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) n (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.

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.

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.

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.

Small matrix modular path integral: iterative quantum dynamics in space and time

2021 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Quantum Dynamics ◽  
Matrix Decomposition ◽  
Propagation Time ◽  
Molecular Aggregates ◽  
Space And Time ◽  
Small Matrix

This work presents a small matrix decomposition of the modular path integral for spin arrays or molecular aggregates, which leads to an iterative treatment with respect to the units that comprise the system and the propagation time.

scholarly journals From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexandre Belin ◽  
Benjamin Withers
Keyword(s):  
Quantum Theory ◽  
Initial Data ◽  
Path Integral ◽  
Coherent States ◽  
Microscopic Theory ◽  
Delta Function ◽  
Common Method ◽  
Single Trace

Abstract A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.

From Classical to Quantum Mechanics

2021 ◽  
pp. 207-219
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Classical Theory ◽  
Constrained Systems ◽  
Experimental Results ◽  
Basic Assumptions ◽  
Original Approach

In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.

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.

The quantum theory of space and time

Nature ◽  
1982 ◽  
Vol 297 (5862) ◽  
pp. 166-166
Author(s):  
C.J. Isham
Keyword(s):  
Quantum Theory ◽  
Space And Time

QUANTUM THEORY OF WORMHOLES

1993 ◽  
Vol 08 (12) ◽  
pp. 1089-1101 ◽  
Author(s):  
PEDRO F. GONZÁLEZ-DÍAZ
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Low Energy ◽  
Neutrino Masses ◽  
Quantum Field ◽  
Distribution Law ◽  
Effective Interactions ◽  
Multiply Connected ◽  
Low Energies ◽  
Euclidean Action

We re-explore the effects of multiply-connected wormholes on ordinary matter at low energies. It is obtained that the path integral that describes these effects is given in terms of a Planckian probability distribution for the Coleman α-parameters, rather than a classical Gaussian distribution law. This implies that the path integral over all low-energy fields with the wormhole effective interactions can no longer vary continuously, and that the quantities α2 are interpretable as the momenta of a quantum field. Using the new result that, rather than being given in terms of the Coleman-Hawking probability, the Euclidean action must equal negative entropy, the model predicts a very small but still nonzero cosmological constant and quite reasonable values for the pion and neutrino masses. The divergence problems of Euclidean quantum gravity are also discussed in the light of the above results.

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