ARCUS:  The World Formula and its Solutions

Consequently constructed using the results of Albert Einstein and Max Planck leading to the Unified Field Theory

The Preaching
The force worked out on 07-05-2000, Protocosm force problem solved on 02-09-2001

A real particle is a spatial wave falling down by itself and standing up to the amplitude. It is oscillating. While this, the radius R is moved between next to zero and to the amplitude Ro. I call this particle a primary quantum. There would be pure gravitational quanta and pure electric quanta. Then we would explain gravitational particles and electric charges. But charges really are coupled at gravitational particles this way we find both kinds of particle quanta in one system of symbiosis of nature. Now I had the idea after all that the phenomenon of spatial vibrating was the fundament of the exchange of momenta. During this, the primary wave quanta would be exchanged between real particles and charges. Wave quanta themselves aren't particles. Therefore I don't speak of "virtual particles" like present physics does. Particles as real quanta and primary oscillators are always just transmitters and receivers of spatial wave quanta forming gravitation and electrostatics! I presented the following theses:

  1. If you enlarge the elongation R up to the amplitude Ro virtually over Ro, then you get the particle as transmitter of a spherical wave or a so-described spatial wave.
  2. The larger now the extension radius ri of the spatial wave is, the smaller is the momentum mass mi acting there, which was exactly measured with rest mass mo or rest charge eo at the amplitude Ro.
  3. When two elementary masses exchange their momenta, the force between both is arising while both distances ri are multiplied now to ri.
  4. Each force between compact masses and charges is combined of all elementary vectors of the exchange between the elementary oscillators.
  5. For this behavior the rest mass mo and the rest charge eo are valid as primary wave quantum of the momentum exchange between oscillators.
  6. But also secondary wave quanta of magnet fields, mw and ew, are acting this way, but not totally spherical.

So I consequently followed: The center of gravity of a compact mass is just a virtual center, because it represents the resulting force FR of all the interaction forces Fi over their interaction radii ri between microcosmic oscillators.

The gravitation force Fg = FR of this compact mass is vectorially added from single forces Fi at each particle interaction.

This way interacting momentum masses are streaming from all directions of the universe to all the given masses. The general inertia is shown now as if a medium would "stream" to the earth but in the same amount off of the earth, too. In every inertia equilibrium the momentum masses should be the same into all directions.

Then I made the equations:

Jo = 1h = mo c Ro


as conservation of angular momentum Jo follows:

Jo = 1h = mi c ri


from which follows:

mi = mo Ro / ri (hyperbolic)



xo = mi ri = mo Ro torque xo in conservation



mi / Ro = mo / ri

or the terms of momenta:

pi = po Ro / ri = mi c = mo c Ro / ri


At the position of interaction with the other quantum (mass or elementary charge) only the momentum mass mi is effectively working which was at the amplitude after equ. (7):

Fg = G mo mo / ri


Fg = G mi mi / Ro


Fg = Fa = mo a


Fo = Mo ao with ao = - G Mo / Ro


Fo = - G Mo Mo / Ro


Mo is the internal mass of a quantum at the surface Ro. Both are acting after the coupling constant a3. Additionally my theory found the relations:

Fo = - c4 / G


Mo = h c / G mo


Fo = - h c / G mo Ro


Fo = - h c / G mo Ro mi ri


xo = mo Ro

xo = mi ri

Analysis: G = - c4 / Fo

Fg = mo mo c4 / ri Fo ~ F / Fo


Therefore mc/r multiplied with mc/r is already F or

F1 F2 / Fo


Fg =


moc / Fo




Fg =


E2 / Fo

E = FA ri



Fg =


FA2 / Fo

standard equ. of forces


Each mass has its own force FAn, which has the relationship with elementary force!

With equ. (5) we get:

Fg = mi1 c mi2 c / Fo Ro

Eo = Fo Ro


Mo = Eo /c

Fg = mi1 c mi2 c / Mo Ro

pi = mi c


Fg = pi1 pi2 / Mo Ro with the torque

Do = Mo Ro


The gravitation force Fg after Newton is the result of two momenta pi at the radius ri acting with the momentum mass mi, referred to the constants of the quantum, the particle or the elementary charge as oscillator like Fo, Ro or Mo.


But it obviously has no importance for calculations of forces. It only shows like force is made.

What is valid for gravitation force must be valid for electric charge following my theory, because the elementary charge represents an elementary quantum spatially vibrating in the same way like a particle mass and transmitting a spherical wave into the exchange space. I calculate:

mo = eo kq


Fg = ei1 c ei2 c kq / Moq Roq


pi = ei c kq


Just here the local momenta are exchanged.

How are the relations at secondary wave quanta?

If a mass or a charge would rotate elementary, then they would form secondary momenta with the secondary velocity v and the secondary rotation radius Rrot. We get the secondary quanta, which exchange their momentum masses into the space, too, but now not as spherical wave but as a spatial wave of two directions (two maxima) of the acting dipole what is a magnet field. We get the first twist of geodetic lines of the primary wave quanta by this first kind of rotation. If the plane of rotation is rotating once more around itself, then the dipole directions change at the receiver. We get a frequency of the secondary exchange wave. This second twist leads to the x-frequent exchange wave. Also here the conservation of angular momentum is valid:

J(n) = nh = mw(n) c Rw(n) = mo v Rw(n) / g = gmo v Rrot(n)


mw(n) = f (n), f(R w(n)), f(mo), f(v), f(g)

g = (1 v / c)1/2

(Gamma factor of special relativity theory)

mA = mo / g

indicated mass, retardation mass, observer indicated the impacting mass

mB = g mo with pB(n) = mB(n) v = mb(n) c

Mass in movement, observer is flying along the moving mass

mw(n) = mo v / c g


The local secondary wave momentum exchange is then:

