unpublished, “ Can We Travel to the Past? Irreversible Physics along Closed Timelike Curves ”, arXiv: 1912.04702. doi:10.48550/ARXIV.1912.04702

causation: backward | determinism: causal | quantum mechanics | quantum mechanics: retrocausality | space and time: being and becoming in modern physics | time machines | time travel

Copyright © 2023 by Christopher Smeenk < csmeenk2 @ uwo . ca > Frank Arntzenius Tim Maudlin

• Accessibility

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2023 by The Metaphysics Research Lab , Department of Philosophy, Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

Quantum Mechanics Proves 'Back to the Future' Is B.S.

But the Avengers' method of time travel totally checks out.

• Like in certain mathematical conditions , the timeline can overcome some disruptions.
• No one can take Back to the Future away from you.

In trippy new research, scientists say they’ve confirmed what they call the Avengers: Endgame model of time travel.

They did this by running a quantum time travel simulation that runs backward and forward, letting them “damage” the past and see what resulted. And, as they say, the devil is in the details—the experiment involves an extremely simplified idea of a “world,” and is only the very first step toward demonstrating any big ideas about causality.

🤯 The universe is a mindf#!@. Let's explore it together.

In a statement, sponsoring Los Alamos National Laboratory likens the movie Back to the Future , where Marty McFly must carefully not disrupt the timeline of his own inception, to the idea of the “butterfly effect.” The idea is simple: Because of the complex way time moves and how causality “ripples out” in unexpected or just unfathomable ways, stepping on a butterfly in the past could change the entire world you try to return to.

Games with procedurally generated worlds use a reverse butterfly effect to create those worlds—a randomized “seed,” which is a string of characters that determines different variables. In Songbringer , for example, the player makes up their own six-letter seed and then plays through the world they created. Since the randomness is an illusion based on high numbers, entering the same seed makes the same world over and over.

But what if the world is, to some extent, self healing? This is where the Endgame version of events comes into play, and where the quantum experiment begins. In this version of events, no matter what “seed” shifted the world—what information was included, left out, or examined—the timelines would all eventually converge. The Avengers can go back, gently meddle, and return to the present without making a ripple.

This may sound like the same narrative handwaving that enables all time travel stories, but the Los Alamos experiment came to the same conclusion.

Here’s the scenario: Alice and Bob, two agents in a system, each have a piece of data—a qubit , or quantum bit. Alice sends her data backward in time, where Bob measures it, altering it in accordance with the Heisenberg uncertainty principle. What happens when the qubit returns?

In their simulations, the researchers found the qubit didn't change—or even affect—the original timeline. They used a series of quantum logic gates and an operator called a Hamiltonian, which in quantum mechanics is a measurement of potential and kinetic energy. Here’s where the idea stops being the stuff of sci-fi watercooler talk and starts to sound real. From the paper :

“The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. We show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol.”

In other words, the nature of the time-affected operator they studied is such that it ends up affecting information that travels through it, and for some far-off application like quantum internet, that fact could end up making a big difference.

If researchers know they can “rewind” the information to see how it looked originally without changing the outcome, they may be able to guarantee fidelity of data in a situation previously thought to result in, well, some digital broken eggs.

Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all. 

.css-cuqpxl:before{padding-right:0.3125rem;content:'//';display:inline;} Science .css-xtujxj:before{padding-left:0.3125rem;content:'//';display:inline;}

Tardigrades Could Extend Humanity’s Shelf-Life

Fish in Florida Are Spinning Out of Control

Why People Will See Mind-Blowing Colors on April 8

There May Be a Moonshine Cave Under a NASCAR Track

A Genetic Discovery Changed Bird Evolution

Scientists Are Searching for Quantum Gravity

Global Warming Is Slowing Earth’s Rotation

What To Know About the 2024 U.S. Solar Eclipse

8 Ways to Power Your Home With Renewable Energy

Beethoven’s DNA Scored Low for Musical Ability

A Wonder Clock Has Rocked the Scientific World

Advertisement

Why rethinking time in quantum mechanics could help us unite physics

Inspired by experiments showing entanglement over time, not just space, physicist Vlatko Vedral is reconsidering the way we think of time in quantum mechanics. The new approach treats space and time as part of one entity and could help us unravel black holes and make quantum time travel possible

By Vlatko Vedral

23 August 2022

Janelle Barone

I WOULD like to take you with me, just for a minute or two, on a journey through space and time. We are minding our own business, watching the stars and galaxies zip by, when, suddenly, an invisible force draws us in. The closer we get to its source, the faster we move. Eventually, we are moving so quickly that time slows. We become extremely heavy and nothing can stop us – we are hurtling towards a black hole .

On our approach, we start to see streaks of light curving around a dark centre . This is the event horizon, the point beyond which gravity is so great that nothing, not even light, can escape.

But our journey must end here. Putting aside the torture it would place on our bodies to go further, we can’t even imagine what lies beyond this point. At the centre of a black hole, our best description of gravity, the general theory of relativity , breaks down and our other great theory of nature, quantum mechanics , must kick in. We have reached a place where our two best ways to describe the universe – relativity on the larger scale, quantum mechanics on the very small – come together in some way we don’t yet understand. Trying to unify these remains one of our greatest challenges.

However, there are now glimmers of hope. Recently, I have been developing an idea that might get us somewhere by making quantum mechanics more like general relativity. With the help of some experiments, it could lead us to the centre of our black hole, and to a unified theory at last.

Sign up to our weekly newsletter

Receive a weekly dose of discovery in your inbox! We'll also keep you up to date with New Scientist events and special offers.

To continue reading, subscribe today with our introductory offers

No commitment, cancel anytime*

Offer ends 2nd of July 2024.

*Cancel anytime within 14 days of payment to receive a refund on unserved issues.

Inclusive of applicable taxes (VAT)

Existing subscribers

More from New Scientist

Explore the latest news, articles and features

Climate change can disturb the accuracy of trees’ biological clocks

Subscriber-only

Environment

Great apes threatened by mining for electric vehicle batteries, i might be an astrophysicist, but i'm still learning about stargazing, sound tracks: a fascinating archaeological history of music, popular articles.

Trending New Scientist articles

Can we time travel? A theoretical physicist provides some answers

Emeritus professor, Physics, Carleton University

Disclosure statement

Peter Watson received funding from NSERC. He is affiliated with Carleton University and a member of the Canadian Association of Physicists.

Carleton University provides funding as a member of The Conversation CA.

Carleton University provides funding as a member of The Conversation CA-FR.

View all partners

• Bahasa Indonesia

Time travel makes regular appearances in popular culture, with innumerable time travel storylines in movies, television and literature. But it is a surprisingly old idea: one can argue that the Greek tragedy Oedipus Rex , written by Sophocles over 2,500 years ago, is the first time travel story .

But is time travel in fact possible? Given the popularity of the concept, this is a legitimate question. As a theoretical physicist, I find that there are several possible answers to this question, not all of which are contradictory.

The simplest answer is that time travel cannot be possible because if it was, we would already be doing it. One can argue that it is forbidden by the laws of physics, like the second law of thermodynamics or relativity . There are also technical challenges: it might be possible but would involve vast amounts of energy.

There is also the matter of time-travel paradoxes; we can — hypothetically — resolve these if free will is an illusion, if many worlds exist or if the past can only be witnessed but not experienced. Perhaps time travel is impossible simply because time must flow in a linear manner and we have no control over it, or perhaps time is an illusion and time travel is irrelevant.

Laws of physics

Since Albert Einstein’s theory of relativity — which describes the nature of time, space and gravity — is our most profound theory of time, we would like to think that time travel is forbidden by relativity. Unfortunately, one of his colleagues from the Institute for Advanced Study, Kurt Gödel, invented a universe in which time travel was not just possible, but the past and future were inextricably tangled.

We can actually design time machines , but most of these (in principle) successful proposals require negative energy , or negative mass, which does not seem to exist in our universe. If you drop a tennis ball of negative mass, it will fall upwards. This argument is rather unsatisfactory, since it explains why we cannot time travel in practice only by involving another idea — that of negative energy or mass — that we do not really understand.

Mathematical physicist Frank Tipler conceptualized a time machine that does not involve negative mass, but requires more energy than exists in the universe .

Time travel also violates the second law of thermodynamics , which states that entropy or randomness must always increase. Time can only move in one direction — in other words, you cannot unscramble an egg. More specifically, by travelling into the past we are going from now (a high entropy state) into the past, which must have lower entropy.

This argument originated with the English cosmologist Arthur Eddington , and is at best incomplete. Perhaps it stops you travelling into the past, but it says nothing about time travel into the future. In practice, it is just as hard for me to travel to next Thursday as it is to travel to last Thursday.

Resolving paradoxes

There is no doubt that if we could time travel freely, we run into the paradoxes. The best known is the “ grandfather paradox ”: one could hypothetically use a time machine to travel to the past and murder their grandfather before their father’s conception, thereby eliminating the possibility of their own birth. Logically, you cannot both exist and not exist.

Read more: Time travel could be possible, but only with parallel timelines

Kurt Vonnegut’s anti-war novel Slaughterhouse-Five , published in 1969, describes how to evade the grandfather paradox. If free will simply does not exist, it is not possible to kill one’s grandfather in the past, since he was not killed in the past. The novel’s protagonist, Billy Pilgrim, can only travel to other points on his world line (the timeline he exists in), but not to any other point in space-time, so he could not even contemplate killing his grandfather.

