The Penrose interpretation of quantum mechanics…
…states that the mass of a system affects the system’s ability to maintain quantum coherence. This is the basis for some theories of quantum gravity. Above the Planck mass, which is ~1E-8kg, a system can no longer maintain coherence for any measureable time, due to the onset of gravitational interactions.
This has been irritating me for a while. Let’s think about superconductors: Does the effective ‘mass’ of the superconducting condensate affect the coherence time of it’s macroscopic wavefunction?
1 mol of a metal contains ~ 6e23 conduction electrons
which have a mass of ~ 5e-7 kg
which is greater than the Planck mass. But I don’t see any reason why a macroscopic superconducting wavefunction cannot be established in a large single crystal of a material such as Niobium/Lead/Aluminium. You can demonstrate the Meissner effect with a huge lump of superconductor:
I haven’t been able find much information about this. Maybe that’s why I think I’m just being dumb here. So I guess the question would be: Is there a fundamental limit on the size of a superconducting macrocopic quantum wavefunction? Does the distribution of mass affect the wavefunction, i.e. are the gravitational effects seen by the QM wavefunction on average reduced by the distributed mass of the surrounding condensate? Does superconductivity, being a collective phenomenon, somehow negate the entire thing? I don’t know the answer to this problem so I thought I’d throw it out there 🙂