Time Travel into the Past: How can a wormhole be transformed into a time machine?

In 1988, Kip Thorn and his students published a technical article about traversable wormholes (see here). In their article, they conjectured that if the laws of physics were to permit traversable wormholes they would probably also permit such a wormhole to be transformed into a time machine, which violates causality. This would allow for travel into the past. More than 25 years later, Thorn was involved with the movie Interstellar from its inception and he helped the producer Christopher Nolan and others weave science into the film’s fabric. However, according to Thorn, today almost thirty years have gone by and, the preponderance of evidence still suggests that traversable wormholes are an impossibility.

Wormhole creation would be governed by the laws of quantum gravity. A seemingly plausible scenario entails quantum foam (“foamy” topologies of space-time on length-scales of the order of the Planck length 1.3 x 10-33). One can imagine an advanced civilization pulling a wormhole out of the quantum foam, enlarging it to classical size, and threading it with exotic matter to hold it open. Of course, says Thorn, we do not understand the quantum gravity laws that control the foam, the pull, and the stages of enlargement. Moreover, we do not understand exotic matter very well either.

Thorn suggests the following thought experiment. I am paraphrasing here. Suppose both California desert and Dublin are connected by a wormhole. The two mouths of the wormhole are synchronized. Since the California desert and Dublin are not moving with respect to each other, I in the California desert can synchronize my clock with that of my friend in Dublin. Hence clocks remain synchronized inside the throat and between the two mouths regardless of the outside time. While a wormhole is a single unit connected by a throat, its two mouths open onto places that are totally different from each other. The wormhole throat itself is a single reference system. According to special relativity, we can, therefore, synchronize clocks in this reference system.


Mouth in California Desert                             Mouth in Dublin

The images seen through a wormhole’s mouths. Photos by Catherine MacBride and Mark Interrante.

Both mouths look like crystal balls. When I look into my California desert mouth, I see a distorted image of a street in Dublin. That image is brought to me by light that travels through the wormhole from Dublin to California, rather like light traveling through an optical fiber. When you look into your Dublin mouth, you see a distorted image of the trees in the California desert.

In Thorn, Kip, The Science of Interstellar, W. W. Norton & Company, p. 133.

Imagine a situation where the wormhole has been created by an advanced civilization in some future year, say 3000. On January 1, 3000 the wormhole’s two mouths, A and B, are at rest with respect to each other. Subsequently, mouth A remains at rest in Dublin, while mouth B, in California desert, accelerates to near-light speed, then reverses its motion and returns to its original location. Suppose the advanced beings produce this motion by pulling on mouth B gravitationally. I, therefore, take mouth B for a round trip and travel outside the wormhole with mouth B moving at relativistic velocities. Mouth A will not have moved since nothing has been pulling on it. The two mouths A and B of the wormhole are moving with respect to each other, and the wormhole throat now has mouth A at one end and a hole B at the other end. Hence the geometry of the wormhole throat does not change during the whole trip of mouth B so that the length of the wormhole’s throat remains fixed.

Since the two mouths move with respect to each other, time dilation creates a time difference between the clocks next to each mouth. The motion of the mouth is like that of the twins in the standard special-relativistic twin paradox. Outside the wormhole, mouth B ages less than mouth A, but inside the wormhole, the clocks are still synchronized; mouth A and hole B are at rest relative to each other and therefore, both entrances of the wormhole will age equally. If I have traveled with mouth B at close to the speed of light, I might find myself ensconced for many years in the future after returning to my original location in California desert.

I finally return to California desert with mouth B and find I have aged only one day (namely, on the date January 2, 3000, as measured by my own time – my proper time). Suppose that I find myself, on returning to California desert, to have arrived on, say, January 1, 3010 (according to the standard special-relativistic twin paradox). This is the date that appears on the calendar on the wall of an abandoned creepy cabin in the desert. Stepping through mouth B in California desert on January 1, 3010 and emerging out of A in Dublin will take me back in time. I will emerge from A and find that it is January 2, 3000. This is so because it is as seen from Dublin and my clock remains synchronized with the clock in mouth A. Recall that I have aged only one day during the trip (on my subsequent return to California desert, the date was January 2, 3000, as measured by my own time).

Consequently, by traversing the wormhole from mouth B to mouth A, one can travel backward in time, namely one can traverse a closed timelike curve. The same relative aging that occurs in the twin paradox produces, here, closed timelike curves that loop through the wormhole. However, that traveler could never go further back into the past than the year 3000. No traveler can ever go further back in time than the original date of creation of the wormhole.

Fur further reading see my book: General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists.

How do science fiction writers explain traversable wormholes? In The Strange Days at Blake Holsey High science fiction television program, a group of science students (science club) at a private boarding school have discovered that their science teacher’s office floor has a traversable wormhole that connects major time periods and therefore deposits a traveler back in time to October 4, 1987, April 11, 1977, and October 4, 1879 (when Blake Holsey High and the wormhole were founded). One of the students is getting sucked into the wormhole:







Einstein, Gödel and Time Travel

In January 1940 Gödel left Austria and emigrated to America, to the newly founded Institute for Advanced Study, located in Princeton University’s Fine Hall. Princeton University mathematician, Oskar Morgenstein, told Bruno Kreisky on October 25 1965 that, Einstein has often told him that in the late years of his life he has continually sought Gödel’s company, in order to have discussions with him. Once he said to him that his own work no longer meant much that he came to the Institute merely to have the privilege to be able to walk home with Gödel (Wang, Hao Reflections on Kurt Gödel, MIT Press, 1987, 31).


Image of Einstein and Gödel.

