Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 30/01/2017 08:24:11

I caught the tail end of a trail on BBC Radio 4 that had Brian Cox saying that "the apple doesn't fall to the floor. Instead the floor rises to meet the apple..."
What was he getting at?

Neither is fundamental. Both the apple and the floor accelerate towards their mutual centre of gravity.
The accelerating force on both is F = GMm/r^{2} where M is the mass of the earth, m the mass of the apple, and r the distance between their centres.
Now we also have Newton's Law F = ma where a is acceleration. Since M>>m, the apple will accelerate much more rapidly than the planet, and the mutual centre of gravity is somewhere below the surface of the planet, so an observer standing on the earth will notice the apple falling, but not the floor rising.
Relativity has its place in criminal evidence: "The accused attacked my boot with his face, m'lud."

He was talking about 'accelerations'. In Einsteins terms a uniform constant acceleration is equal (equivalence principle) to a 'gravity'. That meaning that if one ignore the Earths spin the gravity we experience here is the exact same phenomena as I would meet inside a rocket constantly uniformly accelerating at one gravity. It also make the idea of there being no 'true golden standard' more plausible. The only way we can define a uniform motion is relative some arbitrarily chosen point, saying that this is 'still' and so we find a motion relative it. But there is no way to prove it, it's all relative your pick of measurement. In such terms it becomes meaningless to define this acceleration as being a real motion, even though you normally think of the apple as being the one 'accelerating', which it does relative your choice of being 'still', namely the Earth you (are at) rest on/with.
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It's not that it is doubting motion, motion/acceleration do exist. It's just questioning what it means.
Ponder this one Chris, and see where it takes you :)
If you were in a rocket accelerating at one constant gravity in a otherwise empty 'universe', would you have a weight?
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Better point out that there are two kinds of 'accelerations' defined main stream. the one with the apple accelerating is called a 'gravitational acceleration', impossible to differ from a 'uniform motion' if you were inside that apple as it 'fell' (weightlessness) whereas the one with the rocket accelerating is defined by you finding a weight standing on a scale. Then again, what about Mach principle, and if it is correct, at what scale would it end? Will you still have a weight? To that one also should add that the difference then between the geodesic expressed by our 'accelerating apple' versus Earth is just that, that the equivalence principle actually demand earth to accelerate in a equivalent manner to a rocket. The apple doesn't 'accelerate' at all, defined through a 'black box scenario', If it did the 'weightlessness' one experience with falling wouldn't be there. So, looked at that way it then becomes the Earth that has a acceleration, not the apple. It's just in a 'free fall' following a geodesic, maybe that was how he looked about it?
Still, if you were in a rocket accelerating at one constant gravity in a otherwise empty 'universe', would you have a weight?
Why?
Or expressed otherwise, relative what?
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A further point to ponder is that neither of those states, Earths 'acceleration' versus the apples 'acceleration', expend any measurable 'energy'. The 'rocket' though will expend energy, but, relative what? Actually my last point is arguable, we 'know' a rocket spend energy, but how would you prove it inside that black box (rocket). By standing on a scale? Thinking of it you actually might be able to argue that spending energy always have to be relative something else which brings us back, rather nicely, to Mach principle.
Yes, I think Mach had a very good point in his ideas, it's all relative something else.

So which of you two is correct? I must admit that I am finding the Newtonian argument easier to comprehend...

A relativistic approach, if correct, must yield the same result as a newtonian one at low speeds, because that is what is observed.
Anyone who has experienced free fall will recognise the sensation as quite different from one of constant velocity within a gravitational field.

Heh Alan :)
""The accused attacked my boot with his face, m'lud." enjoyed that one although the boot is the culprit accelerating in this case, is it not? Unless the other one threw his face upon it?
(Can one even write it that way "let me throw my face around and see")
And Alan is quite correct, he usually is.

