ℱ(P) quantum mechanics

2020 ◽  
Vol 17 (09) ◽  
pp. 2050130
Author(s):  
Homa Shababi ◽  
Andrea Addazi
Keyword(s):  
Quantum Mechanics ◽  
Large Class ◽  
Uncertainty Principle ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Quantum Algebra ◽  
Functional Operator ◽  
Lifshitz Theory ◽  
Commutative Space ◽  
Heisenberg's Uncertainty Principle

We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as [Formula: see text]. We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of [Formula: see text] models can introduce superluminal modes in the quantized theories. We also show that the Hořava–Lifshitz theory is related to a large class of [Formula: see text] Quantum Mechanics.

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.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

scholarly journals Why does uncertainty come in quantum mechanics?

2021 ◽  
Author(s):  
Muhammad Yasin
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Research Paper ◽  
Main Topic ◽  
Heisenberg's Uncertainty Principle

In 1927 Heisenberg has invented the uncertainty principle. The principle of uncertainty is, "It is impossible to determine the position and momentum of a particle at the same time."The more accurately the momentum is measured, the more uncertain the position will be. Just knowing the position would make the momentum uncertain. Einstein was adamant against this principle until his death. He thought that particles have some secret rules. Einstein thought, "The uncertainty principle is incomplete. There is a mistake somewhere that has resulted in uncertainty. Many did not accept Einstein then. But I'm sure Einstein was right then, there are secret rules for particles. Heisenberg's uncertainty principle is also 100% correct . I recently published a research paper named "Quantum Certainty Mechanics"[1], which shows the principle of measuring the momentum and position of particles by the quantum certainty principle. Why uncertainty comes from certainty is the main topic of this research paper. When the value of the energy absorbed by the electron in the laboratory is calculated, the uncertainty is removed. The details are discussed below.

scholarly journals Hoe zeker is Heisenbergs onzekerheidsprincipe?

2021 ◽  
Vol 113 (1) ◽  
pp. 137-156
Author(s):  
Jeanne Peijnenburg ◽  
David Atkinson
Keyword(s):  
Quantum Mechanics ◽  
Recent Work ◽  
Uncertainty Principle ◽  
Copenhagen Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Uncertainty Principles ◽  
Werner Heisenberg ◽  
Heisenberg's Uncertainty Principle

Abstract How certain is Heisenberg’s uncertainty principle?Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.

scholarly journals Devepment of the Incompatibility between Einstein's General Relativity and Heisenberg's Uncertainty Principle

2018 ◽  
Author(s):  
Alexandre GEORGES
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Scientific Community ◽  
Relativistic Particle ◽  
Mathematical Proof ◽  
Werner Heisenberg ◽  
Time Dilatation ◽  
Heisenberg's Uncertainty Principle ◽  
Einstein’S General Relativity

Are General Relativity and Quantum Mechanics incompatible? Each in their world, that of the infinitely large and that of the infinitely small, they did not seem to interfere as long as they avoided each other. However, it is their fundamental oppositions that prevent the scientific community from achieving a unification of physics. The proposal of this paper is to provide a mathematical proof of incompatibility, beyond the fact that they have fundamentally different principles, between the foundations of General Relativity and Quantum Mechanics, namely the deformation of the space-time geometry and the Uncertainty Principle. It will thus be possible to provide an absolute limitation in establishing a unifying theory of physics, if any. Moreover, while respecting the conditions fixed by the Uncertainty Principle, it will be tempted to determine with accuracy and simultaneity, the position and the speed of a non-relativistic particle, by application of relativistic principles and bypassing the problems raised by such an operation. The Uncertainty Principle as stated by Werner Heisenberg will be then, in the light of observations made on the measurement of the time dilatation and in accordance with its own terms, refuted by the present. - Physics Essays, Volume 31, Issue 3 (September 2018), Article 12 - https://physicsessays.org/browse-journal-2/product/1667-12-alexandre-georges-incompatibility-between-einstein-s-general-relativity-and-heisenberg-s-uncertainty-principle.html

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

2020 ◽  
pp. 133-156
Author(s):  
Jim Baggott
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Laboratory Experiments ◽  
Space Time ◽  
Spectral Lines ◽  
Planck’S Constant ◽  
Classical Space ◽  
Planck's Constant

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

Uncertainty in quantum mechanics: faith or fantasy?

2011 ◽  
Vol 369 (1956) ◽  
pp. 4864-4890 ◽  
Author(s):  
Roger Penrose
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Uncertainty Principle ◽  
Quantum Level ◽  
Diverse Range ◽  
Absolute Truth ◽  
Quantum Uncertainty ◽  
Level Of Activity ◽  
Heisenberg's Uncertainty Principle

The word ‘uncertainty’, in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very ‘truth’ into question. This article addresses the issue of quantum ‘uncertainty’ from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.

Exploration of the unification of fields

2019 ◽  
Vol 32 (3) ◽  
pp. 399-410
Author(s):  
Ge Guangzhou
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Quantum Mechanics ◽  
Field Equation ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Space Time ◽  
The State ◽  
State Function ◽  
Tensor Equation

This article may be deemed as an exploration on the unification of fields as well as a discussion of the completeness in physics. This author tended to support the viewpoint of Einstein and believed that the Uncertainty Principle should be in itself incomplete, and that the representation of the state function ψ should not be complete in quantum mechanics. Following a series of discussions, including the hypothesis of a new quantum, the relativity of electromagnetic field, and the general equivalence principle, this author proposes here a new field equation called Hamilton’s tensor equation (HTE). Acting as the complete presentation of Einstein’s field equation and as an extension of Hamilton’s principle, what this new field equation (HTE) has revealed is that the “virtuality” of space‐time, rather than its curvature, is what determines the distribution and movement of matter and energy. Based on this new field equation (HTE), the author has extended the study to include the unification of fields, a model of new particle, and the phenomenon of black hole.

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