[chris (OP)]

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?

[alancalverd]

Neither is fundamental. Both the apple and the floor accelerate towards their mutual centre of gravity.

The accelerating force on both is F = GMm/r² 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."

[yor_on]

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.
=

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?
==

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?

===

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.

[chris (OP)]

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

[alancalverd]

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.

[yor_on]

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.

[PmbPhy]

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 non-uniform g-fields 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.

[JohnDuffield]

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 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 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, though he referred to a gravitational field "of quite special form".   

[zx16]

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 earth-tremors in apple-orchards?

[CPT ArkAngel]

"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...

[zx16]

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

[yor_on]

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

[yor_on]

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.
=

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.

[JohnDuffield]

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.

[jeffreyH]

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.

[JohnDuffield]

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 best-tested theories we've got, as per Clifford Will's Confrontation between General Relativity and Experiment. 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.

[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. We still don't know how to explain it, although that doesn't make it wrong.

[timey]

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?

[yor_on]

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 :)

[jeffreyH]

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 best-tested theories we've got, as per Clifford Will's Confrontation between General Relativity and Experiment. 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.