Another question about Gravity -- Does the apple attract the Earth?

[TheQuestionGuy14]

So recently I asked a question about a model of gravity I saw. Turns out I was misinterpretating it, it was the wronv source to use.

Here is a video by PBS ( ) talking about what I was trying to say, that is that some people say 'The Earth rises to catch an apple, not vice versa. But, it doesn't really make any sense to me. If every time anything fell, and the Earth moved to catch it, wouldn't the Earth stray off orbit if it accelerated to catch something, let's say 200 kilometers away; which is still in Earth's orbit. So I was just wondering if the Earth really does move, or is it a simplified term trying to explain The Equivalence Principle? Thanks.

 

[PeroK]

So recently I asked a question about a model of gravity I saw. Turns out I was misinterpretating it, it was the wronv source to use.

Here is a video by PBS ( ) talking about what I was trying to say, that is that some people say 'The Earth rises to catch an apple, not vice versa. But, it doesn't really make any sense to me. If every time anything fell, and the Earth moved to catch it, wouldn't the Earth stray off orbit if it accelerated to catch something, let's say 200 kilometers away; which is still in Earth's orbit. So I was just wondering if the Earth really does move, or is it a simplified term trying to explain The Equivalence Principle? Thanks.

At 35s, he says it is "more appropriate to think of the apple as stationary", which is a) nonsense and b) contradicts the fundamental concept that all motion is relative.

I would ignore this video as fatuous and misleading.

 

[BvU]

Hi guy,

Earth strays 'a little' from its orbit but the orbit of the center of mass of (earth + object) does not.

 

[russ_watters]

So recently I asked a question about a model of gravity I saw. Turns out I was misinterpretating it, it was the wronv source to use.

Here is a video by PBS ( ) talking about what I was trying to say, that is that some people say 'The Earth rises to catch an apple, not vice versa. But, it doesn't really make any sense to me. If every time anything fell, and the Earth moved to catch it, wouldn't the Earth stray off orbit if it accelerated to catch something, let's say 200 kilometers away; which is still in Earth's orbit. So I was just wondering if the Earth really does move, or is it a simplified term trying to explain The Equivalence Principle? Thanks.

Every time you jump, you have both a takeoff and a landing. They are equal and opposite, so there is no net effect on the Earth's orbit.

 

[BvU]

Best way to convince yourself is to wonder why we have high tides twice per day and only one moon

 

[Ibix]

Locally, you are free to regard the Earth's surface as rising up at 10ms^-2 and an apple as not moving. That makes sense: an accelerometer attached to the apple reads nothing while one attached to the floor reads 1g. However, that picture doesn't really work globally. The Earth would have to be expanding at an accelerating rate, and that isn't consistent with observation.

I think this is a general observation about general relativity - models that make sense locally can be flat wrong when you try to globalise them. The reason (at least in this case) is that the floor-is-rising model is essentially a flat spacetime model. The apple follows a geodesic path, so can be regarded as "at rest or moving at constant velocity" as Newton's first law would put it, while the floor accelerates for some reason that we don't examine too closely. Maybe it has rockets. The model works fine as long as you don't push it far enough that the non-flatness of spacetime doesn't come back to bite you. And it does bite if you start talking about the whole Earth.

 

[PeroK]

Locally, you are free to regard the Earth's surface as rising up at 10ms-2 and an apple as not moving.

Why should acceleration imply motion (velocity)?

 

[TheQuestionGuy14]

Locally, you are free to regard the Earth's surface as rising up at 10ms^-2 and an apple as not moving. That makes sense: an accelerometer attached to the apple reads nothing while one attached to the floor reads 1g. However, that picture doesn't really work globally. The Earth would have to be expanding at an accelerating rate, and that isn't consistent with observation.

I think this is a general observation about general relativity - models that make sense locally can be flat wrong when you try to globalise them. The reason (at least in this case) is that the floor-is-rising model is essentially a flat spacetime model. The apple follows a geodesic path, so can be regarded as "at rest or moving at constant velocity" as Newton's first law would put it, while the floor accelerates for some reason that we don't examine too closely. Maybe it has rockets. The model works fine as long as you don't push it far enough that the non-flatness of spacetime doesn't come back to bite you. And it does bite if you start talking about the whole Earth.

