25 pages; for 'Everett @ 50,' S. Saunders, J. Barrett, A. Kent, D. Wallace (eds.), Oxford, 2009. Revised version involves some clarification in the formulation and minor corrections
We argue that the intractable part of the measurement problem -- the 'big' measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the 'truthmaker' for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the 'big' measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW 'collapse' theorists who add structure to the theory and propose dynamical solutions to the 'big' measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.
About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper and, following Frauchiger and Renner, I show that the Everett interpretation leads to modal contradictions in 'Wigner's-Friend'-type scenarios that involve 'encapsulated' measurements, where a super-observer (which could be a quantum automaton), with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures th…
Quantum Mechanics (QM) has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of quantum phenomena. Today, even though we have reached a standardized version of QM which is taught in Universities all around the world, there is still no consensus regarding the conceptual reference of the theory and, if or if not, it can refer to something beyond measurement outcomes. In this work we will argue that the reason behind the impossibility to reac…
Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement problems (simply called the big and the small measurement problems), with a different degree of relevance and, second, that the analysis of a quantum measurement is a problem only if other assumptions, taken by Pitowsky and Bub to be unnecessary 'dogmas', are assumed. Here I critically discuss this unconventional stance on the measurement problem and argue that…
In recent works, Časlav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the interpretation, they sharpen and clarify it.
The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here that these three theorems are valid for classical mechanics with a nonstandard kinetic energy. This brings some information about the connections between the quantum and classical worlds. Constraints about the functional form of the kinetic energy are also discussed.
The Hatsopoulos-Gyftopoulos resolution of the Schroedinger-Park paradox about the concept of "state" in quantum statistical mechanics
在量子统计力学的现有公式中（以及在其量子信息理论解释中），一个很少被认识到的基本困难破坏了个体“状态”的概念。这个困难是E.薛定谔在1936年和仔细阅读J. L。公园，上午。《物理学杂志》，第36卷，211（1968）。为了解决这个问题，我们要么拒绝不健全的状态概念，要么认真地重新表述量子理论和统计学的作用。我们重申了困难，并讨论了1976年G.N. Hatsopoulos和E. P. Gyftopoulos，创始物理学家，第6卷，15，127，439，561（1976）中所述。
We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field.
We bring together two topics (quantum mechanics and time passage) with the goal of clarifying questions about each. Specifically, we claim that the formalism of quantum mechanics provides an answer to the question: "What is time passage?".
We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt regarding whether or not the hermiticity of the hamiltonian operator is sufficient to justify a simplification of the expression of the macroscopic-observable time derivative that promotes the one usually found in quantum-mechanics textbooks. The study develops by considering the simple quantum system "particle in one-dimensional box". We propose theoretical arguments to support the incompleteness of the Ehrenfest's theorem in the formulation he gav…
We discuss the epistemological features of the Ghirardi, Rimini and Weber proposal to modify quantum mechanics in order to overcome the objectification problem, that means the transition between the quantum and the classical level of description of natural phenomena. We shall show that the GRW is a realistic theory, but in a way quite different from Einstein realism or other kinds of realism proposed in the past, such as the Many World Interpretation or the Bohmian Mechanics.
What is the quantum system? Consider the wavefunction of the electron, what we call single particle wave-function and assume that it contains N wave packets. If we pass all the wave packets through an electric field, all are deflected, as if each one of them contains an electron. However, if we bring any two wave packets to travel close to one another, they do not repel one another, as if at least one of them contains no charge. In trying to solve the measurement problem of the quantum mechanics (QM), different interpretations were proposed, each one coming with a particular ontology. However,…
To investigate the dynamical behavior of a quantum system embedded in a memory environment, it is crucial to obtain the knowledge of the reservoir spectral density. However, such knowledge is usually based on a priori assumptions about the environment. In this paper, we put forward a method to obtain key information about the reservoir spectral density of an optomechanical resonator without additional assumptions about the spectral shape. This is achieved by detecting and analysing the optical transmission rate of the emitted light. In the weak optomechanical singlephoton coupling regime, we e…
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a "quantum theory without observers," alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics fo…
Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations, translations, and dilations are quotiented out. This reformulation of mechanics naturally leads to a relational notion of time as well, in which a history of the universe is just a curve in shape space without any reference to a special parametrization of the curve given by an absolute Newtonian time. When relational mechanics (classical or quantum) is regarded as f…
In this paper the detailed investigation of one of the most interested models in the non relativistic quantum mechanics of one massive particle i.e., introduced by G. Poeschl and E. Teller in 1933 is presented. This model includes as particular cases two most popular and valuable models: the quasi free particle in the box with impenetrable hard walls (i.e., the model with confinement) and Bloch quantum harmonic oscillator, which is unconfined in space; both models are frequently and effectively exploited in modern nanotechnology e.g., in quantum dots and magnetic traps. We give the extensive a…
In this comment we answer to the recent critique of our article [arXiv:2208.11793] about Relational Quantum Mechanics (RQM) by Aurélien Drezet [arXiv:2209.01237]. Here we point out that our critical analysis of RQM was precisely based on the most recent formulation of RQM, and that the theses found in the critique are based on neither RQM assumptions nor on our arguments.
In the mid-19th century, both the laws of mechanics and thermodynamics were known, and both appeared fundamental. This was changed by Boltzmann and Gibbs, who showed that thermodynamics can be *derived*, by applying mechanics to very large systems, and making simple statistical assumptions about their behavior. Similarly, when Quantum Mechanics (QM) was first discovered, it appeared to require two sets of postulates: one about the deterministic evolution of wavefunctions, and another about the probabilistic measurement process. Here again, the latter is derivable from the former: by applying u…
The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas from the gedankenexperiment of Wigner's friend it has been argued that, when combined with the assumptions of locality and no-superdeterminism, regarding a measurement as an absolute event is incompatible with the universal validity of quantum mechanics. We consider a weaker assumption: is the measurement event realised relatively to the observer when he only …
Brukner and Pienaar have critiqued the Relational Quantum Mechanics of Rovelli, and together with Di Biagio, the latter has replied. I point out a few places where, in my view, that reply needs clarification.
A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review and compare several realist interpretations of the wave function. They fall into three categori…
