Gravity and Spin
Posted: Thu Apr 10, 2008 5:28 am
I am a bear of very small brain, and it takes me a long time to work some things out, so please forgive me if I ramble.
The idea that 'gravity is rotation' - or at least 'gravity is curvature', which seems the same thing to me - seems to come up a lot, both in conventional Einsteinian Relativity and in various spooky aether systems. But I still can't really get a sensible idea into my head of how this equivalence works.
Take ordinary rotation, for instance. If you spin a 3D object, we notice a few things:
1) We get a force pulling objects attached to the rim of the spinning thing, to the centre (centripetal) through whatever it is that connects us to that centre (the molecular bonds of the material, I guess). The inertia of the orbiting object reacts against this and this 'fictitious' force of inertia (fictitious because it's zero in an inertial frame) pushes outwards. The result is that the orbiting object 'feels' an outward push. This is often called 'artificial gravity', but it's not at all like gravity in many ways.
2) You can only spin or orbit in a two-dimensional plane. Centripetal/centrifugal force is therefore a two-dimensional force. Gravity, however, is three-dimensional. It's like orbiting at the same speed in an infinite number of directions at once - or at least in all three dimensions. And not in a tumble, but a smooth sort of spherical orbit. What's up with that?
3) If you reverse the spin of an object, you do *not* get a reversed centripetal/centrifugal force. But gravity is the opposite - it sucks us in. You can't artificially generate through ordinary 2D spin of a 3D object, a force like gravity that 'sucks things toward the centre' (even though centripetal force 'pushes things toward the centre' but is felt as an outward push). So as well as being 3D, gravity is like a sort of 'anti-spin' - it's like not us but the whole rest of the universe is spinning around us, flinging us inward toward our centre of mass. Does that make sense either?
4) Physicists like to talk about 'inertial frames of reference' versus 'accelerated frames', of which 'rotating frames' are a special case. Rotating frames seem to be considered kind of icky and best avoided - hence that whole business about 'it's not really centrifugal force, it only seems like that from a rotating frame; but the real truth of what's happening is in the inertial frame, where it's clearly centripetal'.
But a) actually there are no inertial frames in nature, *everything* rotates, from atoms to stars - things that seem to be 'moving straight' are just orbiting in a very large circle. So shouldn't we treat rotating frames as more primitive, more 'natural', than inertial ones?
And b) how does the rotating frame 'know' that it's rotating? It's not like it's got anything to compare against, has it?
If you take a piece of rock in space, and give it a push (strap a disposable rocket on the side) in a straight line, it'll accelerate briefly then go back to being (relatively) inertial again. No constant energy expenditure.
But if you take that same rock, strap the same rocket on at an angle so it imparts a spin, and light it up - the same amount of energy gets burned, the same amount of work gets done, but that rock now starts spinning around its own centre of mass - and that means it is now in a permanently accelerated frame of reference.
Same amount of energy, totally different result. What's up with that?
And how does it know it's rotating, anyway? Okay, I can see how rotation could be considered a kind of mechanical stress; we've somehow warped the curvature (spacetime, even) of that rock, such that the atoms on one side want to go left and the atoms on the other want to go right... or whatever. So we've dumped that rocket energy into the chemical bonds, maybe.
But still. That a rock 'knows' that it's rotating around itself, with no external cues, that it even 'feels' a stress at all, means that somehow it must have a connection to an absolute rest point inside it, at its centre of mass. It must have something to compare *against*.
But in physics, even the ordinary Newtonian kind, we don't believe there exists such a thing as a priviledged reference frame, surely. But we do, in rotating frames. Seriously, what's up with that?
Best as I can figure, even Mach's principle doesn't make sense of this; it just shrugs and says 'it's just so, there's a spooky connection, maybe gravity, maybe with all the rest of the mass of the universe'. But that still assumes that gravity travels instantaneously; that my spinning rock can immediately feel a kickback from the Whole Darn Universe.
5) If gravity is not quite the same thing as spin in two dimensions of a 3D object - but if it is somehow a kind of curvature, or spin - is it conceivable that it might be something like a spin in four dimensions?
I have no idea what I mean by that, which is why I apologise. But I'm wondering if it might have something to do with Hamilton's quarternions, which seem to me to be all about the idea of 'extension plus rotation' (from complex numbers, expressed in polar coordinates, which I can almost grok) extended to something like 'an extension in time plus three dimensions of rotation in space'.
More about quaternions if I make any more sense of them, and if anyone is interested.
6) Since spin is a purely mechanical quantity, no electric or magnetic forces needed, is it possible that there might be ways to think of a mechanical coupling between ordinary 2D spin and '4D spin' - as Laithwaite seemed to believe was possible, and as Keely and Carr seem to talk about?
