Burkhard Heim on Antigravity
(c) Robert Neil Boyd
[R. N. Boyd]:

1965: Burkhard Heim, as director of the German Research Institute of Field Physics at Goettingen, Germany revealed that, by direct experimentation, he had discovered a positive lead to antigravity. The discovery involved an intermediate field, neither electromagnetic nor gravitational.

The results, Heim stated, if applied to space flight, would be direct levitation, conversion of electricity into kinetic energy without any waste, and "immunizing he occupants and the structures of such vehicles against any effects from acceleration of the vehicle, however great and violent."

Do we know what Heim's "intermediate field" is? Is it related to hyperspace?

[B. Goeksel]:

Heim's intermediate field is called Mesofield.

Here are some excerpts which seem to fit well in the recent discussions on aether theories (compare also with Tucker's gravi- charges and the work of Prof. Kussner. Prof. Tucker will present at the coming Utah BPP conference.)

"Due to the existence of field mass, the gravitational force in Heim's theory is the solution of a so-called "transcendental" equation, i.e. an algebraic equation having no simple solution.

"In addition to the normal gravitational field described by Eq. (2) the field mass give rise to a second gravitational field, whose relation to the first is very similar to the relation between magnetic and electric fields. In the literature the second field sometimes is referred to as the "mesofield". In free space the two fields are orthogonal to each other.

The result of this is a set of equations governing the two dissimilar gravitational fields quite analogous to those describing the electromagnetic fields (Maxwell's equations). The main difference is the appearance of the field mass in the gravitational equations in the place where zero appears in Maxwell's equations. The zero in the latter is due to the non-existence of magnetic monopoles.

This difference renders Heim's gravitational equations less symmetric than the electromagnetic ones. The same lack of symmetry also applies to a unified field theory, combining electromagnetism and gravitation, which cannot be more symmetric than its parts."

[B. Goeksel]:

I am no expert in Heim's theory but suppose that there are more similarities to the work of Prof. Kussner. Heim is also predicting neutral electrons. Neutrinos could be the link between both fields. I don't know what this is:

"Additionally there appear three pairs of neutrinos with small masses and a neutral electron. The inertia of elementary particles consist of 4 zones with differently degrees of steps of condensation, respectively densities. The dense zones (two in mesons and three in baryons) can be interpreted as quarks, since high energetic particles will be scattered by them."

p. 46: "With rotating magnetic fields it seems impossible to generate gravitation fields. But it is hoped, that in a near future someone will find out how to bring FREE IONS INTO ROTATION IN CRYSTALS, which will yield a sufficient strength of magnetic fields. Instead of rotating magnetic coils one could think to use time-dependable curves like linear increasing SHORT-CUT CURRENTS which are used in rail- guns. In a device to generate high magnetic field pulses the rails could form in a SPIRAL IN A FLAT CYLINDER. To get an effective acceleration field it would be required to have a sandwick-pack of several of such plates in which the pulses are generated time- displaced."


There is another, newer Jefimenko book with title "Electromagnetic Retardation and Theory of Relativity: New Chapters in the Classical Theory of Fields" which we should study. It is also quoted in the Russian book mentioning the work of Shipov.

Heim's Mesofield seems to be identical to the cogravitational field described in Prof. Jefimenko's book "Causality, Electromagnetic Induction and Gravitation". It is based on the work of Heaviside.

"The theory starts out from a set of relations very similar to Maxwell's equations, describing the interrelations between electric, magnetic, and gravitational field, including the mesofield. The mesofield only acts on moving masses and bears about the same relation to the gravitational field as the magnetic field does to the electric field."

curl E = -dB/dt
curl g=0

curl g = - b dB/dt
whereby b is a coupling constant
epsilon: vacuum permittivity
alpha: permittivity of space to gravity
as namely suggested by W. K. Allan

curl g = -dK/dt

Heim's mesofield is coupled through b to the magnetic field: dK/dt = -b dB/dt

This is a 4D approximated electrogravitational equation of Prof. Auerbach. The original equations are hyperdimensional. Gravitons are located in 5th and 6th dimension according to Heim. More from the 4D approximation:

"Two coupled equations of the set describe the phenomena of antigravity. In Section 2 the first of these is solved separately because the resulting solution is simple and tractable, allowing modifications to be made with relative ease. The solution of both coupled equations is derived in Section 3. Section 4 contains a brief discussion of the antigravitational field and of the electromagnetic fields accompanying antigravity. In order to keep mathematics in the main text to a minimum full mathematical details are presented in Appendices A and B.

The antigravitational force turns out to be of measurable proportions only if the mass of the entire earth is utilized for repelling the device that generates the antigravity field. For this reason the theory to follow will be applied from the outset to methods of flight propulsion.

