Orthodox Quantum Mechanics

Orthodox Quantum Mechanics is an algorithm which is used by physicists to make predictions about the outcomes of experiments.

There will always be voices (even from otherwise reasonable people) insisting that it's simply not the role and purpose of physics to provide a coherent and objective description of nature.
Detleff Durr and Dustin Lazarovici

The orthodox (Copenhagen) school of Quantum Mechanics does not attempt to provide a coherent and objective description of nature, so it is not satisfactory to me.

It would seem that the theory [quantum mechanics] is exclusively concerned about "results of measurement", and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of "measurer"? Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for some better qualified system ... with a Ph.D.? If the theory is to apply to anything but highly idealized laboratory operations, are we not obliged to admit that more or less "measurement-like" processes are going on more or less all the time, more or less everywhere. Do we not have jumping then all the time?
J.S. BELL
Against "Measurement"

Some say that the transition that one makes from classical to quantum is that properties of particles are now represented by operators. I do not have a problem with the idea of particles being represented by operators. This transition has also given rise to some beautiful mathematics. However, it is necessary for one to ask themselves what this mathematics tells us about reality. For example, we translate a classical system of particles into mathematics by representing their positions as vectors in three dimensional space. At any point we desire, (for example, after we have solved the ODE for their motion), we may "translate back into reality" by saying the positions of our particles are given by these vectors. Quantum mechanics makes no effort to translate its operators back to reality.

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.
Niels Bohr

Instead of reality, orthodox quantum mechanics translates its operators back into "our knowledge of reality". The ontology of orthodox quantum mechanics reeks heavily of idealism, which is the belief that the only things which truly exists are our perceptions of the external world. This ontology also depends on a notion of consciousness, which has yet to be defined and studied properly by physicists.

You see, the quantum mechanical description is in terms of knowledge. And knowledge requires somebody who knows.
Rudolf Peierls

Idealism as an ideology is fine, unless one is attempting to study the universe. Idealism rejects the notion of "the external world", but we cannot reject the thing we mean to study!

Given that a rock is a creation of my understanding, how is it possible that I might be killed by a falling rock, since in that case I would be smashed by one of my own notions? Can one commit suicide with the help of one's own concepts? Or be surprised and assasinated by it?
Jean-Francois Revel

Solipsism cannot be refuted. But if such a theory were taken seriously it would hardly be possible to take anything else seriously. So much for the social implications. It is always interesting to find that solipsists and positivists, when they have children, have life insurance.
John Bell

A great deal of damage has been done to the physics community by this subtle introduction of idealism into our theories of the universe, and it is unclear how long it will take for us to recover.

Formerly, the cruelty, the meanness, the dusty fretful passion of human life seemed to me a little thing, set, like some resolved discord in music, amid the splendour of the stars and the stately procession of geological ages. What if the universe was to end in universal death? It was none the less unruffled and magnificent. But now all this has shrunk to be no more than my own reflection in the windows of the soul through which I look out upon the night of nothingness. The revolutions of nebulae, the birth and death of stars, are no more than convenient fictions in the trivial work of linking together my own sensations, and perhaps those of other men not much better than myself. No dungeon was ever constructed so dark and narrow as that in which the shadow physics of our time imprisons us, for every prisoner has believed that outside his walls a free world existed; but now the prison has become the whole universe. There is darkness without, and when I die there will be darkness within. There is no splendour, no vastness, anywhere; only triviality for a moment, and then nothing. Why live in such a world? Why even die?
Bertrand Russell

Bohmian Mechanics

If you don't enjoy the philosophical baggage that comes with the Copenhagen interpretation, I might recommend an alternative. Bohmian mechanics does attempt to provide a coherent and objective description of nature, and it makes the exact same predictions as the orthodox school.

if we cannot disprove Bohm, then we must agree to ignore him.
J. Robert Oppenheimer

In addition to Bohmian mechanics, I am also a fan of the Many Worlds Interpretation (or at least, my interpretation of it). This interpretation amounts to a "Many Worlds" version of Bohmian mechanics, where there are infinitely many non-interacting worlds in which particles are guided by the wavefunction. This interpretation lacks the distinguishing "branching" that Many-Worlds features. Many worlders will argue that the introduction of particle's positions are unnecessary. But point particles don't make sense unless they have positions. Bohmians will argue that there is no need for many worlds. But I argue that it is a neat way to interpret the quantum equilibrium hypothesis.

