[yor_on (OP)]

This is the sentence getting me stuck "  But this gain is exactly balanced by a larger negative gravitational energy as it comes closer to Earth’s center, "

Well, with a greater 'negative energy' at the surface it doesn't ring right to me. Unless you ignore Relativity and just use Newton where 'gravity' is a force, but even then you need to explain how that 'gravitational 'negative' energy'' increase with the ball 'at rest' in the middle of Earth. And using Newton for it can't be right.

[Bill S]

http://curious.astro.cornell.edu/physics/140-physics/the-theory-of-relativity/general-relativity/1059-if-gravity-isn-t-a-force-how-does-it-accelerate-objects-advanced 

Undoubtedly there is some good stuff in this article, I intend looking when I have time.  However, I find the opening assertion off-putting:

Einstein said there is no such thing as a gravitational force.

Lots of other people have said it, but not, I understand, Einstein.

[yor_on (OP)]

You have to put a distinction between the theory and what Einstein wanted Bill.  EM is a 'force'  and Einstein wanted relativity to become one too. But he failed to incorporate it, and so have everybody else.
=

Maybe it's better to say he wanted it to be a field, thinking of it.

[yor_on (OP)]

That you see it used as a 'force' doesn't imply that relativity agree. We want it to be fields, so we interpret it that way. But a geodesic is something without 'forces' acting on it according to the way I see it, and as I think, relativity. We see the apple fall and we call it a force, it 'accelerates' with time. But not in relativity, not from a 'black box' perspective, in that one you're unable to find any acceleration, and you're 'weightless'.
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Let's see what more we do, ok?

We give it a 'potential energy' that doesn't exist inside that black box.
We call it (gravity) a 'negative energy' as it works against the 'fields' we've already found to exist.
I'm sure I can think up more examples of how we treat it.
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And the whole point of this thought exercise is why I started to differ between what I call 'global' versus 'local' interpretations. It seems I'm in a minority doing so, but I still think it's as important as your 'frame of reference'.

[Bill S]

 

That you see it used as a 'force' doesn't imply that relativity agree.

There are certainly experts who are adamant that gravity is a force.  I’ve quoted Dr Baird before:  “Yes, gravity is a force. But it is a force that is more completely described by spacetime curvature and not Newton's law.”

Are you saying this is wrong?

Just a thought from one whose maths/geometry is abysmal:

 A geodesic is defined as the most direct route in curved spacetime.  Thus, a geodesic seems to have a lot in common with a straight line.  Could it be that a straight line in Euclidian geometry is equivalent to a curved line in the non-Euclidian geometry of curved spaces? 

Would it follow from that that, given an appropriate change in geometry, no force, and therefore no expenditure of energy, is required to alter the course of an object?   

[yor_on (OP)]

Yes, I think that might be a third interpretation, don't know how many that use it as it contain a contradiction in terms. It joins forces with gravity without defining how. https://en.wikipedia.org/wiki/Force

" In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F. "

'gravity' neither push on you or pull in a geodesic, and there are a untold amount of geodesics in one single patch of space depending on uniform motion (relative speeds) and mass. It's called 'curved SpaceTime' but there are no 'forces' curving it, in contrast to f.ex a stream that you force to change direction. A acceleration is a force, uniform motion is not.

[Halc]

A geodesic is defined as the most direct route in curved spacetime.  Thus, a geodesic seems to have a lot in common with a straight line.  Could it be that a straight line in Euclidian geometry is equivalent to a curved line in the non-Euclidian geometry of curved spaces?

I fire a bullet at a target in space, or lob a softball.  Both get from me to the target by different curved spatial paths. The answer is that both do not get to the same target event since if the me-shooting/throwing is the same event, the arrival event at the target is not.

Geodesic BTW describes the trajectories that airliners take to get from A to B on the non-Euclidean surface of Earth, which appear to be curved lines on a flat map, but in fact can be determined by pulling a string from A to B on a globe.  Similarly, a geodesic path in spacetime is such a straight line.

Would it follow from that that, given an appropriate change in geometry, no force, and therefore no expenditure of energy, is required to alter the course of an object?

