# Faster than light in glass

• richengle
But the light waves outside the glass will travel faster, yes.Yes, although I am not sure if the simulation is accurate.

#### richengle

i made a simulation of waves in glass and in air. my simulation has led me to believe that if light begins in glass, it can travel to the air, and then move much faster, and then go back into the glass at a point further down. Could this happen in real life?

here is the video of my simulation, and the blue waves are for in glass, the white, for air... you can see the waves begin in the glass/red side, and move out, striking to air,,,, and start moving much faster, and reintroducing waves ahead of the original wavefront... could this really happen?

richengle said:
Summary:: if you have a source of light that begins in glass, can it move out of the glass, and exceed its speed in glass, and then return... see video

i made a simulation of waves in glass and in air. my simulation has led me to believe that if light begins in glass, it can travel to the air, and then move much faster, and then go back into the glass at a point further down. Could this happen in real life?

here is the video of my simulation, and the blue waves are for in glass, the white, for air... you can see the waves begin in the glass/red side, and move out, striking to air,,,, and start moving much faster, and reintroducing waves ahead of the original wavefront... could this really happen?

I didn't bother to watch the video. Of course light's velocity is higher in air than glass. That is not rocket science. Light's velocity in air is slightly less than c (the velocity in a vacuum).

I don't see why it would re-enter the glass, unless the surface isn't flat or there's some subtle diffractive effect I haven't thought about. And the reflection looks wrong - it should be very weak below the critical angle and strong above it. So I wonder what it is you are simulating.

But the light waves outside the glass will travel faster, yes.

richengle said:
Summary:: if you have a source of light that begins in glass, can it move out of the glass, and exceed its speed in glass, and then return... see video
Yes, although I am not sure if the simulation is accurate.

richengle said:
my simulation has led me to believe
You have things the wrong way rounds here. A simulation cannot tell you anything that you didn't put in first. It can give you good pictures or results if the theory is right. If your simulation 'allows' speeds higher than c then it's fundamentally in error.
Fun though.

berkeman
sophiecentaur said:
You have things the wrong way rounds here. A simulation cannot tell you anything that you didn't put in first. It can give you good pictures or results if the theory is right. If your simulation 'allows' speeds higher than c then it's fundamentally in error.
Fun though.
Its not faster than light, its like, the light escapes the "swamp" of slow speed in glass, and runs for a bit on the fast track of air,,, then runs back into the swamp of the glass at a further position down than the head of the wave that stayed in glass

Ibix said:
I don't see why it would re-enter the glass, unless the surface isn't flat or there's some subtle diffractive effect I haven't thought about. And the reflection looks wrong - it should be very weak below the critical angle and strong above it. So I wonder what it is you are simulating.

But the light waves outside the glass will travel faster, yes.
it is originally from simulating ripples in water. Each cell affects surrounding cells. So cells at the border will poll cells in the other region. The "glass" region polls every third time, thus waves move slower there.

would you happen to have a better simulation by chance?

I don't have a simulation. But I think that if you wish to simulate light, you need to simulate an EM field not a body of water. The equations are not the same.

vanhees71 and sophiecentaur
In real life, there is nothing special about "faster than light" in this case. You just have a flat interface between two regions and a ratio of refractive indices. Snell's law will work just fine and will tell you whether or not you have total internal reflection.

vanhees71
richengle said:
Summary:: if you have a source of light that begins in glass, can it move out of the glass, and exceed its speed in glass, and then return... see video

my simulation has led me to believe that if light begins in glass, it can travel to the air, and then move much faster
The difference in speed of waves doesn't involve acceleration so decrease and increase in wave speed doesn't violate any intuitive ideas about an object with mass suddenly speeding up when it exits a dense medium.
This is a common source of confusion.

