Do photons, phonons and electrons have mass?

[PeterDonis]

Has the emitted photon a longer wavelength?

You are pushing the heuristic picture to the point where it breaks down.

 

[AndreasC]

It isn't.
Yes.
As noted, this is a heuristic picture. It's not 100% accurate.
In the sense that photons still have zero rest mass inside a medium, to the extent the "photon" concept makes sense inside a medium, yes.

Alright, but what is actually happening? It is a question I've had, it's just that every class I've had so far has left me with that impression. Is it beyond the scope of this thread?

 

[PeterDonis]

what is actually happening?

The only ultimate answer to any question like that is, we don't know. We can't directly observe the micro-level details of light propagation in a medium. The best we can do is construct models and compare their predictions with observed data.

The most fundamental model we currently have would be quantum field theory; the QFT answer to your question is that the quantum EM field is interacting with the quantum electron field in each atom in a way that makes the expected "speed" of propagation from a source on one side of the medium to a detector on the other side (as shown by the probability amplitude for detection as a function of the time lapse from source to detection) slower than the speed of light in vacuum. The "photons getting absorbed and re-emitted" heuristic is more or less based on perturbative QFT, but all of the caveats about virtual particles (about which we have several good Insights articles) apply to that heuristic.

Is it beyond the scope of this thread?

Going into more detail about how QFT models light propagation in a medium would be best done in a new thread, yes.

 

[AndreasC]

The "photons getting absorbed and re-emitted" heuristic is more or less based on perturbative QFT, but all of the caveats about virtual particles (about which we have several good Insights articles) apply to that heuristic.

Would you mind linking me to some of said articles?

 

[PeterDonis]

Would you mind linking me to some of said articles?

https://www.physicsforums.com/insights/?s=virtual+particles

 

[Vanadium 50]

You can think of light moving through matter as photons slamming into atoms, being absorbed and then being emitted again, many times over.

Sure, you can think of it, but you'd be wrong.

If this were true, the refractive indices in gasses would depend on pressure, but not temperature. They depend on both. If this were true, the refractive index of graphite would be much lower than diamond (because of densities). In fact, it's higher.

I note that we have drifted quite some way from the original topic, perhaps because multiple people have attempted to answer the original question but have instead injected their own misunderstandings into the thread.

 

[AndreasC]

Sure, you can think of it, but you'd be wrong.

If this were true, the refractive indices in gasses would depend on pressure, but not temperature. They depend on both. If this were true, the refractive index of graphite would be much lower than diamond (because of densities). In fact, it's higher.

I note that we have drifted quite some way from the original topic, perhaps because multiple people have attempted to answer the original question but have instead injected their own misunderstandings into the thread.

We drifted away from the original topic because the op asked how light appears to slow down when it passes through matter even though its speed is supposed to be always the same. I tried to answer to the best of my knowledge but someone explained that it is not entirely correct. Now after that I started looking around a bit and I found out that there is actually a section of the FAQ of this website which discusses this and explains why my version is incorrect. Imo the FAQ is a little bit harder to find than it should for a FAQ but beyond that, OP can look there!

 

[berkeman]

I found out that there is actually a section of the FAQ of this website which discusses this and explains why my version is incorrect. Imo the FAQ is a little bit harder to find than it should for a FAQ but beyond that, OP can look there!

Link?

 

[Lord Jestocost]

You can think of light moving through matter as photons slamming into atoms, being absorbed and then being emitted again, many times over. This process has the effect of slowing down the propagation of the wave as a whole but each individual photon still moves at c while being scattered from atom to atom, it's just that this whole process makes it take longer to get to the other side of the material.

When light travels through a medium like a glass plate, it appears to slow down. The apparent "slower speed" is the result of the superposition of two radiative electric fields:
The incoming light, traveling at speed c, and the light re-radiated by the atoms in the medium (oscillating charges driven by the incoming light) in the forward direction, traveling at speed c, too.

The superposition shifts the phase of the radiation in the air downstream of the glass plate in the same way that would occur if the light were to go slower than c in the glass plate. In case one wants to understand the essential aspects of the phenomena, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". (http://www.feynmanlectures.caltech.edu/I_31.html). On Bruce Sherwood’s homepage (https://brucesherwood.net/) you find an article “Refraction and the speed of light” dealing with this question, too.

 

[AndreasC]

Link?

