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alpha_wolf
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Does a rappidly spinning mass experience an effect in GR that is equivalent to mass dilation in SR? I so, would it have a stronger gravitational field than at rest?
No. There is a GR effect, but it is not equivalent to the SR effect. The GR effect is to induce cross terms in the gravitational force. SR is just a special case of GR; it does not account for graviational effects.alpha_wolf said:Does a rappidly spinning mass experience an effect in GR that is equivalent to mass dilation in SR?
I believe so. But also a different gravitational field (i.e. gravetomagnetic).alpha_wolf said:... would it have a stronger gravitational field than at rest?
I sould have written "similar", not "equivalent".. What I meant was an increase in mass or something like that due to angular velocity, similar to how mass increases due to linear velocity in SR.turin said:No. There is a GR effect, but it is not equivalent to the SR effect. The GR effect is to induce cross terms in the gravitational force. SR is just a special case of GR; it does not account for graviational effects.
Hmm.. is there some simple formula that would relate the generated gravitaional field (in terms of force strengh - I don't care much about the resulting spacetime geometry..) to the rest mass, radius, and angular velocity of the body, assumming it some simple shape like an infnitely thin ring? Or is this one of those devilish calculations that leave one's lower jaw at approximately ground level?I believe so. But also a different gravitational field (i.e. gravetomagnetic).
The SR effect is a GR effect, since GR contains SR. I thought that you were asking for something that GR would predict that SR would not. There is a relativistic mass increase that SR predicts for a spinning mass without appealing to GR. GR predicts an added magnetic-ype effect.alpha_wolf said:What I meant was an increase in mass or something like that due to angular velocity, similar to how mass increases due to linear velocity in SR.
Assuming an "ordinary" situation like the Earth rotating, you use the weak field approximation. I haven't done the calculation, but I'm sure you can find it all over the place in textbooks and papers. Look for PN1 (1st order post Newtonian approximation). As an example, Einstein gives a brief treatment in The Meaning of Relativity that shows the emergence of a vector type potential.alpha_wolf said:.. is there some simple formula that would relate the generated gravitaional field ... the rest mass, radius, and angular velocity of the body, assumming it some simple shape like an infnitely thin ring?
This termonolgy isn't really GR incantation. If you know what magnetism is, then just take the straightforward analogy thatalpha_wolf said:...could you expand a bit on the cross terms in the gravitational field and the gravetomagnetic effect? I'm afraid I'm not very familiar with GR terminology...
Oh.. I didn't know SR handles rotating bodies..turin said:The SR effect is a GR effect, since GR contains SR. I thought that you were asking for something that GR would predict that SR would not. There is a relativistic mass increase that SR predicts for a spinning mass without appealing to GR. GR predicts an added magnetic-ype effect.
I understand the verbal meaning, but I don't quite get the physical meaning of the term.. how does this effect work?This termonolgy isn't really GR incantation. If you know what magnetism is, then just take the straightforward analogy that
electric:magnetic::gravitational:gravetomagnetic
A word of caution though. The analogy is only an approximate analogy. It arrises from some low order approxiation of Einstein's equation.
You mean something like a vector cross product?You can think of the cross terms as products of unlike vector components.
Well, in some contexts SR has to be finagled quite a bit (a rotating frame of reference being one of them) in order to apply, so this can be misleading. It is usually not a good idea to rely on SR to consider non-inertial reference frames. If you are willing to suspend the curvature of space-time (i.e. in the absense of "modern" gravitation), then you can get away with treating a rotating body in SR by considering it from an inertial frame (i.e. the frame against which the body rotates). You actually get quite an interesting result: even using SR, you can realize that the 3-D geometry in the rest frame of the body is non-Euclidean (i.e. curved). To be more specific, the SR treatment results in the geometrical ratio of C/D > π in the rest frame of a rotating body (I think it's greater than).alpha_wolf said:Oh.. I didn't know SR handles rotating bodies...
