B How does GR explain increase/decrease in speed?

[Dale]

I agree this is a problem with Galilean relativity as well.
It is a problem when everything is relative and there is no absolute reference frame.

If you want I can open another thread about KE in GR.

I think that you need to learn about KE in Newtonian physics first.

Do you understand, in Newtonian physics, that KE is frame variant? For example, if a car accelerated from 0 m/s wrt the Earth to 100 m/s then its KE increased in that frame, but there is also a frame where that exact same car at the exact same moment accelerated from -100 m/s to 0 m/s and therefore lost KE? This is not GR, this is Newtonian physics.

 

[Nugatory]

Let's remove the atmosphere and do this in a vacuum to simplify things.

If the feather and the apple fall at the same rate, because the acceleration depends only on the Earth's mass, then the Earth's acceleration upwards must also be the same in both cases. But if we switch perspectives, then the Earth's acceleration must only depend on the mass of the feather or the apple, which are different, so how can the Earth's acceleration upwards be the same in both cases?

The upwards acceleration of the Earth's surface is unrelated to the mass of the apple or the feather so is the same in both cases.

The apparent difference between the acceleration towards the feather and the apple is completely due to the air pushing the feather upwards more than the apple, so if we remove the atmosphere that difference would disappear. Remember how astronaut David Scott dropped a hammer and a feather while standing on the airless surface of the moon? The moon's surface hit them both at the same time.

 

[PeterDonis]

Ball falling to quasar:
KE from Big Bang -> PE of ball -> KE of ball towards quasar

The KE from the Big Bang is irrelevant if we are talking about a ball falling to a quasar. The PE of the ball is just a function of whatever distance it happens to be from the quasar when it starts falling. That is the PE that gets converted to KE, in Newtonian terms, as the ball falls.

I use it in the sense of defining a (0,0,0,0) from which all events are measured.

Ok, so by "frame of reference" you mean "coordinate chart". That's fine.

The piece of wood has a certain strength which will only be breached by an impacting object if the difference in KE/momentum between the object and the wood is at least a certain amount.

Yes. Phrasing things in terms of the difference between the objects makes it clearer that you are talking about something that is frame-independent.

Initially, the apple is hanging motionless above the wood, so they have zero relative KE and momentum

Yes. Again, the term "relative" here makes it clear what frame-independent fact we are talking about.

At the point of impact, if the apple punched through the wood, then there is at least that minimum amount of KE/momentum difference between the two. This fact, too, must be explained by all observers, regardless of their frame of reference.

Yes.

Where did this difference in KE/momentum come from, using a purely geometric explanation?

The fact that the wood and the apple are following different paths through spacetime, that intersect with a particular relative KE/momentum. The apple's path is a geodesic--it is the straightest path the apple can follow in its local region of spacetime. The wood's path is not a geodesic; it is being accelerated towards the apple by the surface of the Earth. So, geometrically, the wood's path is curved and the apple's path is straight, and the path curvature of the wood's path ("path curvature" is just the geometric way of saying "proper acceleration") means that the two paths meet at an angle; the angle is the geometric representation of the relative KE/momentum between the two. Under the conditions of the problem, the angle is large enough to provide sufficient relative KE/momentum for the apple to punch a hole in the wood.

 

[Jakaha]

I think that you need to learn about KE in Newtonian physics first.

Do you understand, in Newtonian physics, that KE is frame variant? For example, if a car accelerated from 0 m/s wrt the Earth to 100 m/s then its KE increased in that frame, but there is also a frame where that exact same car at the exact same moment accelerated from -100 m/s to 0 m/s and therefore lost KE? This is not GR, this is Newtonian physics.

I know KE is relative. In any model of physics without an absolute reference frame, of course velocity and all derived quantities will be relative.
My question is not about the relativity of KE, but how pure geometry can explain the addition/removal of KE from an object.
It may well be that GR is silent on the subject and that's fine. I wanted to know if GR says anything.

 

[Jakaha]

The upwards acceleration of the Earth's surface is unrelated to the mass of the apple or the feather so is the same in both cases.

The apparent difference between the acceleration towards the feather and the apple is completely due to the air pushing the feather upwards more than the apple, so if we remove the atmosphere that difference would disappear. Remember how astronaut David Scott dropped a hammer and a feather while standing on the airless surface of the moon? The moon's surface hit them both at the same time.

