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Faster-than-c signals, special relativity, and causality

Stefano Liberati, Sebastiano Sonego, Matt Visser

Abstract

Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate -- indeed, does not exclude -- faster-than-c signalling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which is perhaps the most plausible candidate for a physically sound realization of these phenomena. We demonstrate that in this case the faster-than-c aspects are ``benign'' and constrained in such a manner as to not automatically lead to causality violations.

Faster-than-c signals, special relativity, and causality

Abstract

Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate -- indeed, does not exclude -- faster-than-c signalling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which is perhaps the most plausible candidate for a physically sound realization of these phenomena. We demonstrate that in this case the faster-than-c aspects are ``benign'' and constrained in such a manner as to not automatically lead to causality violations.

Paper Structure

This paper contains 16 sections, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Special relativity
  3. Lorentz transformations without light
  4. Fluid-dynamical analog
  5. Physical coordinates
  6. What is $C$?
  7. Causality
  8. Tachyons and causal paradoxes
  9. Scharnhorst photons preserve causality
  10. Effective metric
  11. Stable causality
  12. Definition: Stable causality.
  13. Theorem:
  14. A paradox with multiple pairs of moving plates?
  15. Chronology protection
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Spatial distances as measured in the reference frame $\cal K$; see equation (\ref{['xi']}).
  • Figure 2: A causal paradox using tachyons. The dotted line represents the set of events which are simultaneous with ${\cal E}_1$ according to the reference frame ${\cal K}'$. The tachyonic signal from ${\cal E}_1$ to ${\cal E}_2$ travels to the future with respect to ${\cal K}'$, and to the past with respect to $\cal K$.
  • Figure 3: Tachyon propagation without causal paradoxes. Both signals travel to the future in at least one reference frame.
  • Figure 4: Wavefront (or line of constant phase) for a light signal emitted at the point $P$. Note that the wave vector ${\bf k}$ forms a non-vanishing angle $\theta-\varphi$ with the direction of propagation.