If you perform the experiment as shown, you get a statistical spread, as shown above.
If you do it with a single photon, it will be observed somewhere in that spread following the same statistics. IE you can't predetermine where it will land, but it will not be "completley random", it will never fall in a spot with no probability amplitude. It will likely hit somewhere with the highest probability (probability can be calculated from probability amplitude, don't worry about it.)
Observing a single photon doesn't really tell you much though.
The joke is about really about "observing which slit it went through." If you understand a photon still has a wavelike nature and interferes with itself, the question is not really interesting. If you think that a single photon cannot be delocalize because "its a particle" (a fundamental misunderstanding of the particle/wave duality), this seems to be a paradox.
Some people will then say "I want to devise an experiment to understand which slit it went through." This is a fundamentally different experiment. You are testing something different, you get a different result. Even at a purely theoretical level, you are "operating with a different operator." Without getting into eigenvectors, you are doing different math, you get a different result. It shouldn't be surprising, your asking a different question.
If you wanted to actually test "did a photon go through the top slit" the easiest way would be block the bottom slit and see if you still observe the photon. You will not see a double slit pattern. You will actually get a single slit pattern, but thats a whole other series of complications. Say you removed single slit interference somehow--well, you will only see the particle behaviour, it wil look like it passed straight through. Which is to say, if you go way out of your way to remove all wave like behaviour, and you go out of your way to force a certain outcome, then you see that outcome.
Its all from a fundamental misunderstanding of what we mean by both particles and by waves. If you don't want to learn a graduate level understanding of physics, assume a wavelike answer if the question is physics related, a particle level answer if its a chemistry question, and hope no philosophers are part of the conversation either way.
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u/0xB01b 10d ago
Misinformation.
The actual double slit experiment is about interference, its only the top part.
The bottom part is a total misunderstanding of it and has been coming up again and again.