scholarly journals Answering Mermin’s challenge with conservation per no preferred reference frame

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
W. M. Stuckey ◽  
Michael Silberstein ◽  
Timothy McDevitt ◽  
T. D. Le
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Reference Frames ◽  
Relativistic Quantum ◽  
Symmetry Plane ◽  
Real Space ◽  
Relativistic Quantum Mechanics ◽  
General Reader ◽  
Famous Paper ◽  
Preferred Reference Frame

Abstract In 1981, Mermin published a now famous paper titled, “Bringing home the atomic world: Quantum mysteries for anybody” that Feynman called, “One of the most beautiful papers in physics that I know.” Therein, he presented the “Mermin device” that illustrates the conundrum of quantum entanglement per the Bell spin states for the “general reader.” He then challenged the “physicist reader” to explain the way the device works “in terms meaningful to a general reader struggling with the dilemma raised by the device.” Herein, we show how “conservation per no preferred reference frame (NPRF)” answers that challenge. In short, the explicit conservation that obtains for Alice and Bob’s Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their “mysteries” is the restricted Lorentz group.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

scholarly journals DOUBLE SPECIAL RELATIVITY WITH A MINIMUM SPEED AND THE UNCERTAINTY PRINCIPLE

2012 ◽  
Vol 21 (02) ◽  
pp. 1250010 ◽  
Author(s):  
CLÁUDIO NASSIF
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Uncertainty Principle ◽  
Vacuum Energy ◽  
Background Field ◽  
Uncertainty Relations ◽  
Minimum Speed ◽  
Fundamental Understanding ◽  
Low Energies ◽  
Preferred Reference Frame

The present work aims to search for an implementation of a new symmetry in the spacetime by introducing the idea of an invariant minimum speed scale (V). Such a lowest limit V, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the spacetime at the subatomic level for very low energies close to the background frame (v ≈ V), providing a fundamental understanding for the uncertainty principle, i.e. the uncertainty relations should emerge from the spacetime with an invariant minimum speed.

scholarly journals Spacetime Quantum Reference Frames and superpositions of proper times

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 508
Author(s):  
Flaminia Giacomini
Keyword(s):  
Hilbert Space ◽  
Reference Frame ◽  
Degrees Of Freedom ◽  
Reference Frames ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Dynamical Evolution ◽  
Quantum Superposition ◽  
Local Frame ◽  
Physical Systems

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.

scholarly journals A SIMPLER SOLUTION OF THE NON-UNIQUENESS PROBLEM OF THE COVARIANT DIRAC THEORY

2013 ◽  
Vol 10 (07) ◽  
pp. 1350027 ◽  
Author(s):  
MAYEUL ARMINJON
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Uniqueness Problem ◽  
Diagonal Form ◽  
Dirac Theory ◽  
Tetrad Field ◽  
Gauge Transformations ◽  
Gamma Field ◽  
Preferred Reference Frame ◽  
Generally Covariant

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

scholarly journals Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 692 ◽  
Author(s):  
William Stuckey ◽  
Michael Silberstein ◽  
Timothy McDevitt ◽  
Ian Kohler
Keyword(s):  
Information Theory ◽  
Special Relativity ◽  
Reference Frame ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum States ◽  
The World ◽  
Preferred Reference Frame ◽  
Bell Basis ◽  
Tsirelson Bound

To answer Wheeler’s question “Why the quantum?” via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., “Why the Tsirelson bound?” We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser–Horne–Shimony–Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub’s question addresses Fuchs’ desideratum that we “take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity].” Thus, the answer to Bub’s question per Fuchs’ desideratum is, “the Tsirelson bound obtains due to conservation per NPRF”.

scholarly journals Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

2017 ◽  
Vol 11 ◽  
pp. 29-44 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Dirac Equation ◽  
Yukawa Potential ◽  
Relativistic Quantum ◽  
Star Product ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Real Space ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Shift Method

Energy levels of one electron atoms have been re-examined by applying an alternative perturbative scheme in solving the modified Dirac equation (m.d.e.) for the modified Yukawa potential model with a arbitrary spin-orbit quantum number (see equation in the paper) by means Bopp’s shift method instead to solving (m.d.e.) with star product, in the framework of noncommutativity three dimensional real space (NC: 3D-RS). It is observed that the obtained corrections of energies are depended on the new discrete atomic quantum numbers (see equation in the paper) under spin-symmetry and pseudospin symmetry and two infinitesimal parameters (see equation in the paper) which induced by position-position noncommutativity. Furthermore, in limit of parameters (see equation in the paper), the new energy equations for modified Yukawa potential are consistent with the results of ordinary relativistic quantum mechanics for ordinary Yukawa potential. Keywords: Yukawa potential, noncommutative space, star product, Bopp’s shift method and Dirac equation.

scholarly journals The analogy of equation of rotation in complex plane with the Dirac equation, and its foundation

2018 ◽  
Vol 182 ◽  
pp. 02108
Author(s):  
Mohammed Sanduk
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Special Relativity ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Position Vector ◽  
Partial Observation ◽  
Complex Vector ◽  
Kinematical Model ◽  
Comparison Table

The Three Wave Hypothesis (TWH) has been proposed by Horodecki in 1981. Sanduk attributed TWH to a classical kinematical model of two rolling circles in 2007. In a previous project in 2012, it is shown that the position vector of a point in a system of two rolling circles can be transformed to a complex vector under the effect of partial observation. The present work tries to develop this concept of transformation. Under this transformation, it is found that the kinematical equations of the motion of point can be transformed to equations analogise the relativistic quantum mechanics equations. Many analogies have been found and are listed in a comparison table. These analogies may sagest that both of the quantum mechanics and the special relativity are emergent, and are of the same origin.

scholarly journals Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021 ◽  
Vol 9 ◽  
Author(s):  
Philipp A. Höhn ◽  
Alexander R. H. Smith ◽  
Maximilian P. E. Lock
Keyword(s):  
Quantum Dynamics ◽  
Reference Frames ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Probability Interpretation ◽  
Temporal Reference ◽  
Recent Method ◽  
Frame Dependence ◽  
Quantum Clocks ◽  
Positive Operator Valued Measure

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

scholarly journals No Preferred Reference Frame at the Foundation of Quantum Mechanics

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 12
Author(s):  
William Stuckey ◽  
Timothy McDevitt ◽  
Michael Silberstein
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Reference Frame ◽  
Reference Frames ◽  
Quantum Probability ◽  
Relativity Principle ◽  
Foundation Of Quantum Mechanics ◽  
Invariant Measurement ◽  
Preferred Reference Frame ◽  
Spin Measurements

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance and Continuity, at the foundation of those axiomatic reconstructions, maps to “no preferred reference frame” (NPRF, aka “the relativity principle”) as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance and Continuity. Consequently, the “mystery” of the Bell states is understood to result from conservation per Information Invariance and Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

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