Archive for April, 2008

Background to Paper 105

April 30, 2008


Subject: Background to Paper 105
Date: Wed, 30 Apr 2008 09:47:13 EDT

The background to paper 105, in which the metric element is derived from the Bianchi identity, is the use of a symmetric metric, but without assuming that the connection is torsion free. The metric compatibility connection is used implicitly because if a connection is metric compatible the metric is always parallel transported. Then the invariant in paper 105 is constructed but without assuming a torsion free connection. So this completes a series of technical notes to the general readership explaining the background to papers 93 to 110. The basic dynamical equation is no longer EH but the four vectro equations derived from the Bianchi identity and its Hodge dual.

Spherically Symmetric Spacetime

April 30, 2008


Subject: Spherically Symmetric Spacetime
Date: Wed, 30 Apr 2008 07:53:58 EDT

One of the most general line elements of the spherically symmetric spacetime is given by Carroll in his eq. (7.13) of his 1997 online notes. This was evaluated in paper 93 of _www.aias.us_ (http://www.aias.us) . Carroll then automatically neglects torsion by computing the Christoffel symbols of this metric. Our Maxima code in paper 93 was checked in this way for correctness. Carroll then gives the non-zero elements of the Riemann tensor for this line element, and again our Maxima code reproduced Carroll’s results. Finally or code was checked to reproduce Carroll’s Ricci tensor. Carroll then uses the Ricci flat condition, in which all elements of Ricci are zero. Our code was again checked in this way. The result of the Ricci flat assumption for the spherically symmetric line element is the CORRECT Schwarzschild solution of 1916, in which Schwarzschild’s alpha is denoted mu by Carroll in his eq. (7.26). The reason for the structure of the Schwarzschild line element is that it is a line element of spherically symmetric spacetime for zero torsion in which the Ricci tensor is assumed to be zero. The Einstein Hilbert equation does not enter into the analysis.

Finally the mu of this pure geometrical solution is assumed to be – 2GM / c squared.

However, the Einstein Hilbert field equation is

R sub mu nu – (1/2) R g sub m nu = k T sub mu nu

and in a Ricci flat spacetime:

T sub mu nu = 0

The 00 element of this tensor is the mass density, so in a Ricci flat spacetime there is no mass density anywhere in the spacetime. Therefore the identification of mu with -2GM / c squared assumes the existence of a mass M where there there is no mass M. Such a procedure was not used by Schwarzschild.

In paper 93 we computed a particular curvature tensor which appears on the right hand side of

D sub mu T sup kappa mu nu = R sub mu sup kappa mu nu

This curvature tensor is non-zero in general for the Christoffel connection, whereas the torsion is always zero for the same Christoffel connection. So the use of this connection conflicts with the Hodge dual of the Bianchi identity in general.

In the weak field limit ( r goes to infinity) we have (T sub mu nu = 0, no EH equation used)

g00 = – grr = – (1 + mu / r)

This is identified with the weak field limit of EH (T sub nu nu NOT zero, EH equation used):

g00 = -grr = – (1 + 2 phi)

where phi is the Newtonian:

phi = – GM / r

It is obvious that this is self contradictory because in one case T sub mu nu is zero (no EH used) and in the other case it is not zero (EH used). So this procedure, on scholarly examination, makes no sense at all, and in papers 93 to 100 we set out to revise it completely to include torsion self-consistently.

