Some questions about the Doppler Effect at high velocities

[neanderthalphysics]

Hey all.

Question 1:
Let's say we start with a red wavelength photon, that is absorbed by an atom and raises the atom to an excited state. The atom is then accelerated. After reaching a high velocity (say 0.1c), the photon is emitted. I would have thought that the energy of the emitted photon is solely dependent on the difference in energy levels of the ground/excited state.

How can it be that depending on the location of the observer relative to the atom, a different color photon is emitted? So if the atom is moving towards you, the emitted photon is blue shifted, while if the atom is moving away from you, the photon is red shifted. Or am I understanding something wrong here?

Question 2:
Let's say we have a CuO crystal, whose absorption spectrum is shown below. (Ref: http://jtasr.com/latest-articles.php?at_id=166 )
As we can see, it is highly absorbent in the middle-UV region. Let's say we are in a room which is illuminated with monochromatic red light. We then shoot a crystal of CuO at high velocity through the room.

So, if I understand correctly, one face of the crystal that is experiencing blue shifting of the red light, will at some point become absorbent to the red light. Light coming from the back of the crystal is red shifted, and passes through the crystal. Effectively, by shooting the crystal at relativistic velocities, we have produced a "diode" that selectively allows light through it depending on direction. Is this correct?

Question 3:
If we have a CuO atom, and likewise accelerate it to high velocities, does the absorption spectra of the CuO atom depend on which direction the incident photon hits it?

Question 4:
What happens if we have an optical computer which we then accelerate, Star Trek style, to near relativistic velocities?

 

[DaveC426913]

I would have thought that the energy of the emitted photon is solely dependent on the difference in energy levels of the ground/excited state.

It is. In the reference frame of the atom.

The freq of the photons absorbed and emitted from the atom are fixed. But we - who are moving relativistically wrt to the atom - see a Doppler shift.

So, if I understand correctly, one face of the crystal that is experiencing blue shifting of the red light, will at some point become absorbent to the red light. Light coming from the back of the crystal is red shifted, and passes through the crystal.

No. All it means is that the crystal experiences more reddish light impinging upon it from the rear and more bluish light impinging from the front. That doesn't change which frequencies it will absorb.

 

[Orodruin]

I would have thought that the energy of the emitted photon is solely dependent on the difference in energy levels of the ground/excited state.

This is only true in the rest frame of the emitting atom. In general, a photon’s energy is frame dependent. Energy is not an intrinsic property of a photon.

If we have a CuO atom, and likewise accelerate it to high velocities, does the absorption spectra of the CuO atom depend on which direction the incident photon hits it?

In what frame?

What happens if we have an optical computer which we then accelerate, Star Trek style, to near relativistic velocities?

Nothing. It is going to use wavelengths etc that are based on the rest frame of the computer. There is nothing in that frame that you can use to determine that you are traveling at high velocity. There is no absolute velocity.

 

[DaveC426913]

It is going to use wavelengths etc that are based on the rest frame of the computer. There is nothing in that frame that you can use to determine that you are traveling at high velocity.

Yeah. This is a more generalized answer.

Examine your experiments from the POV of the crystal - whether in a computer or otherwise. It is stationary, and the observers are moving past it at .1c. All your problems will go away.

 

[Ibix]

If you are wondering where the energy comes from for the red/blue shifted photon, note that the emitting atom will recoil slightly. How much its energy changes when it does so is also frame dependent, and this frame-variance accounts for the different photon energies measured in different frames.

 

[jartsa]

No. All it means is that the crystal experiences more reddish light impinging upon it from the rear and more bluish light impinging from the front. That doesn't change which frequencies it will absorb.

We see red light going through in one direction and not in the other direction.

We who consider the light to be red.

 

[DaveC426913]

We see red light going through in one direction and not in the other direction.

We who consider the light to be red.

Hrm. We see light emitted in both directions. The light moving in the direction of the relativistically-moving crystal is blue-shifted. The light moving sternward is red-shifted.

 

[jartsa]

Hrm. We see light emitted in both directions. The light moving in the direction of the relativistically-moving crystal is blue-shifted. The light moving sternward is red-shifted.

For light to be absorbed its photons must have enough energy to excite and accelerate an atom. Red light can't be absorbed by an atom that is fleeing fast enough.

This is a bit hard to formulate, but the photon must have enough energy for those two tasks. If absorption happens, then the kinetic energy of the fleeing atom will also increase.

 

[Ibix]

I think care is needed with reference frames. I believe the original context was omnidirectional red light in a frame where the crystal is moving. In the frame of the crystal, then, there is highly anisotropic light whose frequency and intensity is strongly dependent on direction.

In the frame of the crystal, it passes light from one side because the frequency is drection dependent and its absorption spectrum is not. In the "lab" frame, the crystal passes light from one side because the light is isotropic but the absorption spectrum of the crystal is direction dependent.

It's much easier to work in the crystal frame.

 

[DaveC426913]

For light to be absorbed its photons must have enough energy to excite and accelerate an atom. Red light can't be absorbed by an atom that is fleeing fast enough.

This is a bit hard to formulate, but the photon must have enough energy for those two tasks. If absorption happens, then the kinetic energy of the fleeing atom will also increase.

Yup. I get where you're coming from.
There's an issue here of state of the ambient radiation. On needs to define whether it's controlled (say, all red) or whether its from the universe at large, in which case, we can assume a range of radiation incliding blue and red, even if it's skewed.