Palle Yourgrau writes in his book A World Without Time:

“Within a few years the deep footprints in intellectual history traced by Gödel and Einstein in their long walks home had disappeared, dispersed by the harsh winds of fashion and philosophical prejudice. A conspiracy of silence descended on the Einstein-Gödel friendship and its scientific consequences. An association no less remarkable than the friendship between Michelangelo and Leonardo – if such had occurred – has simply vanished from sight”. (Yourgrau, Palle A World Without Time: The Forgotten Legacy of Gödel and Einstein, Basic Books, 2005, 7).

In fact, cinquecento Florence the cradle of renaissance art, led to competition among the greatest artists, Leonardo di ser Piero da Vinci and Michelangelo di Lodovico Buonarroti Simoni. And in 1504 the two greatest artists of the Renaissance Leonardo and Michelangelo became direct rivals.


Scuola di Atene, Raphael. Plato (Leonardo) and Aristotle (not Michelangelo).

We can readily admit that, the comparison Yourgrau made between Leonardo’s “friendship” with Michelangelo and Gödel’s daily walk to and from the Institute of Advanced Studies with Einstein is a comparison between two very different things.


Picture of Gödel and Einstein

In Princeton, in 1949, Gödel found that Einstein’s theory of general relativity allows the existence of closed timelike curves (CTCs), paths through spacetime that, if followed, allow a time traveler to interact with his/her former self (Gödel, Kurt, “An example of a new type of cosmological solutions of Einstein’s field equations of gravitation, Reviews of Modern Physics 21, 1949, 447-450).

He explained (Gödel, Kurt, “A remark about the relationship between relativity theory and idealistic philosophy, in: Albert Einstein – Philosopher-Scientist, ed. Paul . A. Schilpp, 1949, pp. 555-562; pp. 560-561):

“Namely, by making a round trip on a rocket ship in a sufficiently wide curve, it is possible in these worlds to travel into any region of the past, present, and future, and back again, exactly as it is possible in other worlds to travel to distant parts of space. This state of affairs seems to imply an absurdity. For it enables one e.g., to travel into the near past of those places where he has himself lived. There he would find a person who would be himself at some earlier period of his life. Now he could do something to this person which, by his memory, he knows has not happened to him. This and similar contradictions, however, in order to prove the impossibility of the worlds under consideration, presuppose the actual feasibility of the journey into one’s own past”.


Einstein replied to Gödel (in: Albert Einstein – Philosopher-Scientist, ed. Paul. A. Schilpp, 1949, pp.687-688):

“Kurt Gödel’s essay constitutes, in my opinion, an important contribution to the general theory of relativity, especially to the analysis of the concept of time. The problem here involved disturbed me already at the time of the building up of the general theory of relativity, without my having succeeded in clarifying it. Entirely aside from the relation of the theory of relativity to idealistic philosophy or to any philosophical formulation of questions, the problem presents itself as follows:


If P is a world-point, a ‘light-cone’ (ds2= 0) belongs to it. We draw a ‘time-like’ world-line through P and on this line observe the close world-points B and A, separated by P. Does it make any sense to provide the world-line with an arrow, and to assert that B is before P, A after P?

Is what remains of temporal connection between world-points in the theory of relativity an asymmetrical relation, or would one be just as much justified, from the physical point of view, to indicate the arrow in the opposite direction and to assert that A is before P, B after P?

In the first instance the alternative is decided in the negative, if we are justified in saying: If it is possible to send (to telegraph) a signal (also passing by in the close proximity of P) from B to A, but not from A to B, then the one-sided (asymmetrical) character of time is secured, i.e., there exists no free choice for the direction of the arrow. What is essential in this is the fact that the sending of a signal is, in the sense of thermodynamics, an irreversible process, a process which is connected with the growth of entropy (whereas, according to our present knowledge, all elementary processes are reversible).

If, therefore, B and A are two, sufficiently neighbouring, world-points, which can be connected by a time-like line, then the assertion: ‘B is before A,’ makes physical sense. But does this assertion still make sense, if the points, which are connectable by the time-like line, are arbitrarily far separated from each other? Certainly not, if there exist point-series connectable by time-like lines in such a way that each point precedes temporally the preceding one, and if the series is closed in itself. In that case the distinction ‘earlier-later’ is abandoned for world-points which lie far apart in a cosmological sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Gödel has spoken”.

Seth Lloyd suggests that general relativistic CTCs provide one potential mechanism for time travel, but they need not provide the only one. Quantum mechanics might allow time travel even in the absence of CTCs in the geometry of spacetime. He explores a particular version of CTCs based on combining quantum teleportation (and quantum entanglement) with “postselection”. This combination results in a quantum channel to the past. The entanglement occurs between the forward – and backward going parts of the curve. Post-selection replaces the quantum measurement, allowing time travel to take place: Postselection could ensure that only a certain type of state can be teleported. The states that qualify to be teleported are those that have been postselected to be self-consistent prior to being teleported. Only after it has been identified and approved can the state be teleported, so that, in effect, the state is traveling back in time. Under these conditions, time travel could only occur in a self-consistent, non-paradoxical way. The resulting post-selected closed timelike curves (P-CTCs) provide time-travel (Quantum time machine) that avoids grandfather paradox. Entangled states of P-CTCs, allows time travel even when no space-time CTC exists. Such quantum time travel can be thought of as a kind of quantum tunneling backwards in time, which can take place even in the absence of a classical path from future to past.


But on March 3 1947, Einstein wrote the famous lines to Max Born: “I cannot make a case for my attitude in physics which you would consider at all reasonable. I admit, of course, that there is considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance”. (Einstein to Born March 3 1947, letter 84). And at about the same time Professor John Archibald Wheeler recounted the time he was presenting Einstein with a new method of looking at quantum mechanics. The aging Einstein listened patiently for 20 minutes. “Well, I still can’t believe God plays dice”, he replied, adding, “but may be I’ve earned the right to make my mistakes”…