Abstract
In this paper, I present a new analysis of the meaning of the phase in quantum mechanics. First, I give a simple but rigorous proof that the global phase is not real in \(\psi\)-ontic quantum theories. Next, I argue that a similar strategy cannot be used to prove the reality of the global phase due to the existence of the tails of the wave function. Finally, I argue that the relative phase is not a nonlocal property of two regions together, and adding a relative phase to one local branch of a superposition only changes the local properties at the boundary of the region of the branch.
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Notes
For example, if the \(\psi\)-epistemic view requires that two wave functions that differ only in the global phase are compatible with the same ontic state or physical state, then it will be obvious that the global phase is not real, since the two wave functions that differ in the global phase do not represent different physical states.
If the wave function is complete, then the wave function uniquely determines the physical state, and thus different physical states cannot be represented by the same wave function. If the wave function is not complete and there are hidden variables, different physical states that include the same hidden variables cannot be represented by the same wave function either.
Locality for product states says that for two systems being in a product state, the ontic state of one system (e.g. a particle) in one region is not affected by the other system in the other region (e.g. a system which implements a unitary transformation there) via action at a distance, and it holds true in existing \(\psi\)-ontic quantum theories such as Bohmian mechanics, the many-worlds interpretation and collapse theories of quantum mechanics [5].
Since the density and the flux density can be measured locally for an ensemble of identically prepared systems, the relative phase can also be measured locally (cf. [6]).
References
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Acknowledgements
I wish to thank Dustin Lazarovici, Lev Vaidman and David Wallace for helpful discussion. This work was supported by the National Social Science Foundation of China (Grant No. 16BZX021).
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Gao, S. Why the Global Phase is Not Real. Found Phys 54, 19 (2024). https://doi.org/10.1007/s10701-024-00754-w
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DOI: https://doi.org/10.1007/s10701-024-00754-w