# A few questions on neutrinos supposedly travelling faster than light

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I was discussing with my friends the implications of neutrinos travelling faster than light (be it real or hypothetical). See http://www.bbc.co.uk/news/science-environment-15791236

So far I've got the following background knowledge:

Michelson-Morley found that the speed of light was the same in all frames of reference.

Einstein claimed that nothing could exceed the speed of light and formalized the theory of relativity based on that maximum speed.

I'm not sure why this claim is valid. What special property of light makes this obvious?

If something CAN travel faster than light, what are the implications?

Isn't it just a matter of correcting $c$ in $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$?

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A few history corrections-

M-M did not find that the speed of light was the same in all frames of reference. They found that we were not moving through an aether; it had been previously determined that we could not be at rest with respect to it (from observation of stellar aberration, Bradley, 1725). Their null result was a mortal wound for the idea of an aether, though the death still took a few decades.

Einstein did not base relativity on a claim that nothing could exceed the speed of light — that's a conclusion, and really it's a pop-sci rephrasing of a conclusion. He used the idea that light had a constant speed in all inertial frames that was embedded in Maxwell's equations and applied it to kinematics. The result of that is that kinetic energy of massive objects diverges at v=c, so nothing massive can accelerate past that speed. Massless particles travel at that speed. An implication of that is causality.

If something can travel faster than c, the implications will depend on what exactly is happening. Within relativity you need imaginary terms for either mass or energy, and the question becomes what that means. There are undoubtedly a number of theoretical models in existence that are extensions of relativity but are untested; I don't know what possibilities that particle/high-energy physics might have (such as "neutrinos break some symmetry"). I think the only conclusion you can draw is that if this holds up, whatever new model is developed, it still has to reduce to relativity in the cases we have already seen, much like relativity reduces to classical Newtonian physics in the limit of low speed and gravity. (Unless causality is tossed, in which case all previous experimental results will change)

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Do you know of any site or text going through, step by step, what Einstein did to derive his theory?

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Do you know of any site or text going through, step by step, what Einstein did to derive his theory?

Here's a translation of the paper Elektrodynamik bewegter Körper

http://www.fourmilab.ch/etexts/einstein/specrel/www/

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If we were traveling at 1/2 c, following a beam of light, the light would appear to be traveling away from us at c.

If there was a neutrino beam traveling next to the beam of light at near light speed, slowly falling behind the light beam, would it appear to us that the neutrino beam was traveling at just under 1/2 c?

If by chance the neutrino beam was also traveling at c, would it appear to be traveling away from us at c or 1/2 c?

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