In Search For The True Relationship Between General Relativity And Quantum Mechanics
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Despite huge research efforts, the relation between the two big theories of the 20th century – General Relativity and Quantum Mechanics is still not clearly understood. The idea that all interactions are fundamentally quantum, albeit extremely successful with all non-gravitational interactions, seems to fail in case of gravitation as we are still far away from a convincing quantum theory of gravity. Therefore any insight into how our two fundamental theories of Nature interrelate is of a great value.

Less understood of the two is quantum mechanics. Especially the mechanism which connects quantum mechanics with our everyday life world, the so-called quantum-to-classical transition. It embraces such well-known problems as wave-function collapse, the measurement problem, and Schroedinger’s cat problem. One prominent approach, gaining recently more and more popularity, to deriving our classical world from the first principles of quantum theory is decoherence theory. In brief, it acknowledges that isolated systems are only idealizations of real-life situations, where each system interacts with an environment, for example, is illuminated by light. It is then this interaction with the environment and inability to observe the whole of the environment which can lead to a suppression of certain quantum features (coherences) and effectively to a classical behavior of the system in question.

Decoherence, although a powerful tool, does not, however, solve all the problems. For example, it does not explain the objective character of the everyday world. This aspect has been pioneered by W. H. Zurek and collaborators under the quantum Darwinism idea, which is a more elaborate and realistic form of decoherence. In essence, it says that to become objective, information about the system, e.g. its position, must be stored in many, perfectly readable copies in the environment (redundant encoding). The idea has been further developed by the Gdańsk group, which uniquely identified a quantum state structure responsible for this form of objectivity and known as Spectrum Broadcast Structure (SBS). The power of this result lies in the fact that the philosophical notion of objectivity becomes expressed very precise and rigorously in the language of quantum states. This opens a possibility that the objective character of the world is in a sense some specific property of quantum states.

What we studied in our work is a theoretical, gravity-induced decoherence mechanism proposed by I. Pikovski and collaborators [Pikovski I et al. 2015, Nature Phys., 11, 668]. The basic idea is that gravitational field may be responsible for decoherence and thus in a sense drive the quantum-to-classical transition. The idea itself is not new and was proposed some time ago by L. Diosi [Diosi L 1987, Phys. Lett. A 120, 377] and then by R. Penrose [Penrose R 1996, Gen. Relativ. Gravit. 28, 581]. However, the modern take on it is qualitatively new as it does not require an immediate departure from the usual, linear Schroedinger equation, which governs the evolution of quantum systems. And this linearity is in fact at the core of the quantum theory, responsible for many of its peculiar phenomena, e. g. quantum entanglement.

The idea of Pikovski et al., called time-dilation decoherence, is strikingly simple: Since time flows differently at different heights in gravitational field (e. g. that of the Earth, a fact experimentally established with a fantastic precision), then a bunch of harmonic oscillators placed in the gravitational field will have different periods at different heights. This, in turn, creates a height-period correlation, which in turn leads to decoherence of the center-of-mass (CM) of the oscillators if we are unable to observe each of them individually. As an example, one can think of a large molecule with many oscillatory degrees of freedom which we do not observe but only monitor the molecule’s CM position in the gravitational field. Easily said, harder done – putting this idea into rigorous form requires some non-trivial and rather brave steps. The resulting mechanism is rather weak due to the weak nature of the gravitational interaction and thus requires a large number of internal degrees of freedom, say 1023.

However, as we mentioned earlier, decoherence alone cannot explain all of the classical features. We, therefore, asked a question if the time-dilation decoherence leads to some form of objectivization? For that, we studied if and how information about the center-of-mass height is transferred to the internal, oscillatory degrees of freedom. As the tool we used the SBS structures mentioned above, as the description on the level of quantum states they provide is the most fundamental we have.

As a result, we found that indeed the gravitation-mediated decoherence leads to the redundant encoding of the height information in large groups of internal degrees of freedom, at least for short times. This information is then in principle accessible to independent observers, which can extract it without disturbing neither the CM position nor their partners. All this leads to a certain form of objectivity of the CM height – many observers can find it out without a disturbance. As we mentioned, the studied gravity-induced decoherence and objectivization mechanism is at this stage only a theoretical proposal. Whether it is an actual phenomenon of Nature or not must be verified in an experiment.

These findings are described in the article entitled Information transfer during the universal gravitational decoherence, published in the journal General Relativity and Gravitation. This work was led by Jarek Korbicz and Jan Tuzimski from the Gdańsk University of Technology.

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