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In a lot of interpretations of Quantum Mechanics they believe that the wave function is "real". But what does that mean? Are they saying that the wave function of an elementary particle (electron/photon) is a real wave, like a water wave, oscillating in space time?

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  • $\begingroup$ Realism is not a physical concept. Strictly speaking it's not even a scientific concept. Try to use the term "realism" in biology on "evolution". Is "evolution" real in any physical sense? Would you feel a need to conjure up an invisible "evolution field" to explain natural selection? How about an "entropy field" in thermodynamics? $\endgroup$
    – CuriousOne
    Sep 9 '15 at 23:28
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    $\begingroup$ "oscillating in space time" - wavefunctions 'live' in configuration space, not spacetime. In other words, the wave function for an N particle system lives in a 3N dimensional $(\mathbf x_1, \mathbf x_2, ..., \mathbf x_N)$ configuration space. $\endgroup$ Sep 10 '15 at 1:06
  • $\begingroup$ try looking into the work by Cavalcanti et al, sec [o] on this page ("superclassical/ emergent QM"), also another Physics question refd there $\endgroup$
    – vzn
    Sep 10 '15 at 1:08
  • $\begingroup$ @AlfredCentauri My apologies that my answer wasn't clear, I'd be happy to re-edit my post if you have suggestions about what was unclear. $\endgroup$
    – Timaeus
    Sep 10 '15 at 2:16
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No one thinks the wavefunction of nonrelativistic quantum mechanics is a wave in space and time. No one that wants to agree with observations that is.

If someone is a realist about the wavefunction of nonrelativistic quantum mechanics then they start out by making a mathematical model by having the model include a wavefunction. Which when there are $n$ particles is a function from $\mathbb R^{3n}$ into a tensor product of the spin states of every particle in the universe (there are other alternatives that are mathematically just as good). They would identify two waves that are the same except an overall nonzero complex scalar multiple.

They would then postulate that it evolves according to some dynamical laws, such as the Schrödinger equation.

They would then explain how features of the mathematical model correspond to experimental set ups and the results of experiments and observations.

Just like Newtonian mechanics might model things as a path in configuration space that satisfies a dynamical law (and maybe some other principles for when the favored dynamical laws fail) and then explain how features of the mathematical model correspond to experimental set ups and the results of experiments and observations.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Sep 10 '15 at 4:28
  • $\begingroup$ Timaeus, I suggest moving those comments to the chat room. I'll come back and delete them after a little while. $\endgroup$
    – David Z
    Sep 10 '15 at 5:05

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