# Speed of light in the vacuum

1. Nov 17, 2014

### sunrah

I'v been troubled by something. Einstein's second postulate determines the speed of light in empty space to be a constant c, measured by all observers to be the same.

So I was thinking, it is possible to slow light by making it pass through a dense medium like water or glass. If we imagine such a medium in an absolute vacuum, with speed of light in the medium being c' < c, then what happens at the interface of the medium with the vacuum when a photon leaves the medium and enters the vacuum.

According SR, the speed of light in a vacuum must always be measured as c. This means the velocity-time graph is discontinuous at this point which, to me at least, is unphysical. I mean, we're not talking about discrete orbits in a hydrogen atom here. Can someone explain this please?

2. Nov 17, 2014

### A.T.

The same what happens when light passes the interface of two different media:
http://en.wikipedia.org/wiki/Refraction

Why is this unphysical?

3. Nov 17, 2014

### sunrah

Hi,

I don't understand how refraction is relevant. Can't we imagine a situation where the angle of incidence is zero?

Also, my thinking is that a change in velocity must always occur over time, however small the interval, unless we are idealising the situation.

4. Nov 17, 2014

### A.T.

Refraction is a consequence of a change in phase velocity. You don't need vacuum for that.

All of physics is idealising the situation. If you want to know how light changes phase velocity on subatomic length scales it gets into quantum mechanics.

5. Nov 17, 2014

### sunrah

Hi, I know what refraction is. What I'm saying is we don't need to consider it because we can imagine a situation where the angle of incidence is zero.

Yes, I would like to know how light changes phase velocity, if that is relevant to the problem I have posted, for which btw I still would like an answer. Either the change in velocity is instantaneous or gradual (albeit fast). According to special relativity there would be no delay, but as I say, this seems to me to not represent reality. If there are other examples of non-continuous velocity in mechanics/electrodynamics then I'd like to here about them too. I was hoping to encourage discussion of this so I could better understand the problem.

6. Nov 17, 2014

### Staff: Mentor

A bouncing ball. All idealized elastic collisions. Reflection of light.

All of these, and your refraction/velocity question, have in common that we can idealize the surfaces involved to be perfectly smooth planes, the materials to be uniformly homogeneous, and so forth. And as A.T. says above... All of physics is about idealizing the situation properly.

SR says no such thing. That's an idealization that we can choose to make or not make, in both classical and relativistic mechanics.

7. Nov 17, 2014

### sunrah

Is a bouncing ball really a case of instantaneous change in velocity, or is the change in momentum applied over time? I understand that we make idealisations in physics, perhaps I'm not expressing myself properly, but what really bugs me is that Einstein says that all observers measure the speed of light in the vacuum to be c. So am I faced with accepting an instantaneous change in velocity at the medium-vacuum interface without further argument? Would sincerely like to know.

8. Nov 17, 2014

### Staff: Mentor

the idealized solution to a bouncing ball most certainly does involve an instantaneous trandsfer of momentum and change in velocity.

We're making a similar idealization when we talk about light enering a medium: we could do the problem the hard way and treat the medium as if it were a whole bunch of individual atoms separated by vacuum, calculate the behavior of the light in the medium as it propagates through the vacuum between atoms and interacts with the charged particles in these atoms. We end up with the exact same results as if we just said the phase velocity was different in the medium, except at the boundary itself. At the boundary, one way we get an instantaneous change in phase velocity, the other way we get a hugely complicated calculation that gives us a nearly instantaneous change in phase velocity.

9. Nov 17, 2014

### sunrah

Okay, that's interesting. So there is a non-instantaneous description of velocity change at the interface as well. Do you wonder why the photon returns to c after leaving the medium? Newton would say there was a resultant force, but that implies quite a lot here doesn't it??

What was the calculation you were talking about? I have a physics BSc. but it's been a while, thanks

10. Nov 17, 2014

### ghwellsjr

Are you thinking that an individual photon travels through space at c and then it slows down while traveling through a transparent medium and then speeds back up to c when it leaves the medium?

11. Nov 17, 2014

### sunrah

Yes, but I was hoping someone would tell me it's wrong because of the post you quoted. If a photon were to accelerate like that, then I really don't know what force would be responsible for it. On the other hand, if the photon doesn't return to c after leaving the medium, then how does that affect special relativity? Thanks

12. Nov 17, 2014

### Staff: Mentor

What's wrong is that you should be thinking of light as an electromagnetic wave.

It sounds as if you're thinking that light is made of particles called photons, and a beam of light is a bunch of photons travelling along, sort of like the way a herd of sheep is made up of a bunch of individual sheep running past. That model is seriously wrong. You can just barely get away with using it with light in a vacuum, but it is hopelessly misleading when it comes to interactions with matter.

That's why, many posts back, A.T. said "if you want to know how light changes phase velocity on subatomic length scales it gets into quantum mechanics".

If you want to understand what a photon is (trust me, it is nothing like what you think it is) you should try Feynmann's "QED: The strange theory of light and matter"

13. Nov 17, 2014

### ghwellsjr

https://www.physicsforums.com/threads/do-photons-move-slower-in-a-solid-medium.511177/ [Broken] which basically states that a photon travels at c through the medium but interacts with the material of the medium so that it is "re-emitted" after a delay many times during its progress. So it never actually slows down and therefore doesn't have to speed back up to c.

Last edited by a moderator: May 7, 2017