# B Classical equations and light

1. Jan 1, 2018

### JulianM

What should I use then for light which has been slowed to "non-relativistic" velocities? I presume that only relativistic equations would still have to apply?

2. Jan 1, 2018

### PeroK

The speed of light is always $c$. You can't slow it down.

3. Jan 1, 2018

### JulianM

Sure you can. C is only for a vacuum.

4. Jan 1, 2018

### Orodruin

Staff Emeritus
You are trying to open an entirely different can of worms here. The dispersion relation for light in a medium is not the same as that in vacuum. You really cannot say that light in a medium is massless.

5. Jan 1, 2018

### PeroK

That's a very different scenario. In a medium photons interact with the medium, are absorbed and may be re-emitted. That's what causes the apparent change in speed. You can't directly use equations for undisturbed motion in this case.

6. Jan 1, 2018

### Orodruin

Staff Emeritus
I must say that I really dislike this quite popular heuristic. I do not think it adequately describes what is going on and leads to misconceptions and misunderstandings.

Either way, I generally recommend staying away from ”photons” when discussing classical relativity and instead look at the dispersion relation of plane EM waves in the medium.

7. Jan 1, 2018

### Mister T

$\vec{p}=\left(\frac{E}{c^2}\right) \vec{v}$

Your confusion is over when we can use equations that apply to massive particles versus equations that apply to massless particles. The equation I wrote above applies to both, as does the one previously mentioned in this thread: $E^2=(pc)^2+(mc^2)^2$.

The equation $\vec{p}=\gamma m\vec{v}$ applies only to massive particles. For low speeds $\gamma \approx 1$ and we can write $\vec{p}=m \vec{v}$.

Up until now we have been discussing a single massless photon moving at speed $c$ through a vacuum. Once you start looking at collections of photons you see that the collection can and usually does have mass. Having a beam of light scatter as it passes through a medium involves the photons interacting with the atoms that make up the medium. You can try to understand that, but modelling the light as a collection of massive particles moving at speeds less than $c$ will not work in the sense that the model will not be consistent with the way we see light actually behaving.
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8. Jan 1, 2018

### ZapperZ

Staff Emeritus
Furthermore, the CHANGE in the apparent speed of light in a medium is because we tend to measure the group velocity of light! This automatically means that we measure not the speed of a photon, but rather the speed of a collection of LARGE number of photons, which we collectively call "light" or EM wave. This is what we typically measure as the speed of light.

Zz.