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A variable electrical field produces a variable magnetic field, which in turn produces a variable electrical field, and so on, leading to an electro-magnetic wave, which is eventually what light is all about. "Variable" means "variable with respect to time". This is my understanding of light from classical physics.

However, relativity tells us that whatever travels at the speed of light does not "experience" time, i.e. its 4-dimensional space-time velocity vector has no "time" component (the object travels only through space, not through time).

How does this blend with the classical physics definition of electromagnetic wave? How can a "variation with respect to time" occur if the object does not experience time at all?

agdev84
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    How does physics explain anvils crashing to the ground when anvils don't have the sensory apparatus to experience crashes? – WillO Mar 17 '21 at 14:08
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    How does a photon experience space and time? – mmesser314 Mar 17 '21 at 14:16
  • @mmesser314, BioPhysicist: thanks for the suggestion. However, I'm not interested in how an hypothetical observer travelling at the speed of light "sees" the world around him, which is roughly the subject of the suggested thread. What I'm asking is how can a time-dependent object even exists, if its time is supposed to be "frozen". – agdev84 Mar 17 '21 at 20:36
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    its 4-dimensional space-time velocity vector has no "time" component Where did you learn that? (It’s not true.) – G. Smith Mar 17 '21 at 20:37
  • @WillO: of course by "experiencing" I don't mean "sensing". This is also why my question is not the same as "How does a photon experience space and time". It wasn't easy for me to come up with a synthetic title for my question, I did the best I could (I'm not a physics expert). How should I rephrase that? – agdev84 Mar 17 '21 at 20:43
  • @agdev4 : But my point is that the thing you do mean by "experiencing" is exactly as irrelevant as any other kind of experiencing, including sensing. – WillO Mar 17 '21 at 20:47
  • @G.Smith: I'm not a physics expert, but I'm roughly referring to this video: https://youtu.be/UKxQTvqcpSg (at about 5:50). I may have interpreted it wrong. – agdev84 Mar 17 '21 at 20:52

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The time varying properties are determined by the observer, who does experience time. The electromagnetic wave (or photon) just "is" -- it has no inherent properties. Those are all ascribed to it by observers. For example, the frequency of an electromagnetic wave is entirely frame dependent. Two observers moving at different relative velocities to each other will find different values for the frequency of the same EM wave, and depending on the observer any value at all may be found.

Eric Smith
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  • Thanks for the answer, it shifted my point of view. Classical EM theory is built around an implicit "privileged observer", but no such a thing exists. I guess this is why galilean transformations fail when applied to EM waves. – agdev84 Mar 17 '21 at 21:23
  • Also, when I talked about "variable with respect to time", I should have thought about "whose time"? That's clearly the observer's time, since it's meaningless to talk about a photon's time. I hope I got it correctly. – agdev84 Mar 17 '21 at 21:27
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Lightlike phenomena have two aspects:

On the one hand, they are observed as propagating with speed of light (the observer's representation) On the other hand, their spacetime interval is zero, meaning that their proper time is zero (the "absolute representation").

By consequence, you must distinguish relative observation and the absolute spacetime interval, both are two different descriptions of the same process. The common description of electromagnetic waves shows how they are observed. In contrast, the zero spacetime interval cannot be observed, it may only be found by calculation.

If an electromagnetic wave is emitted by electron A and absorbed by electron B, the spacetime interval between A and B is zero, that means that in this sense A and B are adjacent, even if both electrons are separated in space by millions of light years. The observed process of alternating electric and magnetic fields must be reflected somehow in the absolute representation, and as you are pointing out correctly, no time and no wave is available here for the representation of these processes. By consequence, the answer should be that, according to the "absolute representation", there should be a process located within the electrons themselves, electron A and B. However, according to my knowledge, the process which corresponds to the electromagnetic wave with its alternating electric and magnetic fields has not been described yet in the sense of the "absolute representation".

Moonraker
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