Quantum Mechanics: Myths and Facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.     

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t+dt. An important quantity is the ratio of the probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity Γ ₁/Γ ₂, where Γ ₁ and Γ ₂ are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value Γ ₁/Γ ₂ and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case.     

Outline of a Generalization and a Reinterpretation of Quantum Mechanics Recovering Objectivity

The ESR model has been recently proposed in several papers to offer a possible solution to the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mathematical framework and reinterpreting quantum probabilities as conditional on detection rather than absolute. We provide a new and more general formulation of the ESR model and discuss time evolution according to it, pointing out in particular that both linear and nonlinear evolution may occur, depending on the physical environment.     

Quantum Field Theory and Dense Measurement

We show, using quantum field theory (QFT), that performing a large number of identical repetitions of the same measurement does not only preserve the initial state of the wave function (the Zeno effect), but also produces additional physicaleffects. We first discuss the Zeno effect in the framework of QFT, that is, as a quantum field phenomenon. We then derive it from QFT for the general case in which the initial and final states are different. We use perturbation theory and Feynman diagrams and refer to the measurement act as an external constraint upon the system that corresponds to the perturbative diagram that denotes this constraint. The basic physical entities dealt with in this work are not the conventional once-perfomed physical processes, but their n times repetition where n tends to infinity. We show that the presence of these repetitions entails the presence of additional excited state energies, and the absence of them entails the absence of these excited energies.     

Locality and Measurements Within the SR Model for an Objective Interpretation of Quantum Mechanics

One of the authors has recently propounded an SR (semantic realism) model which shows, circumventing known no-go theorems, that an objective (noncontextual, hence local) interpretation of quantum mechanics (QM) is possible. We consider here compound physical systems and show why the proofs of nonlocality of QM do not hold within the SR model, which is slightly simplified in this paper. We also discuss quantum measurement theory within this model, note that the objectification problem disappears since the measurement of any property simply reveals its unknown value, and show that the projection postulate can be considered as an approximate law, valid FAPP (for all practical purposes). Finally, we provide an intuitive picture that justifies some unusual features of the SR model and proves its consistency.     

Fundamental Problems in the Unification of Physics

We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues.     

Quantum Information in Relativity: The Challenge of QFT Measurements

Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.     

Estimating perturbative coefficients in high-energy physics and condensed matter theory

Using our method to estimate perturbative coefficients in quantum field theory (QFT), we consider several examples in high-energy physics and condensed matter theory. The results, in all cases, are remarkably good for the known terms. We also predict the values of as yet unknown terms. Moreover, we consider the general convergence properties of asymptotic series in QFT.     

Remarks on some new models of interacting quantum fields with indefinite metric

We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic models obtained by analytical continuation from some stochastic processes with Euclidean invariance. As a first step towards scattering theory in indefinite metric QFT, we give a proof of the spectral condition on the translation group for the relativistic models.     

Empirical consequences of the scientific construction: The program of local hidden-variables theories in quantum mechanics

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality.     

Quantum Machine and Semantic Realism Approach: a Unified Model

The Geneva–Brussels approach to quantum mechanics (QM) and the semantic realism (SR) nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general assumptions, and show that Aerts’ quantum machine can be embodied into a macroscopic version of the microscopic SR model, overcoming the seeming incompatibility between the two models. This result provides some hints for the construction of a unified perspective in which the two approaches can be properly placed.     

Minimal Length Effects on Schwinger Mechanism

In this paper,we investigate effects of the minimal length on the Schwinger mechanism using the quantum Geld theory(QFT) incorporating the minimal length.We Grst study the Schwinger mechanism for scalar Gelds in both usual QFT and the deformed QFT.The same calculations are then performed in the case of Dirac particles.Finally,we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length.     

Where is an object before you look at it?

According to the standard interpretation of quantum mechanics (QM), no meaning can be assigned to the statement that a particle has a precise value of any one of the variables describing its physical propertes before having interacted with a suitable measuring instrument. On the other hand, it is well known that QM tends to classical statistical mechanics (CSM) when a suitable classical limit is performed. One may ask therefore how is it that in this limit, the statement, meaningless in QM, that a given variable has always a precise value independently of having been measured, gradually becomes meaningful. In other words, one may ask how can it be that QM, which is a theory describing the intrinsically probabilistic properties of a quantum object, becomes a statistical theory describing a probabilistic knowledge of intrinsically well determined properties of classical objects.In the present paper we try to answer to this question and show that an inconsistency arises between the conventional interpretation of CSM which presupposes objectively existing Newtonian trajectories, and the standard interpretation of QM. We conclude that the latter needs revisiting unnless we wish to adopt a strictly subjective conception of the world around us, implying that macroscopic objects as well are not localized anywhere before we look at them.     

Is Quantum Mechanics Incompatible with Newton’s First Law?

Quantum mechanics (QM) clearly violates Newton’s First Law of Motion (NFLM) in the quantum domain for one of the simplest problems, yielding an effect in a force-free region much like the Aharonov-Bohm effect. In addition, there is an incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. A general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. Alternatives to the Schrödinger equation are considered that might avoid this problem. The meaning of the classical limit is examined. Critical views regarding QM by Schrödinger, Bohm, Bell, Clauser, and others are presented to provide a more complete perspective.     

Theory for frequent measurements of spontaneous emissions in a non-Markovian environment: Beyond the Lorentzian spectrum

The measurement-result-conditioned evolution of a system(e.g., an atom) with spontaneous emissions of photons is described by the quantum trajectory(QT) theory. In this work we generalize the associated QT theory from an infinitely wide bandwidth Markovian environment to the finite bandwidth non-Markovian environment. In particular, we generalize the treatment for an arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove the general existence of a perfect scaling behavior jointly defined by the bandwidth of the environment and the time interval between successive photon detections.For a couple of examples, we obtain analytic results to facilitate the QT simulations based on the Monte-Carlo algorithm. For the case where the analytical result is not available, a numerical scheme is proposed for practical simulations.     

Analog of Formula of Total Probability for Quantum Observables Represented by Positive Operator Valued Measures

We represent Born’s rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born’s rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.     

Minimal Coupling in Koopman-von Neumann Theory

Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 1930s. They basically formalized, via the introduction of a classical Hilbert space, earlier work of Liouville who had shown that the classical time evolution can take place via an operator, nowadays known as the Liouville operator. In this paper we study how to perform the coupling of a point particle to a gauge field in the KvN version of CM. So we basically implement at the classical operatorial level the analog of the minimal coupling of QM. We show that, differently than in QM, not only the momenta but also other variables have to be coupled to the gauge field. We also analyze in detail how the gauge invariance manifests itself in the Hilbert space of KvN and indicate the differences with QM. As an application of the KvN method we study the Landau problem proving that there are many more degeneracies at the classical operatorial level than at the quantum one. As a second example we go through the Aharonov-Bohm phenomenon showing that, at the quantum level, this phenomenon manifests its effects on the spectrum of the quantum Hamiltonian while at the classical level there is no effect whatsoever on the spectrum of the Liouville operator.