Archive for July, 2011

corves of m(r,theta)

Feed: Dr. Myron Evans
Posted on: Thursday, July 28, 2011 3:39 PM
Author: metric345
Subject: corves of m(r,theta)

Many thanks, excellent work again! I will reply in detail tomorrow. These results mean that a function

m = 1 – r0 / r

does not give a precessing ellipse at all. Anther complete disaster for the standard model. The complexity of these graphs shows what happens when one tries to force m of the above type to give a precessing ellipse. I think that these graphs by Horst are already adequate to show the complete collapse of Einsteinian general relativity in yet another way. Will comment in more detail tomorrow. These are very important results because nothing has been used except the assertions of the Einsteinian gr themselves. In other words Einsteinian gr is completely self inconsistent.

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Fitting the m Function to 1 – r0 / r

Feed: Dr. Myron Evans
Posted on: Monday, July 18, 2011 10:50 PM
Author: metric345
Subject: Fitting the m Function to 1 – r0 / r

Many thanks, this version could perhaps be used in your section of UFT 189. What is being done here is to regard the 1 – r0 / r function as an approximation to the solution obtained from geometry. In UFT 190 we could use the geometrical solution (the double exponential solution) to produce orbital functions: the orbital velocity of a planet dr / dt, and then dr / d phi and d phi / dt, angle of deflection and relativistic time delay. In FT 108 a function was found for precessing ellipses spiralling inwards (binary pulsars). As in eq. (4) of UFT 190, d phi / dt can be used to define angular momentum, and this is a link to the theory of whirlpool galaxies, as in previous papers angular momentum is expressed as spacetime torsion. If the double exponential function is approximated by

m (r0, a) = 1 – r0 / r – a / r squared

the orbits of UFT 108 are obtained. What is happening here is that the double exponential function m (R) is being reparameterized in terms of r0 (the constant 2MG / c squared) and a This process could be continued by using

m (r0, a , b) = 1 – r0 / r – a / r squared – b / r cubed – …………..

which should produce a different kind of binary pulsar orbit, and so on.

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Fitting the m Function to 1 – r0 / r

Feed: Dr. Myron Evans
Posted on: Monday, July 18, 2011 4:20 AM
Author: metric345
Subject: Fitting the m Function to 1 – r0 / r

It would be optimal if the m function could be fitted numerically and to machine precision to the function 1 – r0 / r, where

r0 = 2 MG / c squared

Here M is the mass of the sun, G is Newton’s constant and the speed of light. This could be done with a least mean squares fitting algorithm available in most computer packages. This method can be seen in my Algol code of the seventies, (code on www.aias.us) using the Numerical Algorithms Group (NAG) three variable least means squares package. If the logic of Cartan geometry is applied rigorously, the m function is the one that describes orbits. In the solar system, orbits are described in received opinion by 1 – r0 / r. The received opinion is essentially empirical, Schwarzschild did not derive this function and it seems to have been found by trial and error. In note 190(1) I will give the basic method starting with the infinitesimal line element and hamiltonian. The m function as described using a new universal constant R. So by fitting m to 1 – r0 / R the value of R can be found and m determined. The function 1 – r0 / r is known to produce precessing ellipses which reduce to ellipses in the correct limit, and to Newton’s dynamics. However, Newton’s dynamics are now due to the m function, not the Hooke / Newton inverse square law of attraction. This reasoning is another product of the post Einsteinian paradigm shift knwn as ECE theory, and is as big a leap of thought as the Einstein paradigm shift before it.

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Note on the Complementary Function

Feed: Dr. Myron Evans
Posted on: Tuesday, July 12, 2011 5:43 AM
Author: metric345
Subject: Note on the Complementary Function

This is a clear example taken from Stephenson.”Mathematical Methods for Science Students”. The new metric m(r, t) is the complementary function, which is the solution to the reduced equation. The complete solution is the solution of the original constraint equation is the particular integral obtained by Horst using computer algebra. I chose the particular integral to be a very large negative constant (approaching negative infinity) so m sub p vanishes. In this example, eq. (3) is not a solution of eq. (1). This has been checked again by Dr Horst Eckardt using computer algebra. For an example of this method see Marion and Thornton pp. 114 ff. in the well known context of Euler resonance. Transient effects are described by the complementary function, and resonance by the particular integral. So having carried out this final check I think that all is fine. The complete solution is therefore:

m = m sub p + m sub c

where

m sub p = 0

So the new general metric is a kind of fall transient which behaves much better than SM (graphs just sent over by HE).

a189thpapernote.pdf

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note 189(6)

Feed: Dr. Myron Evans
Posted on: Tuesday, July 12, 2011 12:08 AM
Author: metric345
Subject: note 189(6)

To Horst Eckardt:

I thought about this quite a lot over the weekend, and I summed up my thoughts so far in note 189(8), i.e. m is a function of a function, (eq. (1) of note 189(8)) so the chain rules apply as in note 189(8). The key equation is (4), where R is not a function of r, so no chain rule applies. I agree that t and r are linearly independent but as you know, the orbital equation is found as in standard general relativity by the chain rule:

dr / dt = (dr / d tau) (d tau / dr)

It would be very helpful to plot m(r, t) (eq. (1) of note 189(7)) against r, and compare it with a plot of

f(r) = 1 – r0 / r

to see if the two curves can be superimposed by variation of parameters.

The great advantage of this approach is that all orbits can be described in theory by eq. (9) of note 189(7). Naturally I will check all my calculations again today.

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