Faculty of Science, University of Tübingen, Auf der Morgenstelle 8, 72076 Tübingen, F.R.G.

Abstract

Two years before finishing the general theory of relativity, Einstein already arrived at the complete constant-c Telemach theorem. This Einstein-Nordström-Abraham metric, as it can be called, remains valid in the vertical direction in the full-fledged general theory of relativity. A connection to cryodynamics is drawn.

(November 7, 2012)

In a 1913 paper titled “On the present state of the problem of gravitation“ [1], Einstein on the fourth page described the Einstein-Nordström-Abraham formalism as it can be called. The four (and by implication five) findings remain valid in the full-fledged theory arrived at two years later, specifically in the implied Schwarzschild metric.

The evidence:

1) c is globally constant.

Quote: “… the velocity of light propagation is equal to the constant c.” (Fourth line underneath Eq.1’)

2) T is inversely proportional to the gravitational potential. (Unit intervals go up with increasing gravity)

Quote: “However, in our case it is possible that the natural [local] interval d-tau-zero differs from the coordinate interval d-tau by a factor [omega] that is a function of phi [the gravitational potential]. We therefore set d-tau-zero = omega d-tau.” (= Eq.3)

3) L is inversely proportional to the gravitational potential. (Unit lengths go up with increasing gravity)

Quote: “The lengths l and the volumes V, measured in coordinates, also play a role. One can derive the following relation between the coordinate volume V and the natural [local] volume V-zero: Eq.(4)” [In this Eq.(4), the ratio V over V-zero is essentially proportional to 1/omega-cubed – so that L over L-zero is essentially proportional to 1/omega]

4) M is proportional to the gravitational potential. (Unit mass goes down with increasing gravity)

Quote: “… according to Nordström’s theory, the inertia of a mass point is determined by the product m times phi [the gravitational potential]; the smaller phi is, i.e., the larger the masses we gather in the neighborhood of the mass point under consideration, the smaller the inertial resistance with which the mass point opposes a change of its velocity becomes.” (Three lines after Eq.2a)

5) Ch is proportional to the gravitational potential. (Unit charges go down with increasing gravity)

Remark: This corollary to point 4 referring to charge is NOT explicitly mentioned by Einstein but follows trivially from the universal rest mass-to-charge ratio valid for each particle class.

Comment

The same 5 points were almost a century later described in the “Telemach theorem” (T,L.M,Ch) [2]. Here Einstein’s equivalence principle of 1907 (lying behind point 2) was shown to entail all 5 facts. Five years before, the same results had been found to be implicit in the vertical direction of the Schwazschild metric of general relativity [3], a fact which was soon generalized to 3 dimensions by a gifted anonymous author named “Ich” (see [3]). Independently, Richard J. Cook [4] arrived at points 1 – 4 on the basis of general relativity proper and subsequently expressed his full support to point 5 (see [2]).

Historical Conclusion

Historians of science have re-worked the period of 1907 (the discovery of the equivalence principle) to 1913 in which the above results were discovered and beyond [5,6]. Nevertheless the Telemach theorem (if the above results deserve this onomatopoetic name) remained unappreciated for almost a century. The reason deserves to be elucidated by historians.

Outlook

A totally unrelated recent theory – cryodynamics – revealed that the famous big-bang theory of cosmology, based on general relativity without regard to the implied Telemach theorem which via L excludes bounded solutions, needs replacement by a stationary cosmology unbounded in space and time in a fractal manner [7]. This fact may help eliminate the strong professional pressure that existed up until recently in favor of sticking to mathematically allowed but physically unrealistic nonlinear transformations in general relativity. In this way, the recent passive revolt staged against constant-c general relativity by part of the establishment in the field in conjunction with the nuclear-physics establishment can perhaps be overcome. Everyone hopes that no ill effects on the survival of planet earth will follow (the last 8 weeks of increasing the risk even further could momentarily still be avoided).

The reason why the scientific outlook for Telemach is maximally bright lies in a favorable chanceful fact. Cryodynamics is maximally important economically [8]. The same industrial-military complex which so far boycotted Telemach and its precursors will enthusiastically embrace cryodynamics, sister discipline to thermodynamics, because of the unprecedented revenues it promises by its for the first time making possible hot fusion on earth [8]. So if money stood in the way of embracing Telemach, the situation has totally changed by now.

References

[1] Einstein, A., On the present state of the problem of gravitation (in German). Physikalische Zeitschrift 14, 1249 – 1262 (1913). See: The Collected Papers of Albert Einstein, Vol. 4, English Translation, pp. 198 – 222, pages 102 – 103. Princeton University Press 1996.

[2] Rossler, O.E., Einstein’s equivalence principle has three further implications besides affecting time: T-L-M-Ch theorem (“Telemach”). African Journal of Mathematics and Computer Science Research 5, 44 – 47 (2012), http://www.academicjournals.org/ajmcsr/PDF/pdf2012/Feb/9%20Feb/Rossler.pdf

[3] Rossler, O.E., Abraham-like return to constant c in general relativity: “R-theorem” demonstrated in Schwarzschild metric. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics 2, 2012, http://www.nonlinearscience.com/paper.php?pid=0000000148

[4] Cook, R.J., Gravitational space dilation (2009), http://arxiv.org/pdf/0902.2811v1.pdf

[5] Castagnetti, G., H. Goenner, J. Renn, T. Sauer, and B. Scheideler, Foundation in disarray: essays on Einstein’s science and politics in the Berlin years, 1997, http://www.mpiwg-berlin.mpg.de/Preprints/P63.PDF

[6] Weinstein, G., Einstein’s 1912 – 1913 struggles with gravitation theory: importance of static gravitational fields theory, 2012, http://arxiv.org/ftp/arxiv/papers/1202/1202.2791.pdf

[7] Rossler, O.E., The new science of cryodynamics and its connection to cosmology. Complex Systems 20, 105 – 113 (2011). http://www.complex-systems.com/pdf/20-2-3.pdf

[8] Rossler, O.E., A. Sanayei and I. Zelinka, Is Hot fusion made feasible by the discovery of cryodynamics? In: Nostradamus: Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems, Advances in Intelligent Systems and Computing Volume 192, 2013, pp 1 – 4 (has appeared). http://link.springer.com/chapter/10.1007/978-3-642-3.….ccess=true

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