A Mechanism for Gravity

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w.i.p 2007.12.10

A MECHANISM FOR GRAVITY

"The nature of nature is natural"

j.s.brandsma

[snr@casema.nl]

Gravity

There is no generally accepted mechanism for gravity, a major shortcoming and one that makes it impossible to really understand "what is going on". This is an attempt to find a mechanism that will provide insight and explain, in the true sense of the word, the various phenomena.

The aim is finding, or devising, a model that can serve as a useful foundation for understanding physics. Studying the inverse square formula, for clues that indicate a possible foundation, resulted in an interesting model. The derivation of the formula for the force of gravity is easy, and it indicates a tangible field with acceptable natural properties.

[01] A Mechanism.

[01-01] The formula for the force of gravity, can be written as:

[01-02]This suggests:

The force F changes proportional to the spherical area A.

Newton about gravity: "It is nonsense to think that one body can affect an other body at distance, that is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.

Einstein: "Space is not a featureless 'ether', but an environment with local properties depending on the distribution of mass". (AE in his 1920 Leyden address.)

[Hence: space is an environment with local properties that bridge that distance!]

An agent is needed to 'carry' the local properties and to bridge distances. This 'carrier' N (with N from eNtities) must, of necessity, be very small and have at least, while maintaining the property "mass", the penetrating power* of a neutrino and still carry the basic, the fundamental, gravitational force.

Lorentz: Indeed one of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms, or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest. (Lorentz, 1906)

With such 'carriers', spread uniformly through space, we conclude that the scalar sum of the forces, of a spherical area, on the centre N is a constant. The vector sum, the resultant, on that N is, of course, zero.

This scalar sum P, of the forces delta-P on the centre N, of a spherical shell with n² N's per square meter, is then:
[01-03]

[01-04]Or for the force delta-F at R:

With two bodies we have: every N in one body attracts every N in the other and vice versa. Mass is the product of the number of N's ( k per kg ) in that body and the mass of one N. The force F between two masses M and m is therefore:
[01-05]

[01-06]Gathering all constants in G:

[01-07]Results in:

For equilibrium there must be two (opposing) types of these particles, suitably arranged. An environment filled with such opposing particles produces Newton's well-known empirical formula for the force of gravity. This is no surprise and would normally be of little value, it gives however, better insight and understanding:

The rotating bucket rotates indeed in relation to space itself.

The abandoning of the instantaneous change of the field-strength.

The problem of 'action at distance' is reduced to sub-atomic level (*).

The difference between space, and the void, the absolute emptiness.

The quantification of gravity.

The velocity correction formula (the FitzGerald/Lorentz formula).

The correct calculation of the perihelion advance of Mercury.

The local properties of space 'curved' by the presence of matter.

The possibility to demonstrate gravity aberration.

(*) Stable equilibrium requires two types of opposing N's. To avoid the obvious problem of bridging distances again, these particles must have some electromagnetic properties to pass energy at the prevailing distances.

Space, an environment, 'curved' and with local properties that depend on the distribution of mass and consequently the void as the absolute emptiness. It may (or may not) be the correct model, but it does show that a model can provide improved insight and thereby transfer existing 'recipes' into something understandable and replace the current 'gespenster' or phantom field for gravity with a tangible field, the Newton Field (NF).

********

THE FITZGERALD/LORENTZ FACTOR

[02] Moving mass, and gravity.

Part [01] does not show Newton's shortcomings, but it indicates that it may have something to do with motion. Moving bodies alter the local strength of gravity. A moving body signals ahead to increase (the strength of its spheres) and to decrease again in the other direction. These adjustments cannot be instantaneous, they must take some time; it seems reasonable to take the velocity of light (c), for this signalling velocity.

Consider a body m changing its velocity (from rest) to v. Signalling this change, in time t, for an N at distance R, gives R = c . t, in the same time m moves a distance v . t.
The reaction-distance R reduces, in the forward direction to R(c-v)/c, and increases, in the opposite direction, to R(c+v)/c. A factor (c-v)/c reduces all distances forward, and (c+v)/c increases all distances in the opposite direction.

That body is no longer in the centre* of its gravity spheres, the forces on it are no longer in equilibrium. Part of the accelerating force is used for this and a modification of Newton's second law is necessary.

(*) This makes it possible to demonstrate gravity aberration with 'plumb' lines. The 'plumb' lines will follow a particular pattern, moving in 24 hour cycles.

The algebra:

This movement of m, within its spheres of gravity, gives R' = R ( 1 - v/c ), and with v / c equal to u, gives a distance s measured from the centre:
[02-01]

The resultant on m is no longer zero. The strength a' at s is the ratio s / R times the strength a at R:
[02-02]

Part of the force F is used to overcome the resulting opposing force. With the ratio, s / R equal to u we have:
[02-03]

[02-04]And from this the forces:

[02-05]Giving an (algebraic!) correction of:

[02-06]And a corrected velocity:

Multiplication of the accelerating force, by a correcting factor (1 -v²/c²), is required.

