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Does interference happen across time?


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Maybe a dumb title for this question, so I'll expand with an example.

Suppose that we have photon source, and diffraction element - like small aperture and a screen. On screen we will observe Airy diffraction pattern arising from photon interference (with it self, or rather wave function interference).

Now let's throw a bit of space-time curvature in the mix, and observe two different paths - one going thru warped space-time, other one thru "normal" space-time. Since path in warped space-time is longer - there will be phase shift and interference pattern should change? Now I come to the real question - is quantum state / wavefunction element of reality :D ? I bet you did not see that one coming :D

What I'm trying to say is - if wavefunction is element of reality (and not just mathematical construct to help explain probabilities), or in another words - photon travels thru both slits (and does not travel at all, but rather wavefunction evolves in time) - what happens to wavefunction in bent space time? We assume that wavefunction evolution is in "flat time", or maybe even "flat space time", but what happens if we need to calculate wavefunction evolution across volume where one part is "flat" and other is bent?

I'm speculating on this one, but one of explanations is that "wavefunction" is sensing space around it self and shapes accordingly. Can it sense time as well and shape accordingly (like looking ahead of time to form or destroy interference patterns)?

I don't seem to be able to reconcile "no path" approach with this. If we look at single photon and two places it can land - one idea is that photon "decided" on "path" and landed in spot A (and quantum eraser shows this is not the case), other idea is that photon "took both paths" to A and B and then "decided" where to interact (decided is dumb word for it - I'm not implying decision making but rather dice roll). If we introduce time into the mix then we can distinguish single path vs all paths, depending on timing of photon arrival?

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"is quantum state / wavefunction element of reality"

As far as I remember, it is not "Cat is dead 100% or Cat is Alive 100%", -
it's always a probability.

So photon will land with some probability on spot A, or B or even Both and that's why time "kinda" has nothing to do with...
And probabilities of all particles make up a full-scale object :)  so even if you even "do not look at the Moon", it still exists. 

P.S. never heard anyone taking into account the space curvature in such a small scales... this is why gravity theory does not work in nanoscales...

Maybe someone with PHD in String or M Theory is able to join for some beer with you! :)
I am writing off! but I would like to listen :)

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1 hour ago, andrew s said:

LIGO is based on gravitatonal waved csysimg interference causing interference.  So yes what count is proper distance which can have space and time components.

Regards Andrew 

Ok, great, it makes sense. But that is confusing me further. I'll try to explain what is causing confusion (It might well be that I should not try to apply mundane logic to it ... :D )

Suppose we have dual slit setup, but path along one slit contains space time curvature which shifts phase due to proper distance, and I suppose interference pattern will no longer be symmetrical in relation to line going between two slits but rather shifted.

But what would happen if we correlated detection time with emission time and took corresponding samples and plotted those - I think that interference pattern would disappear. Or another way to state what's bothering me (just to exclude precise measurement at both ends, and just concentrate on receiver / detector) - if we have setup that fires pairs of photons in close succession (like 1ns apart, and then wait 1ms and repeat) and we record position and time hits at detectors - we would be able to identify first and second photon in each pair - would they still be arriving at 1ns apart, or would that time be different - longer depending on what "percentage" (I know this is silly, but need to describe it somehow) of photon went the longer way?

What I'm wondering is if there are two paths for photon to follow and interfere - and one path is such that it takes longer for photon to reach sensor compared to other - at what time will we detect photon at sensor?

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5 hours ago, vlaiv said:

record position and time hits at detectors - we would be able to identify first and second photon in each pair

Unfortunately, this is not the case in quantum theory (QFT). Photons are described in as being created (i.e. emission) and annihilated (i.e. detection) and when created one is added to the number in the EM field and when annihilated one removed - i.e. there is a number operator. That is about all you can say. There is no position operator for photons so in QFT you can't ask about where it is or what route it took. All QFT will do is allow you to calculate, given a set of emissions, what the probability of detection would be at a given place and time given a specific experimental set up. You can't say which of the photon was detected if there is more than one in the EM field. 

If you what to ask about paths in flat of curved space-time then the best you can do is use the classical Maxwell equations.  For example if you modeled short laser pulses going through your experiment with the timing you propose it would give similar results to QFT prediction just as classical theory if fine for predicting the diffraction pattern of gratings. 

Regards Andrew

NB there are some very special circumstances in which excitations of the EM filed can be localised but this is not generally the case.

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1 minute ago, andrew s said:

Unfortunately, this is not the case in quantum theory (QFT). Photons are described in as being created (i.e. emission) and annihilated (i.e. detection) and when created one is added to the number in the EM field and when annihilated one removed - i.e. there is a number operator. That is about all you can say. There is no position operator for photons so in QFT you can't ask about where it is or what route it took. All QFT will do is allow you to calculate, given a set of emissions, what the probability of detection would be at a given place and time given a specific experimental set up. You can't say which of the photon was detected if there is more than one in the EM field. 

If you what to ask about paths in flat of curved space-time then the best you can do is use the classical Maxwell equations.  For example if you modeled short laser pulses going through you experiment with the timing you propose it would give similar results to QFT prediction just as classical theory if fine for predicting the diffraction pattern of gratings. 

Regards Andrew

NB there are some very special circumstances in which excitations of the EM filed can be localised but this is not generally the case.

Yes, thank you for the answer - I've been just reading about it, along with the idea that under some circumstances you can't really tell how much particles there are (system is in superposition of different particle numbers).

I still need to read a lot about it, don't really get how is speed of light related to it all if there is no position operator for photons. I don't get how creation operator which adds 1 to particular mode of oscillation of field is related to space propagation (what is actually propagating ...).

 

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3 minutes ago, vlaiv said:

I don't get how creation operator which adds 1 to particular mode of oscillation of field is related to space propagation (what is actually propagating ...).

The first half of the quote is quantum theory the second classical. The two don't mix. What you would find is that if you only had one photon then used QFT to calculate the probability of detection at a given detector the arrival time would be strongly peaked at the arrival time given by the speed of light, distance and time of emission.

Regards Andrew

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14 minutes ago, andrew s said:

The first half of the quote is quantum theory the second classical. The two don't mix. What you would find is that if you only had one photon then used QFT to calculate the probability of detection at a given detector the arrival time would be strongly peaked at the arrival time given by the speed of light, distance and time of emission.

Regards Andrew

Ok, what I don't understand then is how to relate "point" of emission, "point" of detection in space and related times to obtain probabilities when looking at quantum field as set of quantum harmonic oscillators - I always assumed those are theoretical constructs representing states - rather than actual waves (wave expression comes from the fact that we have "spinning" complex number - which is solution to differential equation similar to wave motion - sines and cosines, actually not similar but exactly the same via Euler's formula).

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Sorry vlaiv, I don't have the knowledge or skill to explain it more clearly. All I can say is that our theories are models of reality that have the ability to predict outcomes of observation/measurement. 

Regards Andrew

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1 minute ago, andrew s said:

Sorry vlaiv, I don't have the knowledge or skill to explain it more clearly. All I can say is that our theories are models of reality that have the ability to predict outcomes of observation/measurement. 

Regards Andrew

Don't worry - this means only one thing: I need to study the subject deeper until I get the hang of it ...

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