# Is there a gravitational equivalent to magnetism?

1. Jun 30, 2008

### Ray Eston Smith Jr

I understand that magnetic force is a relativistic effect of electric force.
Is there a force which is the relativistic effect of gravitational force?

If a stationary observer sees 2 electrically charged particles moving parallel to each other at the same very high speed relative to himself he will see a "magnetic force" between the 2 particles. But an observer moving along with the charges would only see an electrostatic force between the particles. The "magnetic force" is just a relativistic effect of electric force.

So, what if the particles were uncharged? Shouldn't there be a similar "relativistic- gravitational" force (analogous to magnetism) seen by the stationary observer?

The "relativistic-gravitational" force would be very small, because gravitational force is generally much smaller than electric force (and relativistic force is very small relative to static force except at very high speeds). However, the universe contains massive galaxies moving at high speeds relative to one another. At that scale, the relativistic force should be observable. I think it would be a repulsive force.

On the other hand, maybe the relativistic increase in mass with velocity would provide just enough extra gravitational attraction to exactly counteract the repulsive relativistic force.

2. Jun 30, 2008

### JesseM

Good question, I believe this is what is known as gravitomagnetism, perhaps someone here can explain more about it, or you can google the term to look for more info.

3. Jun 30, 2008

### Ray Eston Smith Jr

Thanks for the link. I don't understand why general relativity has to come into it, but then I don't understand much about general relativity, in general.

4. Jun 30, 2008

### JesseM

Well, the reason the electrical force in a particle's rest frame looks like a magnetic force in a frame where it's moving has to do with relativistic effects, mostly Lorentz contraction. And Newtonian gravity is not a relativistic theory--it isn't invariant under the Lorentz transformation. So I think it makes sense that you'd need to use general relativity, because it's the only relativistic theory of gravity we have.

5. Jun 30, 2008

### rbj

a while ago i was asking the same kinda question on sci.physics.research . i wonder the same question (it seems that when you have an inverse-square field in the static case and the effects of special relativity for the moving case, you should get results analagous to E&M, but there's that pesky factor of 2 that i don't get). anyway GEM is only an approximation to what GR would predict for masses in motion. but it's s'pose to be a good approximation for reasonably flat space-time.

6. Jul 1, 2008

### granpa

---Is there a force which is the relativistic effect of gravitational force?---

frame dragging?

7. Jul 1, 2008

### pmb_phy

Gravitomagnetism is not a relativistic effect of gravity in the sense inquired by the OP. Gravitomagnetism is an analogy between gravity and electromagnetism in that the equations of motion in GR have the same form as Maxwell's equations.

Pete

8. Jul 1, 2008

### JesseM

What do you mean by "in the sense inquired by the OP", though? I understood the OP to be asking if there is an equivalent in gravity to the fact that a radial electric force that one particle feels from another in the particle's rest frame must look like a velocity-dependent nonradial magnetic force in a frame where the particle is moving, because of the way the Lorentz transformation works. I may be wrong, but I had the idea that gravitomagnetism is broadly similar--in a spacetime that isn't too far from flat I think you can still talk about coordinate systems that are close to the inertial frames of SR (part of the 'weak-field approximation'?), and I thought the gravitomagnetic effects appear in a "frame" where the mass is in motion, and depend on the mass' velocity. For example, this paper says:

9. Jul 1, 2008

### pmb_phy

The OP said
The magnetic force is not an analogy of the electric force. It is a different kind of force than the electric force. It even has a different nature to it, i.e. the magnetic force is velocity dependant whereas the electric force is not.

The gravitomagnetic force is not a different force than the gravitational force. In fact they are exacly the same thing, exactly. I.e. the gravitomagnetic force is the gravitational force. Gravitomagnetism is just a paradigm for gravitational force.
We simply have a different opinion as to what the OP was looking for. Its still a good idea for you to mention it though. I just wanted to point out that the gravitomagnetic force is not a different force than the gravitational force.
Thanks for mentioning this. It reminds me of the fact that electric charge is analogous to relativistic mass. I'm looking for analogies like this. Thanks!

Best wishes

Pete

10. Jul 1, 2008

### JesseM

Well, I agree the magnetic force is independent of the electric force and behaves differently, but I took the original poster to mean something like the idea that if you want to construct a theory that includes a force that works like the electric force, then if you want the theory to be Lorentz-invariant you must include a force that works like the magnetism as well, because of the way the electric field vectors transform in different frames. There's a good discussion of this on this page, adapted from a similar section in Purcell's undergraduate textbook Electricity and Magnetism (which is where I first learned about this idea). Perhaps the OP can clarify if this is what was meant by "magnetic force is a relativistic effect of electric force"? If so, then since the behavior or a particle under the influence of a magnetic force can be reinterpreted in terms of the influence of an electric force by transforming into the particle's rest frame, the question is whether there's a similar relation between the "gravitomagnetic" force and the gravitational force.

Last edited: Jul 1, 2008
11. Jul 1, 2008

### pmb_phy

The equivalent here is to point out the relationship between gravitoelectric forces and gravitomagnetic forces.

Pete

12. Jul 1, 2008

### JesseM

Ah, I wasn't aware of the term "gravitoelectric", thanks. I notice now that the wikipedia page on gravitomagnetism mentions the gravitoelectric force, and also describes it as the "static gravitational field (conventional gravity, also called gravitoelectric for the sake of analogy)". So in the weak-field approximation, would I be right in thinking that this is fairly similar to Newtonian gravity? If so this may be what the OP meant by "gravity", since the poster apparently wasn't actually thinking of general relativity when asking the original question, saying in his second post "I don't understand why general relativity has to come into it, but then I don't understand much about general relativity, in general."

13. Jul 3, 2008

### rbj

long ago, i had something to do with that WP article. i added the references to the Mashoon artiicle and the other one. both derived something that looked like Maxwell's equations and the Lorentz force equation, out of GR (for reasonably flat space-time). even though the references are still there, it's been edited so much, that i am not confident that it represents what the original authors of those GEM papers meant.

i thought that the gravitostatic force was exactly corresponding to the coulomb electrostatic force. and since

my understanding is that the "gravito-static" force is just like Newton. inverse-square and doesn't care about relative velocities. i disagree that the magnetic force is independent of the electric force. is not the magnetic force a consequence of the electric force when effects of relativity are considered? is that not also the same about gravito-magnetic effects (just a consequence of the gravito-static force, but with relativistic effects accounted for)?

there's a factor of two difference between the two that i have never understood.