Electron/photon interference pattern questioned

[etamorphmagus]

The interference pattern created by the distribution of particles (electrons or photons) is related to the wave behavior.
We interpret the probability distribution as the intensity distribution of 2 interfering waves.

Say, a single electron travels toward the 2-slits, it diffracts like this:
[PLAIN]http://img42.imageshack.us/img42/9482/65985389.gif

but you see that on the left side, one wave is always before the other wave, and when they reach the "screen" on the bottom left side, they are not yet interfering. This leads me to the conclusion that we can't get interference because the particle's wavefront is left alone without interference (one wave reaches the screen first - without interference).

This of course would tell you from which slit the particle came from - which is impossible. and also not what we see. we see interference.
Is the answer to this problem is that the electron's "wave" is—using Feynman's words—"sniffing" before the electron actually reached the screen to see where it should have higher probability? As if as the electron is emitted from the electron gun, it automatically has its probabilities everywhere. This also doesn't make sense - it's against speed c limit.

Anyone? help?

 

[Upisoft]

The interference pattern created by the distribution of particles (electrons or photons) is related to the wave behavior.
We interpret the probability distribution as the intensity distribution of 2 interfering waves.

Say, a single electron travels toward the 2-slits, it diffracts like this:
[PLAIN]http://img42.imageshack.us/img42/9482/65985389.gif

but you see that on the left side, one wave is always before the other wave, and when they reach the "screen" on the bottom left side, they are not yet interfering. This leads me to the conclusion that we can't get interference because the particle's wavefront is left alone without interference (one wave reaches the screen first - without interference).

This of course would tell you from which slit the particle came from - which is impossible. and also not what we see. we see interference.
Is the answer to this problem is that the electron's "wave" is—using Feynman's words—"sniffing" before the electron actually reached the screen to see where it should have higher probability? As if as the electron is emitted from the electron gun, it automatically has its probabilities everywhere. This also doesn't make sense - it's against speed c limit.

Anyone? help?

The state of the electron passing through the left slit is $$\left|\psi_L\right\rangle$$. In this case the right slit is closed. With left slit closed and right slit opened we have state $$\left|\psi_R\right\rangle$$. When both slits are opened the state is $$\left|\psi_L\right\rangle + \left|\psi_R\right\rangle$$. This is when the electron interferes. The screen at the bottom has nothing to do with it.

 

[tom.stoer]

There is not one single wave front (an infinitesimal this spherical shell) traveling from the slits to the screen. The incoming electron is a plane wave with _infinite_ extension. The same applies to the two outgoing spherical waves; again they have infinite extension. The electron is not located, neither at a specific point, nor on a spherical shell. In this picture the electron is distributed over the whole space.

A physically realistiv picture is to replace these waves (plane wave, spherical wave) by wave pakets. They are better located, but again they are not located at a certain point - because they are waves.

 

[arkajad]

As it was mentioned above by tom.stoer, there are no wave fronts. There is one wave function spread all over the space. Its form is changing wit time. If the source is approximately at a distance d1 from the slits, and the slits are approximately at a distance d2 from the screen, and if the electron has approximately velocity v, the wave function maximum riches the slits after t=d1/v, then it changes its shape, and the maximum of this changes shape reaches the screen after approximately t= d2/v.

My use of "approximately" neglects here many factors like geometry, interaction with the slits and with the screen etc. So it is the zero-order approximation. But it tells the essence of the story.

 

[zonde]

Is the answer to this problem is that the electron's "wave" is—using Feynman's words—"sniffing" before the electron actually reached the screen to see where it should have higher probability? As if as the electron is emitted from the electron gun, it automatically has its probabilities everywhere. This also doesn't make sense - it's against speed c limit.

Assumption that "wave" is already there before electron exits the slit seems to give quite simple resolution.
And it makes sense if you consider that "wave" can be created by ensemble of all (previous) particles going through the slits.

 

[etamorphmagus]

Thank you for all the fine answers but I still haven't got this straight.

As the electron passes the 2 slits Upisoft said that it has a state which is combination of both slits, ok that makes sense. But when you say "they interfere at that moment", does it mean that the interference-map of the electron is created before the electron "passes" those locations?

Also, this question goes very well with this question: Does it take the single electron longer to reach X₂ rather than X₁, time measured from exiting electron gun to detection?
[PLAIN]http://img824.imageshack.us/img824/2448/13338541.gif

 

[arkajad]

As the electron passes the 2 slits ...

When you have just one electron - you have just one dot on the screen. No interference pattern at all.

 

[etamorphmagus]

Well of course, the interference pattern emerges after many electrons, I question the mechanics of that interference as "waves". As I understand the wave-function acts like a wave, but I have some problems with that...