How do you expect geometry to change without force being involved?  As it is, geometry in spacetime is fixed.  Geometry in space might not be, but in spacetime, time is part of the geometry, so there is no 'changing' it.

If you're talking about space, then paths are not straight.  Force is involved, and can be changed by rearranging the objects that exert gravity.

Well, with a greater 'negative energy' at the surface it doesn't ring right to me. Unless you ignore Relativity and just use Newton where 'gravity' is a force, but even then you need to explain how that 'gravitational 'negative' energy'' increase with the ball 'at rest' in the middle of Earth. And using Newton for it can't be right.

At rest just means it has no kinetic energy.  At the center of earth, the maximum energy is needed to get away from Earth.  Escape velocity is about 11.2 km/s at the surface of Earth, but greater from its center since you need more energy just to get the object to the surface.

We see the apple fall and we call it a force, it 'accelerates' with time. But not in relativity, not from a 'black box' perspective, in that one you're unable to find any acceleration, and you're 'weightless'.

This is wrong.  Gravity (without acceleration) is equivalent to acceleration (without gravity), so the apple falls in both black boxes, and in a straight line to boot.  Nothing is weightless in those two cases.  That occurs in freefall, with or without gravity, which are indistinguishable from the box.

[yor_on (OP)]

No Halc, you need to read up on relativity. A black box inside a gravitational potential /'field' has a observer dependent 'gravity', just like that apple 'accelerating'. That's why we differ between a accelerations and a 'gravitational acceleration', in the first case it will be unequivocal acceleration to all observers, the second is observer dependent. I really wish you started checking your sources.

[yor_on (OP)]

It's called a transformation, you 'transform' the 'gravitational field' by choosing frame of reference. Inside the box (ignoring spin) you're 'weightless' following a geodesic. From a observer on f.ex Earth you're in a gravitational field and  also gravitationally accelerating even if ever so slowly. So from inside that box there are no 'forces' acting upon you, although from the observer on Earth it will seem like it.

" In Einstein's theory of general relativity, gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. The gravitational force is a fictitious force. There is no gravitational acceleration, in that the proper acceleration and hence four-acceleration of objects in free fall are zero. Rather than undergoing an acceleration, objects in free fall travel along straight lines (geodesics) on the curved spacetime. " https://en.wikipedia.org/wiki/Gravitational_acceleration

[yor_on (OP)]

Ok, the question still stands?

How should I think of this 'negative energy' at the middle of that sphere. From the balls point of view it's in a geodesic, no forces acting upon it.  And from the idea on a 'gravitational field'' then?

If I use weight as a measure then the surface has a stronger 'field' and so more 'negative energy'.

So?
Anyone that has an idea here?
=

You know, this 'negative energy' of gravity seems to me pretty weird. It's not the same as f.ex Dirac sea.

" The origins of the Dirac sea lie in the energy spectrum of the Dirac equation, an extension of the Schrödinger equation that is consistent with special relativity, that Dirac had formulated in 1928. Although the equation was extremely successful in describing electron dynamics, it possesses a rather peculiar feature: for each quantum state possessing a positive energy E, there is a corresponding state with energy -E. This is not a big difficulty when an isolated electron is considered, because its energy is conserved and negative-energy electrons may be left out. However, difficulties arise when effects of the electromagnetic field are considered, because a positive-energy electron would be able to shed energy by continuously emitting photons, a process that could continue without limit as the electron descends into lower and lower energy states. Real electrons clearly do not behave in this way.

Dirac's solution to this was to turn to the Pauli exclusion principle. Electrons are fermions, and obey the exclusion principle, which means that no two electrons can share a single energy state within an atom. Dirac hypothesized that what we think of as the "vacuum" is actually the state in which all the negative-energy states are filled, and none of the positive-energy states. Therefore, if we want to introduce a single electron we would have to put it in a positive-energy state, as all the negative-energy states are occupied. Furthermore, even if the electron loses energy by emitting photons it would be forbidden from dropping below zero energy.  " https://en.wikipedia.org/wiki/Dirac_sea

Then again, you have this idea of being able to fall past the event horizon, if we assume no tidal forces acting upon you. But that is a geodesic? So, yeah it's weird.