Three basic postulates for Quantum Theory are proposed, namely the Probability, Maximum-Speed and Hilbert-Space postulates. Subsequently we show how these postulates give rise to well-known and widely used quantum results, as the probability rule and the linearity of quantum evolution. A discussion of the postulates in the light of Bell's theorem is included which points towards yet unsolved conceptual problems in the Foundations of Quantum Mechanics.
In a recent comment on the arXiv, Blake C. Stacey criticizes our derivation of the quantum state update rule in Nat. Commun. 10, 1361 (2019). Here we argue that the criticism is unfounded. In particular, and in contrast to Stacey's claims, our proof does not assume linearity.
It is argued that the usual postulates of quantum mechanics are too strong. It is conjectured that it is possible to interpret all experiments if we maintain the formalism of quantum theory without modification, but weaken the postulates concerning the relation between the formalism and the experiments. A set of postulates is proposed where realism is insured. Comments on the Bell theorem are made on the light of the new postulates.
A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable separately. A proposal has been made for doing this, but it is shown to be problematic.
The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is require…
Comment on "Quantum theory based on real numbers cannot be experimentally falsified": On the compatibility of physical principles with information theory for fermions
The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering of the events in the system is not automatically implied based on the values of time, but must be specified explicitly. This suggests the specific logic of events as well as complex character of the function, which describes stochastic behavior of the system, hence the parameters of the system are defined by Hermitian operators in the Hilbert space of functi…
We previously suggested that photon exchange interactions could be used to produce nonlinear effects at the two-photon level, and similar effects have been experimentally observed by Resch et al. (quant-ph/0306198). Here we note that photon exchange interactions are not useful for quantum information processing because they require the presence of substantial photon loss. This dependence on loss is somewhat analogous to the postselection required in the linear optics approach to quantum computing suggested by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)].
Recently D. A. R. Dalvit and S. K. Lamoreaux arXiv:0805.1676 [Phys. Rev. Lett. v.101, 163203 (2008)] suggested the modification of the reflection coefficients in the Lifshitz theory taking into account the screening effects and diffusion currents. We demonstrate that the suggested modification is thermodynamically and experimentally inconsistent.
This is a comment on J. A. Barrett's article ``The Preferred-Basis Problem and the Quantum Mechanics of Everything'' in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called ``hidden'') variables. I point out that it is far from clear, for most observables, what such a postulate is supposed to mean, unless the postulated additional variable is related to a clear ontology in space-time, such as particle world lines, string world sheets, or fields.
In a recent comment [arXiv:2112.05658], Grudka and Wójcik object to some of our earlier claims concerning a link between fundamental postulates of quantum theory and special relativity extended to superluminal frames of reference. In this short reply we refute these criticisms.
We show that the geometric phase for mixed state during a cyclic evolution suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by nowaday techniques.
It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.
It has recently been suggested that an Aharonov-Bohm phase should be capable of detection using beams of neutral polarizable particles. A more careful analysis of the proposed experiment suffices to show, however, that it cannot be performed regardless of the strength of the external electric and magnetic fields.
In a recent paper [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)] an electromagnetic energy-momentum tensor is suggested as an alternative to the Abraham-Minkowski tensor and is applied to calculations of Casimir forces in planar geometries. We argue that the universality of the suggested tensor is doubtful; application of the Raabe-Welsch theory to a simple example in classical electrodynamics shows that their proposed tensor is unable to describe the situation in a simple way. We also show that modified Casimir forces acting on the cavity medium as prescribed by these authors suf…
Starting with a consideration of the implication of Bell inequalities in quantum mechanics, a new quantum postulate is suggested in order to restore classical locality and causality to quantum physics: only the relative coordinates between detected quantum events are valid observables. This postulate supports the EPR view that quantum mechanics is incomplete, while also staying compatible to the Bohr view that nothing exists beyond the quantum. The new postulate follows from a more general principle of quantum relativity, which states that only correlations between experimental detections of q…
In a recent interesting article A. Heuer, G. Pieplow, and R. Menzel discuss a quantum-eraser experiment to investigate the complementarity of wave-like and particle-like behavior of photons. I would like to draw your attention to the fact that the very same experimental setup was suggested in a previous paper, and take advantage of this opportunity to examine some aspects of this controversial subject.
