Canonical Formalism. Keywords: Uncertainty Relation, hidden variables, Ostrogradski’s Canonical Formalism (original) (raw)

The Systematic Measurement Errors and Uncertainty Relation

2006

Inertial effects in non-inertial reference frames are compared with quantum properties of tests objects. The real space-time and perfect inertial reference frame can be compared accurate to the uncertainty relation. Complexities if describing micro-object in non-inertial reference-frames are avoidable using Ostrogradski's Canonical Formalism.

Quantum reference systems: A new framework for quantum mechanics

Physica A-statistical Mechanics and Its Applications, 1997

The new concept of quantum reference systems is introduced, and a corresponding new foundation of nonrelativistic quantum mechanics is given in terms of a set of postulates. The resulting theory gives an explanation for the measurement without assuming an a priori classical background. Schrrdinger's cat paradox and the Einstein-Podolsky-Rosen paradox gain resolution, too. It is also shown that, despite the violation of Bell's inequality, quantum mechanics is a local theory.

A model of extended mechanics and nonlocal hidden variables for quantum theory

2009

Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary reference frames postulating the description of body dynamics by differential equations with higher derivatives of coordinates with respect to time but not only of second order ones and follows from Mach principle. In that case the Lagrangian L(t, q,q,q, ...,q (n) , ...) depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if n-th derivative of the body coordinate with respect to time is a constant (i.e. finite). First, kinematic state of a free body is postulated to invariable in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the n-th order derivative of coordinate with respect to time, then the body dynamics is describes by a 2n-th order differential equation. For example, in a uniformly accelerated reference frame all free particles have the same acceleration equal to the reference frame invariant, i.e. reference frame acceleration. These bodies are described by third-order differential equation in a uniformly accelerated reference frame.

Chapter 3 Quantum Theory in Space-time I-frames

Why do we need space-time descriptions? Well, quantum states are basic elements of abstract Hilbert space and as such they do not have space-time localization. Abstract quantum mechanics provides a general framework that would cover all possibilities a system may show up; it is a foundational construct but one does not get hints to construct actual models for most operators. The only thing one can require in abstract space is existence that is ensured by endowing the framework with a definite mathematical structure. But the world of laboratory experiments imposes space-time frameworks.

Relativistic Quantum Mechanics through Frame-Dependent Constructions

This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions and framedependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, a many-maps theory based on such constructions fails to provide dynamical explanations for local quantum events. Here the hiddenvariable dynamics used in the frame-dependent constructions is just a rule that serves to characterize the set of all possible spacetime maps. While not having dynamical explanations of the values of quantum-mechanical measurement records is a significant cost, it may prove too much to ask for dynamical explanations in relativistic quantum mechanics.

The Quantum Mechanical Frame of Reference - Part 2: The Third Logical Type

In Part 1 the properties of QBism are shown to be natural consequences of taking quantum mechanics at face value, as does Everett in his Relative State Formulation (1957). In Part 2 supporting evidence is presented. Parmenides' (Palmer, 2012) notion that the physical world is static and unchanging is vividly confirmed in the new physics. This means the time evolution of the physical world perceived by observers only occurs at the level of appearances as noted by Davies (2002). In order to generate this appearance of time evolution, a moving frame of reference is required: this is the only possible explanation of the enactment of the dynamics of physics in a static universe. Such a frame of reference can only be a fundamental property of the unitary system as a whole, of different logical type to the quantum state. Thus an ontological category in addition to physical existence is required to complete the science. At this level of logical type, all multiply instantiated copies of an inside view constitute a single entity. Thus the superposition proposed in Part 1 is inevitably effected; and the nature of physical reality on the inside view is as described in QBism.

Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance

Annals of Physics, 1996

The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter—e.g., elapsed time—may be determined via arbitrary data analysis of arbitrary measurements onNidentically prepared

Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics

Nonreflexive quantum mechanics is a formulation of quantum theory based on a non- classical logic termed nonreflexive logic (a.k.a. ‘non-reflexive’). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are individuals in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical (mainly metaphysical) motivations and consequences of it.