This article is an easy-reading version of our Physicality article.

Introduction

After working on some problems in mathematical physics, we saw an opportunity to design a way for the foundations of physics to be expressed as minimally as possible.

Consistency with accepted science

Although this sounds pretentious, it is respectful to the work done so far on the Standard Model, which has proven correct, for the areas it is intended. Indeed, we reconcile with standard physics, and our purpose is to find a way of originating the assumptions of the Standard Model from some first principles, without necessarily using the Standard Model constructs and free parameters. The relevant standard details emerge as our configurations are grown and explored for their observable effects.

This article describes physicality, or the things that make up what is physical, what those things are doing when they are not physical (when they are ‘hiding’!), how things can behave fairly consistently, and then seem to randomly interact.

Existing formulations

Quantum field theory is a statistical method, which does not usually tell you want happens in an exact experimental configuration. Instead, it quantifies the possible results you might get from similar configurations including some unknowns. It uses fields to contain energy and states, optionally-charged fermions, force-carrying particles to communicate between fermions, and coupling constants to define how much of one quantity transfers to another entity. Quantum mechanics, as used in this way, with the unknowns included, is non-deterministic, in that it does not tell you exactly what nor when your result will be, for any given input.

How are we thinking differently?

Our design is deterministic, and it claims to be able to hold all information that can define a system, such that its future states can be computed from a complete description, if you’re lucky enough to have one. Analytically, we can rebuild the constructs that QM enjoys, like fields, vacuum, wavefunctions, etc.

Our 'trick' is to go smaller than a fermion; we break it up, and find that a relatively simple construction can lead us to an expression of fermions, bosons, their interactions, and their observable effects, without needing to convert between incompatible algebras or pictures. We do this without discarding quantum mechanics, and continue to find ways that the existing standard work can be correct in its designed context.

The Foundations

We’ll start with the foundations. There are just six rules, which are enough to describe a dynamic framework for matter and energy. This first step is to define a basic unit of information.

1. Waves and bosons

Waves are scalar, bound in pairs as oscillating bosons

We’ve defined a boson, which has two waves, and only two waves. These waves cannot be separated, and they will always be bound together in the boson. No other waves can merge with these in the boson.

Fig.1: Boson propagation. See also: time.

This unit does some things that are important for us. First, it is an entity. It is not a physical entity yet, because we later define what ‘physical’ means, and it needs a few more conditions to be satisfied.

This entity has a mass-energy value, encoded by the two component waves. Later, we’ll see that this value is conserved, and influences interactions.

Harmonic oscillator

If you know a bit of Newtonian physics, you might have spotted that this resembles a harmonic oscillator with the same two components. Each wave is simply a sine wave, so you can address its properties either by its phase angle $φ$ , or, more ambiguously, the value of the phase angle (some value on the $b$ axis).

Unlike an oscillator, we don’t privilege either wave, so the boson is a superposition of states. Depending which wave is chosen as the reference, we can obtain spin-up or spin-down (spin being the sign of the oscillator’s angular momentum).

The rules below will read into some of the properties of this boson, and show how they express themselves in physical systems.

2. Equivalence

d φ = d s = d t

These bosons (waves) propagate at light speed, and only at light speed. The wave phase progresses as it extends from its source, and it does so at a constant rate. You could say that the oscillator itself defines time and distance, as it changes phase.

We do not assume any background space for this boson to propagate. Fundamentally, it’s just a changing phase value, extending in one spatial dimension, marking time implicitly. However, it might be easier to visualise this as a bubble in 3D space, whose surface is expanding outwards at the speed of light. Having zero thickness, the bubble is infinitesimally thin, and if you’ve defined a space, it sweeps over any defined points in that space. Nothing really exists inside or outside of this surface, and nothing, not even space itself, can be meaningfully addressed unless it is a boson surface.

3. Quantization and localization

(A_{1} or A_{2}) = (B_{1} or B_{2}) = - b

Bosons collapse into a fermion where waves from two different bosons have value $- b$ at a unique point:

Fig.2: Fermion Event.

This provides opportunities for the continuous waves to generate a discrete point. It’s a quantization condition. Importantly, this is the only point where the two bosons share this condition, so they are coupled uniquely at this point. Immediately before and after this point, the bosons had no unique position, only a phase value, offset from their respective sources. We may construct an uncertainty principle from this behaviour.

It remains as a fermion for precisely zero time, before resuming as bosons, radiating from that point. The waves emerging from that point are entangled quanta.

4. Exclusion

Waves having the same phase and source are excluded

Fig.3: Conserved re-constitution
of an electron-type fermion.

Waves having the same phase and source are non-unique, so are excluded from interactions. This occurs immediately after every fermion, because two of the waves will have the same phase, and they originated from the same source point. There is no way to distinguish them. The exclusion is only removed when one of the two bosons is removed from the radiating shell, which happens when the one of the non-excluded waves couples to another boson (fig.3: $t_{2}$ ). We map this to electro-weak symmetry breaking.

5. Mass-energy

ρ = - b e^{- i (φ_{B} - φ_{A})}

We define mass-energy as a function of the phases of the waves in a boson. This means that the boson carries the mass-energy as it radiates. When the boson collapses (rule 3), the mass-energy is relocated and conserved.

You might have noticed that the oscillator of fig.1 is not ideal; one of its phases is offset slightly, so that it does not have a circular phase picture. This phase offset gives the boson mass-energy. Next, we’ll see how this helps collapse bosons, and generate gravitational fields.

6. Phase operator

φ_{modulated} = φ_{carrier + ρ}; ρ = \sum_{i=1}^{n} ρ_{i}

Fig.4: Phase Modulation from ρ, on introduction of a shell to wave Z.

While propagating, mass-energy is a phase operator where it overlaps other bosons. If bosons overlap, they will co-modulate at the overlap, and enable a wider phase window for collapse. The implied behaviour is that large masses will collapse at smaller radius than smaller masses, where an environment of bosons is present.

The modulation advances or retards the collapse by a fraction of Planck length, which looks like a curvature of space.

We assume that the vacuum is simply the bosons radiated from other fermions, rather than a continuous field.

Emergent physics

We’ve only just mentioned the vacuum, which is where it gets interesting, and we see lots of physics emerging, like the gravitational field, a context for charge, implicit Compton radius, and a picture of coherence that applies to trivial particles and black holes alike. You can find further reading in our 2014 paper, and a concise list of emergent properties in our introduction.