[Paper Review] Time, E8, and the Standard Model

D. J. Jackson|arXiv (Cornell University)|Sep 6, 2017

Noncommutative and Quantum Gravity Theories37 references6 citations

TL;DR

This paper proposes that the fundamental structure of physical reality emerges from a single dimension of time, with its multi-dimensional extension leading to the exceptional Lie group E₈ as the unifying symmetry. By constructing spacetime and particle symmetries from time's geometric and algebraic properties, the theory predicts the Standard Model gauge group and suggests E₈ as the complete symmetry group, offering testable predictions for new physics beyond the Standard Model.

ABSTRACT

Based upon the unique and simple starting point of the continuous flow of time a physical theory is derived through an analysis of the elementary arithmetic composition and symmetries of this one-dimensional progression. We describe how the explicit development of the theory leads to a prediction of the unique and largest exceptional Lie group E8 as the full `symmetry of time', and hence as the unification group for the physical theory. This proposal results from the identification of a series of esoteric properties of the Standard Model of particle physics from a series of intermediate augmentations in the `multi-dimensional form of time'. These physical properties derive from the breaking of the full symmetry of time through the necessary interposition of an external 4-dimensional spacetime arena, itself constructed from a 4-dimensional form of time, as the background to all observations. The basic conceptual picture is presented together with reviews of a number of references regarding E8 structures which may provide a significant guide in pursuing the goal of converging upon a complete unified theory.

Motivation & Objective

• To establish a physical theory grounded solely in the continuous flow of time, without assuming extra spatial dimensions.
• To demonstrate how the symmetries and structures of the Standard Model arise from the algebraic and geometric extension of one-dimensional time.
• To justify E₈ as the maximal symmetry group of time, unifying spacetime, gauge symmetries, and matter fields.
• To identify testable predictions for new physics beyond the Standard Model, such as additional gauge symmetries or a dark sector.
• To position the theory as a falsifiable alternative to extra-dimensional models, particularly in light of the absence of supersymmetry or mirror states.

Proposed method

• Derives physical structures from the arithmetic and symmetry properties of real numbers representing time, using quadratic and higher-order forms to generate spatial and spacetime geometries.
• Constructs a 4-dimensional spacetime arena via a 4-dimensional form of time, breaking the full symmetry of time to yield Lorentz invariance and local inertial frames.
• Uses the algebraic structure of octonions and the exceptional Jordan algebra to realize E₆, E₇, and ultimately E₈ symmetries from time-based multi-dimensional forms.
• Identifies the 248-dimensional representation of E₈ as the full symmetry of time, with the Standard Model gauge group embedded within it via specific subgroup decompositions.
• Applies the E₈(-24) real form to describe the full time structure, projecting onto a 4D spacetime manifold to recover known particle multiplets and their quantum numbers.
• Analyzes symmetry breaking patterns from E₈ to E₇(-25), E₆, and finally to the Standard Model group, with residual components potentially corresponding to new physics.

Experimental results

Research questions

• RQ1 Can a complete physical theory be derived from the one-dimensional flow of time alone, without assuming extra spatial dimensions?
• RQ2 How do the symmetries and particle content of the Standard Model emerge from the multi-dimensional extension of time?
• RQ3 What is the role of the exceptional Lie group E₈ in unifying spacetime, gauge symmetries, and matter fields?
• RQ4 What testable predictions arise from the E₈ symmetry structure, particularly regarding new gauge symmetries or a dark sector?
• RQ5 How does the absence of supersymmetry or mirror states in this framework affect its consistency with current experimental constraints?

Key findings

• The theory predicts that the full symmetry of time is the exceptional Lie group E₈, derived from the multi-dimensional algebraic extension of one-dimensional time.
• The Standard Model gauge group SU(3)×SU(2)×U(1) is embedded within E₈, with the full E₈ symmetry breaking to this subgroup via a specific projection onto a 4D spacetime manifold.
• The E₈(-24) real form contains an additional SU(2)×U(1) gauge symmetry beyond the Standard Model, suggesting the possibility of new gauge bosons.
• The Higgs field's 4-vector magnitude |v₄| is linked to electroweak symmetry breaking, implying potential non-standard dynamics in the Higgs sector.
• Residual components in the 248-dimensional E₈ representation (up to ~50) may correspond to a dark sector, potentially detectable in high-energy or cosmological observations.
• The theory is falsifiable: the absence of supersymmetric partners or mirror states would contradict its core assumptions, making it empirically testable.