If flat parts of the Earth rise up to catch things, then why don't we just see chunks of Earth rising up all the time, when we observe things fall? That's what confuses me.

 

[Khashishi]

I would ignore this video as fatuous and misleading.

It's not a bad video at all. The only issue is terminology: when the video says "true acceleration" it should say "proper acceleration" instead. And instead of saying that gravity doesn't exist, he should say gravity is a fictitious force, meaning it is a result of non-inertial reference frames. These non-inertial reference frames can be very useful and shouldn't be considered "wrong".

 

[PeroK]

It's not a bad video at all. The only issue is terminology: when the video says "true acceleration" it should say "proper acceleration" instead. And instead of saying that gravity doesn't exist, he should say gravity is a fictitious force, meaning it is a result of non-inertial reference frames. These non-inertial reference frames can be very useful and shouldn't be considered "wrong".

It has horribly misled the OP!

 

[PeroK]

If flat parts of the Earth rise up to catch things, then why don't we just see chunks of Earth rising up all the time, when we observe things fall? That's what confuses me.

1) All motion is relative.

2) In the reference frame of the Earth, the apple falls to Earth.

3) In the reference frame of the apple, the Earth moves.

4) This is true in both Newtonian gravity and GR.

5) In the most natural coordinates in which to study the Earth-apple system: Schwarzschild coordinates centred on the Earth (the ball being a test particle whose gravitational effects on local spacetime are negligible): the surface of the Earth is at rest (in these coordinates) and the apple accelerates (in these coordinates).

6) In this interpretation: a (real) force is required to keep an object at rest (in Schwartzschild coordinates).

People who say it's more natural or appropriate to consider the apple at rest end up with a lot of explaining to do.

The question is this:

Does the video help or hinder your understanding of GR? Is it done to be clever and provocative or enlightening?

 

[Ibix]

Why should acceleration imply motion (velocity)?

It doesn't necessarily. You are free to regard the surface as accelerating and the apple as stationary, or vice versa. Either makes sense and may be useful in different circumstances. Note that inertial observers get to use special relativity in its nice simple form, however.

If flat parts of the Earth rise up to catch things, then why don't we just see chunks of Earth rising up all the time, when we observe things fall? That's what confuses me.

Here you are doing exactly what I said not to - trying to extend a local model to a global one. If you put your apple tree in a room, there is no experiment you can do that will tell you whether you are in a room on Earth or in a rocket under power - except opening the door and looking. As long as you stay in the room, you cannot know whether the floor is rising up to meet the apple or if the apple is falling to the floor. Since you cannot tell the difference, is there actually a difference?

As soon as you open a door, however, you can see a difference. If the Earth were actually a massless spherical shell it would have to be expanding rapidly to produce an effect like gravity, and it clearly isn't. So I can't use that local model globally. That does not stop you from closing the door again and using a local model.

Basically, you are free to say that the you fell down and broke your nose, or that the floor came up and broke your nose. Neither view is wrong (as long as you restrict your thinking to a reasonably small patch of spacetime). It may be advantageous to adopt one view over the other in a particular circumstance.

 

[Ibix]

2) In the reference frame of the Earth, the apple falls to Earth.

3) In the reference frame of the apple, the Earth moves.

Note that the reference frame of the Earth's surface is not inertial whereas the apple's frame is. That makes a difference to mathematical simplicity.

5) In the most natural coordinates in which to study the Earth-apple system: Schwarzschild coordinates centred on the Earth (the ball being a test particle whose gravitational effects on local spacetime are negligible): the surface of the Earth is at rest (in these coordinates) and the apple accelerates (in these coordinates).

I'd challenge the notion that this is always the most appropriate frame. Globally, yes. Locally, maybe not. You are, in a Newtonian analogy, asserting that it is always more appropriate to use $F=GMm/r^2$ than $F=mg$. As long as I bear in mind that the latter incorrectly implies a uniform field and remember the limitations, that's fine and saves me a few multiplications that I already know the answer to.

People who say it's more natural or appropriate to consider the apple at rest end up with a lot of explaining to do.

I wouldn't go as far as "more natural". But picking a local inertial frame certainly has advantages, as long as I remember that "local" qualifier.

