Exceed speed of light: always exceeded speed of light?

Trinitiet

Hi,

Now we have the "faster than speed of light" neutrinos, I was wondering the next philosophical question:

If we presume it is indeed correct they are faster than speed of light, would all observers of these neutrinos, no matter in what inertial frame of reference they are in, measure these neutrinos faster than the speed of light? Or does an inertial frame exist where in the speed of these neutrino's are indeed slower than the speed of light?

Thanks

Trinitiet

clem

If a particle is superluminal in one Lorentz frame, it is superluminal in all Lorentz frames.

phinds

We do not have FTL neutrinos. What we have is a very meticulously done experiment that pretty much everyone, particularly the people who did the experiment, believes has a measurement error in it but the error has not yet been found.

Trinitiet

Sorry, that's what I meant ;) But I was just considering the case IF it were true :p

Trinitiet

Thank you, what is the basis for this statement? I tried to use the normal special relativity Lorentz transformaties for velocities, but I seem to get imaginary velocities.

ghwellsjr

You are correct, there is no room for superluminal velocities in Special Relativity so there is no room for your philosophical question in Special Relativity.

Trinitiet

Is this a possible solution to superluminal neutrinos?

Landau and Lifchitz formulated the two postulates of special relativity as the following:
1/ All laws of physics should be the same in every inertial frame
2/ There's a maximal propagation speed for physical interactions

The second postulate does not talk about the speed of light, it just says there is a maximal speed. If we change all Lorentz transformations formulas and change every c from the speed of light to a new c, the speed of superluminal neutrinos; we can get superluminal speeds but all equations remain the same, just the value of c is changed.

Snip3r

Do we know speed of neutrinos is invariant in all reference frames?

Trinitiet

Sorry indeed, that was quite a stupid proposal of mine

georgir

Apologies for resurrecting this, but I just had to post when I saw this in the "similar threads" on another post I just made.

Actually, I think you made a mistake. There is no way to get imaginary velocities, as there are no square roots in the normal lorentz transformation for velocity, u' = (u-v) / (1- uv/c^2)

You get imaginary results if you try to go to a FTL reference frame, but you should get normal (though always FTL, sometimes negative) results if you transform a FTL velocity from one sub-lightspeed frame to another. Except in the special case where you get division by zero, which is the reference frame where that FTL speed seems infinite.

An example for exactly this kind of "FTL velocity" is looking at the intersection point of a gilloutine's two edges. With a small angle between the edges and a large (but still far under c) falling velocity this intersection point is travelling faster than light. And in some moving reference frames it will appear travelling in the other direction, or in one frame it will even seem like the edges are parallel and touch simultaneously everywhere.

ghwellsjr

Sure, you can plug a FTL velocity into the velocity addition formula and get a FTL result but that is why Einstein stipulated in his 1905 paper, section 5, that the velocities you plug in cannot be FTL. But you can't get to a FTL velocity unless at least one of them is already FTL. Even if you add c and c, you still get just c.

And as to your gilloutine example, nothing is traveling FTL. Do a search of "scissors" for lots of discussion about this subject, such as, Superluminal.

yuiop

It has already been correctly stated that if a particle is super-luminal in one reference frame then it is super-luminal in all reference frames. What you might not know is that while it requires infinite energy to accelerate a sub-luminal particle to the speed of light, it takes infinite energy to slow a superluminal partical to the speed of light. The speed of light is a barrier in both directions.

Also, as a side note, if a particle is super-luminal in one reference frame then it is possible to find other reference frames where the particle goes backwards in time and causality is violated.