Quantum Phase Mechanics: A Hypothesis

Some of my beliefs regarding the theory which underlies both Quantum Mechanics and Special Relativity...

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Quantum Mechanics is derivable from Special Relativity
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Site last modified: 2015-Apr-25



Note: This is a work in progress...if you notice errors, please let me know.

Abbreviations
QM=Quantum Mechanics
SR=Special Relativity
GR=General Relativity

Introduction

There are still several fundamental problems with the interpretation of Quantum Mechanics. Admittedly, it is arguably the most successful theory in all of physics, but there are a number of paradoxical and unintuitive results that occur when the formalism is blindly followed. It is my opinion that QM as currently formulated is not a final theory. I believe that there is a deeper structure which gives QM as a statistical approximation, just as Classical Mechanics is an approximation of QM for systems composed of many particles.

Let's begin with the measurement problem.

A "observed" system makes a discontinuous "jump" into a single eigenstate of the measurement observable. Which of the final states will be selected is currently an unknown and unknowable in standard QM.

However, this system + observer is just a subset of a larger "unobserved" system, which evolves deterministically according to the Schrodinger equation, or more accurately the Klein-Gordon or Dirac equations, its relativistic cousins. Based on this, the device for making a measurement "selection" should reside within the QM formalism, without having to ad hoc in a new "hidden variable".

Everything is made of quantum particles. I do not subscribe to Bohr's artificially drawn line between quantum and classical systems.

I propose that the overall phases of single quantum particles are the devices by which measurement selections are made.


What are the properties which support this?

1) QM has been enormously successful over the past years for predicting all kinds of phenomena. Any successor theory must give the same results within the valid regime of QM. The overall phase does not change the probabilistic predictions of QM.

Let |S> = eia |s>, then <S|S> = <s|e-ia eia |s> = <s| e-ia+ia |s> = <s| e0 |s> = <s|s>

Hence, as stated in so many QM books, the overall phase plays no role in the probabilistic predictions of QM. However, this does not rule out the possibility that the overall phase could play some role in which eigenstate is selected in a measurement process. It simply puts a condition on the allowed values that the phase might take - it must obey a statistical law if one repeats "identical up to a phase factor" experiments.


2) The overall phase is a relativistic invariant. Thus, all inertial observers will agree on phase values.

Phi = KR = wt - kr

Also, this relation gives the phase values as the particle moves through spacetime. Other relativistic invariants include such things as c-speed of light, m0-rest mass, hbar-Planck's constant, q-electric charge, etc.  Note that in the particle's own rest-frame, the overall phase will change according to wt. Thus the phase is always "spinning" around the time axis. If a particle has a constant K, one can show that:

Phi(K=K0) = (m0c2 / hbar) T + K0R0

This description shows how the phases of separate particles could maintain a phase entanglement. If the particles are of equal rest mass and if they begin at the same spacetime event point, then their respective phases change at the same rates according to each one's proper time.


3) When one considers free particle scattering theory, the result is that the only change in the wave function at large distances is a change in the phase of the outgoing wave. Think about this. We are repeating "identical up to a phase factor" experiments with two particles. We have a target particle at a certain location. We shoot a moving particle at it with the same velocity from the same location in each setup. QM can not predict the exact outcome of this simple experiment, just the scattering cross-section probabilities. What can determine the actualized outcome? There is apparently some sort of phase interaction that occurs in the collision. Perhaps the differing overall initial phases of the particles involved in the same experimental configuration are what account for the different possible outcomes of the same experiment.


References (on 4-Vectors in SR & QM in SR)
Classical Dynamics of Particles & Systems, 3rd Ed., Jerry B. Marion & Stephen T. Thornton (Chap14)
Classical Electrodynamics, 2nd Ed., J.D. Jackson (Chap11,12)
Classical Mechanics, 2nd Ed., Herbert Goldstein (Chap7,12)
A First Course in General Relativity, Bernard F. Schutz (Chap1-4)
Fundamental Formulas of Physics, Donald H. Menzel (Chap6)
Introduction to Electrodynamics, 2nd Ed., David J. Griffiths (Chap10)
Introduction to Special Relativity, 2nd Ed., Wolfgang Rindler (All) (**pg60-65,82-86**)
Lectures on Quantum Mechanics, Gordon Baym (Chap22,23)
Modern Elementary Particle Physics: The Fundamental Particles and Forces?, Gordon Kane (Chap2+)
Path Integrals and Quantum Processes, Mark Swanson (var)
Quantum Electrodynamics, Richard P. Feynman (Lec7-rest)
Quantum Mechanics, Albert Messiah (Chap20)
Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians, Anthony Sudbery (Chap7)
Relativistic Quantum Fields, Mark Hindmarsh
The Theory of Spinors, E'lie Cartan (var)
Topics in Advanced Quantum Mechanics, Barry R. Holstein (Chap3,6,7)
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Quantum Mechanics is derivable from Special Relativity
See QM from SR-Simple RoadMap