2. Dipole Solution of the First Equation

2.1 The Basic Equation

The equation to be solved in this section is

curl g = -b dB/dt (1) where
g = gravitational field
B = magnetic field
b = coupling constant

Reading from right to left, Eq. (1) states that a space- and time-dependent magnetic field B induces a space- and time-dependent gravitational field. As is well known, it also induces an electric field, but the electric field has been omitted from Eq. (1) because it acts on electrical charges only. In the absence of charges it is legitimate to drop the electric field from the equations.

The gravitational field acts on masses such that the product mg represents a real force if m denotes a mass. A force always acts in some direction, implying that g is a directed quantity. The same is true with regard to the magnetic field B.

In Eq. (1) the direction of g is seen to depend on that of B. Since the latter is to be produced artificially, care must be taken to ensure a direction of B inducing a repulsive gravitational field, and not an attractive one. The fact that this is possible demonstrates the great advantage of g over ordinary gravity, whose direction is always attractive and cannot be manipulated in any way whatsoever. Gravitational and antigravitational forces merely differ in the plus- or minus-signs in front of them. For this reason the term "gravitational" in this report will often be used collectively to denote both types of forces.

Of essential importance with regard to the expected strength of antigravity is the magnitude of b in Eq. (1). Its value is given by

b=sqrt (epsiolon0/alpha)=8.625*10^-11 coul/kg .

epsilon0=vacuum permittivity (8.854*10^-12 farad/m) alpha=permittivity of space to gravity (1.19*10^9 s^2kg/m^3)

b is a coupling constant between the magnetic field B and the gravitational field g. Obviously, it is extremely small, so that even a strong B will induce a vanishingly small gravitational field. However, this is no course for concern, because the same occurs in ordinary gravity, where a mass m creates an exceedingly weak gravitational field around itself, to which it is coupled by the small gravitational constant gamma. Gamma is seen to be somewhat smaller than b. Nevertheless, when the weak gravitational field of m interacts with the huge mass of the earth, the result is an attractive force - the weight of m - which is not small by any means. Evidently, the enormous mass of the earth more than compensates for the weak gravitational field of m. By analogy, it may be argued that the weak g-field of Eq. (1), interacting with the earth, should result in a relatively strong antigravitational force, roughly equal in magnitude to that of ordinary gravity. Unfortunately, this hypothesis is not supported by the facts for reasons that will become clear later on.

Equation (1) can be solved after deciding on a magnetic field B suitable for generating antigravity. B is produced by an alternating current, since it has to be time-dependent. The field lines of B are known to be perpendicular to the current, while the field lines of g are perpendicular to those of B. Two possible arrangements meeting all necessary requirements are shown schematically in Fig. 1.

In Fig. 1a a rectangular current loop composed of many wires is connected to an alternating current source. The wires pass through a cylinder made of highly permeable material, such as iron. The current induces a strong magnetic field B, whose field lines encircle the vertical portions of the loops in a plane perpendicular to them. The permeable material serves to increase the field strength of B. A strong B is needed because antigravitational force is directly proportional to it. The curved field lines, belonging to g, in turn are induced by B. The gravitational force acts on any mass in the direction of the arrows tangentially to the field lines.

A second arrangement is shown in Fig. 1b, where many windings surround a toroidal core of highly permeable material. The magnetic field lines are circles inside the torus, while the field lines of g at some distance from the magneti are the same as in Gif. 1a. In the configuration of Fig. 1 a end effects may cause a slightly modification of the gravitational field relative to the field of Fig. 1b. ...

2.3 The Vertical Field Component in Dipole Approximation

An exact solution of Eq. (1) for the gravitational field g induced by the magnetic fields of Figs. 1a or 1b may be derived in the form of an infinite series of terms. If the height of the craft above the earth's surface is large compared to the dimensions of the magnet, which usually is the case, the first two terms of the series express the solution with sufficient accuracy for our purpose. The gravitational field resulting from this approximation is known as a dipole field.

The vertical component of the gravitational field is given by the expression

g_z=- (b mu0 3 cos^2theta - 1)/(16 pi^2 r^3) V (mu/mu0) dI/dt, (3)

where r and theta are the coordinates of the point at which g_z is evaluated, as shown in Fig. 4, V is the volume of the magneti, mu/mu0 is the relative permeability of its iron core, mu0 is the permeability of free space, I is the current producing the magnetic field, and dI/dt is the time derivative of I. Note the 1/r^3- dependence of g_z. Ordinary gravity depends on 1/r^2, i. e., it diminishes more slowly and remains stronger throughout the earth's volume . This leads us to suspect that antigravity may be a weaker force than normal gravity.

2.4 The Gravitational Force

The last step in the calculation consists in evaluating the actual force acting on the magnet. To this end g_z of Eq. (3) is multiplied by the average density of the earth, rho_m (5500 kg/m^3, is here the error?) and integrated over the earth's volume (an integration is a mathematical summation over many small elements). The force F resulting from this is

F=-3.16 * 10^-14 (R^3/(R+h)^3) V (mu/mu0) dI/dt, (4)

where R is the earth's radius (R=6.378*10^6 m), and h is the height of the magnet above the earth's surface.