This factor is, for the resulting velocity, equal to the factor of Fitzgerald/Lorentz and the SRT. It is, however, quite different in application. It will e.g. produce a transverse component when the field, in the direction of movement, is not symmetrical, so 'instantaneously' causing the various orbits.

The temporarily retained energy of motion, due to m.a.u,² is known as inertia.

It -this velocity correction factor- can only be used, but without further limitations, to adjust the changes in velocity. It does not require -or provide proof for- the special effects of the SRT on mass, time or length.

The correction ought to be applied to acceleration (and deceleration) in general, but it only produces an observable difference with higher velocities as, for instance, in Mercury's orbit.

********

THE PERIHELION ADVANCE OF MERCURY

[03] Mercury's Advance.

The orbit of Mercury is an ellipse with eccentricity e = 0.2056. Though this means a secondary main axis only 2 % less ( b = .98 a), this 'new' correction-factor is, in contrast to the SRT factor, applicable to the changes in the velocities of Mercury.

There is a decrease in velocity in the accelerating part of the orbit, and the satellite 'falls' to a lower orbit. This 'falling' to a lower orbit increases the velocity again. In the decelerating part of the orbit the satellite 'climbs' to a higher orbit, reclaiming the 'lost' energy. The increase/decrease in velocity brings the satellite to the same elliptical orbit but with the axes rotated through a small angle.

The algebra:

[03-01]The correction to the orbital velocity ( v / c = u ) is:

[03-02]This can, ( v << c ), be written, with acceptable accuracy, as:

[03-03]Giving an acceleration of:

[03-04]And a small change of a:

The factor u² is a variable and changes with the radius. The expression for the velocity, (with a" the semi-major axis),is:
[03-05]

The factor, GM/a", in the expression for the velocity is a constant and does not effect the variation in the acceleration. The expression for the radius is:
[03-06]

The average value for the cosine factor, over one complete orbit, is zero, making the average velocity, (with h = GM / c²) :
[03-07]

The angle -the ratio change in acceleration to acceleration- indicates the change in direction for the tangent, the radius of curvature (right angle to the tangent), and so for the orbit. The angle, delta-ľ, is cumulative, making ľ for the complete orbit:
[03-08]

With the available data:

ľ = 6 x 3.14159 x 1477 / ( 57.9 x 10⁹ ) x ( 1 - 0.20562² ) = 0.499 x 10^-6 radian.*

And for 100 years, in agreement with observations:

0.499 x 10^-6 x 206265" x 100 x 365.25 / 87.96 = 43 "

Not a featureless ether, but an 'environment' that has local properties, that depend on the presence of matter.

* The angle found, 0.1" per orbit, clearly justifies the shortcuts in the mathematics.

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REMARKS

General.

The objective is to understand the mechanism that explains physics in terms understandable for the non-specialist who is interested in "how it really works".

One can also interpret these difficulties -explaining results properly- as an indication that the basic assumptions, the foundations of physics, are missing or that the assumptions are not altogether correct. The interpretation problems must originate in the basic assumptions.

A basic model is needed that provides answers that are more satisfactory, a model that is less fanciful than the ones on offer. This model has, of course, to produce the same (or similar) results. Comparison and checking is necessary, which leads, in turn, from one subject to another.

Gravity

With all that in mind, a gravitational field, that produces the Newton forces, was devised. It makes no claim that it is the real and only possible field, only that it is useful and a definite possibility. No more, no less. The probability that it 'really is like this' obviously increases with the success it has in explaining well-known phenomena.

The resulting model is easily understood, it does not need extra dimensions or other unnatural concepts, and a -realistic- understanding and insight of the various processes, is now possible. It does show that a model can provide insight where that was impossible before.

Especially noteworthy: the relativity theories are not needed for an understanding of nature.

Details of how the N's 'produce' the -varying- effects of gravity is conjecture; electromagnetism seems a possibility. The arrangement of the N's can be similar to that of CsCl crystals, where each Cs atom is at the centre of a cube with 8 Cl atoms at the corners of that cube, and vice versa for the Cl atoms. A displacement from the centre for the N's, which are held very tightly in position, can produce the local difference in strength.

Movement of e.g. the earth through the field of the sun means then adding, to the properties of the 'resident' N's, the properties of the earth N's at that particular locality etc.

Calculations indicate a very small mass for the N's; a mass of 4.85 × 10^-35 kg, (137x137~18780 N's per electron). The N's are held very tight indeed, as indicated in the section The Hydrogen Atom. While we now have a tangible field, the N's are small enough to accept the possibility of a passage of ordinary matter through this field.*

Curvature of space can now be understood in real terms as a property of this Newton-field.
A geodesic is the curved path that a body follows when the forces along the line of movement do not balance. It is a straight path when they do balance.

The Newton-field is not continuous, but discrete, with a resulting vector at each N.

[*] From the Nobel-price winner (1902):
I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. (Lorentz, 1906)

Indeed one of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms, or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest. (Lorentz, 1906)

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