This is getting perhaps a bit off topic so maybe we can move it to a new thread?
In any case, please see my post #50.
I would say the experiment on the moon would give different results if we have a sufficiently sensitive instrument to detect the minuscule time difference between the feather and the hammer.

My reasoning is simple: imagine the whole thing from the pov of the feather/hammer. Each of them has a completely different curvature and the moon falling into them will have a different acceleration.

 

[PeterDonis]

how pure geometry can explain the addition/removal of KE from an object.

Pure geometry explains the paths that all freely falling objects take through spacetime, and how those paths intersect. Pure geometry plus knowledge of forces applied (such as the force applied by the Earth to objects in contact with it) explains the paths that all objects, freely falling or not, take through spacetime, and how those paths intersect. Knowledge of how all the paths intersect is equivalent to knowledge of all the KE/momentum of objects relative to each other when they intersect. That's all there is to it.

 

[Dale]

I know KE is relative. In any model of physics without an absolute reference frame, of course velocity and all derived quantities will be relative.

OK, so let's then talk about KE in non inertial frames. (Still in Newtonian physics)

Suppose that you are in a non inertial frame, specifically, one that is uniformly accelerating in a straight line. In that non inertial frame, an inertial object starting at rest will accelerate, continuously gaining KE. Where did that KE come from?

 

[PeterDonis]

I would say the experiment on the moon would give different results if we have a sufficiently sensitive instrument to detect the minuscule time difference between the feather and the hammer.

In making this claim, you are claiming that GR is false in a regime where its predictions have been confirmed to many decimal places. That doesn't seem like good ground to stand on to me (pun intended).

My reasoning is simple: imagine the whole thing from the pov of the feather/hammer. Each of them has a completely different curvature and the moon falling into them will have a different acceleration.

No, they don't have "different curvature" in any sense. They are both freely falling objects, at rest relative to each other, so their paths are parallel geodesics of the same local spacetime geometry. That means the Moon's surface accelerates the same relative to both of them.

 

[Jakaha]

In making this claim, you are claiming that GR is false in a regime where its predictions have been confirmed to many decimal places. That doesn't seem like good ground to stand on to me (pun intended).

I don't think my statement contradicts GR. In fact I am saying that GR demands the feather and hammer fall at different rates. The whole thing makes more sense if you think of the moon falling into the feather or the hammer.

No, they don't have "different curvature" in any sense. They are both freely falling objects, at rest relative to each other, so their paths are parallel geodesics of the same local spacetime geometry. That means the Moon's surface accelerates the same relative to both of them.

As I wrote, it's about changing your point of view. Forget that the moon is a massive body.

Think of the feather and its curvature of space-time. Now see the moon reacting to that curvature and accelerating.

Now imagine a different scenario with the hammer and its curvature and calculate the moon's acceleration.

You will get different values because the feather and the hammer have different masses, i.e. curvature.

 

[Jakaha]

The KE from the Big Bang is irrelevant if we are talking about a ball falling to a quasar. The PE of the ball is just a function of whatever distance it happens to be from the quasar when it starts falling. That is the PE that gets converted to KE, in Newtonian terms, as the ball falls.

And where did this PE come from?
Answer: the KE that the Big Bang provided when it separated the ball and the quasar by sending them their separate ways billions of years ago.

The fact that the wood and the apple are following different paths through spacetime, that intersect with a particular relative KE/momentum. The apple's path is a geodesic--it is the straightest path the apple can follow in its local region of spacetime. The wood's path is not a geodesic; it is being accelerated towards the apple by the surface of the Earth. So, geometrically, the wood's path is curved and the apple's path is straight, and the path curvature of the wood's path ("path curvature" is just the geometric way of saying "proper acceleration") means that the two paths meet at an angle; the angle is the geometric representation of the relative KE/momentum between the two. Under the conditions of the problem, the angle is large enough to provide sufficient relative KE/momentum for the apple to punch a hole in the wood.

The wood is the same as the Earth. There is no extra acceleration. Think of a planet made of wood, if it makes the problem simpler.