 

[arkajad]

When you have many electrons, say one after another. then the time that the electron hits the screen will be also random. But, on average, it will take longer to hit x2 than to hit x1, though I doubt if that can be measured with the measurement techniques of today. When it will be possible to measure these things - such experiments can decide between alternative descriptions of quantum phenomena.

 

[jtbell]

Say, a single electron travels toward the 2-slits, it diffracts like this:
[PLAIN]http://img42.imageshack.us/img42/9482/65985389.gif

but you see that on the left side, one wave is always before the other wave, and when they reach the "screen" on the bottom left side, they are not yet interfering.

Your diagram is incomplete. A procession of wavefronts emerges from each slit, and each wavefront from slit #1 can interfere with any wavefront from slit #2 that it happens to "cross." You seem to be thinking that wavefront #n from slit #1 can interfere only with wavefront #n from slit #2.

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Double_slit_diffraction.svg/500px-Double_slit_diffraction.svg.png[/URL]

In the diagram above, there is a maximum wherever two black lines or two white lines cross, and a minimum wherever a white line crosses a black line.

 

[etamorphmagus]

When you have many electrons, say one after another. then the time that the electron hits the screen will be also random. But, on average, it will take longer to hit x2 than to hit x1, though I doubt if that can be measured with the measurement techniques of today. When it will be possible to measure these things - such experiments can decide between alternative descriptions of quantum phenomena.

So is it possible that it will take say 1 second to hit X₁ with one electron, and 2 seconds with a different electron?

Your diagram is incomplete. A procession of wavefronts emerges from each slit, and each wavefront from slit #1 can interfere with any wavefront from slit #2 that it happens to "cross." You seem to be thinking that wavefront #n from slit #1 can interfere only with wavefront #n from slit #2.

In the diagram above, there is a maximum wherever two black lines or two white lines cross, and a minimum wherever a white line crosses a black line.

I know I did not finish the diagram, thank you for the better one. As you can see on your diagram, on the right and left sides, there is a area where one wave (4 wavelengths actually according to that diagram) is chasing the other and there is no interference, so when the "wavy" electron spreads and reaches the detector, at first it has probability to be detected without interference. That is what I want to understand.

 

[arkajad]

So is it possible that it will take say 1 second to hit X₁ with one electron, and 2 seconds with a different electron?

Sure, but such a huge difference will not happen very often.

 

[etamorphmagus]

How is it that there are time differences though anyway? Now I have a hard time understanding the probability for particle detection on screen for location AND time.
The wave-function represents the value of the electron that if squared gives the probability, but it is not like a ripple-tank that pumps ripples on the water, it is a single wavefront, it is a single electron.

Just to make it clear, how does the single electron gives the probability that is proportional to wave-intensity in a ripple tank?

 

[arkajad]

How is it that there are time differences though anyway?[?QUOTE]

This would have to take us beyond what is considered to constitute the mainstream physics.

 

[Upisoft]

How is it that there are time differences though anyway? Now I have a hard time understanding the probability for particle detection on screen for location AND time.
The wave-function represents the value of the electron that if squared gives the probability, but it is not like a ripple-tank that pumps ripples on the water, it is a single wavefront, it is a single electron.

Just to make it clear, how does the single electron gives the probability that is proportional to wave-intensity in a ripple tank?

The wave-function depends on how the particle is interacting. In your example there are 2 interactions (measurements). First is the interaction at the slits. There the particle is measured for position. Any macro object will pass either through left or through right slit (if the slits are big enough). That is not the case with the electron. You can draw its position probability density function as having 2 spikes at the slits and zero elsewhere. That's perfectly possible solution for position and can be interpreted either as an electron passing through both slits, or as an electron that had chance to pass through one of the slits or the other. If you stop thinking about the electron as macro particle having defined position and start thinking of it as if it has only wave-function defined all the time then you can understand why it "interferes" with itself. The electron changes its wave-function from what it was before passing through slits to what it is after passing through them. And when you calculate that function and then calculate the momentum probability density function you will see it is wave-like with all sorts of maximums and minimums. Putting screen behind the slits just confirms that calculation.

 

[arkajad]

The wave-function depends on how the particle is interacting. In your example there are 2 interactions (measurements). First is the interaction at the slits.

I would rather distinguish a measurement from an interaction. If passing through the slits was to give us some additional actualization of what is only potential, that would additionally influence time evolution. Passing through the slit is described by a standard potential. It is just an interaction, not a measurement. Measurement always results in irreversible macroscopic change. If we would make the slits to register something about the passing electron - that would cause additional changes in pattern on the screen.