Sure! https://www.physicsforums.com/insights/do-photons-move-slower-in-a-solid-medium/

 

[vanhees71]

From a QFT point of view an in-medium photon is a photon-like quasiparticle which is described by the in-medium photon Green's function. If you want to visualize a photon (no matter whether in vacuum or in medium) it's rather better to think in terms of waves, and the wave properties are described by the corresponding propagator. If the propagator is sufficiently peaked in energy-momentum space you have a "quasiparticle" which can be described by a dispersion relation $E=E(\vec{p})$, which you can find by looking for poles of the Green's function. Whether or not the photon has an effective mass is decided by this dispersion relation.

In a homogeneous medium you usually have two such "plasmon modes", a longitudinal and a transverse one with different dispersion relations.

Interestingly in a superconductor the photons really get a mass due to the Higgs mechanism, caused by the formation of a charged condensate of Cooper pairs. This mass is responsible for the Meissner effect and defines the penetration length of the London theory (which is a possible effective electrodynamics in superconductors). That's why the Higgs mechanism has been first formulated by Andersen in thinking about spontaneous symmetry breaking in condensed-matter physics.

 

[Vanadium 50]

We drifted away from the original topic because the op asked how light appears to slow down when it passes through matter even though its speed is supposed to be always the same.

Which message?

 

[AndreasC]

Which message?

#17 and #22.

 

[mfb]

binis didn't start the thread, and I already asked to stay on topic as response to that.

 

[AndreasC]

binis didn't start the thread, and I already asked to stay on topic as response to that.

Oh sorry then, I got confused.

 

[vanhees71]

Wasn't the original question, whether photons, phonons, and electrons have mass?

Well, I tried to answer that in #46 assuming that the OP is familiar with what these (quasi-)particles are and that we are taking about QFT (relativistic for photons of course, but for quasiparticles like photons it also makes sense for non-relativistic QFT).

 

[Demystifier]

These articles have energy but do they have mass?

If you print them then they obviously have, but if you read them as pdf's on a computer screen, then it's a very nontrivial physical question.

 

[TeethWhitener]

(NB—Thread had no prefix, so possibly answering this at the wrong expertise level.)

Some phonons (specifically optical phonons) have a non-zero energy at the center of the Brillouin zone (at zero momentum), so I suppose you could call this the “rest energy” of those phonons—and associate it with a rest mass. I’m not sure what that gains you, though.

 

[TonyP0927]

Electrons don't come at rest. Electron rest mass is the mass of an electron as measured when its speed is zero relative to an observer. A photon never comes at rest thus its rest mass is 0. But why can't be the rest mass of a photon be measured when its speed is zero relative to the observer?

Photons have zero mass and are not at rest in any reference frame. If you are trying to determine how photons are affected by gravity, the equivalent property for mass would be $\frac {hf} {c^2}$ .

 

[vanhees71]

And this leads to wrong conclusions. Gravity should be treated within GR, and a naive photon model, i.e., treating the em. wave as a massless point particle has its justification in the eikonal approximation of the Maxwell equation in a spacetime background. E.g., you get the famous deflection of light on the Sun, which lead to Einstein's fame in the public in 1919, when Eddington et al confirmed the prediction of this deflection from GR. The naive idea to just take $hf/c^2$ as the mass of the photon in a Newtonian gravitational field leads to only half the value, but of course the value from GR turned out to be right.

The reason, why for "photons" the Newtonian approximation gets wrong by a factor 2 precisely is the fact that it is always a relativistic object. That's why the Newtonian solution for the Kepler motion in a Newtonian (weak) gravitational field is correct for slow massive objects as testparticles in a gravitational field is a (very) good approximation to the full general-relativistic solution but not for relativistic "objects" like photons.

 

[TonyP0927]

Not always i.e. inside glass they are moving slower,and inside heavy water of a nuclear reactor very slow.

That's because the photon is being absorbed and re-emitted by the atoms it runs into, however in-between the atoms, it travels a c.

 

[Vanadium 50]

Why do people jump on to old threads only to post incorrect things? Especially when this was put to rest on the previous page?

If this were true, the refractive indices in gasses would depend on pressure, but not temperature. They depend on both. If this were true, the refractive index of graphite would be much lower than diamond (because of densities). In fact, it's higher.

 

[TonyP0927]

And this leads to wrong conclusions. Gravity should be treated within GR, and a naive photon model, i.e., treating the em. wave as a massless point particle has its justification in the eikonal approximation of the Maxwell equation in a spacetime background. E.g., you get the famous deflection of light on the Sun, which lead to Einstein's fame in the public in 1919, when Eddington et al confirmed the prediction of this deflection from GR. The naive idea to just take $hf/c^2$ as the mass of the photon in a Newtonian gravitational field leads to only half the value, but of course the value from GR turned out to be right.

