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.
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.
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 .
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.
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,
Carver Mead, Collective Electrodynamics: Quantum Foundations of Electromagnetism, The MIT Press:
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 .
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