The Origin of Gravity
The Origin of Gravitation

The acceleration of a free falling particle is caused by the refraction of its
oscillating components by a cloud of exchange particles.
This also explains the weakness of gravity and the attracting-only effect;
and it includes all phenomena of General Relativity

1   Abstract.

It is a well proven fact that the speed of light is reduced in a gravitational field. As a consequence, a light beam which passes a big object is bent towards the object. This bending process is quantitatively explained by the refraction of light at the gravitational potential. - The same happens every light-like particle.

From the spin and from the magnetic moment of an elementary particle it can be concluded, that the constituents of such particle oscillate permanently at the speed of light c. For the electron this was determined by Paul Dirac in 1928. If the effect of refraction is applied to this oscillation within an elementary particle, it yields the correct gravitational acceleration of a free physical object in a gravitational field.

This evaluation does not only yield the gravitational behaviour of an object at rest but also explains the acceleration of fast objects in a gravitational field, which is normally explained by Einstein’s general relativity ("curvature of space-time"). The refraction of light-like objects by the field is an equivalent, but easier, replacement for Einstein’s model of a curved space-time.

And, very surprisingly, you will find that the mass of an object is not the cause of its gravitational field.

This consequence has the potential to eliminate the problems of Dark Matter and Dark Energy, and additionally the very grave problem of Quantum Gravity.

The structure of particles used here is called the Basic Particle Model.
 

2  Bending of a Light Beam Passing a Massive Object

The speed of light is not constant in the vicinity of matter but depends for e.g. the sun on the gravitational potential in the following way:

(2.1)

where c is the speed of light in the gravitation-free space, c_red is the reduced speed of light in the field, G is the gravitational constant; M is the mass of the source, which is traditionally said to cause the gravitational potential; r is the distance to the centre of the gravitational source. The power p is ¹/₂ or 1 depending on the direction of motion in respect to the centre of gravity; that means it is 1 for the radial direction and ¹/₂ for the tangential one.

This equation was experimentally determined the first time by the Shapiro experiment in 1970 for small changes
of c.

(Remark: The equation (2.1) can also be derived using Einstein’s general relativity. We do not use Einstein at this place but use instead the experimental result as such. Later we will derive the equation by physical considerations in contrast to structural ones of Einstein.)

From classical optics it follows that a light beam, which passes an area in which the speed of light depends on the position, is bent towards the area where the speed of light is lower.

Figure 2.1: A light-like object deflected by a massive object
 

The deflection of a light beam passing the sun was correctly given for the first time by Albert Einstein. He predicted the gravitational acceleration of the photon to be twice the value of the Newtonian acceleration (as it was for the first time predicted by von Soldner in 1801). This was historically taken as an important proof of Einstein’s concept of a 4-dimensional curved space-time. We will, however, see that Einstein’s concept is not necessary to achieve this result. A calculation, which is based on the classical assumption of refraction, yields the same result.

2.1 The Amount of Deflection

Here now follows a brief collection of equations, which describe the deflection of the path. A detailed deduction of the refraction process is given in the Appendix A (pdf-version).

The first step necessary is a derivative of c with respect to the direction y - perpendicular to the path of the particle (y being equivalent to d at the vertex). And we define x as the distance of the point of consideration to the vertex of the path.

We can now describe r by the components x and y:

(2.2)

Then taking into account the dependency of the reduction of c from x and y, which follows in a somewhat complex way from equations (2.1) and (2.2), we get

(2.3)

(2.4)

(2.5)

(2.6)

(2.7)

-  G = 6.674 · 10^-11  m³ kg^-1 s^-2
-  M = 1.989 ·10³⁰ kg
-  c = 2.998 · 10⁸ m s^-1
-  d = 6.95 · 10⁸ m

1.75 arc-sec .

2.2       The Acceleration

Next we will need the acceleration of the beam at the vertex of the path. The acceleration a within the beam follows from the deflection angle α in the way:

(2.8)

(2.9)

(2.10)

3   Reference of Gravity to the Basic Particle Model

3.1 The Structure of Elementary Particles

The above chapter was about gravity at fast motion. Next we have to understand the effect of gravity to an object at rest.

