Comments by "Dr Gamma D" (@DrDeuteron) on "Most Radioactive Men Ever" video.
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OK, ppl. this is getting out of hand. Yes, the speed of light is constant, and nothing (including information) can go faster, and anything with mass must go slower.
The speed of light can measure w/o light, all you need to do is measure the permittivity (epsilon_0) and permeability (mu_0) of free space, and find c = 1 /sqrt(e0*u0).
The permittivity measure the strength of the coupling of the electric field to charge (mu does the magnetic part).
So...in a medium like air or water or glass, the electric field of the lightwave polarizes the atoms/molecules, thereby creating little dipoles of charge, thereby increasing the local coupling of the field to charge (epsilon > epsilon0)
This makes light travel slower in a medium. Nevertheless, it is still dispersion less for constant "n(f)" (though it usually does disperse, hence: rainbows).
So it's not "ionized particles" that cause Cherenkov, it's "ionizing particles", which are energetic charge particles.
As they pass through the medium, their electric field is strong enough to ionize the nearby molecules/atoms in the medium. The point of ionization follows the particle, which is faster than the speed of light in the medium, which is c/n, where n is the index of refraction. Hence the similarity to sonic booms, where the air pressure disturbance position is moving faster than sound, so at a forward point, you hear (see) all the sound (light) from everywhere at once...that's just trigonometry.
In air, n = 1.000278 (see: The Particle Data Group). that c/n is totally out of reach for nuclear fission; however, in water n ~ 1.5: so you can Cherenkov in water and not in air with fission/beta-decay. (Beta decay is a few MeV, while the threshold for electrons in air is 21 MeV, which is a number I used in 1989 and have not since recalculated).
Air glow is caused by scintillation: ionized air recombines with free electrons and emits blue light in random directions. In these accident cases, its neutrons knock protons out, which then ionize. Very deadly. 1 neutron can blast a lot of atoms before tossing energy. Think: golf ball bouncing of bowling ball, golf ball keeps moving.
Cherenkov is focused in a forward cone with opening angle arc-cos(1/n). Moreover, the spectral power depends on n (bigger=better) and the photon energy, so it is strongly weight to blue (and even more in the ultraviolet). It is cut-off at the point where the Cherenkov photon energy can ionize the atom...otherwise it would extend to X-ray like synchrotron radiation.
An even whackier effect is called "Transition Radiation", which requires ultra-relativistic particles traversing a boundary between 2 media.
Finally: the comment about space expanding faster than light is not relevant. The speed of light is constant for all observers in flat spacetime locally. No matter how fast you go, the speed of light always moves a "c" in all directions...so which way do you go to reach "c"? It's a hyperbolic geometry.
In curved / expanding space time. There is no unique way to even define the relative speed of distance objects. Nevertheless, if two particles/people/galaxies are moving apart fast then "c", then they are separated by a horizon: either a black hole's event horizon, or the cosmological horizon.
Source: Me. I did get the highest degree (PhD) in the hardest subject (Nuclear Physics) from the worlds toughest school, and I built Cherenkov detectors for several projects in high background environments (read: scintillation). So it's hella studied. Re: general relativity, I am not an expert, but both my teacher and one of my fellow students won Nobel Prizes for black holes, so: osmosis of genius?
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