Photon states should not evolve?

[PeterDonis]

I thought $d \tau^2$ could always be regarded as a proper time, because in the reference frame of the "particle" there's no spatial displacement.

This will be true if the particle has nonzero rest mass and $d\tau^2$ is an interval along its worldline. But the definition of $d\tau^2$ makes no such assumptions. What you're describing is just one particular special case.

because if it is space-like the "proper time" would be negative?

The square root of $d\tau^2$, assuming you were using a timelike signature convention, would not be negative for a spacelike interval, it would be imaginary.

However, this is still focusing on superficial features instead of the fundamental definition. The fundamental definition just says that timelike, null, and spacelike intervals are physically different. How that difference is modeled in the math depends on your choice of signature convention--note that I specified a timelike signature convention above, which means that timelike intervals have positive $d\tau^2$ and spacelike intervals have negative $d\tau^2$. Conversely, the spacelike signature convention means that timelike intervals have negative $d\tau^2$ (the symbol $ds^2$ is normally used in this case--but as I said before, it's often used in the timelike signature case as well) and spacelike intervals have positive $d\tau^2$. Either way, null intervals have zero $d\tau^2$.

 

[Tio Barnabe]

This will be true if the particle has nonzero rest mass and $\tau^2$ is an interval along its worldline.

This is going against what is said in Weinberg's book. I remember a part of the book that says for light the LHS of the equation $d \tau^2 = \ ... \$ is equal to zero.

 

[PeterDonis]

This is going against what is said in Weinberg's book.

No, it isn't. I said "if the particle has nonzero rest mass". For something with zero rest mass, like light, the interval along the worldline is zero, yes, but the term "proper time" is not a proper description of it, for that very reason--because the worldline is null, not timelike.

 

[Tio Barnabe]

No, it isn't. I said "if the particle has nonzero rest mass". For something with zero rest mass, like light, the interval along the worldline is zero, yes, but the term "proper time" is not a proper description of it, for that very reason--because the worldline is null, not timelike.

So, also, is the statement that times stop at the speed of light incorrect?

 

[PeterDonis]

is the statement that times stop at the speed of light incorrect?

I would say it's "not even wrong", because it assumes that the concept of "proper time" or "elapsed time" is even meaningful for light, or anything that moves at the speed of light.

 

[Dale]

Hmmm, good to know. I thought $d \tau^2$ could always be regarded as a proper time, because in the reference frame of the "particle" there's no spatial displacement. So $d \tau^2 = dt^2$ in the particle reference frame.?

If $d\tau^2=0$ then there is no particle reference frame.

 

[Dale]

Since an object can always be chosen such that the absorbed photon is in the same state as when it was emitted, and emission and absorption are the only times a photon's state can be observed, there is no requirement for a photon's state to evolve over time.

This is wrong. The wave function representing the photons state evolves over time according to the schrodinger equation. At least in standard QFT it is required.

 

[PeterDonis]

The wave function representing the photons state evolves over time according to the schrodinger equation. At least in standard QFT it is required.

Just to clarify: the Schrodinger equation is non-relativistic, and you can't really apply it to photons/light. (You can apply it to atoms or particles interacting with an electromagnetic field, but the field itself will be modeled as an external potential.) A better way of expressing what I think you're trying to express here would be that, in QFT, you can't assume that, if the photon field (electromagnetic field) is in a given state at a particular event, it will be in the same state at any other event that is null separated from that event.

 

[PeterDonis]

This is wrong.

To clarify a bit further: I was interpreting @Carrock's use of the term "photon" classically, i.e., it should really be "very short pulse of EM radiation", which we can model as a "particle" with a well-defined 4-momentum vector which is null. Given a known null 4-momentum vector, and some chosen value for energy, we can always find a local inertial frame at any event on the null worldline of the photon in which the inner product of that 4-momentum vector and the timelike basis vector of the frame yields the chosen value. If we imagine a series of such local inertial frames all along the null worldline, we could say that, in these frames, the photon's energy is "unchanged" as it travels.

The problem, as I pointed out in response, is that in order to know which frames these are, you have to already know the photon's 4-momentum, and in most cases of practical interest, you don't. Also, even if you do, the frame given by the above prescription might not be the one you actually care about.

 

[Carrock]

Hard to find a reference, but I've seen claims that photons experience change in some way, but time does not pass for them.

Um, have you read this thread? We've already discussed such claims and why they're not valid.

Um, have you read the post you quoted from? ( https://www.physicsforums.com/threads/photon-states-should-not-evolve.925675/page-4#post-5847397 )

Carrock: Saying that 'the concept of "time" does not apply to them' also often leads to incorrect inferences.
PeterDonis: How So?
Carrock: Hard to find a reference, but I've seen claims that photons experience change in some way, but time does not pass for them.

