Now I would like to apply the reasoning of the last post to the case of verifying macroscopic superpositions of the metric. It’s been 4 years since I’ve touched GR, so I’m going to rely heavily on E&M concepts and pray I don’t miss any key changes in the translation to gravity.
In the two-slit experiment with light, we don’t take the visibility of interference fringes as evidence of quantum mechanics when there are many photons. This is because the observations are compatible with a classical field description. We could interfere gravitational waves in a two-slit set up, and this would also have a purely classical explanation.
But in this post I’m not concentrating on evidence for pure quantum mechanics (i.e. a Bell-like argument grounded in locality), or evidence of the discrete nature of gravitons. Rather, I am interested in superpositions of two macroscopically distinct states of the metric as might be produced by a superposition of a large mass in two widely-separated positions. Now, we can only call a quantum state a (proper) superposition by first identifying a preferred basis that it can be a superposition with respect to. For now, I will wave my hands and say that the preferred states of the metric are just those metric states produced by the preferred states of matter, where the preferred states of matter are wavepackets of macroscopic amounts of mass localized in phase space (e.g. L/R). Likewise, the conjugate basis states (e.g. L+R/L-R) are proper superpositions in the preferred basis, and these two bases do not commute.
There are two very distinct ways to produce a superposition with different states of the metric: (1) a coherent superposition of just gravitational radiation [continue reading]
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