Parallels between gravity and EM

[KipIngram]

One of my books on EM theory brings the theory forth by starting with Coulomb's Law and special relativity and then proceeds to show how those things together require the existence of a magnetic field and so forth.

 

Coulomb's Law and Newton's formula for gravity are both inverse square laws, so it seems an entirely parallel development could be done starting with Newton's formula and special relativity. And yet in sense EM and gravity are very different, with one being a "real" force field in GR terms and the other being an aspect of spacetime geometry.

 

How valid is this, and how far can it be taken? Is it off track from the start because Newton's theory isn't really "right" but is rather just a good approximation? Does it "work up to a point," and give us a correct derivation of gravity waves and so on?

 

I've also seen some references to early work on unifying EM and gravity (Kaluza's 5D approach, and so on). How worthwhile is a study of that material? I guess reviewing any work is educational, but would it really lead me forward, or more off into the weeds?

 

Thanks,

Kip

 

[zztop]

One of my books on EM theory brings the theory forth by starting with Coulomb's Law and special relativity and then proceeds to show how those things together require the existence of a magnetic field and so forth.

 

Coulomb's Law and Newton's formula for gravity are both inverse square laws, so it seems an entirely parallel development could be done starting with Newton's formula and special relativity. And yet in sense EM and gravity are very different, with one being a "real" force field in GR terms and the other being an aspect of spacetime geometry.

 

How valid is this, and how far can it be taken? Is it off track from the start because Newton's theory isn't really "right" but is rather just a good approximation? Does it "work up to a point," and give us a correct derivation of gravity waves and so on?

 

I've also seen some references to early work on unifying EM and gravity (Kaluza's 5D approach, and so on). How worthwhile is a study of that material? I guess reviewing any work is educational, but would it really lead me forward, or more off into the weeds?

 

Thanks,

Kip

 

You are thinking Gravitoelectromagnetism

[KipIngram]

Thanks - this line from there:

 

While Maxwell's equations are invariant under Lorentz transformations, the GEM equations were not. The fact that ρ_g and j_g do not form a four-vector (instead they are merely a part of the stress–energy tensor) is the basis of this problem.

 

was particularly helpful.

[zztop]

Thanks - this line from there:

 

While Maxwell's equations are invariant under Lorentz transformations, the GEM equations were not. The fact that ρ_g and j_g do not form a four-vector (instead they are merely a part of the stress–energy tensor) is the basis of this problem.

 

was particularly helpful.

you are welcome

[kjelleman]

Gravitoelectromagnetism shows that you may formulate GR in the same form as Maxwell's equation within the same approximation scheme, i.e. low speed, weak field.

Why is this so?

The reason is that magnetism and induction are due to uniform and accelerated motion of charges and are actually motional consequences (same as relativistic effects). The corresponding effects therefore appear in GR which basically sums up the motional consequences starting from Newton's force law. The corresponding effects of magnetism and induction therefore also appear there.

For example, in the parallel motion of two massive objects the attraction is smaller than when being at rest. This is equivalent two the parallel motion of two charges where the reduction of the force is called magnetism.

This is an important aspect of GR since it provides a conceptual understanding of its basic mechanisms.

[Sooryakiran]

Hello,

I would like to bring to your notice the following points.

As far as we know,

 

Mass is continuous where as charge is quantised.

Mass varies according to relativity and charge is invariant ( perhaps due to quantities )

Since charge is invariant, we need another force to balance electric force that is dependent on velocity so that the time dilation equation is satisfied. This force is magnetic force. You may combine time dilation and other equations of relativity with electrostatics to obtain equations of magnetism.

 

Since mass is already dependent on velocity, there is little chance for the existence of gravitomagnetism.

 

As always nature has something to surprise us.