Why does light travel slower in water?

[student34]

I always thought it was from individual water molecules absorbing and reabsorbing light, but this explanation in a video from Fermilab is very strange to me .

What is this "new wave" he speaks of; wouldn't it be light too? If so, then this light is now slower than the speed of light, which makes no sense.

 

[ergospherical]

I think the idea of the video is correct. One can show that Maxwell's equations admit plane wave solutions with phase velocity $1/\sqrt{\epsilon \mu}$. In most cases $\mu \sim \mu_0$, so it's only required to consider the dependencies of $\epsilon$. You could say that an electron paired to a positive core obeys a damped, driven oscillatory equation of motion of the form\begin{align*}
\ddot{x} + 2\gamma \dot{x} + \omega_0^2 x = eE(t)/m
\end{align*}with $E(t)$ varying harmonically with time, and this equation is then easily solved for $x(t)$. If there are $n$ such oscillators per unit volume, then the polarisation of the medium is related to the electric field by $P = ne\bar{x} = \chi \epsilon_0 E$, which enables you to determine $\epsilon = \epsilon_0(1+\chi)$; this depends on the freqency $\omega$ of the electric field.

 

[student34]

I think the idea of the video is correct, but not fleshed out. One can show that Maxwell's equations admit plane wave solutions with phase velocity $1/\sqrt{\epsilon \mu}$. In most cases $\mu \sim \mu_0$, so it's only required to consider the dependencies $\epsilon$.

Following the approach of the video, you could say that an electron paired to a positive core obeys a damped, driven oscillatory equation of motion of the form\begin{align*}
\ddot{x} + 2\gamma \dot{x} + \omega_0^2 x = qE(t)
\end{align*}with, say, $E(t)$ varying harmonically with time, and this equation is then easily solved for $x(t)$. If there are $n$ such oscillators per unit volume, then the polarisation of the medium is related to the electric field by $P = ne\bar{x} = \chi \epsilon_0 E$, which enables you to determine $\epsilon = \epsilon_0(1+\chi)$; this depends on the freqency $\omega$ of the electric field.

But what is this "new wave"? Is it light, or what?

 

[phinds]

But what is this "new wave"? Is it light, or what?

both waves, and the resultant composite wave, are electromagnetic waves which, at a certain range of frequencies, we call light. The words are a human construct and don't matter to nature at all.

What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.

 

[student34]

both waves, and the resultant composite wave, are electromagnetic waves which, at a certain range of frequencies, we call light. The words are a human construct and don't matter to nature at all.

What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.

But aren't all EM waves light, which are suppose to travel at the speed of light?

 

[phinds]

But aren't all EM waves light, which are suppose to travel at the speed of light?

Yes, but you aren't paying attention to the COMPOSITEness of the resultant wave as explained by the math in post #2. The waveform of the incident light is combined with the created electromagnetic wave from the electrons.

Also, NO, not ALL EM waves are "light". As I said in the first place "light" is a term we usually only apply to that range of EM frequencies that stimulate our optical nerves.

 

[PeroK]

But aren't all EM waves light, which are suppose to travel at the speed of light?

Light in vacuum travels at the speed of light in vacuum, denoted by $c$. Light in a medium travels at $\dfrac c n$, where $n$ is the refractive index of the medium. Note that $n = 1$ for vaccum.

A postulate of special relativity is that light travels at $c$ in vacuum, as measured in any IRF. There is no postulate that light travels at $c$ in water.

 

[sophiecentaur]

If so, then this light is now slower than the speed of light, which makes no sense.

c only applies in a vacuum. Anything present will slow it down.

individual water molecules absorbing and reabsorbing light,

A simple approach: A light wave passing a molecule will only be 'absorbed' under certain conditions. What we all learned about the Hydrogen Atom absorbing or emitting some specific wavelengths doesn't apply for most wavelengths and most atoms, molecules, liquids or solids. Particularly, when light passes through a solid or liquid (very dense), it interacts with all the material along its path and slows down noticeably but Energy loss is not significant - unlike actual absorption processes. Coming out of the other side, c is re-established. There is no mechanical 'deceleration' and 'acceleration' as with particles that have mass so the change of speed need not worry you.

 

[DaveE]

I think these Sixty Symbols videos are good:

 

[Ibix]

this light is now slower than the speed of light, which makes no sense.

One important thing to realize about $c$ is that it is the speed of light in vacuum, although those last two words are often omitted for brevity. I would say Lincoln probably would have been wise to have included them in this particular video, but he has more YouTube followers than I do. Either way, light in a medium not traveling at the speed of light in a vacuum is not an oxymoron.

But what is this "new wave"? Is it light, or what?

I would describe that "new wave" as "a light wave in a medium". Take a look at the diagrams around 8:30 (and the earlier ones around 7:03) in Lincoln's video, where he's showing two waves adding to make a third. I would say that those diagrams are actually the reverse of the argument he's making. I would say that his argument is that if you take the real electromagnetic field present in the medium (analogous to the third wave) and subtract something that looks like a light wave in vacuum (analogous to the first wave), the remainder (analogous to the second wave) turns out to look like the wave that would be emitted by atomic electrons that just happened to be oscillating as if they'd been driven by the light.

So Lincoln's "new wave" is the physical reality - a light wave in a medium. The other two waves are notional - we can't physically split an EM field into two separate EM fields, only split the mathematical description into two separate terms. But the split up terms do provide some physical insight.

 

[student34]

Thanks everyone

 

[Psnarf]

All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?

 

[PeroK]

All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?

Maxwell's equations represent the classical theory of Electromagnetism. No photons, no probabilities.