 

[DrChinese]

How is it that there are time differences though anyway? Now I have a hard time understanding the probability for particle detection on screen for location AND time.
The wave-function represents the value of the electron that if squared gives the probability, but it is not like a ripple-tank that pumps ripples on the water, it is a single wavefront, it is a single electron.

Just to make it clear, how does the single electron gives the probability that is proportional to wave-intensity in a ripple tank?

It may help to picture the probability function as being "real". It evolves "as if" it is a physical effect, and this explains the observed results over a series of trials.

 

[etamorphmagus]

How is it that there are time differences though anyway?[?QUOTE]

This would have to take us beyond what is considered to constitute the mainstream physics.

Maybe in a nutshell?

The wave-function depends on how the particle is interacting. In your example there are 2 interactions (measurements). First is the interaction at the slits. There the particle is measured for position. Any macro object will pass either through left or through right slit (if the slits are big enough). That is not the case with the electron. You can draw its position probability density function as having 2 spikes at the slits and zero elsewhere. That's perfectly possible solution for position and can be interpreted either as an electron passing through both slits, or as an electron that had chance to pass through one of the slits or the other. If you stop thinking about the electron as macro particle having defined position and start thinking of it as if it has only wave-function defined all the time then you can understand why it "interferes" with itself. The electron changes its wave-function from what it was before passing through slits to what it is after passing through them. And when you calculate that function and then calculate the momentum probability density function you will see it is wave-like with all sorts of maximums and minimums. Putting screen behind the slits just confirms that calculation.

I know what it means that the electron interferes with itself. I imagine 2 waves propagating through the slits, and when the 2 waves first reaches the screen there are 2 points that the wave touches the screen on. You see what I mean? The probability is on those 2 points at first!
But if you let the waves propagate for some time and THEN you use THAT interference map, that is what you see on the screen for real as a distribution.

 

[DrChinese]

I know what it means that the electron interferes with itself. I imagine 2 waves propagating through the slits, and when the 2 waves first reaches the screen there are 2 points that the wave touches the screen on. You see what I mean? The probability is on those 2 points at first!
But if you let the waves propagate for some time and THEN you use THAT interference map, that is what you see on the screen for real as a distribution.

When you perform the experiment, you consider some time window. You cannot really say "when" the wave originated and "when" it arrived. If you could, you would be obtaining information and that might color the results so that there is no interference.

 

[arkajad]

Maybe in a nutshell?

In an nutshell: you need an extension of QM that would allow you to describe the behavior of an individual system under a continuous observation and not only tell you about averages of quantum observables after an infinite number of instantaneous measurements.

 

[Upisoft]

I would rather distinguish a measurement from an interaction. If passing through the slits was to give us some additional actualization of what is only potential, that would additionally influence time evolution. Passing through the slit is described by a standard potential. It is just an interaction, not a measurement. Measurement always results in irreversible macroscopic change. If we would make the slits to register something about the passing electron - that would cause additional changes in pattern on the screen.

It depends what you call measurement. If you call measurement something that gives you knowledge only of single real value, then you are correct. In my terms measurement means "obtaining information". And passing the electron through the slits definitely has this effect.

 

[arkajad]

And passing the electron through the slits definitely has this effect.

No, You do not get any additional information that you did not have before. Unless you change your experiment in such a way as to obtain an additional information. Such a change would then influence the interference pattern.

 

[Upisoft]

No, You do not get any additional information that you did not have before. Unless you change your experiment in such a way as to obtain an additional information. Such a change would then influence the interference pattern.

Of course you do obtain information. At slits you cannot have just any position probability density function. It must be function that has 2 peaks at the slits and zero elsewhere. That limits possible wave-functions after the slit. Knowing these limits means obtaining information.

 

[arkajad]

You do not get any additional information. The new information that you did not have before performing the experiment. If you do get - it is that the fact that you did not get any - which is the same as no information at all.

 

[Upisoft]

You do not get any additional information. The new information that you did not have before performing the experiment. If you do get - it is that the fact that you did not get any - which is the same as no information at all.

If you did not get any information you have no basis to distinguish between 1-slit and 2-slit. Therefore the final result should be the same. But in reality you can tell the difference, therefore you obtain information.

 

[arkajad]

When you set the experiment to have one slit - you know it has one slit. When performing the experiment it is rather rare that you get a second slit - unless your electron is energetic and makes a new hole in your equipment.

 

[Upisoft]

When you set the experiment to have one slit - you know it has one slit. When performing the experiment it is rather rare that you get a second slit - unless your electron is energetic and makes a new hole in your equipment.

And how could you know how many slits are there if you cannot obtain information from it? And if you are able to obtain information and you are able to know how many slits are there when you set up your experiment, what makes you special and deny the electrons the ability to obtaining that information?

 

[arkajad]

what makes you special and deny the electrons the ability to obtaining that information?

