Time dilation of photon vs wave movements

[Ultron]

There is one thing which seems like paradox to me. So there is a photon which is a particle and wave at the same time (wave-particle duality). Lets imagine that this photon flies with the speed c next to Earth. As it has the velocity of c, the time dilation is (nearly) infinite, so the time stands still for the photon compared to Earth reference frame.
But even when the time is standing still for photon, at same time it makes wave oscillations each second during the fly.
So when it reaches Alpha Centauri in 4 years on Earth, it is a practically zero time for photon, but it makes trillions of oscillations as wave until reaching Alpha Centari, so it is not kind of sitting still due to the zero time elapsed.

Anybody knows how to explain it?

 

[Schneibster]

Sure.

The wave/particle duality requires that one perform all analysis either in the wave domain or the particle domain. In either domain, the other domain is meaningless. Therefore talking about "frequency" when analyzing photons simply is mathematically impossible.

In your example, you talk about the photon (a particle), but then you try to talk about frequency (a characteristic of waves); this is the source of the apparent paradox.

I'll also point out that in the frame of the photon, time cannot pass so "frequency" (measured in s e-1, or "per-seconds") is meaningless. In Earth's frame, the frequency has meaning because time can pass in that frame.

 

[paddoboy]

There is one thing which seems like paradox to me. So there is a photon which is a particle and wave at the same time (wave-particle duality). Lets imagine that this photon flies with the speed c next to Earth. As it has the velocity of c, the time dilation is (nearly) infinite, so the time stands still for the photon compared to Earth reference frame.
But even when the time is standing still for photon, at same time it makes wave oscillations each second during the fly.
So when it reaches Alpha Centauri in 4 years on Earth, it is a practically zero time for photon, but it makes trillions of oscillations as wave until reaching Alpha Centari, so it is not kind of sitting still due to the zero time elapsed.

Anybody knows how to explain it?

Actually, in the photon's frame of reference, time and distance[space] do not exist [due to maximum time dilation and length contraction.
A photon therefor in its FoR, could traverse the whole universe in an instant.

 

[Ultron]

Im not sure we understand each other. I will try it in some more simplified version. The photon should not be moving while frozen in time dilation, but it still moves sideways all the time in form of wave. Maybe it is mathematically impossible, but it happens in reality. And to say that we cant mix the wave and particle aspect is not answer is is just covering up the fact that we dont know how exactly it works, because it is obvious that it happens both in the same time (from the viewpoint of the photon). But maybe somebody here knows better.

 

[Schneibster]

Im not sure we understand each other. I will try it in some more simplified version. The photon should not be moving while frozen in time dilation, but it still moves sideways all the time in form of wave. Maybe it is mathematically impossible, but it happens in reality. And to say that we cant mix the wave and particle aspect is not answer is is just covering up the fact that we dont know how exactly it works, because it is obvious that it happens both in the same time (from the viewpoint of the photon). But maybe somebody here knows better.

You're confusing two frames, and that's not going to work.

In the photon's frame, the photon does not move. In that frame, also, time does not pass so the units frequency is defined in (per-seconds) would require you to divide by zero; that's about as basic a "don't do that" as there is in all of mathematics.

In the Earth's frame, the photon moves.

You have to pick one frame and stick with that frame or your results will be inconsistent.

 

[Janus58]

Im not sure we understand each other. I will try it in some more simplified version. The photon should not be moving while frozen in time dilation, but it still moves sideways all the time in form of wave. Maybe it is mathematically impossible, but it happens in reality.

No, it doesn't. You seem to have the idea that the photon travels in a sinuous path, this is not the case. This is not what is meant by photons having wave-like properties.

And to say that we cant mix the wave and particle aspect is not answer is is just covering up the fact that we dont know how exactly it works, because it is obvious that it happens both in the same time (from the viewpoint of the photon). But maybe somebody here knows better.

There is nothing being "covered up", because the "paradox" you are implying is based on a misconception on your part.

 

[Q-reeus]

There is one thing which seems like paradox to me. So there is a photon which is a particle and wave at the same time (wave-particle duality). Lets imagine that this photon flies with the speed c next to Earth. As it has the velocity of c, the time dilation is (nearly) infinite, so the time stands still for the photon compared to Earth reference frame.
But even when the time is standing still for photon, at same time it makes wave oscillations each second during the fly.
So when it reaches Alpha Centauri in 4 years on Earth, it is a practically zero time for photon, but it makes trillions of oscillations as wave until reaching Alpha Centari, so it is not kind of sitting still due to the zero time elapsed.

Anybody knows how to explain it?

Ignore comments in earlier posts mentioning 'the photon's FoR' as though there could be such a thing. No, there can't. In the limit of 'catching up' to a photon, it ceases to exist, since given photon E = hv, v (frequency) becomes zero, hence there is no energy E, hence no photon 'in it's own frame'.

Consider instead a high energy massive particle say an electron. It also has a wavelike character given by it's de Broglie wavelength lambda = h/p, with p the momentum relative to some given frame of reference. Which relation has experimental confirmation as in electron diffraction optics. But this wavelike character is an interaction involving always relative motion between particle and whatever it interacts with. It's just how things are in the quantum world. In the nominal electron rest frame, de Broglie relation formally implies an infinite wavelength but that becomes meaningless - given there will be a non-zero particle ZPE related to the Heisenberg uncertainty principle. Hence there will always be some fuzziness about what is exactly an electron rest frame.
Try reading these two Wikipedia articles:
https://en.wikipedia.org/wiki/Matter_wave
https://en.wikipedia.org/wiki/Zero-point_energy

 

[paddoboy]

Ignore comments in earlier posts mentioning 'the photon's FoR' as though there could be such a thing. No, there can't.