I caught the tail end of a trail on BBC Radio 4 that had Brian Cox saying that "the apple doesn't fall to the floor. Instead the floor rises to meet the apple..."
What was he getting at?
He's talking about the principle of equivalence from general relativity. He's expressing the fact that he has a less than perfect knowledge of the principle of equivalence or its meaning. Mind you, I'm not saying that I have either a complete or perfect knowledge of GR. But I do know the meaning and interpretation of the equivalence principle. All one can say with GR is that a uniformly accelerating frame of reference is equivalent to a uniform gravitational field. For nonuniform gfields this principle holds locally. This means that it's not possible to distinguish which is which. In fact all you can say is that the observed distance between floor and apple is decreasing at an accelerating rate.

I caught the tail end of a trail on BBC Radio 4 that had Brian Cox saying that "the apple doesn't fall to the floor. Instead the floor rises to meet the apple..." What was he getting at?
I saw that too, and was a little irritated by it because it isn't correct. Like pmb says, what he was getting at was the principle of equivalence*. Standing on the surface of the Earth is like being in an accelerating rocket, but it isn't exactly the same. In both situations light curves downwards and you can feel a force on your feet, but for different reasons. If you have a dig around in the Einstein digital papers you can find Einstein's 1920 Leyden Address where he referred to a gravitational field as a place where space was "neither homogeneous nor isotropic". That's why light curves downwards, rather like sonar waves curve downwards (http://www.dosits.org/people/history/1920/) in the deep ocean. You then fall down because of the wave nature of matter, or alternatively you feel a force on your feet because you're standing on the ground. Hence standing still in inhomogeneous space is like accelerating through homogeneous space. However the surface of the Earth is most definitely not accelerating upwards.
* see this page (http://einsteinpapers.press.princeton.edu/vol7trans/156?highlightText=%22nowhere%20precisely%20realized%22) from the Einstein digital papers where Einstein says special relativity is nowhere precisely realized in the real world. The same is true of the principle of equivalence, because it only applies to a region of infinitesimal extent, and you can't transform away the Earth's gravitational field. See Einstein saying so here (http://www.bartleby.com/173/20.html), though he referred to a gravitational field "of quite special form".

Apples fall from trees at varying and random intervals. If the ground had to respond every time by thrusting upwards, wouldn't there be frequent earthtremors in appleorchards?

"because it only applies to a region of infinitesimal extent"
The fact that g is not a constant at all is too often forgotten when people try to give explanations about how gravity works. If you are in a free fall above the earth, g (the acceleration) increases as you approach the ground. In most practical situations, it is so small that you don't have to take care of it.
As Pete said, in the context of Relativity, you can only say that the distance is shrinking. Space is a relative concept in Relativity... :)

But surely, if the floors of appleorchards rose up every time an apple fell, the ground would be in constant upheaval?

'Ahh Xc, you forget the 'uniform' there. Consider a uniform unicorn, make it symmetric, then let it fall.
What do you see?

Yes, Einstein used the word variable, but then he also used geodesics, so you will have to prove without doubt that the geodesic light follows doesn't become a longer path from the reference frame of the observer. And then we come to the situation where he involves a free fall. Free falls exist in gravitational fields , actually :) that's where they make themselves known. Without gravity SR rules, and everything becomes our 'free fall/uniform motion', or a equivalence if one like. And there light is a constant. It's incredibly much simpler to use 'c' as a constant than to deem the universe to become hodgepodge 'patches' of different 'time dilations' depending on your speed and mass. The last meaning that those time dilations are observer dependent, meaning that two different observers of a same patch will see two different 'time dilations' due to speed and mass. To get it to work John I think you will need to find a way to invalidate relativity, because what you seem to search after is a 'golden standard' from where we then can agree on 'real speeds' and mass.
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There exist one 'standard' of sorts though, but that's not the 'whole universe'. It's strictly local, and in that one all clocks agree, the proof of it is joining a same frame of reference. You can do that everywhere inside our universe though, and it will hold.

Yes, Einstein used the word variable, but then he also used geodesics...
The recurring theme is that Einstein said one thing, and people like Brian Cox say something that flatly contradicts not just Einstein, but the hard scientific evidence too. The surface of the Earth is not accelerating upwards! Pointing this out and giving reference to the Einstein digital papers isn't invalidating relativity. To be blunt, it's invalidating the popscience tosh that is presented as relativity.

