Is the wave-function description of photon location incomplete?

[San K]

Is the wave-function description, even though a good one, for photon location (evolving in time-space) incomplete?

How can probabilities self-interfere?

probability theory would say - either the photon goes from x slit or y slit, but not both

a coin is either heads or tails but not both (ignoring the case where the coin lands/stands on its circumference)

the result of a rolled dice result is a whole number (1, 2, ...6) but not 2.5, or 5.4 etc

the dice cannot land on one of its 12 (?) edges

 

[Bill_K]

How can probabilities self-interfere?

Probabilities can't, but probability amplitudes can. Probabilities are real numbers between 0 and 1. Probability amplitudes are complex numbers, and so the result of adding two of them can be less than either one separately.

probability theory would say - either the photon goes from x slit or y slit, but not both

It isn't probability theory that says this, it's classical mechanics. Quantum mechanics, on the other hand, says that the photon travels all possible paths, and the probability amplitudes from every possible path must be added together.

 

[San K]

thanks Bill_K. agree with what you said.

how far/long do wave-functions last?
do they go to infinity provided there is no other interaction/disturbance/interference?
i.e. if we have an isolated mach-zhender interferometer say 1 km square (i.e. each arm was 1 km in length), would interference still occur?

http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer

 

[Zarqon]

The answer to your question on interference is that it is given by the coherence length of the photon, which is basically the distance the photon travels during its coherence time. The coherence time is in turn related to the spectral content of the photon.

For example, an atomic transition that produced the photon have an uncertainty of it's energy levels, and this is transferred over to an energy/frequency uncertainty of the photon. Being built from multiple frequencies, the phase of the photons are only well defined for a certain time before they have dephased, and this time is given approximately by 1/df , where df is the width of the frequency content.

 

[f95toli]

Also, note that a photon does not HAVE a wavefunction in the usual sense of the word (you can't wrote down a SE for a photon). Moreover, a photon does not have a position operator so you can't talk about "where" a photon is at all; it is simply not a valid concept.
There are other -related- quantities one can use for photons, but they are all fairly non-intuitive.

 

[andrien]

here is a thread on the related topic
https://www.physicsforums.com/showthread.php?t=659614

 

[San K]

Thanks Zargon, on the information on coherence length
Thanks f95toli, it will take time to digest the new information/knowledge
Thanks Andrien, again a lot of information, will take time

what started as a simple photon, does not sound that simple anymore...;)

the deeper you go, the more the knowledge expands like the expansion of the universe...;)

 

[San K]

The answer to your question on interference is that it is given by the coherence length of the photon, which is basically the distance the photon travels during its coherence time. The coherence time is in turn related to the spectral content of the photon.

For example, an atomic transition that produced the photon have an uncertainty of it's energy levels, and this is transferred over to an energy/frequency uncertainty of the photon. Being built from multiple frequencies, the phase of the photons are only well defined for a certain time before they have dephased, and this time is given approximately by 1/df , where df is the width of the frequency content.

How long does quantum entanglement last?

Does the coherence length/time effect quantum entanglement (even thought coherence and entanglement are complimentary)

does having multiple frequencies (building up the phase of a photon) suggest a unit smaller than a quantum/photon?

 

[Zarqon]

How long does quantum entanglement last?

Does the coherence length/time effect quantum entanglement (even thought coherence and entanglement are complimentary)

Normally, entanglement in photons are not dependend on the coherence of them. This is because typically, other degrees of freedom are used, such as time-bin qubits or polarization qubits. Neither of those depend on the temporal coherence. That being said, if one were to use some type of frequency encoding, then yes I assume the temporal coherence would come in, just as it does for atomic qubits, which most often do use encodings that are sensitive to temporal decoherence.

does having multiple frequencies (building up the phase of a photon) suggest a unit smaller than a quantum/photon?

This is a strangely worded question. The quantization of photon energy (or anything really) depends on the boundary conditions of your system that interacts with them (think different longitudinal modes in a cavity). There is no conceptual problem to just choose a different system that has smaller (energywise) quanta than your original system.

With regards to the spread of energy (multiple frequecies) you can rather think of it as the uncertainty of how large your quanta actually are.