# Question about "Rest frame of a photon" FAQ

#### Wes Tausend

Gold Member
[Moderator's note: This thread has been separated out from the FAQ entry since questions or suggestions about FAQ entries should not be cluttering up the FAQ entries themselves.]

I've read that in relativity the concept of the rest frame of a photon doesn't make sense. Why is that?

A rest frame of some object is a reference frame in which the object's velocity is zero. One of the key axioms of special relativity is that light moves at c in all reference frames. The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c (velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense.

The following forum members have contributed to this FAQ:
D H
Dale
Fredrik
Pallen
I would like to suggest that it might be more proper to base the "rest frame of a photon" theory explanation entirely on the PF Rules regarding conventional public peer-review and just say we follow Einstein because of that. It seems preferable to leave it open, rather than adding a weak member derived theory of "what it looks like".

If energy and matter are interchangeable and certainly directly related (they are), it seems to me that if we reduce the theoretical situation to one elementary particle of matter and one elementary particle of energy related by a certain speed in our universe, that they could inexplicably move relative rather than exclusive to one another. Most important, if we are to properly follow the Copernican principle, the two could (and should) be reasoned to be relative to one another.

So unless the fundamental FAQ-given reasoning is made more rigorous in depth, we should just fall back on Einstein's limited SR where he apparently believed (or at least states as axiom) a particle of energy is somehow immune to the conventional foundation principle of relativity as one of his first principles. Einstein didn't fully explain why relativity should only work this one way, just that it does (at the least) unfortunately work in a rather non-intuitive manner. So why should we need to try to improve his explanation to reject ordinary relativity, while also accidently flying in the face of our PF rules?
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To accentuate my point on why I think the FAQ reasoning weak, let me re-word the original PF FAQ premise argument in terms of faulty pre-Copernican era reasoning:
Q: I've read that in relativity the concept of the rest frame of a star doesn't make sense. Why is that?
A: A rest frame of some object is a reference frame in which the object's velocity is zero. One of the key axioms of Ptolemy's (Aristotle's) relativity is that a star moves across the sky in all reference frames. The rest frame of a star would require the star to both be at rest (velocity=0) and moving at high speed across the sky. That of course is contradictory. In other words, the concept doesn't make sense.

Using the "known firmament" as his first principle, Aristotle argues that obviously earth appears to be standing still and thereby must be considered at rest. He concludes in error, therefore only stars move. According to Aristotle, and our present FAQ, what it initially looks like... must be what it is. The FAQ reasoning might appeal to us, but in light of the Copernican principle, I find it fundamentally weak.

Wes

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#### Ibix

It seems preferable to leave it open, rather than adding a weak member derived theory of "what it looks like".
It's not a "weak member derived theory". It's a direct consequence of the second postulate that you cannot have an inertial frame in which light is at rest. This result may be wrong - but only if relativity is not an accurate description of reality. And we have no evidence of that, despite over a century of search. This is why your Aristotle/Ptolemy analogy fails. We have plenty of evidence that their cosmology is wildly inaccurate, so whether or not something contradicts its principles is physically irrelevant.

Arguably the article should end "...doesn't make sense in our modern understanding of physics." But that's all.

#### Mister T

Gold Member
I would like to suggest that it might be more proper to base the "rest frame of a photon" theory explanation entirely on the PF Rules regarding conventional public peer-review and just say we follow Einstein because of that.
But that would be a false statement! We do not base it on a peer-review of Einstein's 114 year old publication. We base it on the overwhelming amount of experimental evidence that's been collected during the intervening years.

It seems preferable to leave it open, rather than adding a weak member derived theory of "what it looks like".
I suppose I don't understand this statement. The phrase "what it looks like" appears nowhere in the answer to the FAQ.

If energy and matter are interchangeable and certainly directly related (they are),
But they aren't! Energy is a property of matter. Energy is a human invention, matter is not.

Perhaps you have the misconception that the $m$ in $E_o=mc^2$ stands for matter. It doesn't. It stands for mass, which is also a property invented by humans. One of the main consequences of Einstein's famous mass-energy equivalence is that mass is not, as it had been previously thought, a measure of the amount of matter.

it seems to me that if we reduce the theoretical situation to one elementary particle of matter and one elementary particle of energy [...]
There is no such thing as an elementary particle of energy. Plus, Nature doesn't often behave the way it seems it ought to.

So unless the fundamental FAQ-given reasoning is made more rigorous in depth, we should just fall back on Einstein's limited SR where he apparently believed (or at least states as axiom) a particle of energy is somehow immune to the conventional foundation principle of relativity as one of his first principles.
Neither of the two postulates contradicts the other. Moreover, experimental evidence confirms that Einstein got it right.

#### Wes Tausend

Gold Member
I'm not saying Einstein got it wrong. To the contrary, I'm saying he got it right... but there may be two relative coordinate systems to consider as philosophically and mathematically correct just as there are two ways to look at the differences between heliocentrism and geocentrism. I am saying Einstein might accidently be incomplete.

