Double slit experiment & time (action at a distance?)

[earlofwessex]

hi, Please help me understand this...


could you set up the double slit experiment (light, one photon at a time) in such a way that you could measure the time between a photon leaving the gun and arriving at the detector?

you could then calculate the path the photon took, so would the interference not be there?


Thanks very much

 

[xts]

that you could measure the time between a photon leaving the gun and arriving at the detector?

Measure with what precision?
In most experiments you may measure it, or even it is measured pretty precisely (picoseconds), why should it spoil the interferenence?
If you mean measuring the time so precisely to distinguish which way the photon took: no, it is impossible. So precise measurement would broaden the spectrum that much, so the pattern wouldn't be seen.

 

[earlofwessex]

yes, i meant accurately so as to determine which way the photon went.

So precise measurement would broaden the spectrum that much, so the pattern wouldn't be seen.

thanks, could you explain that a little more? what does broaden the spectrum mean?

 

[Drakkith]

yes, i meant accurately so as to determine which way the photon went.



thanks, could you explain that a little more? what does broaden the spectrum mean?

The more accurately you measure the position, the less accurate the future momentum is. And for a photon the momentum = energy and determines frequency.

See here: http://en.wikipedia.org/wiki/Uncertainty_principle

 

[edpell]

I think this is a good question.

In a standard two slit experiment the two paths differ by a few wavelength. So you have to measure the time to wavelength/c but the particle is of a size of a wavelength, I think getting its start and stop to a fraction of a wavelength will be not physically possible.

But we could use a two path setup with a one nanosecond difference between the two paths. Would we get constructive interference if the delta is an integer multiple of the wavelength? Destructive interference if the delta is integer plus one half times the wavelength? It would be easy to measure a time difference of one nanosecond. I think the answer is no interference effect will be seen because the two paths are NOT indistinguishable.

When does indistinguishable turn into distinguishable? How many wavelength difference?

 

[Demystifier]

could you set up the double slit experiment (light, one photon at a time) in such a way that you could measure the time between a photon leaving the gun and arriving at the detector?

you could then calculate the path the photon took, so would the interference not be there?

Even if you could measure this time, you couldn't really calculate the path from it. Or at least not without taking additional assumptions on motion of photons that you cannot directly verify by experiments.

 

[earlofwessex]

Thanks, I'm not sure I understand what the HUP has to do with this? I want to measure the time at the point where the photon hits the detector, its momentum doesn't matter after this time, just the position

Even if you could measure this time, you couldn't really calculate the path from it. Or at least not without taking additional assumptions on motion of photons that you cannot directly verify by experiments.

Thanks, are you saying that photons do not nessasarily travel in a straight line or at speed c?

Just to clarify, I am imagining. A photographic plate as a detector and some kind of camera pointed at it or vibration sensor attatched to it. Basically a measurement not local to the slit

 

[xts]

are you saying that photons do not nessasarily travel in a straight line or at speed c?

No we are (well.. I am) saying that it make no sense to think about photons traveling along such or other path. You may only say that the photon left the source at some time (with some accuracy, more precisely you determine the time, less certain is photon colour) and reached the target at some other time (again, with limited accuracy)

 

[Drakkith]

Thanks, I'm not sure I understand what the HUP has to do with this? I want to measure the time at the point where the photon hits the detector, its momentum doesn't matter after this time, just the position

Thanks, are you saying that photons do not nessasarily travel in a straight line or at speed c?

Just to clarify, I am imagining. A photographic plate as a detector and some kind of camera pointed at it or vibration sensor attatched to it. Basically a measurement not local to the slit

The problem is that we cannot determine when the photon leaves the emitter. The only thing we can do is say that over X time, Y photons will leave the emitter on average. And if you set up a detector to measure when the photons leave the emitter, then you alter them.

 

[earlofwessex]

No we are (well.. I am) saying that it make no sense to think about photons traveling along such or other path. You may only say that the photon left the source at some time (with some accuracy, more precisely you determine the time, less certain is photon colour) and reached the target at some other time (again, with limited accuracy)

sorry, I still don't understand...

if the difference in paths was greater than the combined error bars of the time measurement, then why could you not say " if the photon went through hole 1, it must have gone faster than C, therefore it must have gone through hole 2" (assuming the measurements supported that classically)

The problem is that we cannot determine when the photon leaves the emitter. The only thing we can do is say that over X time, Y photons will leave the emitter on average. And if you set up a detector to measure when the photons leave the emitter, then you alter them.

Ah ok. is there some fundamental principle at work here? at the very least could we not switch the emitter on for such a short time that if a photon was emitted, the "X time" was minimal?

 

[edpell]

"are you saying the photons do not travel in a straight line?"

If they did all the photons through slit A would land at one set position on the screen and likewise for slit B there would be no interference. But photons are waves and the wave expands in a circle after leaving the slit.

 

[edpell]

Thinking in terms of Feynman all paths and least action, I think, we get interference if the two paths have the same action or if the difference in the action for the two paths is small ( a few h bar). We do not get interference if the difference in the action along the two paths is large (many h bar).

 

[earlofwessex]

"are you saying the photons do not travel in a straight line?"

If they did all the photons through slit A would land at one set position on the screen and likewise for slit B there would be no interference. But photons are waves and the wave expands in a circle after leaving the slit.

ah ok thanks. i was thinking the interference came from random kicks to the direction at the slit.
does the wave front propagate at exactly c?

edit: Feynman all paths and least action is way above me, so ill take your word for it.
trigonometry now: does the difference in shortest paths vary with the distance between the slit and the detector, all other things being held constant?

 

[edpell]

does the wave front propagate at exactly c?

Yes.

 

[Drakkith]

Ah ok. is there some fundamental principle at work here? at the very least could we not switch the emitter on for such a short time that if a photon was emitted, the "X time" was minimal?

I'm not sure how, but I think either the momentum or position of the photon would be less known as you bring the X time down. Anyone know?

 

[edpell]

Yes one can do one photon at a time two slit interference. One can make the time the emitter is on be a short interval. The photomultiplier at the screen can be feed into a timing circuit to get the arrival time.

Since a photon is a wave where on the wave are we measuring from the first1%, 10%, 50%, 90%, 99%? if the wavelength is 5000 angstroms then the time from front of the wave to back of the wave is 1E-13 seconds. Since the path length differ by one wavelength for the first maxima we need accuracy of say 0.3E-13 sec. Can we be sure the photo detector always firers on the first 30% of the wave? Does it sometimes fire on the last 30%? This is a phyiscs question that I am not sure of the answer.

 

[Demystifier]

Thanks, are you saying that photons do not nessasarily travel in a straight line or at speed c?

Exactly! For example, recent weak measurements of photon trajectories suggest that they do not. On this forum, we have discussed these measurements here:
https://www.physicsforums.com/showthread.php?t=503861

 

[Cthugha]

Y if the wavelength is 5000 angstroms then the time from front of the wave to back of the wave is 1E-13 seconds.

The wavelength is not a natural measure of the spatial extent of a photon. If you want to have a quantity that closely resembles the "volume" taken by a photon the next best choice is the coherence volume. Even for single photons the probability to detect it is not restricted to an area with dimensions of the order of the wavelength, but usually much larger dimensions.