The universe in Slaughterhouse-Five is consistent with everything we know. The second law of thermodynamics works perfectly well within it and there is no conflict with relativity. But it is inconsistent with some things we believe in, like free will — you can observe the past, like watching a movie, but you cannot interfere with the actions of people in it.

Could we allow for actual modifications of the past, so that we could go back and murder our grandfather — or Hitler ? There are several multiverse theories that suppose that there are many timelines for different universes. This is also an old idea: in Charles Dickens’ A Christmas Carol , Ebeneezer Scrooge experiences two alternative timelines, one of which leads to a shameful death and the other to happiness.

Time is a river

Roman emperor Marcus Aurelius wrote that:

“ Time is like a river made up of the events which happen , and a violent stream; for as soon as a thing has been seen, it is carried away, and another comes in its place, and this will be carried away too.”

We can imagine that time does flow past every point in the universe, like a river around a rock. But it is difficult to make the idea precise. A flow is a rate of change — the flow of a river is the amount of water that passes a specific length in a given time. Hence if time is a flow, it is at the rate of one second per second, which is not a very useful insight.

Theoretical physicist Stephen Hawking suggested that a “ chronology protection conjecture ” must exist, an as-yet-unknown physical principle that forbids time travel. Hawking’s concept originates from the idea that we cannot know what goes on inside a black hole, because we cannot get information out of it. But this argument is redundant: we cannot time travel because we cannot time travel!

Researchers are investigating a more fundamental theory, where time and space “emerge” from something else. This is referred to as quantum gravity , but unfortunately it does not exist yet.

So is time travel possible? Probably not, but we don’t know for sure!

• Time travel
• Stephen Hawking
• Albert Einstein
• Listen to this article
• Time travel paradox

Communications and Events Officer

Lecturer (Hindi-Urdu)

Director, Defence and Security

Opportunities with the new CIEHF

School of Social Sciences – Public Policy and International Relations opportunities

April 26, 2023

Is Time Travel Possible?

The laws of physics allow time travel. So why haven’t people become chronological hoppers?

By Sarah Scoles &

yuanyuan yan/Getty Images

In the movies, time travelers typically step inside a machine and—poof—disappear. They then reappear instantaneously among cowboys, knights or dinosaurs. What these films show is basically time teleportation .

Scientists don’t think this conception is likely in the real world, but they also don’t relegate time travel to the crackpot realm. In fact, the laws of physics might allow chronological hopping, but the devil is in the details.

Time traveling to the near future is easy: you’re doing it right now at a rate of one second per second, and physicists say that rate can change. According to Einstein’s special theory of relativity, time’s flow depends on how fast you’re moving. The quicker you travel, the slower seconds pass. And according to Einstein’s general theory of relativity , gravity also affects clocks: the more forceful the gravity nearby, the slower time goes.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

“Near massive bodies—near the surface of neutron stars or even at the surface of the Earth, although it’s a tiny effect—time runs slower than it does far away,” says Dave Goldberg, a cosmologist at Drexel University.

If a person were to hang out near the edge of a black hole , where gravity is prodigious, Goldberg says, only a few hours might pass for them while 1,000 years went by for someone on Earth. If the person who was near the black hole returned to this planet, they would have effectively traveled to the future. “That is a real effect,” he says. “That is completely uncontroversial.”

Going backward in time gets thorny, though (thornier than getting ripped to shreds inside a black hole). Scientists have come up with a few ways it might be possible, and they have been aware of time travel paradoxes in general relativity for decades. Fabio Costa, a physicist at the Nordic Institute for Theoretical Physics, notes that an early solution with time travel began with a scenario written in the 1920s. That idea involved massive long cylinder that spun fast in the manner of straw rolled between your palms and that twisted spacetime along with it. The understanding that this object could act as a time machine allowing one to travel to the past only happened in the 1970s, a few decades after scientists had discovered a phenomenon called “closed timelike curves.”

“A closed timelike curve describes the trajectory of a hypothetical observer that, while always traveling forward in time from their own perspective, at some point finds themselves at the same place and time where they started, creating a loop,” Costa says. “This is possible in a region of spacetime that, warped by gravity, loops into itself.”

“Einstein read [about closed timelike curves] and was very disturbed by this idea,” he adds. The phenomenon nevertheless spurred later research.

Science began to take time travel seriously in the 1980s. In 1990, for instance, Russian physicist Igor Novikov and American physicist Kip Thorne collaborated on a research paper about closed time-like curves. “They started to study not only how one could try to build a time machine but also how it would work,” Costa says.

Just as importantly, though, they investigated the problems with time travel. What if, for instance, you tossed a billiard ball into a time machine, and it traveled to the past and then collided with its past self in a way that meant its present self could never enter the time machine? “That looks like a paradox,” Costa says.

Since the 1990s, he says, there’s been on-and-off interest in the topic yet no big breakthrough. The field isn’t very active today, in part because every proposed model of a time machine has problems. “It has some attractive features, possibly some potential, but then when one starts to sort of unravel the details, there ends up being some kind of a roadblock,” says Gaurav Khanna of the University of Rhode Island.

For instance, most time travel models require negative mass —and hence negative energy because, as Albert Einstein revealed when he discovered E = mc 2 , mass and energy are one and the same. In theory, at least, just as an electric charge can be positive or negative, so can mass—though no one’s ever found an example of negative mass. Why does time travel depend on such exotic matter? In many cases, it is needed to hold open a wormhole—a tunnel in spacetime predicted by general relativity that connects one point in the cosmos to another.

Without negative mass, gravity would cause this tunnel to collapse. “You can think of it as counteracting the positive mass or energy that wants to traverse the wormhole,” Goldberg says.

Khanna and Goldberg concur that it’s unlikely matter with negative mass even exists, although Khanna notes that some quantum phenomena show promise, for instance, for negative energy on very small scales. But that would be “nowhere close to the scale that would be needed” for a realistic time machine, he says.

These challenges explain why Khanna initially discouraged Caroline Mallary, then his graduate student at the University of Massachusetts Dartmouth, from doing a time travel project. Mallary and Khanna went forward anyway and came up with a theoretical time machine that didn’t require negative mass. In its simplistic form, Mallary’s idea involves two parallel cars, each made of regular matter. If you leave one parked and zoom the other with extreme acceleration, a closed timelike curve will form between them.

Easy, right? But while Mallary’s model gets rid of the need for negative matter, it adds another hurdle: it requires infinite density inside the cars for them to affect spacetime in a way that would be useful for time travel. Infinite density can be found inside a black hole, where gravity is so intense that it squishes matter into a mind-bogglingly small space called a singularity. In the model, each of the cars needs to contain such a singularity. “One of the reasons that there's not a lot of active research on this sort of thing is because of these constraints,” Mallary says.

Other researchers have created models of time travel that involve a wormhole, or a tunnel in spacetime from one point in the cosmos to another. “It's sort of a shortcut through the universe,” Goldberg says. Imagine accelerating one end of the wormhole to near the speed of light and then sending it back to where it came from. “Those two sides are no longer synced,” he says. “One is in the past; one is in the future.” Walk between them, and you’re time traveling.

You could accomplish something similar by moving one end of the wormhole near a big gravitational field—such as a black hole—while keeping the other end near a smaller gravitational force. In that way, time would slow down on the big gravity side, essentially allowing a particle or some other chunk of mass to reside in the past relative to the other side of the wormhole.

Making a wormhole requires pesky negative mass and energy, however. A wormhole created from normal mass would collapse because of gravity. “Most designs tend to have some similar sorts of issues,” Goldberg says. They’re theoretically possible, but there’s currently no feasible way to make them, kind of like a good-tasting pizza with no calories.

And maybe the problem is not just that we don’t know how to make time travel machines but also that it’s not possible to do so except on microscopic scales—a belief held by the late physicist Stephen Hawking. He proposed the chronology protection conjecture: The universe doesn’t allow time travel because it doesn’t allow alterations to the past. “It seems there is a chronology protection agency, which prevents the appearance of closed timelike curves and so makes the universe safe for historians,” Hawking wrote in a 1992 paper in Physical Review D .

Part of his reasoning involved the paradoxes time travel would create such as the aforementioned situation with a billiard ball and its more famous counterpart, the grandfather paradox : If you go back in time and kill your grandfather before he has children, you can’t be born, and therefore you can’t time travel, and therefore you couldn’t have killed your grandfather. And yet there you are.

Those complications are what interests Massachusetts Institute of Technology philosopher Agustin Rayo, however, because the paradoxes don’t just call causality and chronology into question. They also make free will seem suspect. If physics says you can go back in time, then why can’t you kill your grandfather? “What stops you?” he says. Are you not free?

Rayo suspects that time travel is consistent with free will, though. “What’s past is past,” he says. “So if, in fact, my grandfather survived long enough to have children, traveling back in time isn’t going to change that. Why will I fail if I try? I don’t know because I don’t have enough information about the past. What I do know is that I’ll fail somehow.”

If you went to kill your grandfather, in other words, you’d perhaps slip on a banana en route or miss the bus. “It's not like you would find some special force compelling you not to do it,” Costa says. “You would fail to do it for perfectly mundane reasons.”

In 2020 Costa worked with Germain Tobar, then his undergraduate student at the University of Queensland in Australia, on the math that would underlie a similar idea: that time travel is possible without paradoxes and with freedom of choice.

