Concerning the Classical Electromagnetism and Gravitation Constants

[FysixFox]

In classical electromagnetism, Coulomb's constant is derived from Gauss's law. The result is:

k_e = 1/4πε = μc^2/4π = 8987551787.3681764 N·m²/C²

Where ε is the electric permittivity of free space, μ is the magnetic permeability of free space, c is the speed of light in a vaccuum, and 4π is because of how Coulomb's constant is calculated (εEA=Q and F=qE ergo F=qQ/εA, and since A=4πr² then F=1/4πε * Qq/r²).

(on an unrelated side note, the symbol for pi looks funny and I'm not sure if I like it, it's not majestic enough and it looks awkward if I use itex tags to do it... okay, back to topic at hand)

The equations for electrostatics and gravity have been compared with almost no end. Even Tesla went so far as to attempt to attribute gravity to electromagnetism (though I don't think he ever published his theory, he just mentioned it). What I'm most interested in is the gravitational constant, G. Working backwards from G, could we perchance find the permeability/permissivity of a vacuum with respect to gravitation just as k_e does for electromagnetism?

Starting with G and assuming that G = 1/4πε, we find that 1/4πG = ε. The result is 1.1924*10⁹ kg s² / m³. Now since ε = 1/μc², that means 1/εc² = μ. The result for this is 9.3314*10^-27 m / kg.

What interests me the most is if this could split classical gravitation into two forces that act as one, just as magnetism and electricity do to form electromagnetism.

Thoughts? Or am I barking up the wrong tree? This thought just occurred to me and I ran straight here to ask about it. :)

 

[UltrafastPED]

Maxwell's equations unified two seemingly different forces: electricity and magnetism.

This union is usually presented as four linear partial differential equations in terms of the electric and magnetic field vectors, and coupled by the fields. There are source terms for the electric field - the electric charge, which comes in two forms, positive and negative, but no sources for the magnetic field: there are no magnetic charges in Maxwell's theory.

From Maxwell's theory the Lorentz transforms of Special Relativity can be derived; the equations are invariant under this transform, but not under the Galilean transform of Newtonian mechanics. This insight leads to additional formulations of Maxwell's laws which perhaps looks simpler at first glance, but all of the same physics is encoded.

See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html
And for a nice introduction: http://www.maxwells-equations.com/

Newton's Universal Law of Gravitation has a single "charge": mass; thus it lacks some of the intricate structure of the electromagnetic equations. Of course the Newtonian system is also incomplete: it needs some changes to make it compatible with Special Relativity. When Einstein was done with this work he had created General Relativity, our modern theory of gravitation.

This consists of ten non-linear partial differential equations, coupled in the metric. Space and time are again coupled, as in Special Relativity, but now the coupling is more complex.

While there is no direct analog to magnetism in Newton's theory, there are many obvious similarities to static electricity: the law for gravitation and Coulomb's law for electric charges are identical in form except for mass only coming in one form of charge: always attractive, never repulsive.However, there are some magnetic analogs with Newton's theory, and more With General Relativity; this can be called gravitomagnetism: https://en.wikipedia.org/wiki/Gravitoelectromagnetism

 

[FysixFox]

Interesting... I wasn't taught anything about Maxwell in school, though I have heard of him somewhere before. So basically, gravity DOES have two components that behave similarly to the electric and magnetic forces, but they're so unnoticeable that it's rarely mentioned to us physics noobs. Interesting! :D

But since the GEM equations in the article were only "in a particular limiting case," doesn't that mean you'd have to apply General Relativity to Maxwell's Equations to apply the equations to gravity properly?

 

[UltrafastPED]

But since the GEM equations in the article were only "in a particular limiting case," doesn't that mean you'd have to apply General Relativity to Maxwell's Equations to apply the equations to gravity properly?

Maxwell's equations don't need to be changed; they are OK as is. They already obey Special Relativity.

The analogy isn't perfect, and is appears when the gravitating body is rotating. In General Relativity this effect shows up directly as "frame dragging".

 

[FysixFox]

Maxwell's equations don't need to be changed; they are OK as is. They already obey Special Relativity.

The analogy isn't perfect, and is appears when the gravitating body is rotating. In General Relativity this effect shows up directly as "frame dragging".

Ah, I see. Thank you! :)