J(n) = nh = mi(n) c ri(n)


pi(n) = pw(n) Rw(n) / ri(n)


pw(n) = mw(n) c


pi(n) = mi(n) c


Analogously (3) is valid:

mi(n) = mw(n) Rw(n) / ri(n)


and the secondary dipole forces are analogously (6) and (7):

Fgw = G mw(n) mw(n) / ri(n)


Fgw = G mi(n) mi(n) / Rw(n)


Now one can form the forces (w8) and (w9) over the wave mass mb(n), too. Then we get the analogon on the action of rest masses and/or rest charges. Therefore I didn't derive them completely:

FgB = G mb(n) mb(n) / ri(n)


FgB = G mi(n) mi(n) / Rrot(n)


Here it's possible now to underrun the wave amplitude Rw(n) with the distance ri(n) going to the center of the rotating mass (or to the rotating charge).

The force Fgw would go to infinite singularly if the distance would reach zero.

But what is a distance here? If there is something, the distance never can reach zero! But what is there? The answer our theory gives to us: if there is no stable quantum like a particle acting with its amplitude, so there must be a protocosm - the early stage of a quantum in unstable or better in divergently open form. Because in this feature of protocosms is no mass which would have made it for divergent contracting but only field energy, we call it field protocosm. It realizes a divergent field force Fo(PK) next to Fo and also an intrinsic internal amplitude of Ro(PK).

This way a rotating field, the so-called magnetic field is a complete analogon to the primary field of masses and charges, no matter if it's caused gravitationally or electrically. You see that the attraction between magnets aims to the center laying inside of the causing orbit, no matter how and on what orbit they are ever made during the rotation of masses or charges. While this, the force and the spacetime curvatures increase to finite maxima. These protocosms are strongly larger at superconductors.

Now an equation should be found which describes the central protocosm.. At first I take the well-known equation of the gravitational horizon ro:

ro = 2 G Mo / c


The external radius of the protocosm ro is dependent on the internal mass Mo.

Now we could substitute the momentum mass mi(n) in the distance ri(n) of the center of rotation from equ. (w7) instead of the internal mass Mo, just as it would make the protocosm (PK) from wave functions:

ro(PK) = 2 G mw(n) R w(n) / ri(n) c


Here we see: If the velocity is increasing the relativistic momentum mass mw(n) is also increasing, while the wave amplitude Rw(n) is decreasing. Therefore the horizon ro(PK) is only still dependent on the distance ri(n). When the distance decreases, a value can be reached which is finally the same as the horizon. This statement doesn't help us going on.

Now we substitute the internal mass Mo directly by the wave masse mw(n), this equation follows:

ro(PK) = 2 G mw(n) / c = 2 G mo v / g c


Here the horizon ro(PK) is a function of the decelerated mass mo, of the velocity v and of the gamma factor g of the special relativity theory.

You see: the horizon grows along the increasing mass, but essentially it grows along the velocity which is changed or totally stopped by movement of this mass. The g.m. protocosm is then dependent on the special-relativistic conditions of the velocity changes (the same is valid for electric charges and their e.m. protocosms)!

This kind of protocosms can only be build if an INTERACTION was just running.

If there aren't an interaction then the mass mo rotates as movement mass mB(n) on its orbit (see equ.(w1)).

We can make the movement momentum mass mb(n) from it:

mb(n) = mo v g /c


Now we set it into the horizon and get this:

ro(PK) = 2 G mb(n) / c = 2 G mo v g / c


Just now the gamma factor acts as soon as relativistic velocities appear working against the increase of the horizon with given mass and increasing velocity. From this I see the parallel to the general relativity theory. Here the adjustment of a gravitational horizon is only dependent on the intensity of the resting mass (see equ. (w10)).

So we conclude:

  1. The protocosm from wave masses mw(n) is made from interactions especially from relativistic velocity changes.
  2. This protocosm of the moved masses mb(n) is made from the intensity of the masses or/and of the charges which are non-relativistically moved.

For superconductors is then valid:

  1. for b): If there a current is flowing, it makes a non-relativistic protocosm from intensity. Since present currents are too low, the shielding effect of that protocosm is also too low.
  2. for a): If the superconductor additionally rotates, you can support a relativistic interaction by strong deceleration which forms a bigger protocosm having a stronger shielding similar with Podletnikov's effect with about 2%.

Who will come along? Who wants to build a stronger superconductor with more initial intensity? Who wants to increase the rotation velocity and its retardation relativistically?

Who makes this, who will produce a protocosm of real effectiveness.


But if we found a description of the central protocosm, then we had the proof for strong space curvatures in each force centers. The more we could amplify them, the more curvatures we would get into larger areas of our space. This would allow us to change physical magnitudes after Einstein's relativity. I saw here the action of the superconductivity which doesn't only "shield" the gravitation how Podletnikov and different scientists suspected, but which curves the spacetime effectively. Just now, exactly between two points the synthetic space curvature is acting, no matter what distance they ever have (influence of the other forces and curvatures neglected first). It shifts the action of gravitation, of electromagnetism, and it shifts the time. At 2%, a clock already should be slow by 29 minutes per day next to the superconductor.

From my acknowledge I see my copyright to be the originator and the discoverer of the protocosms, even of the synthetic protocosms, which qualities we can examine and use later. How these properties look like I will tell you another time another place.

All rights reserved: Arcus (Heinz-Joachim Ackermann, since1998)