The measurement problem in quantum mechanics has the character of a fundamental incompleteness within that theory similar to the incompleteness of axiomatic systems in mathematics, discovered and elaborated by Gödel and others. The difficulty of describing the measurement process by the time-dependent Schrodinger equation may reflect the limitations of formal language , and quantum theory may thus require a formalism consisting of two levels of description, one for the dynamics and one for measurement, levels whose relationship resembles that of a calculus and meta-calculus.
The measurement problem in quantum mechanics has the character of a fundamental incompleteness within that theory similar to the incompleteness of axiomatic systems in mathematics, discovered and elaborated by Gödel and others. The difficulty of describing the measurement process by the time-dependent Schrodinger equation may reflect the limitations of formal language , and quantum theory may thus require a formalism consisting of two levels of description, one for the dynamics and one for measurement, levels whose relationship resembles that of a calculus and meta-calculus.
The measurement problem is one of the greatest unsolved mystery of the foundations of quantum mechanics. This paper is an exploration of the underlying subtleties of this phenomenon from the standpoint of the quantum mechanical interpretations that are available to us at the moment. First, we revisit the infamous double slit experiment and contrast between the observer dependent and observer independent effects on the measurement process. In this regard, we have tried to establish a causal relationship between the observer's consciousness and the collapse of the wave function. The point is justified through the application of Godel's incompleteness theorems. Finally, we perform a thought experiment which shall validate our conclusions.
Abstract We use the Wigner’s friend story to characterize the quantum measurement problem. On the standard formulation of quantum mechanics, whether a physical system is measured determines which of the theory's two dynamical laws obtains. For this reason, the logical consistency of the theory depends on one specifying strictly disjoint conditions for when when each law obtains, which means that one needs to say precisely what constitutes a measurement. But since the term measurement occurs in the standard theory as an undefined primitive term, the theory is at best incomplete. We see precisely how this conceptual incompleteness threatens the logical inconsistency of the theory and why, on even the most charitable reading, it entails that the theory is empirical incomplete. We end by considering why its empirically incompleteness is extremely difficult to test.
Quantum Measurement problem studied in Information Theory approach of systems selfdescription which exploits the information acquisition incompleteness for the arbitrary information system. The studied model of measuring system (MS) consist of measured state S environment E and observer O processing input S signal. O considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for O derived by the algebraic QM formalism which exploits Segal and C∗-algebras. From Segal theorem for systems subalgebras it's shown that such restricted states VO=∣Oj><Oj∣ describes the classical random 'pointer' outcomes Oj observed by O in the individual events. The 'preferred' basis ∣Oj> defined by O state decoherence via O - E interactions.
Einstein's article on the EPR paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not Heisenberg's uncertainty principle, which he accepted, but the experimental non-separability of spatially separate systems. The same problem was also recognized, years later, by one of us, as part of an axiomatic analysis of the quantum formalism, which revealed an unexpected structural limitation of the quantum formalism in Hilbert space, preventing the description of separate systems. As we will explain, this limitation does not manifest at the level of the states, but of the projectors describing the properties, in the sense that there are not enough properties in the formalism to describe separate systems. The question remains whether separability is a possibility at the fundamental level and if a formalism should integrate it into its mathematical structure, as a possibility. To aid our intuition, we offer a reflection based on a powerful analogy between physical systems and human conceptual entities, as the question of separability also arises for the latter.
Abstract Einstein’s article on the Einstein-Podolsky-Rosen paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not Heisenberg’s uncertainty principle, which he accepted, but the experimental non-separability of spatially separate systems. The same problem was also recognized, years later, by one of us, as part of an axiomatic analysis of the quantum formalism, which revealed an unexpected structural limitation of the quantum formalism in Hilbert space, preventing the description of separate systems. As we will explain, this limitation does not manifest at the level of the states, but of the projectors describing the properties, in the sense that there are not enough properties in the formalism to describe separate systems. The question remains whether separability is a possibility at the fundamental level and if a formalism should integrate it into its mathematical structure, as a possibility. To aid our intuition, we offer a reflection based on a powerful analogy between physical systems and human conceptual entities, as the question of separability also arises for the latter. This article is part of the theme issue ‘Newton, Principia, Newton Geneva Edition (17th–19th) and modern Newtonian mechanics: heritage, past & present’.