# Trying to understand gravitomagnetism

1. Nov 6, 2005

### koroljov

I know special relativity, but not general relativity.
I am trying to understand gravitomagnetism (at least in simple terms).
I have read some of the information google gave me, and I would like to know wether my understanding is corect.
1) Gravitomagnetism has nothing to do with magnetism. They just gave it that name because of the analogy with electromagnetism.
2) 1/r^2 laws are not lorentz invariant. Since all laws have to be lorentz invariant, all 1/r^2 laws must be accompanied by a velocity-dependent field (the magnetic field for electromagnetism and the gravitomagnetic field for gravity).
Is this correct? Or am I totally wrong?

2. Nov 6, 2005

### masudr

The most accurate Lorentz-invariant theory of gravity we have today is General Relativity (GR) which has more to it than starting off with a $1/r^2$ force and then seeing how it transforms in different inertial frames. Instead we postulate the equivalence principle, and look at all frames, not just the inertial ones. Throw in a bit of geometry, algebra and analysis, and you're there - the full formalism of GR.

3. Nov 6, 2005

### rbj

one crude way i have to look at it (which is not totally accurate, but i, too, don't understand the mathematical detail of GR) is to imagine the analogy of E&M to GEM. in E&M you have this inverse square law (w.r.t. distance) which also has proportionality to the magnitude of the two charges. you can take the static E&M physics, toss in SR and show, at least in one thought experiment, how magnetic effects come out of that. from that, you can generalize further and get Maxwell's Equations. and from that, you get the speed of propagation of the electromagnetic action to be $$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$$. and the force on a small test charge is governed by the Lorentz Force Equation.

now replace that with (newton's) gravitation, but continue to apply the effect on the static inverse-square forces of SR. what you get is something that looks like Maxwell's Equations but with mass or mass density replacing charge or charge density and $$\frac{1}{4 \pi \epsilon_0}$$ being replaced by $$-G$$. and likewise, the force on a small test mass is something like Lorentz force equation but with $$q$$ getting replaced by $$m$$.

there's a wikipedia article on the subject you might want to look up.

4. Nov 6, 2005

### pervect

Staff Emeritus
This is basically on the right track. I'm not sure offhand if one can definitively say that the extra force terms must be proportional to velocity. However, one can say that a purely 1/r^2 force is not compatible with special relativity because it does not transform properly.

Certainly a velocity dependent force is one of the simplest resolutions, and is the one that both Maxwell's equations and GR compute.

Another quibble is the whole issue of "forces" in GR - GR is not technically formulated in terms of forces between particles in the usual treatments. There are some treatments which take a different approach, though, so this issue is probably not major.

5. Jun 10, 2006

### Ian Rumsey

Gravitomagnetism?
Is this not the field radiated by rotating mass?
Is it not the force that causes tides?
Is it not present in the atom due to the rotating mass of the electron?
Is it not a medium through which instant communication may be made between all things, at all times?
In simple terms Koroljov, this is Gravitomagnetism.

6. Jun 10, 2006

### vanesch

Staff Emeritus
7. Jun 10, 2006

### Robert100

While I have a BS in physics, I don't know anything about this topic other than what I have read in popular texts. As such, I'd like you to address a point made in the Wikipedia Gravitomagnetism article. The article states:

"Gravitomagnetism (sometimes Gravitoelectromagnetism), abbreviated GEM, refers to a set of formal analogies between Maxwell's field equations and an approximate reformulation of the Einstein field equations for general relativity, valid under certain conditions. For instance, the most common version of GEM is valid only far from isolated sources, and for slowly moving test particles."

"The effects of such a gravitational field, often loosely referred to as gravitomagnetic effects, are among the last basic predictions of general relativity not yet directly tested. A group at Stanford University is currently analyzing data from the first direct test of GEM, the Gravity B satellite experiment. Frame-dragging is often mentioned as a gravitomagnetic effect, but the Lense-Thirring effect (precession) may be a more appropriate example."

Should we regard this phrasing as this correct? Is frame-dragging technically an example of GEM at all, or is it simply not the best such example?

In the Wikipedia article on frame-dragging GEM is hardly mentioned. (I am thinking that this may be a deficiency in the article, but I would like your views.)

Robert

8. Jun 10, 2006

### Robert100

I have a question about the wording of the Wikipedia article on gravitoelectromagnetism (GEM). Their article states:

Despite the electromagnetism in gravitoelectromagnetism, and despite the similarity of the GEM force law to the Lorentz force law, gravitomagnetism should not be confused with any of the following:

* claims to have constructed anti-gravity devices,
* Eugene Podkletnov's claims to have constructed gravity-shielding devices and gravitational reflection beams,
* the so-called Electric Universe "theory", which claims to identify gravity as a form of electromagnetism.