Yes, Einstein used the word variable, but then he also used geodesics...
The recurring theme is that Einstein said one thing, and people like Brian Cox say something that flatly contradicts not just Einstein, but the hard scientific evidence too. The surface of the Earth is not accelerating upwards! Pointing this out and giving reference to the Einstein digital papers isn't invalidating relativity. To be blunt, it's invalidating the popscience tosh that is presented as relativity.
So what you are saying is relativity is immutable. The last word. Just as communism was the end of history. Nothing Einstein said can ever be wrong. Just let me know if this is your position. Then we can have a real debate.

So what you are saying is relativity is immutable. The last word. Just as communism was the end of history. Nothing Einstein said can ever be wrong. Just let me know if this is your position. Then we can have a real debate.
Er, no. Einstein was famously wrong about the expanding universe. But I will say this: general relativity is one of the besttested theories we've got, as per Clifford Will's Confrontation between General Relativity and Experiment (https://arxiv.org/abs/1403.7377). I will also say Einstein never ever said the surface of the Earth is accelerating upwards. And since the diameter of the Earth is still 12,742 km I will say this too: Brian Cox is talking popscience nonsense.

Why do you say that his example is wrong John? Earths gravity is a equivalence to a acceleration according to the equivalence principle, and that is a foundation from Einsteins GR. We still don't know how to explain it, although that doesn't make it wrong.

I will also say Einstein never ever said the surface of the Earth is accelerating upwards. And since the diameter of the Earth is still 12,742 km I will say this too: Brian Cox is talking popscience nonsense.
When a rocket is launched into space, the force the rocket exerts upon the earth displaces the planet's position in space.
(fortunately this displacement is corrected by our planet's gravitational position in relation to the sun, otherwise who knows where we would be in the Milky Way by now)
Therefore, similarly but in reverse, when the apple falls from the tree, the force of attraction of both M of the planet in relation to m of the apple, and m of the apple in relation to M of the planet are at play.
It is a clear fact that the force that M exerts on m is far greater than the force m will exert on M, and therefore the m of the apple moves towards the planet faster than the M of the planet moves towards the m of the apple.*
So Brian Cox is not talking popscience nonsense atall, and is stating a justifiably relevant truth, that is otherwise a meaningless trivia...
... And you are right, Einstein did not say that the earth is accelerating upwards, and neither has anyone else!
*The more interesting consideration is that the apple, when still attached to the tree, is attached only by a thin stalk. Amazingly this stalk not only stops the apple from falling to the ground, (until it doesn't), but also stops the planet from falling towards the apple. Or, hmmm (rubs chin)... is it the trunk and branches of the tree that does that?

Heh :)
Timey, I would suggest that the apple is 'at rest' with Earth, hanging from the branch. And actually, I'm one of them not being sure on what acceleration is. The example Brian use is slightly controversial but he's not the first guy using it. I've seen it before. If you think of it you will see that both relativity as well as QM uses minuscule 'patches' to describe nature, as for example earth (a curved surface) becoming 'flat' to a high degree when using the correct 'magnification'. That's a direct analogy in my mind to the idea of GR translating to SR. I'm still wondering what motion is :)

So what you are saying is relativity is immutable. The last word. Just as communism was the end of history. Nothing Einstein said can ever be wrong. Just let me know if this is your position. Then we can have a real debate.
Er, no. Einstein was famously wrong about the expanding universe. But I will say this: general relativity is one of the besttested theories we've got, as per Clifford Will's Confrontation between General Relativity and Experiment (https://arxiv.org/abs/1403.7377). I will also say Einstein never ever said the surface of the Earth is accelerating upwards. And since the diameter of the Earth is still 12,742 km I will say this too: Brian Cox is talking popscience nonsense.
So the apple according to you has no gravitational mass and therefore no gravitational field. So cannot influence any other object. Since apples travel at the speed of light no one can possibly eat apples. Am I in the ballpark with you thinking John. If not can you describe your version of the field theory that allows non interaction of the apple with other masses.