To understand further implications of the refraction process for the phenomenon of gravity, we have to investigate the general structure of matter, which means, the structure of elementary particles.

From the dynamic parameters of an elementary particle, its spin and its magnetic moment, and also from its relativistic behaviour it follows that a particle is built by sub-particles, called here 'basic particles', which orbit each other at the speed or light c as shown in figure 3.1.

3.2 Conditions for the Refraction of an Elementary Particle

In textbooks, which deduce gravitational lensing in a classical way, the refraction of light or light-like particles in a situation of varying speed of light is normally explained by a pair of photons or a pair of particles. We have, however, to assume that also a single object is subject to refraction. So, also a basic particle is subject to refraction in the appropriate situation.

This is a necessary assumption at this place to make the following considerations work. It can be logically understood from the view of the particle, if we assume that even a basic particle has an expansion (kind of a charge cloud, which may be arbitrarily small) or it is in a process of permanent oscillation.

3.3 Gravity for an Object at Rest

3.3.1 Gravitational Acceleration in a Special Orientation

If an elementary particle is placed in a gravitational field, its basic particles are subject to refraction as explained above. This refraction causes the basic particles to deviate from their circular path. This will in turn cause a movement of the entire elementary particle.

If we take an elementary particle oriented in such a way that its orbital axis points towards the source of gravity, then the refraction causes the basic particles to spiral towards the source of gravity. So the entire elementary particle will move into the direction of the source. Due to the refraction, the pitch angle of the basic particles, α, will steadily increase. This causes the elementary particle to perform an accelerated motion towards the gravitational source.
 

Figure 3.2: Progressive spiralling downwards
 

3.3.2 Gravitational Acceleration in Arbitrary Orientations

In the general case the orientation of the axis is at an arbitrary angle θ with respect to the vertical direction
(see figure 3.3).

Figure 3.3: General orientation of a particle
 

which is the well known result for the classical case (Newton).
 

4  The Equivalence Principle

4.1 Equivalence Classically

The (weak) equivalence principle treats the fact that every object undergoes the same gravitational acceleration independent of its mass.

In order to explain this fact, Newton has introduced the equivalence principle, saying that there exists an inertial mass and a gravitational mass. Both types of mass are said to be equivalent to a high degree, and as a consequence the gravitational force onto an object is strictly proportional to the inertial force, and so every object undergoes strictly the same acceleration in a certain gravitational field.

Einstein had, when he developed general relativity, adopted this principle and made it to one of the pillars of his theory.

Neither Newton nor Einstein ever made the attempt to explain this phenomenon on a physical basis.

5  The Schwarzschild Solution

The work with Einstein’s field equations is an extremely challenging task. A short time after Einstein published general relativity, Karl Schwarzschild presented a solution for the simplified, less general situation of a spherically symmetric field, like the one of the sun, which is a very frequent case in astronomy. The experiments and observations cited in the literature as proofs for Einstein’s general relativity refer usually to the results of the Schwarzschild solution.

An elementary particle is, according to the Basic Particle Model, built by two sub-particles orbiting each other. Their temporal behaviour is given by special relativity, from which the following equation results for the proper time of an object in motion:

In a gravitational field this time behaviour changes. The understanding of this change directly guides us to the Schwarzschild solution.

We first split the speed into a radial and a tangential component as the Schwarzschild solution is normally presented in polar coordinates:

6   The Cause of Gravity

We have seen that gravity is in fact not a force but a refraction process. And the cause of the refraction is the varying speed of light c in the vicinity of matter.

6.1 Varying Speed of Light

Equation (2.1) is the basis to explain all phenomena of gravity. Now we have to understand this dependency.

The reduction of c can be explained by the exchange particles, which build the binding field of the basic particles.

