elastic, universe, Weinberg angle, gravitational constant, neutrino oscillation, PMNS-matrix, grand unified theory, GUT, alternative to string theory

The elastic universe theory provides a concept for the interpretation of the existing models of fundamental physics. The interpretation reveals new relationships that ultimately lead to new results.

Basics

Basics without mathematics:
Some basics of today's physical model are summarized in a separate article. The text is aimed at interested readers who want to refresh their knowledge of the standard model of physics (without mathematics). For further details, the text contains some external links and references.
You can find the article using this link.

Mathematical basics:
The mathematics applied in this work is developed in three articles. These texts are addressed to physicists and mathematicians:

I: Geometric Interpretation of the Minkowski Metric
II: Properties of the map between Euclidean and Minkowski space
III: Application of local gauge theories to fluid mechanics

Results

In this work three hypotheses are presented. Their mathematical elaboration and interpretation so far provides the quantitative results listed in the table, as well as a multitude of qualitative insights into the symmetries and nature of matter.

Comparison of the physical constants measured in the experiment with the values calculated according to the elastic universe theory:

Physical constants:
Description:	Unit:	Symbol:
Gravitational constant	$\left[10^{-11}m^{3}kg^{-1}s^{-2}\right]$	$G$
Weinberg angle (Q=0)	$[\;]$	$\mathrm {sin} ^{2}\,\theta _{W}$
Neutrino mixing angle 12	Failed to parse (syntax error): {\displaystyle [°]}	$\theta _{12}$
Neutrino mixing angle 23	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [°]}	$\theta _{23}$
Neutrino mixing angle 13	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [°]}	$\theta _{13}$
Neutrino mixing phase	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [°]}	$\delta$

Experimental measurement:
Value:	3σ-error- interval:	Source:
6.674 08	± 0.000 93	^[1]
0.2397	± 0.003	^[2]
33.56	31.38 → 35.99	^[3]
41.6	38.4 → 52.8	^[3]
8.46	7.99 → 8.90	^[3]
261	0 → 360	^[3]

Calculation according to the elastic universe theory:
Value:	3σ-error- interval:
6.673 192 3	± 0.000 000 3
0.237 33	± 0.000 06
35.28	± 0.08
42.42	± 0.08
8.65	± 0.04
323.13	± 0.02

All calculated values are more precise than those measured experimentally and are within the 3σ-error-interval of the experiments.

Idea/ Theses

The three theses of the elastic universe theory are gradually worked out in four chapters and the results are calculated in the process. The chapters and their appendices are in separate articles and are accessible through the Contents. Here, the basic idea of the theses is shortly presented:

Third hypothesis: Elementary particles are not point-like but they possess a very small, yet finite (four dimensional) volume.
What follows:
The most important difference between the point-particle and the particle with volume is that the latter has a shape, which can be isotropic (like the point), but it can also have anisotropic shear terms. In a first approximation this means that an isotropic (four dimensional) sphere with equal radii in all directions turns into an anisotropic (four dimensional) ellipsoid with four unequal radii. The anisotropic terms can then be separated from the isotropic ones: this corresponds to the common decomposition of tensors into isotropic and trace free terms.

The key here: at a fixed volume the shear is determined by three residual, linearly independent parameters (radii). This means that there are three independent shear-parameters for each fixed volume, and therefore three configurations, which only distinguish themselves by their anisotropic properties. For illustrative purposes, see the following schematic diagram:

This allows the following interpretation:
A particle possesses a small 4-dimensional volume. The isotropic volume term (first parameter) corresponds to the electric charge and is constant for any particular particle. Photons interact with this isotropic part.

Yet the particle also possesses an anisotropic shear term, which is determined by three independent parameters. These parameters correspond to the three generations of particles. The anisotropic state can change, yet an anisotropic interaction is necessary to do this. This is the case for neutrinos and weak interaction, but not for photons, which is why photons cannot change the generations of the particles. Neutrinos are particles which do not possess an isotropic term, but only a shear term.

