Horst Eckardt

Alpha Institute for Advanced Study (

explainable through standard physics. In this paper we show how Einstein-Cartan-Evans theory is able to

explain the mechanism. Resonances of ambient spacetime are created to transfer energy from spacetime itself

to the devices, so that energy is con-served. The concept is applied to two main types of devices: electrical

solid state devices and magnetic self-rotating motors. The description is kept on a level requiring only

knowledge in vector analysis and basic differential equations.

provide energy only for a limited number of years. The environmental problems caused by these energy

sources are enormous, in particular global climate warming is already an observable fact today. Therefore,

governments and environmental research groups are looking for replacements for such fuels. A wide range is

considered, from biologically generated fuel to solar and wind energy. It is a common feature of all these

replacement substances and methods that energy in the form of heat or electric power cannot be obtained in

sufficient quantities out of them. For example, one would have to cover huge land areas with solar cells or wind

turbines, which is not possible in industrialized countries. A basic solution of this problem has to be found but it

is still not in sight from the official research in energy techniques.

In order to face the energy crisis all possibilities for finding new energy sources have to be evaluated, even if

the success is not directly obvious from the very start. This is done, for example, with nuclear fusion reactors,

but many other areas are not being researched seriously. Among the latter is the so-called vacuum energy, and

a number of inventions which are considered as non-existent or fakes in the eyes of the official science

community. This is in misjudgement of the fact that the physical vacuum is known to be far from empty and to

have a high energy density. This possible energy source is presently ignored by the scientific establishment

because the physical basic principles for this are not sufficiently understood.

Meanwhile, however, a growing number of inventions has emerged whose mechanisms are not explainable by

standard physics. Some of them are being developed to production quality so that such alternative energy

devices will be commercially available in the near future. The question arises regarding why these devices are

able to create usable energy, apparently “from nothing”. Since conventional science cannot give an explanation

for these devices, inventors have to rely on suppositions which are, in the best case, physics-based ad-hoc

assumptions, or in other cases some kind of philosophical principles which lie outside scientific methods.

The dilemma is being resolved by the Einstein-Cartan-Evans (ECE) theory. This is the only known scientific

theory which is able to give an explanation of these devices on the basis of physics, by means of a sound

mathematical method. ECE theory is an extension of Albert Einstein´s general relativity, through the ideas of the

French mathematician Élie Cartan, developed around 1922. Myron W. Evans brought this into a final form in

2003. The unified theory results to be a new basis of all areas of physics. Existing fields such as quantum

physics and Newtonian mechanics emerge as special limits of the new theory. In addition, new mechanisms

evolve being hitherto unknown, in particular mechanisms for extracting energy from spacetime. The spacetime

takes over the role which in the past was ascribed to the vacuum.

According to ECE theory, energy can be extracted from spacetime without sacrificing energy conservation. The

mechanism is based on a resonant coupling of the device with the spacetime itself. This effect is described in

this paper where it is applied to two types of devices: electrical solid state structures and magnetic motors.

Details are found in the scientific papers [1] - [6]. In this article we try to spot the essential points and present

them on a level which is understandable for engineers.

input power can be enhanced up to a factor of 100,000. This effect, of energy extracted from spacetime, does

only appear in configurations where a certain resonance condition has been met. So for an understanding of

the process it is necessary to find possible resonances in the underlying physics. The structure of solids is

mainly determined by the Coulomb law, which describes the interaction between atomic nuclei and electrons, as

well as the electrons among each other. The electric field E of a charge density

law:

(1)

where the field

(2) .

These are elementary equations of classical electrodynamics of Maxwell and Heaviside and there is no

resonance, as is well known.

Now ECE theory comes into play. According to ECE, gravitation is curvature of spacetime and electromagnetism

is spinning spacetime. The curvature is described as introduced by Einstein in his theory of general relativity in

1915. This means that space is curved in presence of masses (or more precisely: energy distributions).

Consequently, Eucledian geometry cannot be used to describe a curved spacetime, Riemannian geometry has

to be used. Consideration of curvature requires a modification of differential calculus in Riemannian space: An

additional term called Christoffel symbol, or Christoffel connection, is required and added to the partial

derivatives which occur, for example, in Eqs. (1) and (2).

