I'm taking advantage of this pause in the discussion to address the question about tachyons, a fascinating and complex topic. In the postscript, I'll provide some information about tachyons, but I'd like to briefly engage all participants with this question, that interests me too:
Bohm proposed an interpretation of Entanglement, ensuring that the principle of causality remained intact. However, if we were to admit the existence of compact dimensions and tachyons, would it still be necessary to uphold the relativistic origin of this principle?
PS. I've come across two different formulations that deserve attention:
Tachyons and Relativity: Some studies explore the possibility of tachyons by extending the concept of causality without drastically altering special relativity. An interesting example is this article:
https://arxiv.org/abs/hep-th/9607232. The basic idea is to modify the understanding of causality to allow for the existence of particles that travel faster than light, without completely overturning special relativity.
Compact Dimensions and String Theory: Another perspective, as presented in this article:
https://www.mdpi.com/2076-3417/9/24/5406, does not focus directly on tachyons, but introduces the possibility of extra "compact" spatial dimensions. This concept is central to string theory, where it's hypothesized that there are additional dimensions curled up on themselves at microscopic scales.
Personally, I find the idea of compact dimensions particularly interesting, as it integrates perfectly with string theory. It's seems that tachyons posed a problem in the early versions of this theory, but they have been eliminated in the more recent formulations. Compact dimensions, on the other hand, are a fundamental feature of the theory and play a crucial role in determining the properties of particles and forces. In practice, these extra dimensions connect distant points in space through very short "shortcuts."
A question arises spontaneously: could these "shortcuts" be used by tachyons? Although modern superstring theory does not predict tachyons, the possibility that they could exploit compact dimensions to move between distant points in space-time remains a fascinating hypothesis.
I hope this brief overview is helpful for those who wish to delve deeper into the subject. As far as I'm concerned, I don't have enough skill to deal with the topic.