Subject: Fwd: AW: Consequences of Discarding Torsion
Date: Sat, 30 Aug 2008 11:00:32 EDT

Good idea! This will lead to the further contradiction in the torsionless geometry:

D ^ R tilde not equal to zero

when

T tilde = 0 and D ^ T tilde = 0

This could also be shown by computer algebra of all solutions of the Einstein equation. I wil lwrite these out in tensor notation. The reason for this is that (paper 88):

D ^ (D ^ T) := D ^ (R ^ q)

becomes

D ^ R = 0

when T is zero. This is what the standard physics calls the second Bianchi identity. All line elements that are exact solutions of the Einstein equation should obey the second Bianchi identity by construction. We know that R tilde ^ q is not zero (paper 93), so:

D ^ (R tilde ^ q) is not zero

i.e.

D ^ R tilde is not zero

but

D ^ ( D ^ T tilde )

is zero for all solutions of the Einstein field equation.

One could probably derive a fourth identity:

D ^ (D ^ T tilde) := D ^ (R tilde ^ q)

I do not know if it is of any usefulness.

Horst

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The neglect of torsion is the arbitrary assumption (initially made for convenience):

T = 0 – (1)

So the Cartan geometry of the previous note reduces to

D ^ q = 0 (2)

R = D ^ omega (3)

D ^ T := R ^ q = 0 (4)

Without going into any details, it is seen that this is a drastic assumption, and there is no justification for it. The Bianchi identity reduces to

R ^ q = 0 (5)

an equation that was first given by Ricci and Levi-Civita. For some reason it is known in the standard physics as the “first Bianchi identity”. All of Einsteinian general relativity is based on this incorrect geometry. The correct Bianchi identity is given by Cartan:

D ^ T := R ^ q (6)

and neither side of eq. (6) is zero in general. During the course of development of ECE theory (2003 to present) two more identities have been highlighted. These both derive staightforwardly from eq. (6). They are:

1) The dual identity

D ^ T tilde := R tilde ^ q (7)

2) The derivative identity

D ^ (D ^ T) := D ^ (R ^ q) (8)

Here tilde means the well known Hodge dual transformation in four dimensions. The geometry used by Einstein is:

R tilde ^ q =? 0 (9)

and

D ^ R =? 0 (10)

Eq. (10) is known in the standard physics as “the second Bianchi identity”. It is however an incorrect equation, so the =? sign is used in eq. (10). Eq. (9) is also incorrect. The Einstein field equation merely claims that the incorrect eq. (10) is proportional to a quantity in physics. So the whole Einsteinian general relativity is irretrievably incorrect. This has actually been suspeced for ninety years bu tis shown with great clarity by eq. (7) (see papers 93, 95, 100 and 117, and “Criticisms of the Einstein Field Equation”). The ECE theory derives all the equations of physics using the correct geometry due to Cartan. All this is easy to understand, and this major progress in modern physics is being deliberately ignored by the standard faction, who are merely transient dogmatists of no real significance in the history of science.

Civil List Scientist