Closed-Semi Time Loop

« Relativity at the physical level is also present in general relativity. It is one of the basic principles that theoretically makes semi-closed time loops possible. »

Indeed, if there is in fact an absolute simultaneity at the physical level—and thus a present moment for the Universe—then it becomes impossible to travel back in time. Marc Lachièze-Rey, in his very instructive book Voyager dans le temps : la physique moderne et la temporalité, examines the consequences of the formalism of general relativity. He notes that the latter theoretically allows semi-closed time loops—for example the case of a billiard ball that could, in theory, hit its duplicate in its own past. It is somewhat hasty to claim that there is no paradox, because one would end up with two billiard balls instead of one. It is due to the implicit presence of the principle of relativity of simultaneity at the physical level that, at a certain point, the theory loses its footing and drifts into science fiction.

Marc Lachièze-Rey, in his book, examines several theoretical possibilities of time loops; I leave it to physicists or mathematicians to comment. But even if one is not able to follow the mathematical reasoning, one can approach semi-closed time loops by asking on which conceptual principles they rely. For certain types of time loops, Marc Lachièze-Rey speaks of acceleration, curvature of space, and wormholes. Starting from this, I asked myself how it could be possible, within the theory, for a body to travel backwards in time.

Here is how I understand things, using these three elements:

First, when a body accelerates, according to the principle of relativity of simultaneity at the physical level, time “unfolds for the body,” but, according to its line of simultaneity for certain distant events, it is supposed to be able to move backward in time ^[1].

Next, in the presence of space curved by a massive object, a body can retrace its steps “without changing direction.” As a result, on the way back, one would not need to apply the principle of relativity of simultaneity. Thus, the backward movement in time, carried out along a line of simultaneity during acceleration, would not be cancelled out.

Finally, with a wormhole as a spacetime shortcut, the body could move extremely quickly from one region to another and, through this means, reach very rapidly a distant region of spacetime. It could therefore, in theory, quickly find itself near the regions of spacetime for which it moved backward in time—according to its line of simultaneity—during its acceleration.

Semi-closed time loops would thus, within the framework of general relativity, be theoretically possible. Physicists nevertheless wonder whether they are practically possible. It remains quite surprising that the initial principles of the theory allow them. There is the possibility of a time curve that would allow me to return to my past, giving rise to the grandfather paradox: « What happens if I kill my grandfather before my father was conceived? » Naturally, one immediately feels immersed in full science fiction. Yet this approach would be permitted by certain equations of physics. But, according to Marc Lachièze-Rey, there would be something that prevents “killing my grandfather,” namely the principle of consistency; in short, « none of the predictions of the theory can contradict logic » ^[2]. This argument does not seem very convincing to me, because it appears to be a way of compensating for a flaw in the theory—regarding its basic principles—by adding something later on. One can no doubt also situate general relativity within a broader conceptual framework that would make semi-closed time loops impossible. Nonetheless, the formalism of general relativity, left to itself, would allow them. This may be a good indication of the need to reform the theory with respect to its foundational principles. (...^[3] )

Conclusion

From these considerations, it follows that the principle of relativity of simultaneity at the physical level is present, at least implicitly, in both theories of relativity, even if at some point physicists no longer notice it. This illustrates that it is essential to reform this theoretical framework in depth, showing that there must necessarily be an absolute simultaneity at the physical level, with the consequences that this entails concerning the invariance of the speed of light ^[4], the representation of spacetime, and the analysis of motion. And theoretical physicists should not overlook this issue for many more years. It would be enough for theorists like Étienne Klein or Marc Lachièze-Rey—who are particularly addressed in this letter—or others, to take hold of this subject for the question to be definitively resolved.

Notes

1. Nantes Utopiales, 1–6 November 2017, LA FLÈCHE DU TEMPS — https://www.youtube.com/watch?v=Ya0EU6jINiQ  ↑
2. Ibid.  ↑
3. Marc Lachièze-Rey, Voyager dans le temps : la physique moderne et la temporalité, p. 199, Science ouverte, Seuil.  ↑
4. With the idea of an absolute simultaneity, one understands that there is a constant adaptation of the speed of light to the spatial configuration—a massive body modifying this configuration. Therefore, in the presence of a low-mass object moving through space, in certain situations, there should be a difference in the speed of light if one takes two reference points sufficiently distant from the object. Of course, one must ask whether, from an operational point of view, a significant measurement can be achieved. This constant adaptation of the speed of light to the spatial configuration supports a relational approach to space and motion.  ↑

Excerpt from a circular letter cited in the book Et il survolait les eaux — vers une nouvelle vision du monde physique ?