Goldberg agrees with them in a way. “I definitely fall into the category of [thinking that] if there is time travel, it will be constructed in such a way that it produces one self-consistent view of history,” he says. “Because that seems to be the way that all the rest of our physical laws are constructed.”

No one knows what the future of time travel to the past will hold. And so far, no time travelers have come to tell us about it.

A beginner's guide to time travel

Learn exactly how Einstein's theory of relativity works, and discover how there's nothing in science that says time travel is impossible.

Everyone can travel in time . You do it whether you want to or not, at a steady rate of one second per second. You may think there's no similarity to traveling in one of the three spatial dimensions at, say, one foot per second. But according to Einstein 's theory of relativity , we live in a four-dimensional continuum — space-time — in which space and time are interchangeable.

Einstein found that the faster you move through space, the slower you move through time — you age more slowly, in other words. One of the key ideas in relativity is that nothing can travel faster than the speed of light — about 186,000 miles per second (300,000 kilometers per second), or one light-year per year). But you can get very close to it. If a spaceship were to fly at 99% of the speed of light, you'd see it travel a light-year of distance in just over a year of time. 

That's obvious enough, but now comes the weird part. For astronauts onboard that spaceship, the journey would take a mere seven weeks. It's a consequence of relativity called time dilation , and in effect, it means the astronauts have jumped about 10 months into the future. 

Traveling at high speed isn't the only way to produce time dilation. Einstein showed that gravitational fields produce a similar effect — even the relatively weak field here on the surface of Earth . We don't notice it, because we spend all our lives here, but more than 12,400 miles (20,000 kilometers) higher up gravity is measurably weaker— and time passes more quickly, by about 45 microseconds per day. That's more significant than you might think, because it's the altitude at which GPS satellites orbit Earth, and their clocks need to be precisely synchronized with ground-based ones for the system to work properly. 

The satellites have to compensate for time dilation effects due both to their higher altitude and their faster speed. So whenever you use the GPS feature on your smartphone or your car's satnav, there's a tiny element of time travel involved. You and the satellites are traveling into the future at very slightly different rates.

But for more dramatic effects, we need to look at much stronger gravitational fields, such as those around black holes , which can distort space-time so much that it folds back on itself. The result is a so-called wormhole, a concept that's familiar from sci-fi movies, but actually originates in Einstein's theory of relativity. In effect, a wormhole is a shortcut from one point in space-time to another. You enter one black hole, and emerge from another one somewhere else. Unfortunately, it's not as practical a means of transport as Hollywood makes it look. That's because the black hole's gravity would tear you to pieces as you approached it, but it really is possible in theory. And because we're talking about space-time, not just space, the wormhole's exit could be at an earlier time than its entrance; that means you would end up in the past rather than the future.

Trajectories in space-time that loop back into the past are given the technical name "closed timelike curves." If you search through serious academic journals, you'll find plenty of references to them — far more than you'll find to "time travel." But in effect, that's exactly what closed timelike curves are all about — time travel

This article is brought to you by  How It Works .

How It Works is the action-packed magazine that's bursting with exciting information about the latest advances in science and technology, featuring everything you need to know about how the world around you — and the universe — works.

There's another way to produce a closed timelike curve that doesn't involve anything quite so exotic as a black hole or wormhole: You just need a simple rotating cylinder made of super-dense material. This so-called Tipler cylinder is the closest that real-world physics can get to an actual, genuine time machine. But it will likely never be built in the real world, so like a wormhole, it's more of an academic curiosity than a viable engineering design.

Yet as far-fetched as these things are in practical terms, there's no fundamental scientific reason — that we currently know of — that says they are impossible. That's a thought-provoking situation, because as the physicist Michio Kaku is fond of saying, "Everything not forbidden is compulsory" (borrowed from T.H. White's novel, "The Once And Future King"). He doesn't mean time travel has to happen everywhere all the time, but Kaku is suggesting that the universe is so vast it ought to happen somewhere at least occasionally. Maybe some super-advanced civilization in another galaxy knows how to build a working time machine, or perhaps closed timelike curves can even occur naturally under certain rare conditions.

This raises problems of a different kind — not in science or engineering, but in basic logic. If time travel is allowed by the laws of physics, then it's possible to envision a whole range of paradoxical scenarios . Some of these appear so illogical that it's difficult to imagine that they could ever occur. But if they can't, what's stopping them? 

Thoughts like these prompted Stephen Hawking , who was always skeptical about the idea of time travel into the past, to come up with his "chronology protection conjecture" — the notion that some as-yet-unknown law of physics prevents closed timelike curves from happening. But that conjecture is only an educated guess, and until it is supported by hard evidence, we can come to only one conclusion: Time travel is possible.

A party for time travelers 

Hawking was skeptical about the feasibility of time travel into the past, not because he had disproved it, but because he was bothered by the logical paradoxes it created. In his chronology protection conjecture, he surmised that physicists would eventually discover a flaw in the theory of closed timelike curves that made them impossible. 

In 2009, he came up with an amusing way to test this conjecture. Hawking held a champagne party (shown in his Discovery Channel program), but he only advertised it after it had happened. His reasoning was that, if time machines eventually become practical, someone in the future might read about the party and travel back to attend it. But no one did — Hawking sat through the whole evening on his own. This doesn't prove time travel is impossible, but it does suggest that it never becomes a commonplace occurrence here on Earth.

The arrow of time 

One of the distinctive things about time is that it has a direction — from past to future. A cup of hot coffee left at room temperature always cools down; it never heats up. Your cellphone loses battery charge when you use it; it never gains charge. These are examples of entropy , essentially a measure of the amount of "useless" as opposed to "useful" energy. The entropy of a closed system always increases, and it's the key factor determining the arrow of time.

It turns out that entropy is the only thing that makes a distinction between past and future. In other branches of physics, like relativity or quantum theory, time doesn't have a preferred direction. No one knows where time's arrow comes from. It may be that it only applies to large, complex systems, in which case subatomic particles may not experience the arrow of time.

Time travel paradox 

If it's possible to travel back into the past — even theoretically — it raises a number of brain-twisting paradoxes — such as the grandfather paradox — that even scientists and philosophers find extremely perplexing.

Killing Hitler

A time traveler might decide to go back and kill him in his infancy. If they succeeded, future history books wouldn't even mention Hitler — so what motivation would the time traveler have for going back in time and killing him?

Killing your grandfather

Instead of killing a young Hitler, you might, by accident, kill one of your own ancestors when they were very young. But then you would never be born, so you couldn't travel back in time to kill them, so you would be born after all, and so on … 

A closed loop

Suppose the plans for a time machine suddenly appear from thin air on your desk. You spend a few days building it, then use it to send the plans back to your earlier self. But where did those plans originate? Nowhere — they are just looping round and round in time.

Sign up for the Live Science daily newsletter now

Get the world’s most fascinating discoveries delivered straight to your inbox.

How It Works has a special formula for making learning fun by answering questions on science, space, history, technology, transport and the environment with engaging articles, in-depth special features, global science news, and topical interviews. With impressive cutaway illustrations that show how things function, and mindblowing photography of the planet’s most inspiring spectacles, How It Works represents the pinnacle of engaging, factual fun for a mainstream audience keen to keep up with the latest tech and the most impressive phenomena on the planet and beyond. Written and presented in a style that makes even the most complex subjects interesting and easy to understand, How It Works is enjoyed by readers of all ages.

Get fantastic offers by subscribing to the digital and/or print edition now. Subscribers get 13 issues per year!

See photos of NASA's suitcase-sized rovers that will soon map the moon's surface

Why NASA is launching 3 rockets into the solar eclipse next week

Mpox cases are far outpacing last year's numbers, CDC reports

Most Popular

By Anna Gora December 27, 2023

By Anna Gora December 26, 2023

By Anna Gora December 25, 2023

By Emily Cooke December 23, 2023

By Victoria Atkinson December 22, 2023

By Anna Gora December 16, 2023

By Anna Gora December 15, 2023

By Anna Gora November 09, 2023

By Donavyn Coffey November 06, 2023

By Anna Gora October 31, 2023

By Anna Gora October 26, 2023

• 2 'You could almost see and smell their world': Remnants of 'Britain's Pompeii' reveal details of life in Bronze Age village
• 3 Where does the solar system end?
• 4 Chemicals that make babies smell sweet and teens smell 'goat-like' revealed
• 5 'You probably didn't inherit any DNA from Charlemagne': What it means when your DNA 'matches' a historic person's
• 2 James Webb telescope confirms there is something seriously wrong with our understanding of the universe
• 3 How much does Earth weigh?
• 4 'You probably didn't inherit any DNA from Charlemagne': What it means when your DNA 'matches' a historic person's

Physical Review A

Covering atomic, molecular, and optical physics and quantum information.

• Collections
• Editorial Team

Treating time travel quantum mechanically

John-mark a. allen, phys. rev. a 90 , 042107 – published 9 october 2014.

• Citing Articles (19)
• INTRODUCTION
• MODELING TIME TRAVEL WITH QUANTUM…
• D-CTCs AND P-CTCs
• ALTERNATE THEORIES
• ACKNOWLEDGMENTS

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and “postselected” CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the “equivalent circuit model”—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of “transition probability” CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

• Received 22 January 2014

DOI: https://doi.org/10.1103/PhysRevA.90.042107

©2014 American Physical Society

Authors & Affiliations

• Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
• * [email protected]

Article Text (Subscription Required)

References (subscription required).

