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).

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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.

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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.

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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”.

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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:

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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.

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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”…

 

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