The speed of a "photon" in a multipath experiment?

[alikim]

Let's say here are two ways for a photon to go between point A and B and a detector at B detects photons with some probability based on interference.

Mathematically, it's calculated by carrying phases along each path and then adding them up regardless of how much time it takes to travel along each path and after what time the interference will appear.

But in practice, if one path is much much longer than another, how long do you have to wait after a photon passed point A till the moment of detection at B?

Is there a formula for the speed of this process that happens between A and B?

 

[Simon Bridge]

In this setup you only know that there has been an emission and a detection.
You are asking about the time elapsed between the two.

If you know the path, then it is the path-length divided by the speed of light.
But actually you don't, so you need to use statistics:
The mean time between emission and detection will be the weighted average path-length divided by the speed of light.
Complicated by the fact that there are many emission events that do not generate a detection (those photons hit the barrier instead) ... and how do you tell if a particular detection event was due to the emission event immediately preceding it, or the one before (and the photon just took a more convoluted path)?

 

[alikim]

In this setup you only know that there has been an emission and a detection.
You are asking about the time elapsed between the two.

If you know the path, then it is the path-length divided by the speed of light.
But actually you don't, so you need to use statistics:
The mean time between emission and detection will be the weighted average path-length divided by the speed of light.
Complicated by the fact that there are many emission events that do not generate a detection (those photons hit the barrier instead) ... and how do you tell if a particular detection event was due to the emission event immediately preceding it, or the one before (and the photon just took a more convoluted path)?

As far as I understand, in case of light traveling through a layer of glass, for example, the speed of light in the glass (calculated through integration along all infinite possible paths between the point of entry and point of exit) is a definite value that doesn't have statistical nature, i.e it's always the same for any photon that manages to go through and that is detected on the other side, it's not a mean value of some kind of distribution of speeds.

So in case of only two paths I expect to have a definite value as well, not a mean time.

Obviously, each photon is separated in time from another to give it enough time to travel to the detector and to be or not to be detected before the next photon is emitted.

The same way as any multi-path experiment is done with one photon present "in the air" at a time by whatever means it is done.

 

[Simon Bridge]

As far as I understand, in case of light traveling through a layer of glass, for example, the speed of light in the glass (calculated through integration along all infinite possible paths between the point of entry and point of exit) is a definite value that doesn't have statistical nature, i.e it's always the same for any photon that manages to go through and that is detected on the other side, it's not a mean value of some kind of distribution of speeds.

The speed of light in a vacuum is a constant ... it is a definite speed.
It is not the speed that is statistical but the elapsed time between emission and detection.
Clearly this must depend on the path taken at least - longer times for longer paths.

So in case of only two paths I expect to have a definite value as well, not a mean time.

Consider Feynman's example of a long plane mirror with source and detector, and consider those photons that are reflected.
The shortest path is one where the trajectory forms equal angles for incidence and reflection - however, the longest path may arbitrarily long, depending on the size of the mirror. The math would have to work for mirror's light-years wide. For all paths to be traversed in the same time as the shortest would require some photons to travel faster than the speed of light, which is a contradiction.
http://vega.org.uk/video/subseries/8

Obviously, each photon is separated in time from another to give it enough time to travel to the detector and to be or not to be detected before the next photon is emitted.

You'd hope so - at least, use a source that is so diffuse that the chances of a second photon lingering on a weird trajectory is very small.

Note: the "usual experimental setup" is designed more to reduce the possible effect of two photons interfering with each other. A strong diffraction pattern means we need to have a precise frequency for the photons, so we sacrifice knowledge of the exact time that each photon was emitted.

The trouble with the experiment you are thinking of is that you would need to measure the time the photon was emitted and detected with great accuracy. Unfortunately, a great accuracy in the timing of the emittion means a large uncertainty in the frequency of the emitted photon. This would destroy the interference pattern. There's a lay discussion:
http://physics.stackexchange.com/qu...l-time-of-photons-in-a-double-slit-experiment

But you may be thinking of something more like this:
http://www.physic.ut.ee/instituudid/efti/loengumaterjalid/opt/optika/young timeresolved_Garcia.pdf

 

[vanhees71]

You have to clearly define what you mean by "speed of photon". It's not so clear to me what you are talking about. Also be particularly careful with physics papers typed with M$ Word!

