Why when not observed in the double slit experiment, do we see light in places we do not see light when observed?

Question

The double slit experiment with a single electron provides a different result when observed and when unobserved. When unobserved we see an interference pattern, and when observed we just see 2 lines. When the experiment is unobserved we see an interference pattern at all points, e.g exactly between the 2 slits we may see a fringe, but when observed there is nothing there.

If when observed and the wave function is collapsed, the wave function stays collapsed, that would explain this result. When collapsed the photon behaves instead like a particle, meaning that it does not diffract around the slit but can only travel in a straight line. Unfortunately, this doesnt seem to be correct. A google search says that the wave function is only briefly collapsed (distance of 1 hydrogen atom), so the photon should go back to acting as a wave.

Is the reason just that the common illustrations are exaggerated and there is less of a obvious 2 line pattern?

Answer 1

When unobserved we see an interference pattern, and when observed we just see 2 lines. When the experiment is unobserved [...] e.g exactly between the 2 slits we may see a fringe, but when observed there is nothing there.

That's not true, though it's a common mistake. Here's an incorrect picture of the experiment from Sean Carroll's blog:

Here's a correct illustration from The Feynman Lectures:

What you get when there's a detector at one or both slits is the sum of $I_1$ and $I_2$, and what you get without a detector is $I_{12}$. Note that $I_1+I_2$ is large wherever $I_{12}$ is large; in fact, $I_{12} \le 2(I_1+I_2)$ everywhere. So it's not possible for a point on the screen where there is almost no light when the detector is present to receive a large amount of light when the detector is absent.

Answer 2

It does not matter that the thing you are studying is a photon, so I will speak of the general particle.

There is no Hamiltonian whereby position localisation are eigenfunctions (but somewhat spread out ones are, e.g. QHO, H atom solutions, etc). As long as you have travelling solutions, they would be somewhat wavy.

When you perform a localisation observation on the particle, the eventual evolution of the particle will look as if it were to start from a wavefunction that was localised to the place you looked at. In this case, that is one of the slits. The particle would behave as if it were everywhere in that one slit, and nowhere else. Then it will propagate as a wave from then on.

That is how we are supposed to get two Gaußian spreads, what you call as two lines. Those are not sharp lines, but the important part is that you do not see the interference pattern of many peaks and troughs. The lack of interference pattern is particularly obvious.

It can be exaggerated, as in, it can be one big blob with a slight variation in brightness, but it is not too exaggerated. You can sometimes see the two lines separately. The important part is, again, that you do not see the interference fringes.

Answer 3

I think we need to clarify what do you mean by "observed". The outcome of the two-slit experiment is the same regardless if you look at it or not. The only thing that matters is the experimental setup.

If you want to know which slit the particle passed through you need to place some sort of detector at the slits. This modified setup, with detectors at the slits would not generate an interference pattern. I assume that you have such a setup in mind when you refer to an "observed" experiment.

OK, so we have two different experiments, Experiment 1 consisting of a particle source, a barrier with two slits and a screen and Experiment 2 consisting of a particle source, a barrier with two slits, two detectors placed at the slits and a screen.

The pattern we see on the screen is determined by the way the incoming electrons interact with the barrier. In the Experiment 1 the barrier does not have detectors and some electrons are scattered between the slits. In the Experiment 2 the barrier has detectors and no electron is scattered between the slits. We can therefore conclude that the presence of those detectors is causing the electrons to change their paths.

I don't think that imagining the electron as changing from a particle to a wave and back is the right way to think about what happens, since such a change needs to be non-local (the wave needs to "collapse" instantly at a point) which is in conflict with relativity.

Answer 4

I agree that the Double Slit (DS) with photons is conceptually similar to the DS with an electron (or other quantum particle types). However, there are experimental & theoretical variations on the DS with photons that cannot be easily performed for other particle types. And this gives us more insight. Let's take the case of photons one at a time to build up a pattern, and vary our knowledge of "which slit" information. We CAN do this without affecting the total number of photons which will hit the screen.

As you know, the general rule is that if you could NOT know which slit the photon goes through, there will be interference. If you could know which slit the photon goes through, there will NOT be interference. It does not matter if you actually know the which slit information, it is enough that you could know it. And it is possible to vary continuously between these two extremes and get corresponding variation in the pattern (i.e. a mixture of interference and no interference).

The method we consider is when we place polarizers over each slit. a) If the polarizers are aligned parallel, there WILL be interference. b) If the polarizers are aligned orthogonal (crossed, perpendicular), there will NOT be interference. Parallel: it is NOT possible to extract which slit information. Orthogonal: it IS possible to extract which slit information. Either way, 50% of the photons will be blocked by the polarizers. So the total light detected remains constant.

Also, you may choose to look at the b) scenario as follows: there can be no interference between the slits if they are sending through the "portion" of the possible "paths" (for lack of a better description - insert your preferred description here) that are themselves now orthogonal. By definition pretty much, these cannot self interfere. Of course they can self interfere in the a) scenario.

Note that there is no mention of "collapse" or "localization". There is no need to refer to point particles or similar. So yes with a "*"; the answer is that in the DS with photons (or whatever), detection will occur much greater in some places when there is self-interference ("unobserved") than when there is no such interference ("observed"). As pointed out by @benrg, the diffraction that occurs when there is no self-interference places some light everywhere. So it might be more accurate to say: When observed, we see light in places we do not see when unobserved. You can compare Figures 8 and 9 in the experimental reference below to see this is the case. References:

Theory: Polarized Light https://books.google.com/books?id=w6PMBQAAQBAJ&pg=PA271&lpg=PA271&dq=double+slit+interference+polarizers+Fresnel&source=bl&ots=MumGUCvweh&sig=7wit8bq5xXkunYoHpnbB3hL3YXw&hl=en&sa=X&ved=0CB0Q6AEwAGoVChMI-tm_ueGNyQIVBigeCh1SLwwt#v=onepage&q=double%20slit%20interference%20polarizers%20Fresnel&f=false

Experiment: Young’s double-slit experiment with single photons and quantum eraser https://sciencedemonstrations.fas.harvard.edu/files/science-demonstrations/files/single_photon_paper.pdf

Answer 5

The double slit experiment is a mostly a thought experiment, intended to illustrate the wave and particle properties of particles/light. There exist some literal physical realizations of such experiments, but most discussions are still aim at being pedagogical, rather than taking into account all the possible effects that may take place. In this sense, quantitative statements like the wave function is only briefly collapsed (distance of 1 hydrogen atom), so the photon should go back to acting as a wave are generally out of context.

When discussed as an experiment with electrons, the experiment simply aims at showing the interference: how electrons, classically thought of as particles, actually represent wave properties, if described quantum mechanically.

Light, on the other hand, is classically a wave, which exhibits interference and diffraction. Notably, diffraction can be even observed with a single slit/pinhole/whatever (image source):

What makes double slit experiment special in case of light is when the light intensity is very low (so low that photons pass one by one) - in which case the interference pattern may vanish, demonstrating that photon is a particle. (Note that saying photons pass one by one makes sense only after we proved that photon is a particle.) There is nothing wrong with photon still interfering from a single slit - the interference pattern is clearly different from the light passing through two slits.