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Wave Function Collapse Revealed

by John G. Cramer

Alternate View Column AV-210
Keywords: wave function collapse, wave mechanics, matrix mechanics, QED, NCT, QFT, renormalization, 2nd quantization, 
Published in the January-February-2021 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 09/07/2020 and is copyrighted ©2020 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

In doing these AV columns I don't usually write about my own work, partly because I'm perhaps too close to be objective.  However, this time I've decided to make an exception.  I want to tell you about a paper that Prof. Carver Mead (CalTech) and I just published in the open-access journal Symmetry.  To set the stage, let us begin with a bit of physics history.


The story starts with the birth of quantum mechanics in the mid-1920s, the physics era when Erwin Schrödinger produced wave mechanics and Werner Heisenberg produced matrix mechanics, rival theories of quantum phenomena that seemed very different and incompatible in the ways they described (or avoided describing) the inner workings of Nature at the scale of atoms.   Schrödinger built on Maxwell's existing wave theory describing light, applying the same differential equation methods to describe particles that have mass, like electrons and protons.  He was able to show that the energy levels and emitted photons of the hydrogen atom could be accurately calculated, including the mysterious energy shifts and level splittings that had been observed when electric and magnetic fields were applied to hydrogen.

Heisenberg took a more radical and unorthodox approach, rejecting any pictures of physical process.  He concentrated instead on what he called "laundry lists", tables that tabulated only observable quantities (energy, angular momentum, etc.) that could be measured. To him, these had a greater reality than unmeasurable intermediate variables, and these became the focus of his work.  He invented what he at first called a "crazy algebra" that allowed him to combine a pair of such lists to produce a third list of measurable quantities that were correct but were not a part of the input.

His older colleague Max Born soon realized that Heisenberg, who had no mathematical training in the subject, had reinvented the mathematics of matrix algebra.  Heisenberg's new matrix mechanics approach to quantum phenomena, while providing no pictures or insights into underlying mechanisms and focusing exclusively on measurement-outcome probabilities, allowed one to calculate quantum phenomena very economically.  It also worked well in treating complicated systems, because it was easy to extend the matrices to many-dimensional spaces that described all the measurable properties of many-particle systems and included extra quantities like spin.  On the other hand, Schrödinger's wave mechanics was stuck in three-dimensional space and had problems with systems having more than a few components.

Both of these theories had a common problem: when a measurement was made and/or information was gained about a quantum system, it was necessary to change the wave functions or matrices describing the system to reflect the new situation.  This change was called "wave function collapse."  Schrödinger tried and failed to make his wave functions collapse as part of the process.  For matrix mechanics wave function collapse simply required adding another rule to the cannon.  Neither theory provided a mechanism for wave function collapse.  For both theories it had to be "put in by hand" as a rule that must be applied after measurement.

For a time in the late 1920s it appeared that physics had two rival and incompatible versions of physical reality at the quantum level.  Subsequently, Schrödinger and Dirac showed that wave mechanics and matrix mechanics were equivalent, two sides of the same coin, in the sense that both always gave the same results.  But there were important differences.

The Heisenberg matrix approach led to a new quantum theory of light and electromagnetic phenomena called quantum electrodynamics or QED.  QED introduces a further theoretical twist called "second quantization", in which space is considered to be filled with tiny harmonic oscillators that interact with photons.  QED was very successful in calculating a large range of quantum phenomena, but it had some intrinsic problems.  It treated electrons as charged point-like objects, leading to super-intense electric fields at small distances giving infinite self-energy.  These infinities had to be subtracted away by a process called "renormalization" (see my AV Column in the January-February-2020 issue of Analog) to use QED.  Further, the little space-filling harmonic oscillators each have an irreducible zero-point energy, which would fill space with energy and lead to a cosmological constant that was 120 orders of magnitude greater than that observationally established by modern cosmology.  This is by far the largest disagreement between theory and experiment in the history of physics, yet QED remains our standard theory of quantum electromagnetism taught in physics graduate schools.


In the late 1950s to 1970s, Ed Jaynes of Stanford and later Washington University (St. Louis, MO) attempted to combine classical Maxwell's equations with Schrödinger's wave mechanics to perform quantum calculations using what he called "neo-classical theory" (NCT).  Over a large range of experimental results, NCT made predictions identical to those of QED, but without the burdens of point-like electrons and second quantization.  The work on NCT went very well for a time and led to major new insights into phenomena like masers and lasers.

Then, in the early 1970s came the new Einstein-Podolsky-Rosen (EPR) entangled-photon experiments that demonstrated violations of Bell's inequalities and the intrinsic nonlocality that is present in quantum mechanics (and in Nature itself).  QED had no problem with EPR nonlocality, because it only delivered final results and was not required to provide any underlying mechanism to connect entangled particles.  By contrast, Jaynes' NCT, from the nature of its detailed approach, was required to provide a mechanism for nonlocality, and it offered none.  Therefore, its predictions failed critical EPR experimental tests.

From that point on NCT, having been experimentally falsified, was essentially cast aside, leaving QED with no serious rivals. Schrödinger's wave mechanics did continue to be used in a limited way (by me and others) to analyze two-body nuclear and atomic scattering and reactions.  Some electrical engineers used it to understand the behavior of electrons and holes in semiconductors, leading to LEDs and solid-state lasers.  However, the mainstream of quantum physics marched forward under the twin flags of QED and its particle-physics descendant, quantum field theory (QFT).  Both of those theories have the intrinsic problems of including infinities that require renormalization and of spectacularly over-predicting the value of the cosmological constant.  In a recent column (Jan-Feb-2020 Analog) I reported on convincing theoretical arguments concluding that when some final Theory-Of-Everything that unites gravitational and quantum phenomena is finally formulated, QED and QFT cannot be a part of it or be derived from it, because of their renormalization requirement.  Physics needs a new direction.


