## Welcome

Welcome, this site contains a somewhat disjointed approach to the problem of the interpretation of quantum mechanics. It is a continuation of earlier versions, started 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).

One avenue that I have chosen to follow as a starting point is making use of computer simulations of quantum experiments to demonstrate the viability of William Duane's 1923 hypothesis for crystal diffraction. Although Duane's work does not, at first sight, look to connect in a ready-made way to the mathematics of contemporary quantum wave equations his approach is interesting because it depends on, and is consistent with, special relativity and early work on quantum theory by Einstein.

Duane showed how Einstein's work on the photoelectric effect provides a model for quantised exchange of momentum that can be applied to the diffraction of X-rays by crystals. This model allows the problem to be treated as a discrete particle scattering problem and provides a marked difference from conventional explanations that rely on particles behaving as if their interactions incorporate behaviours similar to classical waves. In contrast, Daune was able to derive the same scattering relationships that were derived by Bragg's wave model, "*based on quantum ideas without reference to interference laws.*" (www.pcontent/9/5/15nas.org/8).

Duane's work was extended by Gregory Breit (www.pnas.org/content/9/7/238) to explain how diffraction through gratings and slits can also be analysed using discrete momentum transfers.

While it is well known that classical wave mechanics can be successfully applied to calculate interference patterns that match the observed particle scattering patterns, Duane's scattering model also produces the same results, calling into question the soundness of the conventional assumption that classical wave interference has to be incorporated into explanations of quantum mechanics.

Duane's work shows how scattering by crystals and gratings (with Breit, including the notorious 'double slit') can be straightforwardly modelled by treating the reactions of the scattering object as being constrained to a quantized set of possible reactions while the incident particles are treated as a localised entities that obey the rules of energy and momentum conservation.

Unlike classical mechanics which is fully deterministic, Duane's model requires quantized momentum transfers that depend on the state and structure of the scattering object and this feature leads to an uncertainty in outcomes and places the same constraints on determining particle position at the time of interaction while still being able to observe the scattering pattern, as the wave model. The major difference is that while the position cannot be measured (which requires some form of additional interaction), the particles do have definite positions and trajectories.

If Duane's model is viable, then the various attempts to reconcile how it is that discrete localised particles can temporarily operate as distributed classical waves, could well be spurious.

By employing standard quantum theory to calculate the possible reactions of an extended object, Duane's approach looks to provide a better fit to the mathematical formalism of contemporary quantum mechanics than the tortuous rationalisations of wave-particle duality, where the incident particle is thought to mysteriously 'explore' the scattering object as a classical wave.

Because Duane's model keeps the incident particle as a discrete entity throughout, a simple model can be constructed with particles following definite trajectories before and after the interaction. As can be seen in the simulation, the ability of this simple model to reproduce Laue scattering patterns is striking in both simplicity and beauty.

In essence, taking Duane's approach involves shifting our view as to what the mathematical equations of quantum theory represent without throwing the 'baby out with the bathwater'. The primary shift in viewpoint is to challenge the conventional view that the equations completely represent the behaviour of incident particles that individually explore all avenues through a classically passive scattering object, and then later magically turn up as discrete localised objects on detection.

Despite the radical differences between interpretations based on interference/wave-particle duality, (e.g. 'pilot wave'/collapse'/'multiple realities'), these interpretations have a common basis. All contain attempts to couple observed scattering patterns to the same type of interference processes that classical waves undergo. As if there is a one-to-one correspondence between the mathematical tools of quantum theory and the interference of classical waves.

In contrast, Duane showed that if one treats the possible momentum reactions that an extended object can make as being a discrete and quantized, then the set of reactions that are required to reproduce the observed crystal scattering can be tied to the crystal geometry using the same quantum rules that Niels Bohr had deduced for the angular momentum of atomic orbitals.

### Motivation

Ever since I encountered the work of one of the pioneers of quantum mechanics, Paul Dirac, through actually attending a lecture delivered by Dirac himself at the University of Canterbury in 1975, I have been convinced that there is something wrong, not with quantum mechanics, but with the way quantum theory is presented within an opaque and bewildering cocoon of 'philosophical' and, in my view, pseudo-scientific rationalisation, that does not actually describe how quantum theory works.

*[Note: Dirac's lecture was one of a series of lectures that were recorded and are now available on Youtube.]*

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.

Ideas of wave-particle duality, or particles undergoing classical wave interference, are not only disconnected from formal quantum theory, I would argue that they do not even begin to explain the connections that Dirac had uncovered.

Dirac produced outstanding work. He developed the mathematics of quantum spin, explained the spectrum of Helium (which defied Schrodinger's equation), and predicted the existence of antimatter, all by applying relativity to quantum theory.

None of this work is even remotely addressed by ideas of multiple instances of universes, a wave-function the 'collapses' on observation, or a non-local 'quantum potential'.

Dirac's visit left me convinced that the central role of relativity must be no accident, providing 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.

### The Basis of Mainstream Interpretations

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*). Despite the apparent divergence, there is a common set of underlying assumptions.

In particular, one assumption is located within almost all of them: The assumption that some form of wave-like interference process must be the key to explaining quantum phenomena.

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 these premises, 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 would have to be hidden from us because we directly observe localized particles, which is not consistent with the non-local nature of the interference of classical waves.

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 instances of reality 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 every type of particle (i.e. photon & matter).

Classical interference occurs when a wave interacts with a structure and spreads out with segments taking different routes to superimpose at the point detection. The detected pattern is the integral across all possible paths from the location of the interaction through to the point of detection.

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, by focussing on the alternatives that are left to us as a consequence of deciding in advance that the answer is interference, we exclude consideration of the possibility that classical interference is the route we must take to comprehend quantum phenomena.

In quantum experiments such as the double-slit experiment, the form of observed discrete scattering patterns matches a wave interference pattern. Once we decide that an interference model is the only possible way of reproducing the observed pattern, we are forced to accept whatever ad-hoc mechanisms seem to 'most reasonable', no matter how 'weird' or 'counter-intuitive'.

A system of epicycles and deferents forms a possible way to explain of orbital mechanics because it can always be made to give the right answers if we add just enough ad-hoc steps. In the same way, interference can be made to fit as a possible explanation of quantum mechanics. However, in both these cases, one cannot use the fact that one has chosen a model that we know will always give the right answer, 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".

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".

### Simulation

The intention here is to use software models to demonstrate how quantum theory can be used to explain what we see, without incorporating an interference mechanism. The starting point is the work of William Duane, an Ameican physicist who produced a working hypothesis of crystal diffraction, **"without reference to interference laws"**.

Duane's work is very interesting because it shows that crystal diffraction can be modeled in a way that retains definite particle trajectories rather than alternating back and forth between diffuse wave behaviour, and discrete particle interactions. The following video provides an overview of to how Duane's model works for crystal diffraction and shows how it produces results consistent with both quantum, and classical physics.

This video illustrates what can be accomplished by separating the dynamics of light/photons, from the dynamics of matter particles while still applying 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.