# Tachyon is just a general term for some hypothetical particle that travels faster than the speed of light. According to the theory of special relativity that particle must have an imaginary mass. It also can never slow down, but actually loses energy to speed up. The tachyon lives in a strange upside down world indeed.

Is this actually a prediction of special relativity?

In general, special relativity is not in the business of predicting particles. That is left to quantum theories.

Special relativity describes observed behaviour.

Special relativity is actually a theory about the symmetry of space and time. That symmetry has consequences for effects that we observe. Probably the most well-known consequence is the famous mass-energy equivalence principle.

One of the fundamental consequences of special relativity is that it could not sustain both the notions of causality and simultaneity. In particular, special relativity was found to incompatible with the notion of simultaneity. However, causality was fundamental to the theory. This is the principle of locality, that requires causal influence spread out at an invariant speed.

No experiment has ever demonstrated a violation of causality, which in turns means the no influence has ever been observed to travel faster than the speed of light.

A tachyon, as a particle with imaginary mass, would violate causality if it could be detected. However, that’s putting the cart before the horse.

Special relativity is a theory based on two axioms. The mathematical consequences of the two axioms are the machinery of the theory. We put numbers in and the theory chugs along and outputs another number, which we interpret. However, the mathematical machinery is not reality. It is just a model that we use. Thus all the machinery of mathematical logic need not apply to reality. For example, just because we have developed the mathematics of complex analysis, doesn’t mean that complex or imaginary solutions are relevant or valid in all cases. What an imaginary solution means is that we would need to extend our theory beyond the real numbers into the complex plane. Surely there must be some motivation to make such a leap?

Extension of the theory of special relativity to the complex plane as well as potential violations of causality are two reasons why tachyons are really just a concept. (I should note that complex numbers are used in special relativity, specifically to describe the space-time metric, so the discussion about complex numbers is not necessarily as strong as the causality requirement. However, not all mathematical solutions need be physical solutions.)

Next we should look at superluminal propagation in the scientific literature. The work by Steinberg, Kwiat and Chaio on superluminal tunnelling highlights the most curious aspects of quantum mechanics. These papers are published with provocative titles designed to interest editors and readers alike. However, the authors are very careful to point out that none of their experiments violate causality. The details as to why this is the case is deeply rooted in very careful examinations the quantum theory.

Take for example the case of superluminal tunnelling time reported for single photons. This is a very beautiful experiment that was carefully conducted using an entangled photon source to provide a way of efficiently detecting single photons. A very clear and statistically significant result was reported. Moreover, there was no observed change in the shape of the photon wavepacket aside from a shift corresponding to faster than light tunnelling.

It just so happens that the faster than light tunnelling result was still consistent with Einstein locality. This seems paradoxical! However, the devil is in the detail.

The single photon tunneling experiment is that of a post-selective weak measurement (that’s jargon). That means that most of the photons are not detected, but those that are happen to be those that are detected earlier. This is possible because the actual timing of the photon arrival is not infinitely narrow. The photon wavepacket allows for a range of detection times and the experiment just happens to be able to select/detect the small fraction that arrive earlier. The upshot of this is that it is not possible to use this tunnelling effect to transmit signals faster than the speed of light.

What experiments like this illustrate is that scientists are continually probing the limits to their theories and understanding. Afterall, that’s their job. Sometimes, they try to hype their result using evocative and engaging language. In fact this is becoming more common and can result in confusion amongst the general populace about what was actually achieved. The common problem is that while the devil is in the detail, most people are not interested in the detail and just absorb the hype. Scientists tend to use evocative language to hype the importance of their research to other scientists, who generally will read the detail. It’s the science communicators who should be more careful in how they convey the research to a wider public.

The gist of this is that the work on superluminal propagation has nothing to do with “tachyons”. Even the work using terms as “tachyonlike” are not trachyons, but materials that exhibit properties that can be shown to have “effective” imaginary mass. All of these materials are nevertheless compatible with causality are described in the special theory of relativity.

All this talk of tachyons may sound confusing, but that’s because the devil is in the detail…

If any real tachyons are ever discovered, you’d really know about it…

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