Vol. 90, Iss. 4 — October 2014

Access Options

• Buy Article »
• Log in with individual APS Journal Account »
• Log in with a username/password provided by your institution »
• Get access through a U.S. public or high school library »

Authorization Required

Other options.

• Buy Article »
• Find an Institution with the Article »

Download & Share

Schematic diagram for the standard form circuit described in the text. The n CR and m CV qubits are shown entering the gate labeled by unitary U . The double bars represent the time-travel event and may be thought of as two depictions of the same spacelike hypersurface, thus forming a CTC. The dashed lines represent the spacelike boundaries of the region in which time travel takes place; CV qubits are restricted to that region.

Circuit diagram for the unproven theorem circuit of Ref. [ 16 ] in the standard form. The book qubit is labeled B , mathematician labeled M , and time traveler labeled T . The input to the circuit is taken to be the pure state | 0 〉 B | 0 〉 M . The notation used for the gates is the standard notation as defined in Ref. [ 14 ] and describes a unitary U = s w a p M T c n o t B M c n o t T B .

The equivalent circuit model. (a) A circuit equivalent to the standard form of Fig.  1 with V = s w a p U . (b) The same circuit “unwrapped” in the equivalent circuit model. There is an infinite ladder of unwrapped circuits, each with the same input state ρ i . To start the ladder, an initial CV state σ 0 is guessed. The CV state of the N th rung of the ladder is σ N . The output state ρ f is taken after a number N → ∞ of rungs of the ladder have been iterated.

Schematic diagram illustrating the protocol defining the action of P-CTCs as described in the text. When Alice measures the final state of the B and A qubits to be | Φ 〉 , the standard teleportation protocol would have Bob (who holds the other half of the initially entangled state) then holding the state with which Alice measured the A system. There are two unusual things about this situation: first, that Bob's system is the same one that Alice wants to teleport, just at an earlier time, and, second, that Alice can get the outcome | Φ 〉 with certainty and so no classical communication to Bob is required to complete the teleportation.

Sign up to receive regular email alerts from Physical Review A

• Forgot your username/password?
• Create an account

Article Lookup

Paste a citation or doi, enter a citation.

• The Inventory

Physicists Say Time Travel Can Be Simulated Using Quantum Entanglement

“whether closed timelike curves exist in reality, we don’t know.".

The quantum world operates by different rules than the classical one we buzz around in, allowing the fantastical to the bizarrely normal. Physicists have described using quantum entanglement to simulate a closed timelike curve—in layman’s terms, time travel.

Before we proceed, I’ll stress that no quantum particles went back in time. The recent research was a Gedankenexperiment , a term popularized by Einstein to describe conceptual studies conducted in lieu of real tests—a useful thing when one is testing physics at its limits, like particles moving at the speed of light. But a proposed simulation involves “effective time travel,” according to the team’s recent paper in Physical Review Letters, thanks to a famously strange way that quantum particles can interact.

That interaction is called quantum entanglement , and it describes when the characteristics of two or more quantum particles are defined by each other. This means that knowing the properties of one entangled particle gives you information about the other, regardless of the distance between the two particles; their entanglement is on a quantum level, so a little thing like their physical distance has no bearing on the relationship. Space is big and time is relative, so a change to a quantum particle on Earth that’s entangled with a particle near a black hole 10 billion light-years away would mean changing the behavior of something in the distant past.

The recent research explores the possibility of closed-timelike curves, or CTCs—a hypothetical pathway back in time. The curve is a worldline—the arc of a particle in spacetime over the course of its existence—that runs backwards. Steven Hawking posited in his 1992 “Chronology protection conjecture” paper that the laws of physics don’t allow for closed timelike curves to exist—thus, that time travel is impossible. “Nevertheless,” the recent study authors wrote, “they can be simulated probabilistically by quantum-teleportation circuits.”

The team’s Gedankenexperiment goes like this: Physicists put photonic probes through a quantum interaction, yielding a certain measurable result. Based on that result, they can determine what input would have yielded an optimal result—hindsight is 20/20, just like when you can look over a graded exam. But because the result was yielded from a quantum operation, instead of being stuck with a less-than-optimal result, the researchers can tweak the values of the quantum probe via entanglement, producing a better result even though the operation already happened. Capiche?

The team demonstrated that one could “probabilistically improve one’s past choice,” explained study co-author Nicole Yunger Halpern, a physicist at the National Institute of Standards and Technology and the University of Maryland at College Park, in an email to Gizmodo, though she noted that the proposed time travel simulation has not yet taken place. 

In their study, the apparent time travel effect would occur one time in four—a failure rate of 75%. To address the high failure rate, the team suggests sending a large number of entangled photons, using a filter to ensure the photons with the corrected information got through while sifting out the outdated particles.

“The experiment that we describe seems impossible to solve with standard (not quantum) physics, which obeys the normal arrow of time,” said David Arvidsson-Shukur, a quantum physicist at the University of Cambridge and the study’s lead author, in an email to Gizmodo. “Thus, it appears as if quantum entanglement can generate instances which effectively look like time travel.”

The behavior of quantum particles—specifically, the ways in which those behaviors differ from macroscopic phenomena—are a useful means for physicists to probe the nature of our reality. Entanglement is one aspect of how quantum things operate by different laws.

Last year, another group of physicists claimed that they managed to create a quantum wormhole—basically, a portal through which quantum information could instantaneously travel. The year before, a team synchronized drums as wide as human hairs using entanglement. And the 2022 Nobel Prize in Physics went to three physicists for their interrogation of quantum entanglement, which is clearly an important subject to study if we are to understand how things work.

A simulation offers a means of probing time travel without worrying about whether it’s actually permitted by the rules of the universe.

“Whether closed timelike curves exist in reality, we don’t know. The laws of physics that we know of allow for the existence of CTCs, but those laws are incomplete; most glaringly, we don’t have a theory of quantum gravity,” said Yunger Halpern. “Regardless of whether true CTCs exist, though, one can use entanglement to simulate CTCs, as others showed before we wrote our paper.”

In 1992, just a couple weeks before Hawking’s paper was published, the physicist Kip Thorne presented a paper at the 13th International Conference on General Relativity and Gravitation. Thorne concluded that, “It may turn out that on macroscopic lengthscales chronology is not always protected, and even if chronology is protected macroscopically, quantum gravity may well give finite probability amplitudes for microscopic spacetime histories with CTCs.” In other words, whether time travel is possible or not is a quandary beyond the remit of classical physics. And since quantum gravity remains an elusive thing , the jury’s out on time travel.

But in a way, whether closed-timelike curves exist in reality or not isn’t that important, at least in the context of the new research. What’s important is that the researchers think their Gedankenexperiment provides a new way of interrogating quantum mechanics. It allows them to take advantage of the quantum realm’s apparent disregard for time’s continuity in order to achieve some fascinating results.

The headline and text of this article have been updated to clarify that the team describe a way that time travel can be simulated; they did not simulate time travel in this experiment.

More: Scientists Tried to Quantum Entangle a Tardigrade

Suggestions or feedback?

MIT News | Massachusetts Institute of Technology

• Machine learning
• Social justice
• Black holes
• Classes and programs

Departments

• Aeronautics and Astronautics
• Brain and Cognitive Sciences
• Architecture
• Political Science
• Mechanical Engineering

Centers, Labs, & Programs

• Abdul Latif Jameel Poverty Action Lab (J-PAL)
• Picower Institute for Learning and Memory
• Lincoln Laboratory
• School of Architecture + Planning
• School of Engineering
• School of Humanities, Arts, and Social Sciences
• Sloan School of Management
• School of Science
• MIT Schwarzman College of Computing

Physicists harness quantum “time reversal” to measure vibrating atoms

Press contact :, media download.

*Terms of Use:

Images for download on the MIT News office website are made available to non-commercial entities, press and the general public under a Creative Commons Attribution Non-Commercial No Derivatives license . You may not alter the images provided, other than to crop them to size. A credit line must be used when reproducing images; if one is not provided below, credit the images to "MIT."

Previous image Next image

The quantum vibrations in atoms hold a miniature world of information. If scientists can accurately measure these atomic oscillations, and how they evolve over time, they can hone the precision of atomic clocks as well as quantum sensors, which are systems of atoms whose fluctuations can indicate the presence of dark matter, a passing gravitational wave, or even new, unexpected phenomena.

A major hurdle in the path toward better quantum measurements is noise from the classical world, which can easily overwhelm subtle atomic vibrations, making any changes to those vibrations devilishly hard to detect.

Now, MIT physicists have shown they can significantly amplify quantum changes in atomic vibrations, by putting the particles through two key processes: quantum entanglement and time reversal.

Before you start shopping for DeLoreans, no, they haven’t found a way to reverse time itself. Rather, the physicists have manipulated quantumly entangled atoms in a way that the particles behaved as if they were evolving backward in time. As the researchers effectively rewound the tape of atomic oscillations, any changes to those oscillations were amplified, in a way that could be easily measured.

In a paper appearing today in Nature Physics , the team demonstrates that the technique, which they dubbed SATIN (for signal amplification through time reversal), is the most sensitive method for measuring quantum fluctuations developed to date.