The main result of integration is the quotient R^3/(R+h)^3 in Eq. (4). Its magnitude is nearly equal to unity, because in general h is much smaller than R. When calculating the normal weight of an object a similar force appears in the result, but there the denominator equals (R+h)^2 instead of (R+h)^3. Thus, if R is measured in meters, the quotient in Eq. (4) is about 6 million times small than the corresponding factor in ordinary gravity. Equation (4) confirms our suspicion that artificial gravity is a much weaker force than gravity. Clearly, a fairly strong antigravitational force F can be attained only if the remaining quantities in Eq. (4) are made as large as reasonably possible.

2.5 Elimination of the Time Dependence

There now arises a new problem. The current I must be alternating. The simplest alternating current is sinusoidal and corresponds to the expression,

I = I_0 sin(wt)
w = 2 pi f .

Here I_0 is the maximum current, t is the time, w (omega) is the angular frequency, and f is the frequency of oscillations. As a example, if f=100 Hz then w=200 pi = 628 radians/second. According to Eq. (4) the force F is proportional to dI/dt which, with I given by Eq. (5), is

dI/dt=I_0 w cos(wt) . (6)

When this is substituted into Eq. (4) the extra w in Eq. (6) increases F substantially. One certainly should be careful not to lose w again in subsequent mathematical operations. In our example f is equal to 100 Hz, but frequencies in the megahertz (MHz) range can easily be attained (ignoring self-inductance). This will result in very large values for w, leading to an enormous increase in the antigravitational force F.

Unfortunately, this increase is only an illusion, because cos(wt) in Eq. (6) alternates between positive and negative values as time progresses, and so does F. If a negative value refers to antigravity, then a positive F result, F constantly alternates between an attractive and a repulsive force, whose average value is exactly zero. No sustained flight is possible under those circumstances.


Only one solution to the problem has come to mind so far, but hopefully there are others, and perhaps more elegant ones. The solution is to let the magneti rotate about a horizontal axis, together with its gravitational field, as shown in Fig. 5 for the cylinder of Fig. 1a. The rotational frequency must be the same as the current frequency, with the magnet rotating as coswt, i.e. 90° ahead of the sine-current.


Instead of using just a single magnet one uses two of them, rotating about the same axis but in opposite directions, as shown in Fig. 6. This immediately eliminates the gyroscope effect. Both magnets rotate with equal angular frequency w, which must be the same as the current frequency. The second magnet is required to have a definite phase relation with respect to the first: Its axis must be horizontal when the axis of the first magnet is vertical and vertical when the first magnet is horizontal.

Furthermore, a cosine current has to flow through the second magnet. As a result of counterrotation, a wcos^2wt-term is introduced into the field of the first magnet as before, and an wsin^2qt-term appears in the field of the second. When the two fields are added together the resulting force is proportional to

F=w(sin^2wt+cos^2wt) = w,

because the sum of the squares is always equal to unity. The total antigravitational force now becomes,

F=-3.16*10^-14 (R^3/(R+h)^3) V (mu/mu0) i_0 w . (9)

This equation represents the ideal situation, for now F is antigravitational due to the minus-sign in front and entirely independent of time. Being constant, F is ideally suited for counteracting the constant weight of the craft. V in this and all subsequent formulas is the volume only one of the two counteracting magnets.



V=1 m^3

I_0=600.000 A

I_0 is calculated on the basis of 60A per wire of 1 square millimeter cross-sectional area and 10.000 windings. Due to saturation effects in the permeable material the high value of mu/mu0 is not really compatible with the large number of ampere turns, I_0. However, when dealing with the futuristic topic of antigravity one may, perhaps, be allowed to use values representing an extrapolation into the future.

--> F = -2.13 * 10^5 g(k,h) (13)

For g(k,h) it is best to choose the first maximum reached at a frequency of 13.03 Hz. This frequency of rotation is attainable even by large magnets. The maximum of the g-function at h=100 m and k=2.73*10^-7 m^-1, corresponding to a frequency of 13.03 Hz.

1st maximum: g(k,h)=8.193 *10^-7 m^-1. When this figure is substituted into Eq. (13) the final result is,

F=0.175 Newton=17.5 gram-weight


The optimum is reached at f=2.25 Mhz, leading to an optimum antigravitational force of 0.267 Newton or 26.7 grams.


5. Conclusion

The theory outlined in the present study has demonstrated the feasibility of generating antigravity by means of time-dependent magnetic fields, albeit of very modest strength. Basically, this was to be expected, since otherwise the effect would have been detected long ago.

The smallness of induced antigravitation may be disappointing, but it is due in a large measure to purely technological inadequacies, which some day may be overcome. New concepts could be instrumental in bringing sufficiently strong antigravitation within reach of a future technology. Electronic generation of standing antigravitational waves and the elimination of all iron cores certainly would be steps in that direction.

Just again read the book "Behind the Flying Saucer" by Frank Scully. It was published in the year 1950. They are talking about magnetic force line crossing etc.