These and other claims are considered pseudophysics by mainstream science. Gravitoelectromagnetism, on the other hand, is firmly part of our gold standard theory of gravitation, general relativity, has testable predictions, and is in the final stages of being directly tested.​

I understand fully that the article is trying to explain the distinction between real science and pseudoscience, but I am wondering if the text is worded too strongly. If GEM is real, then it truly is a gravitational force, and if it can act (in some cases) as gravitational repulsion, then would it not count as "anti-gravity"?

However, I also want to make clear that the wording of a phrase doesn't always capture the intent of what the phrase really means. Just because we could define "anti-gravity" in this way doesn't mean that physicists actually do so. I'm under the impression that physicists usually avoid the term "anti-gravity"; they'd only use that term if a new force was discovered that actually was distinct from gravity and counter to it. (As such, that would make the phrasing of the Wikipedia article correct and useful.)

Robert

9. Jun 10, 2006

### rbj

there is, BTW, a little dispute at Wikipedia about the Gravitomagnetism article. it needs a real expert to go there and fix it up. it also should have the primary name changed to Gravitoelectromagnetism (with Gravitomagnetism redirecting to it), but i lost that fight a couple of months ago because not enough physicists came to set the "popularists" straight about the terminology. but i think those references to pseudophysics are correct.

first of all, GEM is not the "first principle" in gravitation. GR is (to our present state of knowledge). but, given certain conditions, that is reasonably flat space-time and reasonably slow speeds relative to whatever observer, the Einstein GR equation can be manipulated to form equations that look just like Maxwell's Equations with charge density replaced by mass density and with $1/(4 \pi \epsilon_0)$ replaced by $-G$. those are th GEM equations and they're only an approximation to reality unlike Maxwell's which is presently believed to be pretty much exactly reality (dunno if unification theories would say that).

just as the (electro)magnetic field is not really a "new" or different action from the electrostatic field (it is a manifestation of the electrostatic field where the effect of relativity to what the "stationary" observer sees is accounted for), in GEM, the gravitomagnetic field is the same as the gravitostatic field (but with the consequences of relativity considered).

as with the electromagnetic field, any "repulsive" gravitomagnetic field does not exceed the attractive gravitostatic field (the regular old Newtonian "gravity" field). it only reduces the gravitostatic field, but that is really just a model. there is only the gravitostatic field, but because of relativity, an observer believes he/she sees the acceleration due to gravity being reduced (due to time-dilation) and attributes that reduction of acceleration to a repulsive gravitomagnetic force that acts in the opposite direction to the gravitostatic force. but there is no net repulsion, no net anti-gravity.

there is no net anti-gravity. we would need negative mass charges to make anti-gravity (or to construct gravity shielding) and, because of the equivalence of inertial mass to gravitational mass, a negative mass will repel everything (negative or positive masses) and a positive mass attracts everything (negative or positive mass). so imagine what would happen in free space if you had two masses of equal magnitude and opposite sign separated by some distance? (it's a little paradox, which is why i don't think we really ever see globs of negative mass around in the universe. perhaps in conceptual particles, but not little piles of in on the street.)

both the electromagnetic and gravitomagnetic forces are pseudo-forces to account (without reference to SR) for an observed reduction in electrostatic or gravitostatic forces. (and, to be really correct, so is the gravitostatic force also a pseudo-force, although Newton might not agree.)

that's my spin on it.

Last edited: Jun 10, 2006
10. Jun 10, 2006

### Robert100

Thanks very much, rbj. Frankly, that's the clearest explanation yet I've seen of this issue.

I hope that I'm this clear when I explain analagous issues to my students in physics. (They come into my class believing that there is some mysterious "centrifugal force" which pulls spinning objects outwards. Between demos and step-by-step Socratic dialogues, I try to get them to understand that it is only a fictitious force. The only real forces, in such cases, are actually inward, which blows their minds.)

Robert

Robert

11. Jun 11, 2006

### rbj

just remind them that when they are in a car going around a corner (say, to their left) that it is the car door or seat or seatbelt that is pushing on their body from the right that is accelerating them to the left.

if you are interested, i posted a few times a special case that shows, for this particular setup with two infinite and parallel lines of charge, how the magnetic field is precisely the same as the sole electrostatic field but with SR considered. this result of this thought experiment is consistent with both know classical E&M (Maxwell and Lorentz force equation) or with just the E-field but with SR considered.