Predictions, limitations & falsifiability

QFT, QED, Allgemeine Relativität, elastisch, Materialgesetz, GUT, Gravitation, Wechselwirkungen

Status of the work

Up to now, no part of this work has been peer reviewed, and it is in the open access sense a publication on the green way. All hypotheses, propositions and results are to be taken with great care. Constructive criticism, suggestions and other inputs are welcome anytime. The easiest way is to contact the author directly by e-mail.

 

Predictions/ Results

The elastic universe theory makes multiple qualitative predictions:

• Existence of 3 lepton generations and relationship between these generations.
• Interpretation of the Minkowski metric.

 

Further predictions are available in the approach:

• Interpretation of QED.
• Interpretation of GR.
• Existence of a relationship between GR und QED.

 

The calculated numerical results can be directly experimentally verified:

Physical constant:   Description:   Unit: Symbol: Gravitational constant [math]\displaystyle{ \left[10^{-11}m^3 kg^{-1} s^{-2}\right] }[/math] [math]\displaystyle{ G }[/math] Weinberg angle (Q=0) [math]\displaystyle{ [\;] }[/math] [math]\displaystyle{ \mathrm{sin}^2 \,\theta_W }[/math] Neutrino mixing angle 12 [math]\displaystyle{ [°] }[/math] [math]\displaystyle{ \theta_{12} }[/math] Neutrino mixing angle 23 [math]\displaystyle{ [°] }[/math] [math]\displaystyle{ \theta_{23} }[/math] Neutrino mixing angle 13 [math]\displaystyle{ [°] }[/math] [math]\displaystyle{ \theta_{13} }[/math] Neutrino mixing phase [math]\displaystyle{ [°] }[/math] [math]\displaystyle{ \delta }[/math]

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

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 quantities are more precise than the experimentally measured ones and lie within the 3σ-error-interval of the experiments.

 

Falsifiability

Dispersion

Each lattice with a finite lattice length [math]\displaystyle{ a }[/math] creates – as opposed to vacuum – a non linear relationship between angular frequency [math]\displaystyle{ \omega }[/math] and wavenumber [math]\displaystyle{ k }[/math] of waves (dispersion relation). So far, however, the universe shows a linear dispersion for electromagnetic waves [math]\displaystyle{ \omega(k) = c \cdot k }[/math], where [math]\displaystyle{ c }[/math] is the measured speed of light. This means that all frequencies of electromagnetic waves move with the same velocity [math]\displaystyle{ c }[/math] in vacuum, yet in a lattice higher frequencies are slower.

This means that the lattice theory only makes sense if the lattice is so small that its influence on the dispersion relation is below today's measurement capabilities.

This problem exists for all theories which initially assume a quantised spacetime, so also for Loop Quantum Gravity (LQG). In this case, the problem was already studied . As an upper limit for the size of lattice structures, this research suggests that the lattice length must be of the same order of magnitude as the Planck length, so [math]\displaystyle{ a \leq l_P =\sqrt{\frac{\hbar\,G}{c^3}}\approx 1.616\cdot10^{-35}m }[/math].

Schematically: In red is the dispersion through a linear chain as a model for lattice structures. In the case of wavelengths close to the lattice length [math]\displaystyle{ a }[/math], the dispersion changes considerably from the meascured vacuum dispersion (blue). If one gives the model a lattice length close to the Planck length, then today's known wavelengths (green), left on the illustration, move far beyond the lattice length. This is a situation where the two descriptions are almost undistinguishable.

Granulation

A further argument, which limits the possibilities of lattice structures, has to do with granulation. Object which are at great distances would appear blurred or "grainy" because of the lattice.

No study is known which considers this argument, but it could give an upper bound to the length of the lattice structure.

Causality

The postulated interpretation of the Minkowski metric and the hypothetically possible existence of a universal observer raises the question to whether causality is ensured. To this end, see the discussion.

 

References

 

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