# Photon's frame of refernce

Sorry if this has been asked, but I did a search and didn't find a relating topic.

This thought came to me a few days ago when a friend asked me about time dilation. Time beats slower and distance is shorter for a moving reference frame with respect to a non-moving reference frame, and the amount of each is dependent upon the speed.

So, for a photon that travels at c, would time not pass and would all space be a single point in the photon's moving reference frame with respect to the non-moving reference frame?

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Photons don't have reference frames. By postulate, photons travel at c in all reference frames. Thus there are no reference frames in which photons are at rest.

I've seen a few arguments on PF to the effect that a photon doesn't have a frame of reference where it is at rest. But the inability to provide a map, as these arguments go, from an inertial frame to a hypothetical frame of reference, is only weak evidence of nonexistance.

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pervect
Staff Emeritus
We've really had this discussion several times. See for instance https://www.physicsforums.com/showpost.php?p=1254103&postcount=8

It's basically an error to attribute the usual sort of reference frame to an object moving at the speed of light.

If one has some basic knowledge of the concept of the Lorentz interval, it is easy to see why. The Lorentz interval between any two points of the worldline of an ordinary observer is timelike. Thus such an observer experiences time along their worldline. The Lorentz interval along any two points of the wordline of a photon is null. A null interval is neither timelike, nor spacelike. Thus a photon does not experience "time in the same sense that a person or any object made out of matter does.
But while a photon doesn't "experince time", it is possible to mark out regular intervals along its worldline.....

So a photon doesn't experience time, but in some abstract sense it "experiences" a null coordinate - at least, one can distinguish regular intervals along a photon's worldline. But in spite of the fact that these intervals are regular in some sense, they should not be confused with time. The intervals are not timelike - they are null intervals, neither timelike nor spacelike.

How does that answer anything, pervect?

So, for a photon that travels at c, would time not pass
and asks how the measure of space in an inertial frame maps to the measure of space in the comoving frame of a photon,
and would all space be a single point in the photon's moving reference frame with respect to the non-moving reference frame?

I've seen a few arguments on PF to the effect that a photon doesn't have a frame of reference where it is at rest. But the inability to provide a map, as these arguments go, from an inertial frame to a hypothetical frame of reference, is only weak evidence of nonexistance.
When I claimed above that the photon has no reference frame, I did not argue anything about maps. I pointed out that such a frame would directly contradict the second postulate. That should clearly end any debate, unless it was something other than Relativity you were wanting to talk about.

Fredrik
Staff Emeritus
Gold Member
He's also talking about the "photon's frame of reference" as if there's a standard definition of "this object's rest frame" that works for all objects including photons. This is certainly not the case. A good answer should explain the standard definition for massive particles and explain why it doesn't work for photons. I included such an explanation in the thread I mentioned in this quote:
See my posts in this thread about the "photon's point of view". In particular, #8 and #14.

The concept of "proper time" is only defined along those curves in spacetime that represent speeds <c, so the concept of "proper time" isn't really relevant here. We could of course define the proper time of a null curve (a curve that represents speed c) to be =0, but it's a pretty pointless thing to do for several reasons, one of them being that no clocks can travel at that speed anyway.

Fredrik. We've gone over this before, of course. thank you, I've reread your posts. You might also feel free to read my posts at the end of the same thread.

One can spend a great deal of time showing how one cannot make sense of the question using some particular reasoning. But the best we can do, in support of the negative, is say that we cannot make sense of it, rather than sense cannot be made of it.

If I become sufficiently motivated, I might go over my notes to see if I found a sensible answer to this.

A.T.
I think It is OK to say that proper time doesn't pass for photons. I'm not convinced by the arguments why the concept of proper time is completely inapplicable to photons:
Fredrik said:
The concept of "proper time" is only defined along those curves in spacetime that represent speeds <c,
Here you a linking the concept of proper time which is a measurable physical quantity with one particular abstract mathematical concept: the Minkowski spacetime. There are other geometrical interpretations than Minkowski's, like the space-popertime diagram, where the proper time of photons is simply zero.
Fredrik said:
one of them being that no clocks can travel at that speed anyway.
We also cannot place an observer at infinity, but will still use his proper time to define gravitational time dilation. And how do you know that photons are not clocks?

Fredrik
Staff Emeritus
Gold Member
Fredrik. We've gone over this before, of course. thank you, I've reread your posts. You might also feel free to read my posts at the end of the same thread.
I took a quick look at them, but didn't examine every detail. When you define your new variables a and b, you're really just saying that we take the photon's world line to be the time axis of a new coordinate system, and then you pick another straight line to be the spatial axis. This is of course fine, but you need to be aware of two things: a) the result isn't an inertial frame, and b) after you have chosen the time axis that way, the photon will be stationary in your new coordinate system, no matter what other choices you make in your definition (e.g. what curve to use as the spatial axis). So if you're going to say that a particular coordinate system is "the photon's rest frame" (rather than one of infinitely many rest frames for the photon), you're going to have to come up with a very good reason.

One can spend a great deal of time showing how one cannot make sense of the question using some particular reasoning. But the best we can do, in support of the negative, is say that we cannot make sense of it, rather than sense cannot be made of it.
I think that what's interesting is that neither the theory we're talking about, nor the standard definitions used by people working with it, has made sense of it. The possibility that some weird definitions might give this concept meaning isn't very interesting to me.

