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I'm curious about the fact that it is impossible to consider a frame of reference where a photon is the reference itself (meaning a frame of reference where this photon can't move).

I looked for answers in other SE questions. In the first one: Frame of reference of the photon? I read:

there is no frame of reference for the photon because there is no frame of reference in which the photon is at rest.

This surprises me. Indeed, the Galilean principle of relativity says:

The laws of mechanics have the same form in all inertial frames.

Looking to an answer of a similar question in SE (which is Would time freeze if you could travel at the speed of light? ), I also read:

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection.

Unfortunately, those complete explanations are too complicated for me.

Does anyone have a more simple way to explain why it is impossible to consider a photon as a frame of reference? I'm really curious about how a photon would "see" the universe around him.

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  • $\begingroup$ For starters, one of the postulates of Special Relativity is that light has the same speed $c$ in all inertial frames of reference. This already precludes the existence of a frame in which the photon is at rest. Then you might ask why one should postulate that, and probably the best answer is that it is because it works. It is what we observe, have tested with several experiments and found to be obeyed. $\endgroup$
    – Gold
    Commented Aug 23, 2022 at 14:49
  • $\begingroup$ One more post along the same lines that may help - A photon travels in a vacuum from A to B to C. From the point of view of the photon, are A, B, and C at the same location in space and time? $\endgroup$
    – mmesser314
    Commented Aug 23, 2022 at 14:59
  • $\begingroup$ What is your candidate for a frame in which a photon is at rest? $\endgroup$
    – WillO
    Commented Aug 23, 2022 at 17:15
  • $\begingroup$ @WillO the candidate would be the photon itself $\endgroup$
    – user343933
    Commented Aug 23, 2022 at 17:34
  • $\begingroup$ A photon is not an example of a frame. $\endgroup$
    – WillO
    Commented Aug 23, 2022 at 18:01

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Does anyone have a more simple way to explain why it is impossible to consider a photon as a frame of reference?

The simplest that I can think of is the following:

  1. an object’s reference frame is one where it is at rest, $v=0$
  2. by the 2nd postulate light moves at $v=c$ in all inertial frames

It is a logical contradiction for something to both move at $v=0$ and $v=c$ at the same time in the same frame. Therefore such a frame is a logical impossibility.

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  • $\begingroup$ Why can't we just say that, relative to all reference frames, except that of light itself, light always travels at $c$, but from the reference frame of light, everything else moves at $c$? Sure, it's more wordy, but I don't see why it would be invalid. $\endgroup$
    – Mikayla Eckel Cifrese
    Commented Jul 30, 2023 at 21:16
  • $\begingroup$ @MikaylaEckelCifrese can you prove mathematically that such a thing is even possible? I have never seen such a proof and I doubt a valid frame with those properties exists even just mathematically/hypothetically $\endgroup$
    – Dale
    Commented Jul 30, 2023 at 21:57
  • $\begingroup$ well I don't know -- that's why I'm asking. Why wouldn't it be possible? $\endgroup$
    – Mikayla Eckel Cifrese
    Commented Jul 30, 2023 at 22:03
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    $\begingroup$ @MikaylaEckelCifrese I have never seen such a frame defined, nor do I know how to define it. I have not read everything, but I have read enough that the fact that I have never seen it makes me doubt that it is possible $\endgroup$
    – Dale
    Commented Jul 30, 2023 at 22:16
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The crux of the matter is that photons do not exist in the the Galilean principle of relativity which says,"The laws of mechanics have the same form in all inertial frames." It is classical mechanics that obeyed by macroscopic particles , but not elementary particles. Quantum mechanics had to be invented in order to fit the data and observations at the level of small dimensions to which elementary particles belong.

Actually before the formulation of Maxwell, light itself was not considered an electromagnetic effect. When the disparate laws existing for electricity and magnetism were bound up in one mathematical theory by Maxwell, it was found that light was an electromagnetic wave, and it carried energy and momentum and its velocity in vacuum ( the velocity of the energy representing light) would always be c, as far as the equations went. This directly led to the Lorenz transformations, inherent in the Maxwell equations.

At the time, there was the conjecture by Newton of the corpuscular nature of light:

the corpuscular theory of light states that light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus. This was based on an alternate description of atomism of the time period.

The two concepts for light came together with quantum mechanics and quantum field theory, where it is the photons, the particles that build up light that move always with velocity c and cannot have a classical frame of reference at rest.

An intuition of how photons can build up the classical light can be seen in an answer of mine here ; The difference between photons always having velocity c, and the experimental possibility of slowing down the velocity of light in a medium is consistent with this.

You ask:

I'm really curious about how a photon would "see" the universe around him.

Elementary particles do not "see", they interact, as in the link with the single photons, with the boundary conditions.

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I think Anna V's answer is complete and needs no additions, but this is a bit too much of an answer to just place as a comment.

We can retrieve a modern physics version of Galilean relativity by promoting laws of mechanics to general laws of physics (which include all the laws of mechanics known to classical physics as special cases of more general laws), and rephrasing inertial frames to the synonym rest frames. Doing so logically rules out the existence of a photon frame-of-reference along two different avenues based on the requirement that the laws of physics remain the same.

1: the laws of physics include/imply a fixed speed of light, hence if the laws of physics are the same in all rest frames, there can be no rest frame comoving with light: $v_\gamma \triangleq c \implies v_\gamma \ne 0$

2: the laws of physics define the different properties of objects, e.g. velocity, invariant mass, momentum, kinetic energy, etc, as they relate to each other. A body of invariant mass $m$ with a relative velocity of $c$ to some rest frame has undefined energy and momentum, therefore no such rest frame exists.

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The tangent vector to the worldline of a photon is orthogonal only to multiples of itself. Therefore it cannot be part of an orthogonal frame.

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  • $\begingroup$ Could you provide a graph please ? I don't remember what a worldline is $\endgroup$
    – user343933
    Commented Aug 23, 2022 at 17:33