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In some media, mass-carrying particles can go faster than light:

Cherenkov radiation, ... is electromagnetic radiation emitted when a charged particle... passes through a dielectric medium at a speed greater than the phase velocity of light in that medium

How does this happen? I would imagine that light faces the least resistance to motion and that other charged mass-carriers have more stuff to impede their speed.

Why are the particles allowed to exceed the speed of light for other media when they are not allowed to in a vacuum?

Qmechanic
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Jesvin Jose
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3 Answers3

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Cherenkov radiation is generated by charged particles which are faster than the local speed of light in an optical medium, which is always lower than the speed of light in vacuum. So if the local speed of light in an optical medium is given by c_medium = c_vacuum/n, where n is the refractive index, a particle with c>v>c_medium can generate Cherenkov radiation, even though it is slower than the actual speed of light in vacuum. Such particles can be found in cosmic rays and are made copiously in our accelerator facilities, where Cherenkov detectors are used often to detect them. The optical media used in Cherenkov detectors do slow particles down, of course. The Cherenkov light requires energy, which has to come out of the kinetic energy of these relativistic particles. Typically, however, particles can travel several meters, and sometimes many miles trough Cherenkov media before they have lost all of their energy.

CuriousOne
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Why are the particles allowed to exceed the speed of light for other media when they are not allowed to in a vacuum?

Light is represented by electromagnetic radiation which in its simpler form is mathematically described by a sine or cosine wave, classically. The classical light is built up by photons which are the quantum of electromagnetic radiation and are the mediators of any interaction between charged particles. A charged particle entering a medium immediately starts interacting with the field of the atoms and molecules in the medium by exchanges of virtual photons, which we should keep in mind.

A sine or cosine wave mathematical description is not a good description for complex electromagnetic interactions . What is a good representation for an electromagnetic interaction is a wave packet, i.e. combination of sines and cosines which can carry information by the phase and amplitude about the particle passing through

The wave packet allows a mathematical description for an information carrying bundle (particle passing at x,y,z,t) with sines and cosines but two definitions of velocity are needed, the group velocity, which is the peak of the bundle moving in space,

wave packet

and the phase velocity , which is the velocity of the individual sine wave component comprising the wave packet/bundle, as it is made up by a function that expands into sine and cosine functions.

In a medium there is dispersion , and phase velocity , (i.e. how fast the sine and cosines comprising the wave packet are moving) can be different from the group velocity.

It is the group velocity in the medium that measures the velocity of light in the medium, i.e. how fast the information is given to the medium that a charged particle is passing is known to the medium with the group velocity:

The wave packets of photons exchanged between the particle and the electromagnetic field of the atoms comprising the medium and say " charged particle passing" , are slower than the velocity of the particle, because of the index of refraction of the medium. The particle itself is not directly constrained by the index of refraction ( unless it is a photon) and can move faster than the group velocity of the electromagnetic wave packets that send the information that it is passing.

As the other answers say this can generate Cerenkov radiation (analogous to sonic booms), those exchanged wave packets stop being virtual and turn real, dissipating the energy from the wave packet.

For electromagnetic wavepackets in vacuum the two velocities are the same because there is no dispersion .

anna v
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  • so would these no-longer--virtual photons be considered coming from the particle or the medium? – jiggunjer Dec 05 '16 at 04:39
  • @jiggunjer The energy is supplied by the the energy of the particle passing through, if there were no particle or if it did not have kinetic energy there would be no radiation, thus it is the particle , from energy considerations. – anna v Dec 05 '16 at 04:56
  • That was my thought too. But I've read online (reddit) that the difference between bremstrahlung and Cherenkov is that the photons come from the medium with Cherenkov, because the medium is dielectric, whereas with bremsstrahlung it doesn't matter if the medium is polarizable. – jiggunjer Dec 05 '16 at 07:36
  • @jiggunjer it is all a matter of pov . the medium is part of the boundary conditions. Both for brems and for Cerenkov the particle provides the energy. – anna v Dec 05 '16 at 07:51
  • I think this answer should be marked as “answer” Since it tries to address the actual question asked by the OP. Even so the point that comes closest to answering is the statement that “light/photons are slower in a medium ‘due to the refractive index’ whereas the particle is not hampered by this impediment” – thentangler Jul 11 '21 at 08:28
  • Perhaps the above statement can be expanded upon. I was under the impression that light is faster than any particle (vacuum or not), because of the mass component of the particle. Photons are massless. Even if the group velocity is lower in the medium, wouldn’t the particle still be relatively slower due to interactions with its mass in the medium? – thentangler Jul 11 '21 at 08:39
  • @thentangler Photons always move with velocity c even in a medium, the way elecromagnetic waves are composed of photons is complicated . Have a look at how this em interference pattern is built up one photon at a time.The single photons seem random in the beginning, but the classical interference appears. https://www.sps.ch/artikel/progresses/wave-particle-duality-of-light-for-the-classroom-13/ . So in a transparent medium the build up of classical em is different than in vacuum, and the classical light group velocity can be lowered. – anna v Jul 11 '21 at 08:57
  • see my answer here https://physics.stackexchange.com/questions/643540/doppler-effect-in-slow-light/643557#643557 – anna v Jul 11 '21 at 08:58
  • I am familiar with the Youngs double-slit experiment, which is what your SPS link basically talks about. I still dont understand how a particle with mass can travel faster than speed of light in a medium. Especially now that you say that the velocity of light is c even in a medium. Is it because of intereference that the speed is decreased? – thentangler Jul 11 '21 at 14:32
  • I said the velocity of photons is c, NOT of light in the medium, because in a medium the velocity one measures of light is the group velocity that can really be very slow ( I gave the links) . cosmic ray and collider particles can be very much faster than the light group velocity in a transparent medium, so as to get Cherencov radiation. Even in water reactors one sees Cherencov radiation see this https://reactor.mst.edu/cerenkov/ – anna v Jul 11 '21 at 14:59
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Why are the particles allowed to exceed the speed of light for other media when they are not allowed to in a vacuum?

No particle can have relative speed greater than c, period. This is 'built-in' to the geometry of spacetime.

But, a particle can travel faster, relative to some medium, than electromagnetic waves propagate in the same medium.

Do you see the distinction? Such a particle isn't travelling faster than c relative to the medium.

If you see this, then your question may be why material particles can have a speed relative to the medium faster than light propagates in the medium.

Consider the neutrino which is exceedingly 'reluctant' to interact with matter whereas photons readily interact with charged particles. See, for example, this answer.

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Alfred Centauri
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