The difficultly: Despite the propagation delay, gravity always points to where the object should be, instead of where it was when the gravity was "emitted".
The explanation: Just like the object itself is moving, the gravitational field (or electric/magnetic field) is ALSO moving! It moves at exactly the same speed, and in the same direction as the object which created it.
It's "disconnected" from the source - so if the source suddenly changes direction the field it emitted doesn't know about it, and continues to point to where it expected the object to be.
More technical:
Why wormholes are impossible, and why you can not create a single magnetic monopoles:
What about conservation of momentum? If an object is pulled to where the other object is expected to be, not where it is, then momentum exchange between the two of them would seem to not add up!
But it works because you can never create a gravitational or electric field from nothing. You can only move them around, so the momentum always catches up.
What about a magnetic field? You can create those from nothing - ah, but you can only create magnetic dipoles, with opposing fields, so again it works.
But, you can never create a magnetic monopole because you would suddenly have a magnetic "charge" where none existed before and the momentum would not add up. What you can do is create two monopoles, of opposite poles. (So this implies a conservation of magnetic pole, just like conservation of electric charge - assuming monopoles exist.)
What about wormholes? They have the same momentum problem - an object suddenly appears where none was before and it pulls on other objects. You could then move it away before it gets pulled in turn by those objects, and that would violate conservation of momentum. So you can't do that.
And, faster than light objects would have the exact same problem - they could move out of the area before they properly shared the momentum. So I suspect they can't exist either. (Unless there is some complicated math I didn't think of which "fixes" it.)
Say some advanced civilization can move around some large mass - an asteroid, a planet, a black hole, whatever, we'll just call it "the big mass". They can, at will, fly it back and forth between two distinct positions we'll call 0 and 1.
And let's say some distance away - a light-year, say - they have an facility where they can measure with excruciating precision the force of gravity on a test mass. After isolating out all other known gravity sources, they can use the remaining vector of gravitation force to compute the current position of the original big mass - and whether it's at position 0 or position 1.
Assuming they can drag around the big mass from one position to the other in a short amount of time, shouldn't the people at the remote facility be able to detect where the big mass is long before light could reveal its position? Couldn't they use those observations to receive a low-bandwidth, but faster-than-light message?
The gravitational field points at where the object would be, given its current velocity.
This is not to say that the object will actually end up there. If the velocity changes, the gravitational field changes direction according to the new velocity. The change propagates at the speed of light.
(I made this from the "Moving Charge" java physics applet
at http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/Mo... .
It's a demo of the physics of electric charges, not general relativity, but the essence
of the idea is the same even if the field equations are different. This follows directly from the central idea of relativity: the physics of uniform constant motion is the same as no motion, if you're moving along at the same speed.)
The point charge (mass for gravity) in the center is first moving slowly to the right, then suddenly changes direction to move slowly to the left. (The small red vector indicates velocity.)
The white lines represent the direction of the field, that is, the direction an object would be pulled.
Near the point source, the field lines point to where it is. Far away, the news hasn't arrived yet that it's motion has changed, and so they point to where it would have been. During the brief acceleration when the source changed direction, the field lines connecting these two regions are "kinked" strongly - that's the radiation, which propagates outward at the speed of light.
A second object would feel a sideways pulse as the wave (kink) passed by.
> Assuming they can drag around the big mass from one position to the other in a short amount of time, shouldn't the people at the remote facility be able to detect where the big mass is long before light could reveal its position?
No, the remote facility won't notice the thing moved until the gravity wave hits and that only moves at the speed of light. If it's a light year away, it'll take a year before the remote facility notices the shift.
I think this is actually a brilliant exercise in though. I have no idea what the answer is, and it's likely impossible to ever cancel out the effects of every other source of gravity within a 1 light-year radius, but it seems like in theory, if the force due to gravity propagates faster than the speed of light, your suggestion may hint at a method of communication that exceeds the speed of light.
No. The change in gravitational fields propagates at the speed of light. The gravitational force vector for a star in the sky N light years away points to where the star was N years ago.
