The famous gedanken experiments of quantum mechanics have played crucial roles in developing the Copenhagen interpretation. They are studied here from the perspective of standard quantum mechanics, with no ontological interpretation involved. Bohr's investigation of these gedanken experiments, based on the uncertainty relation with his interpretation, was the origin of the Copenhagen interpretation and is still widely adopted, but is shown to be not consistent with the quantum mechanical view. We point out that in most of these gedanken experiments, entanglement plays a crucial role, while its buildup does not change the uncertainty of the concerned quantity in the way thought by Bohr. Especially, in the gamma ray microscope and recoiling double-slit gedanken experiments, we expose the entanglement based on momentum exchange. It is shown that even in such cases, the loss of interference is only due to the entanglement with other degrees of freedom, while the uncertainty relation argument, which has not been questioned up to now, is not right.
Weak values inferred from weak measurements have been proposed as a tool to investigate trajectories of pre- and post-selected quantum systems. Are the inferences drawn from the weak values about the past of a quantum particle fully true? Can the two-state vector formalism predict everything that the standard formalism of quantum mechanics can? To investigate these questions we present a "which-path" gedanken experiment in which the information revealed by a pre- and post-selected quantum system is surprisingly different from what one would expect from the weak values computed using the two-st…
Quantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, we show that the interplay between relativity theory and quantum entanglement has intriguing consequences for the spacetime surrounding elementary particles with spin. Classical and quantum gravity theories predict that a spin-generated magnetic dipole field causes a (slight) bending to the spacetime around particles, breaking its spherical symmetry. Motivated by the apparent break of spherical symmetry, we propose a very general gedanken experi…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation of the series yields some particular eigenvalues and eigenfunctions in exact analytical form. The former can be organized in such a way that one obtains suitable information about the whole spectrum of the model.
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new aspect of this work is a discussion of how symmetries of a quantum system induce homomorphisms of the relevant semiheaps and ternary algebras.
Kochen-Specker theorem and experimental test on hidden variables
最近的一项建议，实验测试量子力学对非上下文隐藏变量理论[物理学评论快报。80，1797（1998）]被示出与目前已知的Kochen-Specker定理的最小证明有关[Phys. Lett. A 212，183（1996）]。这个证明包含了18个关于四维物理系统的是非问题，这些问题被组合成9个互不相容的测试。当这些测试被认为是关于一个两部分两态系统的测试时，那么量子力学和非上下文隐变量对其中的八个做出了相同的预测，但对第九个做出了不同的预测。因此，这第九个测试将允许我们在一个（gedanken）单次实验中区分量子力学和非上下文隐变量理论。
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 …
Marcella in 2002 published a "quantum-mechanical" treatment of the famous single- and double-slit interference experiment in classical wave optics by a simple assumption that quantum mechanical wave function is a constant anywhere within a slit. Rothman and Boughn in 2011 commented that Marcella introduced no quantum physics into the problem other than\ a symbol substitution $p=\hbar k$, and the used essentially the classical wave optics. In present comment, we point out that though Marcella made a fundamental mistake, the problem is nevertheless remediable to give the satisfactory quantum mec…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given state. The operational tangibility of the framework assures that the resultant general relations admit natural operational interpretations and characterisations, and thereby perhaps most importantly, their experimental verifiability. In view of the universal formulation, Heisenberg's original philosophy of the uncertainty principle, most typically exemplified in …
作为旧量子理论的续篇，在对新量子力学的“教科书“解释进行了全景式的介绍之后，在爱因斯坦和尼尔斯·玻尔以来的各种建议的背景下，对自哥本哈根解释以来的量子理论的概念基础进行了回顾，旨在阐明与其基础有关的可能的新方面，其固有的“不完整性”的关键问题是A）测量，和B）量子非定域性。本文还简要介绍了与量子芝诺效应有关的测量问题，即量子芝诺效应和反芝诺效应。新方面的投入来自一些重要的印度专家：S.M. Roy，V. Singh ; D. B. Misra; C.S.乌尼克里希南
The so-called information-thermodynamics link created by a thought experiment of Szilard became a core of the modern orthodoxy in the field of quantum information and resources theory in quantum thermodynamics. We remind existing objections against standard interpretation of Szilard engine operation and illustrate them by two quantum models: particle in a box with time-dependent thin potential barrier and the spin-boson model. The consequences of the emerging superselection rules for thermodynamics and foundations of quantum mechanics are discussed. The role of non-ergodic systems as informati…
The Bell theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper, we show, however, that the proof of the Bell theorem involves a subtle, though crucial, …
Historically, Ehrenfest's theorem (1927) is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form. Next, we highlight its generalizations to the relativistic Dirac particle, and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.
Schrödinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently. It is shown that the notion of classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. In accordance with Raggio's theorem, the impossibility of evolving the product state of a composite system made up of a classical …
Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective
Howard University（霍华德大学）；Landeshauptstadt München, Seminar TMG Universität, Referat für Bildung und Sport（慕尼黑市，TMG大学研讨班，教育与体育局）；Arizona State University（亚利桑那州立大学）
