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I'm trying to explain an FM or AM radio receiver using photons.

When the photons are absorbed by the antenna, they arrive in discrete pulses, where in the case of FM, each wave front contains photons of the same energy (frequency) and the following wave fronts contain photons of different energies. When these photons land on the antenna in succession, the difference in energies, and therefore difference in induced voltages, is proportional to a sound signal in which the radio deciphers.

And it is essentially the same for AM, except each wave front has a different density of photons, and therefore the current modulates, not the voltage.

Is this correct? If so, wouldn't you theoretically be hearing a slightly (very slightly) sped up version of the signal if you were driving towards the radio tower, and a slightly slowed down version when driving away (since the photons are landing in succession at a faster/slower rate)?

Thanks

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mfb
Mentor
I'm trying to explain an FM or AM radio receiver using photons.
Why?
Photons are quantized excitations of the electromagnetic field. The field is the fundamental thing. Photons are quantum-mechanical objects, they are not particles that could hit your antenna at a specific time, and working with them just makes everything much more complicated.

Is this correct? If so, wouldn't you theoretically be hearing a slightly (very slightly) sped up version of the signal if you were driving towards the radio tower, and a slightly slowed down version when driving away
Yes, due to the Doppler shift, but in practice you'll lose the signal long before that becomes notable (because the carrier frequency gets shifted, too).
(since the photons are landing in succession at a faster/slower rate)?
No. Simply increasing the power of the emitter would do that as well, but would not influence your radio signal.

How about this. Lets say you have a sensitive apparatus that can detect extremely weak radio signals. At some point your going to have to stop talking about the collective behavior of the photons and start talking about the photons themselves. So I'm wondering how it works at the level of the photon. When the signal is frequency modulated, how does that translate to the individual photons? After a photon is emitted, its individual frequency isn't modulating, so how does the absorption of photons translate to the oscillating signal that the radio receives?

Photons are quantum-mechanical objects, they are not particles that could hit your antenna at a specific time...
Could you expand on this? Why couldn't they hit at a specific time? I've taken my undergraduate QM so feel free to be technical... to a certain point :). When a photon is absorbed, it is absorbed at specific time, is it not?

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bhobba
Mentor
Could you expand on this? Why couldn't they hit at a specific time? I've taken my undergraduate QM so feel free to be technical... to a certain point :). When a photon is absorbed, it is absorbed at specific time, is it not?
That's the domain of Quantum Field Theory and what a quantum field is, is nothing like that.

Anything you have read about photons outside a QFT text is likely way oversimplified to the point its probably downright wrong. For example it doesn't reside in a Hilbert space, but rather a Fock space:
http://en.wikipedia.org/wiki/Fock_space

If you would like to see the correct description fortunately these days books are now appearing on QFT accessible to undergraduates with just a first course on QM:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

If you modulate the RF signal you modulate the field. Since that is described by a Fock space at the level of individual photons its pretty meaningless.

Thanks
Bill

If you would like to see the correct description fortunately these days books are now appearing on QFT accessible to undergraduates with just a first course on QM:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

If you modulate the RF signal you modulate the field. Since that is described by a Fock space at the level of individual photons its pretty meaningless.
You know I've been looking for something to do over winter break and I think I'm gonna order that book. Thanks for the suggestion.

But I'm still a little confused. How is the energy transferred to the electrons in the antenna? It has to be a quantum transfer of energy, right? So we have to use the notion of quanta at some point. I'm just curious about the manner and pattern in which these photons transfer their energy to the electrons in the antenna.

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bhobba
Mentor
But I'm still a little confused. How is the energy transferred to the electrons in the antenna? It has to be a quantum transfer of energy, right? So we have to use the notion of quanta at some point. I'm just curious about the manner and pattern in which these photons transfer their energy to the electrons in the antenna.
It's the standard quantum thing. The quantum EM field gets entangled with the atoms in the antenna and a photon gets absorbed just like the quantum em field in the double slit gets entangled with the screen and a flash will occurs at some point.

Thanks
Bill

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How about this. Lets say you have a sensitive apparatus that can detect extremely weak radio signals. At some point your going to have to stop talking about the collective behavior of the photons and start talking about the photons themselves.
It has been argued that for multi-atom light sources (which an antenna inevitably is), it's not possible to originate single photon states:

http://www.fli-leibniz.de/www_kog/research/physics/SPIE.pdf [Broken]

Presumably the same applies to radio antennas:

Greulich et al said:
I don't know much condensed matter quantum theory, but I would imagine that for reception, there is some similar constraint on the interaction between the field and the gas of conduction electrons in the metal?

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f95toli