Does The Speed Of Light Change In Different Mediums

Cosmic Lollipop

Based on Maxwell equations, nosotros can make up one's mind the speed of calorie-free equally:

$$c=\frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$

Where ##\epsilon_{0}## is the electric permittivity of vacuum and ##\mu_{0}## is the magnetic permittivity of vacuum. This annotation makes me believe that in other mediums those parameters can acquire other values, implying that the speed of an electromagnetic wave changes depending on the medium and that goes confronting Einstein's second postulate of special relativity. What am I missing?

PeterDonis

implying that the speed of an electromagnetic wave changes depending on the medium

Yep. Light tin travel slower in a medium than it does in vacuum.

that goes confronting Einstein's second postulate of special relativity.

No. The speed of light in vacuum is the only thing that needs to be invariant in SR.

Cosmic Lollipop

Yes. Light tin travel slower in a medium than it does in vacuum.
No. The speed of lite in vacuum is the only thing that needs to exist invariant in SR.

And then hypothetically we can detect a medium where a mechanical wave is faster than an electromagnetic one. Is that correct?

mitochan

Yes, actually. For an case charged particles moving faster than light speed in a medium e.g. water, cause Cherenkov radiations. It is like a daze wave past supersonic jet airplane.

vanhees71

Indeed, the phase velocity in an isotropic medium is ##c_n=c/n##. This can exist ##<c## (normal dispersion) or ##>c## (dissonant dispersion). There'due south no speed-limit for ##c_n##. It doesn't contradict relativity, considering one can show that the signal velocity (i.e., the velocity of the moving ridge front end of a signal) is alwasy ##\leq c## (Sommerfeld 1907, Sommerfeld and Brillouin 1914).

If a charged particle moves in a medium with ##c_n<c## Cherenkov radiation occurs. This was predicted before relativity has been theoretically predicted by Heaviside (1888) and by Sommerfeld (1904) for a particle faster than low-cal in the vacuum, which is of class impossible due to relativity, and the theory of Cherenkov radiation in affair is due to Frank and Tamm (1937, Nobel prize 1958). The first experimental ascertainment is due to M. Curie (1910) in a solution of radium.

https://en.wikipedia.org/wiki/Cherenkov_radiation

PeroK

implying that the speed of an electromagnetic wave changes depending on the medium and that goes against Einstein's second postulate of special relativity. What am I missing?

2d postulate (invariance of c)

As measured in any

inertial frame of reference, low-cal is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting trunk. Or: the speed of light in complimentary space has the aforementioned value c in all inertial frames of reference.

See:

https://en.wikipedia.org/wiki/Postulates_of_special_relativity#Postulates_of_special_relativity

Note the conditions that light is travelling through empty space and is measured in an inertial frame of reference.

MikeeMiracle

This 1 used to get me too. Individual photons ever travel at C, but if there is a medium the light is passing through those photon'southward get captivated and re-emitted, thus the "wave" of light passing through a medium like water is slower than C. In water I believe the "wave" of calorie-free travels at 0.75C.

Vanadium 50

but if in that location is a medium the lite is passing through those photon's go absorbed and re-emitted

Quondam wives tale. This is non what happens. I suggest a forum search.

Does The Speed Of Light Change In Different Mediums

Speed of light in dissimilar mediums

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