Archive for June, 2011

Self Consistency of Riemann Geometry

Feed: Dr. Myron Evans
Posted on: Thursday, June 23, 2011 11:19 AM
Author: metric345
Subject: Self Consistency of Riemann Geometry

I evaluated the mu = nu = 1 condition in note 186(7), giving eq. (8). In my opinion, the way to interpret that equation is that metric compatibility contradicts the commutator method. The former gives a finite gamma sup 1 sub 11 and the latter shows that a gamma sup 1 sub 11 leads to zero torsion and curvature and a flat spacetime and a zero gamma sup 1 sub 11. So I concluded that for any g sub 11, eq. (9) has no meaning and metric compatibility can only be used with an antisymmetric connection, otherwise Riemann geometry itself is self inconsistent. The SM gives an accurate description of the relativistic Kepler problem, so cannot be abandoned. In the latest note I suggested a perturbation of the SM, and it works fine.

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Orbit of a Binary Pulsar

Feed: Dr. Myron Evans
Posted on: Monday, June 20, 2011 2:53 AM
Author: metric345
Subject: Orbit of a Binary Pulsar

In the new cosmology of UFT 186 (in prep), there is a small correction to the Hooke / Newton force (inverse square law of universal gravitation) in this type of orbit. The inverse square law does not quite hold and this is also true in the relativistic Kepler problem. This type of non Hooke / Newton phenomenon seems to have been picked up in the solar system by NASA recently in some satellites. The new cosmology gives the Hooke / Newton force as being the relevant antisymmetric connection within the rest energy, m c squared:

F = – m c squared gamma

a great simplification and strengthening of the old cosmology, which has been quietly discarded for all practical purposes. The old icons are still there, but we are now into the post Einstein paradigm. Curvature has been eliminated from cosmology in UFT 186, leaving torsion. The spacetime torsion is twice the antisymmetric connection, so universal gravitation is due exclusively to torsion. The Einstein field equation has been discarded as fogma (foggy dogma). There are still some who think the world is flat, but to any thinker the old cosmology has had its day. This is physics, the old gives way to the new.

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186(8): Complete Results for Gravitational Metric

Feed: Dr. Myron Evans
Posted on: Sunday, June 19, 2011 7:10 AM
Author: metric345
Subject: 186(8): Complete Results for Gravitational Metric

These results are collected in Table 1, and they show that gravitation is due entirely to spacetime torsion. Curvature plays no role in solar system gravitation. The only equation needed to show this is the metric compatibility equation (2). The metric used is the simplest solution of the orbital theorem of UFT 111, the old “Schwarzschild metric” of the relativistic Kepler problem of the solar system. Therefore the solar system is described entirely by one one connection, antisymmetric in its lower two indices. Twentieth century cosmology went completely wrong from the very beginning, and is essentially meaningless. This is because of the incorrect assumption of a symmetric metric, and an over complicated use of three metric compatibility equations. Only one is needed, equation (2), and the commutator equation (4) shows that the connection must be antisymmetric in order to give a non zero torsion. The Hookian force (inferred by Robert Hooke and wrongly attributed to Isaac Newton) is defined by:

F = – m c squared gamma sup 0 sub 10 = – m M G / r squared

for r >> r sub 0.

a186thpapernotes8.pdf

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Torsion Based Cosmology

Feed: Dr. Myron Evans
Posted on: Saturday, June 18, 2011 5:25 AM
Author: metric345
Subject: Torsion Based Cosmology

It is instinctively obvious that the motions of planets around the sun and of stars around the centre of a galaxy are due to torsion of spacetime. It has just been demonstrated in notes 186 that curvature plays no part in the cosmology of the solar system – the relativistic Kepler problem. This is a completely non-Einsteinian result, yet is based on exactly the same metric (the so called Schwarzschild metric (SM)). This metric was not derived by Schwarzschild in his 1916 papers, he gave different results with no singularities. The new method of notes 186 gives the inverse square law exactly in the limit r >> r sub 0 where:

r sub 0 = 2 MG / c squared

So the solar system is described by spherically symmetric spacetime and by only one element of the spacetime torsion. The next step is to apply this method to a whirlpool galaxy, building on previous papers. All the UFT papers are easily and quickly accessible with google and there is an index on the home page of www.aias.us. We now have a method of deriving the antisymmetric connection from the SM (so called). So all four field equations of the engineering model can be applied with this known connection. Similar remarks apply to electrodynamics. For background I recommend:

S. P. Carroll, “Spacetime and Geometry: an Introduction to General Relativity” (Addison Wesley, New York, 2004), chapters 1 – 3 on geometry, but chapters 4 onwards are just dogma.

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Comparison of UFT 113 and UFT 186

Feed: Dr. Myron Evans
Posted on: Saturday, June 18, 2011 4:12 AM
Author: metric345
Subject: Comparison of UFT 113 and UFT 186

The same result is obtained as UFT 113, eq. (27):

F = m c squared T

where F is force and T is spacetime torsion in barebones notation with all indices removed. UFT 113 eq. (53) gives the relation between torque and torsion. So the driving torques used in UFT 183 and 184 are due ultimately to spacetime torsion. However, UFT 113 still accepted the received opinion that the connection be symmetric. It was realized in UFT 122 ff. that the connection is antisymmetric. UFT 186 sets the clock back to 1900 and starts again, improving a great deal the entire output of the twentieth century in general relativity. Knowing the torsion gives the torque and the angular momentum, and in several UFT papers the whirlpool galactic dynamics are explained straightforwardly with torsion without use of a dark matter that has never been observed.

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Final Version of Note 186(4)

Feed: Dr. Myron Evans
Posted on: Saturday, June 18, 2011 1:26 AM
Author: metric345
Subject: Final Version of Note 186(4)

I dropped a minus sign which is reinstated in eq. (12). It is seen that this is precisely the inverse square law of attraction within a factor m c squared, where m is the mass of the attracted particle. The formula (1) is defined only for sigma = alpha = mu, and for rho not equal to mu. The inverse square law is

F = – m M G / r squared

so we find that

F = m c squared T sup 0 sub (10)

and universal gravitation is due to Riemann torsion. The inverse square law was discovered by Robert Hooke of Christ Church College Oxford, not by Isaac Newton of Trinity College Cambridge. This is clearly stated by John Aubrey in his well known book “Brief Lives”. Newton developed the theory in “Principia Mathematica Philosophiae Naturalis” (1687) but Hooke inferred it originally. Newton developed fluxions independently with Leibniz.

a186thpapernotes4.pdf

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