Can the wave function be considered a real wave?

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ajv
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In QM, the wave function is a wave in hilbert space. But is it possible that it is a physical wave in physical space? I think that there are a few interpretations/theories of QM that describe it as a physical wave.
 

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What exactly do you mean by "physical wave"?
 
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And what exactly do you mean by "physical" space? How many dimensions the physical space is supposed to have?
 
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