According to the Basic Particle Model, the binding field is the field of the strong interaction, which is – also according to the model – the universal force in our world affecting all existing particles. These exchange particles, which effect an attraction or a repulsion in a random way, interact as well with every light-like particle. They cause such a particle to be deflected towards the origin of the exchange particle (which is the basic particle) or away from it. So the light-like particle performs a random walk as depicted in figure 6.1. As a result the average speed of the light-like particle is reduced, even though the microscopic speed is still the speed of light c.

Figure 6.1: Disturbed way of a light-like particle
 

This understanding is in contrast to the conventional physics, but it helps to overcome the principle problems of present gravitational physics..   

Remark: There is an apparent conflict here to the fact that the forces within an elementary particle in the binding function have a limited range. This seems not to conform with the unlimited range of the effect of gravity. The solution is that the binding field is set up as a multi-pole field by a composition of monopole charges of the strong force. The exchange particles of those monopole charges, which cause the disturbance of the path of a light-like particle, have an unlimited range as we know it similarly about electric charges.

6.2 Speed Reduction in Detail

The reduction of c is, as mentioned above, caused by the continuous deflection of the light-like particle. This reduction will now be determined.

We have to consider two orthogonal cases, the motion in the tangential direction with respect to the centre of gravity, and in the radial direction. In the tangential direction the reduction is

as this is a crossway disturbance of the path. In the radial direction it is

which is greater than in the former case as it is a longitudinal disturbance of the path.

The effective amount of the influence onto the speed depends on two facts

1. The influence of a single exchange particle
2. The rate of exchange particles.
    

We have used here N to denote the number of elementary particles causing the gravitational field to reflect the fact that this influence is independent of the mass of a particle. And so we have to use a different gravitational constant denoted here as g.

The deduction is given in detail in appendix C of the pdf-version.

1. Dark Matter: It is presently not understood, why a rotating galaxy has a stable configuration. By conventional calculations the mass within the galaxy can only explain ca. 1/6 of the necessary centripetal acceleration. - If we assume, that not the mass of the stars is the cause of the gravitational field but e.g. the number of elementary particles, which build the stars, then we are close to a solution without assuming things like "dark matter" or undetected elementary particles.
2. Dark Energy, which is a phantom as the acceleration .of supernovae is only a seeming evaluation result. The acceleration in fact disappears if it is accepted that the speed of light was greater at former times. This latter assumption by the way solves also other open problems of the cosmology. For details look here
3. Quantum Gravity: According to chapter 6 the phenomenon of gravity is a very weak side effect of the strong interaction. As on the other hand strong interaction is fully covered by quantum mechanics, any discrepancy between QM and gravity is disappears.

Figure 7.1: Equilibrium conflict at the galaxy NGC 3198
(The radius of the galaxy is 10 kpc)

In order to keep both accelerations in a balance, it follows for the orbital speed v that

This is the reason for the curvature of the red dotted line in figure 7.1, and so it provides the contribution to the gravitational field, which is elsewhere assigned to the so called "Dark Matter".
 

8  Conclusion

We have shown that gravity is not the force # 4 but a refraction process effective on all particles. The refraction approach conforms to the results of the Einsteinian way at least up to the Schwarzschild solution, as it is demonstrated here. And it is easy enough to be taught at a college level.

This approach provides answers to several open questions about gravity:
 

1. The weakness of this effect (which is primarily not a force)
2. The attracting-only effect.

The investigation of the cause of the related processes explains

1.The phenomenon called Dark Matter
2.The open conflict with quantum mechanics called Quantum Gravity.

The related understanding of relativity in general solves the apparent problem of Dark Energy in a very easy - and physical - way.

Generally speaking, there is no longer a need for the assumption of a 4-dimensional curved space in order to explain the phenomena named above. In addition we have to accept that the mass of an object is not the cause of the object's gravitational field.

An explanation for the 'Origin of (inertial) Mass' is also available.

NOTE:

The concept of the Basic Model of Matter was presented initially at the Spring Conference of the German Physical Society (Deutsche Physikalische Gesellschaft) on 24 March 2000 in Dresden by Albrecht Giese.

(Secondary title: The Origin of Gravitation)

Appendices