This article is an easier-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

This work is respectful of 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, oscillators, and bosons

Waves are scalar, bound in pairs as oscillators, as a boson shell

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

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

The oscillator unit does some important things 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 classical mechanics, 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 a harmonic oscillator, we don’t privilege either wave, so the oscillator 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 show the properties of this oscillator, and how they express themselves in physical systems.

2. Equivalence

d φ = d s = d t

These oscillators (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.

Fundamentally, we do not assume any background space for this oscillator to propagate. It’s just a changing phase value, extending in one spatial dimension, marking time implicitly: a clear relationship in Noether's Theorem.

It might be easier to visualise this as a bubble or shell in flat 3D space, with the shell expanding outwards at the speed of light. Having zero thickness, the shell 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 such a shell surface.

3. Quantization and localization

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

Oscillators collapse into a fermion where waves from two different shells 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 have no unique position, only a phase value, offset from their respective sources. If we apply statistics in larger systems, we can 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.

Also, with time as a given, and phase and space being equivalent in the first order, the no-action default state is to be constantly propagating, so everything propagates and all propagation is inherently thermodynamic.

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 the waves that caused the collapse will have the same phase, and they originate from the same source point at the new fermion. There is no way to distinguish them. The exclusion is only removed when one of the two oscillators is removed from the radiating shell, which happens when the one of the non-excluded waves couples to another oscillator (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 as a function of the phases of the waves in an oscillator. This means that the shell carries the mass as it radiates. When an oscillator in the shell collapses (rule 3), the oscillator's mass 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, which looks like potential energy in its behavior. Next, we’ll see how this helps collapse other shells, and generate gravitational fields.

6. Phase operator

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

Fig.4: Phase Modulation from $ρ$ changes the effective phase of W, 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 shell 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 can look like a curvature of space.

We define the the vacuum as the shells of oscillators radiated from other fermions, rather than a continuous field. Our vacuum is therefore not homogeneous, and may vary with the distribution of matter in space, and evolve with time.

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 with mass, and a picture of coherence that applies to trivial particles and black holes alike. You can find further reading in our papers, and a concise list of emergent properties in our introduction.