# Does a photon not having a reference frame result in logical inconsistency? [duplicate]

So, I know that SR makes two statements. One is the first assumption it has:
"Speed of light is the same with respect to all reference frames".

Second, the statement:
"A photon cannot have a reference frame".
(Please correct me if the statements I wrote are not accurate.)

Aren't these two statements a bit paradoxical?
One first says that Speed of this thing is the same with respect to all frames. And then says speed is not defined wrt to it's own frame, because there is no such frame.

The comparison has already been made in assumption one. It's not logical to say in the next statement the opposite, and say that no we are just not comparing with it's own reference frames. It's a contradiction.

Are Physics textbooks not accurate enough? or have I made a mistake somewhere in my thinking.

I don't really want to be correct, but just want to know my mistake.

But, so far, it seems like a Philosophical mistake in SR.

Any statement is only valid under the assumption applied on top of it.

I understand that the photon cannot have a frame of reference, but what I am pointing to, is that a comparison with "All" reference frames has already been made earlier. Before this statement is established that "Photon cannot have a frame of reference".

You cannot compare without defining. This seems like a paradoxical set of statements.

If you look at the current answers, this is exactly what I am referring to. We have a reason from statement 1 itself for statement 2 to be true, but if statement 2 is true, then it violates part of statement 1, because both cannot be absolutely true together.

I agree that statement 2 will follow from statement 1, but if statement 2 follows, then statement 1 cannot be absolutely true, because it was stated first. Statement 2 follows from it through reasoning.

Let me illustrate what I think could be wrong:
We make statement 1: "Speed of light is same wrt to all reference frames"
These statements are a subset of statement 1:
Statement A: " Speed of light is same wrt to A reference frame"
Statement B: " Speed of light is same wrt to B reference frame"
Statement C: " Speed of light is same wrt to it's own reference frame".

If 1 is true, then A, B , and C all are true, so far.

But, now we say that it follows from 1, that C cannot be true, because there can be no reference frame for photon. This constitutes a contradiction, because C has already been said to be True.

## marked as duplicate by Qmechanic♦Nov 1 '17 at 6:21

• No they are not the two basic statements of SR. en.wikipedia.org/wiki/Special_relativity – Rob Jeffries Nov 1 '17 at 1:51
• Possible duplicate of Does a photon in vacuum have a rest frame? – GPhys Nov 1 '17 at 2:01
• @GPhys That question never had an answer directly on this point. The answer instead dealt only with the rest mass of the photon. – StephenG Nov 1 '17 at 2:09
• @novice It's not paradoxical. The speed of light is constant in all reference frames. There is no reference frame for photons. So "all reference frames" does not include reference frames for photons, because there ARE no reference frames for photons. It's like saying "All countries have flags. There are no countries on the moon." Is that a contradiction? Or is that just two separate facts? – Jahan Claes Nov 1 '17 at 4:35
• @StephenG Er ... a rest frame is one in which the momentum is zero. For photons such a condition only occurs when energy is also zero which is to say when there is no photon. That is, there is no such thing as the rest frame of a photon because they are have no mass. The two ideas are inseparable inside the structure of relativity. – dmckee Nov 1 '17 at 5:13

One should be aware that there exist logical frames of reference in addition to the mathematical ones used in studying physics. These are a meta-level on the model's level. Example of meta-levels: the alphabet is one level, the words written with the alphabet is another level, the meaning carried by the words is a third level. Whenever paradoxes appear it is because one mixes levels of reference.

So, I know that SR makes two statements. One is the first assumption it has: "Speed of light is the same with respect to all reference frames".

Second, the statement: "A photon cannot have a reference frame". (Please correct me if the statements I wrote are not accurate.)

At the level of your two statements , SR makes many more statements:

"inertial mass increases with velocity"

"time is different in different reference frames"

Depending on the variables used similar statements can appear in the set of statements. All the statements depend on the underlying mathematical level of SR, and may be similar or connected through it.

Aren't these two statements a bit paradoxical?

