Space in quantum mechanics seems to be modeled as a triplet of real numbers, i.e. a continuum. Same happens in special relativity. General relativity I do not know (nor field theories). And then we apply the Pythagorean theorem and triangle inequality and so forth...(adsbygoogle = window.adsbygoogle || []).push({});

I have a few general questions:

1) Is space (3d or Minkowski) theonlycontinuum?

If a quantum mechanical operator describing an observable has a continuous spectrum (partially at least),

i.e. the observable is allowed to take, in principle, real values,

then is this always an end result of the assumption that space is continuous?

Or are there seemingly continuous observables that are not related to space?

An example: Bound electrons in a hydrogen atom have discrete spectra, both theoretically and experimentally, but free ones have seemingly continuous, and the Coulomb law plays a role there theoretically, and the fact that space would be a continuum.

2) Is it so that based on experiments, space in QM can always be assumed to have locally euclidean metric?

Thanks

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# Observables vs. continuum and metric?

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