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Consistent description of microscopic phenomena by macroscopic observers in quantum theory

Alexey A. Kryukov

Published May 12, 2021• 0 citations
Publisher

Abstract

Abstract Quantum mechanics is the foundation of modern physics that is thought to be applicable to all physical phenomena, at least in principle. However, when applied to macroscopic bodies, the theory seems to be inconsistent. Wigner's friend and related thought experiments demonstrate that accounts by different observers described by the rules of quantum mechanics may be contradictory. Although still highly debated, such experiments seem to demonstrate an incompatibility of quantum mechanics with the usual rules of logic. Alternatively, one of the hidden assumptions in the thought experiments must be wrong. For instance, the argument is invalidated if macroscopic observers cannot be considered as physical systems described by the rules of quantum theory. Here we prove that there is a way to apply the rules of quantum mechanics to macroscopic observers while avoiding contradictory accounts of measurement by the observers. The key to this is the random noise that is ever present in nature and that represents the uncontrollable part of interaction between measured system and the surroundings in classical and quantum physics. By exploring the effect of the noise on microscopic and macroscopic bodies, we demonstrate that accounts of Wigner, the friend and other agents all become consistent. Our result suggests that the existing attempts to modify the Schrodinger equation to account for measurement results may be misguided. More broadly, the proposed mechanism for modeling measurements underlies the phenomenon of decoherence and is shown to be sufficient to explain the transition to Newtonian physics in quantum theory.

DOI
10.21203/rs.3.rs-501056/v1

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Abstract Quantum mechanics is the foundation of modern physics that is thought to be applicable to all physical phenomena, at least in principle. However, when applied to macroscopic bodies, the theory seems to be inconsistent. Wigner's friend and related thought experiments demonstrate that accounts by different observers described by the rules of quantum mechanics may be contradictory. Although still highly debated, such experiments seem to demonstrate an incompatibility of quantum mechanics with the usual rules of logic. Alternatively, one of the hidden assumptions in the thought experiments must be wrong. For instance, the argument is invalidated if macroscopic observers cannot be considered as physical systems described by the rules of quantum theory. Here we prove that there is a way to apply the rules of quantum mechanics to macroscopic observers while avoiding contradictory accounts of measurement by the observers. The key to this is the random noise that is ever present in nature and that represents the uncontrollable part of interaction between measured system and the surroundings in classical and quantum physics. By exploring the effect of the noise on microscopic and macroscopic bodies, we demonstrate that accounts of Wigner, the friend and other agents all become consistent. Our result suggests that the existing attempts to modify the Schrodinger equation to account for measurement results may be misguided. More broadly, the proposed mechanism for modeling measurements underlies the phenomenon of decoherence and is shown to be sufficient to explain the transition to Newtonian physics in quantum theory.
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios.
It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce a variant of the Wigner's friend experiment in which a multiparticle quantum system is observed by the friend. The friend undergoes rapid decoherence through her interactions with the environment. In the usual version of this thought experiment, decoherence removes the need for Wigner to treat her as a quantum system. However, for our variant we prove theoretically and observe experimentally that there exist partitions of the subsystems in which the friend is entangled with one of the particles in assistance with the other particle, as observed by Wigner. Importantly, we show that the friend is indispensable for the entanglement to be observed. Hence Wigner is compelled to treat the friend as part of a larger quantum system. By analyzing our scenario in the context of a quantum key distribution protocol, we show that a semi-classical description of the experiment is suboptimal for security analysis, highlighting the significance of the quantum description of the friend.
We briefly review the difficulties of the standard version of quantum mechanics in accounting for all kinds of physical processes (in particular both the micro and the macroscopic ones) and we argue that to overcome such difficulties one has to give up the superposition principle, i.e., to break the linear nature of the theory. We then show that the simple introduction of terms violating the linearity of the deterministic evolution of the standard theory has physically unacceptable consequences. Taking this into account we are led to modify the quantum dynamics by adding to Schrödinger’s equation, besides nonlinear terms, a coupling with an appropriate noise. We show that, with such a move, one can work out a theory which is internally consistent and it allows to account, in a quite simple and physically appealing way, for natural processes including the measurements and the classical behavior of macroscopic bodies. On the basis of our analysis, we are led to conclude that the consideration of the noise represents a crucial element for understanding the laws of nature.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.
By assuming (i) a universal, observer-independent quantum state, by considering (ii) measurement processes with wave function collapse as part of quantum mechanical time evolution (also within isolated systems), and by (iii) clearly distinguishing the state of a quantum system from the knowledge of conscious observers about this state, we suggest a modified Copenhagen interpretation of quantum mechanics that resolves Wigner's Friend and extended Wigner's Friend paradoxes. The suggested interpretation leads to differences in some outcome probabilities compared to previous analyses which, in principle, make it possible to falsify the suggested modifications or the previous analyses (or both). The fundamental problem of the incompleteness of quantum mechanics in the Copenhagen interpretation regarding the lack of a precise definition and a mechanistic description of the measurement process (including the collapse of the wave function) is not addressed in this study. However, the argumentation regarding the resolution of Wigner's Friend paradoxes also applies to attempts for such a mechanistic description using collapse models with stochastic extensions to the Schrödinger equation or trying to model wave function collapse with unitary time evolution and irreversibility of the measurement process resulting from quantum statistical mechanics.