 

[PeroK]

Note that the reference frame of the Earth's surface is not inertial whereas the apple's frame is. That makes a difference to mathematical simplicity.

I'd challenge the notion that this is always the most appropriate frame. Globally, yes. Locally, maybe not. You are, in a Newtonian analogy, asserting that it is always more appropriate to use $F=GMm/r^2$ than $F=mg$. As long as I bear in mind that the latter incorrectly implies a uniform field and remember the limitations, that's fine and saves me a few multiplications that I already know the answer to.
I wouldn't go as far as "more natural". But picking a local inertial frame certainly has advantages, as long as I remember that "local" qualifier.

Well, we'll have to disagree about that. We are talking here about the replacement theory of gravity. That cannot be understood from LIF's, which although important, cannot be used generally to explain the theory. The theory requires that we take into account the source of the gravity, which is missing from the LIF, which by definition is a region of flat spacetime.

 

[A.T.]

...or is it a simplified term trying to explain The Equivalence Principle? Thanks.

Yes. The Earth's surface has a proper acceleration upwards, which is something different than "movement". See the green apple still hanging on the tree in the below video: In Einstein's model it must experience a net force upwards (and the corresponding proper acceleration), in order to stay at a fixed height.

 

[Mister T]

Here is a video by PBS

PBS otherwise has a reputation for excellence. These videos are not consistent with that reputation. They are an embarrassment, there have been several people who come on PF asking questions about them because they were seriously misled by the errors.

 

[Nugatory]

If flat parts of the Earth rise up to catch things, then why don't we just see chunks of Earth rising up all the time, when we observe things fall?

If you're the falling object, that is exactly what you see... The surface of the Earth is accelerating towards you until either your parachute opens or the Earth smashes into you.

 

[PeroK]

If you're the falling object, that is exactly what you see... The surface of the Earth is accelerating towards you until either your parachute opens or the Earth smashes into you.

I still think it is somewhat misleading to suggest that this is an explanation of gravity. Once you have made the change of reference frame to the free falling object, where do you go from there? You have a LIF with flat spacetime and a large object (for some reason beyond the scope of your LIF) accelerating towards you.

And, if you consider the path of a light ray, you have no LIF to move to. The deflection of light round a star cannot be explained by a LIF in this way.

Is there a serious textbook on GR that teaches gravity in this way: from the LIF of free falling objects? Rather than from the global, non-inertial Schwarzschild (or other) coordinates?

 

[PeterDonis]

I still think it is somewhat misleading to suggest that this is an explanation of gravity.

It isn't a complete explanation of the global properties of spacetime in the presence of gravity. But it is an explanation of the local behavior of "gravity". More precisely, it's an explanation of why, locally, "gravity" doesn't exist; there is no "force" pulling the apple down. The apple is just in free fall. The only force present is the force pushing up on the surface of the Earth, preventing it from also being in free fall, and causing it to collide with the freely falling apple.

The deflection of light round a star cannot be explained by a LIF in this way.

Locally, yes, it can. Locally, the path of light is straight in an LIF, but the LIF is free falling towards the star. And locally, with respect to an observer who is "hovering" at a fixed altitude above the star (and hence is accelerating upward), the path of light bends towards the star.

The global path of the light ray can't be completely explained with a single LIF, true; but that's because there is no single LIF that covers the entire trajectory of the light ray. But that's equally true for any object. Globally, in the presence of gravity, spacetime is curved, not flat; but another way of putting it is that globally, in the presence of gravity, the LIFs centered on different events do not "fit together" the way they do in a globally flat spacetime; instead, they "fit together" in a way that shows spacetime curvature (just as on the surface of the Earth, globally, the locally flat patches do not "fit together" the way they do on a flat plane; they fit together in a way that shows the curvature of the surface).

Is there a serious textbook on GR that teaches gravity in this way: from the LIF of free falling objects?

Yes. MTW spends considerable time on this aspect, and also on how all the local LIFs "fit together" in a way that shows spacetime curvature.

 

[pervect]

To make life simple, we totally ignore the back-reaction on the Earth when we drop the apple. Then, Nugatory's post catches the essence of what's being said. From the viewpoint of the apple, you see the surface of the Earth (and the rest of it, for that matter) accelerating towards you, from your viewpiont, in the apple.

