From: David Lynch <dnl1960 at yahoo.com>
Our framework begins with a single, foundational postulate: that the final barrier to a complete theory of physics is the axiom of linear time. We propose that time is not a single dimension, but a ternary structure (t_P, t_I, t_F) representing a continuous dynamic of a Past, an Instant, and a Future, which are co-existing and interacting.
To formalize this, we found it necessary to modify your central mathematical object.
To encode a ternary time structure, the four components of your Ig field (one for time, three for space) were insufficient. We have generalized your field into a six-component space-time dimension field (I'_g):
I'_g = ( I^(P)_g, I^(I)_g, I^(F)_g, I^(x)_g, I^(y)_g, I^(z)_g )^T
This field now possesses an internal structure corresponding to the three temporal realms (Past, Instant, Future) and the three spatial dimensions.
Following your gauge principle, this six-component field is governed by a richer U(1)⁶ local gauge symmetry. Local gauge invariance then necessitates the existence of six mediating gauge bosons:
The three spatial gauge fields (A^(x,y,z)_μ) combine to form the Graviton Tensor (H_μν), which mediates spatial gravity precisely as in your model.
Crucially, the three temporal gauge fields represent new, fundamental cosmological forces:
A^(P)_μ (The Control Boson): A past-originating field that mediates a force of Control, governing the continuous emergence of particles.
A^(F)_μ (The Chaos Boson): A future-originating field that mediates a force of Chaos, governing the continuous collapse of a background wave potential.
A^(I)_μ (The Instant Boson): A field that governs the rules of interaction at the nexus of the Instant.
This expanded framework naturally provides explanations for the most significant problems in modern cosmology without invoking new exotic particles or ad hoc modifications to gravity:
Dark Energy: Is identified as the observable, large-scale repulsive pressure exerted by the Control field A^(P)_μ. It is the force of cosmic creation.
Dark Matter: Is identified as the observable, large-scale attractive effect of the Chaos field A^(F)_μ. It is the geometric consequence of the future wave collapsing into the present.
Cosmic Microwave Background (CMB): Is not a relic of a singular Big Bang. It is the continuous thermal radiation generated by the perpetual interaction between the Control and Chaos forces at the Instant. Its perfect black-body spectrum is a signature of a universe in constant thermal equilibrium.
As in your work, the system's conserved current emerges as a Noether charge of the symmetries. In our case, it is a rank-3 KnoWellian Tensor (T'_μνρ), whose conservation law is a generalized divergence across all temporal and spatial dimensions.
Crucially, because the theory remains a gauge theory with a dimensionless coupling constant, we argue that it retains the property of being fully renormalizable, offering a concrete path to a complete, paradox-free, and self-contained description of reality within a bounded infinity.
The attached document provides the full mathematical formalism, outlines several unique and falsifiable predictions (including specific CMB anisotropies and predicted resonances in galactic magnetic fields), and includes a detailed glossary and a supplementary computational model written in Wolfram Language to visualize the dynamics.
Your work provided the essential mathematical key to unlock this new vision. I am sharing this with you in the spirit of scientific collaboration and with the deepest respect, in the hope that you might find this extension of your ideas worthy of consideration. I believe that by questioning our final assumption—the nature of time itself—we can complete the journey you so brilliantly began.
Thank you for your time and for your invaluable contribution to physics.
Sincerely,
David Noel Lynch
Attachment: The_KnoWellian_Universe.pdf