I will also say Einstein never ever said the surface of the Earth is accelerating upwards. And since the diameter of the Earth is still 12,742 km I will say this too: Brian Cox is talking popscience nonsense.
When a rocket is launched into space, the force the rocket exerts upon the earth displaces the planet's position in space.
(fortunately this displacement is corrected by our planet's gravitational position in relation to the sun, otherwise who knows where we would be in the Milky Way by now)
Therefore, similarly but in reverse, when the apple falls from the tree, the force of attraction of both M of the planet in relation to m of the apple, and m of the apple in relation to M of the planet are at play.
It is a clear fact that the force that M exerts on m is far greater than the force m will exert on M, and therefore the m of the apple moves towards the planet faster than the M of the planet moves towards the m of the apple.*
So Brian Cox is not talking popscience nonsense atall, and is stating a justifiably relevant truth, that is otherwise a meaningless trivia...
... And you are right, Einstein did not say that the earth is accelerating upwards, and neither has anyone else!
*The more interesting consideration is that the apple, when still attached to the tree, is attached only by a thin stalk. Amazingly this stalk not only stops the apple from falling to the ground, (until it doesn't), but also stops the planet from falling towards the apple. Or, hmmm (rubs chin)... is it the trunk and branches of the tree that does that?
What an excellent post. Good on you!

You could think of it this way, and it would indeed make for a very cool software is someone was able to write it. Let's assume that Brian mean exactly what is stated above. "the apple doesn't fall to the floor. Instead the floor rises to meet the apple..."
Now, this software would have to be calibrated for mass, relative motion and rotations. But it should treat it as a view from another 'dimension', in which Earth, as well as all other mass, actually accelerate in the way we normally think of it. One have to remember that the apple is in a free fall, it's weightless, the same as an astronaut in space. Anything accelerating 'for real' will express itself with inertia and gravity. You going for a ride must notice how an acceleration presses you against the seat for example. None of that exist with our apples 'acceleration', the same is not possible to state for Earth though. There you feel a constant uniform acceleration of approximately one gravity acting upon you the whole time. It would be a experience playing with such a program :)

Heh :)
Timey, I would suggest that the apple is 'at rest' with Earth, hanging from the branch. And actually, I'm one of them not being sure on what acceleration is.
Yes  that is clearly the case. The whole tree is at rest with respect to the planet, and is only in motion with the planets motion  this being why the M of the planet does not accelerate 'upwards' towards the m of the falling apple, nor the m of the falling apple accelerate 'downwards' towards the planet.
Consider that the long term coordinates of both the location of the apple attached to tree by a stalk, and the location on the planet that the tree is growing from, are not only hurtling through space around the sun, but spinning from a position closer to and further away from the sun.
The location of both the attached apple observed at rest with respect to the planet, and the bottom of the apple tree attached to this location on the planet, will be tracing out 2 aligned curving cork screw trajectories as the planet carries out it's orbit of the sun.
I have my own theory on gravitational 'acceleration' which I will not talk about 'here', (it's on New Theories)
But... considering that our planet is in relative motion to the sun, and that however fast the sun is moving through space, that our planet must not only keep up with the speed that the sun is moving through space at, but also move fast enough to orbit the sun as it keeps up, we must be moving through space faster than the sun is.
Similarly, where the moon orbits the planet, it must be moving through space faster again relative to the speed the earth is orbiting the sun at.
We can now take this remit all the way to the doorstep of the black hole that resides in the middle of the Milky Way and state the black hole as the slowest moving mass in our galaxy, with all orbiting masses moving faster, (because they must also circle around, as well as keep up), and masses orbiting those masses moving faster still...
(although the outer regions of galaxies are seemingly orbiting at the same speed as the inner regions, which is weird)
...Therefore  ascertaining an exact speed for any mass is already a challenge, without even considering time dilation effects.
Going back to the apple now falling from the tree. Interestingly, the apple 'should' theoretically fall ever so slightly slower in the day time than it will at night, because the sun's gravitational force will be acting 'against' the fall in the daytime and 'with' the fall during the night.
And the falling apple should follow a slightly curved trajectory due to the speed the planet is moving through space at, in conjunction with the fact of the planets spin.
Bringing SR into the picture  the apple, when at the top of the tree, is moving faster through space than the apple that has already fallen to the ground is. The apple on the ground 'should', according to SR, observe, (if it's sensitive enough), that the apple on the tree is ever so slightly length contracted, and that the apple's tiny clock is running a tad slow, but the (very sensitive) apple on the ground will notice that the apple on the tree's clock is running a tad fast.
The effects of SR motion related time dilation are cancelled out by the greater extent of the GR gravitational time dilation effects at that h from M.
At a certain orbital radius from M, the parameters switch where the SR time dilation effects cancel out the GR gravitational time dilation effects, and time will be the same for an apple at the top of a 'very' tall tree (chuckle) orbiting Earth at that radius, as time will be for the apple on the ground.
Further out than this radius, 'an orbital' will experience a slower time relative to the apple on the ground, due to SR effects being greater than GR effects because of the speed required to upkeep that orbital at that radius.