The technique could improve the accuracy of current state-of-the-art atomic clocks by a factor of 15, making their timing so precise that over the entire age of the universe the clocks would be less than 20 milliseconds off. The method could also be used to further focus quantum sensors that are designed to detect gravitational waves, dark matter, and other physical phenomena.

“We think this is the paradigm of the future,” says lead author Vladan Vuletic, the Lester Wolfe Professor of Physics at MIT. “Any quantum interference that works with many atoms can profit from this technique.”

The study’s MIT co-authors include first author Simone Colombo, Edwin Pedrozo-Peñafiel, Albert Adiyatullin, Zeyang Li, Enrique Mendez, and Chi Shu.

Entangled timekeepers

A given type of atom vibrates at a particular and constant frequency that, if properly measured, can serve as a very precise pendulum, keeping time in much shorter intervals than a kitchen clock’s second. But at the scale of a single atom, the laws of quantum mechanics take over, and the atom’s oscillation changes like the face of a coin each time it is flipped. Only by taking many measurements of an atom can scientists get an estimate of its actual oscillation — a limitation known as the Standard Quantum Limit.

In state-of-the-art atomic clocks, physicists measure the oscillation of thousands of ultracold atoms, many times over, to increase their chance of getting an accurate measurement. Still, these systems have some uncertainty, and their time-keeping could be more precise.

In 2020, Vuletic’s group showed that the precision of current atomic clocks could be improved by entangling the atoms — a quantum phenomenon by which particles are coerced to behave in a collective, highly correlated state. In this entangled state, the oscillations of individual atoms should shift toward a common frequency that would take far fewer attempts to accurately measure.

“At the time, we were still limited by how well we could read out the clock phase,” Vuletic says.

That is, the tools used to measure atomic oscillations were not sensitive enough to read out, or measure any subtle change in the atoms’ collective oscillations.

Reverse the sign

In their new study, instead of attempting to improve the resolution of existing readout tools, the team looked to boost the signal from any change in oscillations, such that they could be read by current tools. They did so by harnessing another curious phenomenon in quantum mechanics: time reversal.

It’s thought that a purely quantum system, such as a group of atoms that is completely isolated from everyday classical noise, should evolve forward in time in a predictable manner, and the atoms’ interactions (such as their oscillations) should be described precisely by the system’s “Hamiltonian” — essentially, a mathematical description of the system’s total energy. 

In the 1980s, theorists predicted that if a system’s Hamiltonian were reversed, and the same quantum system was made to de-evolve, it would be as if the system was going back in time.

“In quantum mechanics, if you know the Hamiltonian, then you can track what the system is doing through time, like a quantum trajectory,” Pedrozo-Peñafiel explains. “If this evolution is completely quantum, quantum mechanics tells you that you can de-evolve, or go back and go to the initial state.”

“And the idea is, if you could reverse the sign of the Hamiltonian, every small perturbation that occurred after the system evolved forward would get amplified if you go back in time,” Colombo adds.

For their new study, the team studied 400 ultracold atoms of ytterbium, one of two atom types used today’s atomic clocks. They cooled the atoms to just a hair above absolute zero, at temperatures where most classical effects such as heat fade away and the atoms’ behavior is governed purely by quantum effects.

The team used a system of lasers to trap the atoms, then sent in a blue-tinged “entangling” light, which coerced the atoms to oscillate in a correlated state. They let the entangled atoms evolve forward in time, then exposed them to a small magnetic field, which introduced a tiny quantum change, slightly shifting the atoms’ collective oscillations.

Such a shift would be impossible to detect with existing measurement tools. Instead, the team applied time reversal to boost this quantum signal. To do this, they sent in another, red-tinged laser that stimulated the atoms to disentangle, as if they were evolving backward in time.

They then measured the particles’ oscillations as they settled back into their unentangled states, and found that their final phase was markedly different from their initial phase — clear evidence that a quantum change had occurred somewhere in their forward evolution.

The team repeated this experiment thousands of times, with clouds ranging from 50 to 400 atoms, each time observing the expected amplification of the quantum signal. They found their entangled system was up to 15 times more sensitive than similar unentangled atomic systems. If their system is applied to current state-of-the-art atomic clocks, it would reduce the number of measurements these clocks require, by a factor of 15.

Going forward, the researchers hope to test their method on atomic clocks, as well as in quantum sensors, for instance for dark matter.

“A cloud of dark matter floating by Earth could change time locally, and what some people do is compare clocks, say, in Australia with others in Europe and the U.S. to see if they can spot sudden changes in how time passes,” Vuletic says. “Our technique is exactly suited to that, because you have to measure quickly changing time variations as the cloud flies by.”

This research was supported, in part, by the National Science Foundation and the Office of Naval Research.

Share this news article on:

Related links.

• Vladan Vuletic
• Research Laboratory of Electronics
• Department of Physics

Related Topics

• Quantum mechanics
• Dark matter
• National Science Foundation (NSF)

Related Articles

New type of atomic clock keeps time even more precisely

Physicists create new form of light

Scientists set traps for atoms with single-particle precision

Vanishing friction

Thousands of atoms entangled with a single photon

Previous item Next item

More MIT News

Researchers 3D print key components for a point-of-care mass spectrometer

Read full story →

Unlocking new science with devices that control electric power

Drinking from a firehose — on stage

A new computational technique could make it easier to engineer useful proteins

MIT researchers discover “neutronic molecules”

Training manufacturing technologists to be future shop floor leaders

• More news on MIT News homepage →

Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, MA, USA

• Map (opens in new window)
• Events (opens in new window)
• People (opens in new window)
• Careers (opens in new window)
• Accessibility
• Social Media Hub
• MIT on Facebook
• MIT on YouTube
• MIT on Instagram

Time Travel May be Possible Inside the Quantum Realm

Time travel may be possible after all, particularly in the quantum realm. And based on recently published research, this may include moving both backward and forward in time.

BACKGROUND: BUT ISN’T TIME TRAVEL IMPOSSIBLE?

In classical physics, the movement of time is more or less described as a movement from a more organized state to a less organized state. Physicists called this entropy. Such movement can be seen in everyday systems like the rotting of food or the growing of a tree, or the simple process of a meal cooking on the stove. 

Due to this seeming unidirectional aspect to the movement of time, often called time’s arrow, most physicists agree that traveling backwards in time would violate a number of known processes and properties of physics, likely making it all but impossible outside of science fiction .

By comparison, moving forward in time is relatively straightforward. Simply speed up to as close to the speed of light as possible, thereby taking advantage of the relativistic effects that will cause time on the outside world to travel significantly faster than it will for you. In short, if you travel close enough to the speed of light, you will age significantly slower than the world around you, meaning that for all intents and purposes, you will have traveled into the future.

Now, based on new research published in the journal Communications Physics , traveling to the past may be back on the proverbial time travel table.

ANALYSIS: TO TRAVEL BACKWARDS YOU FIRST MUST GO QUANTUM

According to a recent press release ; “a team of physicists from the Universities of Bristol, Vienna, the Balearic Islands and the Institute for Quantum Optics and Quantum Information (IQOQI-Vienna), has shown how quantum systems can simultaneously evolve along two opposite time arrows – both forward and backward in time.”

This unique ability is governed by the quantum principle of superposition, where a single particle of matter can exist in two different states at the same time. According to the researchers behind the latest study, this unique state of matter also allows for the travel of time in both directions, forward and backward.

“We can take the sequence of things we do in our morning routine as an example,” said the study’s lead-author Dr. Giulia Rubino from the University of Bristol’s Quantum Engineering Technology Labs (QET labs). “If we were shown our toothpaste moving from the toothbrush back into its tube, we would be in no doubt it was a re-winded recording of our day. However, if we squeezed the tube gently so only a small part of the toothpaste came out, it would not be so unlikely to observe it re-entering the tube, sucked in by the tube’s decompression.”

“Extending this principle to time’s arrows,” added Rubino, “it results that quantum systems evolving in one or the other temporal direction (the toothpaste coming out of or going back into the tube), can also find themselves evolving simultaneously along both temporal directions.” 

Basically, if this quantum sized hypothetical “toothpaste” can evolve along two different paths as allowed by superposition, then it is possible that one of those paths results in the toothpaste moving back into the tube, essentially going back in time to a previous, less entropic state. According to Rubino, it is precisely this process that his team’s research shows.

“In our work, we quantified the entropy produced by a system evolving in quantum superposition of processes with opposite time arrows,” explained Rubino. “We found this most often results in projecting the system onto a well-defined time’s direction, corresponding to the most likely process of the two.”

In short, most of the time things moved forward in time, just as researchers and classical physics would predict. However, sometimes the opposite happened.

“And yet,” he added, “when small amounts of entropy are involved (for instance, when there is so little toothpaste spilled that one could see it being reabsorbed into the tube), then one can physically observe the consequences of the system having evolved along the forward and backward temporal directions at the same time.”

In conclusion, based on the size and timing of the event, the quantum realm may possess its own equivalent of a five second rule , allowing the movement back in time to a less entropic state in certain circumstances. But what does this mean in the macro world?

OUTLOOK: SO FLUX CAPACITOR OR NO FLUX CAPACITOR?

Like many things that occur in the quantum realm, the findings of this latest research may be counter-intuitive. However, the researchers behind the study say it is a real, actual principle operating inside the quantum world that may have real, macro-world level impacts.

