## 3-dimensional implications of a black hole

thanks MFB and IamLoser, now I'm engaged in this - http://www.phys.uu.nl/~thooft/theorist.html - and I will do it. I have not retained my math knowledge well enough some am starting from the beginning.

 Quote by wetwonder If you were doing an EVM outside the space shuttle, and tethered to the exterior of the shuttle was a cubic meter of lead and a cubic meter of a sea sponge, are you saying the cubic meter of lead wouldn't have less space within it than the sea sponge? Or if it was a cubic meter of lead vs. a cubic meter of balsa wood that the lead wouldn't have less space within it?
do you mean "empty space"?
 I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."

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 Quote by wetwonder I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."
The sea sponge is filled with empty holes that have nothing but vacuum, while the lead is one continuous solid object. You could add air or liquid into the sponge, and this may or may not mean it now takes up more space than before depending on how you choose to look at it.
 I don't see how, but the sea sponge is a bad example because there are too many preconceptions about its structure. So put the sea sponge aside and use a cubic foot of solid wood instead. If the cubic foot of solid wood and cubit foot of lead are both tethered off the space shuttle, there would be more space within the dimensions of the wood than the lead. If the lead and the wood were to run into each other at a high speed, the wood will show a perceptible dent (without any splintering off in this eg.) - there is still the same amount of wood, but it's been compressed by its mass displacing space inside. The lead may have a tiny dent, so it displaced much less space then the wood, partly because there was less space available to displace.

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 Quote by wetwonder I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter.
What you describe is called "vacuum". If you call vacuum "space" (which has a specific and different meaning), you are confusing others, so please do not do that.

 I wasn't thinking of an imaginary sense of "volume."
But everyone else did, probably.
 "space" is, as I understand it, a way to conceptualize the relationships between objects in other words, it's not really a "something", instead it's just a very intuitive way to understand reality I think you're using the word "space" and "volume" interchangeably

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 Quote by wetwonder If the cubic foot of solid wood and cubit foot of lead are both tethered off the space shuttle, there would be more space within the dimensions of the wood than the lead.
This depends HIGHLY on what you define "space" and "vacuum" to be. If you think the space between electrons and the nucleus is empty, and that fundamental particles are point-like, then the vast majority space that matter occupies is indeed empty. However, if you view particles as occupying the portion of space where their wavefunction says they are most likely to be found, and you view forces between particles as "something", then matter is not mostly empty space. It gets even more complicated if we delve into QED and QCD and bring virtual particles and such into it.

 If the lead and the wood were to run into each other at a high speed, the wood will show a perceptible dent (without any splintering off in this eg.) - there is still the same amount of wood, but it's been compressed by its mass displacing space inside. The lead may have a tiny dent, so it displaced much less space then the wood, partly because there was less space available to displace.
I think this goes back to the sponge issue. Wood is not fully solid. It has water and gasses inside it and is made up of complex molecules. If you really want to compare to objects, lets compare Aluminum and Lead. Aluminum has an atomic radius of 143 picometers, while lead is 175 pm. Yet lead has much more mass even though it is larger, giving it a much higher density. You could say that there is less empty space inside lead if you want to. But let me ask you this. Where is a particles "surface"? How can we say how big it is?
 Nice good example, aluminum and lead. (I'll be more careful also with my use of space and volume.) There must actually be space all over the place inside a mass, being warped by all the matter in there and making gravities pulling every which way relative to the relationship of the matter - otherwise there would be no structure, no order. And one must have more space inside its dimensions than the other - differentiating the characteristic/structures of the two.

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 Quote by wetwonder Nice good example, aluminum and lead. (I'll be more careful also with my use of space and volume.) There must actually be space all over the place inside a mass, being warped by all the matter in there and making gravities pulling every which way relative to the relationship of the matter - otherwise there would be no structure, no order. And one must have more space inside its dimensions than the other - differentiating the characteristic/structures of the two.
The structure of all objects on our scale is dominated by electromagnetic interactions, not gravity. Molecules are held together by balancing the attraction and repulsion of their atoms. Only when you get to very large objects such as moons, planets, etc does gravity start to play a dominant role.

I can't say much on there being more spacetime inside an object, as I don't know.

 Quote by wetwonder I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."
Your concept is perfectly OK, but that is not the way physicists think of it. They generally think of space as "existing" and matter passing through space having no effect on space.

Either way of looking at it makes sense. They way I see it, either way works equally well, so you may as well use the same definition everyone else does in order to avoid misunderstandings.

I have a policy of refusing to argue about definitions. I'll just use whatever definition the other guy wants. (Political discussions in particular often devolve into endless arguments about definitions. Since definitions are arbitrary, to me this seems pointless.)

Some is sure to point out that according to Einstein matter and space do affect one another, but this is so complicated and hard to work with that physicists avoid using this theory. Instead they stick with Isaac Newton's much simpler ideas, which are almost always accurate enough.