In GR, gravity is not a force.
https://en.wikipedia.org/wiki/Geodesics_in_general_relativity
Two parallel laser beams do not attract each other, but antiparallel beams do... What is the difference? Relative speed!
Consider an orbit following an elliptical geodesic around the Earth. Then consider a particle following this geodesic as having a relative speed to an inertial observer. Then consider that this relative speed has two components: one external, which is the standard relative speed of the particle to the observer and a second internal speed, which is the relative timerate of the particle to the observer.
https://en.wikipedia.org/wiki/Ellipse
As the particle approach the major axis, the internal speed increases and the external speed decreases. As the particle approach the minor axis, the internal speed decreases and the external speed increases. The sum of both velocities must be the speed of light.
The geodesic of a photon can only be circular if you don't consider the imperfect symmetry of the Earth gravitational field, because it has no internal speed (timerate). There is no elliptical geodesic for light if you consider only a single attractive pole. It is not the case for particles with proper masses...
http://iopscience.iop.org/article/10.1088/13672630/18/2/023009
Allow flashplayer to watch the video.
The internal speed is transverse so C^{2}= v_{1}^{2} + v_{2}^{2}
Where v_{1} is the external speed and v_{2} is the internal speed.

Hmm yes CPT, but what are you thinking of? That gravity isn't a force? Yep, that's the way I usually look at it, but then again, consider 'potential energy'.

Why do you say that his example is wrong John? Earths gravity is a equivalence to a acceleration according to the equivalence principle, and that is a foundation from Einsteins GR.
The man falling off the roof gave Einstein his happiest thought and led to the equivalence principle, but take a look at Pete's paper Einstein's gravitational field (https://arxiv.org/abs/physics/0204044). See the Synge quote on page 20:
"I have never been able to understand this principle…Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line … The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of spacetime geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute spacetime faced".
Einstein used the principle of equivalence to appreciate that a gravitational field is like accelerating through space. But the equivalence principle only applies to a region of infinitesimal extent. That means it applies to no region at all. So a gravitational is not exactly the same as accelerating through space. In the former situation you aren't moving and space is inhomogeneous. In the latter situation you're moving faster and faster and space is homogeneous.
We still don't know how to explain it, although that doesn't make it wrong.
I know how to explain it. So does Don Koks.

Why do you say that his example is wrong John? Earths gravity is a equivalence to a acceleration according to the equivalence principle, and that is a foundation from Einsteins GR.
The man falling off the roof gave Einstein his happiest thought and led to the equivalence principle, but take a look at Pete's paper Einstein's gravitational field (https://arxiv.org/abs/physics/0204044). See the Synge quote on page 20:
"I have never been able to understand this principle…Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line … The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of spacetime geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute spacetime faced".
Einstein used the principle of equivalence to appreciate that a gravitational field is like accelerating through space. But the equivalence principle only applies to a region of infinitesimal extent. That means it applies to no region at all. So a gravitational is not exactly the same as accelerating through space. In the former situation you aren't moving and space is inhomogeneous. In the latter situation you're moving faster and faster and space is homogeneous.
We still don't know how to explain it, although that doesn't make it wrong.
I know how to explain it. So does Don Koks.
That actually made sense. I am impressed.

