Albert Einstein Elie Cartan Myron W. Evans
Einstein, Cartan and Evans – Start of a New Age in Physics?
Laurence G. Felker,
Reno, Nevada, USA
Although physicists have struggled in vain for over a half-century to encompass all natural forces within a unified
theory, chemical physicist Myron W. Evans has now succeeded. Based on the fundamental insights of Albert
Einstein and Elie Cartan, Evans’ theory takes the geometry of space-time itself as the origin of all forces of Nature.
As Einstein attributed gravitation to the curvature of space-time, the new theory attributes electromagnetism to the
torsion or twisting of space-time. The possibility of reciprocal interactions between gravitation and electromagnetism
-- which possibility is denied in current mainstream physics -- leads to predictions of new physical effects which could
be used to produce power and energy from space-time.
For centuries, physicists and philosophers sought a unified description of all phenomena of Nature. We know today
that the world at the sub-microscopic quantum scale behaves very differently than our familiar macroscopic
experience. In particular, theories of gravitation have been irreconcilable with quantum theory. Therefore, one
expects that, if gravitation could be unified with quantum theory, wholly new insights would result. It now appears that
this unification has been achieved, but not in the manner expected by previous generations of scientists. This
unification predicts fundamental new effects – for example, the production of energy (or power) without need for
input of other primary energy. This prediction, among others, is creating great interest in professional and scientific
circles. We now review the origins of this unification.Albert Einstein in 1915 published a theory of the gravitational
interaction; he called this the theory of General Relativity, and today it provides the basis for our understanding and
exploration of the cosmos at large. In 1905, Einstein had already produced the theory of Special Relativity, which
rests upon the well-known postulate of “constancy of the speed of light“ in vacuum. During the last thirty years of his
life, Einstein looked for a still more comprehensive unified theory which could cover all known natural forces. He
spent the years from approximately 1925 to 1955 in this search, but did not reach his desired goal. Since the
discovery of quantum mechanics in the 1920’s, the majority of physicists busied themselves with this, and not with
General Relativity. The fact that quantum mechanics is consistent only with Special Relativity, but not with General
Relativity, was overlooked or ignored. In addition, while quantum mechanics is successful in describing the electron
sheath of atoms; it is not a suitable theory for the high mass-densities which occur within atomic nuclei. Other
notable progress toward unified theory in the 20th century consisted of a unification of electromagnetism with the
weak nuclear force, via an extension of the formalism of quantum mechanics. Gravitation has remained, until today,
outside the Standard Model of particle physics.
Elie Cartan is less well-known than Einstein. He was a French mathematician who exchanged ideas with Einstein
concerning many details of General Relativity. Cartan’s original insight was that electromagnetism could be derived,
via differential geometry, from the geometry of space-time – more or less in parallel with Einstein’s insight that
gravitation could be derived from space-time geometry.
A successful unification, however, was not achieved by Cartan and/or Einstein. The unification was finally achieved
in the year 2003 by Myron Evans who, trained as a chemical physicist, brought fresh insight to the problem. Evans
held several academic professorships in England and the USA, before he was forced to withdraw because of his
unorthodox views, and he now works as a “private researcher“ in his homeland of Wales. From there, he conducts
the “Alpha Institute for Advanced Study“ (AIAS), which presents his ideas to the public as a world-wide team or
working-group. A popular-scientific presentation is in . Recently concentrating its work on energy production from
the vacuum -- a topic which established science avoids – the AIAS website generates large interest, as shown by the
steady increase in web-page statistics on the AIAS site . Many well-known universities and research
establishments world-wide have visited these pages.
1 The four natural forces
To understand the importance of unification, one must start with knowledge of the quantities being unified. It is
widely accepted in physics that all interactions in Nature are manifestations of four fundamental forces. . We
characterize these briefly as follows:
1. The seemingly separate force-fields generated by electrostatic charge and magnetism were united in the 19th
century, largely by Maxwell, into what is now called electromagnetism, or the electromagnetic field.
