We have a mathematical model of physics, which includes things like superpositions of wave-functions. We don't know how or even if they map on to reality, we but do have a habit of talking equating "states" with wave-functions. Then when describing superpositions, we end up with paradoxes like your first sentence.
This goes beyond Einsteinian "the physical world is not what you thought it was" thinking, and starts challenging logic itself. If QM really did challenge logic like that, then we would have to start rebuilding every other field of thought, including even mathematics.
I think it is more reasonable to see if some lateral thinking in QM can make the seeming paradoxes go away.
That whole thinking - that states are well defined, and can be only either one or the other - that's the classic world approximation, it's not reality. You firmly believe in it because your crucial early years, when you were crawling on the floor at your parents' house, were spent in a classic-world-approximation universe. That's why it's so hard for you (and pretty much everyone else) to let go of it.
The quantum phenomena are the more fundamental reality. This classic universe that you think you understand is just an epiphenomenon. Just foam floating on the ocean.
The fundamental reality of the electron is the wave function. States, and everything else, emerge from it. It's not a corpuscle. It's not a wave. It does not behave like ping-pong balls, or like waves in a pond, although it shares a few characteristics. Fundamentally, it's something different. The only way to know that entirely different thing is via the mathematics of quantum mechanics - and whatever intuition you can derive from it after you do the math.
There is no equivalent for that stuff at the human scale of things.
This is a very simplified colloquial way of stating a concept that also makes it seem mysterious. The state of an electron is described by a vector 'v' in a 2D complex vector space. Now, to actually talk about the vector concretely you should choose a basis. Suppose your basis is one in which the vector 'v' is not parallel to any of the basis vectors. Then you can say the vector v is "somewhere in between basis vectors e1 and e2". No magic in the way I have stated it. There is a little bit of fake magic when you start thinking about the random measurement results you get when you measure the electron in state 'v'. But these effects can be simulated in a classical deterministic universe.
The real magic of quantum mechanics is in entanglement which can't be simulated in a classical deterministic universe. But that is a much longer story.
Now to answer your question, yes there is lots of physical evidence that this non-deterministic description of systems is a good model of reality. This comment box is too small to state it. People are currently in the process of determining if this probabilistic description is a good one outside of the mathematical framework of QM. See http://www.nature.com/news/quantum-physics-what-is-really-re...
Personally, I think "simultaneously points both up and down" is a terrible way to describe superpositions. So let me avoid that phrase, and see if I can rephrase your question. Would it be fair to say that you're asking this question?
> Is there any real physical evidence that an electron can be in a superposition of two states, that can only be explained using quantum mechanics?
Surprisingly, the answer to this question is yes. The evidence is the Bell experiment[1].
Mathematical frameworks that assume Quantum Systems are deterministic (only being in state A or B) during unobserved periods have never been validated by experiment. It is great if you have a model, but if that model fails to agree with experimental results.
> Is there any real physical evidence that an electron can be both states at the same time, outside the mathematical framework of QM?
Another way to respond to your question is to consider that the transistors inside the machine you used to post your comment were designed based on QM models of the electron that essentially follow from the Schrodinger Equation (e.g. via Fermi-Dirac statistics [0]).
As far as has been known since 1947, without QM it is extremely unlikely humans would ever have discovered how to build solid state semiconductor devices like the transistor. A key intrinsic feature of QM is superposition.
The double-slit experiment is a famous experiment that provides "tangible" evidence for superposition. [1]
You can't think of an electron as a little ball whose behavior is described by a weird quantum mathematical formula. The universe is really made of quantum mechanics. The electron is actually an excitation in the wave function, a fundamentally quantum object, of which "tiny ball" happens to be a lossy and flawed, but not altogether terrible description.
there are certain experimental results in quantum mechanics that only make sense if you accept things like superposition and entanglement. for example: https://www.youtube.com/watch?v=v657Ylwh-_k
Electron diffraction implies wave behaviour, and wave behaviour implies the superposition principle. Is that good enough evidence or are you looking at experiments measuring entanglement in electrons?
[+] [-] adrianratnapala|9 years ago|reply
We have a mathematical model of physics, which includes things like superpositions of wave-functions. We don't know how or even if they map on to reality, we but do have a habit of talking equating "states" with wave-functions. Then when describing superpositions, we end up with paradoxes like your first sentence.
This goes beyond Einsteinian "the physical world is not what you thought it was" thinking, and starts challenging logic itself. If QM really did challenge logic like that, then we would have to start rebuilding every other field of thought, including even mathematics.
I think it is more reasonable to see if some lateral thinking in QM can make the seeming paradoxes go away.
[+] [-] powertower|9 years ago|reply
Is there any real physical evidence that an electron can be both states at the same time, outside the mathematical framework of QM?
[+] [-] Florin_Andrei|9 years ago|reply
The quantum phenomena are the more fundamental reality. This classic universe that you think you understand is just an epiphenomenon. Just foam floating on the ocean.
The fundamental reality of the electron is the wave function. States, and everything else, emerge from it. It's not a corpuscle. It's not a wave. It does not behave like ping-pong balls, or like waves in a pond, although it shares a few characteristics. Fundamentally, it's something different. The only way to know that entirely different thing is via the mathematics of quantum mechanics - and whatever intuition you can derive from it after you do the math.
There is no equivalent for that stuff at the human scale of things.
[+] [-] abdullahkhalids|9 years ago|reply
This is a very simplified colloquial way of stating a concept that also makes it seem mysterious. The state of an electron is described by a vector 'v' in a 2D complex vector space. Now, to actually talk about the vector concretely you should choose a basis. Suppose your basis is one in which the vector 'v' is not parallel to any of the basis vectors. Then you can say the vector v is "somewhere in between basis vectors e1 and e2". No magic in the way I have stated it. There is a little bit of fake magic when you start thinking about the random measurement results you get when you measure the electron in state 'v'. But these effects can be simulated in a classical deterministic universe.
The real magic of quantum mechanics is in entanglement which can't be simulated in a classical deterministic universe. But that is a much longer story.
Now to answer your question, yes there is lots of physical evidence that this non-deterministic description of systems is a good model of reality. This comment box is too small to state it. People are currently in the process of determining if this probabilistic description is a good one outside of the mathematical framework of QM. See http://www.nature.com/news/quantum-physics-what-is-really-re...
[+] [-] justinpombrio|9 years ago|reply
> Is there any real physical evidence that an electron can be in a superposition of two states, that can only be explained using quantum mechanics?
Surprisingly, the answer to this question is yes. The evidence is the Bell experiment[1].
[1] https://en.wikipedia.org/wiki/Bell_test_experiments
[+] [-] deckar01|9 years ago|reply
https://en.m.wikipedia.org/wiki/Stern–Gerlach_experiment
[+] [-] valarauca1|9 years ago|reply
Mathematical frameworks that assume Quantum Systems are deterministic (only being in state A or B) during unobserved periods have never been validated by experiment. It is great if you have a model, but if that model fails to agree with experimental results.
[+] [-] j1vms|9 years ago|reply
Another way to respond to your question is to consider that the transistors inside the machine you used to post your comment were designed based on QM models of the electron that essentially follow from the Schrodinger Equation (e.g. via Fermi-Dirac statistics [0]).
As far as has been known since 1947, without QM it is extremely unlikely humans would ever have discovered how to build solid state semiconductor devices like the transistor. A key intrinsic feature of QM is superposition.
The double-slit experiment is a famous experiment that provides "tangible" evidence for superposition. [1]
[0] https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics [1] https://en.wikipedia.org/wiki/Double-slit_experiment
[+] [-] unknown|9 years ago|reply
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