The question is does the apple or the Earth move and it seems obvious to me that both move but as the mass of the Earth is something like 10^26 times that of the apple its movement is very small.
This is why Galileo was wrong when he said that the 1Kg cannon ball and the 100Kg fell at the same rate, they do of course if they are released together but if they are released separately and their transit time measured there is a tiny difference

Syhprum  I think this one of the most fascinating aspects of physics...
2 cannon balls of differing weight, when released at the same time, accelerate at the same rate, and will arrive on the ground at the same time  showing that whatever is causing this has nothing to do with gravitational attraction, (ie: F(grav) = M*m/d squared), only gravitational acceleration.
So  releasing the cannon balls separately, with a time interval between, causes a slight difference in travel time...
Question being:
If we subtract the time interval between the release of these cannon balls from the difference in travel time experienced by each, shouldn't the travel time by rights then be equal for both? And if not, then indeed 'why' not?

When they were released separately I had assumed that the first one had completed its transit before the second was released

When they were released separately I had assumed that the first one had completed its transit before the second was released
Really?
I had visualised only a couple seconds time period between the cannon balls being released  and the fact that the first cannon ball (doesn't matter which weight), is observed to be accelerating at a faster rate compared to the second cannon ball (doesn't matter which weight), a couple of seconds in distance behind it.
This being due to the more accelerative location closer to M that the first canon ball is travelling in compared to the less accelerative location the second cannon ball is travelling in further away from M.
If both cannon balls that are of differing weights are released at the same time, and both arrive on the ground at the same time, then when dropped separately both cannon balls will take an equal amount of time, and therefore an equal acceleration of speed, to reach the ground no matter the time period between the releases.
The question is does the apple or the Earth move and it seems obvious to me that both move but as the mass of the Earth is something like 10^26 times that of the apple its movement is very small.
This is why Galileo was wrong when he said that the 1Kg cannon ball and the 100Kg fell at the same rate, they do of course if they are released together but if they are released separately and their transit time measured there is a tiny difference
Therefore, what you have first described can only be a comparison of acceleration between cannon balls that are still in the air, and the lower ball accelerates at a faster rate than the higher ball due to its closer proximity to M in the gravity field of open space in relation to M.
But why?
This is what is observed, but it makes no sense because F(grav) = M*m/d squared does not describe the observation. If it did then the heavier cannon ball would be observed to accelerate faster...
To date, there is no current physics remit that gives 'cause' for this accelerative phenomenon.

In GR, gravity is not a force.
That is a commonly held misconception. In physics there are two kinds of forces; 4forces and inertial forces. In relativity the gravitational force is an inertial force. Some physicists think of inertial forces as being imaginary somehow whereas others, including Einstein and John Stachel think that inertial forces are as real as any force. But in the end its all a matter of definition. As Einstein once wrote, to him the concept of real and not real is like choosing to place somethings in one draw and everything else in another.
For those not familiar with what inertial forces are and what some wellknown experts say about it then please see:
http://www.newenglandphysics.org/physics_world/gr/inertial_force.htm
Here are some of the comments I mentioned
From Grvitation, by Misner, Thorne and Wheeler, Box 6.1, page 164
A tourist in a powered interplanetary rocket feels "gravity." Can a physicist by local effects convince him that this "gravity" is bogus? Never, says Einstein's principle of the local equivalence of gravity and accelerations. ...
I recommend reading the rest of that quote.
From Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122
Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in noninertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]
Here's the most important one by Einstein
Albert Einstein That the relation of gravity to inertia was the motivation for general relativity is expressed in an article Einstein wrote which appeared in the February 17, 1921 issue of Nature [28]
Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolisfield" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of coordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.
Please enjoy. After all I worked extremely hard on that website for everyone. :)

To say that gravity is not a force in GR is just a way to emphasize the dichotomy of Newton's view vs Einstein's. In Einstein's view, gravity is explained by relative spacetime (not specifically curvature). You must try to distance your view from the Euclidean space: The main mistake people do when trying to explain it... It took 10 years for Einstein to come with this new point of view, not for no good reason.
Thank you very much Pete for your Einstein's quote! This is a very good one, I've never read this! I agree totally. And this is related to QM!