2. The weak nuclear force is responsible for radioactive decay. According to the Standard Model of elementary
particle physics, the weak interaction is mediated by the W- and Z- bosons, which are “virtual particles“. Neutrinos
also are known to be involved in the weak interaction. It has been shown that the weak force is essentially
the same as electromagnetism at very high energies. Thus, these two forces are said to be “already united“.
3. The strong nuclear force holds protons and neutrons together. It is carried by gluons and quarks in combination,
although direct experimental proof of their existence was not achieved until recently.
4. Gravitation is the fourth fundamental force, but it does not fit with the theoretical picture of the other three, since it
is regarded (after Einstein's General Relativity theory) as the curvature of space-time, which does not correspond to
a classical force term. On the other hand, General Relativity today has been well-tested experimentally, so that
nobody doubts its validity.
If a unified description and formalism could be given for these four very different forces, many new theoretical
insights and practical applications would result. In addition, mutually reciprocal interactions -- which today’s
mainstream physics does not recognize -- could then be predicted and used. As we will see later, such interactions
open new possibilities for power generation. In view of the urgent global energy crisis, this might be the most
important application of such a unification. The first three fundamental forces concern quantum physics (the world
“in the small“), while the fourth force (gravitation) applies on all scales, including cosmic orders of magnitude.
Therefore, the underlying fundamental problem is to unify General Relativity with quantum mechanics. Conventional
science has explored essentially three different pathways which might achieve this result:
1. Bringing general relativity into quantum physics. The insurmountable difficulty here is that time in quantum physics
is treated as a unique continuous parameter, which is incommensurate with the quantized coordinates of distance
(or spatial displacement).
2. Quantization of General Relativity. But the mathematical formalism for this approach is thus far inconclusive, and
unable to make reference to experimental test
3. Invention of a totally new theory, from which the others follow. The various “string theories” are examples, but they
require un-physical high-dimensional spaces (N>10), and have not produced testable predictions.
The solution comes, surprisingly, in an unexpected way. By extending the Einstein theory along the lines first
suggested by Cartan, Evans shows that all four fundamental forces are derivable from one extended theory. This
represents the long-sought Unified Field Theory. Evans’ approach does not exactly follow any of the three above-
mentioned pathways,although it is closest to the third one in the list.
3 Basis for Evans’ theory
To understand the basis of Evans’ theory, we must review the starting-point of Einstein’s relativity theory. Einstein
postulated that the presence of a massive body or an energy distribution in space (which are really interchangeable,
according to the famous formula E=mc2) changes the geometry of space. Viewed from right-angles within a
Euclidean coordinate system, it “creates” a curvature of space (or, more accurately, space-time). One can write this
directly as a formula:
R = k T
In which R designates the (tensor of) curvature, T the (tensor of) energy-momentum density, and k is a
proportionality constant. The left side of this formula is geometry, the right side is physics. Einstein thus used the
geometry of curvilinear coordinates, which goes back to the mathematician Riemann. This formula implies that
space-time (i.e. the three space coordinates, and time as the fourth coordinate) is a 4-dimensional continuum (or
manifold) whose curvature we perceive as a force (namely gravitation).
Notably, Einstein’s formula did not exploit all possible characteristics of Riemann’s geometry. It turns out that R
describes only the intrinsic curvature of the manifold; in other words, it is limited to describing vectors whose point-to-
point variation lies entirely within the manifold (see Fig. 1A).
A) Curvature B) Torsion
Fig. 1: Curvature and Torsion
In contrast to this, Cartan employed considerations of extrinsic curvature. This means that vectors are also allowed
to vary within (and normal to) the plane tangent to the manifold at any point (see Fig. 1B). Cartan showed that the
extrinsic curvature of space-time could be taken to represent electromagnetism as described by the Maxwell
equations. Unfortunately, Einstein’s use of the mathematical concept of tensors made the relation to Cartan’s
concept of geometry unclear. Cartan used the so-called “tetrad” to represent the manifold’s extrinsic curvature. In
the 3-dimensional case, this reduces to a Cartesian-coordinate “triad”, which moves along with a point in space.
