Photons in the stationary wave?

[bernhard.rothenstein]

Consider that an observer composes two electromagnetic waves of the same frequency propagating in opposite directions in order to obtain a stationary wave. Please tell me a short story about the behaviour of the photons in the transition from propagating waves to a stationary one.
What does detect an observer moving relative to me and watching the experiment I just perform. Thanks.

 

[Meir Achuz]

In QFT, photons are quanta of the EM potential field, just as electrons are quanta of the electron field. In either case, the quanta of a standing wave can be written in terms of quanta of traveling waves in opposite directions.
The photon or electron would be such a superposition. Going to a moving frame, the Doppler frequency shift would be different for each component, so the character of the wave will change. It is a homework exercise to calculate the change. The answer for photons, will be the same as for classical EM plane waves.

 

[bernhard.rothenstein]

stationary wave

In QFT, photons are quanta of the EM potential field, just as electrons are quanta of the electron field. In either case, the quanta of a standing wave can be written in terms of quanta of traveling waves in opposite directions.
The photon or electron would be such a superposition. Going to a moving frame, the Doppler frequency shift would be different for each component, so the character of the wave will change. It is a homework exercise to calculate the change. The answer for photons, will be the same as for classical EM plane waves.

Thank you. That is the way in which I am looking for help on the Forum. We did the homework exercise in order to show the conservation of the number of counted photons.

 

[country boy]

A simple sum of two EM waves with equal but opposite wavenumbers k and -k (kc=frequency) can represent a photon that is moving in either the + or -x direction. The photon is moving at c but its probability current is zero. From a moving frame the two opposite k's will not be the same because of their doppler shifts, but the photon will still be moving at c in either the + or -x' direction. The probability current is flowing at v. It is clear that there is still only one photon. As more photons are added to the state the number is likewise conserved between the rest and moving frames.

The nodes of the standing wave form a stationary ruler and the oscillations of the amplitude between nodes provide a set of stationary clocks. When viewed from a moving frame, the doppler shifts of the two component waves make the moving nodes appear closer together by the Lorentz contraction and the oscillations become slower by the relativistic time dilation. The observer at rest can construct a moving node ruler and moving oscillation clocks by using two oppositely moving waves of different frequency. Stationary and moving space-time grids can be built in this way with light waves.

 

[bernhard.rothenstein]

special relativity in the stationary wave

A simple sum of two EM waves with equal but opposite wavenumbers k and -k (kc=frequency) can represent a photon that is moving in either the + or -x direction. The photon is moving at c but its probability current is zero. From a moving frame the two opposite k's will not be the same because of their doppler shifts, but the photon will still be moving at c in either the + or -x' direction. The probability current is flowing at v. It is clear that there is still only one photon. As more photons are added to the state the number is likewise conserved between the rest and moving frames.

The nodes of the standing wave form a stationary ruler and the oscillations of the amplitude between nodes provide a set of stationary clocks. When viewed from a moving frame, the doppler shifts of the two component waves make the moving nodes appear closer together by the Lorentz contraction and the oscillations become slower by the relativistic time dilation. The observer at rest can construct a moving node ruler and moving oscillation clocks by using two oppositely moving waves of different frequency. Stationary and moving space-time grids can be built in this way with light waves.

Thanks for the interesting idea you offer.
So far as I know relativists make a net distinction between observers equipped with rods and synchronized clocks located at differfent points in space confronted with effects like time dilation and length contraction, and observers located at a given point in space collecting information about events taking place at different points in space form the light that arrives at the point where they are located confronted with effects like Doppler or aberration.
Do you consider that the observer you propose is an uptodated first kind of observer?
I have to think if the lengths involved transform by contraction or by Doppler effect?
Kind regards

 

[country boy]

The two observers in my example, moving and at rest, each collect information from measurements at various locations in their respective frames. The measurements at each location are made by observers or recording/transmitting devices. Since the central observer who collects the information from distant points can compile it over a period of time, his results are not affected by times-of-flight from the distant points. He is probably not like the second type of observer you describe above. Instead, the many observers or devices at distributed locations are like your first type of observer.