If having a viewpoint on the apple seems a bit strange, one might consider a larger "apple", such as the international space station. Being in orbit is just a slightl extension of the notion of falling. (The initial velocity of the orbiting object is different from the initial velocity of an object falling straight down, but both can be reasonably described as falling).

So then we ask - what is gravity like on the ISS? The lowest order answer is that there is none. One will see remarks that one is weighless on the ISS, and videos of astronauts floating in space, dropping pens which don't move.

In order for this viewpoint to make sense, we have to make certain approximations. The viewpoint of the apple (or the ISS) is only simple in a sufficiently near the apple (or sufficiently close to the center of the ISS).

The motivations for considering the "viewpoint of the apple" may not be obvious, especially since we need to admit that said viewpoint is limited in scope because it doesn't cover all of space-time. Nevertheless, it can be useful in treating some of the concepts we need to motivate GR.

 

[Dale]

The deflection of light round a star cannot be explained by a LIF in this way

But many other things can. Like gravitational redshift, such as the Pound Rebka experiment, and several related scenarios.

 

[PAllen]

Actually, the deflection of light can be explained in in an LIF via the principle of equvalence, and this is exactly how Einstein first made the prediction. The complete path can’t be treated this way, the the local deflection can be.

 

[bhobba]

Actually, the deflection of light can be explained in in an LIF via the principle of equvalence, and this is exactly how Einstein first made the prediction. The complete path can’t be treated this way, the the local deflection can be.

Yes - but only locally - which is why he got half the correct answer which requires the EFE's and its associated space-time curvature. He made the prediction before he had fully developed GR, and was simply lucky they were not done before he found the right answer.

Thanks
Bill

 

[PAllen]

Yes - but only locally - which is why he got half the correct answer which requires the EFE's and its associated space-time curvature. He made the prediction before he had fully developed GR, and was simply lucky they were not done before he found the right answer.

Thanks
Bill

But the answer can be completely correct locallly. The factor of 2 (more generally 1 + beta squared, it isn’t specific to light) only shows up globally.

 

[bhobba]

But the answer can be completely correct locallly. The factor of 2 (more generally 1 + beta squared, it isn’t specific to light) only shows up globally.

Of course - that's what I meant - sorry if what I said wasn't clear

Thanks
Bill

 

[itfitmewelltoo]

So recently I asked a question about a model of gravity I saw. Turns out I was misinterpretating it, it was the wronv source to use.

Here is a video by PBS ( ) talking about what I was trying to say, that is that some people say 'The Earth rises to catch an apple, not vice versa. But, it doesn't really make any sense to me. If every time anything fell, and the Earth moved to catch it, wouldn't the Earth stray off orbit if it accelerated to catch something, let's say 200 kilometers away; which is still in Earth's orbit. So I was just wondering if the Earth really does move, or is it a simplified term trying to explain The Equivalence Principle? Thanks.

I don't know what the equation is in relativity but in Newtonian physics [1] it is

F = G * (M1*M2)/r^2.

The force is proportional to the product of both masses.

The force exerted on each is equal. Because each have different masses, they experience different accelerations and change to velocity.

From what you have said about the video, I think the point it is making is that the Earth also moves. And it does, but only a very small amount. [1] (Newtonian physics is as valid as it ever was and relativity must be consistent with Newton, just more precise)

 

[PeterKinnon]

It is perhaps better to picture the apple and Earth as producing a distortion of space-time such that they accelerate towards each other in proportion to their masses. This coalescence minimizing the distortion. Bearing in mind, of course, that the apple-earth is not an isolated system.

 

[bhobba]

I don't know what the equation is in relativity

Newtonian Gravity has the force produced on a mass and that force acts directly on another mass. And we have the particle moves from f=ma. In GR a mass curves space-time according to the Einstein Field Equations, and we have another rule masses follow geodesics. But GR is in fact much more elegant - how masses move is derivable from the field equations themselves:
https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.21.408

This is very elegant, but really weird - its the only known example, to the best of my knowledge anyway, where the motion is determined only by the field - no other rule needed how the particle moves in the field.

Very interesting but not that well known fact about relativity.

