No Preferred Reference Frame at the Foundation of Quantum Mechanics

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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Gravity as entanglement, entanglement as gravity

10.31226/osf.io/4z56f ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Reference Frame ◽

Common Sense ◽

Reference Frames ◽

General Covariance ◽

The Universe

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, the latter is that of quantum mechanics and information.Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant.That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics.e

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Gallilei covariant quantum mechanics in electromagnetic fields

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171285000643 ◽

1985 ◽

Vol 8 (3) ◽

pp. 589-597 ◽

Cited By ~ 2

Author(s):

H. E. Wilhelm

Keyword(s):

Quantum Mechanics ◽

Electromagnetic Fields ◽

Electromagnetic Waves ◽

Wave Equations ◽

Reference Frames ◽

Schroedinger Equation ◽

Relativity Principle ◽

Covariant Quantum ◽

Electromagnetic Potentials ◽

Galilean Relativity

A formulation of the quantum mechanics of charged particles in time-dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocitywis in magnitude comparable with the velocity of lightc. The electromagnetic substratum velocitywoccurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.

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Knowledge of Quantum Hidden Variables Enables Backwards-In-Time Signaling

Applied Sciences ◽

10.3390/app11104477 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4477

Author(s):

Avishy Carmi ◽

Eliahu Cohen ◽

Lorenzo Maccone ◽

Hrvoje Nikolić

Keyword(s):

Quantum Mechanics ◽

Reference Frame ◽

Hidden Variables ◽

Bohmian Mechanics ◽

The State ◽

Bell’S Theorem ◽

Relativity Theory ◽

Bell's Theorem ◽

Preferred Reference Frame ◽

Superluminal Signaling

Bell’s theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics.

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887813500278 ◽

2013 ◽

Vol 10 (07) ◽

pp. 1350027 ◽

Cited By ~ 7

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.

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

Scientific Reports ◽

10.1038/s41598-020-72817-7 ◽

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.

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GENERAL REFERENCE FRAMES AND THEIR ASSOCIATED SPACE MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887811005051 ◽

2011 ◽

Vol 08 (01) ◽

pp. 155-165 ◽

Cited By ~ 13

Author(s):

MAYEUL ARMINJON ◽

FRANK REIFLER

Keyword(s):

Quantum Mechanics ◽

Reference Frame ◽

Reference Frames ◽

Deformable Body ◽

Three Dimensional ◽

Differentiable Manifold ◽

Hamiltonian Operator ◽

Formal Definition ◽

General Reference ◽

Time Coordinate

We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we assume, moreover, that the time coordinate is fixed. This is necessary for quantum mechanics, because the Hamiltonian operator depends on the choice of the time coordinate. Our definition allows us to associate rigorously with each reference frame F, a unique "space" (a three-dimensional differentiable manifold), which is the set of the world lines bound to F. This also is very useful for quantum mechanics. We briefly discuss the application of these concepts to Gödel's universe.

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The isomorphism of Minkowski space and the separable complex Hilbert space and its physical interpretation

10.31226/osf.io/jc7v9 ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

Hilbert Space ◽

Quantum Mechanics ◽

Quantum Information ◽

Special Relativity ◽

Minkowski Space ◽

Reference Frame ◽

Physical Interpretation ◽

Complex Hilbert Space ◽

Axiom Of Choice ◽

The Axiom Of Choice

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”.

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The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information

10.20944/preprints202106.0197.v1 ◽

2021 ◽

Author(s):

Vasil Penchev

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Quantum Information ◽

Standard Model ◽

Reference Frame ◽

General Principle ◽

Wave Functions ◽

Principle Of Relativity ◽

Elementary Wave ◽

The Standard Model

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

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Path integral implementation of relational quantum mechanics

Scientific Reports ◽

10.1038/s41598-021-88045-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Jianhao M. Yang

Keyword(s):

Quantum Mechanics ◽

Reference Frame ◽

Path Integral ◽

Measurement Theory ◽

Entanglement Entropy ◽

Quantum Probability ◽

Frame Theory ◽

Probability Amplitude ◽

Relational Quantum Mechanics ◽

Measured System

AbstractRelational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born’s Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation effort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and influence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory.

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Allocentric to Egocentric Spatial Switching: Impairment in aMCI and Alzheimer's Disease Patients?

Current Alzheimer Research ◽

10.2174/1567205014666171030114821 ◽

2018 ◽

Vol 15 (3) ◽

pp. 229-236 ◽

Cited By ~ 8

Author(s):

Gennaro Ruggiero ◽

Alessandro Iavarone ◽

Tina Iachini

Keyword(s):

Alzheimer’S Disease ◽

Alzheimer's Disease ◽

Reference Frame ◽

Reference Frames ◽

Memory Task ◽

Spatial Representations ◽

The Novel ◽

Spatial Memory Task ◽

Switching Condition ◽

Normal Controls

Objective: Deficits in egocentric (subject-to-object) and allocentric (object-to-object) spatial representations, with a mainly allocentric impairment, characterize the first stages of the Alzheimer's disease (AD). Methods: To identify early cognitive signs of AD conversion, some studies focused on amnestic-Mild Cognitive Impairment (aMCI) by reporting alterations in both reference frames, especially the allocentric ones. However, spatial environments in which we move need the cooperation of both reference frames. Such cooperating processes imply that we constantly switch from allocentric to egocentric frames and vice versa. This raises the question of whether alterations of switching abilities might also characterize an early cognitive marker of AD, potentially suitable to detect the conversion from aMCI to dementia. Here, we compared AD and aMCI patients with Normal Controls (NC) on the Ego-Allo- Switching spatial memory task. The task assessed the capacity to use switching (Ego-Allo, Allo-Ego) and non-switching (Ego-Ego, Allo-Allo) verbal judgments about relative distances between memorized stimuli. Results: The novel finding of this study is the neat impairment shown by aMCI and AD in switching from allocentric to egocentric reference frames. Interestingly, in aMCI when the first reference frame was egocentric, the allocentric deficit appeared attenuated. Conclusion: This led us to conclude that allocentric deficits are not always clinically detectable in aMCI since the impairments could be masked when the first reference frame was body-centred. Alongside, AD and aMCI also revealed allocentric deficits in the non-switching condition. These findings suggest that switching alterations would emerge from impairments in hippocampal and posteromedial areas and from concurrent dysregulations in the locus coeruleus-noradrenaline system or pre-frontal cortex.

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