“The theory of relativity is concerned with the connection between the descriptions of phenomena as viewed from two different coordinate systems which are in motion relatively to each other” –Einstein.
The theory of temporal mechanics is concerned with the source of the connection in the theory of relativity.
I suspect that this image appears at the desk of many physicists working. Their body of work impacts all fields of physics. Yet, the conflict between quantum mechanics and relativity that they created appears to still exist after 100 years. These theories can be put into the same geometric language removing this illusion of conflict.
Time is more than a real number. Time is also a circle. Einstein’s postulates provide for a temporal connection. It is possible to constructing particles by twisting this connection. The fields of physics are then just the casual response to curvature induced by these twists. As the twists are quantized, the particles and their field interactions are quantized.
Time must have an internal structure large enough to hold the Higg’s field, where the external winding seen in Schrödinger’s equation has a conjugate winding. A simulation of a particle is presented showing locked external dual windings. Their underlying color and Higg’s-electroweak motion are depicted in the color of the windings.
A clock is any physical system whose state evolves with stable, periodic trajectories on the temporal manifold \mathcal{M}_\tau, such that each complete cycle defines a unit of experienced time in the emergent external spacetime \mathcal{M}_4.
Temporal Mechanics postulates:
Postulate 1.
Time oscillation is universal: every physical system possesses intrinsic periodic structure associated with motion on the internal temporal manifold \mathcal M_\tau.
Postulate 2.
The internal temporal sector is encoded geometrically by a compact manifold \mathcal M_\tau together with a rank-3 Hermitian bundle E\to\mathcal M_\tau carrying a U(3) structure.
Postulate 3.
The determinant line L_{\det}=\det E realizes the universal temporal U(1) phase, and this line is phase-locked to the auxiliary line L^sc of an external \mathrm{Spin}^c(1,3) structure.
Postulate 4.
The observed Lorentzian causal structure on \mathcal M_4 is an emergent external realization of the locked temporal phase.
Postulate 5.
The traceless sector of the internal U(3) structure carries the nonabelian geometric data from which color, electroweak, Higgs, and flavor structure are modeled.
The description of time and its holonomies follow the fiber construction with an emergent Lorentzian group. Using a fiber to describe time with \mathcal G = U(3)\times_{U(1)} \mathrm{Spin}^c(1,3) and a bundle that holds the Standard Model as \mathcal E_\tau = T\mathcal M_\tau \oplus T^*\mathcal M_\tau.
Seeing everything as temporal relationships forming connections that have curvature formed by a phase locked between a temporal manifold and a Lorentzian manifold is more natural than inventing mass, charge, hyper-charge, spin, or other quantum properties to explain our external observations. We could be nothing more than temporal connection twisted into periodic structures by the holonomies of time.
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For us believing physicists, the distinction between past, present, and future is only a stubbornly persistent illusion.
Albert Einsetin