Ineluctable Link between Torsion and Curvature

April 30, 2008


Subject: Ineluctable Link between Torsion and Curvature
Date: Wed, 30 Apr 2008 06:57:43 EDT

This is well known to scholars of geometry and topology (e.g. Carroll chapter three), and comes from the action of an operator, called the commutator of covariant derivatives, on the general vector in n dimensions. The most rigorous application of this theorem is to be found in the well read paper 109, posted earlier this month. The commutator is sometimes called the round trip operator, and is well known in field theory. Gauge theory was developed from it as in Ryder’s book, “Quantum Field Theory” (Cambridge 1996). The commutator defines the torsion tensor and the curvature tensor. The torsion differential form and the curvature differential form of Cartan are defined from the tensors by multiplying them with a tetrad. EH was developed before this was known in geometry, and EH used the symmetric Christoffel connection, which is defined on the basis of the metric compatibility condition and the symmetric metric. However, the commutator acting on a vector does not assume metric compatibility and does not assume a symmetric metric, so does not assume the Christoffel connection. Prior to paper 93 on _www.aias.us_ (http://www.aias.us) it was thought that the torsion could be omitted from gravitational theory. However papers 93 to 110 prove that it cannot be omitted without violating the Hodge dual of the Bianchi identity. The complete argument is given in paper 109. The duality invariance in four dimensions of the Bianchi identity means that in four dimensions, the original identity and its Hodge dual have the same mathematical structure. So all field equations of ECE are duality invariant. The fundamental reason for this is that the Hodge dual in four dimensions of a two-form (rank two antisymmetric tensor) is another two-form. The Cartan torsion is a vector valued two-form, and the Cartan curvature is a tensor valued two-form. Each is antisymmetric in its last two indices.

Finally, the Riemann tensor is a type of curvature tensor in which the connection is the Christoffel connection. In general neither the metric nor the connection are symmetric.

EH versus ECE

April 30, 2008


Subject: Relativistically Corrected Orbits: EH versus ECE
Date: Wed, 30 Apr 2008 06:30:18 EDT

The standard argument here is that the Schwarzschild metric (so called) produces the inverse r attractive (negative sign) part of the potential, plus the positive valued repulsion potential of an orbit, plus the relativistic correction that produces the perihelion advance. Then tests of gr set out to measure the preihelion advance accurately using satellites or binary pulsar observations. The Christoffel connection is used throughout in the standard model, and torsion is zero implicitly, or just not mentioned at all. It is then claimed that EH predicts the perihelion advance very accurately, and these claims are merely repeated as data get more precise. The ECE theory counter argues these claims by showing that the Christoffel connection is geometrically self-contradictory (as in the previous note) and that torsion always enters into the basic equations of gravitation (notably the gravitomagnetic equations obtained directly from the Bianchi identity with torsion). ECE shows for example that the acceleration due to gravity g is a well defined scalar torsion within a factor of proportionality. ECE also shows that the Schwarzschild alpha is not predictive, it is an adjustable parameter, so the basis of the predictive claims of EH is undermined completely. What really happens is that a Ricci flat geometry, producing a parameter called alpha by Schwarzschild, is adjusted to produce Newtonian dynamics in a given limit. A source mass M is introduced depsite the fact that a Ricci flat geometry contains no source mass M, another self-contradiction of EH. Finally ECE shows that an angular momentum generates torsion through the rotation generator. In an orbit of any kind, rotation is present. There is a non-zero angular velocity of the orbit (the Kepler laws). Therefore in any orbit space-time torsion is non-zero. The Christoffel connection of the standard model implies zero torsion, a self contradiction.

So satellite data should be used to test ECE (and other new theories) but not EH, for the above reasons and several others. In fact (_www.santilli-galilei.com_ (http://www.santilli-galilei.com) and _www.aias.us_ (http://www.aias.us) ) EH has been criticised many times by many leading scientists since inception. The standard modellers essentially indulge in propagandist, public consumption, material which just states that EH is a very precise predictive theory, or similar incorrect statements. In fact EH is not predictive at all, and is internally self-inconsistent. To develop a self-consistent theory of precise satellite data requries torsion and curvature, the basic elements of Cartan’s self-consistent geometry.

The Bianchi Identity in ECE Theory

April 30, 2008


Subject: The Bianchi Identity in ECE Theory
Date: Wed, 30 Apr 2008 05:35:30 EDT

The Bianchi identity as developed by Cartan is:

D ^ T := R ^ q

and as first shown in paper 15 (the most read ECE paper this month) is a rigorous identity consisting of a cyclic sum of three curvature tensors being identically the same as the cyclic sum of the fundamental definitions of these same three curvature tensors in terms of the gamma connection. Not carefully that the latter is more general than the Christoffel connection. This is proven in all detail in one of the appendices of paper 15. This proof is used again in paper 109, which proves rigorously the Hodge dual of the Bianchi identity:

D ^ T tilde := R tilde ^ q

These are in essence two expressions of the Bianchi identity, which is duality invariant. In paper 88 the rigorously correct expression of the so-called “second Bianchi identity” of the standard model was given. In paper 93 the Hodge dual identity was used to show the fatal internal inconsistency of the geometry of the EH equation. The latter geometry is:

T = 0, R ^ q = 0

whcih is fortuitously self consistent with the Bianchi identity, but the internal inconsistency is:

T tilde = 0, R tilde ^ q NOT zero in general

which is inconsistent with the Hodge dual of the Bianchi identity.

Paper 103 then produced a form of the field equation of realtivity in which torsion is accounted for correctly. Finally paper 110 shows that the torsion generator is the rotation generator within a factor of proportionality. The Bianchi identity is the basis of the homogeneous tensorial field equation of ECE, and the Hodge dual identity is the basis for the inhomogeneous tensorial field equation of ECE. These split into four vector equations. In dy namics these are the rigorously self-consistent “gravitomagnetic equations”, as they are obscurely known in the standard model, and in electrodynamics they are the rigorously self-consistent field equations, with a mathematical structure that is the same as the Maxwell Heaviside field equations, but written in a more general space-time with curvature and torsion both present, and with a non-zero connection.

ECE gives an internally consistent, duality invariant, structure for the field equations of dynamics and electrodynamics.

Orbital Theory

April 30, 2008


Subject: Orbital Theory
Date: Wed, 30 Apr 2008 04:57:54 EDT

The standard modellers will argue, predictably, that the Christoffel symbol and Schwarzschild metric (as they call it) produce the relativistic corrections in orbital theory (e.g. precession of the perihelion). However this is counter argued by the fact that the Christoffel connection is now known to contradict the Hodge dual of the Bianchi identity, so the Christoffel connection is a logical self-contradiction at a basic geometrical level. Steve Crothers has also given a counter argument in that Ricci flat solutions are pure geometry, and they contradict the Einstein equivalence principle. So we should use the satellite data (which are of course precise and interesting) to test ECE, because we already know that EH is self-contradictory and obsolete. Thirdly as just mentioned, Schwarzschild’s alpha from a Ricci flat solution is a loose parameter, not a predicting entity. All the so called precision tests of general relativity are now known to contain these fatal internal contradictions and fitted paramater alpha of a vacuum solution. So they all have to be overhauled systematically. In paper 108 which Horst is working on at present, we will give the rigorously consistent ECE description of the orbits of binary pulsars, without using gravitational radiation. The precision tests of gr are usually said to be: bending of light by gravity, percession of the perihelion, the orbits of binary pulsars, and the Lense Thirring effect. It is now known that they must all be based on torsion and curvature.

The intolerance of the standard mdollers to new ideas is also tediously predictable. For example our very well read and accepted paper 93 was dismissed by an anonymous referees as, sic, “a loony paper”. There was a seplling mistake, it shoul dhav ebeem “loonie”, which is slang of “insane”. When the editor was challenged by an objection to this offensive charade he in turn became dismissive and intolerant, and finally abusive. This episode is recorded word for word on the _www.aias.us_ (http://www.aias.us) blog. What has happened is that these people (who seek to censor and dismiss without reading, let alone understanding) have been by-passed by intense study worldwide of the entire contents of the _www.aias.us_ (http://www.aias.us) site.

Civil List Scientist

note 111(2)

April 30, 2008


Subject: Fwd: note 111(2)
Date: Wed, 30 Apr 2008 04:35:39 EDT

Good idea. In fact this is the key point, a rotation of any lien element generates torsion. For example there are torsion generators around each axis because there are rotation generators around each axis. The most general definition of tetrad is used – the matrix linking two vectors. The R parameter is related to the shell radius. In all these precision tests of general relativity there is the problem of identifying the alpha parameter of Schwarzschild (1916) with 2MG / c squared. This is actually a curve fitting exercise, not a prediction, because the alpha parameter for the vacuum comes from pure geometry as you know (the Ricci flat solution). So the purely geometrical alpha was FITTED by othe rpeople (not Schwarzschild himself) to 2MG / c squared to reproduce Newtonian dynamics. There is no prediction of Newtonian dynamics in Schwarzschild’s original 1916 vacuum solution. Similarly the commutators of two Lorentz boost generators give a torsion generator. The Christoffel connection gives zero torsion. So there is an internal contradiction in using a Christoffel connection in general relativity whenever there is rotational motion. Also in paper 93 of course we found a basic internal contradiction in the EH geometry, after an exhaustive analysis. I recall that you inferred this contradiction independently in the context of the Lense Thirring effect. If the standard modellers try to assert that rotation does not generate torsion, then they are forced back on asserting arbitrarily that a tetrad can only be used in centrally directed gravitational theory. This is counter argued by noting that the Cartan geometry is valid for any tetrad, i.e. any tensor linking any two vectors.

To the general readership: this is what I mean by an inductive discussion of a thread of thought. This is how all the ECE papers were developed. Sometimes a newspaper article or similar is useful, but the inductive approach to such an article is to apply ECE theory to it, because after all, we are developing ECE theory. Colleagueas are of course encouraged to apply ECE theory to any problem they may note in any kind of literature. At that point I can enter into an inductive discussion. It is especially important at present to apply ECE to new energy devices in a rigorously systematic manner, and this is expemplified in the papers on such devices on _www.aias.us_ (http://www.aias.us) .

In Eq. (2) which refers to the original papers of the Lense Thierring effect: Is R the radius of the rotating shell? I cannot see that this parameter should have any effect, except it defines the total mass or mass density. Consequently, your derivation does not need such a parameter. From the comparison of results (eqs. 21/22) one sees that R must be in the order of coordinate radius r, for example when looking at the poles of the sphere (sin theta = 0). If this comparison is meaningful at all depends on the interpretation of R, I think. Perhaps it would make sense to write down the general formulas for obtaining the rotational torsion from a given transformation matrix (i.e. tetrad). You did it already in part in paper 109. Or better to start with a given symmetric metric as you already proposed. The steps could be automised then.

Horst

Tired Gamma Ray Photons

April 29, 2008


Subject: Fwd: Tired Gamma Ray Photons
Date: Tue, 29 Apr 2008 12:53:43 EDT

http://www.nytimes.com/2008/03/21/science/space/21bangw.html

Myron,

How do you put this gamma ray event together with the Tired Photon model?

Spritzer telescope observes Gamma Ray events, which I suspect would be converted into microwave or thereabouts by a half universe travel.

Thanks,

Marco

In general I don’t respond very much to newspaper articles sent to me because usually I am developing a line of thought with scholars such as Horst Eckardt who have a complete understanding of ECE. Newspaper articles and popular science press articles frequently distort facts, contain no equations, and sometime little or no scholarly detail. Photon mass is predicted by ECE, which is all I can comment on this website. So I tend to just redistribute articles sent to me, or just glance at them. if there is anything of relevance to what I am doing I make a short comment. My usual method is to look for accurate and detailed scholarly papers, and to develop my own line of thought on a given subject. Tired light is a theory based on a Yukawa potential. In ECE teh photon mass comes out of the wave equation.

Food and Fuel

April 29, 2008


Subject: Food and Fuel
Date: Tue, 29 Apr 2008 12:45:15 EDT

InterestingBest, Gareth

Is Global Warming Fueling World Hunger?Washington Post

The food price shock now roiling world markets is destabilizing governments, igniting street riots and threatening to send a new wave of hunger rippling through the world’s poorest nations. … Much of the increase is being absorbed by middle men — distributors, processors, even governments — but consumers worldwide are still feeling the pinch. The convergence of events has thrown world food supply and demand out of whack and snowballed into civil turmoil. … To quell unrest, countries including Indonesia are digging deep to boost food subsidies and rationing certain staple foods. The U.N. World Food Program has warned of an alarming surge in hunger in areas as far-flung as North Korea and West Africa. The crisis, it fears, will plunge more than 100 million of the world’s poorest people deeper into poverty, forced to spend more and more of their income on skyrocketing food bills. “This crisis could result in a cascade of others . . . and become a multidimensional problem affecting economic growth, social progress and even political security around the world,” U.N. Secretary General Ban Ki-moon said. A big reason for higher wheat prices, for instance, is the multiyear drought in Australia, something that scientists say may become persistent because of global warming. But wheat prices are also rising because U.S. farmers have been planting less of it, or moving wheat to less fertile ground. That is partly because they are planting more corn to capitalize on the bio-fuel frenzy. In other words, the crisis may have its genesis on two ends of the same problem: Global Warming causing droughts causing poor harvests, and people shifting resources to create alternatives to forestall or reverse Global Warming.

_________________________________________________________________ Be a superhero and win! Play the Iron Man Mashup Game http://www.ironmanmashup.co.uk=

This illustrates the urgent need to stabilize fuel prices. It would be optimal if a car, train or ship coudl be run off a combination of magnegas and new energy devices.

BepiColombo mission

April 29, 2008


Subject: Fwd: BepiColombo mission
Date: Tue, 29 Apr 2008 08:32:46 EDT

Many thanks! I find this very interesting and will forge a few ECE apeprs in preparation for these experiments. We can regard these satellite experiments as providing us with very precise data with which to test ECE theory, not EH theory. As you know, some fundamental principles of relativity are retained in ECE, such as the equivalence principles, local Lorentz invariance and constancy of the speed of light, constancy of G and c, of e and h bar, and so on, but others are firmly rejected as in papers 93 to 110. As in paper 108 we are able to explain things in ECE more simply and self-consistently. Similarly we should regard the large hadron collider results soon to emerge from CERN as testing ECE theory, not the obsolete standard model. With ECE we are also able to explain why gravitatonal radiation has not yet been detected by LIGO. Gravitational radiation can exist in ECE, (wave equation), but again it cannot be produced from an incorrect geometry such as that of EH. Nothing physical can be predicted with an incorrect and self-inconsisetnt geometry. It is safe to extrapolate accurately from four years of feedback data for _www.aias.us_ (http://www.aias.us) . These unique data provide an excellent statistical sampling by now, (daily for four years), and show very clearly that ECE will be studied more and more by the younger generation such as yourself. The use of computer algebra cannot be challenged objectively. The basic flaw in EH was hard to find, but we found it in the exhaustive analysis reported in paper 93 and its plots and Maxima code. We have already fixed this flaw with the use of torsion, and have already explained binary pulsars and the Cassini / Pioneer anamaliees, Thomas precession and Lense Thirring effects with the use of torsion. So these new satellite data are going to be most interesting. We are ready for them with ECE theory.

Dear prof. Evans,

here is link to ESA mission BepiColomgo which is planed to be launched in year 2013 and one of its goal is to proof several relativistic predictions (equivalence principle and special and general relativity). Cite “*Measurements would allow the estimation of key parameters in alternative theories.*”

http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=40836

Best Regards

Karel


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