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Einstein’s Pseudotensor - a Meaningless Concoction of Mathematical Symbols
Stephen J. Crothers 23 January 2020
sjcrothers@plasmaresources.com

Abstract: In an attempt to make his General Theory of Relativity comply with the usual conservation of energy and momentum for a closed system which a vast array of experiments has ascertained, Mr. A. Einstein constructed, ad hoc, his pseudotensor. That it is not a tensor is outside the very mathematical structure of his theory. Beyond that, it violates the rules of pure mathematics. It is therefore a meaningless concoction of mathematical symbols.

Proof of a Meaningless Concoction of Mathematical Symbols The Riemann-Christoffel symbol of the second kind is denoted Γαβγ, defined by,

Γαβγ

=

1 gαω 2

∂gωγ ∂xβ

−

∂gγβ ∂xω

+

∂gβω ∂xγ

(1)

Note that Γαβγ is not a tensor and is composed solely of the components of the metric tensor and their first derivatives. Mr. Einstein’s pseudotensor is denoted tσα, defined by [1],

tσα

=

1 κ

1 2

δασgµνΓλµβΓβνλ

−

gµνΓαµβΓβνσ

(2)

where κ is a constant. Although tσα is not a tensor, Mr. Einstein and his followers claim that it acts ‘like a tensor’ under linear transformations
of coordinates, so it is, they claim, meaningful, both mathematically and physically. Since it acts ‘like a tensor’ it can be
contracted ‘like a tensor’, to produce an invariant t, thus,

t

=

tαα

=

1 κ

gµν

Γλµβ

Γβνλ

(3)

From eq.(1) it is easily seen that the invariant eq.(3) is a first-order intrinsic differential invariant; that is, it is an invariant

composed solely of the components of the metric tensor and their first derivatives. But the pure mathematicians proved [2, 3],

in 1900, that first-order intrinsic differential invariants do not exist. Thus, Mr. Einstein’s pseudotensor is a meaningless

concoction of mathematical symbols and therefore cannot be used to represent anything and cannot be used to do calculations.

Nevertheless, Mr. Einstein and his followers use it to represent the energy-momentum of his gravitational field and hence his

gravitational waves, and, miraculously, do calculations with it; a feat beyond the capacity of pure mathematics and rational

thought.

General Relativity cannot localise its alleged gravitational energy, so Mr. Einstein’s gravitational waves do not exist [3,4].

This is the more so since Mr. Einstein’s claim [5] that form-invariance of the Theorem of Pythagoras under Lorentz trans-

formation is form-invariance of his expanding spherical wave of light, is false. Under Lorentz transformation his spherical

wave of light is an expanding translated ellipsoidal wave of light with a non-static centre [6]. Consequently the ideological

and occult Theory of Relativity is logically inconsistent and therefore false [6, 7].

References
[1] Einstein, A., The Foundation of the General Theory of Relativity, Annalen der Physik, 49, (1916).
[2] Ricci-Curbastro, G., Levi-Civita, T., Me´thodes de calcul diffe´rentiel absolu ET leurs applications, Matematische Annalen, B. 54, p.162, (1900).
[3] Levi-Civita, T., Mechanics. - On the Analytical Expression that Must be Given to the Gravitational Tensor in Einstein’s Theory, Rendiconti della Reale Accadmeia dei Lincei 26: 381, (1917), eprint: http://arxiv.org/pdf/physics/9906004
[4] Crothers, S.J., General Relativity: In Acknowledgement Of Professor Gerardus ’t Hooft, Nobel Laureate, 4 August, (2014), http://vixra.org/pdf/1409.0072v9.pdf
[5] Einstein, A., On the electrodynamics of moving bodies, Annalen der Physik, 17, p.891, (1905).
[6] Crothers, S.J., Special Relativity and the Lorentz Sphere, Physics Essays, V.33, No.1, p.15, (2020), http://vixra.org/pdf/1911.0013v2.pdf
[7] Crothers, S.J., On the Logical Inconsistency of the Special Theory of Relativity, American Journal of Modern Physics, Vol.6, No.3, pp.43-48, (2017), http://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170603.12.pdf http://vixra.org/pdf/1703.0047v6.pdf

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