A Novel Approach to Extra Dimensions

Jackson, David

doi:10.48550/arxiv.1603.07552

Cited by 6 publications

(40 citation statements)

References 15 publications

(43 reference statements)

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“…Further, it is possible to avoid dealing directly with such infinitesimal quantities and express equation 3 itself in terms of generally finite quantities by dividing both sides by (δs) p and defining the n-dimensional vector v n with components v a = δx a /δs for the limit δs → 0. This leads directly to the general homogeneous polynomial form (as described for [3] equation 2.9 and [4] equation 11):…”

Section: Time and Spatial Dimensionsmentioning

confidence: 99%

“…3, as described more generally for equation 5. The set of four variables {r a } ∈ R 4 can be identified with an initial set of four coordinates {x µ } ∈ R 4 , with x µ = δ µ a r a (Greek indices {µ, ν, . .…”

Section: Geometry Of the Spacetime Manifoldmentioning

confidence: 99%

“…This combines the vector representation of SL(2, C) on h 2 ∈ h 2 C and the spinor representation on ψ ∈ C 2 , together with the scalar denoted n ∈ R (in line with the notation used for the same expression in [4] equation 19), in a single symmetry transformation that preserves L(v 9 ) = 1 of equation 18. Hence the choice of a preferred SL(2, C) implies a symmetry breaking pattern aligned with the isomorphism of vector spaces:…”

Section: Extra Dimensions and Symmetry Breakingmentioning

confidence: 99%

“…This is the point of view adopted for the present work in which we argue that a unified framework, sharing many of the properties of Kaluza-Klein theories, can be founded simply upon the structure of the one dimension of time alone, as represented by the real line. While the full development of this theory has been presented in [3] with the uncovering of properties of the Standard Model described in [4], which summarises ([3] chapters 6-9), here we elaborate upon the foundations of the theory and the elementary geometric structures involved as arising from the simple starting point of one dimension. Being largely self-contained this paper both summarises and expands upon the contents of ([3] chapters 2-5), with further discussion of the underlying conception of the theory in section 2 and a more direct and explicit construction of the relation between the external and internal curvature presented here in section 4.…”

Section: Introductionmentioning

confidence: 99%

“…Combining the motivations of section 2 with geometric arguments adapted from the Kaluza-Klein theories of section 3, a means of constructing a relationship between the external spacetime geometry and the internal curvature for the present theory is proposed in section 4. We further compare and contrast the new approach with Kaluza-Klein theory in section 5, where we also relate this work to references [3] and [4] and allude to the further development of the theory.…”

Section: Introductionmentioning

confidence: 99%

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Construction of a Kaluza-Klein type Theory from One Dimension

Jackson

2016

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We describe how a physical theory incorporating the properties of fields deriving from extra-dimensional structures over a four-dimensional spacetime manifold can in principle be obtained through the analysis of a simple initial structure consisting of the one dimension of time alone, as represented by the real line. The simplicity of this starting point leads to symmetries of multi-dimensional forms of time, from which a geometrical structure can be derived which is similar to the framework employed in non-Abelian Kaluza-Klein theories. This leads to a relationship between the external and internal curvature on the spacetime manifold unified through the underlying constraint of the one dimension of time for the theory presented here. We also describe how the symmetry breaking structure is compatible with the Coleman-Mandula theorem for the subsequent quantisation of the theory.

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Section: Time and Spatial Dimensionsmentioning

confidence: 99%

Section: Geometry Of the Spacetime Manifoldmentioning

confidence: 99%

Section: Extra Dimensions and Symmetry Breakingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Construction of a Kaluza-Klein type Theory from One Dimension

Jackson

2016

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The Dark Energy Sector of Generalised Proper Time

Jackson¹

2022

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Generalisation from the local 4-dimensional spacetime form for a proper time interval provides an alternative basis for a unified theory contrasting with the more familiar approach of appending extra dimensions of space. In both cases the main goal is to derive a structure of matter that accounts for empirical observations from the properties of the additional components. Previous work has focussed upon the direct and significant connections that this new approach makes with the Standard Model of particle physics while also providing a link with dark matter models. In this paper we elaborate on how a further sector of generalised proper time, incorporating the key component of negative pressure, can account for the apparent dark energy fuelling the accelerating large-scale expansion of the universe. Through comparison with existing dark energy models we elucidate the elementary composition of this sector, its potential relation to an effective cosmological constant term, and the nature of possible interaction with the visible and dark matter sectors.

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Time, E8, and the Standard Model

Jackson¹

2017

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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 E 8 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 E 8 structures which may provide a significant guide in pursuing the goal of converging upon a complete unified theory.

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A Novel Approach to Extra Dimensions

Cited by 6 publications

References 15 publications

Construction of a Kaluza-Klein type Theory from One Dimension

Construction of a Kaluza-Klein type Theory from One Dimension

The Dark Energy Sector of Generalised Proper Time

Time, E8, and the Standard Model

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