[hamdani yusuf (OP)]

According to QM, a photon carries a unit of energy according to its frequency through formula E=hf. Since h is a constant, no new information is obtained in calculating the energy because it's a dependent variable.
But we know that photon has other characteristics independent of its frequency, such as phases and polarization states.
Increasing the amplitude of EM wave is usually interpreted as increasing the number of photon with the same frequency, phase, and polarization state.
 
Are there other known characteristics of a photon?

[hamdani yusuf (OP)]

Due to Doppler's effect, light from moving source toward/away from receiver appears to have higher/lower frequency. Is it possible to distinguish if a photon with a particular frequency is produced by a stand still source with that frequency or a moving source with higher/lower frequency?

[Bored chemist]

Due to Doppler's effect, light from moving source toward/away from receiver appears to have higher/lower frequency. Is it possible to distinguish if a photon with a particular frequency is produced by a stand still source with that frequency or a moving source with higher/lower frequency?

No
They are identical.

[hamdani yusuf (OP)]

No
They are identical.

If the receiver also moves when getting hit by those photons, would it get identical measurements?

[hamdani yusuf (OP)]

But we know that photon has other characteristics independent of its frequency, such as phases and polarization states.

Polarization states alone carry some information as a complex number, which worths more than just one bit.
https://en.wikipedia.org/wiki/Jones_calculus#Jones_vector

[Halc]

If the receiver also moves when getting hit by those photons, would it get identical measurements?

Different.  Energy of a photon and thus its frequency and wavelength are all frame dependent quantities. So is the direction that it is moving, and thus its velocity and momentum.

[hamdani yusuf (OP)]

If the receiver also moves when getting hit by those photons, would it get identical measurements?

Different.  Energy of a photon and thus its frequency and wavelength are all frame dependent quantities. So is the direction that it is moving, and thus its velocity and momentum.

Let's say a source sends a 1 TeraHertz photon to a receiver. The receiver is moving towards the source at 0.5c. What is the frequency and wavelength detected by the receiver?

[Halc]

Let's say a source sends a 1 TeraHertz photon to a receiver. The receiver is moving towards the source at 0.5c. What is the frequency and wavelength detected by the receiver?

Assuming the 1THz is relative to said source, about 1.3 THz as measured by the approaching receiver. The light appears blue shifted.
Same light velocity in this case (as compared to a receiver that is stationary relative to the 1THz source), but different frequency, wavelength, energy and momentum.  You need an example with more than one dimension to get a velocity change.

[hamdani yusuf (OP)]

Let's say a source sends a 1 TeraHertz photon to a receiver. The receiver is moving towards the source at 0.5c. What is the frequency and wavelength detected by the receiver?

Assuming the 1THz is relative to said source, about 1.3 THz as measured by the approaching receiver. The light appears blue shifted.
Same light velocity in this case (as compared to a receiver that is stationary relative to the 1THz source), but different frequency, wavelength, energy and momentum.  You need an example with more than one dimension to get a velocity change.

What is the formula did you use to get the answer?

[Halc]

Let's say a source sends a 1 TeraHertz photon to a receiver. The receiver is moving towards the source at 0.5c. What is the frequency and wavelength detected by the receiver?

Assuming the 1THz is relative to said source, about 1.3 THz as measured by the approaching receiver. The light appears blue shifted.

What is the formula did you use to get the answer?

I don't know the formula, so I worked it out.
Did a Lorentz transform to the frame of the receiver, which has the source emitting a 1THz/λ photon, where λ is 1.1547, yielding 866 GHz.  Then I did a Doppler calculation on that which is apparently multiplying it by (1+0.5c) to get 1.3
I figured that out by considering it to be a continuous beam and just counting the waves that come in over the span of one nanosecond, assuming the source to be initially half a light nanosecond away and 'here' after that time.

So I guess the 'formula' in this case (linear motion with V = recession velocity) is (1-Vcos(θ))√(1-V²). V is in units of c. Somebody let me know if I did that wrong, because I didn't look it up anywhere. The cos(Φ) is 1 in our case, but isn't if the emitter motion isn't directly towards the receiver. Φ is computed at the location of the emitter of the current photon being received, not the current location of it at the time of receiving the photon.

[Hayseed]

Light has handedness.  A single photon with the same energy can be right handed or left handed.  So you can give a single photon a left or a right.    OR a 1 or a 0.

The "photon" is actually the torque part of the EM emission, which does not change with distance.

[evan_au]

Is it possible to distinguish if a photon with a particular frequency is produced by a stand still source with that frequency or a moving source with higher/lower frequency?

It is possible to correct for Doppler shift if you know the relative velocity of the emitter and receiver. If you are talking about a spaceship and the control center, that relative velocity will be known fairly accurately.

You would not try and send a message on a single photon - it could hit a speck of dust and be lost.
- If the laser beam from the transmitter is 100km in diameter when it reaches the receiver, and the receiver is using a telescope 1m across to receive the signal, you will miss almost all the photons.
- The good thing about photons is that they are relatively easy to produce in large quantities.

From a communications viewpoint, typically, you would send a message with:
- A certain bandwidth. The center of this bandwidth tells you the Doppler shift offset
- A certain timing. There is a clock signal embedded in the signal that allows you to extract a synchronization signal from what is received. Synchronous reception allows you to carry more data
- A certain number of bits per symbol. This is selected based on the noise in the signal (if the Signal-to-Noise ratio is worse, you send fewer bits per symbol).
- A certain duration: The more information you need to transmit, the longer the duration
- A certain schedule: One receiver has to monitor many transmitters. You want to transmit at the time you know the receiving telescope will be pointed at you (and not on the other side of the planet, or obscured by the Moon, for example)
- Enough photons so that you will on averagereceive more than one photon for each symbol you are transmitting
- For those cases where you receive 0 photons for some symbols, you add an error-correcting code, which allows you to reconstruct the missing symbols (providing there aren't too many of them). Normally the most advanced error correcting codes are tried first in space systems, as they have more challenging error conditions than most terrestrial applications (except maybe for spies communicating covertly).
- These days, when computer memory is relatively cheap, you store the data until you have confirmation that the signal has been received before deleting it. You retransmit the segments that could not be reconstructed (because too many symbols were lost for them to be recovered by the error-correcting code)

[hamdani yusuf (OP)]

It is possible to correct for Doppler shift if you know the relative velocity of the emitter and receiver. If you are talking about a spaceship and the control center, that relative velocity will be known fairly accurately.
You would not try and send a message on a single photon - it could hit a speck of dust and be lost.

In the thought experiment, the sensor has detected a photon. We don't know how much other photons have been sent by the source which are lost or undetected.
Can we infer the motion of the source by merely analyzing that detected photon?