 

[mfb]

The concept you are looking for is the coherence length of the emitted light. The short version: if your delay is shorter than the coherence length you get interference, otherwise you do not. But it is a gradual process, nothing with a sharp border. There is no speed involved, apart from the speed of light from A to B, which is the speed of light.

Also be particularly careful with physics papers typed with M$ Word!

Better ignore them completely.

 

[alikim]

...But you may be thinking of something more like this:
http://www.physic.ut.ee/instituudid/efti/loengumaterjalid/opt/optika/young timeresolved_Garcia.pdf

More like this. If I understand it right, here they measured travel time of a photon between the slit and points on the screen where interference maximums are and proved that up to their camera resolution the flight time is consistent with the speed of light. I understand that there is always some distribution of measurement results but in this case it has a strong peak at where the speed of light is.

What I'd like to know is what results do you get in the same experiment but with two slits instead of one.

You emit photons and register them with the camera as they did in the article but now there is a shorter straight path from one slit to the maximum on the screen and a longer one from another slit.

What the flight time measurements will look like? Distributed evenly between the shorter and longer times with each photon randomly arriving between the two or is it going to show a peak around the average time?

 

[mfb]

If your flight time measurement is too precise (which needs a precise start time), then your paths are not coherent any more and you lose interference. You get two separate peaks in flight time. If your measurement is not very precise, it is possible (but not guaranteed) to have interference and a broad distribution centered around the average of the expected flight times.

 

[Strilanc]

Someone correct me if I'm wrong.

I assumed that the specific path integral approach described by Feynman in this lecture was for computing the incidence rate that the system would converge to if you left it running arbitrarily long. i.e. the different path lengths are being added together not because it takes the same time for photons to traverse them, but because earlier possible emission times were interfering with later possible emission times.

A consequence of this idea is that if you only left the photon emitter on in short bursts, with long wait times in between, you'd in principle be able to see different incidence rates due to the lack of interference. Is that right?

 

[Simon Bridge]

If I understand it right, here they measured travel time of a photon between the slit and points on the screen where interference maximum...

They timed pulses of light from source to detector, and, in another experiment, timed individual photons arriving.
If they say they sent a single photon through the apparatus, I missed it.

 

[vanhees71]

Someone correct me if I'm wrong.

I assumed that the specific path integral approach described by Feynman in this lecture was for computing the incidence rate that the system would converge to if you left it running arbitrarily long. i.e. the different path lengths are being added together not because it takes the same time for photons to traverse them, but because earlier possible emission times were interfering with later possible emission times.

A consequence of this idea is that if you only left the photon emitter on in short bursts, with long wait times in between, you'd in principle be able to see different incidence rates due to the lack of interference. Is that right?

I'm not sure what Feynman did in his popular lecture, but one should be aware that photons in the path-integral approach do not involve path integrals over particle trajectories, as is possible to define in non-relativistic quantum mechanics (or also with a grain of salt also for massive relativistic particles), is a parth integral over fields as in any QFT, i.e., many-body approach (where here "body" has to be taken in quotation marks, because photons don't have anything in common with a "body" in any classical sense).

 

[alikim]

If your flight time measurement is too precise (which needs a precise start time), then your paths are not coherent any more and you lose interference. You get two separate peaks in flight time. If your measurement is not very precise, it is possible (but not guaranteed) to have interference and a broad distribution centered around the average of the expected flight times.

So if I have interference and I get a flight time as an average between two paths it is explained by a large error in the flight time measurement, in particular the uncertainty in the start time?

 

[mfb]

You reversed the logic. If your setup allows to measure the flight time accurately, then you won't get interference. If your setup produced light with a long coherence length, then you get interference, but then "the flight time" is not a well-defined quantity any more, and your measurements will have a large spread.