Electromagnetism is described by Cartan torsion as suggested by Cartan in 1922. This requires an additional

change in differential calculus. Instead of the Christoffel connection, the so-called spin connection is to be used

in order to describe spinning of spacetime adequately. This makes the equations which represent the laws of

nature “generally covariant”, i.e. they keep their form in any coordinate system, in a curving and spinning

spacetime. This is not the case for classical electrodynamics.

The formalism can be simplified [3] to a vector of spin connection ω which can be imagined to be an axis of

rotation in some simple cases. Since electromagnetism is spinning spacetime, we can apply now the Cartan

torsion to Eqs. (1) and (2). The first equation remains as is while in the second the spin connection term is to be

added to the partial derivatives (gradient operator):

(3) ,

(4) . .

Inserting (4) into (3) gives

(5)

where

which is obtained in the limit

(6) .

In Eq. (5) we have arrived at a differential equation of the Bernoulli type, which is in one dimension:

(7) ..

This is a well known equation of a forced oscillation with resonance frequency ω0 and damping factor α. And

f(x) is the “driving force”. The difference with Eq. (5) is that here the coefficients are constant.

Eq. (5) can be rewritten in spherical polar coordinates. We assume ω and Φ to be spherically symmetric, i.e. we

consider only the radial coordinate

(ω→0) one obtains that the radial component of ω has the form

(8)

and (5) can be rewritten as

(9) .

Assuming an oscillatory form of the charge density

(10)

with a spatial frequency (wavenumber)

oscillator. Lastly, the non-constant coefficients are responsible for this behaviour. In Fig. 1 the resonance

curves are shown. The red curve describes an ordinary resonance according to Eq. (7) while the green curve

shows the resonance behaviour of Eq. (9) describing the resonant Coulomb law. It can be seen that more than

one resonance frequency occurs and the resonances are relatively sharp. These peaks are due to spin

connection resonance which is not present in Maxwell-Heaviside theory.

In order to obtain energy from spacetime, the Coulomb potential of atoms, molecules or solids has to be brought

to spin connection resonance. What happens to the electronic states of an atom is shown in Fig. 2. The energy

eigenvalues of atomic Hydrogen have been calculated in presence of a small oscillatory charge density serving

as a driving force. The resulting ECE Coulomb potential has been added to the proton core potential of the H

atom. It can be seen that all energy eigenvalues are shifted upwards at the main resonance. This means that

the valence electron is pushed out of the atom, becoming a free electron. In a solid this means that the electron

is lifted to the conduction band by resonance and becomes part of a current source which can do external work.

As we have seen spin connection resonance is obtained by applying a periodic charge density oscillation. The

wavelength has to be comparable to the atomic distances. Such charge density oscillations can, for example, be

evoked by spin waves in ferromagnetic materials. A detailed treatment of these effects requires application of

developed methods for solid state physics, for example Density Functional Theory.

At the end of this section let us recall the excitation mechanism for Coulomb resonance (Fig. 3). The oscillating

part in the mechanical driven oscillation is a mass, in ECE Coulomb law it is the electrical potential. The

restoring force of the spring corresponds to the spin connection, and the oscillating driving force is provided by

the charge density. In mechanics, a driven oscillation is an open system, the energy is transferred to the mass

by the driving force. In the ECE Coulomb case the charge density remains unchanged while energy is

transferred to the system (potential is increased). So this is also an open system as far as spacetime is not

considered. Ignoring this fact leads to the erroneous assumption of a system driven through perpetual motion.

But in the same way as a mechanical resonating mass is by no way a

system under consideration. Energy is transferred from spacetime serving as an external reservoir in the same

way as a mechanical driving force delivers the energy. So energy is perfectly conserved.

reproducible way ([11], see also Fig. 4, [11]). The functioning of these devices cannot be explained by Maxwell-

Heaviside electrodynamics. Again we give an explanation through ECE theory.

