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In quantum mechanics time is a classical background parameter and the flow of time is universal and absolute. In general relativity time is one component of four-dimensional spacetime, and the flow of time changes depending on the curvature of spacetime and the spacetime trajectory of the observer. How can these two concepts of time be reconciled?

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They already are reconciled in some sense, in Quantum Field Theory, where time and space are placed on equal footing. But of course this is only the union of Special Relativity and quantum theory, not General Relativity. In QFT we work with a fixed metric background and deal with Lorentz transformations, and this works extraordinarily well in regimes where gravity is weak. We can even do QFT in curved spacetimes to make predictions about Hawking radiation or inflationary physics, but this is only an approximation of a full theory of quantum gravity. We don't yet have this full theory of quantum gravity which incorporates GR and QFT.

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It is immediately reconciled at low speeds. There is no need to go to quantum gravity whatsoever and also not even to quantum mechanics. If you check how time is understood in classical mechanics, you already can convince yourself that time in such regime is absolute, thus I believe you are trying to understand this difference. You can then later go to QM mechanics without change since the relevant parameter here is speed, not sizes.

We have a theory we trust at all speeds (not all scales), namely general relativity which reduces locally to special relativity (SR). On the other side we have (classical or quantum) mechanics where we speak about lower speeds, where we use a Newtonian notion of time (absolute), in other words there is always a laboratory frame where time flows.

The reason why time must become a part of space-time at higher speeds has to do with (the speed of light being the same in all frames) the specific form of the Lorentz transformations, which mixes space with time. If you take the limit of low speeds you will be able to neglect such term and therefore conclude that all frames will share the same time coordinate. You obtain then equations which are again symmetric under Galilean transformations and thus time becomes absolute again to all observers.

To sum up, at low speeds time becomes again absolute, meaning it is not mixed in a complicated way with space components and allowing all frames to share the same time variable. This in turn means your equations will reduce properly to those treating time as an external parameter.

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  • $\begingroup$ To be clear, we can do quantum physics at high speeds with Lorentz transformations & all etc, it's just QFT. I know you know this, but it wasn't present in the answer. $\endgroup$
    – Eletie
    Commented Dec 23, 2020 at 11:57
  • $\begingroup$ I believe the question is addressing the different apparent nature of time that exist. There is no need to use any QFT effects to understand why relativity reduces to an absolute time flow at low speeds, thus also matching with classical mechanics where the treatment is already absolute. So for this question QM is playing no role, I will extend the answer to make this point clear. $\endgroup$
    – ohneVal
    Commented Dec 23, 2020 at 12:02

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