scholarly journals The Arithmetic of Uncertainty unifies Quantum Formalism and Relativistic Spacetime

2020 ◽  
Author(s):  
John Skilling ◽  
Kevin Knuth
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Three Dimensions ◽  
One Dimension ◽  
Lorentz Transformations ◽  
Mathematical Structures ◽  
Modern Physics ◽  
Relativistic Spacetime ◽  
The Universe ◽  
Dimensions Of Space

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

scholarly journals Generation of families of spectra in PT -symmetric quantum mechanics and scalar bosonic field theory

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120049 ◽  
Author(s):  
Steffen Schmidt ◽  
S. P. Klevansky
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Complex Analysis ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Bosonic Field ◽  
Symmetric Quantum ◽  
The Difference ◽  
Do So

This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H = p 2 + x 2 (i x ) ϵ , H = p 2 +( x 2 ) δ and H = p 2 −( x 2 ) μ . In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display symmetry. To do so, simple arguments that use the Wentzel–Kramers–Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and -symmetric quantum theory.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

1988 ◽  
Vol 03 (07) ◽  
pp. 645-651 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Meaning ◽  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Interpretation Of Quantum Mechanics ◽  
Probabilistic Interpretation ◽  
The Universe ◽  
Classical Picture

A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.

scholarly journals Consistent description of microscopic phenomena by macroscopic observers in quantum theory

2021 ◽  
Author(s):  
Alexey Kryukov
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Random Noise ◽  
Thought Experiments ◽  
Newtonian Physics ◽  
Measurement Results ◽  
Modern Physics ◽  
Measured System ◽  
Physical Phenomena

Abstract Quantum mechanics is the foundation of modern physics that is thought to be applicable to all physical phenomena, at least in principle. However, when applied to macroscopic bodies, the theory seems to be inconsistent. Wigner's friend and related thought experiments demonstrate that accounts by different observers described by the rules of quantum mechanics may be contradictory. Although still highly debated, such experiments seem to demonstrate an incompatibility of quantum mechanics with the usual rules of logic. Alternatively, one of the hidden assumptions in the thought experiments must be wrong. For instance, the argument is invalidated if macroscopic observers cannot be considered as physical systems described by the rules of quantum theory. Here we prove that there is a way to apply the rules of quantum mechanics to macroscopic observers while avoiding contradictory accounts of measurement by the observers. The key to this is the random noise that is ever present in nature and that represents the uncontrollable part of interaction between measured system and the surroundings in classical and quantum physics. By exploring the effect of the noise on microscopic and macroscopic bodies, we demonstrate that accounts of Wigner, the friend and other agents all become consistent. Our result suggests that the existing attempts to modify the Schrodinger equation to account for measurement results may be misguided. More broadly, the proposed mechanism for modeling measurements underlies the phenomenon of decoherence and is shown to be sufficient to explain the transition to Newtonian physics in quantum theory.

scholarly journals General Quantum Theory: II ----Measuring & Identical Theorems, Origins & Classifications of Entanglements and Solution to Crisis of Wave Collapse

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Yi-You Nie
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Statistical Mechanics ◽  
Particle System ◽  
Square Root ◽  
Classical Statistical Mechanics ◽  
Wave Particle Duality ◽  
Wave Collapse ◽  
Modern Physics

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

scholarly journals Reality and Super-Reality: Properties of a Mathematical Multiverse

Axiomathes ◽  
2019 ◽  
Vol 30 (4) ◽  
pp. 453-478
Author(s):  
Alan McKenzie
Keyword(s):  
Quantum Theory ◽  
Mathematical Structure ◽  
Self Awareness ◽  
Complete Structure ◽  
Mathematical Structures ◽  
Structural Environment ◽  
Parallel Universes ◽  
Definition Of ◽  
Rudimentary Form ◽  
The Universe

Abstract Ever since its foundations were laid nearly a century ago, quantum theory has provoked questions about the very nature of reality. We address these questions by considering the universe—and the multiverse—fundamentally as complex patterns, or mathematical structures. Basic mathematical structures can be expressed more simply in terms of emergent parameters. Even simple mathematical structures can interact within their own structural environment, in a rudimentary form of self-awareness, which suggests a definition of reality in a mathematical structure as simply the complete structure. The absolute randomness of quantum outcomes is most satisfactorily explained by a multiverse of discrete, parallel universes. Some of these have to be identical to each other, but that introduces a dilemma, because each mathematical structure must be unique. The resolution is that the parallel universes must be embedded within a mathematical structure—the multiverse—which allows universes to be identical within themselves, but nevertheless distinct, as determined by their position in the structure. The multiverse needs more emergent parameters than our universe and so it can be considered to be a superstructure. Correspondingly, its reality can be called a super-reality. While every universe in the multiverse is part of the super-reality, the complete super-reality is forever beyond the horizon of any of its component universes.

Transition in spacetime

2014 ◽  
Vol 6 (2) ◽  
pp. 1202-1210
Author(s):  
Mostafa Mohamed Korany
Keyword(s):  
Spatial Dimension ◽  
The Other ◽  
Three Dimensions ◽  
Theory Of Relativity ◽  
Spacetime Dimension ◽  
Time And Space ◽  
Temporal Dimension ◽  
The Universe ◽  
Dimensions Of Space

The universe has two main dimensions spatial dimension (consists of three dimensions directional X, Y, Z) and the other dimension is the temporal dimension. Time and space are linked strongly inseparable so we will consider the time and place one Is the dimension of spacetime (as proved Einstein in his theory of relativity). Spacetime dimension includes the temporal dimension and spatial dimension (the three dimensions of space).  Spacetime dimension two (real spacetime – Vision spacetime).  Spacetime has two cases:    1- Navigate spacetime       2- The change in spacetime. spacetime is Personally like a fingerprint and it always variable ( everyone has Personally spacetime and there are not find two of spacetime are the same.

5. Mysteries of the quantum

2021 ◽  
pp. 93-109
Author(s):  
David Wallace
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Properties ◽  
The State ◽  
Successful Theory ◽  
Modern Physics ◽  
Faster Than Light ◽  
Non Locality

This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.

Purpose, Freedom, and the Laws of Nature

2018 ◽  
Author(s):  
Sean M. Carroll
Keyword(s):  
Quantum Mechanics ◽  
Laws Of Nature ◽  
Arrow Of Time ◽  
Modern Physics ◽  
The Universe ◽  
Individual Human

Sean M. Carroll notes that, despite popular stereotypes of existential “philosophers sitting in cafes, smoking cigarettes and drinking apricot cocktails” and neuroscientists decked out in lab coats, there is an undeniable connection between existentialism and science. This is perhaps easy to see with biology and neuroscience, but the connection goes beyond this. Carroll maintains that, “An honest grappling with the questions of purpose and freedom in the universe must also involve ideas from physics and cosmology.” He goes on to argue that if we want to create purpose and meaning at the scale of individual human lives, we must understand the nature of the larger universe of which we are a part. After discussing what modern physics can tell us about determinism, quantum mechanics, the arrow of time, and emergence, Carroll concludes by exploring the existential implications of these insights for freedom and meaning.

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