The reason, why for "photons" the Newtonian approximation gets wrong by a factor 2 precisely is the fact that it is always a relativistic object. That's why the Newtonian solution for the Kepler motion in a Newtonian (weak) gravitational field is correct for slow massive objects as testparticles in a gravitational field is a (very) good approximation to the full general-relativistic solution but not for relativistic "objects" like photons.

There is really nothing Newtonian about light; in fact, it is the basis of relativity (all of us are moving at the speed of light, just not through space as much as through time as illustrated by a space-time light cone diagram).

Many physicists define m as strictly rest mass, but for undergrad physics students, m is taught as representing effective mass for simplicity as relativity is a new concept for most of the students. Defining m as the rest mass, for light, m=0.

It's probably more accurate to think of massless particles in terms of momentum. BTW, the famous equation E=mc² is actually not the complete equation. The complete equation is E²=(pc)² + (mc²)² . For a photon, the rest mass is zero so this equation reduces to E²=(pc)² + 0 or simply E=pc where p=h/λ. Basically for photons, it's not the mass; it's the momentum.

 

[vanhees71]

Where does this strange claim about "we'd all move with the speed of light" come from? I guess, it's paraphrasing the mathematical identity that the four-velocity of a particle obeys always $u_{\mu} u^{\mu} = c^2$, but it is misleading to say everything moves with the speed of light.

It's not many physicists but all physicists that define $m$ as strictly the invariant mass. For massive particles it's the rest mass. For photons the mass is 0 and thus never a rest mass, because a photon moves always with the speed $c$ (in the vacuum). Of course photons are no massless particles in a literal sense. They cannot even localized, because there's no position operator for them in the strict sense. That's why I said that the naive photon picture as used in GR has to be understood in the sense of the iconal approximation of the Maxwell equations (see, e.g., Landau&Lifshitz vol. 2).

I think at no level of teaching one should tell students of the 21st century about several different sorts of "relativistic masses". Einstein comitted this sin only in the very beginning of relativity around 1905 but then stated one should use mass only as the invariant mass.

 

[PeterDonis]

it is the basis of relativity (all of us are moving at the speed of light

This is not the "basis of relativity". It is a particular viewpoint which, while it can be said to have some basis in the actual math (see below), is never found in actual textbooks or peer-reviewed papers, but only in pop science books, articles, and TV shows.

Even the basis in the actual math is questionable. As @vanhees71 notes, one can observe that the invariant length of the 4-velocity $u^\mu$ of an object with nonzero rest mass is $\sqrt{u^\mu u_\mu} = c$, and the square root of this could be thought of as the "speed through spacetime" of the object. However, the main point of doing this, according to the pop science sources where this viewpoint appears, is so that we can say that, as the velocity of the object relative to some chosen frame increases, more of the object's "speed through spacetime" becomes "speed through space" instead of "speed through time". And the limiting case of this is claimed to be a light ray, which moves at $c$ "through space" and therefore doesn't move "through time" at all.

However, this nice-seeming viewpoint conceals a critical flaw: the invariant length of a light ray's 4-momentum is zero, not $c$. There is no continuity between the case of nonzero rest mass (4-velocity with invariant length $c$) and zero rest mass (4-momentum with invariant length $0$) of the kind that is claimed by this viewpoint.

There have been plenty of previous PF threads on this (often prompted by one of Brian Greene's TV specials where he pushes this viewpoint), but it's been a while since the last one.

 

[vanhees71]

That's a very important point. As the analysis of the representation theory of the proper orthochronous Poincare group in the context of relativistic QFT reveals, the massless case is special, and the limit "$m \rightarrow 0$" is anything but trivial. That's also the mathematical reason for the fact that one must not think about photons as pointlike objects traveling with the speed of light wrt. any (inertial) reference frame.

The correct semiclassical point of view of the "photon", as usually treated in GR textbooks, is that this is in fact the eikonal approximation of Maxwellian electrodynamics. It describes the behaviour of wave vectors in the sense of geometric optics. The point-particle-photon picture can sometimes be a shortcut in deriving interesting things about em.-wave propagation (e.g., in the GR context the gravitational bending of light) but it must not be mistaken as a point-particle interpretation of photons. This was an erroneous point of view in the early days of the "old quantum theory", which is out of date for at least 97 years!