Do you understand how magnetism arrises from electrostatics? Around the beginning of the 20th century, the mathematical formulation of physics acquired a powerful criterion: covariance. In order for the low order (but not the lowest order) gravitational field equations to maintain their covariant nature, magnetic-type manifestations of the gravitational interaction must exist. This is quite similar to the reason why Maxwell's equations unite the electric and magnetic fields, and this similarity is why most people refer to the generalization as gravetomagnetism.alpha_wolf said:I understand the verbal meaning, but I don't quite get the physical meaning of the term.. how does this effect work?
Yes.alpha_wolf said:You mean something like a vector cross product?
Ah, ok. I.e. gravitomagnetism relates to gravity like magnetism relates to electrostatics, and not that gravity somehow creates a megnetic force of sorts... Hmm, yea, the latter would mean that the grand unification theory has already been found, at least partially.turin said:Do you understand how magnetism arrises from electrostatics? Around the beginning of the 20th century, the mathematical formulation of physics acquired a powerful criterion: covariance. In order for the low order (but not the lowest order) gravitational field equations to maintain their covariant nature, magnetic-type manifestations of the gravitational interaction must exist. This is quite similar to the reason why Maxwell's equations unite the electric and magnetic fields, and this similarity is why most people refer to the generalization as gravetomagnetism.
Beware, some may try to obscure the meaning to just that.alpha_wolf said:... not that gravity somehow creates a megnetic force of sorts...
alpha_wolf said:Does a rappidly spinning mass experience an effect in GR that is equivalent to mass dilation in SR? I so, would it have a stronger gravitational field than at rest?
alpha_wolf said:Does a rapidly spinning mass experience an effect in GR that is equivalent to mass dilation in SR? I so, would it have a stronger gravitational field than at rest?
turin said:No. There is a GR effect, but it is not equivalent to the SR effect. The GR effect is to induce cross terms in the gravitational force. SR is just a special case of GR; it does not account for graviational effects.
rtharbaugh1 said:I would rewrite the question as follows: Does a rapidly spinning mass have greater gravitational attraction than an otherwise identical mass that is not spinning?
rtharbaugh1 said:I imagine an experiment as follows: a pair of large massive disks in free space (no extraneous mass or charge fields) is set to rotate in the plane of the disks about an axis through the centers of mass, rather like spinning a pair of wheels on an axle. Does the attraction measured as a compressive force on the axis between the two disks vary with the rate of rotation of the disks? Does it make a difference if the disks are rotated in the same or in opposite directions?
It seems to me that if the disks are rotated they should show some attractive force along the axis.
The theory of general relativity (GR) describes gravity as the curvature of space-time caused by massive objects, while special relativity (SR) describes gravity as a result of the warping of space and time by massive objects. In GR, gravity is a manifestation of the curvature of space-time, while in SR, gravity is a result of the mass of an object warping the space it occupies.
A rapidly spinning mass causes a dragging effect on the surrounding space-time which results in a distortion of the gravitational field. This phenomenon is known as frame-dragging and is predicted by general relativity. It means that the space and time around a rapidly spinning mass are dragged along with it, affecting the gravitational field in its vicinity.
Yes, the effects of a rapidly spinning mass on the gravitational field have been observed through various experiments, such as the Gravity Probe B mission by NASA. This mission measured the frame-dragging effect of Earth's rotation on the surrounding space and confirmed the predictions of general relativity.
The frame-dragging effect caused by a rapidly spinning mass can cause objects in its vicinity to experience orbital precession, where their orbits deviate from what would be expected in a non-spinning mass. This can also affect the stability of satellites and other objects orbiting the spinning mass.
While the frame-dragging effect may not have immediate practical applications, it is important for our understanding of gravity and the universe. However, there are some proposed concepts that could utilize this effect, such as using rotating black holes as power sources for spacecraft propulsion systems.