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What might happen were the speed of light to be exceeded is a subject of hot debate in the philosophy of modern physics. Therefore, this is of interest to philosophy.

The most straight-forward way I know for expressing relative motion is the Lorentz equation, and I assert the most straight-forward answer would be to attempt to extend its results past the speed of light. Therefore, I am referencing the Lorentz equation for this question.

My studies of interest in regards to this are the following articles by physicists:

Einstein's special relativity beyond the speed of light

Revisiting Barry Cox and James Hill's theory of superluminal motion

On the infeasibility of superluminal velocities as an extension of relativity

The implication of Cox-Hill's proposal is that there are two possible simple extensions to the Lorentz formulation. Although I do not understand the details yet, that idea seems intuitive in a very notional way, since the Lorentz equation normally gives complex values (which we represent as two parts) past the speed of light. Cox-Hill mention, if I understand them right, that their extension possibilities might both be true in a sense, and represent a bifurcation of relativity theory into two equally likely possibilities. I am not quite clear on what observable facts actually bifurcate once the notion of spacetime is extended in this way; it may be clearer to Cox-Hill, however.

My question regards precedent: Has anything been written, probably in metaphysics or philosophy of space and time, regarding the possibility of choice at/near/past the speed of light or at pure energy (as observed relatively)?

(Please do not reference science fiction, unless it has a reference in academic philosophy. If you propose your own idea, please try to keep it brief and give as many good references as you can.)

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Not really an answer, but some comments:

Archaic Physics

The speed of light in Relativity is seen as a maximal speed that a massless object can travel at in the vacuum; in fact it must travel at this speed.

A massless object doesn't interact with the gravitational field; so one can say that it feels no 'resistance'.

Interestingly this is reminiscent of an argument in Aristotles Physics, which is probably due to the atomists that bodies in the Void (not as Non-Being but privation of Body, or perhaps as a Continua of Places) must all travel at the same speed as they do not feel any resistance.

Theoretically, one can consider that the speed of light as a barrier through which particles cannot pass through; this so that causality isn't violated. Thus superluminal particles have been investigated.

Tachyons

Feinberg proposed a model of these that had negative energy, and imaginary mass which he called tachyons; but in fact these fields were later understood as not permitting superluminal speeds; and represent an instability important in the mechanism of the Higgs field; and in fact this field is a tachyon, so has imaginary mass and negative energy; at least at first, the instability 'condenses' and then the field is no longer tachyonic.

Another way to investigate super-luminal particles in a sense, is to allow c to vary; and I recall very vaguely possibilities where these were linked to ideas of inflation - c varies with time; another interesting angle is to have the Plank length as an observer invariant; one theory along these lines is by Maguijo/Smolin, called doubly-special relativity.

  • This seems to be a crux, but I have not made sense of it: "...the speed of light as a barrier through which particles cannot pass through; this so that causality isn't violated. Thus superluminal particles have been investigated." – dwn Jan 31 '15 at 18:00
  • Does this mean that the particles cannot be observed? or does it mean that they, due to an indefinite causality, can be regarded as existing across spacetime? or something else? – dwn Jan 31 '15 at 20:50
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    "A massless object doesn't interact with a gravitational field." This is untrue. Massless objects are affected by gravity according to general relativity. According to Newton's law of gravity there is no interaction, but this is obsolete. – Matt Samuel Feb 1 '15 at 16:09
  • @dwn: I think the full story is quite complicated and I'm not familiar with all the arguments; kinetic energy increases to infinity for a massful particle accelerated to c; so its a barrier in that direction; particles that travel at c have no time/time becomes indefinite - a second becomes infinite/time stops, so their proper time, if it exists is not observable; so in sense, the particle becomes 'unobservable'. – Mozibur Ullah Feb 2 '15 at 16:38
  • @MattSamuel: this is true; but I was thinking in terms of SR and not GR. – Mozibur Ullah Feb 2 '15 at 16:40

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