Similarities between the theories of electromagnetism and gravity

[kostik]

In the theory of electricity and magnetism, which follows from Coulomb's inverse square law, the magnetic field and force arises from moving charge due to considerations of special relativity and different moving frames of reference.

 

Therefore, since Newton's and Coulomb's laws are identical in form (both inverse square), with the exception of the constants involved, and the fact that Coulomb's law allows for charge and force to have the same or opposite signs, why is there NO analog to magnetism in the theory of gravity? Why doesn't a moving mass (or "mass current") give rise to another velocity-dependent force on a nearby test-mass, as a moving charge does to a nearby test-charge? Why do Maxwell's equations have no analog for gravity, when the fundamental laws - Coulomb's Law and Newton's law - are identical in form?

[EdEarl]

Physicists observe and explains things, properties of things, and relationships among them. Why things are as they are is not observable. Some have speculated that there are infinitely many universes, each with different laws of physics, and that our universe is the way it is by chance. Others speculate a grand programmer simulated our universe and us, some say a god or gods made the universe. Each of us is a few atoms bouncing around an insignificant planet orbiting a small star in a common galaxy; it is our fate to wonder why and not to know.

[ajb]

You can linearise the Einstein field equations and these look close to Maxwell's equations. You can then start to discuss the formal similarities properly. I have not looked into this closely, but frame-dragging effects can be viewed as an analouge of magnetism for gravity. But you will have to look up the details yourself.

[swansont]

!

Moderator Note

 

Speculation on the dependence on r^2 has been split

http://www.scienceforums.net/topic/77788-inverse-square-law/

 

 

[kostik]

My question is more straightforward and really just about the mathematical development of the theory, not philosophical. If the magnetic field and Maxwell's equations are derived SOLELY from Coulomb's law plus special relativity, then why don't we end up in exactly the same place with respect to gravity? Why doesn't a test-mass experience a velocity-dependent perpendicular force near a "current" of mass, analogous to the Lorentz force law?

 

The only difference between Coulomb's and Newton's laws is that the force can be attractive or repulsive, whereas in gravity the force is always attractive. I suspect that must be the factor that somewhere causes the theories to diverge .... but it's not obvious exactly where it happens.

Edited July 28, 2013 by kostik

[swansont]

Newtonian gravity and E&M follow the same form for one of the E&M equations, the one called Gauss's law. i.e. the divergence of the field is given by the enclosed charge (mass). We do not see the rest of the behavior for Newtonian gravity — e.g. the curl of the gravitational field does not give rise to a changing gravitomagnetic field, and a time-varying gravitational field likewise produces nothing relating to a gravitomagnetic field.

 

Except, as ajb notes, that there are effects in GR.

[studiot]

If you want to study the comparison at undergraduate level I recommend the book by Professor Hammond of Southampton University

 

Electromagnetism for Engineers.

 

His treatment uses the similarities (and differences) between gravity and coulomb's law to introduce electromagnetism.

 

It is very readable.

 

You should look for the SI/Metric edition.

Edited July 28, 2013 by studiot

[kostik]

I found some Internet discussion of this topic under "gravity magnetism". Apparently the fact that charge comes in two types, + and -, is indeed what causes the theories to split. If you bring three charges together, at least two of them must repel each other, unlike gravity. One web site expounded that if you try to carry out the formulation for Maxwell's equations based on gravity you would end up with a formula for gravitational radiation that carries away negative energy, which is impossible.

[Strange]

You might be interested in this:

Gravitoelectromagnetism: A Brief Review

http://arxiv.org/abs/gr-qc/0311030v2

Edited August 2, 2013 by Strange

[swansont]

You might be interested in this:

Gravitoelectromagnetism: A Brief Review

http://arxiv.org/abs/gr-qc/0311030v2

 

Note that this is listed as General Relativity and Quantum Cosmology, i.e. this is not a matter of Newtonian gravitation following the form of Maxwell's equations.

[roger4464]

Note that this is listed as General Relativity and Quantum Cosmology, i.e. this is not a matter of Newtonian gravitation following the form of Maxwell's equations.

I found some Internet discussion of this topic under "gravity magnetism". Apparently the fact that charge comes in two types, + and -, is indeed what causes the theories to split. If you bring three charges together, at least two of them must repel each other, unlike gravity. One web site expounded that if you try to carry out the formulation for Maxwell's equations based on gravity you would end up with a formula for gravitational radiation that carries away negative energy, which is impossible.

''The word impossible in physics Should never be used''.... Roger Dynamic Motion

[pantheory]

In the theory of electricity and magnetism, which follows from Coulomb's inverse square law, the magnetic field and force arises from moving charge due to considerations of special relativity and different moving frames of reference.

 

Therefore, since Newton's and Coulomb's laws are identical in form (both inverse square), with the exception of the constants involved, and the fact that Coulomb's law allows for charge and force to have the same or opposite signs, why is there NO analog to magnetism in the theory of gravity? Why doesn't a moving mass (or "mass current") give rise to another velocity-dependent force on a nearby test-mass, as a moving charge does to a nearby test-charge? Why do Maxwell's equations have no analog for gravity, when the fundamental laws - Coulomb's Law and Newton's law - are identical in form?

 

Magnetism follows the inverse square law when considered as a point source of pull or push, but when considering the entire magnet as a dipole, it is more akin to a inverse cube law.

 

http://blazelabs.com/inversecubelaw.pdf

 

Although in both cases of magnetism and gravity the entire mass of the magnet or gravitational mass is considered in the formulations, mass is proportional to the volume and the inverse cube law may relate to the mass as it changes in relationship with the volume (4/3 pi r³ ). On the other hand the inverse square law of gravity may be more akin to surface area and emanations from the surface area as it relates to the mass (4pi r²). I think this might be a clue to their kinship. You also might consider the possibility of kinship between the equivalency principle of gravity, as it might relate to moving electrical charges concerning magnetism.

Edited August 15, 2013 by pantheory