A reconstruction of quantum theory for nonspinning particles

• URL: http://arxiv.org/abs/2202.13356v2
• Date: Tue, 27 Dec 2022 14:44:13 GMT
• Title: A reconstruction of quantum theory for nonspinning particles
• Authors: Ulf Klein
• Abstract summary: This work is based on the idea that the classical counterpart of quantum theory (QT) is not mechanics but probabilistic mechanics. We represent $M$ as an irrotational field, where all components $M_k$ may be derived from a single function $S (q, t)$. In the fourth work of this series, a complete representation of $M$ will be used, which explains the origin of spin.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work is based on the idea that the classical counterpart of quantum theory (QT) is not mechanics but probabilistic mechanics. We therefore choose the theory of statistical ensembles in phase space as starting point for a reconstruction of QT. These ensembles are described by a probability density $\rho (q, p, t)$ and an action variable $S (q, p, t)$. Since the state variables of QT only depend on $q$ and $t$, our first step is to carry out a projection $p \Rightarrow M (q, t)$ from phase space to configuration space. We next show that instead of the momentum components $M_{k}$ one must introduce suitable potentials as dynamic variables. The quasi-quantal theory resulting from the projection is only locally valid. To correct this failure, we have to perform as a second step a linearization or randomization, which ultimately leads to QT. In this work we represent $M$ as an irrotational field, where all components $M_{k}$ may be derived from a single function $S (q, t)$. We obtain the usual Schr\"odinger equation for a nonspinning particle. However, space is three-dimensional and $M$ must be described by $3$ independent functions. In the fourth work of this series, a complete representation of $M$ will be used, which explains the origin of spin. We discuss several fundamental questions that do not depend on the form of $M$ and compare our theory with other recent reconstructions of QT.

Related papers

• Heading towards an Algebraic Heisenberg Cut [0.0]
  We show that early signs of macroscopic behaviour appear before infinity. This lays the grounds for justifying the inclusion in quantum physics of the ITP formalism.
  arXiv  Detail & Related papers  (2024-12-21T10:39:40Z)
• Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits [9.979018524312751]
  The quantum Mpemba effect (QME) describes the counterintuitive phenomenon in which a system farther from equilibrium reaches steady state faster than one closer to equilibrium. Here we propose the intrinsic quantum Mpemba effect (IQME), defined using the trajectory length traced by the quantum state as a more appropriate measure of distance. This work deepens our understanding of quantum state evolution and lays the foundation for accurately capturing novel quantum dynamical behaviour.
  arXiv  Detail & Related papers  (2024-11-27T15:00:59Z)
• The composition rule for quantum systems is not the only possible one [0.0]
  We argue that the composition postulate deserves to be experimentally scrutinised independently of the other features of quantum theory. We formulate a family of operational theories that are solely distinguished from standard quantum theory by their system-composition rule.
  arXiv  Detail & Related papers  (2024-11-24T19:31:13Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• A new indeterminacy-based quantum theory [0.0]
  I propose a novel interpretation of quantum theory, which I will call Environmental Determinacy-based (EnDQT) Unlike theories such as spontaneous collapse theories, no modifications of the fundamental equations of quantum theory are required to establish when determinate values arise. EnDQT may provide payoffs to other areas of physics and their foundations, such as cosmology.
  arXiv  Detail & Related papers  (2023-10-06T04:05:38Z)
• Space-time-symmetric quantum mechanics in 3+1 dimensions [0.0]
  In conventional quantum mechanics, time is treated as a parameter, $t$, and the evolution of the quantum state with respect to time is described by $hat H|psi(t)rangle=ihbar fracddt|psi(t)rangle$. In a recently proposed space-time-symmetric (STS) extension of QM, position becomes the parameter and a new quantum state, $|phi(x)rangle$, is introduced.
  arXiv  Detail & Related papers  (2023-08-08T16:27:43Z)
• Connecting classical finite exchangeability to quantum theory [45.76759085727843]
  Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. It is well known that both theorems do not hold for finitely exchangeable sequences.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• Step-by-step derivation of the algebraic structure of quantum mechanics (or from nondisturbing to quantum correlations by connecting incompatible observables) [0.0]
  This paper provides a step-by-step derivation of the quantum formalism. It helps us to understand why this formalism is as it is.
  arXiv  Detail & Related papers  (2023-03-08T19:27:24Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
  We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
  arXiv  Detail & Related papers  (2022-05-30T18:01:34Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Complementarity in quantum walks [0.08896991256227595]
  We study discrete-time quantum walks on $d$-cycles with a position and coin-dependent phase-shift. For prime $d$ there exists a strong complementarity property between the eigenvectors of two quantum walk evolution operators. We show that the complementarity is still present in the continuous version of this model, which corresponds to a one-dimensional Dirac particle.
  arXiv  Detail & Related papers  (2022-05-11T12:47:59Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models [0.0]
  Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. We use infinite matrix product state techniques to study DQPTs in spin-$S$ $mathrmU(1)$ quantum link models. Our findings indicate that DQPTs are fundamentally different between the Wilson--Kogut--Susskind limit and its representation through the quantum link formalism.
  arXiv  Detail & Related papers  (2022-03-02T19:00:02Z)
• A reconstruction of quantum theory for spinning particles [0.0]
  We show that spin is not a purely quantum mechanical phenomenon, as has long been assumed. This phenomenon occurs before the transition to quantum theory (QT) We derive the Pauli-Schr"odinger equation, the correct value $g=2$ of the gyromagnetic ratio, and clarify some other open questions.
  arXiv  Detail & Related papers  (2022-02-27T13:42:47Z)
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans\"atze [13.651587339535961]
  We develop a framework for convolutional quantum circuits with SU$(d)$symmetry. We prove Harrow's statement on equivalence between $nameSU(d)$ and $S_n$ irrep bases.
  arXiv  Detail & Related papers  (2021-12-14T18:03:43Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Bohr meets Rovelli: a dispositionalist account of the quantum limits of knowledge [0.0]
  I argue that the no-go theorems reflect on a formal level those practical and experimental settings that are needed to come to know the properties of physical systems. I show that, as a consequence of a relationist and perspectival approach to quantum mechanics, the quantum state of the universe regarded as an isolated system cannot be known in principle.
  arXiv  Detail & Related papers  (2020-01-13T22:45:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.