## Welcome

Welcome, Please note: This a personal website and a work in progress. If you have comments or queries, a note via the contact page would be appreciated.

I began working on earlier versions of this site in the late 1990's as an outlet for curiosity as to the relationship between Albert Einstein's Special Theory of Relativity, and the dynamics of Quantum Mechanics (QM).

## Motivation

That curiosity had its beginnings around the time I encountered the work of one of the pioneers of quantum mechanics, Paul Dirac, through my studies and then by actually attending a lecture delivered by Dirac himself, at the University of Canterbury in 1975. The lecture was one of a series of lectures that were recorded and are now available on Youtube.

Dirac's visit coincided with my second-year studies, when I was first encountering the formalism of quantum mechanics, and struggling to relate the formalism to some sort of working "picture" as to what these equations correspond to in terms of physical mechanisms. Like many, I was puzzled by an apparent disconnect between the diverse "explanations" of quantum mechanics (i.e. interpretations), and the workings of the mathematical tools that that are used to "do" quantum mechanics.

The ideas of wave-particle duality that occurs as part of an introduction to quantum mechanics does not allow one to readily see a clear progression from explanation downwards into theory, as is often found in other areas of physics. For example, Newton's concepts regarding the motion of free-falling objects, lead in a clear and elegant manner to the classical equations of orbital mechanics, whereas wave-particle duality is used the other way, to attempt to explain how to work up from the mathematical model to our everyday experience.

As I recall, our lecturers were quick to point out that such quantum interpretations are suspect, and that the formal theory is in a sense "phenomenological", in that it provides a very good, and powerful mathematical description that matches the observed phenomena, **but may not be a direct representation** of the phenomena. Not so much a "shut up and calculate" situation, rather guidance to set aside the interpretation and put effort toward developing an understanding and familiarity with the mathematical tools, their uses, and limitations.

When interpretations are set aside, the power and clarity of Dirac's work stands out. That work involved applying special relativity to quantum theory, and provides strong evidence of a direct link between quantum mechanics and relativity. Dirac's work produced astounding results, including the mathematics of quantum spin, the spectrum of Helium (which defied Schrodinger's equation), and predicted the existence of antimatter.

Dirac's visit left me with the idea that the central role of relativity must be no accident, it provides compelling evidence that Einstein's Special Relativity (SR) is at the very core of quantum mechanics, and holds the key to explaining why quantum mechanics looks the way it does. Despite the apparently "open and shut" case to the contrary, the mathematical relationships indicate that relativity should be at the core of any explanation as to why quantum mechanics works the way it does, rather than be at odds to with it.

In other areas in physics, special relativity plays a fundamental role. In addition to being the foundation for general relativity, there are very clear-cut relationships between special relativity and electrodynamics, and special relativity and classical mechanics, with the latter being an approximation to relativistic relationships. In the case of electromagnetic theory, one can take electrostatic forces and by applying special relativity, predict the magnetic field and Maxwell's equations.

Despite this central position, the concept that quantum mechanics could be the result of the relativistic nature of reality, runs counter to conventional accounts of quantum theory. Typically, such accounts seek to explain quantum effects as some hidden-from-view interference process that comes about as dimensions and energies reduce in scale.

### The Basis of Mainstream Interpretations

In order to understand how the mainstream view that quantum mechanics is incompatible with relativity, despite the obvious role of relativity within quantum mechanics, it pays to understand how the basic assumptions and premises that underpin those mainstream interpretations are put together.

Please note that I want to be clear that the structure of the mathematical formalism of quantum mechanics is not being examined here, we are looking at the rationale behind accepted "interpretations" of quantum mechanics and asking if they are actually obstructing the understanding QM, rather than helping.

A striking feature of mainstream interpretations of quantum mechanics is that they are quite diverse (*e.g. wave-particle duality with collapse/pilot wave, or a multiverse of branching realities where everything happens*). They are nothing like each other, yet despite the divergence, they look to be formulated on top of a common set of underlying assumptions.

One assumption in particular is there within almost all of them, the assumption that a single type of wave-like interference process explains all classes of quantum behavior.

This assumption arises from taking two steps. First, by taking the position that scattering patterns that match the patterns produced by waves, provides incontrovertible evidence that the patterns can only be produced by a wave interference mechanism (however hidden). Second, that the same type of "wave process" is responsible for all classes of quantum interaction.

After accepting this starting position, only then do the interpretations diverge and begin to compete with each other on the basis of the "reasonableness" of the various ad-hoc (and in my view unfalsifiable) mechanisms that each requires in order to rescue the wave interference mechanism from the fact that its operation is perplexing, and would have to be hidden from us because we see only localized particles, yet wave interference is non-local.