Ok, I'm not sure what's happening on this site anymore? One can't ignore practical experiments, the equivalence principle is actually tested, and will be tested again https://news.cnrs.fr/articles/theprincipleofequivalenceputtothetest (https://news.cnrs.fr/articles/theprincipleofequivalenceputtothetest). the tests we've made so far "The best modern limits, based on, e.g., laser ranging of the Moon to measure how fast it falls around Earth, show that EP holds within a few parts in a trillion (10 (to) 12). This is fantastically accurate, yet the possibility remains that the equivalence principle could fail at some more subtle level." Now this extremely subtle level might or might not exist but to me the equivalence principle still is well and good.
=
Btw what happened to all the attachments (options) we could 'edit in' mathematically? Can't see them anymore. only 'Attach' seems to exist?

There is nothing wrong with the Equivalence Principle. A more complete theory should give the same results. The term 'equivalence' is not the same as 'equal'.
For a photon, the gravitational field is moving with it in the direction of motion. There is no gravitational field in front and behind it because gravity moves at the same speed. I have never found Einstein's explanation of the Equivalence Principle for a photon. I suspect that is why he used the term 'Equivalence' and not 'Equal'. Though Einstein did many thought experiments with photons to establish his theory, the photon is not completely integrated in it.
Another interesting article:
https://phys.org/news/201407equivalenceprincipleeffectsspingravitycoupling.html

Timey
Once the 100Kg cannon ball has fallen to the ground the mass of the Earth has increased hence the force accelerating the 1Kg cannon ball which is proportional to the product of its mass and that of the Earth has also increased so its transit time will be reduced

Timey
Once the 100Kg cannon ball has fallen to the ground the mass of the Earth has increased hence the force accelerating the 1Kg cannon ball which is proportional to the product of its mass and that of the Earth has also increased so its transit time will be reduced
Hmmm... (rubs chin)
Yes, that is clever, but still gives no cause for the m of either airborne cannon ball not affecting the rate of m's acceleration with regards to M, this being original M, or original M plus 100KG or 10KG cannon ball, no matter which was dropped first, because either would affect the value of M, and therefore *presumably* the accelerative factor  under the remit you propose.
The accelerative factor being...?

Getting back to the original question, surely we find that when an apple falls onto the ground, there is no measurable upward movement of ground towards the apple.
I mean even if we attached very sensitive motiondetectors to the ground. Would they detect an upward movement towards the apple?
Well obviously not. The ground just lies still. It doesn't move. It simply attracts the moving apple. Which is what Newton said over three centuries ago.
If an object moves, it gets drawn towards another static object.

But you see zx16, Syphrum and I were indeed referring to the apple m versus M in our conversation.
In your post, you completely disregard the fact of F(grav)=m*M/d^2.
The reason why this question arises of "does the apple fall to the ground, or does the ground fall towards the apple", is entirely due to the fact that F(grav)=m*M/d^2 does not describe inertial free fall.

Why do you say that his example is wrong John? Earths gravity is a equivalence to a acceleration according to the equivalence principle, and that is a foundation from Einsteins GR.
The man falling off the roof gave Einstein his happiest thought and led to the equivalence principle, but take a look at Pete's paper Einstein's gravitational field (https://arxiv.org/abs/physics/0204044). See the Synge quote on page 20:
"I have never been able to understand this principle…Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line … The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of spacetime geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute spacetime faced".
Einstein used the principle of equivalence to appreciate that a gravitational field is like accelerating through space. But the equivalence principle only applies to a region of infinitesimal extent. That means it applies to no region at all. So a gravitational is not exactly the same as accelerating through space. In the former situation you aren't moving and space is inhomogeneous. In the latter situation you're moving faster and faster and space is homogeneous.
We still don't know how to explain it, although that doesn't make it wrong.
I know how to explain it. So does Don Koks.
Quite so John, it's about 'test particles'. That doesn't make it wrong though.

When I think of that it leads me to QM :)
In a general sense the whole treatment is equivalent to magnifying something into its 'simplest constituents'. The same way you can take a curvature, magnifying it, and end up with a approximately 'flat line'. That is what you will end up with imagining it.