The Woolly Mammoth Will Be Back In 6 Years, Says New Start-Up in Partnership with Harvard University

“Although this idea seems rather nonsensical when applied to our day-to-day experience, at its most fundamental level, the laws of the universe are based on quantum-mechanical principles.”

This revelation also likely means that macro level systems that are affected by processes in the quantum realm, like the ability of birds to sense the Earth’s magnetic field using a quantum mechanical process , may be able to take advantage of these uniquely quantum effects. Apparently, this now includes time travel.

“Although time is often treated as a continuously increasing parameter, our study shows the laws governing its flow in quantum mechanical contexts are much more complex,” said Rubino. ”This may suggest that we need to rethink the way we represent this quantity in all those contexts where quantum laws play a crucial role.”

Okay, somebody call Doc Brown. Anyone seen the keys to my DeLorean?

Follow and connect with author Christopher Plain on Twitter: @plain_fiction  

share this!

April 3, 2024

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

fact-checked

peer-reviewed publication

trusted source

Researchers visualize quantum effects in electron waves

by Markus Bernards, Goethe University Frankfurt am Main

One of the most fundamental interactions in physics is that of electrons and light. In an experiment at Goethe University Frankfurt, scientists have now managed to observe what is known as the Kapitza-Dirac effect for the first time in full temporal resolution. This effect was first postulated more than 90 years ago, but only now are its finest details coming to light.

It was one of the biggest surprises in the history of science: In the early days of quantum physics about 100 years ago, scholars discovered that the particles which make up our matter always behave like waves. Just as light can scatter at a double slit and produce scattering patterns, electrons can also display interference effects.

In 1933, the two theorists Piotr Kapitza and Paul Dirac proved that an electron beam is even diffracted from a standing light wave (due to the particles' properties) and that interference effects as a result of the wave properties are to be expected.

A German–Chinese team led by Professor Reinhard Dörner from Goethe University Frankfurt has succeeded in using this Kapitza-Dirac effect to visualize even the temporal evolution of the electron waves, known as the electrons' quantum mechanical phase. The study is published in the journal Science .

"It was a former doctoral researcher at our institute, Alexander Hartung, who originally constructed the experimental apparatus," says Dörner. "After he left, Kang Lin, an Alexander von Humboldt fellow who worked in the Frankfurt team for four years, was able to use it to measure the time-dependent Kapitza-Dirac effect." To do so, it was necessary to further develop the theoretical description, too, as Kapitza and Dirac did not take the temporal evolution of the electron phase specifically into consideration at that time.

In their experiment, the scientists in Frankfurt first fired two ultrashort laser pulses from opposite directions at a xenon gas. At the crossover point, these femtosecond pulses —a femtosecond is a quadrillionth of a second—produced an ultrastrong light field for fractions of a second. This tore electrons out of the xenon atoms, i.e., it ionized them.

Very shortly afterward, the physicists fired a second pair of short laser pulses at the electrons released in this way, which also formed a standing wave at the center. These pulses were slightly weaker and did not cause any further ionization. They were, however, now able to interact with the free electrons, which could be observed with the help of a COLTRIMS reaction microscope developed in Frankfurt.

"At the point of interaction, three things can happen," says Dörner. "Either the electron does not interact with the light—or it is scattered to the left or to the right."

According to the laws of quantum physics, these three possibilities together add up to a certain probability that is reflected in the wave function of the electrons: The cloud-like space in which the electron—with a certain probability—is likely to be, collapses, so to speak, into three-dimensional slices. Here, the temporal evolution of the wave function and its phase is dependent on how much time elapses between ionization and the moment of impact of the second pair of laser pulses.

"This opens up many exciting applications in quantum physics. Hopefully, it will help us to track how electrons transform from quantum particles into completely normal particles within the shortest space of time. We are already planning to use it to find out more about the entanglement between different particles that Einstein called 'spooky,'" says Dörner.

Journal information: Science

Provided by Goethe University Frankfurt am Main

Explore further

Feedback to editors

Automated bioacoustics: Researchers are listening in on insects to better gauge environmental health

4 hours ago

New sunflower family tree reveals multiple origins of flower symmetry

11 hours ago

Researchers determine structure of new metal tellurate material with potential uses in solar energy and more

Evolution in action? New study finds possibility of nitrogen-fixing organelles

12 hours ago

How brown rats crawled off ships and conquered North American cities

Examining groundwater's role in ecosystem sustainability

Matador bugs use their own red flags to ward off predators

For mining in arid regions to be responsible, we must change how we think about water, say researchers

Pollen is a promising sustainable tool in the bone regeneration process

13 hours ago

Fuel cells: Oxidation processes of phosphorous acid revealed by tender X-rays

Relevant physicsforums posts, how would someone see light from something like a flashlight in a tunnel.

21 hours ago

Explanation for homemade digital microscope's optical systems?

Mar 23, 2024

Was Thomas Young wrong?

Mar 13, 2024

Horizon and Curvature Observations

Laser and nano-holes experiment, measure the transmission curve and wavelengths of colored mineral glass.

Mar 11, 2024

More from Optics

Related Stories

Trillionths of a second: Photon pairs compress an electron beam into short pulses

Jun 19, 2023

Photon-like electrons in a four-dimensional world discovered in a real material

Mar 14, 2024

Researchers solve puzzle of Compton scattering: New approach for testing theories in quantum mechanics

Apr 15, 2020

Zeptoseconds: New world record in short time measurement

Oct 16, 2020

Interplay of free electrons: Tailored electron pulses for improved electron microscopy

Oct 13, 2023

Beyond Einstein: Physicists solve mystery surrounding photon momentum

Oct 1, 2019

Recommended for you

Intelligent liquid: Researchers develop metafluid with programmable response

17 hours ago

100 kilometers of quantum-encrypted transfer

Apr 2, 2024

Study unveils a new family of quantum anomalous Hall insulators

Classical optical neural network exhibits 'quantum speedup'

Transmitting entanglement between light and matter in the metropolitan network of Barcelona

Focusing ultra-intense lasers to a single wavelength

Let us know if there is a problem with our content.

Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page. For general inquiries, please use our contact form . For general feedback, use the public comments section below (please adhere to guidelines ).

Please select the most appropriate category to facilitate processing of your request

Thank you for taking time to provide your feedback to the editors.

Your feedback is important to us. However, we do not guarantee individual replies due to the high volume of messages.

E-mail the story

Your email address is used only to let the recipient know who sent the email. Neither your address nor the recipient's address will be used for any other purpose. The information you enter will appear in your e-mail message and is not retained by Phys.org in any form.

Newsletter sign up

Get weekly and/or daily updates delivered to your inbox. You can unsubscribe at any time and we'll never share your details to third parties.

More information Privacy policy

Donate and enjoy an ad-free experience

We keep our content available to everyone. Consider supporting Science X's mission by getting a premium account.

E-mail newsletter

• Collections

• APS Journals

A New Source for Quantum Light

Quantum light sources produce entangled pairs of photons that can be used in quantum computing and cryptography. A new experiment has demonstrated a quantum light source made from the semiconductor gallium nitride. This material provides a versatile platform for device fabrication, having previously been used for on-chip lasers, detectors, and waveguides. Combined with these other optical components, the new quantum light source opens up the potential to construct a complex quantum circuit, such as a photonic quantum processor, on a single chip.

Quantum optics is a rapidly advancing field, with many experiments using photons to carry quantum information and perform quantum computations. However, for optical systems to compete with other quantum information technologies, quantum-optics devices will need to be shrunk from tabletop size to microchip size. An important step in this transformation is the development of quantum light generation on a semiconductor chip. Several research teams have managed this feat using materials such as gallium aluminum arsenide, indium phosphide, and silicon carbide. And yet a fully integrated photonic circuit will require a range of components in addition to quantum light sources.

With the aim of eventually building such a full circuit, Qiang Zhou of the University of Electronic Science and Technology of China and colleagues put their sights on gallium nitride. This material is well known for its use in the first blue LEDs—a development that was recognized with the 2014 Nobel Prize in Physics (see Notes from the Editors: Blue Was the Hardest Color ). Recent work has shown that gallium nitride grown on sapphire can be used for a number of quantum-optical functions, such as lasing, optical filtering, and single-photon detection. “The gallium nitride platform offers promising prospects for advancing photonic quantum chips in the near future,” Zhou says.

To create a gallium nitride quantum light source, Zhou and colleagues grew a film of the material on a sapphire substrate and then etched a 120-µm-diameter ring in the film. In this structure, photons can travel around the ring, similar to the way that sound waves travel around the curved walls of a whispering gallery (see Viewpoint: Tiny Resonators Generate a Large Optical Spectrum ). Next to the ring, the researchers etched a waveguide for transmitting infrared laser light. A coupling between the two optical elements allows some laser photons to pass from the waveguide into the ring.

In the experiments, a detector recorded the spectrum of the waveguide’s output light, revealing discrete dips at multiple wavelengths. Those dips corresponded to resonances in the ring—when a particular photon’s wavelength fits an integer number of times within the ring’s circumference. Resonant photons in the waveguide can enter the ring and become trapped inside.

However, thanks to an effect called four-wave mixing (see Synopsis: Photonic Matchmaking ), pairs of resonant photons entering the ring can sometimes annihilate, causing a new pair of resonant photons (at different wavelengths) to be created and exit through the waveguide. The two photons in each exiting pair are expected to be entangled with each other. To verify this entanglement, the team performed measurements on pairs of coincident photons, showing that they generate an interference pattern—stripes of light and dark fringes—when imaged. (By contrast, nonentangled pairs would produce one broad, bright spot.)

