By revisiting two famous questions concerning the Copenhagen interpretation of quantum mechanics, this article presents a concise analysis of the quantum measurement problems with measuring both microscopic and macroscopic objects. The method used here is mainly based on the concept ``isolated point'' in ``point-set topology''. The findings reported are as follows. (a) Einstein's argument has been misunderstood; he was opposed to the so-called ``inherently probabilistic nature'' attached by the Copenhagen interpretation to quantum mechanics rather than to the use of probability in quantum mechanics. (b) Probability used in Einstein's ensemble interpretation is identical to the quantum-mechanically calculated probability. (c) The wave-functions in Einstein's ensemble interpretation neither describe any single quantum object purportedly possessing mutually exclusive properties simultaneously when nobody looks nor collapse abruptly when an observer performs a measurement.
By revisiting two famous questions concerning the Copenhagen interpretation of quantum mechanics, this article presents a concise analysis of the quantum measurement problems with measuring both microscopic and macroscopic objects. The method used here is mainly based on the concept isolated point'' in point-set topology''. The findings reported are as follows. (a) Einstein's argument has been misunderstood; he was opposed to the so-called ``inherently probabilistic nature'' attached by the Copenhagen interpretation to quantum mechanics rather than to the use of probability in quantum mechanics. (b) Probability used in Einstein's ensemble interpretation is identical to the quantum-mechanically calculated probability. (c) The wave-functions in Einstein's ensemble interpretation neither describe any single quantum object purportedly possessing mutually exclusive properties simultaneously when nobody looks nor collapse abruptly when an observer performs a measurement.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.
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 measurement problem in quantum mechanics has been a cause of much puzzlement over the years. The very idea of having two different versions of reality for the same system has been a cause for much debate. Often quantum mechanics textbooks follow the ‘shut up and calculate’ paradigm. This denies the opportunity for the common student to understand the consequence of one of the most elegant and beautiful aspects of science. The state of the art textbooks give a purely algebraic, perfunctory and monotonous approach where the real consequence of the system is not fully appreciated. A good reason for this is the considerable deviation of the quantum mechanical process from the commonsensical idea of truth, reality and reason. We tend to look at the world in a materialistic, deterministic, causal and objectivistic way. We tend not to accept a world of contradictions. A quantum measurement is essentially an amalgamation of contradictions, mystery and duality. It encompasses an implicit dependence on subjectivity and contradicts with causality as we know it. We look at the world as in the present. But a quantum mechanical measurement is a prediction of the future influenced by the observer or the measurer. This offers a philosophical and pedagogical conundrum. It poses a challenge on not just how our perception of the world might change in addition to providing a big challenge on how to make it compatible with the other successful theories of physics. The most common text book interpretation of quantum mechanics has been the Copenhagen Interpretation suggests the ‘collapse of the wave function’ as a mechanism of transition between duality. But a more bizarre yet elegant theory, extending quantum formalism to the classical domain, called the Many Worlds Interpretation has been catching up very quickly; it stands for the split of the universe when we make a quantum mechanical measurement. Consequently, reality as we is redefined as a universal wave function which is a superposition of several outcomes, which is incompatible with many of the successful concepts of physics and has several problems like the correct idea about probability or basis. We adapt the idea of the universal wave function, but instead suggest a continuum interpretation of quantum mechanics where the universal wave function represents the entire singular universe and the concept of atoms or electrons as conceptually a continuous part of it rather than a distinct separate entity. Such an interpretation could be compatible with other continuum theories like the Superfluid vacuum theory or the Higgs Field.
The foundations of quantum mechanics are reconsidered in relation to the measurement problem. We define two kinds of quantities. The type A quantities are observables obtained experimentally from a single measurement. A dynamical variable is a type A quantity whose measurement selects a set of eigenvalues (EVs) as c-numbers. The type B quantities represent theoretical quantities related to probabilities. State vectors, the wave function, and the probability distribution (PD) are type B quantities. They are derived from an eigenvalue equation such as the Schrödinger equation. A quantum jump (QJ) is the measurement of a dynamical variable to select a set of EVs. The wave function is a theoretical quantity that persists throughout an experiment and therefore does not collapse. After a QJ, a selected set of EVs persists until it becomes macroscopic. However, an eigenstate is a theoretical notion irrelevant to a single measurement and does not exist in reality after a QJ. One experiment is complete when an ensemble of EVs has been obtained and compared with the theoretically predicted PD. To obtain an ensemble, repeated measurements are required in general, but there are some exceptions, like a Bose-Einstein condensate system, for which a single measurement yields a real ensemble.
By revisiting two famous questions about the Copenhagen interpretation of quantum mechanics, this article presents a concise analysis of the quantum measurement problem concerning both microscopic and macroscopic objects. The method used here is mainly based on the concept ``isolated point'' in ``point-set topology''. The findings reported are as follows. (a) Einstein's argument has been misunderstood; he was opposed to the so-called ``inherently probabilistic nature of quantum mechanics'' in the Copenhagen interpretation rather than to the use of probability in quantum mechanics. (b) Probability used in Einstein's ensemble interpretation is identical to the quantum-mechanically calculated probability. (c) The wave-functions in Einstein's ensemble interpretation neither describe any single quantum object purportedly possessing mutually exclusive properties simultaneously when nobody looks nor collapse abruptly when an observer performs a measurement.
The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ``yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter \ensuremath{\epsilon} that quantitatively describes the degree of decoherence. Its value ranges from \ensuremath{\epsilon}=0 (which describes the case in which the two waves are perfectly coherent) to \ensuremath{\epsilon}=1 (which describes the case in which coherence is totally lost); for this reason \ensuremath{\epsilon} is named the ``decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex \ensuremath{\delta} potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit \ensuremath{\epsilon}=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.