Research in Relativistic Q.M

My research in relativistic Q.M pertains to the study of electron-"photon" systems, whose wavefunctions are "multi-time". There are two things to unpack in that sentence. First, what is a photon?

On Photons

In classical Maxwell-Lorentz electrodynamics, a photon is a small disturbance or "bump" in the electromagnetic field. It is not a particle, it is a wave(packet). However, this story changed after the discovery of the Compton effect. Compton's experiment showed that an electron and a photon can "bounce" off each other in a momentum exchange reminiscent of an elastic collision between particles. Physicists started talking about photons as though they were particles but this all happened with some very unfortunate timing. The physics community was still in the midst of an existential crisis regarding particles and cats.

The Compton effect, at its discovery, was regarded as a simple collision of two bodies, and yet the detailed discussion at the present time involves the idea of the annihilation of one photon and the simultaneous creation of one among an infinity of other possible ones. We would like to be able to treat the effect as a two-body problem, with the scattered photon regarded as the same individual as the incident, in just the way we treat the collisions of electrons.

C G. Darwin
"Notes on the Theory of Radiation (1932)"

Since Darwin's time, there have been two major breakthroughs that have allowed us to begin studying electron-photon interactions in the way we originally intended. The first was Bohmian Mechanics, which allows us to treat quantum particles as particles with definite positions. The second breakthrough was made recently by Michael Kiessling and Shadi Tahvildar-Zadeh, wherein their paper titled "On the Quantum Mechanics of a Single Photon" they produced a viable photon wave equation. A photon can therefore be defined as a quantum particle whose wavefunction evolves according to the KTZ equation. Just like a Dirac electron, the photon has a definite position which is guided by its wavefunction.

Multi-Time Wavefunctions

The notion of a single time configuration space is not relativistically covariant. Two space-time events which are equal time in one reference frame will not necessarily be equal time in another. If one starts with a subspace of configuration space-time that is equal times, then undergoes a change in their frame of reference, they will find that the subspace will no longer be in equal times.

To achieve a fully Lorentz covariant theory of a quantum multi-particle system, one must formulate the evolution law of the wavefunction to be on a general configuration space-time. Physicists such as Dirac were aware of this, and chose to ignore it. Specifically, they claimed that one could simply solve for the equal-times wavefunction in a specific frame of reference, then use the Lorentz covariance to of the wavefunction to solve for it in all other frames of reference by performing a Lorentz transformation. Here's a step by step breakdown.

Formulate the wavefunction evolution law on multi-time configuration space-time.
Present the Initial Value Problem for the multi-time wavefunction.
Restrict your wavefunction to the equal-times subspace of configuration space-time, and present the new (and hopefully easier to solve) equal times IVP.
Solve the equal-times IVP.
Use the covariant transformation properties of the wavefunction to solve for any multi-time configuration using the equal-times solutions

The problem lies in step 2. This all assumes that the IVP for the multi-time wavefunction is well-posed. But that may not always be the case, at least we shouldn't take it for granted. Physicists will probably take it for granted, but we as mathematical physicists should actually make sure that it is well-posed.

Compton Scattering as Probability Conservation

Using their newly discovered photon wave equation, Michael Kiessling, Matthias Lienert, and Shadi Tahvildar-Zadeh were able to "derive" Compton Scattering for an electron-photon system in 1 space dimension."Derive" is being used here in the same sense that a mathematical theorem is "derived" from a set of axioms. The physical assumptions taken were very simple; the particles may not cross, and the total probability of the wavefunction must be conserved.

My research has been focused on the generalization of KLTZ's work to the multi-electron case. We ran into some interesting problems. Here is a simulation of a photon between two electrons. This took my computer a whole month to run.

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