I know nothing about electrons obtaining information. I believe we are making experiments with electrons, but who know - maybe they are making experiments with us? But that would take us in a sf area - outside of the bounds of this forum.

 

[Upisoft]

I know nothing about electrons obtaining information. I believe we are making experiments with electrons, but who know - maybe they are making experiments with us? But that would take us in a sf area - outside of the bounds of this forum.

Making sarcastic comments will not help us to progress in understanding each other.

How do you obtain information about the slits? One simple way is to look at them. There is light source emitting photons which then interact with the subject of our argument (barrier with one or two slits in it). Then they being reflected from it and carrying some information (according me) or not carrying any information (according you) hit your retina making some picture. Then the brain processes that image and abstracts the carried information as 1-slit or 2-slits depending what you are looking at. There is clearly information in the image on your retina as the brain is able to process it and then making it abstract and distinguishing the two cases.

If you are correct and the photons do not carry any information from the interaction, then the information is created at the moment when the photons hit your retina. Where does come that instant information from?

 

[arkajad]

Making sarcastic comments will not help us to progress in understanding each other.

I did not notice any effort from your side of understanding my arguments.

What I am stressing is that there is a difference between a measurement and an interaction. If there would be any - the concept of measurement would be unnecessary. Moreover, I want to stress that measurements are being dome without any whatsoever participation of human beings. Very often human beings learn about the results of these measurements thousands of years later (like measurements of the Earth magnetic field).

But I am not going to insist on these points or continue to argue.

 

[Upisoft]

I did not notice any effort from your side of understanding my arguments.

What I am stressing is that there is a difference between a measurement and an interaction. If there would be any - the concept of measurement would be unnecessary. Moreover, I want to stress that measurements are being dome without any whatsoever participation of human beings. Very often human beings learn about the results of these measurements thousands of years later (like measurements of the Earth magnetic field).

But I am not going to insist on these points or continue to argue.

Thank you for making a positive effort. Now I understand where our misunderstanding lies. Difference between a measurement and an interaction is the difference between classical and quantum information. Probably you consider only classical information as being information, while I consider them both. There is some correlation between them. The classical information seems to be a macro effect of the quantum information.

For example you cannot learn if there is 1-slit or 2-slits by simply sending and observing one photon, you need a lot of them to create an image on your retina. You cannot observe the interference if you send only one electron as well, you will need a lot of them.

This also reflects on the information you obtain. In the case of measurement you get information about single real value (the perfect case when you can measure the value with 100% certainty). In the case of interaction you get information about some real function (or perhaps complex function - I'm not quite sure about that).

 

[etamorphmagus]

When you perform the experiment, you consider some time window. You cannot really say "when" the wave originated and "when" it arrived. If you could, you would be obtaining information and that might color the results so that there is no interference.

Ok Dr.Chinese that would solve the problem. This is clearly uncertainty on time.

But it has nothing to do with the time-energy relation for particle decays now, is it?

This time indeterminacy makes sense in the QM world, but what is it connected to? I never saw anyone talk about the point I made here, which is kinda crucial and fundamental.

Thanks.

 

[etamorphmagus]

As a follow up to my last comment + more visual representation of my thoughts:

* I know there is no such thing as a "probability wave" consider this a pulse in the wave function, something like that.

[PLAIN]http://img839.imageshack.us/img839/4782/problem1.gif

Note: I do not speak of the interference of waves, that is obvious, just of the mechanism.

 

[DrChinese]

Consider the initial setup and the final context. There are a large (infinite?) number of ways the photon could travel (and there is interference). So one of these paths is "selected" at random. The time issue is not really relevant in the sense you imply. It is not a series of decisions, each a fraction of a second after the other. One path could be a nanosecond. Another could be many years (say to a nearby star).

 

[etamorphmagus]

Consider the initial setup and the final context. There are a large (infinite?) number of ways the photon could travel (and there is interference). So one of these paths is "selected" at random. The time issue is not really relevant in the sense you imply. It is not a series of decisions, each a fraction of a second after the other. One path could be a nanosecond. Another could be many years (say to a nearby star).

Fine, initial setup and end result! the end result has to be created somehow, and that somehow is the propagating wave-function. does it travel as a wave? yes, or else it wouldn't be called that and wouldn't interfere. I want to understand how the interference map gets to the screen, what I drew was a propagating probability wave, so what's the problem? and what infinite paths? I'm talking about those getting to the detector.

And why not series of decisions? the wave gets to the screen. That means that some probability for finding that particle there exists - if you decide to measure - which you do. So if it is not detected, it will in the next roll or the next roll. Or are you saying time has no relevance here? It is all instantaneous? special relativity for photons and 0 distance 0 time?