This is the point at which our new work appears on the quantum stage.  As some of you know, I am the originator of the transactional interpretation of quantum mechanics (TI) based on the ideas of Wheeler and Feynman, which describes quantum interactions as a "handshake" exchange between a retarded (forward-in-time) quantum wave function and an advanced (back-in-time) quantum wave function.  In my 2016 book, The Quantum Handshake, the TI is explained in detail and is used to describe the underlying mechanisms behind over 26 otherwise paradoxical quantum optics experiments and gedankenexperiments (e.g., two-slit interference, Schrödinger's Cat, the quantum eraser, etc.)

Our new calculation, which combines Schrödinger's version of wave mechanics and Mead's collective electrodynamics approach, was inspired by the TI concept of an advanced-retarded handshake.  In our paper, we have shown that allowing an advanced-retarded electromagnetic wave exchange within the formalism of Schrödinger wave mechanics provides the needed nonlocal mechanism for correctly predicting the outcomes of EPR experiments.  This breathes new life into Jaynes' discarded NCT approach of wave-based quantum electrodynamics.  The falsification roadblock to this alternative to QED has been removed.  For future quantum theory, this represents a first step, opening the door to further progress with this alternative quantum theory that does not use renormalization or second quantization, has no infinities or absurd cosmological predictions, and thus is much more compatible with general relativity.

However, the main point of our paper was to examine a particularly simple case of wave function collapse: the transfer of one photon's worth of energy from one hydrogen atom in its first excited state to another hydrogen atom in its ground state.  We show that when the atoms exchange waves as advanced and retarded four-potentials, the transfer of energy initially rises exponentially and avalanches to the full energy transfer, all done with waves rather than photons.  We have thus accomplished a task that, for all his efforts, Schrödinger had not been able to complete: finding the mechanism for wave function collapse within the formalism of his wave mechanics.  The key trick was the inclusion of advanced waves, which enables both wave function collapse and nonlocal behavior.

The significance of our work goes beyond simply removing the NCT roadblock and providing quantum physics with a collapse mechanism.  It also allows us to examine a previously mysterious quantum process in detail, in a step-by-step way.  In fact, we have been able to produce a movie (see below) of the two hydrogen atoms and the waves connecting them during the process of energy transfer.

In the 1920s and beyond, there was an ongoing debate between Schrödinger and Einstein on one side, and Bohr and Heisenberg on the other, as to whether quantum processes like wave function collapse had any unrevealed structure, or whether they were complete as-is, with nothing more to learn about them.  Our calculations, while only a first step, strongly support the views of Schrödinger and Einstein.

At the present time, at the end of the first two decades of the 21st century, progress in physics has found itself at something of a dead end.  Generations of the best and brightest theoretical physics students have been lured into previously fashionable areas like supersymmetry and string theory, which lead to "multi-verses" that may or may not map into our own reality and which are unable to make any testable falsifiable predictions. The Standard Model of Particle Physics has settled on theories with infinities and absurd cosmological predictions.  Inflation, dark matter, and dark energy are important components of our Standard Model of Cosmology, yet we have essentially no understanding of any of these, beyond experimentally eliminating some of the more obvious candidates.

We desperately need new directions in physics.  We hope that our new "handshake" calculation, with its important insights into an alternative to flawed standard-model QED, may point to one.


John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at:  http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402.

SF Novels by John Cramer:  Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at https://www.amazon.com/Twistor-John-Cramer/dp/048680450X and https://www.amazon.com/EINSTEINS-BRIDGE-H-John-Cramer/dp/0380975106 .  His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: http://www.npl.washington.edu/av .


References:

The Transactional Interpretation of Quantum Mechanics:
John G. Cramer, The Quantum Handshake—Entanglement, Nonlocality and Transactions, Springer: Berlin/Heidelberg, Germany (2016); ISBN 978-3-319-24640-6.

Neo-Classical Electrodynamics:
E. T. Jaynes, "Survey of the Present Status of Semiclassical Radiation Theories", in Coherence and Quantum Optics: Proceedings of the Third Rochester Conference on Coherence and Quantum Optics, held at the University of Rochester, June 21–23, 1972; L. Mandel and E. Wolf, eds.; Springer: Berlin/Heidelberg, Germany, (1973).

Collective Electrodynamics:
Carver Mead, Collective Electrodynamics: Quantum Foundations of Electromagnetism, The MIT Press: Cambridge, MA, USA (2000); ISBN 0-262-13378-4.

The Mechanism of Wave Function Collapse:
John G. Cramer and Carver A. Mead, "Symmetry, Transactions, and the Mechanism of Wave Function Collapse", Symmetry 12 (8), 1373 (2020);
DOI: https://doi.org/10.3390/sym12081373 - 18 Aug 2020;
ArXiv: https://arxiv.org/pdf/2006.11365.pdf .

Movie of Wave Function Collapse:
Download the file Mov4aCM.mov from the link below and set it to "Repeat": https://1drv.ms/u/s!Ap3rYYlMocgZgZxju0KRgd5mTjXK9A?e=qR7mQy


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 This page was created by John G. Cramer on 01/27/2021.