Why do matter waves (as in wave-particle duality) travel faster than light? How is it possible?
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"Matter waves" (such as electrons, which have a relativistic mass) do not travel faster than c (the speed of light in a vacuum). In fact they can never equal c either.
There are rare/special occasions (Cherenkov radiation) in which such a particle can exceed the speed of light in a particular medium, but it is still less than c. In particle accelerators, electrons are regularly accelerated to over 99% of c, but never all the way up to c.
Another interesting thing to understand that even in such circumstances special theory is not violated since they cannot carry any information
It is only the phase speed which appears to move faster than c. This apparent
speed depends on the actual material speed v like, phase speed = c2/v.
This means for instance that the phase speed becomes infinite as the
material speed becomes zero! This may sound all weird but the explanation
is actually simple and beautiful. It's the theory of Special Relativity at work.
I wrote an illustrated explanation which you can read here:
You'll find it as well as you google for: relativistic de broglie wave packet
That's a very interesting and informative paper - thanks!
In QFT, there is a nonzero probability for a particle to propagate faster than light (or, as they say, "outside the light cone"). Read the causality section 2.4 in Peskin and Schroeder for how this is nevertheless compatible with relativity.
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