102 lines
4.0 KiB
Plaintext
102 lines
4.0 KiB
Plaintext
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
|
||
|
||
1
|
||
|