All statements of special relativity can seem paradoxical because our everyday intuitions are dependent on classical Galilean physics. But the set of statements comes from Lorenz transformations and is a meta level to the transformations which have as an axiom the uniqueness of the speed of light.

The second statement is mathematically derived using Lorentz transformations and belongs to the set of statements, not to the mathematics of Lorenz transformations.

I agree that statement 2 will follow from statement 1, but if statement 2 follows, then statement 1 cannot be absolutely true, because it was stated first. Statement 2 follows from it through reasoning.

To recapitulate: statement 2 belongs to the set of statements derivable with the mathematics of Lorenz transformations. Statement 1 is primarily an axiom for defining the mathematics of the Lorenz transformations, and appears in the statements level as a redundancy.

Edit after edit of question:

The statements set is derived and stated by using the mathematics of the mathematical level. (the way a word is written by using the alphabet) In the mathematical level itself there exist singularities. In the link for Lorentz transformations one observes that when the velocity of a particle is c an infinity appears:

Statement A: " Speed of light is same wrt to A reference frame" Statement B: " Speed of light is same wrt to B reference frame" Statement C: " Speed of light is same wrt to it's own reference frame".

So your statement C does not belong to the set of statements derivable from the mathematics, because an infinity appears and C is undefined, so cannot have a reference frame. (that is the origin of the statement) You derive it from statements A and B by logic , mixing a higher level with a mathematical under-level. Logic is not enough to do the mathematics of Lorenz transformations.

• Comments are not for extended discussion; this conversation has been moved to chat. – rob Nov 2 '17 at 13:57

What is the reference frame of an object? It is the frame in which that object is at rest (i.e. it has a speed of zero). If you take the statement

"Speed of light is the same with respect to all reference frames"

to be true, then of course there is no reference frame for the photon: since the speed is the same in all reference frames, there is no reference frame in which the speed is zero.

Regarding your edit: A, B, and C are true assuming those reference frames exist. By making statement C, you are implicitly assuming that the reference frame of the photon exists, and deriving a contradiction from that.

• This is exactly what I am saying. But statement 2 cannot follow from statement 1, because in that statement we have already stated that it has to be the same wrt to "all" reference frames. When we made that statement it was not said that light cannot have a self reference frame. It's like we are trying to make the statement one true afterwards, in hindsight. Taking out the only case where it would be false. – novice Nov 1 '17 at 4:14
• It's a paradoxical statement set. – novice Nov 1 '17 at 4:15
• @novice It "takes out" that case itself. You don't need a separate statement "a photon cannot have a reference frame," because "the speed of light is the same in all reference frames" already implies that. – Chris Nov 1 '17 at 4:56
• Yeah but it also implies that "speed of light be same in ALL reference frames". It implies two things, both paradoxical to each other. Please do refer to Anna's answer as well. – novice Nov 1 '17 at 5:37
• @novice You seem to be taking the word "all" to mean "all things we can imagine, even things that don't exist." The rest frame of a photon does not exist, so it is not part of "all reference frames." – Chris Nov 1 '17 at 7:15

Time loses its meaning in photon's frame of reference. Past, present, future all happen at the same time according to a photon.

Let's consider why: Speed of light should be same in all reference frames. And all observers see light moving in their own frame of reference. But for the photon, the light would be at rest. There is no frame where light is at rest in the special theory of relativity.

• This does not answer my question though. That is just interpretation on top of the math. This seems to be a modelling problem. – novice Nov 1 '17 at 3:36
• Your question is been answered here in more detail: quora.com/… – LostCause Nov 1 '17 at 3:40
• Also, it is not a modeling problem because the special theory of relativity is not built on a premise that photon's don't have a frame of reference. – LostCause Nov 1 '17 at 3:44
• Yeah but the statement being true introduces a paradox. – novice Nov 1 '17 at 3:46
• I have already gone through that link. The question isn't does a photon have a frame of reference, but should. – novice Nov 1 '17 at 3:47