A non-physicist's question on the double-slit experiment

[Quotidian]

OK this question comes from a late-night discussion, er, argument, about the famous double-slit experiment. One of the interesting facts about the double-slit experiment is that the interference pattern that appears on the screen doesn't seem to be affected by the rate at which electrons are fired through the slits. So, even if the electrons (or photons? does it matter?) are fired one at a time, an interference pattern still occurs.

So the question that came up in the argument (and we're all non-physicists, by the way), is whether this means the rate of the discharge of particles doesn't effect the pattern. So whether they're discharged one electron at a time, or at a faster (or is that 'higher'?) rate, then you still get the same pattern.

That was the point of contention in the debate, but none of the participants have enough knowledge of physics to resolve it, so I thought I would bring it here and ask some people who really would know. Thanks.

 

[BvU]

rate of the discharge of particles doesn't effect the pattern.

Correct. The probability of arriving somewhere on the screen is what counts.

 

[Quotidian]

OK - so you could set up the experiment at various rates, and produce the 'interference pattern', and then send a copy of the patterns to a physicist, and the physicist wouldn't be able to deduce the rate at which the particles were fired?

Also - what is that rate? Is it amplitude, or wattage, or something like that? (Sorry if it's a dumb question.)

 

[Mentz114]

OK - so you could set up the experiment at various rates, and produce the 'interference pattern', and then send a copy of the patterns to a physicist, and the physicist wouldn't be able to deduce the rate at which the particles were fired?

Also - what is that rate? Is it amplitude, or wattage, or something like that? (Sorry if it's a dumb question.)

To get the an interference pattern that builds up the individual objects in the 'ensemble' must be identically prepared. A different ensemble, for instance having higher energies per particle, will give a different interference pattern. The gaps/bands will be smaller.

 

[Quotidian]

But you could prepare it in such a way that the interference pattern would remain the same regardless of the rate at which the particles are fired?

 

[BvU]

Yes. 24 hours at 1 per second would give the same pattern as 1 second of 86400.

 

[Quotidian]

Interesting! So energy is a significant variable - if you vary the energy, you vary the resulting pattern - but rate is not. Would that be a valid conclusion, all else being equal?

 

[DrClaude]

Interesting! So energy is a significant variable - if you vary the energy, you vary the resulting pattern - but rate is not. Would that be a valid conclusion, all else being equal?

Yes, but only up to the point where the rate is so high that the interaction between different electrons can no longer be neglected.

 

[Quotidian]

Right! But for some range, the effect is independent of the rate. That makes sense.

So, if you don't mind, a related question. Explanations of the double-slit experiment often show interference patterns in water, to convey the idea of what an 'interference pattern' is:

Would it be possible to emulate the 'rate-independence' of the interference pattern in a water tank? I am thinking that it would not, on the grounds that there is nothing like 'a quantum of water', and so the 'rate' can't be varied in respect of water - only the energy can be varied. Would that be correct?

 

[DrClaude]

Would it be possible to emulate the 'rate-independence' of the interference pattern in a water tank? I am thinking that it would not, on the grounds that there is nothing like 'a quantum of water', and so the 'rate' can't be varied in respect of water - only the energy can be varied.

In the water wave analogy, it is the amplitude of the wave that is related to the rate in the QM case, while the frequency of the source producing the wave is related to the energy in the QM case. There is no "one particle at a time" equivalent for a classical wave.

 

[Quotidian]

Thanks, these replies have been very helpful. The fact that the effect can't be replicated by a physical (water) wave is, I think, due to the interference pattern not actually being 'waves' as such, but something for which the interference patterns of waves is just an analogy.

24 hours at 1 per second would give the same pattern as 1 second of 86400.

The argument that started this was about whether this means that time (being 'rate') is not a factor; which also that means that space (i.e. proximity of particles) is not a factor (as proximity is an aspect of space-time.) So, what is causing the interference pattern is outside, or not a function of, space-time.

 

[DrClaude]

The argument that started this was about whether this means that time (being 'rate') is not a factor; which also that means that space (i.e. proximity of particles) is not a factor (as proximity is an aspect of space-time.) So, what is causing the interference pattern is outside, or not a function of, space-time.

Sorry, but this is gobbledygook.

 

[Quotidian]

Can you explain why? It seems to follow, why doesn't it?

 

[DrClaude]

The argument that started this was about whether this means that time (being 'rate') is not a factor;

Time is not a factor in the sense that the pattern can be accumulated very slowly. So long as the particles cannot interact with each, it doesn't matter how long it takes one particle to go through the double slit apparatus before the next one enters.

which also that means that space (i.e. proximity of particles) is not a factor (as proximity is an aspect of space-time.)

That's a non-sequitur. The fact that time is not a factor has no relation to the fact that space is a factor.

So, what is causing the interference pattern is outside, or not a function of, space-time.

This is where the gobbledygook really is. What does it even mean that the "interference pattern is outside space-time"? The particles move in space-time. The double slit and the detector are in space-time. There is nothing outside of space-time. And there is no need to introduce the relativistic concept of space-time to understand or describe anything that is happening here.

 

[Quotidian]

Well, that was what the argument was about - this is what I came here to resolve. The rate at which the particles are fired doesn't effect the distribution pattern (within limits as explained above). So isn't 'rate' a function of 'time'? So, the particles move in space-time, but the resulting pattern is not affected by the rate at which they're fired.

 

[DrClaude]

Well, that was what the argument was about - this is what I came here to resolve. The rate at which the particles are fired doesn't effect the distribution pattern (within limits as explained above). So isn't 'rate' a function of 'time'? So, the particles move in space-time, but the resulting pattern is not affected by the rate at which they're fired. Whatever it is, that is causing the interference pattern is n

A simple way to see it is that it means that each particle is interfering with itself, not with other particles.

 

[Quotidian]

I don't see how that is any less 'gobbledegook' than what I said. Maybe because it is text-book googledegook?

 

[DrClaude]

I don't see how that is any less 'gobbledegook' than what I said. Maybe because it is text-book googledegook?

I used the word "gobbledygook" because I think it described well what you wrote. You are using technical terms in a way that does not make sense.

 

[Quotidian]

Thanks. I will try again.

As was said above, '24 hours at 1 per second would give the same pattern as 1 second of 86400'. The output (i.e. distribution pattern) and all other factors are equal. There is only one variable in the scenario, which is 'rate'. So this shows that whatever is causing 'the interference pattern' is not a function of the rate.

 

[DrClaude]

No, the interference pattern does not depend on the rate. (Just to be clear: the interference pattern only becomes apparent when a lot of particles have been measured.)

 

[Quotidian]

That is basically all I wanted to establish, so I won't try and engage in further amateur philosophising about it! But this thread has been very helpful, and thanks for it.