Recent experiment by Zhinden et al (Phys. Rev {\bf A} 63 02111, 2001) purports to test compatibility between relativity and quantum mechanics in the classic EPR setting. We argue that relativity has no role in the EPR argument based solely on non-relativistic quantum formalism. It is suggested that this interesting experiment may have significance to address fundamental questions on quantum probability.
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability me…
I. Raptis and R. Zapatrin in the quant-ph/0010104 show possibility to express general state of $l$-qubits quantum register as sum at most $2^l-l$ product states. In the comment is suggested more simple construction with possibility of generalization for decomposition of tensor product of Hilbert spaces with arbitrary dimension $n$ (here simplicial complexes used in the article mentioned above would not be applied directly). In this case it is decomposition with $n^l-(n^2-n)l/2$ product states.
The recently suggested modification of the transverse electric contribution to the Lifshitz formula (S. K. Lamoreaux, arXiv:0801.1283) is discussed. We show that this modification is inconsistent with the data of two precise experiments, and violates the Nernst heat theorem. The preprint's suggestion concerning the resolution of the "apparent violation of the Third Law of Thermodynamics" is shown to be incorrect.
Recently, a substantial amount of debate has grown up around a proposed quantum resolution to the `arrow of time dilemma' that is based on the role of classical memory records of entropy-decreasing events. In this note we show that the argument is incomplete and furthermore, by providing a counter-example, argue that it is incorrect. Instead of quantum mechanics providing a resolution in the manner suggested, it allows enhanced classical memory records of entropy-decreasing events.
This article aims to reconsider E. Schrödinger's famous thought experiment, the cat paradox experiment, and its place in quantum foundations from a new perspective, grounded in the type of interpretation of quantum phenomena and quantum mechanics, which belongs to the class of interpretations designated here as "reality without realism" (RWR) interpretations. Such interpretations have not been previously brought to bear on the cat experiment, including by N. Bohr, whose interpretation in its ultimate forms (as he changes his interpretation a few times) is an RWR interpretation, but who does no…
A chameleonic solution to the cosmological constant problem and the non-equivalence of different conformal frames at the quantum level have been recently suggested [Phys. Rev. D82 (2010) 044006]. In this article we further discuss the theoretical grounds of that model and we are led to a chameleonic equivalence postulate (CEP). Whenever a theory satisfies our CEP (and some other additional conditions), a density-dependence of the mass of matter fields is naturally present. Let us summarize the main results of this paper. 1) The CEP can be considered the microscopic counterpart of the Einstein'…
It is shown that the `arrow of time' operator, M_F, recently suggested by Strauss et al., in arXiv:0802.2448v1 [quant-ph], is simply related to the sign of the canonical `time' observable, T (apparently first introduced by Holevo). In particular, the monotonic decrease of < M_F > corresponds to the fact that < sgn T > increases monotonically with time. This relationship also provides a physical interpretation of the property M_F < 1. Some further properties and possible generalisations are pointed out, including to almost-periodic systems.
It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular interpretation of Shannon's H-function (related to consecutive measurements), and is shown explicitly to fail for other physical interpretations. Further, it is shown that Shannon and von Neumann entropies have in fact a common fundamental significance, connected to the existence of a unique geometric measure of uncertainty for classical and quantum ensembles. So…
In the paper by V.V. Nesvizhevsky et al., Phys. Rev. D 67, 102002 (2003), it is argued that the lowest quantum state of neutrons in the Earth's gravitational field has been experimentally identified. While this is most likely correct, it is imperative to investigate all alternative explanations of the result in order to close all loopholes, as it is the first experiment ever claimed to have observed gravitational quantum states. Here we show that geometrical effects in the experimental setup can mimic the results attributed to gravity. Modifications of the experimental setup to close these pos…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how…
