Mass, Gravity and Inertia

[inflector]

I've been working on the ideas for a theoretical model for gravity, mass and inertia that is based on the idea that all particles are composed of 3-dimensional fractals. The fractal is built of tetrahedrons with six sides made of stretchy strings. The center of the fractal is a single tetrahedron so there are four faces or directions in which the fractal grows. The fractal branches out spherically from the base tetrahedron, with each tetrahedron connected to one larger tetrahedron, and three smaller tetrahedrons. The size of the tetrahedrons is reduced at each level by a factor of [math]1/\sqrt{3}[/math], the size of the strings is likewise reduced by the same factor. So the combined spring constant, k, for any given level would be equal to the sum of the constants for the levels below it. (See the attached diagram for a left-handed fractal in one of the four directions coming off the base tetrahedron).

 

I realize there is a lot of specific potential problems with this idea, and I don't want to address most of them here, as I'm still trying to learn enough of the right math to be able to properly assess the ideas in each of the domains where it touches. So I don't want to go into how this idea relates to particle physics, quantum mechanics, etc., just gravity and inertia for now.

 

For gravity, my idea is that each particle is connected to every other particle in the universe by means of the ends of fractal, i.e. at the very thin ends of the fractal, but that these ends are so thin that we can neither see nor detect them at present under normal circumstances. (See: http://www.fusor.net/board/view.php?bn=fusor_theory&thread=1248718666 for some idea how this might work)

 

For example, if one assumes there are [math]10^{80}[/math] protons in the universe, then this would mean that each proton would be connected to each other proton via a very tiny stretched tetrahedron at the very least at the [math]12^{76}[/math] layer of the fractal (to account for [math]10^{80}[/math] connections) and probably even further out, perhaps even to the extent that the connections are infinite in quantity and in thinness, but nevertheless measurable to some extent because of the mathematical relationship between the thickness and size of the tetrahedrons at each of the layers.

 

For this to be a valid model, clearly there would need to be some relationship between the fractal's tetrahedral string network and the the gravitational attraction of particles in Einstein's General Relativity, i.e. the math for the fractal network would have to end up corresponding to General Relativity for the domain where we have tested General Relativity's validity. Intuitively, I can see how this might work out, but I've got to learn more about Tensor math and GR to know for certain.

 

The equivalence principle is handled quite naturally since both gravity and inertia result from the same thing, tension of the stretchy tetrahedral strings. In the case of inertia, the tension is what creates the need for a force to change momentum. Any given steady-state condition requires and exerts no force because the pull of strings in one direction is matched by the pull of strings in the opposite direction. A change in velocity or direction would require a force because there would be some finite lag in the string tension, i.e. the side coming under greater tension would have no lag and the side that would be loosened would have a lag, so there would be a greater pull on the side coming under greater tension without a corresponding and compensating pull on the side coming under less tension. The degree of tension (i.e. the force) would be proportional to the acceleration. A slow acceleration would require less force because there would be less lag. Only acceleration would affect the balance of the tension because any steady velocity would result in the elimination of the lag and therefore the balancing of the tensions in all directions.

 

Gravity is more complicated, it is a measure of directional tension. For a single particle out in empty space the tension is balanced. As a particle gets nearer to other particles, the tension becomes more directional. A large mass of particles creates more tension, e.g. a planet or star would have more particles and therefore be a source of more tension.

 

Where this idea, which I'll call fractal gravity, diverges from Newtonian gravity is in the measure of the acceleration of gravity. For Newtonian gravity, the acceleration falls off as [math]\frac{1}{r^{2}}[/math], for fractal gravity, in contrast, the acceleration is dependent not only on the proximity to the other mass causing the acceleration but also on the distribution of the surrounding mass. (Again, see: http://www.fusor.net/board/view.php?bn=fusor_theory&thread=1248718666 for greater detail.)

 

This is because the tension of gravity depends on the distribution of all mass, and one can't directly compare the force of gravity between two different objects without considering all the other objects outside the two in question as well. For instance, the gravitational attraction of a star towards the mass of stars in a galaxy would be different depending whether or not the star is located inside the bulk of the mass of the galaxy or out near it's edge.

 

I believe that this is conceptually similar to the way that gravity acts like curved space-time in GR gravity as well, but I'm still learning the math for this and haven't advanced far enough to make any direct comparisons yet.

 

I'm working on the math for GR so I can make comparisons and understand it better. Besides this, any other suggestions for ways in which I might attempt to put some math behind the ideas? Any particular areas I should study? Good books to read?

 

- Curtis

[inflector]

No comments?

[Kyrisch]

The whole thing seems rather unnecessary. Why is your theory more useful than the one accepted at present?

[inflector]

Sorry for the tardy reply. I thought I had subscribed to replies via email and evidently did not.

 

The theory is potentially more useful (if it holds up) for several reasons:

 

1) It offers the potential for explaining the specific mass for each of the basic particles. For this to be true, at a minimum I need to make sure that it models gravity as we have observed it. Obviously, if it can't account for the small subsection of our observations that match GR, it isn't a good theory, so it seems like a good place to start. If it falls apart here, then there's no sense spending years working on it in the future.

 

2) It offers the potential for unifying quantum mechanics and gravity. In particular, the substrate of interconnected strings could be a medium on which pilot waves travel as in deBroglie-Bohm theory (aka Bohmian Mechanics or Pilot Wave theory).

 

3) It offers the potential for other unifications as well.

 

- Curtis