Why Three? The Case for Temporal Triality
The number three appears everywhere in physics — three spatial dimensions, three particle generations, three colours of quark charge. What if time follows the same pattern?
Physicists are comfortable with the number three when it comes to space. Length, width, depth. x, y, z. The three dimensions of a room, a planet, a galaxy. We do not find this suspicious. We have grown up in three spatial dimensions and they feel natural.
We are less comfortable with the number three when it comes to time. Time, in the Standard Model, is one-dimensional. There is one time direction. The equations are written in (3+1)-dimensional spacetime. It does not have to be this way — the mathematics would work fine in (3+3)-dimensional spacetime — but the (3+1) convention fits the observations we currently have, so we have never seriously questioned it.
Here is the question I want to ask: why does the number three keep appearing in physics?
The Three Generations Problem
The Standard Model contains three generations (or "families") of matter particles:
- First generation: electron, electron neutrino, up quark, down quark
- Second generation: muon, muon neutrino, charm quark, strange quark
- Third generation: tau, tau neutrino, top quark, bottom quark
The first generation is the one ordinary matter is made of. The second and third generations are heavier, unstable copies. The muon is essentially a heavier electron that decays in about 2 microseconds. The tau is heavier still.
Why are there three? Not two, not four, not forty? The Standard Model has no answer. The number three is inserted by hand, based on observation. It has no theoretical justification.
Three Colours
Quarks carry a property called "colour charge" — this is not actual colour, just a convenient label. There are three colour charges: red, green, blue. (And their anticolours.) Three, again.
The symmetry group of quantum chromodynamics is SU(3). A three-dimensional symmetry group, for a three-valued charge.
Three Spatial Dimensions
There are arguments from physics and mathematics about why space should be three-dimensional — anthropic arguments about stable orbits, mathematical arguments about the uniqueness of the cross product, analytical arguments about wave propagation. But these are post-hoc rationalisations of an observation, not derivations from first principles.
We live in three spatial dimensions. We do not know why.
A Pattern
Three generations. Three colours. Three spatial dimensions. And, in the Standard Model, the conspicuously lonely one temporal dimension.
One of these numbers is not like the others.
The proposal of Quantime: The Theory of Everything is that the temporal dimension count should also be three, and that the appearance of three throughout physics is not coincidence — it is a structural signature of a (3+3)-dimensional cosmos being viewed through a (3+1)-dimensional perceptual interface.
The three particle generations are shadows of three temporal dimensions. The three colour charges are a compactification artefact. The SO(3,3) symmetry group of full six-dimensional spacetime decomposes, when you project onto a 3+1 interface, into the SU(3) × SU(2) × U(1) gauge symmetry of the Standard Model.
Not by metaphor. By mathematics.
The Obvious Objection
The obvious objection is: if there are two extra temporal dimensions, why can't we see them?
The same reason we can't directly perceive the six extra spatial dimensions of string theory: they are compactified. Curled into loops at the Planck scale. Their effects are not absent — they are translated. They show up as particle families, as colour charge, as the specific symmetry structure of the forces.
We're not looking at a 3+3 universe. We're looking at its projection onto a 3+1 screen. A beautiful, elaborate, four-dimensional shadow of something deeper.
The screen is not the movie.
More on this in Chapter 1 — The Desktop Icon.