I Is time really moving backwards?

[valenumr]

With Newtonian gravity there is a force.

With gravity in General Relativity, the trajectory is only circular in space, not in space-time. But yes, under this model, there is no force.

An ideal (no air resistance) sling spinning at a constant rate has constant energy.

Ok, I'm understanding two disconnects here. First, energy is more of a scalar and momentum is more of a vector.

But second, you are missing my point that an obect in free fall can do nothing other than continue upon its path without an application of energy.

The sling doesn't start spinning at a constant velocity from zero without energy applied, and and planet orbiting a start will continue to do so indefinitely without external forces.

And energy and momentum are measures only relative to observers. The only thing any external observers can agree upon is mass.

 

[jbriggs444]

Ok, I'm understanding two disconnects here. First, energy is more of a scalar and momentum is more of a vector.

Yes. Nicely noted.

But second, you are missing my point that an obect in free fall can do nothing other than continue upon its path without an application of energy.

But this is wrong. Repeating does not make it less so. A moving object in free fall can be deflected by a sideways force without a change in speed.

The sling doesn't start spinning at a constant velocity from zero without energy applied

As I suspected, you want to consider the special case of an object initially at rest that is then subject to a force from God's hand.

 

[valenumr]

Yes. Nicely noted.

But this is wrong. Repeating does not make it less so. A moving object in free fall can be deflected by a sideways force.

As I suspected, you want to consider the special case of an object initially at rest that is then subject to a force from God's hand.

And I will question how you get to the second point without any energy.

 

[Dale]

you are missing my point that an obect in free fall can do nothing other than continue upon its path without an application of energy

We are not missing the point. We are explicitly stating that it is wrong.

The sling doesn't start spinning at a constant velocity from zero without energy applied

It can start spinning from a non-zero inertial velocity without energy applied. And there is always an infinite number of frames where it starts with non-zero velocity.

 

[jbriggs444]

And I will question how you get to the second point without any energy.

With the flick of a pencil. Reference frames are arbitrary. As is energy. Remember it is not invariant.

Edit: From the usual perspective, it is improper to question how the initial conditions of a thought experiment were created. We take them as given. The important part is what happens while the thought experiment is being carried out.

 

[valenumr]

We are not missing the point. We are explicitly stating that it is wrong.

It can start spinning from a non-zero inertial velocity without energy applied. And there is always an infinite number of frames where it starts with non-zero velocity.

I'm pretty confident that there are observations that can be made to contradict this claim.

 

[jbriggs444]

I'm pretty confident that there are observations that can be made to contradict this claim.

You are going to experimentally observe the non-existence of an infinite number of reference frames even though "frames of reference" are abstract mental constructs with no physical existence?

Perhaps we should step back and consider the question: What is a frame of reference?

Me, I usually settle for "coordinate system". @Dale, probably goes for something like "tetrad field".

 

[valenumr]

You are going to experimentally observe the non-existence of an infinite number of reference frames even though "frames of reference" are mental constructs with no physical existence?

Okay, so 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? I mean, you've completely given up the concept of conservation of energy and the conservation of momentum, fundamental physicals principals, in all your arguments. I don't understand why that is.

 

[jbriggs444]

Okay, so 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? I mean, you've completely given up the concept of conservation of energy and the conservation of momentum, fundamental physicals principals, in all your arguments. I don't understand why that is.

As for the twisted space-time, nope. I just consider initial conditions for a thought experiment separate from the running of the thought experiment.

Energy transfer? From what to what? You've not yet closed your system.

Conservation of energy and conservation of momentum? Those are intact. As long as we are dealing with closed systems [and space-times that are friendly].

Can you slow down and explain what you think a frame of reference is and why we cannot use more than one to describe the same physical system?

 

[valenumr]

You are going to experimentally observe the non-existence of an infinite number of reference frames even though "frames of reference" are mental constructs with no physical existence?

Okay, so 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? I mean, you've completely given up the concept of conservation of energy and the conservation of momentum, fundamental physicals principals, in all your arguments. I don't understand why that is

As for the twisted space-time, nope. I just consider initial conditions for a thought experiment separate from the running of the thought experiment.

Energy transfer? From what to what? You've not yet closed your system.