The level of interference—characterized by the amount of contrast between light and dark fringes—is a measure of the degree of entanglement of the photons. The degree of entanglement produced by the gallium nitride ring was comparable to the level measured for other quantum light sources, Zhou says. “We demonstrate that gallium nitride is a good quantum material platform for photonic quantum information, in which the generation of quantum light is crucial,” he says.

“Quantum optics has evolved with a tremendous pace in recent years,” says quantum optics expert Thomas Walther from the Technical University of Darmstadt in Germany. He says that moving forward will require components that are small, robust, efficient, and relatively easy to manufacture. To this end, Zhou and his colleagues have demonstrated that gallium nitride is a promising material for making the pump source, the quantum light source, and the single photon detectors. Having one platform for all these devices “would constitute a major step forward, as this could reduce the cost for manufacturing such systems, as well as make them much more compact and rugged than they are today,” he says.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.

• H. Zeng et al. , “Quantum light generation based on GaN microring toward fully on-chip source,” Phys. Rev. Lett. 132 , 133603 (2024) .

Quantum Light Generation Based on GaN Microring toward Fully On-Chip Source

Hong Zeng, Zhao-Qin He, Yun-Ru Fan, Yue Luo, Chen Lyu, Jin-Peng Wu, Yun-Bo Li, Sheng Liu, Dong Wang, De-Chao Zhang, Juan-Juan Zeng, Guang-Wei Deng, You Wang, Hai-Zhi Song, Zhen Wang, Li-Xing You, Kai Guo, Chang-Zheng Sun, Yi Luo, Guang-Can Guo, and Qiang Zhou

Phys. Rev. Lett. 132 , 133603 (2024)

Published March 29, 2024

Subject Areas

Related articles.

Shielding Quantum Light in Space and Time

A way to create single photons whose spatiotemporal shapes do not expand during propagation could limit information loss in future photonic quantum technologies. Read More »

Erasure Qubits for Abridged Error Correction

Researchers have realized a recently proposed qubit in which the errors mostly involve erasure of the qubit state, an advance that could help simplify the architecture of fault-tolerant quantum computers. Read More »

Another Twist in the Understanding of Moiré Materials

The unexpected observation of an aligned spin polarization in certain twisted semiconductor bilayers calls for improved models of these systems. Read More »

Sign up to receive weekly email alerts from Physics Magazine .

Could the Multiverse Help us Find Alien Life? Expert Paul Sutter Explains

A parallel universe is a fun topic in physics, but it's difficult to understand the concept. That's why Paul Sutter , a theoretical cosmologist, award-winning science communicator, NASA advisor, U.S. Cultural Ambassador, and a globally recognized leader in the intersection of art and science, dives into this topic and helps us understand if parallel universes could help us search for extraterrestrial life.

Hear from Sutter himself as we ask him this question: Are parallel universes possible and can they help us search for extraterrestrial life?

Do Parallel Universes Exist?

Parallel universes are such a tricky topic for me to explore. On the one hand, they are beyond interesting – the possibility of an alternate cosmos right over there is such a mind-meltingly fun idea. But on the other hand, at present we have no way of testing if the multiverse hypothesis is correct, and we're not even sure we can test it, which is a bit difficult to confront.

Read More: Are Strange Space Signals in Antarctica Evidence of a Parallel Universe?

How Does Quantum Physics Relate to the Multiverse Theory?

Let me take a few steps back. The "multiverse" is the very old and generic idea, stretching all the way back to at least antiquity, that our universe is not alone. That there are other worlds/dimensions/realities alongside our own. In modern times, the multiverse appears in two completely separate areas of physics.

One of the places is in quantum mechanics . It turns out that the physics of the really small is dominated by randomness. We can never exactly predict what subatomic particles are going to do at any moment. We can only make guesses about what they might do. We have no idea how this all works. By which I mean that while we have a very sophisticated set of tools for making probability-based predictions, we don't have a picture of what's really going on down there.

Read More: Is the Multiverse Theory Science Fiction or Science Fact?

What Is the Many-Worlds Interpretation of Quantum Mechanics?

There are many "interpretations" of quantum mechanics that offer such pictures, and one of them is known as the Many-Worlds Interpretation . In that interpretation, every time a random quantum event happens (which is…a lot), the universe "splits" into multiple branches, with each branch carrying one of the outcomes of the event.

The other place that the multiverse appears in physics is through our theories of the extremely early universe. For a variety of reasons, cosmologists believe that in the first second after the big bang, the cosmos underwent a period of extremely fast inflation. Some theories of inflation suggest that it never ended. What we call the universe is just a small piece of a much larger cosmos that has been rapidly expanding since well before we came on the scene. Other individual universes can appear in this multiverse, like bubbles of soap in an expanding foam

Read More: How Does Multiverse Theory Relate to Time Travel?

Can we Prove the Existence of a Parallel Universe?

One issue is that we have no idea how to test if these theories of the multiverse are correct or not. The Many-Worlds Interpretation is just that: an interpretation. It's not a theory of physics.

As for the multiverse from inflation, we are working towards finding ways to test inflation itself, but we'll never be able to know if other universes exist outside our own cosmos, because by definition our cosmos is the limit of what we can observe.

Read More: Are We Alone In The Multiverse?

Could Alien Life Exist in Parallel Universes?

What does all of this have to do with alien life? We have no idea if we are alone in the universe or not. In fact, all the evidence we have collected so far indicates that there's nobody else out there, but we haven't exactly been searching for very long.

It's a big universe: our Milky Way is home to around 300 billion stars, and there are about 2 trillion galaxies in the observable universe. The multiverse opens up the possibilities of where life could also exist. Even if the entirety of our cosmos is absolutely devoid of life, and we are the only living creatures in the whole shebang, then the multiverse allows for more room.

For example, there could be another "branch" of quantum possibilities that leads to a universe filled with strange alien lifeforms. Or somewhere out there in the inflation-powered multiverse is a bubble containing life of its own.

Both versions of the multiverse increase the probability of alien life existing somewhere . But I personally can't use this to make a definite statement that life is out there. We can't access the multiverse; we can't go to any other universe or branch and look around. We can guess, which is fun, but it's not scientific.

If we want to know for sure if we are alone or not, then we have to limit ourselves to this universe and this universe alone. But don't worry, with a diameter of over 90 billion light-years, we've got plenty of places to look.

Read More: Fact or Fiction: What Is The Truth Behind Alien Conspiracy Theories?

Article Sources

Our writers at Discovermagazine.com use peer-reviewed studies and high-quality sources for our articles, and our editors review them for accuracy and trustworthiness. Review the sources used below for this article:

Astronomy Magazine . Is the multiverse theory science fiction or science fact?

Britannica . Quantum mechanics.

Stanford Encyclopedia of Philosophy. Many-Worlds Interpretation of Quantum Mechanics.

Simulations of ‘Backwards Time Travel’ Can Improve Scientific Experiments

(Credit: Time is Slipping Away (cropped) from Bennilover on Flick under  CC BY-ND 2.0 DEED )

If gamblers, investors and quantum experimentalists could bend the arrow of time, their advantage would be significantly higher, leading to significantly better outcomes.

JQI affiliate Nicole Yunger Halpern and her colleagues at the University of Cambridge have shown that by manipulating entanglement—a feature of quantum theory that causes particles to be intrinsically linked—they can simulate what could happen if one could travel backwards in time. If such an experiment can be performed, it will be as if the quantum experimentalists are gamblers that can retroactively change their past actions to improve their outcomes in the present.

Whether particles can travel backwards in time is a controversial topic among physicists, but scientists have  previously simulated models of how such spacetime loops could behave if they did exist. By connecting their new theory to quantum metrology, which uses quantum theory to make highly sensitive measurements, the Cambridge team has shown that entanglement can solve problems that otherwise seem impossible.  The study appears in the journal Physical Review Letters .

“ Imagine that you want to send a gift to someone: You need to send it on day one to make sure it arrives on day three,” says lead author David Arvidsson-Shukur, from the Cambridge Hitachi Laboratory.  “ However, you only receive that person ’ s wish list on day two. So, in this chronology-respecting scenario, it ’ s impossible for you to know in advance what they will want as a gift and to make sure you send the right one.

“ Now imagine you can change what you send on day one with the information from the wish list received on day two. Our simulation uses quantum entanglement manipulation to show how you could retroactively change your previous actions to ensure the final outcome is the one you want.”

The simulation is based on quantum entanglement , where the fates of quantum particles are intrinsically linked in a way that never occurs in the physics of relatively large items like people or even grains of sand. Entanglement plays an essential role in  quantum computing —the harnessing of connected particles to perform computations too complex for classical computers.

“In our proposal, an experimentalist entangles two particles,” says co-author Yunger Halpern, who is also a Fellow of the  Joint Center for Quantum Information and Computer Science  and a physicist at the  National Institute of Standards and Technology . “The first particle is then sent to be used in an experiment. Upon gaining new information, the experimentalist manipulates the second particle to effectively alter the first particle’s past state, changing the outcome of the experiment.”

