Photon beyond light speed?(?tachyon?)

[madphysics]

This has bothered me for some time. I must be missing something.

Photons, being the massless particles that they are, have no inertia. So what holds them back from surpassing the "speed limit" at moving around with no time lapse. They would be everywhere simaltaneously. Does something hold them back? A hidden effect of dark matter, perhaps?

Evidence gathered tells us it must be otherwise. But why? What can hold back a massless particle?

Interest in the tachyon is up, and it intrigues me. Any help in this area would definitely be helpful.

 

[mathman]

Photons, being the massless particles that they are, have no inertia.

Photons have no REST mass. However, they have energy. In our coordinate system photons travel at the speed of light, but in the coordinate system of the photon, time never changes.

 

[jtbell]

but in the coordinate system of the photon,

Note that there is no inertial reference frame in which a photon is stationary. Therefore your "coordinate system of the photon" must be something entirely different.

 

[ice109]

Note that there is no inertial reference frame in which a photon is stationary. Therefore your "coordinate system of the photon" must be something entirely different.

the speed of light is the speed of light for ... light?

 

[mathman]

Note to jtbell. What I should have said was: In the reference frame of the photon, everything in its direction has collapsed to one point, i.e. space would be 2 dimensional. This analyisis is taking the Lorentz transformation to the limit - the universe is going at the speed of light relative to the photon.

 

[EnumaElish]

the speed of light is the speed of light for ... light?

I am not a physicist, but that would be my guess. Also guessing that if this wasn't correct then something else would have to "give" -- e.g. our current understanding of how time works would need to be revised.

 

[Timo]

Mathman, I think you should really not have said that since it seems worse than your original statement:

Note to jtbell. What I should have said was: In the reference frame of the photon,...

...which still is not very well defined. I don't see any principal problem constructing a coordinate system where the increase of one coordinate let's you wander along the worldline of the photon. However, you are most likely to shoot yourself in the foot at the next best corner due to the self-perpendicularity of the base vector associated to that coordinate and its (pseudo-)magnitude of zero.
Sidenote: I'm not sure if such a system would even satisfy the mathematical requirements on a coordiante system or map. It seems highly unpractical for the reasons stated, at least. Let's just assume such a coordiante system did exist for the following:

... everything in its direction has collapsed to one point ...

That's not correct. Points in (SR-) spacetime (=events) whose connection vector is lightlike (e.g. two events on the worldline of a free massless particle) always have a "distance" of zero. That value is a so-called Lorentz-scalar and independent of the chosen coordinate system. They are still distinct points, also irrespective of the coordinate system (except if it's the same event, irrespective of coordinate system :rofl:). To rephrase: The points which you state collapsed to one single point already had a "distance" of zero before you switched to the coordinate system in which variation of one coordinate wanders along the photon worldline. They are different events nonetheless.

This analyisis is taking the Lorentz transformation to the limit.

That's probably the crux in it. You seem to assume that the limit v->c exists which is not true (which the divergent gamov-factor already is a hint for). The limit of a rational-valued series doesn't have to exist in the rationals and similarly the limit of a parameter-dependent coordiante transformation doesn't have to be a valid coordinate transformation.