Conservation of energy and conservation of momentum? Those are intact. As long as we are dealing with closed systems [and space-times that are friendly].

Can you slow down and explain what you think a frame of reference is?

I would say any non-accelerating observer to keep it simple, one in free fall in the GR sense, free from external forces.

 

[jbriggs444]

Okay, so 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? I mean, you've completely given up the concept of conservation of energy and the conservation of momentum, fundamental physicals principals, in all your arguments. I don't understand why that is

I would say any non-accelerating observer to keep it simple, one in free fall in the GR sense, free from external forces.

That is wrong. A frame of reference is not an observer. There is more to it than that. Details. We often use an "observer" as a metaphor for a frame of reference -- the coordinate system in which that observer is at rest. In flat space-time, identifying an inertial observer is adequate to identify a unique coordinate system (up to rotation) in which that observer is at rest at the origin.

However, there is no rule that a frame of reference needs to have a physical observer at rest at its origin.

 

[valenumr]

As for the twisted space-time, nope. I just consider initial conditions for a thought experiment separate from the running of the thought experiment.

Energy transfer? From what to what? You've not yet closed your system.

Conservation of energy and conservation of momentum? Those are intact. As long as we are dealing with closed systems [and space-times that are friendly].

Can you slow down and explain what you think a frame of reference is and why we cannot use more than one to describe the same physical system?

What do you mean from what to what? A gravitational field is generated by a mass, the energy is extracted from that field, thus reducing the energy of said mass.

 

[Dale]

I'm pretty confident that there are observations that can be made to contradict this claim.

I am pretty confident that there are not.

I mean, you've completely given up the concept of conservation of energy and the conservation of momentum, fundamental physicals principals, in all your arguments. I don't understand why that is

We have not. But what you still fail to recognize is that forces transfer momentum not energy. Power transfers energy. It is possible to have a non-zero force and a zero power.

 

[valenumr]

OK, fair enough.
That is wrong. A frame of reference is not an observer. There is more to it than that. Details. We often use an "observer" as a metaphor for a frame of reference -- the coordinate system in which that observer is at rest.

Sorry, "observer". I'm pretty sure when I said an observer uninfluenced by outside force we were in agreement.

 

[jbriggs444]

What do you mean from what to what? A gravitational field is generated by a mass, the energy is extracted from that field, thus reducing the energy of said mass.

You spoke of an energy transfer. I asked for clarification -- transfer from what to what.

I am having trouble deciphering what you mean by having the gravitational field subtract from the energy of the object whose mass is responsible for that field. This is supposed to have something to do with maintaining a satellite in orbit about that mass?

 

[jbriggs444]

Sorry, "observer". I'm pretty sure when I said an observer uninfluenced by outside force we were in agreement.

I was extending the benefit of the doubt. We agree that an observer on a geodesic path can define a coordinate system that is approximately inertial over some local region of space-time.

If you want to go from that to talk about this object now being in orbit under the effects of gravity then the local region is necessarily too large for "approximately inertial" to be even remotely correct.

 

[valenumr]

You spoke of an energy transfer. I asked for clarification -- transfer from what to what.

I am having trouble deciphering what you mean by having the gravitational field subtract from the energy of the object whose mass is responsible for that field. This is supposed to have something to do with maintaining a satellite in orbit about that mass?

Satellites in orbit do in fact extract energy from the planet's rotational velocity. But I don't understand your misunderstanding.

 

[jbriggs444]

Satellites in orbit do in fact extract energy from the planet's rotational velocity. But I don't understand your misunderstanding.

They can, yes, through tidal effects. They can also inject energy into the planet's rotation in the same way. They can radiate energy gravitationally. These are minor effects and not what I thought we were discussing.

 

[valenumr]

They can, yes, through tidal effects. They can also radiate energy gravitationally. These are minor effects and not what I thought we were discussing.

I'll just go back to my original point. A physical body will only deviate from the geodesic if energy is applied. That's all I said. It's not a difficult concept.

 

[jbriggs444]

I'll just go back to my original point. A physical body will only deviate from the geodesic if energy is applied. That's all I said. It's not a difficult concept.

But it is still wrong.

 

[valenumr]

I'll just go back to my original point. A physical body will only deviate from the geodesic if energy is applied. That's all I said. It's not a difficult concept.

