scholarly journals Models on the boundary between classical and quantum mechanics

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140236 ◽  
Author(s):  
Gerard 't Hooft
Keyword(s):  
Quantum Mechanics ◽  
Classical Theory ◽  
Classical Logic ◽  
Quantum Systems ◽  
Bell's Theorem ◽  
Vacuum Fluctuations ◽  
Superstring Theory ◽  
Quantum Models ◽  
Physical Laws ◽  
Classical And Quantum Mechanics

Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require ‘conspiracy’. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature ‘conspiracy’, and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.

ALTERNATIVE HAMILTONIAN DESCRIPTION FOR QUANTUM SYSTEMS

1990 ◽  
Vol 05 (15) ◽  
pp. 1229-1234 ◽  
Author(s):  
B. A. DUBROVIN ◽  
G. MARMO ◽  
A. SIMONI
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Dimensional Case ◽  
Hamiltonian Description ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Kähler Structures ◽  
Time Invariant ◽  
Classical And Quantum Mechanics

The existence of time-invariant Kähler structures is analyzed in both Classical and Quantum Mechanics. In Quantum Mechanics, a family of such Kähler structures is found, in the finite-dimensional case it is proven that this family is complete.

scholarly journals CLASSICAL BEHAVIOR IN QUANTUM MECHANICS: A TRANSITION PROBABILITY APPROACH

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1545-1554 ◽  
Author(s):  
N.P. LANDSMAN
Keyword(s):  
Quantum Mechanics ◽  
Transition Probability ◽  
Quantum Systems ◽  
Finite System ◽  
Restricted Class ◽  
Probability Approach ◽  
Classical Behavior ◽  
Poisson Space ◽  
Classical And Quantum Mechanics ◽  
Large Quantum

A formalism is developed for describing approximate classical behavior in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition probability. Both the limit where ħ→0 in a fixed finite system and the limit where the size of the system goes to infinity are incorporated. In either case, classical behavior is seen only for certain observables and in a restricted class of states.

scholarly journals Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Quantum Interference ◽  
Direct Detection ◽  
Energy Levels ◽  
Vacuum Fluctuations ◽  
Heavy Particles ◽  
Evolving Systems ◽  
Gedanken Experiment ◽  
Classical Computer

AbstractFast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

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