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”…



A Century of General Relativity מאה שנה ליחסות הכללית

Hebrew University of Jerusalem celebrates the anniversary of Einstein’s General Theory of Relativity (GTR) in a four-day conference:

Space-Time Theories: Historical and Philosophical Contexts

Monday-Thursday, January 5-8, 2015, in Jerusalem, the van Leer Jerusalem Institute. The conference brings together physicists, historians and philosophers of science from Israel and the world, all working from different perspectives on problems inspired by GTR. It is the first among three conferences planned to celebrate the centenary of Einstein’s General Theory of Relativity, the last of which will take place in the Max Planck Institute in Berlin on December 5, 2015, my next birthday. I am not on the list of speakers of the conference, but it says that admission is free.

בין ה-5-8 לינואר 2015 יתקיים כנס לציון 100 שנה להולדת תורת היחסות הכללית של איינשטיין. הכנס יתקיים במכון ואן ליר בירושלים ליד בית הנשיא. בכנס יישאו דברים היסטוריונים ופילוסופים של המדע שעוסקים בתחום וכן פיסיקאים. הוא הכנס הראשון מבין שלושה שמאורגנים בתחום. הראשון מאורגן באוניברסיטה העברית והאחרון במכון מקס פלאנק: יתקיים בדיוק בעוד שנה ביום ההולדת הבא שלי ב-5 לדצמבר, 2015. אני אמנם לא ברשימת הדוברים של הכנס בירושלים, אבל המודעה מציינת שהכניסה חופשית. בכנס הקודם מ-2005, שציין מאה שנים להולדת תורת היחסות הפרטית של איינשטיין במכון ואן ליר, זכורים היטב דברי הפתיחה של הנשיא ד’אז משה קצב


Einstein wrote Max Born on May 12, 1952:

“The generalization of gravitation is now, at last, completely convincing and unequivocal formally unless the good Lord has chosen a totally different way of which one can have no conception. The proof of the theory is unfortunately far too difficult for me. Man is, after all, only a poor wretch… Even if the deflection of light, the perihelial movement or line shift were unknown, the gravitation equations would still be convincing because they avoid the inertial system (the phantom which affects everything but is not itself affected). It is really rather strange that human beings are normally deaf to the strongest arguments while they are always inclined to overestimate measuring accuracies”.

What did Einstein mean by saying “the gravitation equations would still be convincing…”? “In June 9, 1952 Einstein wrote an appendix to the fifteenth edition of his popular 1917 book Über die spezielle und die allgemeine Relativitätstheorie Gemeinverständlich (On the Special and the General Theory of Relativity). In this appendix he explained:

“I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept “empty space” loses its meaning”.

The centenary of Einstein’s General Theory of Relativity

Einstein’s first big project on Gravitation in Berlin was to complete by October 1914 a summarizing long review article of his Einstein-Grossmann theory. The paper was published in November 1914. This version of the theory was an organized and extended version of his works with Marcel Grossmann, the most fully and comprehensive theory of gravitation; a masterpiece of what would finally be discovered as faulty field equations.


On November 4, 1915 Einstein wrote his elder son Hans Albert Einstein, “In the last days I completed one of the finest papers of my life; when you are older I’ll tell you about it”. The day this letter was written Einstein presented this paper to the Prussian Academy of Sciences. The paper was the first out of four papers that corrected his November 1914 review paper. Einstein’s work on this paper was so intense during October 1915 that he told Hans Albert in the same letter, “I am often so in my work, that I forget lunch”.


In the first November 4 1915 paper, Einstein gradually expanded the range of the covariance of his field equations. Every week he expanded the covariance a little further until he arrived on November 25 1915 to fully generally covariant field equations. Einstein’s explained to Moritz Schlick that, through the general covariance of the field equations, “time and space lose the last remnant of physical reality. All that remains is that the world is to be conceived as a four-dimensional (hyperbolic) continuum of four dimensions” (Einstein to Schlick, December 14, 1915, CPAE 8, Doc 165) John Stachel explains the meaning of this revolution in space and time, in his book: Stachel, John, Einstein from ‘B’ to ‘Z’, 2002; see p. 323).

Albert Einstein as a Young Man

These are a few of my papers on Einstein’s pathway to General Relativity:












Stay tuned for my next centenary of GTR post!

Review: The Cambridge Companion to Einstein

I recommend this recent publication, The Cambridge Companion to Einstein, edited by Michel Janssen and Christoph Lehner.

It is a real good book: The scholarly and academic papers contained in this volume are authored by eminent scholars within the field of Einstein studies.

