In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather possesses profound physical underpinnings. Based on the equivalence, we give a possible solution to the quantum measurement problem. We describe quantum measurement process as two-step physical process: one microscopically controllable process which generates an entanglement between the system being measured and a marking system (or property), and one macroscopic process (uncontrollable microscopically) which detects states (or properties) of the marking system. With the solution, we conclude that the measurement postulate is just a corollary of the completeness of quantum states. Our solution is entirely rooted in the traditional formalism of quantum mechanics, requiring no extensions or modifications to it. We also point out that quantum randomness originates from entanglement, and the collapse of the wave function is a subjective process.
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather possesses profound physical underpinnings. Based on the equivalence, we give a possible solution to the quantum measurement problem. We describe quantum measurement process as two-step physical process: one microscopically controllable process which generates an entanglement between the system being measured and a marking system (or property), and one macroscopic process (uncontrollable microscopically) which detects states (or properties) of the marking system. With the solution, we conclude that the measurement postulate is just a corollary of the completeness of quantum states. Our solution is entirely rooted in the traditional formalism of quantum mechanics, requiring no extensions or modifications to it. We also point out that quantum randomness originates from entanglement, and the collapse of the wave function is a subjective process.
In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.
The description of physical systems obtained in the classical limit of quantum mechanics is not consistent with the one given by classical statistical mechanics. In qantum mechanics the complete description of a physical system is given by specifying the wave function, which evolves completely deterministically. Probability comes into play only when a measurement is made. Classical statistical mechanics, on the contrary, concerns systems whose description is not complete and where probability enters as a consequence of a lack of knowledge. We show that Nelson's stochastic mechanics, whose predictions are identical with those of quantum mechanics, provides nevertheless a unified description of the deterministic and random aspects of quantum mechanics which eliminates the inconsistency outlined above and gives a simple and satisfactory solution to the measurement problem.
The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrodinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrodinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually.
The quantum measurement problem—why and how the deterministic, unitary evolution of quantum states gives rise to definite, stochastic outcomes—has remained unresolved since the inception of quantum mechanics. This paper proposes that wave function reduction is not a separate physical process requiring its own postulate, but an instance of Level-0 projection within the Quantum Blueprint Formalism (QBF). The QBF Level-0 framework describes the constrained transition from a pre-coherent space M_s of distinction configurations to a coherence manifold M_Θ of macroscopic order parameters, governed by three admissibility conditions: local compatibility (A1), preserved Heisenberg structure (A2), and bounded compression (A3). We demonstrate that quantum state reduction exhibits the same formal structure: it is a constrained projection from Hilbert space (possibility space) to eigenstate space (actuality space), subject to conditions structurally isomorphic to (A1)–(A3).
The measurement problem in quantum mechanics (QM) is related to the inability to include learning about the properties of a quantum system by an agent in the formalism of quantum theory. It includes questions about the physical processes behind the measurement, uniqueness, and randomness of obtained outcomes and an ontic or epistemic role of the state. These issues have triggered various interpretations of quantum theory. They vary from refusing any connection between physical reality and a measurement process to insisting that a collapse of the wave-function is real and possibly involves consciousness. On the other hand, the actual mechanism of a measurement is not extensively discussed in these interpretations. This essay attempts to investigate the quantum measurement problem from the position of the scientific consensus. We begin with a short overview of the development of sensing in living organisms. This is performed for the purpose of stressing the relation between reality and our experience. We then briefly present different approaches to the measurement problem in chosen interpretations. We then state three philosophical assumptions for further consideration and present a decomposition of the measurement act into four stages: transformation, conversion, amplification and broadcasting, and, finally, perception. Each of these stages provides an intuition about the physical processes contributing to it. These conclusions are then used in a discussion about, e.g., objectivity, the implausibility of reversing a measurement, or the epistemic status of the wave-function. Finally, we argue that those in favor of some of the most popular interpretations can find an overlap between their beliefs and the consequences of considerations presented here.
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The formulation is fully relativistic and applicable to multi-particle systems. It shall be shown that this new formulation makes the same experimental predictions as quantum field theory, but without having to rely upon the notion of a system evolving in a superposition of quantum states until collapsed by an observation. It is thus free from the problem of deciding what exactly constitutes an observation (the measurement problem) and may therefore be applied just as readily to the macroscopic world as to the microscopic.