Let us take a plane wave Acos(ωt-kx) in a transparent medium with n. The light velocity is c/n. What is the wave solution in a reference frame moving with V=c/n? Isn't it A'cos(k'x') ? And photon energy is not ћω'=0 but ћck'>0?

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Fredrik
Staff Emeritus
Gold Member
I think It is OK to say that proper time doesn't pass for photons. I'm not convinced by the arguments why the concept of proper time is completely inapplicable to photons:

Here you a linking the concept of proper time which is a measurable physical quantity with one particular abstract mathematical concept: the Minkowski spacetime. There are other geometrical interpretations than Minkowski's, like the space-popertime diagram, where the proper time of photons is simply zero.

We also cannot place an observer at infinity, but will still use his proper time to define gravitational time dilation. And how do you know that photons are not clocks?
I can tell that we have pretty different ways of thinking about these things. To me a photon is a mathematical concept defined by a theory, and the definition implies that a photon doesn't have the internal structure it would need to change with time. You're probably talking about "actual photons" in the real world, but I consider that an ill-defined concept, and therefore less interesting to talk about. Also, to me "proper time" is a mathematical property of a curve in Minkowski space, and special relativity is the theory that tells us how to interpret the mathematics of Minkowski space as predictions about results of experiments. If you use another "geometrical interpretation", I would say that you're talking about a different theory. It's an equivalent theory (I hope), but not the same theory, and I tend to interpret questions in the relativity forum as questions about the standard formulations of SR and GR, not as questions about other formulations, or even as questions about the real world (since the concepts we're talking about are defined by the theories we're using).

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Is it in theory impossible to construct an observer out of zero mass particles?

Ich
It is possible in principle, as long as they go in different directions. That's equivalent to the system having rest mass.

Dale
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2020 Award
Woohoo, around and around in circles we go over and over and around and around again and again woohoo!

Maybe somebody mentioned this, but another reason why it's not meaningful to talk about a photon's rest frame is that if it were actually at rest, its momentum would be zero in that frame, so its rest mass would be zero. Then its energy content must be zero, and arguably it wouldn't exist at all. A photon is like a shark, it exists only in motion.

There also is a Heisenburg Uncertainty problem, because if the photon's momentum is exactly fixed (at zero in its rest frame), its location must be entirely unbounded.

Maybe somebody mentioned this, but another reason why it's not meaningful to talk about a photon's rest frame is that if it were actually at rest, its momentum would be zero in that frame, so its rest mass would be zero. Then its energy content must be zero, and arguably it wouldn't exist at all. A photon is like a shark, it exists only in motion.

There also is a Heisenburg Uncertainty problem, because if the photon's momentum is exactly fixed (at zero in its rest frame), its location must be entirely unbounded.
And how about my question in post #12?

And how about my question in post #12?
Agreed.

Dale
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2020 Award
Let us take a plane wave Acos(ωt-kx) in a transparent medium with n. The light velocity is c/n. What is the wave solution in a reference frame moving with V=c/n? Isn't it A'cos(k'x') ? And photon energy is not ћω'=0 but ћck'>0?
Be careful transforming a wave in relativity. The http://en.wikipedia.org/wiki/Four-frequency" [Broken] is (ω/c,k) which is Lorentz covariant, so it transforms like any other four-vector. And its dot product with the four-position of some event is the phase at that event which is a Lorentz invariant scalar.

Thanks for the brief respite from the usual monotony of this repetitive discussion.

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Photons don't have reference frames. By postulate, photons travel at c in all reference frames. Thus there are no reference frames in which photons are at rest.
I've seen a few arguments on PF to the effect that a photon doesn't have a frame of reference where it is at rest. But the inability to provide a map, as these arguments go, from an inertial frame to a hypothetical frame of reference, is only weak evidence of nonexistance.
When I claimed above that the photon has no reference frame, I did not argue anything about maps. I pointed out that such a frame would directly contradict the second postulate. That should clearly end any debate, unless it was something other than Relativity you were wanting to talk about.
Sorry, I missed your last post. Photons have no inertial frame at which they are at rest. That would tend to rule out frames of reference which are inertial. And also comoving. And also those accelerating, I suppose. Is this set exhaustive?

Woohoo, around and around in circles we go over and over and around and around again and again woohoo!
I am not circling.

I took a quick look at them, but didn't examine every detail. When you define your new variables a and b, you're really just saying that we take the photon's world line to be the time axis of a new coordinate system, and then you pick another straight line to be the spatial axis. This is of course fine, but you need to be aware of two things: a) the result isn't an inertial frame, and b) after you have chosen the time axis that way, the photon will be stationary in your new coordinate system, no matter what other choices you make in your definition (e.g. what curve to use as the spatial axis). So if you're going to say that a particular coordinate system is "the photon's rest frame" (rather than one of infinitely many rest frames for the photon), you're going to have to come up with a very good reason.
Thank you. I'll take this all under consideration. Note that neither a nor b are a temporal axis.

I think that what's interesting is that neither the theory we're talking about, nor the standard definitions used by people working with it, has made sense of it. The possibility that some weird definitions might give this concept meaning isn't very interesting to me.
I have not advanced a theory. Personal theories are outlawed under the PF guidlines. I've carefully constrained my analysis to the postulates of special relativity as it should be.

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atyy
Photons have no inertial frame at which they are at rest.
Yes, I think that's the point. You can construct non-inertial frames in which the photon is at rest. http://arxiv.org/abs/hep-ph/9505259