Whether one says that the particles within the world exist in an indeterminate wave-particle state until observation, or one says that the particles have definite trajectories, but the universe as a whole branches into multiple realities where 'everything happens', one is actually addressing the same problem. The problem of explaining how interference could be at work behind the scenes, and how it applies across the board, for all classes of particle.

Wave interference occurs when a wave interacts with a structure and spreads out to form a pattern that forms at the point of detection. The detected pattern is formed by contributions from all components of the original wave and their paths from the interaction to the place of detection. If one takes the probability of finding a particle at some point as being the result of an interference process, then one needs to calculate the value of the interference pattern across the whole of detection space, not just the amplitude at one point of interest. The amplitude of the probability of finding a particle at one point can only be found when one knows the amplitudes across the whole detection space.

If interference is responsible, then one needs to explain how the values for events that never happen affect the likelihood of events that do happen. This applies to both the source and detection locations. One has to explain how a discrete particle can explore the whole region of the scattering structure (i.e. particle goes through all slits) and then the whole region of possible detection, including all pathways between.

Clearly, if quantum mechanics were to be the result of an underlying interference mechanism then yes, it would be logical to conclude that a multiverse of realities, (or perhaps a spooky 'wavefunction' that arises and collapses) would logically follow, and it would seem reasonable to presume that the problem of interpreting quantum mechanics was the problem of explaining how the mechanism of interference can be there, but hidden so we only see indirect evidence such as diffraction patterns made up of discrete events.

However, focussing on the alternatives that are left to us as a consequence of deciding in advance that the answer is interference, shuts out consideration of the possibility that interference may not fully explain the phenomena we observe. That the requirement to add in ad-hoc mechanisms (collapse/branching of reality), mechanisms by the way that are not actually there in the mathematics of QM, would be unnecessary if interference was not the only mechanism that could generate the observed patterns.

A weakness in the logic that leads to the assumption that interference is at work can be seen if we turn the connection between the observed pattern and the presumed mechanism around.

In quantum experiments such as a the double slit, the form of observed discrete scattering patterns matches a wave interference pattern. Now turn that connection the other way about: Because the pattern matches a wave interference pattern, we can be sure in advance any model that utilises an interference mechanisms then the model will produce the right prediction.

However, the fact that we know in advance that the model will be successful in reproducing the pattern does little toward helping us determine if we have the correct model, because it only tells us that this is a *possible* model and does not eliminate the possibility that a different mechanism could produce the same pattern.

Just as a system of epicycles and deferents forms a possible explanation of orbital mechanics because it can be made to give the right answers, the mechanism interference is also a possible explanation of quantum mechanics because we know how to use it to get the right answers (in some significant situations). However, in both examples one cannot use the fact that one has chosen a model that we know will always give the right answers, to conclude that the model is the correct model.

I want to stress that this does not mean that the mathematical relationships, particularly the "wave-function" and mathematical formalism of QM are in any way invalid, rather, I aim to show that difficulties in understanding and interpreting quantum theory may well be the result of mistakenly thinking of the mathematical relationships in quantum theory as if they represent literal "wave functions", just because we have mistakenly convinced ourselves that the underlying mechanism is interference.

In my view, the core relationships in quantum mechanics, do not map directly to models of reality based on quantization of substrates (e.g. segmenting space, time and energy into chunks), underlying randomness, general wave-particle duality, wave-function collapse, or bizarrely, particles "interfering with their other selves" across multiple instances of reality within a "quantum multiverse".

The intention here is to re-examine the simple core steps of logic and inference that have led to the popular and conventional view that wave-particle duality and/or the multiverse are our only options, and point out where the logical fallacies and ad-hoc steps could be.

To do this, I have chosen to use computer modelling (rather than animations) to illustrate and check for consistency with the results of QM experiments, and convince others that there are, alternatives to the conventional approaches.

### Simulation

This video illustrates what can be accomplished by separating the dynamics of light/photons, from the dynamics of matter particles while still applying the the mathematics of quantum mechanics. Instead of assuming that matter temporarily acquires the properties of photons, (and thereby scatter into patterns similar to those made by photons by the mechanism of interference), this video shows how a model based on work by physicists Alfred Landé and William Duane, where discrete photon interactions mediate in particle scattering, can reproduce the experimentally observed results that are conventionally, (and in my view erroneously), attributed to de Broglie waves.

Copyright

Original Content by John K N Murphy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Where feasible, I will do my best to reference and link to open source material for background, examples, and reference.