jbriggs444 said:
In real life, there is nothing special about "faster than light" in this case. You just have a flat interface between two regions and a ratio of refractive indices. Snell's law will work just fine and will tell you whether or not you have total internal reflection.
True. @richengle - you could use ray optics to work out light paths, and join points of equal optical distance to get your wavefront positions. Then you could look up the reflection from interfaces to get the intensity of the wavefronts on different paths. That would be a way to validate whatever you get.

sophiecentaur said:
The difference in speed of waves doesn't involve acceleration so decrease and increase in wave speed doesn't violate any intuitive ideas about an object with mass suddenly speeding up when it exits a dense medium.
This is a common source of confusion.
an increase in wave speed is not an acelleration? wow, isn't it not an increase in momentum? whoa, but that means mass got less if it still is an acelleration... how?

richengle said:
an increase in wave speed is not an acelleration? wow, isn't it not an increase in momentum? whoa, but that means mass got less if it still is an acelleration... how?
It’s not mechanics here and a photon has no mass. The speed in vacuum is c. The momentum is NOT mc. It is h times wavelength for a massless particle.
Just another example of how QM ain’t natural.

richengle
sophiecentaur said:
It’s not mechanics here and a photon has no mass. The speed in vacuum is c. The momentum is NOT mc. It is h times wavelength for a massless particle.
Just another example of how QM ain’t natural.
have you heard of a polariton?

richengle said:
have you heard of a polariton?
Only vaguely but how does that affect the basic question? The relevance of phase and group velocity means that the information transferred when you modulate a light beam will be slower than the simple wave velocity. Afaics, we're dealing with things at a far simpler level, aren't we?

richengle said:
have you heard of a polariton?
Yes but so what? The light (classical wave or corpuscular) travels faster outside the glass. Momentum is certainly conserved in the process but defining the momentum associated with a "photon" in the solid is not simple. So what exactly is your question?

vanhees71
There's a great confusion in the literature about this. It's most clearly answered by using QED at finite temperature to derive the properties of "photons in the medium".

Concerning energy and momentum the debate is more than 100 years old. It's a fight between Abraham's and Lorentz's energy-momentum tensor of the electromagnetic field in a medium (of course in terms of classical physics rather than QT). The salomonic modern resolution is that both are right in different physical contexts and one has to clearly distinguish between canonical and mechanical momentum of the em. field. In addition the interpretation of the energy-momentum balance analysis depends on the (quite arbitrary) split of the total energy-momentum tensor of a dielectric in "field and matter parts".

See, e.g.,

W. Israel, Relativistic effects in dielectrics: An experimental decision between Abraham and Minkowski?, PLB 67, 125 (1977)
https://doi.org/10.1016/0370-2693(77)90824-3

As mentioned before, this effect has met with quite some confusion in the literature. There also textbooks which in my opinion do not get the point right completely.

The main point in my opinion is the confusion about the definition of a signal velocity, which can be proven to not exceed the speed of light (see Jackson / Electrodynamics 2ne ed. §7.11 for a discussion when the definition of a usual group velocity is not sufficient). The "signal" in a scenario like the above, however, is not the fastes wavefront alone, but an adequately defined wavefront in dispersive media that is calculated by some sort of averaging procedure including all parts of the wavepacket.

Without now having calculated everything through: should this not solve the "paradox"?

Sure, that problem is solved for at least 113 years by Sommerfeld in answering a question by Wien concerning anomalous dispersion, where both the phase and the group velocity exceed the speed of light in a vacuum, but particularly the group velocity is just a formal quantity without much physical content in this case, because the saddle-point approximation of the Fourier integral used to derive it as the "speed of a wave packet" doesn't apply in this case.

What's always ##\leq c## (in the usual classical model for dispersion it's ##=c##) is the "front velocity", i.e., the speed the wave front propagates.

All this is of course found in Jackson but also in Sommerfeld, Lectures on Theoretical Physics vol. 4 (optics). I don't know whether the later papers by Sommerfeld and Brillouin are translated into English. In any case it's one of the most elegant applications of complex contour-integration techniques I've ever seen.