I Why special relativity is unsuitable to describe gravity

[MikeGomez]

In the third case, the "floor" will smoothly shift to "ceiling" as you move around, and drilling into it will see a very slow change in force which again drops abruptly to zero once you're through.

I’m confused about what third case you are describing. This isn’t Perter’s third case of an object in freefall.

However, the reason for feeling these forces is quite different, and the consequences can be quite different. For example, if you drill into the "floor" (and fill in behind you) in each case you'll get very different behaviour. On Earth, the force on your feet will first increase then decrease as you drill down (density isn't constant) until you reach the centre, then reverse until it you reach the surface again. In a rotating cylinder, the force will increase (in principle without bound, although material science may have a thing or two to say about that) until you drill through the outer wall, where it falls abruptly to zero. In the third case, the "floor" will smoothly shift to "ceiling" as you move around, and drilling into it will see a very slow change in force which again drops abruptly to zero once you're through.

If you drill a hole all the way through the Earth under your feet, you will switch from an accelerated frame to freefall and (ignoring tidal effects) that would be equivalent to drilling a hole in the case of the rotating cylinder and going into freefall, or drilling a hole in the accelerated elevator and going into freefall.

If you drill the hole in the Earth so that you will weigh more and then less (as you describe due to change in density), then that would be equivalent to increasing/decreasing the rate of rotation of the cylinder, and increasing/decreasing acceleration of the elevator.

So I agree that all possible gravity, artificial or natural, is actually electromagnetic forces making the locally obvious choice of "not moving" frame a non-inertial one. But as soon as you step out of that local paradigm, they can be quite different phenomena.

“Gravity and inertial are phenomenon identical in nature” means that there is no artificial gravity. The fact that these systems are globally different from one another says nothing to dispute that. It's like you're claiming that water that flows in a straight line in a man-made canal is different from water that flows in different directions in a winding river.

 

[Ibix]

I’m confused about what third case you are describing. This isn’t Perter’s third case of an object in freefall.

It is, although I was assuming the extended object is hollow and you are inside it initially. As I recall, a spherical cloud of test particles in a Schwarzschild metric will thin in the r direction and broaden in the tangential plane. An extended object will resist that shape change, with the result that some parts would push outwards and others inwards on a test particle in contact with the surface (either inside or outside).

If you drill a hole all the way through the Earth under your feet, you will switch from an accelerated frame to freefall and (ignoring tidal effects) that would be equivalent to drilling a hole in the case of the rotating cylinder and going into freefall, or drilling a hole in the accelerated elevator and going into freefall.

If you drill the hole in the Earth so that you will weigh more and then less (as you describe due to change in density), then that would be equivalent to increasing/decreasing the rate of rotation of the cylinder, and increasing/decreasing acceleration of the elevator.

I was imagining creating a small cavity or a pit and standing in it, doing an experiment, then drilling further down (that apparently wasn't clear - apologies). And yes, in case (2) you can set any gravity-as-a-function-of-depth profile by adjusting the rotation rate, but if I have two experimenters at different depths who don't alter their positions at the same time you'll be caught at it - either our apparent relative positions will change, or the force will change even for the one who isn't moving. That's the point I was trying to make - the local behaviour may be indistinguishable, but the global behaviour is quite different.

“Gravity and inertial are phenomenon identical in nature” means that there is no artificial gravity. The fact that these systems are globally different from one another says nothing to dispute that. It's like you're claiming that water that flows in a straight line in a man-made canal is different from water that flows in different directions in a winding river.

If you found a straight line channel on Mars, don't you think that the implications would be quite different from those of finding a winding water-carved channel? The "artificial" is simply making a distinction between gravity due to a mass (typically naturally occurring) and gravity due to a spinning something (typically man-made). There's a bit of slop there due to things like a tumbling asteroid, but I don't see it as a terrible bit of terminology.

I agree that the phenomena are locally indistinguishable. Globally, not so much. That's all the point I'm making.

 

[girts]

so from reading this thread I get that plants follow rather precise orbits yet those orbits cannot be described as a pure consequence of gravity if it is looked upon in the boundaries of GR alone? Is this because if we introduce a "light" speed limit also to gravitational forces (or changes in them) then the "action at a distance" phenomenon is also put with respect to gravity and so the gravitational interaction for example between Earth and sun becomes more like a digitalized binary system rather than a purely "analog" one, if I understand the difference meant with this is that by using Newtonian gravity we could simply imagine there being a rope between the sun and Earth (a rope that doesn't stretch for that matter) and so since sun's gravity is many orders of magnitude greater that that of earth, Earth then simply follows sun instantaneously much like a ball being held by a rope and spun around a bearing.I understand that if we look upon this from a GR viewpoint, it must be that the orbit would still resemble that mentioned in the Newtonian case but because there is a delay, any changes in the axis of rotation for sun would result in a change for Earth but slightly later, and since we are talking about large objects which are heavy and have high velocities any such small delayed change would result in rather large fluctuations in the long term and lead to instability in Earth's orbit or maybe the Earth would even escape it's orbit around sun?

But then I have to ask, looking from a GR viewpoint, are the changes in rotation large enough to be felt even when delayed by such large objects as stars and planets? aren't sun "round" enough for it not to cause any noticeable changes in gravitational field given both sun's and Earth's mass and inertia which could then smooth out any such minor changes in the gravitational field? Much like a good filter can filter out any minor ripples in a otherwise DC signal given that the ripples are rather small in amplitude compared to the background steady signal (gravity) ?
Oh and also, don't we already have proof from experiments monitoring cosmological gravitational waves from supernovas or otherwise that show that gravity also travels with "c" ?Or is that only for changes in gravitational field and we are here talking about static gravitational field? But then again is there even such a thing as static gravitational field given that all the planets and stars have some at least minor misalignment or changes in their rotation?
thank you.

 

[PeterDonis]

so from reading this thread I get that plants follow rather precise orbits yet those orbits cannot be described as a pure consequence of gravity if it is looked upon in the boundaries of GR alone?

I don't know where you are getting that idea from. GR explains all of our data about planetary orbits just fine.

For the rest of your post, I think you are speculating too much based on very incomplete knowledge. I would suggest taking some time to study GR instead of trying to guess what it says. Carroll's online lecture notes on GR would be a good place to start:

https://arxiv.org/abs/gr-qc/9712019