More exactly said, the tetrad specifies a tangent space at each point of the Riemann manifold. In this way, one
maintains at each point a Euclidean tangent space (a so-called fiducial space), which greatly simplifies the
description and visualization of physical processes (Fig. 2).
Fig.2: Tangent plane to a curved surface
Despite the value of Einstein’s and Cartan’s insights, a united theory could not yet be formulated, because
experimental indications of how to extend Maxwell’s theory in a manner consistent with General Relativity were still
missing. The crucial connection was found by Evans around 1990 in the spin field or B(3) field.
The decisive empirical effect -- the Inverse Faraday Effect (IFE), i.e. the magnetization of matter by a beam of
circular-polarized electromagnetic radiation, first observed experimentally in 1964 -- could not be explained by
Maxwell-Heaviside electrodynamics, except by introducing an ad-hoc material property tensor.
However, Evans in 1992 was able to derive the IFE directly from first principles (generally covariant unified field
theory, which includes general relativity), and thereby inferred the existence of a previously unknown magnetic field
component -- the B(3) field.
B(3) is, informally, a general-relativistic correction to classical electrodynamics, somewhat analogous to the general-
relativistic correction to Newtonian gravitation needed to explain the perihelion-advance of Mercury.
The index numbers – (1), (2) and (3) -- here refer to the so-called circular basis; and the polarization directions B(1)
and B(2) refer to the directions of transverse polarization of the field. Thus a polarization index must be inserted into
the Maxwell equations. This polarization index corresponds to the tetrad vectors qa in Fig. 2. Finally, this leads
Evans to postulate that the geometrical representation of the electromagnetic vector-potential A should be a
Aa = A(0) qa
where A is the 4 x 4 - matrix of the complete electromagnetic potential, and A(0) is a proportionality factor. The
electric and magnetic fields (combined into the tensor Fa of the total electromagnetic field) then emerge directly from
Cartan’s expression for the torsion Ta:
Fa = A(0) Ta
In this formalism, electrodynamics is completely attributed to the geometrical torsion of space-time. The complete
picture, unifying electromagnetism with gravitation, requires both Riemann curvature and Cartan torsion. The
intrinsic curvature determines gravitation, and the extrinsic curvature (i.e., torsion) determines the electromagnetic
field. This is described in detail by suitable field equations in form of Riemann-Cartan geometry. This theory is now
called Einstein-Cartan-Evans (ECE) theory, after the names of its principal authors.
4 Unification with strong and weak forces
Still to be described is how the remaining two fundamental forces are represented in the ECE theory.
If one analyzes the equations of the theory, it is noticeable that it is formulated for the tangent space of the Riemann
manifold. The number of basis vectors of this space can be selected freely, it needs not be four-dimensional.
Thereby the possibility is offered of selecting such bases which are suitable for the description of quantized action
(e.g. electron spin). Furthermore Evans derived from Cartan geometry a wave equation, which is in principle a
nonlinear eigenvalue equation. Under certain approximation assumptions. this equation becomes linear and predicts
discrete stable states. Those are the “quanta” of energy momentum in quantum mechanics. All quantum-mechanical
theories, in particular Dirac’s electron theory, and the strong and weak interactions, can be deduced in this way as
special cases of the ECE theory.
If we compare this result with the three conventional paths to unification referred to above, it is noticeable that none
of these was actually used. The new theory predicts quantum effects without assuming them (as a postulate) from
the beginning. The first two forces (electromagnetism and weak force) are combined, the third and fourth turn out to
be derivable from other considerations. In short, there are no truly “fundamental forces” because
they all emerge from geometry!
5 Implications for quantum physics
The main implication is that quantum theory in its current form is not a fundamental description of Nature. In
particular, the Heisenberg interpretation and the Correspondence principle are incorrect. The ECE version of
quantum physics rests upon a classical, fully deterministic basis; quantum indeterminacy plays no role. Nevertheless
the equations of quantum mechanics (for instance the Schroedinger equation) are correct and describe classical
statistical processes. It would be a mark against ECE theory if it did not predict this result, because the equations of
quantum mechanics are experimentally verified a thousandfold.
