valenumr said:It is commentary on conservation of momentum and energy.
Imagine a starship that has rotating rings to generate artificial gravity (sci-fi channel stuff) with a central axis. Now, if apply energy or force or work or torque, whatever, to the axis to cause it to rotate WRT to the rings, it is totally possible to know that it is the axis that is rotating and not the rings. You can chose observers who assume the rings rotating WRT the axis or vise versa, but all would end up agreeing the axis was rotating. OTOH, if I applied a torque to the whole ship to really rotate the rings, the axis would not be rotating relative to anyone on the ship. But they would all agree that the ship was rotating due to artificial gravity. Rotating with respect to what? The local geodesic, because all exterior points or constantly moving perpendicular to it. But do you see where the energy was applied?jbriggs444 said:Your claim is wrong in general. An illustrative example would be helpful to work out our disagreement, yes.
Just decide which.valenumr said:... if apply energy or force or work or torque, whatever, ...
The concepts of conservation are fully embodied in Newtons laws. They are not at all discounted in the SM, SR, or GR.weirdoguy said:But conservation of momentum is something more general than "every action has an equal and opposite reaction". In my scenario momentum is conserved (we need to consider momentum of the EM field itself) but Newton's third law is violated.
valenumr said:They are not at all discounted in the SM, SR, or GR.
No. Godel spacetime is a counterexample: objects moving along "comoving" worldlines in this spacetime are moving along geodesics (every point of the object is in free fall), but they have nonzero vorticity, which means they are being "rotated" (not "shear", the shear is zero--the rotation is rigid), but their energy does not change.valenumr said:I suppose we could imagine a really twisted space-time where a body is rotated by shear forces. But does that not still imply an energy transfer?
Your scenario makes no sense. First you say the rings are rotating, then you say you can make the axis "rotate WRT to the rings" as if that makes the rings "not rotating". But that's nonsense; if you didn't do anything to the rings, the rings are still rotating.valenumr said:Imagine a starship that has rotating rings to generate artificial gravity (sci-fi channel stuff) with a central axis. Now, if apply energy or force or work or torque, whatever, to the axis to cause it to rotate WRT to the rings, it is totally possible to know that it is the axis that is rotating and not the rings.
While this is correct, it does not mean what you think it means. Everyone else posting in response to you understands that there are still conservation laws in GR. Continuing to repeat this statement does not make the other things you are saying valid. They aren't.valenumr said:The concepts of conservation are fully embodied in Newtons laws. They are not at all discounted in the SM, SR, or GR.
If I understand your second point correctly, regarding inducing perpendicular spin to the velocity vector, it would induce a torque (say downward)? But this did get off the rails. I'm lost on the point how a body can deviate from a geodesic path without some form of energy transfer.PeterDonis said:No. Godel spacetime is a counterexample: objects moving along "comoving" worldlines in this spacetime are moving along geodesics (every point of the object is in free fall), but they have nonzero vorticity, which means they are being "rotated" (not "shear", the shear is zero--the rotation is rigid), but their energy does not change.
You really, really, really need to stop insisting that your incorrect intuitions are valid. This thread has gone back and forth for several pages now simply because you refuse to consider the possibility that GR does not work the way you think it does.Your scenario makes no sense. First you say the rings are rotating, then you say you can make the axis "rotate WRT to the rings" as if that makes the rings "not rotating". But that's nonsense; if you didn't do anything to the rings, the rings are still rotating.
Also, how would you make an axis rotate? By definition it's the axis, it can't rotate.
A simpler scenario would be starting with the starship not rotating at all (zero vorticity), and applying a torque to make it rotate (nonzero vorticity). This would indeed add some rotational kinetic energy to the starship. But it would do it by applying forces to the different parts of the starship that were parallel to the direction in which those parts of the starship move. Everyone else in this thread already agrees that in this case, energy will be transferred. What they are saying, that you are refusing to recognize, is that if a force is applied perpendicular to the direction of motion, there is no energy transferred (momentum is transferred but energy is not).
For a simple example of a force that transfers zero energy, work out what happens to a charged particle in a magnetic field. The magnetic force is always perpendicular to the particle's velocity (this is obvious from the Lorentz force formula), so the particle's energy does not change.While this is correct, it does not mean what you think it means. Everyone else posting in response to you understands that there are still conservation laws in GR. Continuing to repeat this statement does not make the other things you are saying valid. They aren't.
Keep things simple. Go back to the case of two billiard balls connected by a thread, rotating about one another. Let us put them in a flat space-time. Let us adopt the frame of reference where their combined center of mass is stationary.valenumr said:If I understand your second point correctly, regarding inducing perpendicular spin to the velocity vector, it would induce a torque (say downward)? But this did get off the rails. I'm lost on the point how a body can deviate from a geodesic path without some form of energy transfer.
And re: axis... I suppose I could have said someone just spun a free floating pencil for the first case. Observers would agree as to what actually had angular momentum, No?PeterDonis said:No. Godel spacetime is a counterexample: objects moving along "comoving" worldlines in this spacetime are moving along geodesics (every point of the object is in free fall), but they have nonzero vorticity, which means they are being "rotated" (not "shear", the shear is zero--the rotation is rigid), but their energy does not change.
You really, really, really need to stop insisting that your incorrect intuitions are valid. This thread has gone back and forth for several pages now simply because you refuse to consider the possibility that GR does not work the way you think it does.Your scenario makes no sense. First you say the rings are rotating, then you say you can make the axis "rotate WRT to the rings" as if that makes the rings "not rotating". But that's nonsense; if you didn't do anything to the rings, the rings are still rotating.
