Another double slit question

[Fontwell]

I find science fascinating and baffling in equal measure but I think I had a mini breakthrough moment today regarding the QM double slit experiment. I wonder if someone can confirm my thinking.

Recapping...
The experiment has the following results for patterns detected on a screen:

A full on light and a single slit gives a bright central line that fades away to the edges.

A full on light and two slits give many bands of light and dark - the result of interference i.e. not just the sum of two single slit patterns.

Single photons land in single positions for one or two slots.

Single photons accumulated over time give the same results for two slots as for when the light is full on - an interference pattern.

Single photons accumulated over time and a 'which slot did it go through' detector give rise to the same pattern as would be achieved by adding up the two individual slot patterns - no interference pattern.


So, it is explained that when a single photon meets the two slits it somehow goes through both and its position is then based on a probability wave. When it hits the screen it collapses into a specific location. That collapse is statistical and is based on the probability wave. But when there is a detector to find out which slit the photon went through, this collapses the probability wave, leaving just the pattern of the two slits added together.

Right, my mini breakthrough is this: When we see the interference pattern for two slits with the light full on, we are _not_ seeing a wave interference pattern caused by lots of light waves interfering with each other. We are still seeing the pattern caused by the collapse of individual probability waves. It is just that we are seeing the result of many individual photons having their individual probability functions collapse, all at the same time and for as long as the light shines. In fact, (breakthrough time...) it is just like a speeded up version of the single photon version. That's it!

This makes it different to how, say, water waves interact in swimming pool. For classical sized waves, the energy of the wave's impetus is spread over the whole wave all the time and it adds with the energy of other waves to make bigger peaks and deeper troughs. For the light waves, the energy of a photon might be distributed over a region but when it hits a screen it concentrates back into a small area. Also, the probability waves of different photons don't add together. Instead, the probability waves of individual photons interact with themselves due to the possibility of going through either slot.


Have I got this roughly right? Also, props to anyone prepared to read this

 

[Fontwell]

Damn, I had email notification off and I don't know how to change it with out making another post, so here is another post!

 

[edd]

No, it's really flipping hard to get two photons to unambiguously interfere with one another because basically you need them both to be basically lined up really well. It can be done though.
http://skullsinthestars.com/2008/09/12/interference-between-different-photons-never-occurs-not-1963/ seems like a good blogpost on that subject.

 

[sol invictus]

Right, my mini breakthrough is this: When we see the interference pattern for two slits with the light full on, we are _not_ seeing a wave interference pattern caused by lots of light waves interfering with each other. We are still seeing the pattern caused by the collapse of individual probability waves.

Those aren't mutually exclusive.

It is just that we are seeing the result of many individual photons having their individual probability functions collapse, all at the same time and for as long as the light shines. In fact, (breakthrough time...) it is just like a speeded up version of the single photon version. That's it!

Like edd says, different photons can and do interfere with each other under the right conditions. And in fact in many such cases, for example a laser, the distinction you're trying to draw becomes very fuzzy. A laser doesn't have a definite number of photons in it - there is quantum uncertainty in the photon number. In fact an ideal laser state is a quantum superposition of all possible photon number states (with certain special coefficients). Sent through a double slit, that wavefunction will interfere with itself and produce a diffraction pattern, but you're going to have a hard time deciding (or even defining) whether that interference is due to photons interfering with "themselves" or not.

Still, what you're saying is reminiscent of an important result in quantum mechanics called Ehrenfest's theorem, which says that quantum expectation values obey classical laws.

 

[Fontwell]

OK, I'm trying to deal with the broader mental model I have here and deal with the subtleties later. The broad model that was my breakthrough in understanding was that even in a strong light level and with two slits, what we see on the screen is a pattern caused by (or mainly by, if you must) many individual probability functions collapsing. But anyway, probability functions collapsing.

Previously my mental model was like a swimming pool model, where the waves represented EM waves (not probabilities) interfering with each other and giving the pattern on the screen due to the addition of these EM waves. The bit I could never get was how the photons 'knew' when to be like waves and when to be (a bit) like particles.

After my 'breakthrough' I now think that the photons always behave the same. They spread their probability over a region until they interact with an object, and that causes the probabilities to collapse. This gives a consistent model for all of the apparently inconsistent behaviour of the two slits.

I'm not wanting to deal with special situations and complexities yet, just check that I'm on the right lines. From what you guys have said I get the impression that, although there may be more to be added, my new mental model is a lot closer to the truth than my old one - which quite frankly didn't even make sense to me!

Thanks for the replies and link.

 

[kalen]

I think you have it basically right. What happens quantum mechanically should correspond to what we see classically in the large number limit.

(Note: that EM waves do also interfere with themselves going through a single slit. So, you don't get a bright central line that fades away monotonically to the edges, but a bright central line that goes dark-bright-dark-etc. as you look towards the edges. It's hard to see, and is something that you can normally ignore when you are looking at double slit effects.)