Evans also argues that the Heisenberg Uncertainty relation arose only by a misunderstanding, and is not justifiable.
All physical mass-points of a field theory are actually densities -- i.e. quanta of matter-energy spread over a volume
of space. Thereby the Planck quantum of action is to be divided by the volume, for instance, of the measuring
instrument in which two complementary variables (e.g. position and momentum) are measured. The result can
become arbitrarily small, i.e. the uncertainty can be reduced to powers of ten smaller than previously believed. An
elementary particle, therefore, is neither exclusively a wave, nor exclusively a particle, but possesses characteristics
of both at the same time.
This sounds fantastic as a theory of physics, but exactly that was measured already some years ago . The
experimental refutation of the uncertainty relation was accomplished by mainstream physics.
Fig.3: The Aharonov Bohm effect.
As a further example of an effect which was previously difficult to explain, we consider the Aharonov Bohm effect
(Fig. 3). Two electron beams are diffracted by a double gap, at the screen, a typical interference pattern is
produced. In the diffraction zone is a closed toroidal coil. The magnetic field is circularly closed and thus remains
within the coil. If one now switches on and off the magnetic field, in each case two different interference patterns
result. The closed magnetic field thus has an effect on the electron beams, although these are not in direct contact
with the coil. This appears to be a quantum-mechanical “action at a distance“, which has given rise to many
confusions and unsound speculations.
This problem is treated in ECE theory as follows. The magnetic field of the coil creates a space-time “vortex” (due to
its torsion) which extends into the space outside of the coil itself. The pulling effect of this vortex (i.e. the effect of
vector-potential A) is then able to influence the electron beams. Thus, the apparent “action at a distance” is reduced
formally to local, causal deterministic effect.
Evans points out that torsion is always accompanied by curvature. Since curvature is manifested as gravitational
mass, it follows that the spin of all elementary particles must contribute a component to their gravitational mass.
From the neutrino one knows this already experimentally, even if the standard model fails here. Also photons must
possess a gravitational mass, which is extremely small, however, and is situated below current detection limits.
6 Implications for technology
Typically, new theories lead to practical applications only after many years. In the case of nuclear fusion, the hope of
producing useful power for society’s use remains unfulfilled even after 50 years. In contrast, the ECE theory
suggests direct applications in diverse fields -- in particular, the urgent question of energy production.
The possibility of a new energy source arises from the reciprocal interaction between gravitation and
electromagnetism. According to current standard theory (Maxwell equations) this interaction is not possible.
However, the ECE theory predicts that a gravitational field is always connected with an electrical field, and vice-versa
; this might be called “electrogravitics”. The effect has been known empirically for decades, of course, but until
now has lacked a quantitative description.
That is now possible with assistance of the ECE theory. This application should interest the aircraft and space
In the area of electrical generators, the unipolar generator awaited an adequate explanation since its invention by
Faraday in 1831. This is now completely explainable . Similarly as with the Aharonov Bohm effect, the torsion of
space-time must be considered. In this case it is created due to the mechanical rotation.
The most interesting technical application involves the extraction of energy directly from space-time. One must
understand this as a resonance effect. First the equations of ECE theory show that matter can “transduce” energy
from the surrounding space-time (one sometimes speaks also of “vacuum”). To accomplish this in practice requires
that one fabricate a suitable configuration of space-time, e.g. a skillful mechanical or electromagnetic arrangement.
The configuration must be so arranged that a resonant excitation of the material takes place. One knows from
forced mechanical oscillations that, with suitable excitation frequency, large amounts of power can be transferred to
or from the oscillating system.
Probably many “overunity” inventions on the alternative power scene function this way. In these cases, the inventors
found the resonance mechanism by accident. Therefore, some experiments are not repeatable, because the
fundamental mechanism and critical system parameters, which led to the desired result, are not actually known.
