Undergrad The nature of quantum interference

[Mentz114]

QT would be easier for me to cope with if the interference and diffraction observed experimentally with microscopic objects could be explained entirely by the commutation relations of observables and not by invoking wave properties.

This comes down to the question - if we measure two non-commuting observables nearly simultaneously will the result be subject to interference ? Obviously the answer depends on other things unspecified in this simplification.

For example in the two slit experiment when the particle goes through a slit there is a position measurement with an indeterminacy of at least the distance between the slits. When the particle hits the screen and makes a mark, we have momentum information in x and y ( x being the direction of motion initially ). Do the 'indeterminacy relations' ( as Ballentine puts it) mean that there will be no-go regions of space which will give the dark and light bands characteristic of interference ?

 

[mfb]

In general it does not matter if you measure things nearly simultaneously or with more time in between.

When the particle hits the screen and makes a mark, we have momentum information in x and y ( x being the direction of motion initially ).

If you have a setup where you can measure y precisely enough to distinguish between the two slits, you don't get an interference pattern any more.

Do the 'indeterminacy relations' ( as Ballentine puts it) mean that there will be no-go regions of space which will give the dark and light bands characteristic of interference ?

That is the typical double-slit result, yes.

 

[Mentz114]

In general it does not matter if you measure things nearly simultaneously or with more time in between.
If you have a setup where you can measure y precisely enough to distinguish between the two slits, you don't get an interference pattern any more.

That is certainly what I would expect. Do you have a reference to any equations ? I'm thinking of wave functions overlapping (in phase space, obviously) and interfering in the overlap region. If the indeterminacy is small enough there is no overlap.

That is the typical double-slit result, yes.

I presume you're being (gently) ironic.

 

[mfb]

Do you have a reference to any equations ?

They depend on what exactly you are considering.

I presume you're being (gently) ironic.

It was not meant ironic.

 

[Mentz114]

They depend on what exactly you are considering.It was not meant ironic.

You have not objected to my hypotheseis in the position/momentum case so I will pursue the idea. I have found a paper (which I have yet to read) where the authors use photon interference to verify spin commutation relations (su(2) ?) and I will attempt to use it in another case I'm interested in.

Experimental verification of the commutation relation for Pauli spin operators using single-photon quantum interference
Yong-Su Kim, Hyang-Tag Lim, Young-Sik Ra, Yoon-Ho Kim
Physics Letters A
Volume 374, Issue 43, 27 September 2010, Pages 4393-4396

and

arXiv:1002.3219v2 [quant-ph] 17 Sep 2010