scholarly journals The uncertainty principle, spacetime fluctuations and measurability notion in quantum theory and gravity

2016 ◽  
Vol 10 ◽  
pp. 201-222
Author(s):  
Alexander Shalyt-Margolin
Keyword(s):  
Quantum Theory ◽  
Uncertainty Principle ◽  
Spacetime Fluctuations

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Experimental Accuracy, Operationalism, and Limits of Knowledge – 1925 to 1935

1988 ◽  
Vol 2 (1) ◽  
pp. 147-162 ◽  
Author(s):  
Mara Beller
Keyword(s):  
Quantum Theory ◽  
Uncertainty Principle ◽  
Experimental Accuracy ◽  
Guiding Principle ◽  
Limits Of Knowledge ◽  
Scientific Truth ◽  
Heisenberg's Uncertainty Principle

The ArgumentThis paper analyzes the complex and many-layered interrelation between the realization of the inevitable limits of precision in the experimental domain, the emerging quantum theory, and empirically oriented philosophy in the years 1925–1935. In contrast to the usual historical presentation of Heisenberg's uncertainty principle as a purely theoretical achievement, this work discloses the experimental roots of Heisenberg's contribution. In addition, this paper argues that the positivistic philosophy of elimination of unobservables was not used as a guiding principle in the emergence of the new quantum theory, but rather mostly as a post facto justification. The case of P. W. Bridgman, analyzed in this paper, demonstrates how inconclusive operationalistic arguments are, when used as a possible heuristic aid for future discoveries. A large part of this paper is devoted to the evolution of Bridgman's views, and his skeptical reassessment of operationalism and of the very notion of scientific truth.

scholarly journals LCE Violation for the Relational to Quantum Transition

2021 ◽  
Author(s):  
Chitradeep Gupta
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Quantum Transition ◽  
Arrow Of Time ◽  
Local Conservation ◽  
Conservation Of Energy ◽  
Space And Time

Abstract Quantization historically was never as much a problem as it was a solution to a problem and the problem was the failure of the classical material evolution statement. Under the axiomatic assumption that quantum theory is founded in Heisenberg’s principle and Feynman’s evolution we show that the QM path integral exists at the negation of the evolution of local conservation of energy(LCE) which in its presence fails with arbitrarily many interference terms. Along with LCE violation we uncover another GR-QM contradiction between the local arrow of time and the uncertainty principle. Every contradiction ∼ (p)∩(q) is also a transition in p changing to q. The problem is GR is also caught up in an implication trail and cannot go through multiple parallel changes for LCE violation in presence of the QM path integral. To improve the recovery we go to an alternate projection of GR that has a set of independent frame invariant statements with a Lorentz invariant distinction of space and time.

Einstein Versus Bohr on Reality

2021 ◽  
pp. 161-177
Author(s):  
Steven L. Goldman
Keyword(s):  
Twentieth Century ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Vacuum ◽  
Scientific Theories ◽  
Heisenberg's Uncertainty Principle ◽  
The Universe ◽  
Matter Energy

Ontology is integral to the two most fundamental scientific theories of the twentieth century: quantum theory and the special and general theories of relativity. Issues that drove the development of quantum theory include the reality of quanta, the simultaneous wave- and particle-like nature of matter and energy, determinism, probability and randomness, Schrodinger’s wave equation, and Heisenberg’s uncertainty principle. So did the reality of the predictions about space, time, matter, energy, and the universe itself that were deduced from the special and general theories of relativity. Dirac’s prediction of antimatter based solely on the mathematics of his theory of the electron and Pauli’s prediction of the neutrino based on his belief in quantum mechanics are cases in point. Ontological interpretations of the uncertainty principle, of quantum vacuum energy fields, and of Schrodinger’s probability waves in the form of multiple universe theories further illustrate this point.

scholarly journals QUANTIZATION OF FIELDS BASED ON GENERALIZED UNCERTAINTY PRINCIPLE

2006 ◽  
Vol 21 (16) ◽  
pp. 1285-1296 ◽  
Author(s):  
TOSHIHIRO MATSUO ◽  
YUUICHIROU SHIBUSA
Keyword(s):  
Quantum Theory ◽  
Scalar Field ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Integral Formalism ◽  
Higher Dimensional ◽  
Free Scalar

We construct a quantum theory of free scalar field in (1+1) dimensions based on the deformed Heisenberg algebra [Formula: see text] where β is a deformation parameter. Both canonical and path integral formalisms are employed. A higher dimensional extension is easily performed in the path integral formalism.

scholarly journals Examples of the uncertainty principle

1931 ◽  
Vol 130 (815) ◽  
pp. 632-639 ◽  
Keyword(s):  
Quantum Theory ◽  
Uncertainty Principle ◽  
Formal Theory ◽  
Resolving Power ◽  
Relativity Theory ◽  
Classical Dynamics ◽  
Optical Instruments ◽  
The Subject ◽  
State Of Affairs ◽  
General Synthesis

1. In the general synthesis of classical dynamics with the quantum theory, the Uncertainty Principle plays a most useful part. It is of course only one aspect of the new mechanics, but it is a very helpful one since by its means it becomes easy to see where the old classical ideas broke down. The state of affairs in the quantum theory is not unlike that of the early days of relativity, when most of those who studied the subject felt the need of supporting the formal theory by seeing how the old ideas failed in specific cases. Here the formal theory is very abstract and is not easy to follow intuitively, and the Uncertainty Principle plays much the same rôle as did the examples of clocks and rods in relativity theory. For this reason it is more appropriate for illustrative examples, than for any extreme generality, and though a number of examples have been already given by Heisenberg and Bohr, it may not be amiss to have some more. There are probably some who will have shared my experience that it is often by no means easy to detect how the uncertainty enters into a given experiment, though once detected the arguments are usually very simple. In a recent conversation Professor Bohr criticised some rather careless remarks that I had made, and the present work was undertaken to clear matters up. It may be shortly described as a study of the Uncertainty Principle in connection with electrometers and magnetometers. It may be of interest to point out that the Uncertainty Principle can be regarded from a rather different aspect. The "resolving power" of optical instruments was discussed very fully by Rayleigh on wave principles, but as long as matter was regarded in the classical manner, a mechanical instrument could be considered as capable of measuring quantities with absolute accuracy. Now that we know that matter also has wave properties, there is need of a theory of the resolving power of mechanical instruments, and this is exactly what the Uncertainty Principle supplies.

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