The ECE theory makes it possible to calculate these parameters exactly. The AIAS group is presently studying the
excitation mechanism, via numerical solution of the ECE equations. Experimentally the focus is on resonance
excitation in electrical circuits. If one can obtain power in this way, mechanically moving parts (as in generators) are
not required; and due to the smallness of the source, each electrical appliance could, in principle, be fitted with its
own power supply. The basic components would be cascadeable up to power station size.
A final application is in medical technology. Nuclear magnetic-resonance (NMR) tomography requires very high
magnetic fields, which forces a correspondingly complex design and construction. Instead one could use the Inverse
Faraday Effect (described above) to generate the required magnetic fields in the patient. This requires only
electromagnetic radiation in the radio-frequency range. Large solenoid coils are then not required, and the
NMR apparatus could be built substantially smaller and cheaper.
7 Implications for cosmology
The ECE theory also has implications for astrophysics and cosmology. Expansion of the universe is conventionally
said to be governed by Hubble’s Law, which predicts that galaxies move away from us all the faster, the further they
are distant from us. This is based on the red shift of starlight from the receding galaxies.
However, astronomers have recently found red-shift fluctuations which cannot be reconciled with Hubble’s Law,
although this is not publicly discussed. The ECE theory can explain these deviations easily. One can translate the
ECE equations into a dielectric model. The reciprocal effect between radiation and gravitation is described therein
by introducing a complex-valued dielectric constant. This leads to predictions of refraction of light and absorption. In
areas of the universe with high mass-density, the dielectric constant is larger than in areas of low mass -density.
The absorption of energy within these areas leads to an increased red shift. Such a model goes far beyond the
In Evans’ theory, the cosmic background radiation accounts for absorbed radiation energy, and is not seen as
evidence for the Big Bang, which does not occur in this model. Instead there are expanding and contracting zones of
the universe adjacent to each other.
The ECE theory describes a unification of the four fundamental forces, and their reciprocal interactions, in a simple
unorthodox way. All physics becomes reduced to geometry. The quantum theory is placed on a causal deterministic
basis, while statistical description of processes on the atomic level is preserved.
The important points of the ECE theory are the following:
1. Space-time is completely specified by curvature and torsion. All physics can be derived, via differential geometry,
from these underlying primordial qualities of spacetime.
2. Curvature is the basis of gravitation, and torsion is the basis of electromagnetism. Also, torsion implies curvature,
3. The ECE theory is mathematically based on differential geometry. It relies exclusively on causal connections and
no stochastic processes.
4. The ECE theory rests on three postulates: the curvature postulate of Einstein and the two torsion postulates of
Evans within the electromagnetic sector.
5. The insights of Einstein are even more penetrating than they were believed to be at first. Specifically, Einstein’s
views that “all physics is geometry” and that “quantum mechanics is incomplete” are correct.
6. The Copenhagen interpretation of quantum mechanics is incorrect; the abstract space of quantum theory is the
tangent space of the general relativity.
7. The coupling of electrodynamics with gravitation leads to a large number of new applications.
8. In cosmology, there is neither a Hubble Law, nor a Big Bang.
These ideas are difficult for established university scientists to digest without fundamentally re-orienting themselves.
The Evans theory will receive strong impetus for further development if it actually succeeds opening new energy
sources. Then these ideas will become generally accepted either with or without the support of universities and
 http://www.aias.us, http://www.atomicprecision.com.
 Myron W. Evans, Generally Covariant Unified Field Theory, Part 1. Abramis, 2005, ISBN 1-84549-054-1.
 L.G. Felker, The Evans Equations of Unified Field Theory, preprint on http://www.aias.us.
 www.aias.us/weblogs/log.html .
http://en.wikipedia.org/wiki/Afshar_experiment, http://www.aias.us/Comments/comments01022005.html .
 P.K. Anastasovski et al., Development Of The Evans Wave Equation In The Weak Field Limit: The Electrogravitic
Equation, preprint 2003 (http://www.aias.us/pub/electrogravitic2.pdf) .
 F. Amador et al., Explanation of the Faraday Disc Generator in the Evans Unified Field Theory, paper 43 of the
unified field series, 2005 (http://www.aias.us/pub/a43rdpaper.pdf).