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I want a theoretical opinion about this question:

The relativistic Doppler Shift equation for the light is $$\frac{f_s}{f_o}=\sqrt{\frac{1+\beta}{1-\beta}}$$

where $\beta=v/c$ is the velocity of the observer in terms of the speed of light. So if we assume that we have an infinite length lossless copper cable which can carry frequencies up to 10 Ghz only and this cable has a light emitter and light receiver inside. The light emitter sends light a signal with frequency equal to 1 Thz while moving to the left in a speed very close to the speed of light and the receiver also moving to the left at the same speed.

if we chose the right velocity ($v$) for emitter & receiver then we will have a relative frequency effect such as :

1- The original signal (light) will have frequency equal to 1 Thz.

2- The transmitted signal through the copper cable will be red shifted and will have a reduced frequency equal to 10 Ghz.

3- The received signal will be blue shifted and will have frequency equal to the original signal (1 Thz).

We can see here that the copper cable transmit light signal while in normal conditions it's not possible to do that.

Is it possible for the light (photons) to turns into normal electromagnetic signal?
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Light has a frequency of approx. 1e15Hz. Can light be transmitted in a hollow copper tube? Yes. No need to go relativistic. Can objects move at near the speed of light in a coax cable with inner conductor? No. They can't move in there, at all, not even at walking speed. Does any of this has anything to do with photons? No.

Your experiment does have a "realistic" implementation. Take two observers at rest against each other and a spaceship traveling between them at relativistic speed. Communication is done with light from and to the spaceship, but because of the Doppler shift the ship receives an RF signal with a regular antenna, which it amplifies, sends from aft to stern trough a coax cable and sends out, again, trough an RF antenna. Would that work? Yes, except that one can't make such an ultra-relativistic spaceship.

The relevant related effect in real life is the ultrahigh energy cosmic ray cutoff due to CMB background photons. That one is real and it is an area of active research.

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