The two may reinforce one another, if anything.

Wes

#### PeterDonis

Mentor
I would like to suggest that it might be more proper to base the "rest frame of a photon" theory explanation entirely on the PF Rules regarding conventional public peer-review and just say we follow Einstein because of that.
That would not be an explanation. The purpose of a FAQ entry like this is to actually give an answer to a question, not just say the answer is whatever is published in the peer-reviewed literature.

rather than adding a weak member derived theory of "what it looks like".
I have no idea what you are referring to here.

If energy and matter are interchangeable and certainly directly related (they are), it seems to me that if we reduce the theoretical situation to one elementary particle of matter and one elementary particle of energy related by a certain speed in our universe, that they could inexplicably move relative rather than exclusive to one another. Most important, if we are to properly follow the Copernican principle, the two could (and should) be reasoned to be relative to one another.
I have no idea what you are trying to say here.

unless the fundamental FAQ-given reasoning is made more rigorous in depth, we should just fall back on Einstein's limited SR where he apparently believed (or at least states as axiom) a particle of energy is somehow immune to the conventional foundation principle of relativity as one of his first principles.
Einstein said no such thing. Neither does SR. The fact that the speed of light is the same in all reference frames is perfectly consistent with the principle of relativity.

Also, it appears that you are using the term "particle of energy" to mean "photon". That's not a good usage.

#### Ibix

but there may be two relative coordinate systems to consider as philosophically and mathematically correct
I have no idea what that is supposed to mean.

Lightlike coordinates are of course usable. They just don't define "rest frames of light".

#### PeterDonis

Mentor
there may be two relative coordinate systems to consider as philosophically and mathematically correct
The terms "coordinate system" and "rest frame" do not mean the same thing. Go read post #2 by @Dale in the FAQ thread.

#### Wes Tausend

Gold Member
I have no idea what that is supposed to mean.

Lightlike coordinates are of course usable. They just don't define "rest frames of light".
"but there may be two relative coordinate systems to consider as philosophically and mathematically correct"
Sorry. I should have said two opposing coordinate systems.

#### Wes Tausend

Gold Member
OK, Peter. I'm not sure how he derived this, but I'm done. I'll just accept the FAQ will probably stand as is. Thanks for everyone's replies.

Wes

#### Dale

Mentor
I'm not sure how he derived this
A tetrad is a set of four orthonormal vector fields, one timelike and three spacelike. The integral curves of a tetrad can be thought of as defining the worldlines of a family of physical observers, with the spacelike vector fields defining a set of directions used by those observers.

A coordinate system is a mapping between events in the spacetime manifold and points in R4 with the properties that the mapping must be 1-to-1 and smooth.

You can clearly have a smooth invertible map where the events on a null geodesic share a coordinate value (light cone coordinates are an example), but you can also clearly not have a lightlike vector in a set of one timelike and three spacelike vectors (it can’t be one of the spacelike vectors because it is lightlike and it can’t be the timelike vector for the same reason)

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#### PeterDonis

Mentor
you can also clearly not have a lightlike vector in a set of one timelike and three lightlike vectors
I think you mean a set of one timelike and three spacelike vectors.

There is also another point that might be worth mentioning: why do we define a tetrad as a set of one timelike and three spacelike vectors, all mutually orthogonal? The answer is that there is no other way to satisfy the "all mutually orthogonal" part.

#### PeterDonis

Mentor
I should have said two opposing coordinate systems.
This doesn't make what you are trying to say any clearer. But in any case, coordinate systems are not physics. There will be an infinite number of possible coordinate systems you can choose in any spacetime; but the laws of physics and all physical invariants will be the same regardless of which coordinate system you choose.

#### Dale

Mentor
I think you mean a set of one timelike and three spacelike vectors.
Oops, yes I will correct that

#### Wes Tausend

Gold Member
Thanks Dale. I'll try to understand this. I'm sorely math illiterate beyond trig and pretty rusty at that. But I still have a decent grasp of geometry and ordinary moving spatial dimensions.

Incidentally, I originally came back to comment on the FAQ only because of an invitation to members to participate in workshops. I think I posted late here. Since I think I discovered some unique things on my own, I don't want PF to promote any possible errors to members just in case. Thus my interest in reducing a FAQ statement that I thought might be short-sighted.

I thought I found a lot simpler, I mean really simple, more classic way to look at Einstein's relativities a long time ago. It's mostly why I came here so many years ago. By flipping the movement-at-c coordinates from light to matter, or mass, I seemed to have found more intuitive answers to otherwise strange aspects of SR. This supposedly more intuitive understanding of SR and GR seems to have turned out to be fairly simple in retrospect... just backwards. I just flip it back (translate) when I need to, coming here for instance. To me it is like speaking of sunrise when one also realizes the sun doesn't really do the moving. Either the sun or the earth are at zero coordinates in their respective planetary systems for example. We can mathematically translate the coordinate systems.