Of course there can't. Whoever said we could. It's a thought experiment, and I have mentioned it before along with the comments along the lines of "if it makes any sense to talk about a photon's FoR at all" Still, ideas re time dilation and length contraction to the max, are able to be visualised and explored.
You appear to be scraping the bottom of the barrel in trying to run with that derision.

 

[Q-reeus]

Of course there can't. Whoever said we could. It's a thought experiment, and I have mentioned it before along with the comments along the lines of "if it makes any sense to talk about a photon's FoR at all" Still, ideas re time dilation and length contraction to the max, are able to be visualised and explored.
You appear to be scraping the bottom of the barrel in trying to run with that derision.

In #2 ...in the frame of the photon...
In #3 ...in the photon's frame of reference...A photon therefor in its FoR...
In #5 ...In the photon's frame, the photon does not move. In that frame, also...

So I provide some sense of rigour and clarity by pointing out why there simply *cannot* be such a frame, and, as typically the case, you basically deny writing what in #3 you in particular clearly did write.
And btw, borrowing my 'scraping the bottom of the barrel' which was an accurate and pertinent comment in that recent other thread, may be a sincere form of flattery, but is out of place as used by you here.

 

[paddoboy]

In #2 ...in the frame of the photon...
In #3 ...in the photon's frame of reference...A photon therefor in its FoR...
In #5 ...In the photon's frame, the photon does not move. In that frame, also...

So I provide some sense of rigour and clarity by pointing out why there simply *cannot* be such a frame, and, as typically the case, you basically deny writing what in #3 you in particular clearly did write.
And btw, borrowing my 'scraping the bottom of the barrel' which was an accurate and pertinent comment in that recent other thread, may be a sincere form of flattery, but is out of place as used by you here.

As per usual, you seem to have missed the point.
You do recognise a thought experiment?
Quite unusual though to see you getting so concerned by the "bottom of the barrel" phrase

 

[LaurieAG]

Ignore comments in earlier posts mentioning 'the photon's FoR' as though there could be such a thing. No, there can't. In the limit of 'catching up' to a photon, it ceases to exist, since given photon E = hv, v (frequency) becomes zero, hence there is no energy E, hence no photon 'in it's own frame'.

I gather that doesn't preclude something like geometric representations of the photon streams that occur between rotating sources and an observer over one complete rotation at the time of observation? Does a photon in transit, without interference or distortion along its path, travel in a straight line between its emission point and an observer at velocity c? Does an in transit photon stream exist?

The image below shows the different photon streams that would be apparent from 2 sources rotating around a galactic center of mass that is stationary with respect to an observer who lies at various different angles to the plane of rotation of the 2 sources. Plot A (90 degrees to plane of rotation) is Face On while Plot C is Side On (0 degrees to plane of rotation).

If you are wondering how the images were plotted.
(Plot B 45 degrees to the plane of rotation Top Elevation)

 

[Q-reeus]

As per usual, you seem to have missed the point.
You do recognise a thought experiment?

Yes, and you and your new close buddy obviously got some things right as far as the logical absurdities of 'moving at c' go, but left the false impression 'being in the frame of a photon' was a logically sound pov for such 'thought experiments'. It's not, as explained in #7. Let it ride.

Quite unusual though to see you getting so concerned by the "bottom of the barrel" phrase

Not 'concerned', but 'irritated' will do.

 

[Q-reeus]

I gather that doesn't preclude something like geometric representations of the photon streams that occur between rotating sources and an observer over one complete rotation at the time of observation? Does a photon in transit, without interference or distortion along its path, travel in a straight line between its emission point and an observer at velocity c? Does an in transit photon stream exist?

Leaving aside the imo more extreme QM pov where a photon only exists at points of emission/creation and absorption/annihilation, I see no issue impacting on my observations you quote. Everything in a classical relativistic setting makes sense within that framework. Only light aka massless quanta can and always in every frame move locally at c. Material particles/observers cannot and cannot therefore even in gedanken experiments ever be in the non-existent rest frame of light/photons. Trying to imagine so leads to the vanishing Cheshire cat scenario. As well as the more familiar spacetime extreme distortion stuff.

The image below shows the different photon streams that would be apparent from 2 sources rotating around a galactic center of mass that is stationary with respect to an observer who lies at various different angles to the plane of rotation of the 2 sources. Plot A (90 degrees to plane of rotation) is Face On while Plot C is Side On (0 degrees to plane of rotation)....

Sorry LaurieAG, but I get too dizzy trying to figure it all out there - just my limitation I guess.

 

[Ultron]

Thanks for all replies. What looked inicially as quite easy question resulted in very sophisticated discussion. It seems to me, that in the end it leads to the quantum mechanics description of wave, which is well described in math, but the real mechanism behind it is still discussed. Personally Im fan of Broglie Bohm interpretation.

https://en.wikipedia.org/wiki/Wave–particle_duality#de_Broglie.E2.80.93Bohm_theory