In QED, the quantum mechanical theory of light, there would be an alternative explanation for the speed of light in glass. And, QFT (quantum field theory) would give the most fundamental explanation, involving the interaction of several quantum fields. This would be much more complicated than using Maxwell's equations, which are the coarse-grained consequences of QFT in this scenario.

 

[Ibix]

Photons aren't point particles and no position operator is defined for them, so they don't have an exact location. Learning the maths has been on my to-do list for a while, but my understanding is that even when thinking in quantum terms, "wave" is a nearer description of traveling light than "stream of particles".

 

[gleem]

What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.

I seem to recall that the direction is determined by the boundary conditions at the interface necessary to reconcile the continuity of the EM field at the interface. It is in the math.

 

[sophiecentaur]

Maxwell's equations predict the probability of finding a photon.

I think 'they' would say that's OK but, on the way, a photon can't be said to exist anywhere. A photon is what interacts (in quanta) with an object with mass. That's a particularly hard idea in the case of a transparent substance which passes the energy through it without changing its frequency but absorbing some of the energy. Try to make sense of that in terms of light photons with energy hf passing through glass and just losing 1% of the energy of the beam.

 

[pinball1970]

I seem to recall that the direction is determined by the boundary conditions at the interface necessary to reconcile the continuity of the EM field at the interface. It is in the math.

I tried to read about this (change of direction) before asking. I did not get far on the why. Plenty on how to work it out given the angles.
Without the maths is the why out of reach? I don't understand the time side of it either if I am honest. Compositeness of the waves. Is there a heuristic explanation?

 

[PeroK]

I tried to read about this (change of direction) before asking. I did not get far on the why. Plenty on how to work it out given the angles.
Without the maths is the why out of reach? I don't understand the time side of it either if I am honest. Compositeness of the waves. Is there a heuristic explanation?

There's a heuristic explanation that one side of the wavefront hits the glass first and slows down and sort of pulls the rest of the wavefront round. It's a model that might work better for a physical object, perhaps.

 

[Ibix]

The frequency is constant across the interface and the velocity decreases, so the wavelength must decrease. There needs to be an angle between the propagation directions in order that waves of different wavelengths "match" at the interface.

 

[sophiecentaur]

Plenty on how to work it out given the angles.
Without the maths is the why out of reach?

"without the maths" we can't even work out the price of two litres of petrol at £1.40 a litre. There can be no surprise that, without a bit of Trigonometry, you can't derive Snell's Laws of refraction. Are you suggesting that we should require statements made in the 17th Century to explain Nuclear Physics?

 

[Growler]

I think I can simplify this for you... c = the speed of light in a vacuum, if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons, there is a propagation delay while this transformation from a photon to a more energetic electron and back to a photon occurs. While it may appear that light travels slower, it would be correct to say light propogates slower through water than say through air. photons always travel at c.

 

[Ibix]

if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons,

This is incorrect, as the video in the OP explains.

 

[Growler]

li

All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?

light as demonstrated in the dual slit experiment has both a particle and a wave nature... in fact, everything in the universe has a wave function.

 

[Growler]

This is incorrect, as the video in the OP explains.

Encounter does not equate to collisions, in quantum physics there are no collisions, just interactions. these interactions take time.

 

[DaveE]

I think I can simplify this for you... c = the speed of light in a vacuum, if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons, there is a propagation delay while this transformation from a photon to a more energetic electron and back to a photon occurs. While it may appear that light travels slower, it would be correct to say light propogates slower through water than say through air. photons always travel at c.

OK, then you'll need to explain how a "re-emitted" photon travels in exactly the same direction as the others and is emitted with exactly the same delay as the others. In other words, why doesn't the light disperse in space and time? Also, why is glass equally transparent to many wavelengths, since atomic absorption tends to have specific energy levels?

Watch those videos.

 

[PeroK]

Encounter does not equate to collisions, in quantum physics there are no collisions, just interactions. these interactions take time.

Given that precisely that explanation is debunked in Dr Lincoln's video leaves us less than impressed by your grasp of quantum electrodynamics, I'm sorry to say.

 

[Growler]

OK, then you'll need to explain how a "re-emitted" photon travels in exactly the same direction as the others and is emitted with exactly the same delay as the others. In other words, why doesn't the light disperse in space and time? Also, why is glass equally transparent to many wavelengths, since atomic absorption tends to have specific energy levels?

Watch those videos.

1. it does not travel in "exactly" the same direction, reference diffraction, dispersion, scattering etc. how would you measure the progress of individual photons to determine the delay of each?
2. the absorption of the energy of the photon and the re-emission is just one example of propagating interaction... gravitation plays a role, wave interference etc. it still comes down to propagation delay.

You might consider these interactions "negligible" however consider that time itself is dilated to
a very small extent by the higher gravitational distortion in a denser ambient... even this will manifest an apparent departure from c.

IMHO these videos in one fell swoop both over complicate and over simplify.

 

[sophiecentaur]

since atomic absorption tends to have specific energy levels?

Only for isolated atoms and molecules (gases). In dense materials, the Pauli Exclusion principle applies and the lines become broad bands. The interaction with water is with very high numbers of molecules - all over the wave front. Refraction is also a diffraction effect (as ever) as the wave crosses the boundary.

 

[sophiecentaur]

how would you measure the progress of individual photons to determine the delay of each?

That is actually a flawed concept. Photons do not "progress" as their position and extent is unknown.

 

[Growler]

That is actually a flawed concept. Photons do not "progress" as their position and extent is unknown.

My point exactly