The property of intrinsic mass-energy

The intrinsic mass-energy of a boson is a function of the phase difference of its two component waves (fig.1).

(1)

$\rho =\cos \left({\phi }_B-{\phi }_A\right)=e^{-i\left({\phi }_B-{\phi }_A\right)}$

A negative mass-energy ρ results from a reference wave leading its partner by between ¼-cycle and ¾-cycle; i.e. $\rho <0$, where ρ < 0, where

(2)

π/2 < | φB − φA | < 3π/2.

This value affects the probability that the boson will collapse others, or be collapsed by others.

Bosons as oscillators

The boson's waves can be interpreted as components of a simple oscillator. When these two waves are plotted on orthogonal axes, the mass-energy is equivalent to the elliptical deviation from a circle, such that a circle has a mass-energy of zero.

Mass-energy remains invariant while the boson propagates in the degenerate state, conserving its energy:

(3)

$d\rho /d\phi =0$

Wave collapse

The mass-energy of a boson modulates the phase of any other boson that it overlaps (like a field operator), which widens the 'quantization window' for the phases of those bosons.

In QFT, We may interpret this as an excitation of the field, or an operator of the vacuum energy, so that wherever a boson is propagating, it gives mass-energy to the vacuum, as seen by other bosons.

The implication of this mechanism is that bosons having large mass tend to collapse within a short distance of their source position, and less massive bosons tend to travel far from their source position before being collapsed. We've shown median distance of boson collapse to be inversely proportional to its non-excluded mass, in controlled conditions.[15]

Lighter bosons (typically the flux of vacuum energy) may create quantization conditions for the more massive bosons, which provides further collapse opportunities for them. Conversely, the heavy bosons provide opportunities for the lighter bosons to collapse, when they would have otherwise propagated great distances.

Particle size

Compton radius

This generalizes to a Compton radius, having a 50th percentile radius $r=\left(\ln 2\right)/\rho$ for non-overlapping phases of a shell.

No singularities

The above distribution has no singularity at the origin. Rather than being inversely-proportional to radius, the probability of collapse is based on the interaction of the boson's shell with a quantity of vacuum flux. In three-dimensional space, the boson's shell is the surface of a sphere, with an interaction area.

Our formulation differs from Newtonian and other classical formulations, because it does not have a singularity at radius 0, but instead falls off approaching 0. It is at this distance that Newtonian physics fails, and where ours differs from the Newtonian. This difference may be responsible for corrections like the Yukawa potential.

Degeneracy pressure

The Compton radius establishes an equilibrium distance around which particles will settle, for any given flux density of the environmental vacuum. This equilibrium does not occur in a solely Newtonian distribution. More:

• Degeneracy pressure

Coherence

Conserved particles are more likely to lose coherence if their bosons propagate to a large radius in the presence of a flux.

• Constitution: Coherence

'Massless' photons in QED

In QED we say that photons do not have mass. Our mechanism says they may have mass, but this does not contradict QED, because our photon is transmitted as two separate bosons, which land at their target to each substitute a boson at two fermion instances at the target. This means that there is no change of mass at the target, unless the photon changes the constitution of the target fermion.

As a bonus, this substitution generates a flux from a charged particle, so we have a quantum photoelectric effect.