To be fair, I may have claimed that it should be observable as to which body had energy applied to it due to the deviation, but the two are intertwined.

 

[jbriggs444]

To be fair, I may have claimed that it should be observable as to which body had energy applied to it due to the deviation, but the two are intertwined.

Bullet and gun. Pebble and blob of putty. The deviation from the geodesic may be either [kinetic] energy positive or [kinetic] energy negative.

 

[valenumr]

But it is still wrong.

Aaaaand were back to square one. If you want to throw out GR and fundamental laws of physics that transcend even that... Well..

 

[jbriggs444]

Aaaaand were back to square one. If you want to throw out GR and fundamental laws of physics that transcend even that... Well..

We could step back to Newtonian mechanics. Things are simpler there.

 

[Dale]

A physical body will only deviate from the geodesic if energy is applied. That's all I said. It's not a difficult concept.

It is not difficult but it is wrong. Uniform circular motion remains an obvious counterexample

 

[valenumr]

We could step back to Newtonian mechanics. Things are simpler there.

We could step back to Newtonian mechanics. Things are simpler there.

You do realize that "every action has an equal and opposite reaction" is still a fundamental tenet of physics, right?

 

[Dale]

Bullet and gun. Pebble and blob of putty. The deviation from the geodesic may be either [kinetic] energy positive or [kinetic] energy negative.

Or neutral.

 

[valenumr]

It is not difficult but it is wrong. Uniform circular motion remains an obvious counterexample

I'm really going to need a better explanation, because uniform is a non-deviating path along the geodesic (only there is no such thing, but elliptical orbits).

 

[jbriggs444]

It is not difficult but it is wrong. Uniform circular motion remains an obvious counterexample

To flesh this out a bit, suppose that we have two billiard balls connected by a thread spinning around each other. They are in orbit about the Earth. Their center of mass traces out an approximate geodesic. The two balls individually are each subject to a force. They each deviate significantly from a geodesic path.

Ordinarily, we would not say that much energy transfer is taking place. In particular, in a frame of reference anchored to the center of mass, the energy transfer rate is exceedingly near zero.

 

[Dale]

Aaaaand were back to square one. If you want to throw out GR and fundamental laws of physics that transcend even that... Well..

Nobody is throwing out any laws of physics, we are simply addressing a misunderstanding on your part.

Do you have a bit of calculus background? Can I write simple differential equations and you will be able to follow?

 

[valenumr]

To flesh this out a bit, we have two billiard balls connected by a thread spinning around each other. They are in orbit about the Earth. Their center of mass traces out an approximate geodesic. The two balls individually are each subject to a force. They each deviate significantly from a geodesic path.

Nobody is throwing out any laws of physics, we are simply addressing a misunderstanding on your part.

Do you have a bit of calculus background? Can I write simple differential equations and you will be able to follow?

Yes. It's been a while since I've exercised those skills, but I've had career experience in mathematical modelling, so it's been applied.

 

[valenumr]

Or neutral.

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.

 

[weirdoguy]

You do realize that "every action has an equal and opposite reaction" is still a fundamental tenet of physics, right?

No, it is not fundamental, because it's not always true, especially in relativity. Consider two positive charges moving along perpendicular straigt lines. Consider magnetic forces that they act on each other. Those "action and reaction" forces are perpendicular, hence not opposite.

 

[jbriggs444]

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.

No. Our claim is different. It is that an object may deviate from a geodesic path without a change in energy.

The proviso is that the frame of reference used to evaluate the energy change must not be one in which the object is initially at rest.

That then leads to the discussion of "what is a reference frame". One could also be drawn into a discussion of "what is energy in the context of General Relativity and is it conserved"?

 

[valenumr]

No, it is not fundamental, because it's not always true, especially in relativity. Consider two positive charges moving along perpendicular straigt lines. Consider magnetic forces that they act on each other. Those "action and reaction" forces are perpendicular, hence not opposite.

It is commentary on conservation of momentum and energy. I'm pretty most folks would agree that those are fundamental principles rooted in Newtons laws. Even qft still respects those laws of conservation.

 

[Dale]

Ok, so first some definitions $\vec p$ is momentum and $\vec F$ is force. Force and momentum are related by $\vec F = \frac{d}{dt}\vec p$ so a force is a change in momentum. Note in particular that both force and momentum are vectors.

