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I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur? Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky?

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    $\begingroup$ Nothing theoretical about Cerenkov radiation, and it doesn't require assuming the impossible. Mind you that is due to a moving charged particle. $\endgroup$ – dmckee --- ex-moderator kitten Mar 4 '14 at 1:08
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    $\begingroup$ I know that it is technically impossible for a circle to be square, but if it were possible, what would that circle look like? $\endgroup$ – WillO Mar 4 '14 at 1:22
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    $\begingroup$ The problem with this type of question is the logical structure: (1) I know x is impossible (2) suppose it is possible then (3) what does the theory that says it is impossible predict? Now, as dmckee points out, something can travel faster than light does in a medium but, according to SR, if your speed is less than the speed of light in vacuum in one frame of reference, it's less than the speed of light in any frame of reference. So, if you suppose it is possible to reach or exceed c, you're throwing SR out the window. $\endgroup$ – Alfred Centauri Mar 4 '14 at 1:23
  • $\begingroup$ @Nick: "[...] if it were possible [...]" -- As suggested by the reference(s) to Cherenkov radiation an "object" (such as a charged particle) possibly was "in a medium" (with refractive index different from 1), rather than "in vacuum"; and it may even be said to have "travelled in a medium with some particular speed ($v_p$)." $\therefore$: it might be worthwhile to ask, how to measure whether "a given object had been in a medium", or not; and if so, how to determine "its" $v_p$ $\endgroup$ – user12262 Mar 5 '14 at 23:23
  • $\begingroup$ @dmckee: "Nothing theoretical about Cerenkov radiation" -- There is plenty theoretical about Cherenkov radiation; as may be recognized for instance in the Wikipedia article about the Frank-Tamm formula (which is named for Russian physicists Ilya Frank and Igor Tamm who developed the theory of the Cherenkov effect). However: of course there's nothing hypothetical anymore about Cherenkov radiation. $\endgroup$ – user12262 Mar 6 '14 at 5:53
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To leave an answer that addresses the question, which was answered in comments but comments are not permanent here:

in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur?

It is called Cerenkov radiation and it is continually utilized in high energy physics detectors and cosmic ray experiments.

It is the electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation.

You ask:

Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky?

Light waves are built up in synchrony by a large number of photons. Cerenkov radiation is radiation from one elementary point particle one photon at a time, and the build up into light one sees here :

cerenkovreactor

NRC photo of Cherenkov effect in the Reed Research Reactor.

comes from innumerable electrons with random directions exceeding the speed of light in the medium.

The sonic boom comes from one airplane , a single electron emits Cerenkov radiation practically continuously on its path, similar to the energy dissipation of the sonic boom, but the electron "boom" is a whisper as far as detectors go.

An interesting aside: a veteran particle physicist of the first days of creating beams and experiments, told me that he centered the beam by the Cerenkov light in his eyes.

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