I seemed to have gained a unique, perhaps forbidden, understanding why there is a required high constant speed in the universe... why the Lorentz-Fitzgerald relative contraction ratio must exist... why gravity is, and must be, the same speed as light... why we need a Cosmological Constant and how its related to Dark Energy, Hubble's Constant and the gravitational escape velocity... why gravity is one-way, yet closely related to EMF... and finally, how to make SR & GR more complete and possibly include a simplified, more complete GR atomic theory within.

It's not really new, I think it's already an obvious, but hidden part of SR & GR. Bereft of higher math, I had to use simple inductive reasoning (which seems to be a lost art) based on Einstein's Equivalence and Relative Space by Poincaré. The hardest part is trying to talk about it. The math language barrier, protective PF rules and resistance to any casual change I suppose. I do understand the PF rule reasons.

Dale, I do greatly appreciate the almost tireless efforts you and other mentors spend with everyone, including non-enrolled aging amateur students like myself. Thanks to all again.

Wes

#### Wes Tausend

Gold Member
Wes said: "I should have said two opposing coordinate systems."

This doesn't make what you are trying to say any clearer. But in any case, coordinate systems are not physics. There will be an infinite number of possible coordinate systems you can choose in any spacetime; but the laws of physics and all physical invariants will be the same regardless of which coordinate system you choose.
What I meant is we regard the photon moves at c relative to even a single particle of mass, or us, the observer made of mass. Or can we, should we, say it's also remotely possible all mass moves at c relative to the measurement of any photon. For instance, I suppose in some ways a photon is always stopped in our frame when we realize we have a photon (measure it).

I'm afraid this will not make any more sense to you out of context. It is like I'm foolishly describing a single stitch when there is a longer common thread comprising several stitches that comprise the whole. I'm afraid that's probably as clear as mud too. Darn.

Wes

#### PeterDonis

Mentor
What I meant is we regard the photon moves at c relative to even a single particle of mass, or us, the observer made of mass.
A photon moves at c relative to any object with nonzero rest mass.

Or can we, should we, say it's also remotely possible all mass moves at c relative to the measurement of any photon.
No, because "measurement of any photon" is not meaningful--not at any rate if you are talking about a measurement of relative speed. That would require the photon to be at rest in some inertial frame--or, in the more coordinate-free language @Dale used, it would require the photon's tangent vector to be one of the four members of a tetrad, and that's impossible.

I suppose in some ways a photon is always stopped in our frame when we realize we have a photon (measure it)
I have no idea what you mean by this. Photons move at c relative to all objects with nonzero rest mass, as above.

#### Dale

Mentor
I don't want PF to promote any possible errors to members just in case
I appreciate that desire. In this case the FAQ is not in error. The reasoning is both solid and clear.

Unfortunately, it seems to be universally unconvincing to people enamored of the “rest frame of light” concept. I think that most, like yourself, do not have the formal mathematical background to recognize the FAQ as a straightforward logical proof of the non-existence of reference frames for light.

By flipping the movement-at-c coordinates from light to matter, or mass, I seemed to have found more intuitive answers to otherwise strange aspects of SR.
Without math it is fantastically unlikely that this is correct.

Or can we, should we, say it's also remotely possible all mass moves at c relative to the measurement of any photon
You should probably get the math figured out and work through light cone coordinates to see if this statement is correct.

Edit: I just realized that I made a repeated mistake in my posts above. I repeatedly said “radar coordinates” where I meant “light cone coordinates”. I have gone back and edited my posts.

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#### sweet springs

In OP
"The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c (velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense.”

This way of saying reminds me Barber paradox, "The barber is the "one who shaves all those, and those only, who do not shave themselves." The question is, does the barber shave himself?", with the corresponding of
barber : photon
shave : demonstrate light speed c
those : particle with mass
So the solution could be that massless photon is a special guy who has no beards born or a woman. Please do not take it serious.

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#### Wes Tausend

Gold Member
Thanks again guys. I thought this would go quicker one way or the other. I didn't mean to get this involved if I could present a simple way to explore the FAQ explanation/interpretation just a little further perhaps. I'm satisfied everyone re-thought the FAQ to the best of current ability.

Wes

#### bhobba

Mentor
I would like to suggest that it might be more proper to base the "rest frame of a photon" theory explanation entirely on the PF Rules regarding conventional public peer-review and just say we follow Einstein because of that.
The PF rules do not require everything to have peer reviewed literature as its reference, For example standard textbook material is perfectly valid. You will find a discussion of exactly what an inertial frame is in the first few pages of Landau - Mechanics. It is based on symmetry properties - things have moved on since Einstein's time. It's a good thing to understand as well since not only is relativity based on it, but classical mechanics as well, and provides the underpinning for using Noether's beautiful and powerful theorem.

Thread closed. For those interested in the modern view espoused by Landau start a new thread.

Thanks
Bill

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