The idea that 'gravity is rotation' - or at least 'gravity is curvature', which seems the same thing to me - seems to come up a lot, both in conventional Einsteinian Relativity and in various spooky aether systems. But I still can't really get a sensible idea into my head of how this equivalence works.
Take ordinary rotation, for instance. If you spin a 3D object, we notice a few things:
1) We get a force pulling objects attached to the rim of the spinning thing, to the centre (centripetal) through whatever it is that connects us to that centre (the molecular bonds of the material, I guess). The inertia of the orbiting object reacts against this and this 'fictitious' force of inertia (fictitious because it's zero in an inertial frame) pushes outwards. The result is that the orbiting object 'feels' an outward push. This is often called 'artificial gravity', but it's not at all like gravity in many ways.
2) You can only spin or orbit in a two-dimensional plane. Centripetal/centrifugal force is therefore a two-dimensional force. Gravity, however, is three-dimensional. It's like orbiting at the same speed in an infinite number of directions at once - or at least in all three dimensions. And not in a tumble, but a smooth sort of spherical orbit. What's up with that?
3) If you reverse the spin of an object, you do *not* get a reversed centripetal/centrifugal force. But gravity is the opposite - it sucks us in. You can't artificially generate through ordinary 2D spin of a 3D object, a force like gravity that 'sucks things toward the centre' (even though centripetal force 'pushes things toward the centre' but is felt as an outward push). So as well as being 3D, gravity is like a sort of 'anti-spin' - it's like not us but the whole rest of the universe is spinning around us, flinging us inward toward our centre of mass. Does that make sense either?
4) Physicists like to talk about 'inertial frames of reference' versus 'accelerated frames', of which 'rotating frames' are a special case. Rotating frames seem to be considered kind of icky and best avoided - hence that whole business about 'it's not really centrifugal force, it only seems like that from a rotating frame; but the real truth of what's happening is in the inertial frame, where it's clearly centripetal'.
But a) actually there are no inertial frames in nature, *everything* rotates, from atoms to stars - things that seem to be 'moving straight' are just orbiting in a very large circle. So shouldn't we treat rotating frames as more primitive, more 'natural', than inertial ones?
And b) how does the rotating frame 'know' that it's rotating? It's not like it's got anything to compare against, has it?
If you take a piece of rock in space, and give it a push (strap a disposable rocket on the side) in a straight line, it'll accelerate briefly then go back to being (relatively) inertial again. No constant energy expenditure.
But if you take that same rock, strap the same rocket on at an angle so it imparts a spin, and light it up - the same amount of energy gets burned, the same amount of work gets done, but that rock now starts spinning around its own centre of mass - and that means it is now in a permanently accelerated frame of reference.
Same amount of energy, totally different result. What's up with that?
And how does it know it's rotating, anyway? Okay, I can see how rotation could be considered a kind of mechanical stress; we've somehow warped the curvature (spacetime, even) of that rock, such that the atoms on one side want to go left and the atoms on the other want to go right... or whatever. So we've dumped that rocket energy into the chemical bonds, maybe.
But still. That a rock 'knows' that it's rotating around itself, with no external cues, that it even 'feels' a stress at all, means that somehow it must have a connection to an absolute rest point inside it, at its centre of mass. It must have something to compare *against*.
But in physics, even the ordinary Newtonian kind, we don't believe there exists such a thing as a priviledged reference frame, surely. But we do, in rotating frames. Seriously, what's up with that?
Best as I can figure, even Mach's principle doesn't make sense of this; it just shrugs and says 'it's just so, there's a spooky connection, maybe gravity, maybe with all the rest of the mass of the universe'. But that still assumes that gravity travels instantaneously; that my spinning rock can immediately feel a kickback from the Whole Darn Universe.
5) If gravity is not quite the same thing as spin in two dimensions of a 3D object - but if it is somehow a kind of curvature, or spin - is it conceivable that it might be something like a spin in four dimensions?
I have no idea what I mean by that, which is why I apologise. But I'm wondering if it might have something to do with Hamilton's quarternions, which seem to me to be all about the idea of 'extension plus rotation' (from complex numbers, expressed in polar coordinates, which I can almost grok) extended to something like 'an extension in time plus three dimensions of rotation in space'.
More about quaternions if I make any more sense of them, and if anyone is interested.
6) Since spin is a purely mechanical quantity, no electric or magnetic forces needed, is it possible that there might be ways to think of a mechanical coupling between ordinary 2D spin and '4D spin' - as Laithwaite seemed to believe was possible, and as Keely and Carr seem to talk about?