 

[Jakaha]

OK, so let's then talk about KE in non inertial frames. (Still in Newtonian physics)

Suppose that you are in a non inertial frame, specifically, one that is uniformly accelerating in a straight line. In that non inertial frame, an inertial object starting at rest will accelerate, continuously gaining KE. Where did that KE come from?

In Newtonian physics we talk about forces as the agents of energy transfer.
That is why I am seeking the agent of energy transfer in GR where gravity is no longer a force.

 

[Dale]

In Newtonian physics we talk about forces as the agents of energy transfer.
That is why I am seeking the agent of energy transfer in GR where gravity is no longer a force.

Forces transfer momentum, not energy. They are not completely disconnected, but they are not the same.

Going back to the non inertial frame I asked about previously. Where does the energy come from?

 

[Jakaha]

In fact, both GR and Newtonian gravity say that the feather and the hammer will 'fall' at different rates.
It's just that people forget the feather and the hammer are not 'falling' to the moon.
Rather, the feather and the moon, or the hammer and the moon, are 'falling' to their common center of gravity.

 

[PeterDonis]

Think of the feather and its curvature of space-time.

The spacetime curvature produced by the feather is negligible. So is the spacetime curvature produced by the hammer. That is the basis for the GR prediction that I gave in my last post, which is certainly valid to any accuracy of measurement we are capable of now or in the foreseeable future.

If you insist on including the spacetime curvature due to the feather and hammer, then, as I said in an earlier post, there is no known exact solution in GR that describes the spacetime; you would have to solve it numerically. But there's no point to that if you haven't even gotten a good understanding of the simpler cases that we can solve exactly, like the case where the curvature produced by all bodies except one (the Moon in this case) is negligible. You don't seem to grasp that case yet, so talking about much more complicated cases that we can't even solve exactly is pointless.

 

[Jakaha]

Forces transfer momentum, not energy. They are not completely disconnected, but they are not the same.

Going back to the non inertial frame I asked about previously. Where does the energy come from?

The usual trick would be to imagine a fictitious force acting on the other object and imparting it KE.

As I wrote, in any model of physics without an absolute frame of reference, all velocity-derived attributes will be frame-dependent.

 

[PeterDonis]

And where did this PE come from?
Answer: the KE that the Big Bang provided when it separated the ball and the quasar by sending them their separate ways billions of years ago.

No, this answer is incorrect. The PE of the ball relative to the quasar only depends on its position relative to the quasar. It does not depend on how it got there. I could construct a ball on the spot and drop it towards the quasar, and it would have the same PE as a ball that had existed since the Big Bang.

Also, the concept of potential energy only applies in a static situation anyway--"static" meaning that the body which is the source of gravity, the quasar in this case, is at rest. The universe as a whole is not static, so the concept of "potential energy" in the universe as a whole, looking at how things evolved since the Big Bang, is not even well-defined.

 

[Jakaha]

The spacetime curvature produced by the feather is negligible. So is the spacetime curvature produced by the hammer. That is the basis for the GR prediction that I gave in my last post, which is certainly valid to any accuracy of measurement we are capable of now or in the foreseeable future.

If you insist on including the spacetime curvature due to the feather and hammer, then, as I said in an earlier post, there is no known exact solution in GR that describes the spacetime; you would have to solve it numerically. But there's no point to that if you haven't even gotten a good understanding of the simpler cases that we can solve exactly, like the case where the curvature produced by all bodies except one (the Moon in this case) is negligible. You don't seem to grasp that case yet, so talking about much more complicated cases that we can't even solve exactly is pointless.

Never mind the ad hominems.

I explained why both GR and Newtonian gravity predict that the feather and hammer will 'fall' at different rates towards their common center of gravity.
If you don't understand it, that's fine.

 

[PeterDonis]

I explained why both GR and Newtonian gravity predict that the feather and hammer will 'fall' at different rates towards their common center of gravity.

You "explained" something that, while it is true in principle, is negligible in practical terms and in any case irrelevant to the discussion in this thread. As I said, if we haven't come to a common understanding of the simplest possible case, where there is only one gravitating body and nothing else produces any curvature, then having a productive discussion about more complicated cases is pointless. You have repeatedly failed to address valid questions about the simpler case, so there's no point in continuing the discussion. Thread closed.