One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.
One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown by Bell [1] and Kochen-Specker [2], quantum mechanics portrays a picture of the world in which reality loses its objectivity and is in fact created by observation. Quantum mechanics predicts phenomena which cannot be explained by any theory with objective realism, although our everyday experience supports the hypothesis that macroscopic objects, despite being made of quantum particles, exist independently of the act of observation; in this paper we identify this behavior as classical. Here we show that this seemingly obvious classical behavior of the macroscopic world cannot be experimentally tested and belongs to the realm of ontology similar to the dispute on the interpretations of quantum mechanics [3,4]. For small systems such as a single photon [5] or a pair [6], it has been experimentally proven that a classical description cannot be sustained. Recently, there have also been experiments that claim to have demonstrated quantum behavior of relatively large objects such as interference of fullerenes [7], the violation of Leggett-Garg inequality in Josephson junction [8], and interference between two condensed clouds of atoms [9], which suggest that there is no limit to the size of the system on which the quantum-versus-classical question can be tested. These behaviors, however, are not sufficient to refute classical description in the sense of objective reality. Our findings show that once we reach the regime where an Avogadro number of particles is present, the quantum-versus-classical question cannot be answered experimentally.
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.
Quantum mechanics was developed in the early 20th century as a computational algorithm to organize and predict the strange results of a wide variety of experiments involving the microscopic world (molecules, atoms, elementary particles), which appeared random but had a predictable probabilistic distribution. Despite its overwhelming success, the conceptual foundations of this algorithm remain unclear and extremely controversial. How can we connect the microscopic world described by quantum mechanics with the macroscopic world of our daily experience? What is the role of observers in this connection? Why don't strange quantum phenomena occur on macroscopic scales? How can we explain the nonlocal nature of quantum phenomena? In this article I will present some attempts to answer these and other basic questions, which constitute different theories with completely different worldviews, commenting on their strengths and weaknesses. We will conclude that quantum theory is still under construction, as there is no consensual formulation. Its development is a fundamental problem in contemporary physics, and in thought in general.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment.
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.
After the review by Hauge and Stovneng the old question of "How long does it take to tunnel through the barrier?" has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed scattering (OCS). In this paper we show that this seemingly simple question stands alongside with such fundamental problems of quantum mechanics (QM) as the Schrodinger's-cat and and EPR-Bohm paradoxes. Their common feature is that the states of a scattered particle, a radioactive atom and electron EPR-pair represent pure {\it micro-cat} states. It is widely accepted that the EPR-Bohm paradox implies the non-existence of local hidden variables (LHVs), the cat paradox represents a macro-objectification problem and the tunneling time is an observer-dependent quantity whose definitions must be 'operational'. At the same time, according to the probabilistic approach (Accardi, Khrennikov, Philipp, Hess {\it et al.}) to Bell's inequality that underlies the EPR-Bohm experiments, its experimental violation means simply that it contains probability distributions associated with mutually incompatible statistical data. We argue that this approach must be extended onto micro-cat states because they describe, too, mutually incompatible statistical data. The current practice to interpret the squared modulus of a micro-cat state as the probability density should be recognized as erroneous. It is this practice that makes QM incompatible with classical physical theories and, thereby, makes the micro-world 'unspeakable'. The known 'operational' tunneling-time concepts, elaborated in line with this practice, are logically inconsistent. We argue that the TTP and the cat paradox must be solved at the level of single electrons and atoms, without resorting to environment and measurement contexts. We present a new model of the OCS and solve the TTP on its basis.