Double Slit Experiment: Timing & Reflection Interference

[Andy_K]

Dear All,

I have a couple questions on the double slit experiment I hope you can help shed some light (or photons) on. =)

Arrival Timing of Photons
In a normal double-slit experiment like the above setup, do photons always arrive at the detector at a constant speed (basically, speed of light), or does the arrival time experience fluctuation (albeit an extremely minute one)?

Since the interference pattern is a result of many troughs of (probability) waves, and troughs seem to have a certain order in its propagation (just like in waves, some troughs are in front and some behind), does that mean if a photon is detected at a position created by interference of troughs further back, it would actually arrive at the detector at a slightly later time?

I understand that the "wave" is not physical, but if the interference resembles the characteristics of normal waves, wouldn't that also signify a correlation to the spatial and temporal sequence of troughs?Reflection Interference
If we change some parts of P (please refer to photo below) to become a mirror, so that the photon is either reflected back or detected there, would the reflection's backward "wave" interfere with the forward "waves", or perhaps even cancel it out since it's an opposing "motion"?Thank you for your guidance.

 

[tech99]

[Reflection Interference
If we change some parts of P (please refer to photo below) to become a mirror, so that the photon is either reflected back or detected there, would the reflection's backward "wave" interfere with the forward "waves", or perhaps even cancel it out since it's an opposing "motion"? /QUOTE]
EM waves form an interference pattern above the surface of a mirror.

 

[zonde]

Since the interference pattern is a result of many troughs of (probability) waves

There are no probability waves in Quantum Mechanics. There is a term "probability amplitude", but it's phase does not describe amplitude oscillations. It's phase rather describes rotation in complex plane (mathematically speaking).
You might give a try to Feynmann's (very layman-friendly) book "QED: The strange theory of light and matter".

 

[PeterDonis]

do photons always arrive at the detector at a constant speed (basically, speed of light), or does the arrival time experience fluctuation (albeit an extremely minute one)?

We don't measure the time it takes for the photons to travel through the experiment, so there is no answer to this question. All we measure is the pattern of light and dark at the detector.

 

[Andy_K]

We don't measure the time it takes for the photons to travel through the experiment, so there is no answer to this question. All we measure is the pattern of light and dark at the detector.

May I know if we don't measure because it is not relevant, not possible, or that it will always be the constant speed of light?

 

[Andy_K]

EM waves form an interference pattern above the surface of a mirror.

Does that mean the wave propagating back will interfere with the original forward wave, at spaces between the barrier/slit and detector?

 

[PeterDonis]

May I know if we don't measure because it is not relevant, not possible, or that it will always be the constant speed of light?

Not relevant (since the point of the experiment is to measure the pattern of light and dark at the detector) and not possible (because we can't measure the times at which individual photons leave the source).

 

[tech99]

Does that mean the wave propagating back will interfere with the original forward wave, at spaces between the barrier/slit and detector?

In classical physics terms, which is all I know, yes. Light from the first double slit is interfered with with by light from its image, which is a second double slit located the same distance behind the mirror.

 

[PeterDonis]

Light from the first double slit is interfered with with by light from its image, which is a second double slit located the same distance behind the mirror

This is correct; the QM model of this is basically the same as the classical model as far as the wave interference is concerned.

 

[Andy_K]

Thank you very much for your guidance, Zonde, Tech99 and PeterDonis! I have much to learn :)

You might give a try to Feynmann's (very layman-friendly) book "QED: The strange theory of light and matter".

In classical physics terms, which is all I know, yes. Light from the first double slit is interfered with with by light from its image, which is a second double slit located the same distance behind the mirror.

This is correct; the QM model of this is basically the same as the classical model as far as the wave interference is concerned.

 

[ueit]

Not relevant (since the point of the experiment is to measure the pattern of light and dark at the detector) and not possible (because we can't measure the times at which individual photons leave the source).

Of course you can measure the time of emission. You just turn the source on for a very small amount of time.

Andrei

 

[PeterDonis]

You just turn the source on for a very small amount of time

And then you won't get an interference pattern at the detector; you'll only get a single dot where the single photon that was emitted by the source landed. (Actually, you might not get a photon at all, or you might get two or three, since the source does not emit photons at precise time intervals, there is only a probability of photon emission per unit time.)

 

[vanhees71]

You'll also not get an interference pattern by collecting a lot of photons in this way since if you turn on the source only for a very small amount of time, the energy of the produced photons is very uncertain. So you will get a structureless pattern on your photoplate at the end.

 

[ueit]

And then you won't get an interference pattern at the detector; you'll only get a single dot where the single photon that was emitted by the source landed. (Actually, you might not get a photon at all, or you might get two or three, since the source does not emit photons at precise time intervals, there is only a probability of photon emission per unit time.)

Of course you can repeat the process until the pattern forms.

You'll also not get an interference pattern by collecting a lot of photons in this way since if you turn on the source only for a very small amount of time, the energy of the produced photons is very uncertain. So you will get a structureless pattern on your photoplate at the end.

You don't need to turn off the source, you could just block the light with something.

 

[PeterDonis]

You don't need to turn off the source, you could just block the light with something.

How accurately can you measure the timing of when the light is blocked or not blocked? (The same question would apply to turning the source on and off.)

Also, how do you know you will still get an interference pattern in this way? The usual QM prediction of an interference pattern assumes that all photons from the source make it to the detector.

 

[ueit]

How accurately can you measure the timing of when the light is blocked or not blocked? (The same question would apply to turning the source on and off.)

I think you can measure the timing as accurately as you want. For example you can place a rotating disk with a small slit in front of the source. The rotation speed determines the time interval when the particle is emitted and I see no problem with making that interval as small as you want.

Also, how do you know you will still get an interference pattern in this way? The usual QM prediction of an interference pattern assumes that all photons from the source make it to the detector.

I have never heard of such a requirement and I don't believe it can be true. As far as I can tell QM's prediction is about each particle. Each photon has a certain probability to be detected at each point on the screen. The number of photons that are detected is irrelevant, but, in order to "see" the pattern you need a certain number of them.

 

[PeterDonis]

As far as I can tell QM's prediction is about each particle

The requirement could be stated in an equivalent form that applies to a single photon: the wave function of the photon exiting the source must have no restriction in emission time. (The usual assumption is that the photon is a plane wave.) Your scheme for measuring the time of emission puts a restriction on the emission time, and that changes the wave function of photons exiting the "source" (which is now the original source plus your apparatus for measuring the emission time).

In short, your apparatus changes the wave function of each photon in the experiment, and I think this change will affect the prediction of what will be observed at the detector. I understand that you disagree, but I would like to see something more to back that up than just your opinion. A mathematical treatment would be nice.