# How superluminal motion can lead to backward time travel

Abstract

It is commonly asserted that superluminal particle motion can enable backward time travel, but little has been written providing details. It is shown here that the simplest example of a “closed loop” event – a twin paradox scenario where a single spaceship both traveling out and returning back superluminally – does not result in that ship straightforwardly returning to its starting point before it left. However, a more complicated scenario – one where the superluminal ship first arrives at an intermediate destination moving subluminally – can result in backwards time travel. This intermediate step might seem physically inconsequential but is shown to break Lorentz-invariance and be oddly tied to the sudden creation of a pair of spacecraft, one of which remains and one of which annihilates with the original spacecraft.

## INTRODUCTION

Objects traveling faster than light are discouraged by popular convention in Einstein’s Special Theory of Relativity (Einstein, 1905), which provides a profound, comprehensive, and experimentally verified description of particle trajectories and kinematics at subluminal speeds. Nevertheless, the vast distance to neighboring stars has caused superluminal speeds to continue to be discussed in popular venues. (Studios, 1964) To be clear, this work is not advocating that faster than light speeds for material particles are possible. Rather, the present work takes superluminal particle speeds as a premise to show how closed-loop backward time travel arises in a specific simple scenario.

Physics literature has indicated for many years that superluminal speeds can correspond to backward time travel. (Phillips, 1919) Such claims are pervasive enough to have become common knowledge, as exemplified by a famous limerick published in 1923: “There was a young lady named Bright, Whose speed was far faster than light; She set out one day, In a relative way, And returned on the previous night”.(Buller, 1923)

The possibly of closed-loop time travel within the context of special relativity was later mentioned explicitly in 1927 by Reichenbach. (Reichenbach, 1960) A prominent discussion on the physics of particles moving superluminally within the realm of special relativity was given in 1962 by Bilaniuk Deshpande, and Sudarshan. (Bilaniuk et al., 1962) The term “tachyon” was first coined for faster than light particles by Feinberg (Feinberg, 1967) who also derived transformation equations for superluminal particles. Tachyonic speeds have been suggested multiple times in the physics literature to address different concerns, for example being convolved with quantum mechanics to create pervasive fields (Feinberg, 1967), and to explain consistent results between two separated detectors in quantum entanglement experiments. (Einstein et al., 1935), (Bell, 1966)

The reality of particle tachyons or any local faster-than-light communication mechanism is controversial, at best. Accelerating any material particle from below light speed to the speed of light leads to a divergence in the particle’s energy, a physical impossibility. For $$v>c$$, The Lorentz-FitzGerald Contraction (Lorentz, 1892), (Fras. Fitz Gerald, 1889) $$\sqrt{1-v^{2}/c^{2}}$$ becomes imaginary, leading to relative quantities like mass, distance, and time becoming ill-defined, classically. Simple tachyonic wavefunctions in quantum mechanics either admit only subluminal or non-localizable solutions. (Chase, 1993) Experimental reports of particles moving faster than light have all been followed by skeptical inquiries or subsequent retractions. (all, 2012), (all, 2012) Were tachyonic communications to enable communications backward in time, violations in causality seem to result, a prominent example of which is the Tachyonic Anti-telephone. (Benford et al., 1970) For this reason superluminal communication and backward time travel are thought to be impossible. Experimentally, a recent search of Internet databases for “unknowable-at-the-time” information that might indicate the possibility of backward time travel came up empty. (Nemiroff et al., 2014)

Conversely, the existence of superluminal speeds for phase velocities and illumination fronts that do not carry mass or information are well established. (Griffiths, 1994) The ability of superluminal illumination fronts to show pair creation and annihilation events was mentioned by Cavaliere et al. (Cavaliere et al., 1971) and analyzed in detail by Nemiroff (Nemiroff, 2015) and Zhong & Nemiroff (Nemiroff et al., 2016).

The possibility that a material object could undergo a real pair creation and subsequent annihilation event was mentioned in 1962 by Putnam