A fermion event is a unique point solution of two waves overlapping concurrently with a value −b.
Bosons are spherical shells of zero thickness, and likewise, fermion events are points of zero size.
Our mechanism has distinct definitions for bosons and fermions:
Compositionally, we can construct bosons and fermions from fundamental waves:
This structure provides an ontological unification of waves and particles, providing satisfactory answers to problems in this area.
Fermions are localized snapshots of the continuous journeys of bosons. Fundamentally, fermions and bosons are made of the same stuff, but have different uniqueness properties. The reference waves [fig.1] have a unique positional solution when their bosons become a fermion. In other variables they are indistinguishable, so couple by being co-localized. Conversely, bosons are distinguished by unique source and phase (but not space), are not coupled with other bosons, and have no unique spatial solution (Table 1).
|Property||Pre-interaction Bosons||Fermion||Emitted Bosons|
|Position||Ambiguous (many shells)||Unique||Ambiguous (on‑shell)|
|Phase (reference waves)||Proximate||Identical||Excluded|
|Phase (partner waves)||Distinct||Unique||Available|
This uniqueness can be expressed as an uncertainty relation, of position and the other conjugate-dependent properties (e.g. time, momentum).
Fermions are the only points at which we can observe matter, because these are the only points at which matter interacts or couples. At all other times, matter is propagating at light speed, and may couple again, whether observed or not. As we mention in the gravitation article, the mechanism limits opportunities for matter to interact, "…you cannot measure it more and more precisely; you'd just find fewer (or no) impulses within a smaller sample length, with regular gravitational interactions as background noise. Thus gravitational waves exhibit their own uncertainty relation, between the imparted momentum and the size of the sample."
What we see classically as 'the same fermion' is not continuous at the quantum level. Instead, a persistent fermion state is one that is soon re-constituted after its bosons are emitted, in a cyclic process, using bosons that are the same as (or close enough to) the bosons that originally constituted the fermion. [more...]
This mechanism gives us the ability to show, for example: