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Dr. Myron Evans
Dr. Myron Evans

Notes on the new Evans field and wave equations, and deficiencies of the "standard model"

25 June, 2003

The implications of refuting U(1) electrodynamics, and replacing it with generally covariant electrodynamics, such as O(3) electrodynamics, are of course far reaching. Observation of B(3) in Physical Optics and Interferometry is also important..

Discussion of the Evans field and wave equations (Found. Phys Lett., 16, 367 (2003), in press,, should especially include the role of the tetrad in electrodynamics, weak and strong field theory, and the need for a generally covariant unified field theory. The obvious weaknesses of the standard model, inter-relation of fields and experimental verification, numerical solutions of the Evans equations, and industrial applications are also open to discussion..

Industrial applications include advanced propulsion, specifically the effect of an electromagnetic field on gravitation, and acquisition of electromagnetic energy from spacetime, low temperature fusion, MRI without magnets, and those topics discussed by Dr. K*****, who has industrial plant up and running already.     

It is now realized (M. W. Evans, Found . Phys. Lett., 2003, in press, that the source of electromagnetic energy from spacetime is the scalar curvature R, all forms of energy and curvature being interconvertible. 

The fatal flaws in the standard model and string theory are by now very well known and also widely accepted by reasonable thinkers, i.e. those who base their thinking on objective scientific reality and not subjective preconception or received ideas floated by small elitist communities.

  1. The electromagnetic, weak and strong sectors are not generally covariant, violating the principles of relativity and equivalence of Einstein and Mach.
  2. The U(1) group cannot be the gauge group of the e/m sector.
  3. String theory is flawed in many ways, and according to one eminent physicist, Mendel Sachs, has not produced a single original result.   
  4. Electrodynamics is not a linear theory, as asserted in the standard model.         
  5. The tangent space of generally relativity is a physical space, while the fiber bundle of gauge theory is regarded as just an abstract space.

These flaws in effect prohibit field unification.            

The deeply significant paradigm shift introduced in the novel Evans equations of generally covariant grand unified field theory, classical and quantized, address these fundamental flaws by realizing that the potential for all four fields is the tetrad one form, that the gravitational gauge field is the Riemann form, and that the electromagnetic, weak and strong gauge fields are torsion forms, the field equations are the Maurer Cartan structure relations of differential geometry. The Maurer Cartan equations also inter-relate fields i.e. inter-relate torsion and Riemann forms. All four fields are given the same philosophical significance by realizing that the tangent bundle can be identified with the fiber bundle. O(3) electrodynamics was the first step towards this conclusion. 

I wish to open dialogue between AIAS and other groups on the implications of this equation and to make the AIAS theory more widely known, so that it becomes "mainstream physics" and improves the standard model. The Evans wave equation unifies the four known fields by recognizing that all four sectors must be generally covariant, and non-Abelian in structure. In the standard model only the gravitational sector is generally covariant. Our research at AIAS over the past few years has shown that the electromagnetic sector cannot be U(1), and we have developed an electromagnetic sector which is non-Abelian in structure, and generally covariant. The successful  experimental testing of this theory is archived in the list of my publications, 1998 to 2003, on This work has culminated in the wave equation described already.          

I am interested in developing the implications of the wave equation for example in in particle physics, QED, QCD, field theory, differential equation theory, fluid and non-Newtonian dynamics, non-Newtonian gravitation, MRI , ESR, and NMR technology, low energy fusion, interaction of fields, advanced propulsion technology and in string and brane theory. The various implications in the electrodynamic sector are far reaching and lead to several new technologies, some of which we are developing inside AIAS and some of which has advanced to pilot plant.


The EVANS ANSATZ of classical unified field theory is as follows (Found. Phys. Lett., 16, 367, (2003), and in press and submitted, preprints on

           If the gauge invariant gravitational field be the Einstein field:

          G sup (S) sub mu nu = -(R/4) q sub mu q sub nu  --------------- (1)

then the gauge invariant electromagnetic field is:

          G sup (A) sub mu nu = -Phi(0) (R/4) q sub mu ^ q sub nu.------ (2)

    Here R = -kT is the scalar curvature, k is the Einstein constant, T is the contracted energy momentum tensor of Einstein, Phi(0) is a fundamental magnetic flux (in weber) related to the fundamental Evans potential phi(0) in volts by:

                        partial Phi(0) / partial t = phi(0)

   Eqn. (2) shows that electromagnetic energy is available from space-time provided that Phi(0) is non-zero, and that R is non-zero, and provided that the wedge product of  metric vectors is non-zero. This means that the torsion form of space-time must be non-zero for an electromagnetic field to be non-zero.. 

     The wedge product (Sean Carroll, "Lecture Notes in General Relativity", Univ. Cal., Santa Barbara) eqn. (1.80)) is

       q sub mu ^ q sub nu = q sub mu q sub nu - q sub nu q sub mu


Some Useful Background (Carroll, p. 23) .

      A differential p form is a (0, p) tensor which is completely antisymmetric. Thus scalars are 0 forms, dual vectors are one forms, the antisymmetric tensor is a two form, the current density is a three form and the Levi Civita tensor in 4-D is a four form. Forms can be differentiated and integrated without additional geometrical information. Given a p form A and a q form B the wedge product is a p+q form. A one form in Euclidean space is a vector, so the Hodge dual of the the wedge product of two forms is another one form. In vector notation this is the cross product.

     The tetrad is a one form, the spin connection is a one form but not a tensor, the torsion tensor is a vector valued two form, the Riemann form is a (1, 1) tensor valued two form. The torsion and Riemann forms characterize any given connection.

          The Evans Ansatz thus asserts that if the gauge invariant gravitational field is a Riemann form the gauge invariant electromagnetic field is a torsion form.

           The torsion form is the external covariant derivative of the tetrad. This is the first Maurer Cartan structure relation. The second Maurer Cartan relation defines the Riemann form in terms of the spin connection. Therefore the generally covariant electromagnetic field is defined by the Evans Ansatz and the first Maurer Cartan structure relation.        


Referee two (out of three external academic referees) made some important remarks as follows:

          "This paper deals with the interesting topic of classical gravity and gauge theories (tetrad anholonomic coordinates) which may be important for cosmology and some astrophysical coordinates. An observer measures with respect to the local tetrad coordinate system (in a tangent space or fiber bundle)  and not with respect to a global coordinate system. The general behavior of geometrical structures and physical patterns such as O(3) electrodynamics obtained by the author (M. W. Evans) may be applied to an entire class of (novel, MWE) generalized Einstein field equations.

            The paper is carefully and didactically written, i.e. is self contained, and deserves to be published in Foundations of Physics Letters.

The other two referees were also enthusiastically in favor of immediate publication.            

The importance of the remarks by referee two is that the tangent space of general relativity is identified for the first time in physics and mathematics with the fiber bundle space of Yang Mills gauge field theory. Therefore the up to now abstract gauge field internal space is given a physical meaning in general relativity. This is the key to my suggestion of a novel GUFT theory. This theory has now been well received by nine external referees in three papers.             

These papers show that electromagnetic energy from space-time is possible in general relativity and GUFT. I would be delighted if the MEG received independent laboratory certification.            

 I wish now to develop the theory in several directions, with the AIAS author group, and I am working on a new paper now. The electrogravitic equation is the simplest example of the new GUFT theory.

Myron W. Evans                 
AIAS Director,
25th July 2003

I tend to agree (on the importance of null vectors), I think that Prof. Sir Roger Penrose used null vectors as far back as 1962 to introduce his twistor theory, and there is a close connection to tetrads and spinors.

The relation between the fiber bundle and the tangent spacetime is at the root of my GUFT theory. The fiber bundle in gauge field theory was introduced by your colleague Mills, working with the Nobel Laureate Yang in 1954.  The paper accepted this morning is available in preprint form on


It is also very clear to me at least that the only possible method of describing electromagnetism in general relativity is through the wedge product of metric four vectors. Otherwise we are left with the unpleasant prospect of abandoning the Principle of Relativity.         

The basic reason is that there are only two fundamental forms - the Riemann and torsion forms, available to describe gravitation and electromagnetism respectively. The Riemann form is used in symmetrized general relativity, the torsion form in antisymmerized general relativity.         

This is more or less the same conclusion as arrived at by Sachs, and presumably also Dirac, with whom Sachs worked for a year, and also by Clements, Flower, Crowell and others.

I derived the wave equation simply by covariant differentiation of metric compatibility conditions. The most general of these is the tetrad postulate of differential geometry, which must be compatible with your analytic geometry. The wave equation results in a deeper meaning for general relativity and produces a unification of gravitation and electromagnetism.

The quark colour triplet then emerges as an eigenfunction of the wave equation in SU(3), so the strong force is simply gravitation in SU(3) rather than O(3), as postulated by Petar Anastasovski in his theory of the elements. Similarly the weak force is electromagnetism in SU(2) rather than O(3).                           