As was described in the preceding section, the Cartan torsion of spacetime introduces the spin connection as

an additional quantity occurring in the laws of nature so that they take a generally covariant form. In particular

this holds for the magnetic field. In Maxwell-Heaviside theory the magnetic field B is connected with its

generating vector potential A by the relation

(11) .

In ECE theory this law has to be replaced in the simplest case by

(12)

where ω is the spin connection vector again. In the following we discern between the magnetic field of the

assembly and the magnetic field of the surrounding spacetime itself, denoted by BS. The torque

magnetic dipole moment

(13) .

Under normal conditions there is no resulting torque because of BS = 0. Spacetime is force-free and does not

bear a magnetic field. So there is no rotation of stationary magnets. The situation becomes different if it were

possible to create a magnetic field from spacetime. In order to understand how this can be achieved we have

first to look closer on the fields of the surrounding spacetime. In case of BS = 0 it follows from Eq.(12) that

(14)

where

gaugable quantity but is uniquely defined and has a physical meaning. In case of

(15)

with a wave number

describes a flow with longitudinal vortices (Fig. 5) where streamlines have a helical form. The nearer a

streamline is to the central axis, the more stretched is it and the faster is the flow velocity. In contrast to flows

which are described by the Navier Stokes equa-tion (as for air plane wings) there is no force acting on the

elementary flow volumes. In the case of ECE potential this means that there is no force field present, in

accordance with our prior assumption.

Taking the curl at both sides of Eq.(15) gives

(16) .

Applying the vector identity

(17)

at the left hand side of Eq(16) and assuming that

(18) .

This is a Helmholtz equation for the spacetime surrounding the magnetic assembly. Because of the assumption

of BS = 0 there is no torque on the magnets, they remain at rest. Torque can be created by disturbing the

Beltrami flow. For the Helmholtz equation (18) this means that the balance to zero is no more fulfilled. Assuming

a periodic imbalance leads to

(19)

with a vector

vector and can be interpreted as the frequency of a driving force which the right hand side of the equation

constitutes. If restricted to one coordinate (x) the equation reads

(20) .

In comparison with Eq. (7) it can be seen that this is a differential equation for a resonance without damping

(α = 0). The resonant oscillation occurs in case

condition, A creates a force field according to Eq.(12), which via Eq.(13) creates a torque being big enough to

spin the magnetic assembly and to maintain the rotation. This is the mechanism how spacetime is able to do

work via a resonance mechanism.

In Fig. 6 this is depicted schematically. Fig. 6a shows a stator with Beltrami (force-free) flow of the spacetime

vector potential. The additional rotor magnets in Fig. 6b create vortices of spacetime which are enhanced by

spacetime resonance and evoke a force field according to Eq.(12).

In total we have shown qualitatively how energy can be obtained from spacetime via magnetic assemblies. This

could be the basis for development of an engineering for such devices.

[2] M. W. Evans, “Generally Covariant Unified Field Theory” (Abramis 2005), vol. 1-4 .

[3] M. W. Evans and H. Eckardt, “Space-Time resonances in the Coulomb Law”, paper 61 of the ECE

series on

[4] M. W. Evans and H. Eckardt, “The resonant Coulomb Law of Einstein-Cartan-Evans Field Theory”,

paper 63 of the ECE series on

[5] M. W. Evans, “Spin Connection Resonance (SCR) in magneto-statics”, paper 65 of the ECE series on

[6] M. W. Evans and H. Eckardt, “Spin connection resonance in magnetic motors”, pa-per 74 of the ECE

series on

[7] D. Reed, “Beltrami vector fields in electrodynamics – a reason for reexamining the structural foundations

of classical field physics?”, Modern Nonlinear Optics, Part 3, Second Edition, Advances in Chemical Physics,

Volume 119, edited by Myron W. Evans, John Wiley and Sons, 2001 .

[8] http://www.et3m.net/ .

[9] G. Kasyanov, “Phenomenon of electrical current rotation in nonlinear electric systems, Violation of the

law of charge conservation in the system”, New Energy Tech-nologies, 2(21), pp. 28-30, 2005 .

[10] Johnson permanent magnet motor, US Patent 4151431, 1979 .

[11] http://www.gammamanager.com/ .