Thanks
Bill

 

[PAllen]

Newtonian Gravity has the force produced on a mass and that force acts directly on another mass. And we have the particle moves from f=ma. In GR a mass curves space-time according to the Einstein Field Equations, and we have another rule masses follow geodesics. But GR is in fact much more elegant - how masses move is derivable from the field equations themselves:
https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.21.408

This is very elegant, but really weird - its the only known example, to the best of my knowledge anyway, where the motion is determined only by the field - no other rule needed how the particle moves in the field.

Very interesting but not that well known fact about relativity.

Thanks
Bill

Actually, quite well known. Less well known is that, carefully analyzed, such derivations rely on the dominant energy condition. That is, that small bodies necessarily follow timelike geodesics if and only if the dominant energy condition is true. Otherwise even spacelike trajectories are possible per the field equations. In which case, you could add an assumption about motion to rule this out.

 

[bhobba]

Actually, quite well known.

When I posted a lot of sci.physics.reativity we had a lot of high powered people posting at one time - they gradually disappeared due to the cranks. But back then when I just found out about it and posted could I see a proof - only John Baez and Steve Calip knew about it - of those that posted there of course - and were not cranks. I suspect others did know it but not the proof - so kept quiet. I had to dig it up myself. John and Steve of course knew the proof but also knew I would learn more doing it myself. Of course they were right - that was a lesson I learned there and try to foster here - targeted at the appropriate level of course.

Thanks
Bill

 

[PAllen]

When I posted a lot of sci.physics.reativity we had a lot of high powered people posting at one time - they gradually disappeared due to the cranks. But back then when I just found out about it and posted could I see a proof - only John Baez and Steve Calip knew about it - of those that posted there of course - and were not cranks. I suspect others did know it but not the proof - so kept quiet. I had to dig it up myself. John and Steve of course knew the proof but also knew I would learn more doing it myself. Of course they were right - that was a lesson I learned there and try to foster here - targeted at the appropriate level of course.

Thanks
Bill

As to how well known it is, both Synge’s 1960 book and MTW discuss it. Those are fairly early standard texts.

There are actually many variants of proof. The one you reference is related to work done by Einstein, Infeld, and Hoffman way back in 1938 - the first derivation of particle motion from the field equations. This early type of proof is not affected by the issue of energy conditions because it does not actually apply to matter at all - you assume the vacuum field equations throughout, and are really talking about the motion of BH as stand ins for test particles.

The more complicated problem is showing that matter, in an appropriate limit, follows timelike geodesics. It is this case for which it has turned out that dominant energy condition is both necessary and sufficient for timelike geodesic motion to follow from the field equations, for the limit of small bodies. This line of work starts from Geroch, and the most rigorous derivation is by Gralla and Wald (for a while, several years ago, Sam Gralla was active on these forums).

 

[bhobba]

As to how well known it is, both Synge’s 1960 book and MTW discuss it.

I lost my copy of MTW ages ago - but never really did an in depth study - I preferred Wald which I did study a lot of.

Might have to get a copy again. They do say if you really want to understand GR you need both MTW and Wald. I am going to check now if its in Wald and simply forgot (its been ages since I was into GR). Will get back.

Added Later:
Had a quick scan of Wald. You so and so - looks like I will have to get MTW - again

Thanks
Bill

 

[PAllen]

I lost my copy of MTW ages ago - but never really did an in depth study - I preferred Wald which I did study a lot of.

Might have to get a copy again. They do say if you really want to understand GR you need both MTW and Wald. I am going to check now if its in Wald and simply forgot (its been ages since I was into GR). Will get back.

Added Later:
Had a quick scan of Wald. You so and so - looks like I will have to get MTW - again

Thanks
Bill

Actually, they (Wald) do discuss it briefly, referencing literature, on page 73-4 of the edition I checked. However, they don’t present a full discussion as MTW do (a whole 10 page section, 20.6)

 

[bhobba]

Actually, they (Wald) do discuss it briefly, referencing literature, on page 73-4 of the edition I checked. However, they don’t present a full discussion as MTW do (a whole 10 page section, 20.6)

So it does - on those very pages - but as you say the detail is in references - sneaky.

Relented - got MTW - huge difference in the Kindle price and while its not the best for serious study - if I remember right MTW was so huge it wasn't physically an easy read either so got that one. Talk about HUGE - it took a while to even download.

Thanks
Bill