> The gravitational force vector for a star in the sky N light years away points to where the star would be if kept moving at constant speed for N years.
Interesting. I don't know enough about physics to have a clue one way or the other, but even if it was the prior case (we base our model on where the star is for gravitational computations based on the light we are receiving), that's just what it is -- a model. So if there is a lapse in our understanding that doesn't take into account that the star's gravitational effect on us actually depends on its current position then that may need to be corrected.
to say it's "pulled in a direction where the big mass no longer is" seems incorrect, because above we have "whenever a gravitating object moves inertially, the gravitational acceleration vector at a point removed actually points at where the object actually is at a given instant", due to the cancellaction and abberation effects.
"Indeed, the vector (2.5) does not point toward the “instantaneous”
position of the source, but only toward its position extrapolated from this retarded data" (which is pretty much the same location)
Typical Sci-Fi wormholes have that problem, but there are nevertheless valid GR solutions that look a heckuvalot like wormholes. And they do obey all those conservation laws. One can think of it as the wormhole mouths being objects (made out of space rather than matter) that accumulate and lose conserved quantities like mass and momentum and charge as objects enter or leave them, or you can think of it as lines of force getting stretched out to pass through the wormhole mouths whenever an object moves through them, since the fields can't just shear off.
Incidentally, this generally means that you have to be careful about balancing the mass flow in each direction through your wormhole, lest one mouth develop negative mass (and presumably antigravity) from too much stuff leaving it and the other mouth end up shrouded in a black hole.
> The difficultly: Despite the propagation delay, gravity always points to where the object should be, instead of where it was when the gravity was "emitted".
[citation needed]
My understanding is that it points to where the object was, and that the change propagates at the speed of light as gravitational waves.
That's what you would expect, but it results in unstable orbits.
Instead as the object moves, the gravitational field it emits also moves, so you end up feeling the gravity where you would expect it to be if the field transmitted instantly.
It's when the object emitting the field changes direction that things become interesting.
It is a prediction of some physical theories that magnetic monopoles could exist from the origin of the universe (and it kinda seems like they should, 'cause other than the existence of one kind of charge and the other, there's no good reason to see either half of electromagnetism as more fundamental than the other- both kinds of field can generate the other, and how much of each one you think you have depends on your inertial frame since they're relativistic transformations of each other), but no one has shown that you can make them, pulling the poles of a magnet apart like you can pull electrons away from protons.
The difficultly: Despite the propagation delay, gravity always points to where the object should be, instead of where it was when the gravity was "emitted".
The explanation: Just like the object itself is moving, the gravitational field (or electric/magnetic field) is ALSO moving! It moves at exactly the same speed, and in the same direction as the object which created it.
It's "disconnected" from the source - so if the source suddenly changes direction the field it emitted doesn't know about it, and continues to point to where it expected the object to be.
More technical:
Why wormholes are impossible, and why you can not create a single magnetic monopoles:
What about conservation of momentum? If an object is pulled to where the other object is expected to be, not where it is, then momentum exchange between the two of them would seem to not add up!
But it works because you can never create a gravitational or electric field from nothing. You can only move them around, so the momentum always catches up.
What about a magnetic field? You can create those from nothing - ah, but you can only create magnetic dipoles, with opposing fields, so again it works.
But, you can never create a magnetic monopole because you would suddenly have a magnetic "charge" where none existed before and the momentum would not add up. What you can do is create two monopoles, of opposite poles. (So this implies a conservation of magnetic pole, just like conservation of electric charge - assuming monopoles exist.)
What about wormholes? They have the same momentum problem - an object suddenly appears where none was before and it pulls on other objects. You could then move it away before it gets pulled in turn by those objects, and that would violate conservation of momentum. So you can't do that.
And, faster than light objects would have the exact same problem - they could move out of the area before they properly shared the momentum. So I suspect they can't exist either. (Unless there is some complicated math I didn't think of which "fixes" it.)