[jeffreyH]

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 pop-science nonsense at-all, 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!

[yor_on]

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 :)

[timey]

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 co-ordinates 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.

[CPT ArkAngel]

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 anti-parallel 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/10.1088/1367-2630/18/2/023009
Allow flashplayer to watch the video.

The internal speed is transverse so C²= v₁² + v₂²

Where v₁ is the external speed and v₂ is the internal speed.

[yor_on]

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'.

[JohnDuffield]

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. 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 space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time 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.

[jeffreyH]

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. 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 space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time 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.

[syhprum]

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 

[timey]

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?

[syhprum]

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

[timey]

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.

[PmbPhy]

In GR, gravity is not a force.

That is a commonly held misconception. In physics there are two kinds of forces; 4-forces 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 well-known 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 non-inertial 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 "Coriolis-field" 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 co-ordinates? 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.

[CPT ArkAngel]

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 space-time (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!

[yor_on]

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/the-principle-of-equivalence-put-to-the-test. 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?

[CPT ArkAngel]

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/2014-07-equivalence-principle-effects-spin-gravity-coupling.html

[syhprum]

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]

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...?

[zx16]

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 motion-detectors 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.

[timey]

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.

[yor_on]

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. 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 space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time 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.