Now, energy is a scalar $E$ so it is impossible that $\vec F = \frac{d}{dt}E$ because the left hand side is a vector and the right hand side is a scalar. So we will define a new scalar $P$ called power such that $P= \frac{d}{dt}E$.

What we would like to do is to determine $P$ in terms of $\vec F$. Then $\vec F$ (a vector) will give us the change in $\vec p$ (a vector), and $P$ (a scalar) will give us the change in $E$ (a scalar).

The proof can be found elsewhere, here I will simply assert the result $P=\vec F \cdot \vec v$ where $\vec v$ is the velocity. This is a scalar, like it should be so $\frac{d}{dt}E=\vec F \cdot \vec v$

Now, the part that specifically contradicts your assertion is that it is possible for $\vec F \cdot \vec v =0$ even if $\vec F \ne 0$. This happens if $\vec v$ is perpendicular to $\vec F$ (as in the case of uniform circular motion) or if $\vec v=0$. Hence a force can change momentum without changing energy.

 

[valenumr]

No. Our claim is different. It is that an object may deviate from a geodesic path without a change in energy.

The proviso is that the frame of reference used to evaluate the energy change must not be one in which the object is initially at rest.

That then leads to the discussion of "what is a reference frame".

I've said previously that energy and momentum are observables dependent upon the observer wrt to the observed. But the fact of the matter is deviations from the geodesic can be distinguished by experiment, by all observers. This is acceleration.

 

[jbriggs444]

I've said previously that energy and momentum are observables dependent upon the observer wrt to the observed. But the fact of the matter is deviations from the geodesic can be distinguished by experiment, by all observers. This is acceleration.

Proper acceleration is an invariant. Kinetic energy is not.

 

[valenumr]

OK, fair enough.

Proper acceleration is an invariant. Kinetic energy is not.

See, now we are agreeing. I have said that energy and momentum can be disagreed among observers, but mass is invariant. But. BUT. Acceleration (deviation from the geodesic) is observable and measurable, thus it is possible to tell where energy has been applied. Do you want an illustrative example?

 

[jbriggs444]

See, now we are agreeing. I have said that energy and momentum can be disagreed among observers, but mass is invariant. But. BUT. Acceleration (deviation from the geodesic) is observable and measurable, thus it is possible to tell where energy has been applied. Do you want an illustrative example?

Your claim is not correct in general. In particular, a claim that invariant acceleration means invariant energy transfer is suspect.

Note that there are certainly scenarios where one can find an energy invariant in spite of energy being frame-relative in general. For instance, the energy lost to friction when a bag of cement slides across the bed of a pick-up truck. Despite the kinetic energy of both bag and pick-up truck being frame-relative, the energy lost to friction is invariant. [As I recall, @Dale and I discussed this years ago and he had decided that this scenario led to something invariant even in the context of special relativity]

An illustrative example would be helpful to work out our disagreement, yes.

 

[weirdoguy]

It is commentary on conservation of momentum and energy.

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]

Your claim is wrong in general. An illustrative example would be helpful to work out our disagreement, yes.

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?

 

[A.T.]

... if apply energy or force or work or torque, whatever, ...

Just decide which.

 

[valenumr]

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.

The concepts of conservation are fully embodied in Newtons laws. They are not at all discounted in the SM, SR, or GR.

 

[weirdoguy]

They are not at all discounted in the SM, SR, or GR.

Conservation laws are not, but "every action has an equal and opposite reaction" is and that is what I am saying.

 

[PeterDonis]

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?

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.

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.

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.

The concepts of conservation are fully embodied in Newtons laws. They are not at all discounted in the SM, SR, or GR.

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]

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 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.

 

[jbriggs444]

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.

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.

Neither ball follows a geodesic path. Where is the energy transfer?

Please do not quibble about a time-varying quadrupole moment and gravitational radiation.
Please do not quibble about how this pair of billiard balls came to exist with this state of motion.

 

[valenumr]

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.

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?

 

[Dale]

I'm lost on the point how a body can deviate from a geodesic path without some form of energy transfer.

If a force is applied perpendicular to velocity then there is a deviation from a geodesic without energy transfer. As I showed above