I think that relativity and quantum mechanics would provide some good examples.
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4If you want it CW, you have to flag it for moederator attention. Anyway, even as a CW question I don't really this is a real question... What's the point listing results in various fields of physics that one consider "counter-intuitive" ? – Cedric H. Nov 05 '10 at 11:18
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I agree with Cedric H. The question as stated is completely subjective. "Most counter-intuitive" is really a matter of personal taste. – j.c. Nov 05 '10 at 14:38
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@Cedric: The point is that it collects some of the most interesting problems in physics. If you are unconvinced, look at the equivalent question on Math.StackExchange http://math.stackexchange.com/questions/250/a-challenge-by-r-p-feynman-give-counter-intuitive-theorems-that-can-be-transl – Casebash Nov 05 '10 at 22:32
2 Answers
gets straight from equations, but it is hard to believe it works in reality.

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8@Steve Do you know someone who would intuitively predict the second part of this experiment without knowing the theory? For me, this is a definition of intuitiveness. – Nov 05 '10 at 13:06
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well the time revesality could be expected in any non chaotic system, as well as for example the first law of Newton tells us to expect that a body not subjected to any force, if in motion, will keep going forever.. since we live in a friction world, that does not mean that after a was maybe 4 y.o. i could not intuitively predict what would happen in a no friction condition – Steve Nov 05 '10 at 13:16
If you mean things I'm still scratching my head about, starting from the largest scale, it might be that we, life, the earth, the universe, (in Douglas Adam's words, "everything") is here at all. Different levels of the "Why something rather than nothing question" I suppose, but that's already too defined. We have only developed theories e.g. probability theory on branching trees, quantum chemistry, cosmology in the last 200 years to even partially explain the phenomenology. If someone told you the story from afar, your initial reaction would have to be "No way!" You could say it's not physics (no math and way too broad), but it's definitely physical phenomena.
For something smaller, quantum phenomena, e.g. quantization of spin axis. Is it as Zeilinger suggests ultimately because the electron spin carries only one bit of information?

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2One day my physics prof said that he'd been giving some thought to the problem of existence, and that he'd have a proof ready for the next class. He never showed up again. I've always wondered if that was the point... :-) – Bob Jarvis - Слава Україні Sep 16 '14 at 23:26
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I agree with the heart of your answer, and I won't place the question outside of physics, but it is precisely a question physics has no answer to now, so not really a result... As a side comment, I would argue against saying there is no math behind the question, quite the contrary! – G. Bergeron Oct 19 '17 at 01:36