Several major predictions of the wave equation have emerged already, by e mail discussion in this group over the past few months. These include the inference from general relativity that every particle has a rest volume which is finite, so there are no singularities such as point particles or point charges in nature, and the similar inference (today) that there are no singular cosmologies in nature, so there are no Big Bang cosmologies. Another major prediction is that electromagnetism is a theory whose gauge group is O(n), with n equal to or greater than 3, or SU(n) with n greater than or equal to 2, but if we are to accept general relativity, electromagnetism cannot be a U(1) or O(2) gauge group theory. 

These advances are summarized on as they occur, and distributed by BCC, for security and protection of distribution list privacy.                                    

So historically, Big Bang cosmology is another example of pathological science, i.e. a flawed idea promoted by careerists.

Another example is the Aristotelian view prevalent at the time of Copernicus or Kepler. Even Galileo (who should have known better) described Kepler as a "lunatic", so Galileo was obviously impressed by his great rival and contemporary - the Imperial Mathematician in Prague.

This is all described in impressive scholarly detail by Arthur Koestler in "The Sleepwalkers" published by Hutchinson of London.


The AIAS work supports the possibility of electromagnetic energy from space-time with non-zero torsion as defined in differential geometry. In the same way, gravitational energy is obtained from spacetime with curvature in devices such as hydroelectric power stations, or tripping on a banana skin.


        In respect of advanced propulsion I refer recipients to my paper:

        "The Equations of Grand Unified Field Theory in terms of the Maurer Cartan Structure Relations of Differential Geometry" (Found. Phys. Lett., in press, preprint on                   

          These develop the gravitational and electromagnetic fields through the Evans equation for the tetrad:

                                (d'alembertian + kT) q sup a sub mu = 0

and gives some interrelations between the gravitational and electromagnetic fields. The way that one field influences the other is to be found through the way the tetrad is constructed. For pure electromagnetism the tetrad is constructed with respect to a flat spacetime base manifold, (no gravitation). In the presence of gravitation the base manifold becomes curved, and the tetrad changes. It is this change in the tetrad that gives the influence of gravitation on electromagnetism in generally covariant quantum field theory.

          In order to solve the Evans wave equation (a generally covariant non-linear wave equation) we need computers, a stable research environment, and a highly skilled staff. We may then be able to find some situations in which the influence of electromagnetism on gravitation is sufficient to result in electromagnetically induced lift off .                    

         The electrogravitic equation is the weak field solution of the Evans wave equation, and the electrogravitic equation relates the Newtonian acceleration due to gravity g to the electric field strength E in electrostatics through the Evans potential phi(0) in volts of unified field theory.

            First and foremost we need to test the electrogravitic equation experimentally. 



             The problem with quark theory is that the masses of the

elementary particles are wildly wrong, (out by a factor of two hundred). Also the
evidence for quarks is very tenuous, based on the assumed existence of partons
from low angle scattering. Partons (if they really exist and are not data
artifacts) could be due simply to inhomogeneities inside the proton and neutron.
Electrons are supposed to be elementary and not made up of quarks. This again is
more than a little odd. It means that electrons are described by SU(2) while
protons, neutrons etc. are described by SU(3) quarks.                

                In the new unified theory all elementary particles are

minimum curvatures in the special relativistic limit. Each particle has its own
curvature or mass, and I do not attempt to go further and to try to explain all
these masses with quarks. The experimental evidence for quarks simply is not
strong enough. However if one does accept quarks the new unified theory explains
them as described in my note of this morning.

               String theory is just an elaborate mathematical contrivance,

many dimensions are used, and this makes it automatically unphysical (i.e it
means that it is a not a theory of natural philosophy). Even those working
inside the field of string theory admit its many bizarre weaknesses, and eminent
colleagues like Glashow and Sachs would say that it has not produced anything
that was not already known, and it is in fact incapable of any prediction -
because it uses unphysical dimensions from the start. One cannot predict anything
in physics from unphysical base concepts

             The standard model is a mess made up of incorrect concepts such

as these, and the conventional "GUFT" is a mess made up of group products in
special relativity, the ad hoc Higgs mechanism, and many loose parameters, and
leaves gravitation entirely out of consideration.

             The first genuine attempt at unified field / matter theory is

the AIAS theory

All edited from internal correspondence from AIAS Director, Dr. Myron Evans