Abstract

In this paper, I discuss whether superluminal particles exist in the general relativistic theory of gravity. It seems that the answer to this question is negative. In truth, the result may only represent a difficulty to special but not general relativity, the later allowing both Lorentzian and Euclidian metrics. An Euclidian metric does not restrict speed. Although only the Lorentzian metric is stable, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality.

Highlights

  • IntroductionIt is well known that our daily space-time is approximately of Lorentz (Minkowski) type with a metric diag 1, 1, 1, 1

  • It is well known that our daily space-time is approximately of Lorentz (Minkowski) type with a metricThe above statement is taken as one of the central assumptions of the theory of special relativity and has been supported by numerous experiments

  • Only the Lorentzian metric is stable, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality

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Summary

Introduction

It is well known that our daily space-time is approximately of Lorentz (Minkowski) type with a metric diag 1, 1, 1, 1. Many textbooks [1] state that in the general theory of relativity, any space-time is locally of the type diag 1, 1, 1, 1 , it can not be presented so globally due to the effect of matter. This is a part of the demands dictated by the well known equivalence principle. The reader should notice that already Eddington [2, Page 25] has considered the possibility that the universe contains different domains in which some domains are locally Lorentzian and others have some other local metric of the type or the type diag 1, 1, 1, 1 The stability of those domains was not discussed by Eddington.

Possible Mechanisms of Metric Change
Particle Trajectories in Flat Space
Lorentz Space-Time
Euclidean Space-Time Let us assume an Euclidean space-time with a metric
Some Possible Physical Implications
Conclusion

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