The answer to this question may play the crucial role in dissolving the black hole information loss paradox. Indeed, this paradox results from the apparent conflict between the quantum deterministic principle and Hawking’s black hole radiation, which suggests that since the final quantum state of a physical system falling into a black hole will be mixed (thermal), the information about the initial quantum state of the system will disappear when the black hole evaporates. In other words, the complete information about the quantum state of this system at the initial point in time cannot determine the system’s final quantum state. So, does quantum determinism break down in a process, in which a black hole forms and then evaporates completely?
Article The Computational Limit to Quantum Determinism and the Black...
I am not sure about the limit of determinism of a quantum but for me in-determinism of QM is limitless.
However, there is a precise value (I don't remember it although it can be found in the works of L. Diosi 1985), which is normally regarded as a micro-to-macro divide avoiding localization problems of macro objects. Wonder what happens if one takes a gravitational lump of Penrose and test the information loss paradox.
As I know it very well:-
The limit of quantum mechanics, if Planck constant (h =0) become zero, so that quantum mechanics change to classical mechanics / Newtonian Mechanics.
Contrary to popular believe, quantum theory is deterministic (or it is so according to the majority of the interpretations of it). Being a differential equation (first order in time and second in space), the Schrödinger equation describes the deterministic evolution of the quantum state of a physical system, meaning it determines the system’s future state from the present in a deterministic, predictable manner.
Only during the measurement process an initial coherent superposition of states of the system leads to a definite but unpredictable outcome that cannot be described by a deterministic time evolution.
Nevertheless, even this cannot be considered as a breakdown of quantum determinism since according to decoherence program it is possible to recover the information about the initial coherent superposition lost from the system to the environment by computing with the help of the Schrödinger equation the system’s exact total quantum state.
In contrast to that, during the process of gravitational collapse, quantum determinism breaks down and so information is irretrievably lost. This is especially frustrating because such a loss of information is a direct consequence of relatively non-controversial calculation based on semiclassical gravity that has nothing to do with a quantum treatment of the space–time degrees of freedom, i.e. a quantum theory of gravity.
This is in nutshell the black hole information loss paradox, which in spite of tremendous efforts of many prominent theorists remains unresolved.
Arkady Bolotin:
Yes, you are right being a differential equation with given initial data Schrodinger equation correctly predict the outcome.
But what to do with a deterministic evolution? which only makes sense when one measures or observes it ... Of course in mathematics solutions of differential equations exist even if no one try to find them ... In a decoherence program finding the total quantum state of a system exactly is subject to favorable hypothetical conditions that might not be physically attainable ...
I would need to see those non-controversial calculations that reveal break down of quantum determinism in a gravitational collapse. Could you please give me the references?
Yes, I can. I can point you right to one of the original papers originated the information loss paradox:
Hawking S. Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D, 14, 2460,1976.
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