An Alternative Theory For Gravity

[Aethelwulf]

Similarities to Gravitational and Electromagnetic Forces

 

On the face of it, gravity usually appears quite different to the electrostatic forces, but if one studies the equations, one finds many striking similarities. This has led me to think perhaps (on the fundamental level) gravity is nothing more than electrostatic interaction. It's a bold and quite wild proposal which is why I have posted it in the Alternative Forums.

 

 

Let us begin with a few of these similarities... In Motz' ''On the Gravitational Charge,'' an essay submitted for the Gravity Foundation for FQXI, he states a few similarities, one of them was:

 

[math]F = \frac{\sqrt{G}M_1 \sqrt{G}M_2}{r^2}[/math]

 

This is of course analogous to Coulomb's Force [math]\frac{q_1q_2}{r^2}[/math].

 

He notes, that the gravitational charge will be the source of the gravitational field

 

[math]\frac{\sqrt{G}M}{r^2}[/math]

 

If anyone has noticed, this is actually an analogue of the magnitude of the electric field which is created by a single charge

 

[math]E = \frac{1}{4 \pi \epsilon}\frac{q}{r^2}[/math]

 

Another one to note perhaps, would be the appearance of the gravimagnetic field, given by Motz as [math]\frac{-2 \omega v}{\sqrt{G}}[/math]. It is actually equated to (That is the coriolis force divided by the intrinsic gravitational charge)

 

[math]\frac{F}{\sqrt{G}M} = -\frac{2 \omega v}{\sqrt{G}}[/math]

 

This is actually the gravitational analogue of the equation

 

[math]\mathbf{E} = \frac{F}{q}[/math]

 

which describes the definition of the electric field. So the gravitational case, must be the definition of the gravimagnetic field (gravimagnetic because it is a rotating system ''coriolis'').

 

The Gravitational Force as an Electrostatic Force

 

The gravitational constant G and the Coulomb constant can be expressed in terms of Planck units as

 

[math]G = \frac{k_0 e^2}{\alpha M^2}[/math]

 

and the gravitational force is

 

[math]K_{grav} = \alpha^{-1} k_0 \frac{e_1e_2}{r^2}[/math]

 

Where alpha is the fine structure constant and the mass is the Planck Mass – notice the product of charges and go back to similarities between electromagnetic and gravitational forces. The source of the gravitational field is the gravitational charge, and the charges can be calculated from the elementary charge with masses which exert the attractive gravitational forces – one can say that the gravitational force might be an electrostatic force between two small gravitational charges. This can be given as ratio’s

 

[math]e_1=e \frac{\sqrt{G}M_1}{\sqrt{G}M_p}[/math]

 

and

 

[math]e_2 = e \frac{\sqrt{G}M_2}{\sqrt{G}M_p}[/math]

 

We notice, the gravitational charges make up a dimensionless constant: In nature, only dimensionless constants hold significant physical meaning.

 

Electrostatics really means an equilibrium in the system. A simple system in equilibrium can be thought of using a two particle system. The famous Einstein two-particle universe equation is a good example of a gravitational equilibrium

 

[math]G = \frac{Rc^2}{2M}[/math]

 

And gravitational equilibrium is achieved by

 

[math]\omega^2 R = \frac{GM}{r}[/math]

 

This gravitational equilibrium equation can be found in Motz’ work as well.

 

On the face of it, the gravitational force may very well be an electrostatic interaction between two masses. Certainly above, the relationship of the ratio of the gravitational charge between two elementary charged particles can be allowed in such a fashion where we might be forced to think of gravitational interactions arising from the Coloumb force interaction. On a similar note, Barrow and Tipler) calculated

 

[math]\frac{\alpha}{\alpha_G} = \frac{e^2}{GM_eM_p}[/math]

 

It has a subtle mathematical difference in structure. Perhaps more importantly is that in my equation

 

[math]e_{1,2} = e \frac{\sqrt{G}M_{1,2}}{\sqrt{G}M_{p}}[/math]

 

The part

 

[math]\frac{\sqrt{G}M_{1,2}}{\sqrt{G}M_{p}}[/math] Can be seen as a new predicted physical constant of nature which I will denote as [math]\Gamma[/math].

Edited December 24, 2012 by Aethelwulf

[Aethelwulf]

Sorry about that, I missed out a q/r^2 in my equation

 

[math]E = \frac{1}{4 \pi \epsilon}\frac{q}{r^2}[/math]

[Aethelwulf]

I will call [math]\Gamma[/math] the Electrostatic Coefficient Coupling Constant (ECCC) ... a bit of a mouthful, but it has more to do with the electromagnetic side of things than it does actual gravitational.

 

Keep in mind, in these thoughts, the gravitational force is simply an electrostatic interaction at the fundamental level, so the coupling constant is very similar to

 

[math]\frac{\hbar c}{GM^2} = \alpha_G[/math]

 

(The gravitational fine structure) - [math]\Gamma[/math] is a very fine coupling of electrostatic interactions, effectively playing the role of gravity. Gravity truly would be simply another side of the electric field.

 

And even though [math]\Gamma[/math] is more related to the electric field, it isn't quite the electromagnetic fine structure constant either by definition

 

[math]\frac{e^2}{\hbar c} = \alpha[/math]

 

It is, as the name suggests, a coefficient coupling constant on the elementary charges of systems

 

[math]k_0\frac{e_1 \cdot e_2}{r^2}\Gamma[/math]

 

Which is the Coulomb Force. It defines the ratio of the gravitational charges (masses) of the system and it is a dimensionless coefficient of the elementary charges.

Edited December 24, 2012 by Aethelwulf

[Aethelwulf]

However a small set of calculations can place a large amount of doubt on whether gravitation is an electrostatic force... why? I did say before that theory was a bit wild... calculating the gravitational force (using Newtonian physics) between two electrons, I get

 

[math]5.54 \times 10^{-51}N[/math]

 

The electrostatic force by theory between two electrons is

 

[math]2.30 \times 10^{-8} N[/math]

 

There certainly is a big difference between these two forces, so it does case doubt on whether the gravitational force is even resultant from the electrostatic force.

[Aethelwulf]

It does remain an interesting artifact of the two theories however, that the gravitational force and Coulombs law are so very similar. There have been some theories suggesting that gravity gets stronger and stronger on smaller levels...

Edited December 26, 2012 by Aethelwulf