“ The effect is remarkable, but it happens only one time out of four!” said Arvidsson-Shukur.  “ In other words, the simulation has a 75% chance of failure. But the good news is that you know if you have failed. If we stay with our gift analogy, one out of four times, the gift will be the desired one (for example a pair of trousers), another time it will be a pair of trousers but in the wrong size, or the wrong colour, or it will be a jacket.”

To give their model relevance to technologies, the theorists connected it to quantum metrology. In a common quantum metrology experiment, photons—small particles of light—are shone onto a sample of interest and then registered with a special type of camera. If this experiment is to be efficient, the photons must be prepared in a certain way before they reach the sample. The researchers have shown that even if they learn how to best prepare the photons only after the photons have reached the sample, they can use simulations of time travel to retroactively change the original photons.

To counteract the high chance of failure, the theorists propose to send a huge number of entangled photons, knowing that some will eventually carry the correct, updated information. Then they would use a filter to ensure that the right photons pass to the camera, while the filter rejects the rest of the  ‘ bad’ photons.

“Consider our earlier analogy about gifts,” says co-author Aidan McConnell, who carried out this research during his master’s degree at the Cavendish Laboratory in Cambridge and is now a PhD student at ETH, Zürich. “Let’s say sending gifts is inexpensive and we can send numerous parcels on day one. On day two we know which gift we should have sent. By the time the parcels arrive on day three, one out of every four gifts will be correct, and we select these by telling the recipient which deliveries to throw away.”

“ That we need to use a filter to make our experiment work is actually pretty reassuring,” says Arvidsson-Shukur.  “ The world would be very strange if our time-travel simulation worked every time. Relativity and all the theories that we are building our understanding of our universe on would be out of the window.

“ We are not proposing a time travel machine, but rather a deep dive into the fundamentals of quantum mechanics. These simulations do not allow you to go back and alter your past, but they do allow you to create a better tomorrow by fixing yesterday ’ s problems today.”

Story by Vanessa Bismuth

This story was prepared by the  University of Cambridge  and adapted with permission.

About the Research

Reference publications, nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves.

Help | Advanced Search

Quantum Physics

Title: photonic quantum walk with ultrafast time-bin encoding.

Abstract: The quantum walk (QW) has proven to be a valuable testbed for fundamental inquiries in quantum technology applications such as quantum simulation and quantum search algorithms. Many benefits have been found by exploring implementations of QWs in various physical systems, including photonic platforms. Here, we propose a novel platform to perform quantum walks using an ultrafast time-bin encoding (UTBE) scheme. This platform supports the scalability of quantum walks to a large number of steps while retaining a significant degree of programmability. More importantly, ultrafast time bins are encoded at the picosecond time scale, far away from mechanical fluctuations. This enables the scalability of our platform to many modes while preserving excellent interferometric phase stability over extremely long periods of time without requiring active phase stabilization. Our 18-step QW is shown to preserve interferometric phase stability over a period of 50 hours, with an overall walk fidelity maintained above $95\%$

Submission history

Access paper:.

• HTML (experimental)
• Other Formats

References & Citations

• INSPIRE HEP
• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Magnetic avalanche triggered by quantum effects

Quantum 'barkhausen noise' detected for first time.

Iron screws and other so-called ferromagnetic materials are made up of atoms with electrons that act like little magnets. Normally, the orientations of the magnets are aligned within one region of the material but are not aligned from one region to the next. Think of packs of tourists in Times Square pointing to different billboards all around them. But when a magnetic field is applied, the orientations of the magnets, or spins, in the different regions line up and the material becomes fully magnetized. This would be like the packs of tourists all turning to point at the same sign.

The process of spins lining up, however, does not happen all at once. Rather, when the magnetic field is applied, different regions, or so-called domains, influence others nearby, and the changes spread across the material in a clumpy fashion. Scientists often compare this effect to an avalanche of snow, where one small lump of snow starts falling, pushing on other nearby lumps, until the entire mountainside of snow is tumbling down in the same direction.

This avalanche effect was first demonstrated in magnets by the physicist Heinrich Barkhausen in 1919. By wrapping a coil around a magnetic material and attaching it to a loudspeaker, he showed that these jumps in magnetism can be heard as a crackling sound, known today as Barkhausen noise.

Now, reporting in the journal Proceedings of the National Academy of Sciences (PNAS), Caltech researchers have shown that Barkhausen noise can be produced not only through traditional, or classical means, but through quantum mechanical effects. This is the first time quantum Barkhausen noise has been detected experimentally. The research represents an advance in fundamental physics and could one day have applications in creating quantum sensors and other electronic devices.

"Barkhausen noise is the collection of the little magnets flipping in groups," says Christopher Simon, lead author of the paper and a postdoctoral scholar in the lab of Thomas F. Rosenbaum, a professor of physics at Caltech, the president of the Institute, and the Sonja and William Davidow Presidential Chair. "We are doing the same experiment that has been done many times, but we are doing it in a quantum material. We are seeing that the quantum effects can lead to macroscopic changes."

Usually, these magnetic flips occur classically, through thermal activation, where the particles need to temporarily gain enough energy to jump over an energy barrier. However, the new study shows that these flips can also occur quantum mechanically through a process called quantum tunneling.

In tunneling, particles can jump to the other side of an energy barrier without having to actually pass over the barrier. If one could scale up this effect to everyday objects like golf balls, it would be like the golf ball passing straight through a hill rather than having to climb up over it to get to the other side.

"In the quantum world, the ball doesn't have to go over a hill because the ball, or rather the particle, is actually a wave, and some of it is already on the other side of the hill," says Simon.

In addition to quantum tunneling, the new research shows a co-tunneling effect, in which groups of tunneling electrons are communicating with each other to drive the electron spins to flip in the same direction.

"Classically, each one of the mini avalanches, where groups of spins flip, would happen on its own," says co-author Daniel Silevitch, research professor of physics at Caltech. "But we found that through quantum tunneling, two avalanches happen in sync with each other. This is a result of two large ensembles of electrons talking to each other and, through their interactions, they make these changes. This co-tunneling effect was a surprise."

For their experiments, members of the team used a pink crystalline material called lithium holmium yttrium fluoride cooled to temperatures near absolute zero (equivalent to minus 273.15 degrees Celsius). They wrapped a coil around it, applied a magnetic field, and then measured brief jumps in voltage, not unlike what Barkhausen did in 1919 in his more simplified experiment. The observed voltage spikes indicate when groups of electron spins flip their magnetic orientations. As the groups of spins flip, one after the other, a series of voltage spikes is observed, i.e. the Barkhausen noise.

By analyzing this noise, the researchers were able to show that a magnetic avalanche was taking place even without the presence of classical effects. Specifically, they showed that these effects were insensitive to changes in the temperature of the material. This and other analytical steps led them to conclude that quantum effects were responsible for the sweeping changes.

According to the scientists, these flipping regions can contain up to 1 million billion spins, in comparison to the entire crystal that contains approximately 1 billion trillion spins.

"We are seeing this quantum behavior in materials with up to trillions of spins. Ensembles of microscopic objects are all behaving coherently," Rosenbaum says. "This work represents the focus of our lab: to isolate quantum mechanical effects where we can quantitively understand what is going on."

Another recent PNAS paper from Rosenbaum's lab similarly looks at how tiny quantum effects can lead to larger-scale changes. In this earlier study, the researchers studied the element chromium and showed that two different types of charge modulation (involving the ions in one case and the electrons in the other) operating at different length scales can interfere quantum mechanically. "People have studied chromium for a long time," says Rosenbaum, "but it took until now to appreciate this aspect of the quantum mechanics. It is another example of engineering simple systems to reveal quantum behavior that we can study on the macroscopic scale."

The PNAS study titled "Quantum Barkhausen noise induced by domain wall cotunneling" was funded by the U.S. Department of Energy and the National Sciences and Engineering Research Council of Canada. The author list also includes Philip Stamp, a visiting associate in physics at Caltech and a physics professor at University of British Columbia.

• Quantum Physics
• Spintronics
• Quantum Computing
• Materials Science
• Engineering and Construction
• Nanotechnology
• Quantum mechanics
• Quantum computer
• Quantum entanglement
• Quantum tunnelling
• Introduction to quantum mechanics
• Quantum number
• Absolute zero

Story Source:

Materials provided by California Institute of Technology . Original written by Whitney Clavin. Note: Content may be edited for style and length.

Journal References :

• C. Simon, D.M. Silevitch, P.C.E. Stamp, T.F. Rosenbaum. Quantum Barkhausen noise induced by domain wall cotunneling . Proceedings of the National Academy of Sciences , 2024; 121 (13) DOI: 10.1073/pnas.2315598121
• Yejun Feng, Yishu Wang, T. F. Rosenbaum, P. B. Littlewood, Hua Chen. Quantum interference in superposed lattices . Proceedings of the National Academy of Sciences , 2024; 121 (7) DOI: 10.1073/pnas.2315787121

Cite This Page :

Explore More

• 100 Kilometers of Quantum-Encrypted Transfer
• Intelligent Liquid
• New Approach to Searching for Dark Matter
• We've Had Bird Evolution All Wrong
• Physical Activity Protects Against Chronic Pain
• Australia On Track for Decades-Long Megadroughts
• Speed of Visual Perception Ranges Widely
• 3D Printed Replica of an Adult Human Ear
• Extremely Fast Wound Healing: New Treatment
• Micro-Lisa! Novel Nano-Scale Laser Writing

Trending Topics

Strange & offbeat.