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Suppose one were to perform the same quantum mechanical experiment - say the double slit experiment or any other quantum mechanical experiment with identical conditions, set ups and elements - while providing a mechanism to isolate the systems from ambient conditions, allowing the only varying condition to be the height at which each of the experiments are performed, one closer to Earth and the other far away from it, just like when performing a gravitational time dilation or gravitational redshift experiment.

What are the possibilities that this height variation would actually reveal the difference between the influence of gravitational potential of Earth at different heights on the quantum state involved in the experiment?

DanielFBest
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Precious Adegbite
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The fundamental problem with quantum gravity does not lie in the way that quantum mechanical systems do behave in gravitational fields. In fact, as I am aware, one can do quantum-field-theoretical calculations in curved spacetime. The calculations are messy and impractical, as with most quantum- or many-particle- or many-particle-quantum-theories, but there is no problem with building the fundamental theory when it comes to QM in curved space time.

The problems arise when concerned with the gravitational fields created by the quantum particles themselves, which does not appear to be something which your vaguely described procedure would be expected to yield any insights for.

Still, experimenting with quantum mechanics at different levels of external gravitational influence is a legitimate way of testing current theories and a desirable thing to observe, which I am sure is and has been done before. It is not expected to yield any fundamental new insights though, in particular none about quantum-gravity.

Vincent Thacker
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Zaph
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Just adding to the correct answer of @Zaph:

Many quantum mechanisms absolutely operate at different rates in different gravity wells. I can't picture what might be different in a Double Slit experiment at a different height, as that experiment doesn't commonly include a time component.

Not sure if you realize that the global GPS system is actually a demonstration of the effect of gravity at different altitudes on quantum systems. It does "actually reveal the difference between the influence of gravitational potential of earth at different heights" which are crucial to the proper functioning of the system.

Other things change too. The half life of radioactive isotopes, for example.

DrChinese
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