The first paper introduces the term “Copernican process”, a term invented by scholars to study scientists’ and Einstein’s achievements. The Copernican process describes a complex revolutionary narrative and the book’s side of the divide.

First, Einstein did not consider the relativity paper a revolutionary paper, but rather a natural development of classical electrodynamics and optics; he did regard the light quantum paper a revolutionary paper.

Carl Seelig wrote, “As opposed to several interpreters, Einstein would not agree that the relativity theory was a revolutionary event. He used to say: ‘In the [special] relativity theory it is no question of a revolutionary act but of a natural development of lines which have been followed for centuries'”.

Why did Einstein not consider special relativity a revolutionary event? The answer was related to Euclidean geometry and to measuring rods and clocks. In his special theory of relativity Einstein gave a definition of a physical frame of reference. He defined it in terms of a network of measuring rods and a set of suitable-synchronized clocks, all at rest in an inertial system.

The light quantum paper was the only one of his 1905 papers Einstein considered truly revolutionary. Indeed Einstein wrote Conrad Habicht in May 1905 about this paper, “It deals with the radiation and energy characteristics of light and is very revolutionary”.

A few years ago Jürgen Renn introduced a new term “Copernicus process”: […] “reorganization of a system of knowledge in which previously marginal elements take on a key role and serve as a starting point for a reinterpretation of the body of knowledge; typically much of the technical apparatus is kept, inference structures are reversed, and the previous conceptual foundation is discarded. Einstein’s achievements during his miracle year of 1905 can be described in terms of such Copernican process” (p. 38).

For instance, the transformation of the preclassical mechanics of Galileo and contemporaries (still based on Aristotelian foundations) to the classical mechanics of the Newtonian era can be understood in terms of a Copernican process. Like Moses, Galileo did not reach the promised land, or better perhaps, like Columbus, did not recognize it as such. Galileo arrived at the derivation of results such as the law of free fall and projectile motion by exploring the limits of the systems of knowledge of preclassical mechanics (p. 41).

Einstein preserved the technical framework of the results in the works of Lorentz and Planck, but profoundly changed their conceptual meaning, thus creating the new kinematics of the theory of special relativity and introducing the revolutionary idea of light quanta. Copernicus as well had largely kept the Ptolemaic machinery of traditional astronomy when changing its basic conceptual structure.

Although Einstein did not consider his relativity paper a revolutionary paper, he explained the new feature of his theory just before his death: “the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell‘s equations and was concerned with the nature of space and time in general. A further new result was that the ‘Lorentz invariance’ is a general condition for any theory. This was for me of particular importance because I had already previously recognized that Maxwell‘s theory did not represent the microstructure of radiation and could therefore have no general validity”.

Planck assumed that oscillators interacting with the electromagnetic field could only emit and/or absorb energy in discrete units, which he called quanta of energy. The energy of these quanta was proportional to the frequency of the oscillator.

Planck believed, in accord with Maxwell’s theory that, the energy of the electromagnetic field itself could change continuously. Einstein first recognized that Maxwell’s theory did not represent the microstructure of radiation and could have no general validity. He realized that a number of phenomena involving interactions between matter and radiation could be simply explained with the help of light quanta.

Using Renn and Rynasiewicz phraseology, Planck “did not reach the promised land”, the light quanta. Moreover, he even disliked this idea. Einstein later wrote about Planck, “He has, however, one fault: that he is clumsy in finding his way about in foreign trains of thought. It is therefore understandable when he makes quite faulty objections to my latest work on radiation”.

In an essay on Johannes Kepler Einstein explained Copernicus’ discovery (revolutionary process): Copernicus understood that if the planets moved uniformly in a circle round the stationary sun (one frame of reference), then the planets would also move round all other frames of reference (the earth and all other planets): “Copernicus had opened the eyes of the most intelligent to the fact that the best way to get a clear group of the apparent movements of the planets in the heavens was to regard them as movements round the sun conceived as stationary. If the planets moved uniformly in a circle round the sun, it would have been comparatively easy to discover how these movements must look from the earth”.

Therefore Einstein’s revolutionary process was the following: Einstein was at work on his light quanta paper, but he was busily working on the electrodynamics of moving bodies too. Einstein understood that if the equation E = hf holds in one inertial frame of reference, it would hold in all others. Einstein realized that the ‘Lorentz invariance’ is a general condition for any theory, and then he understood that the Lorentz transformation transcended its connection with Maxwell’s equations and was concerned with the nature of space and time in general.