However, this interpretation raises a few questions:
If the elementary charge corresponds to an isotropic volume, there must be a reason that this value is the same for all particles. This is understood as an indication for the existence of some kind of unitary or elementary volume.

Secondly, something must force the particles into the anisotropic states; it does not make sense that the particles should have any anisotropic parts in vacuum.

Both these properties could be explained seamlessly if the particles were surrounded by some kind of space lattice. Hence the second hypothesis:

Second hypothesis: There exists a smallest (four dimensional) «elementary volume», spacetime is quantized.
What follows:

EN figure harmonic lattice introduction.png

An elementary volume and therefore a finite elementary length leads to the conclusion that the isotropy of spacetime is not conserved on the smallest scale, since the various elementary volumes must somehow arrange, which is only possible in a lattice type structure. In a lattice though, certain directions will inevitably be preferred to others. The simplest model for such lattice structures is the one of a four dimensional, harmonic oscillator lattice, consisting of interlinked harmonic oscillators.

This model is ideally suited to describe the mentioned effects, yet it raises a very basic question: It is geometrically motivated and «lives» in a geometric Euclidean space (a metric space with signature ++++).

Yet the observed spacetime behaves relativistically, in other words, it is described by a Minkowski space (with signature +- - -). This discrepancy must be resolved so that the hypotheses presented so far may hold ground. Therefore the question of the metric, and hence, the nature of space and time will be covered prior to the other hypotheses:

First hypothesis: For a universal observer, space and time behave the same.
In the current theory time and space are linked, yet they are not treated the same. This unequal treatment leads to the effects of special relativity.

In this work, the link between space and time is completed. The presented hypothesis is: Time and space behave the same from the point of view of a universal observer. The observed differences arise because time is measured and perceived differently from man than is space.

Specifically: A human being is a flat observer, he can only see a single point in time. The measurement of time from a human is therefore always based on localised points in time. No human made experiment can measure a time interval directly - for this, one would need at least two points in time - but only the effects which follow from the passing of a time interval in space.

Implication: This allows the separation of the actual effect from its measurement. Relativistic effects arise from the measurement of man. Yet the underlying physics can be carried out independently thereof in the Euclidean space and later be projected onto the space of human perception.

The first hypothesis is covered in Chapter 1.
Chapter 2 is necessary to prepare for the second hypothesis’ treatment of the space lattice, which is introduced in Chapter 3.
The third hypothesis is treated in Chapter 4.

References

↑ 2014 CODATA recommended values, physics.nist.gov, accessed 2.3.2018 [1]
↑ Precision Measurement of the Weak Mixing Angle in Moller Scattering, SLAC E158 Collaboration: P.L. Anthony, et al, 2005, DOI 10.1103/PhysRevLett.95.081601 [2]
↑ ^3.0 ^3.1 ^3.2 ^3.3 Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, Ivan Esteban et. al, Journal of High Energy Physics; Jan 2017, DOI 10.1007/JHEP01(2017)087 [3]

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keywords: elastic, universe, Weinberg angle, gravitational constant, neutrino oscillation, PMNS-matrix, grand unified theory, GUT, alternative to string theory

[CODATA-1] 2014 CODATA recommended values, physics.nist.gov, accessed 2.3.2018 [1]

[SLAC_E158-2] Precision Measurement of the Weak Mixing Angle in Moller Scattering, SLAC E158 Collaboration: P.L. Anthony, et al, 2005, DOI 10.1103/PhysRevLett.95.081601 [2]

[Esteban-3] 3.0 ^3.1 ^3.2 ^3.3 Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, Ivan Esteban et. al, Journal of High Energy Physics; Jan 2017, DOI 10.1007/JHEP01(2017)087 [3]

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Elastic universe theory

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Elastic universe theory

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References

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