Tachyon racing a Photon?

Question

Completely hypothetical question. Let's all ignore the fact that tachyons are only theoretical. Furthermore, let's assume the following (believed) parameters:
1) Tachyons have an imaginary number mass.
2) Because of #1, tachyons travel faster than light.
3) Because of #2, they travel backwards through time.

If a photon and a tachyon were emitted simultaneousely towards a target, which one would get there first? Sure, the tachyon travels faster than a photon, but it also travels backwards through time. Would this time dilation affect the outcome of the race (i.e. would it cause the tachyon to reach the target before being emitted)? Furthermore, what is this answer relative to? Is the answer from the tachyon's local spacetime or the photon's.

Answer 1

I doubt that an answer exist even theoretically for your question, but Zeno and Einstein, not to mention Aristotle and Plato, would have both explanations and critique of your three premises and your questions.

Some of my sophomoric thoughts are:
First to parameter 1. Its impossible from a philosophical viewpoint to form a valid question from something imaginary because imaginary 'errata' and all their properties are 'invalid' by definition. In this specific case we don't know the mass and can only conjecture, since one has never been seen and will theoretically never be measured. This is an invalid argument.
P2. We have no idea whether tachions 'travel' at all, much less are we able to assign to them a property of traveling faster than light. These particles, if they exist at all, are subject to the Uncertainty Principal which rules the measurement and existance of all particles in quantum mechanics. This is an invalid argument.
P3. This is invalid because one cannot reach a valid conclusion using invalid arguments.

Understand that the most important point of the above is that all the premises (arguments) are invalid and therefor any conclusion reached from them is invalid. This is from a purely philosopical viewpoint (talk about 'relativity'!).

And that would bring us to the question about relativity. The response is that the 'outcome' (were it a valid questtion) could be viewed as relative to either or both simultaneously as is the case with all events. I beleive it was Greene who wrote a long book and described relativity in terms of astronauts either floating in space at rest or with various accelerations away from and toward one another that finally allowed me to understand relativity.
At least I think I do a little. LOL

Your question is none-the-less very evocative of deep thought and constructive critique. It is an excellent question!

I believe personally that going back in time is impossible even for tachions. Philosophical analysis leads me to this conclusion. It is akin to accepting that something can be less than zero or that Zeno's hypotheses were and are valid.

A source which links to numerous others that may help people understand the wonderful world of modern physics is:
http://www.damtp.cam.ac.uk/user/gr/public/qg_qc.html

Answer 2

the photon would get first, because tachyon travels back in time