Also, how would you make an axis rotate? By definition it's the axis, it can't rotate.
A simpler scenario would be starting with the starship not rotating at all (zero vorticity), and applying a torque to make it rotate (nonzero vorticity). This would indeed add some rotational kinetic energy to the starship. But it would do it by applying forces to the different parts of the starship that were parallel to the direction in which those parts of the starship move. Everyone else in this thread already agrees that in this case, energy will be transferred. What they are saying, that you are refusing to recognize, is that if a force is applied perpendicular to the direction of motion, there is no energy transferred (momentum is transferred but energy is not).
For a simple example of a force that transfers zero energy, work out what happens to a charged particle in a magnetic field. The magnetic force is always perpendicular to the particle's velocity (this is obvious from the Lorentz force formula), so the particle's energy does not change.While this is correct, it does not mean what you think it means. Everyone else posting in response to you understands that there are still conservation laws in GR. Continuing to repeat this statement does not make the other things you are saying valid. They aren't.
If a force is applied perpendicular to velocity then there is a deviation from a geodesic without energy transfer. As I showed abovevalenumr said:I'm lost on the point how a body can deviate from a geodesic path without some form of energy transfer.
I'm still working through it.Dale said:If a force is applied perpendicular to velocity then there is a deviation from a geodesic without energy transfer. As I showed above
I am still trying to reconcile how anything (macroscopic) can alter course without an energy input.Dale said:If a force is applied perpendicular to velocity then there is a deviation from a geodesic without energy transfer. As I showed above
I am guessing here that taking one's foot off the accelerator, putting the vehicle in neutral and turning the steering wheel counts as an "energy input" in your book?valenumr said:I am still trying to reconcile how anything (macroscopic) can alter course without an energy input.
Did you not follow the explanation above? If so, perhaps start with pointing out the place where you first get confused. We can go from there.valenumr said:I am still trying to reconcile how anything (macroscopic) can alter course without an energy input.
I would recommend pausing until you can finish working through it.valenumr said:I'm still working through it.
Maybe you are confusing energy with force?valenumr said:I am still trying to reconcile how anything (macroscopic) can alter course without an energy input.
That's not a good analogy. Friction dissipates the vehicles energy.jbriggs444 said:I am guessing here that taking one's foot off the accelerator, putting the vehicle in neutral and turning the steering wheel counts as an "energy input" in your book?
We've given you good analogies. But you've ignored them all.valenumr said:That's not a good analogy. Friction dissipates the vehicles energy.
I missed this earlier. No I do not claim that. The external force is indeed required.valenumr said:So you both claim that a fundamental principal of GR, an "observer" in "free fall" along a geodesic can deviate from that path without any external force applied? Ok.
Perhaps I am using the wrong term from the outset, but I also don't see how energy, momentum, and force can be extricated. I'm not saying that energy is used up, just transferred.A.T. said:Maybe you are confusing energy with force?
Going around in circles. I repeat: from what to what? From one billiard ball through a thread to another billiard ball?valenumr said:Perhaps I am using the wrong term from the outset, but I also don't see how energy, momentum, and force can be extricated. I'm not saying that energy is used up, just transferred.
valenumr said:Perhaps I am using the wrong term from the outset, but I also don't see how energy, momentum, and force can be extricated. I'm not saying that energy is used up, just transferred.
From one object to another.jbriggs444 said:Going around in circles. I repeat: from what to what?
So we have these two billiard balls with a thread between them. Please identify the energy transfer.valenumr said:From one object to another.
Look, if you want to idealize a frictionless surface and perfect string, you are modeling a system where nothing loses energy. But if one ball gains energy, the other must lose some.jbriggs444 said:So we have these two billiard balls with a thread between them. Please identify the energy transfer.
Neither ball gains energy. Neither ball loses energy. Both orbit at constant speed. Neither follows a geodesic. Your claim is that because a geodesic is not followed, energy must be transferred. But when challenged on the point, you have no answer.valenumr said:Look, if you want to idealize a frictionless surface and perfect string, you are modeling a system where nothing loses energy. But if one ball gains energy, the other must lose some.
Gravity is indeed a fictitious force in GR, the same way that centrifugal and coriolis are fictitious forces in classical mechanics (and GR). A fictitious force is one that causes proper acceleration, as opposed to coordinate acceleration; if you're not already clear about this essentiall distinction you'l want to look for some of our many threads about proper acceleration.valenumr said:But is not gravitational acceleration in GR a fictitious force? An object traveling along a geodesic is a rest frame? Or is that totally a misunderstanding on my part?
Well, this is the crux.. I'm saying an object deviating from it's geodesic must necessarily change energy. That is all.jbriggs444 said:You keep dodging your own scenario. You have a moving object subject to an external force. What makes you think it must gain energy?
And that is wrong. Again.valenumr said:Well, this is the crux.. I'm saying an object deviating from it's geodesic must necessarily change energy. That is all.
Well, I see your point. It doesn't change energy, but perhaps increases in kinetic energy and loses potential energy or vice versa.jbriggs444 said:And that is wrong. Again.
See subsequent edit in the post you quote. A viable claim would be:valenumr said:Well, I see your point. It doesn't change energy, but perhaps increases in kinetic energy and loses potential energy or vice versa.
But how does it make that transition without energy applied? A rocket doesn't lift ff magically.valenumr said:Well, I see your point. It doesn't change energy, but perhaps increases in kinetic energy and loses potential energy or vice versa.