So you request an example of an incorrect inference; when I provide it you infer I haven't read this thread.

I didn't ask for a reference to show that neutrinos oscillate. I asked for a reference supporting your claim that it is the neutrinos "really evolving" that allows them to oscillate.

I never claimed that it is 'the neutrinos "really evolving" that allows them to oscillate.' Still, the time I wasted searching for a good reference has saved you the necessity of looking for yourself.

refuting "...an object can always be chosen such that the absorbed photon (and absorber I suppose) is in the same state as when it was emitted."

I didn't say this statement was wrong. I just said it wasn't useful, and I explained why. Did you read my post?

I read your posts but don't recall which is the relevant one. I'm not going to trawl through this thread yet again and perhaps pick a post you didn't mean. Perhaps you should read my posts to avoid changing their meaning with misleading editing and inaccurate precis.

I see in post #79 most of your objections seem rather forgotten as well as the reason I introduced this rather old concept in the first place. If you'd posted something like this earlier I'd have clarified this concept; as it is, when I spend this amount of time on a post like this, I know it's time to quit.

 

[Dale]

we could say that, in these frames, the photon's energy is "unchanged" as it travels.

Sure, but the state is more than just the energy. In classical EM the fields evolve over time per Maxwell's equations. In QED the wave function evolves over time per Schrodinger's equation. Either way, the state evolves over time.

 

[Dale]

Just to clarify: the Schrodinger equation is non-relativistic

Hmm, I thought that the Schrodinger equation, in a suitably generalized form, still determines the evolution of the wavefunction. Is it called another name?

 

[PeterDonis]

In QED the wave function evolves over time per Schrodinger's equation.

Not really. See below.

Either way, the state evolves over time.

Agreed, although there are caveats when we are talking about QFT; a better way to put it in QFT would be the way I put it before, that if we know the state of the quantum EM field at a particular event, we cannot just assume that the quantum EM field will be in the same state at any other event that is null separated from the first one.

I thought that the Schrodinger equation, in a suitably generalized form, still determines the evolution of the wavefunction.

In QFT, there isn't a "wave function" in the sense that there is in non-relativistic QM. It's a very different framework conceptually. We should probably start a separate thread in the quantum forum if this needs to be discussed further.

 

[PeterDonis]

you request an example of an incorrect inference; when I provide it you infer I haven't read this thread.

I asked for an example of "the concept of time does not apply to photons" leading to an incorrect inference. You gave me an example of "time does not pass for photons" leading to an incorrect inference. But "time does not pass for photons" implies that the concept of time does apply to photons. So your example was not responsive to my question.

I never claimed that it is 'the neutrinos "really evolving" that allows them to oscillate.'

I suppose that's true; here's what you said:

A particle's state 'really' evolving during flight, like a neutrino, is generally regarded as proof mass is associated with it.

Which is still wrong, as I have already explained in other posts.

 

[PeterDonis]

I read your posts but don't recall which is the relevant one.

It was the exact same one you were already responding to in the quote you gave (your quote starting with "refuting..."), which is from your post #61. In other words, in your post #61, you were responding to the relevant post of mine, which gave the explanation you are looking for.

 

[nitsuj]

That is not correct. "c" is taken as the universal speed limit and it light were found to have mass, "c" would remain the same but would no longer be the speed of light. The point, then, is that light does NOT travel at "c" in various media, so your statement "vacuum or not" is incorrect.

You're right, but think you should read why. By the same interaction light may go faster than light...I mean c.

"If light were found to have mass..." has nothing to do with it.

 

[phinds]

You're right, but think you should read why. By the same interaction light may go faster than light...I mean c.

"If light were found to have mass..." has nothing to do with it.

I don't understand any of this. Can you expound on it please?

 

[nitsuj]

I don't understand any of this. Can you expound on it please?

sure, for light going through something where it is not absorbed and emitted it easiest to think of it as a wave as opposed to a photon. the EM of the light wave when it begins to pass through the medium, such as glass induces a wave in the glass, the sum of these waves is what we see leave the glass, most often this amounts to the original light wave as slowing. This induced wave and original wave can also amount to the the phase velocity bring greater than c.

You should read up on it it's pretty interesting...

 

[phinds]

sure, for light going through something where it is not absorbed and emitted it easiest to think of it as a wave as opposed to a photon. the EM of the light wave when it begins to pass through the medium, such as glass induces a wave in the glass, the sum of these waves is what we see leave the glass, most often this amounts to the original light wave as slowing. This induced wave and original wave can also amount to the the phase velocity bring greater than c.

You should read up on it it's pretty interesting...

Ah. Phase velocity. You're right, I should read up on it, since I keep hearing about it here on PF.