Closed-Semi Time Loops

“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.”

If there is in fact an absolute simultaneity at the physical level — and therefore a present moment for the Universe — then travelling back in time becomes impossible.

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 theory allows, at least formally, semi-closed time loops — for example, the case of a billiard ball that could theoretically strike its duplicate in its own past.

It seems somewhat hasty to claim that there is no paradox merely because one would then have two billiard balls instead of one. In my view, it is through the implicit presence of the principle of relativity of simultaneity at the physical level that the theory eventually loses its conceptual footing and drifts into science fiction.

1. Acceleration

When a body accelerates, the principle of relativity of simultaneity at the physical level implies that time “unfolds for the body.” Yet, according to its new line of simultaneity, certain distant events are supposed to shift backwards in time ^[1].

2. Curved Space

In the presence of space curved by a massive object, a body can retrace its path “without changing direction.” On the return journey, there would therefore be no need to apply the principle of relativity of simultaneity in the opposite direction. The backward shift in time, associated with the earlier acceleration and its line of simultaneity, would not be cancelled.

3. Wormholes

A wormhole would provide a shortcut through spacetime, enabling a body to move extremely quickly from one region to another. In theory, this would allow it to reach a distant region of spacetime that corresponds to the events shifted backwards in time according to its line of simultaneity during acceleration.

Semi-closed time loops would therefore be theoretically possible within the framework of general relativity. Physicists nevertheless continue to ask whether they could ever be physically realised. What remains surprising is that the initial principles of the theory appear to permit them at all.

One may then imagine a timelike curve that would allow a person to return to their own past, giving rise to the grandfather paradox: “What happens if I kill my grandfather before my father was conceived?” One immediately feels immersed in science fiction. Yet this possibility is admitted by certain solutions of the equations.

According to Marc Lachièze-Rey, a principle of consistency would prevent such contradictions: “none of the predictions of the theory can contradict logic” ^[2].

This response does not seem entirely convincing to me, because it appears to compensate after the fact for a weakness in the foundational principles of the theory. General relativity may of course be embedded within a broader conceptual framework that excludes semi-closed time loops. Nevertheless, the formalism of general relativity, considered on its own, appears to allow them. This may be an indication that the theory needs to be reconsidered at the level of its foundational principles ^[3].

Conclusion

These considerations suggest that the principle of relativity of simultaneity at the physical level is present, at least implicitly, in both theories of relativity, even when physicists no longer explicitly recognise its role.

This is why it seems essential to reconsider the theoretical framework in depth and to examine whether an absolute simultaneity must necessarily exist at the physical level. Such a conclusion would have major consequences for the invariance of the speed of light ^[4], for the representation of spacetime, and for the analysis of motion.

The issue therefore deserves to be addressed directly by theoretical physicists. It would be enough for researchers such as Étienne Klein, Marc Lachièze-Rey, or others working on the foundations of time and relativity, to examine this question in depth for the debate to move forward decisively.

A Remark on Time and Clocks

The fact that clocks do not tick at the same rate depending on their spatial position does not imply that time does not exist. It means only that the rate of physical processes depends on spatial conditions, which is very different from denying time itself.

One cannot arbitrarily rule out the possibility that two “identical” clocks, placed in different spatial conditions — for example, on two different floors of the same building — can run simultaneously at different rates. Marc Lachièze-Rey overlooks this distinction.

Related Videos

1. Nantes Utopiales, 1–6 November 2017, LA FLÈCHE DU TEMPS — Watch the video  ↑
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 absolute simultaneity, one understands that the speed of light must continually adapt to the spatial configuration, since a massive body modifies that configuration. In the presence of a low-mass object moving through space, there should therefore be, under certain conditions, a difference in the speed of light between two reference points sufficiently distant from the object. The operational question is whether such a difference could be measured significantly. This continual adaptation of the speed of light to the spatial configuration supports a relational approach to space and motion.  ↑