Since light travels at the speed of light towards a target, the spatial distance to the target seems to be zero, owing to Lorentz transformation. It seems that there is a logical flaw here. Can someone explain that?
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What's the length of a photon? How do you measure it? – John Doty Sep 09 '23 at 19:17
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1Can you explain how it's different from the linked question? Or the one that is marked as a duplicate (namely https://physics.stackexchange.com/q/162477/25301)? – Kyle Kanos Sep 09 '23 at 19:18
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In this question we are dealing with the distance to a given target. In the previous question, we were dealing with the length of the photon. The maths are the same, nevertheless. – Gabriel Ybarra Marcaida Sep 09 '23 at 20:28
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the photon in mainstream physics has no length, it is a point particle. all particles in the table of elementary particles of the standard model are point particles, have no length – anna v Sep 10 '23 at 06:11
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Photon is traveling in its inertial frame of reference. But the target of that photon has a relative velocity. – ssh Sep 10 '23 at 08:08
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@anna-v, what is one photon? When we say photon has energy of hν, does it consist of multiple wavelengths or one wavelength? It is already established that light is an electromagnetic wave. – ssh Sep 10 '23 at 08:14
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@ssh the same holds for all elementary particles and the mathematics of the Lorentz transformation models it.A single photon has an energy hν which mathematically gives a single wavelength value, but it still is a point, and you cannot go the a zero mass center of mass. maybe my answer here helps https://physics.stackexchange.com/questions/273032/what-exactly-is-a-photon/273180#273180 . (The name photon is used in quantum optics within materials and their photons can have mass, but it is another story) – anna v Sep 10 '23 at 08:34
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What you say is only valid in the photon's reference frame. This means that if you were travelling with the photon (which is impossible), you would immediately arrive at the target.
This isn't a problem as you cannot be in the photon's reference frame, so there is no contradiction.
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I hope this answers your question. If not, please point where you see the logical flaw. – Gabriel Ybarra Marcaida Sep 09 '23 at 19:27
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Photon is traveling in its inertial frame of reference. But the target of that photon has a relative velocity. – ssh Sep 10 '23 at 08:16
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If you use the velocity-addition formula (see en.wikipedia.org/wiki/Velocity-addition_formula), you will see that for the photon, the target's velocity will be also $c$. Nevertheless, the target's speed isn't relevant here. – Gabriel Ybarra Marcaida Sep 10 '23 at 09:29
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The speed of light is c relative to any observer in any inertial reference frame. If an observer could travel at the speed of light (which they can not) then the speed of light would still be c relative to them, so they are in fact not a rest with the photon, which is a logical contradiction. The contradiction comes about because an inertial reference frame cannot have a relative velocity of c relative to any other inertial reference frame by definition of the postulates of relativity, so there is no such thing as the point of view of a photon.
KDP
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