I Curved Space-Time

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I don't disagree with this. I just have a hard time with what it means, it's kind of abstract.
You have a non-abstract physical table. That physical table has a flat surface and four legs that are perpendicular to the surface, parallel to each other, and equal in length.

Physics involves geometry. That is spacetime. Yes, we do use mathematical abstractions to represent it in our theories and analyses, but what the abstract math represents is every bit as concrete as the table. Geometry is clearly part of the physical world.
 
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pervect

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I don't disagree with this. I just have a hard time with what it means, it's kind of abstract.
I suspect I fell victim to "Too long, didn't read", aka TL/DR.

So, the chapter title of the Taylor reference I quoted earlier (http://www.eftaylor.com/pub/chapter2.pdf) gives the shortest meaningful answer.

"Distance determines geometry".

There _are_ some fine points that these three words do not cover, but - that's the basic idea.
 
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Orodruin

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But Newtons theory is wrong, it's useful but not perfect. For example, it can't predict the orbit or Mercury. Newtons theory does not try to explain what gravity is. It just makes an approximation (usually a good one) of gravity. General relativity explains gravity more accurately and also "why" gravity is.
This is not accurate. Everything we do in physics is to make models of how the world works. GR in no way makes a claim to know ”why” gravity exists. All it does is to describe gravity through the use of a 4-dimensional curved geometry. Just like Newton’s theory describes gravity as a force. There is no way we can ever know ”why” because, just like an insisting child you can keep asking that question ad infinitum. You can only know that your description is accurate to within experimental uncrrtainties.
 
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Newtons theory is wrong, it's useful but not perfect.
We know that now, but for a long time, as far as everyone knew, it could have been perfect, since no experimental evidence was known that contradicted it. Right now, no experimental evidence is known that contradicts General Relativity; but that doesn't mean there never will be, any more than the fact that there was no known evidence against Newtonian physics in, say, 1800 meant there never would be.
 

PeroK

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Summary: Mass creates curvature in space, but how can nothing have form?

So I understand that mass creates curvature in space-time. But what I struggle with is how nothing has a shape. I picture the space around say a planet, but how does the space (nothing) actual have form? Does anyone have a good intuitive explanation for that?
In a way, saying that spacetime has a "shape" is the intuitive explanation.

What we know, from experiment, is that matter moves in response to other matter. How do we explain this? There are two things to explain. For example:

1) How does a satellite know that the planet is there?

2) How does the satellite know how to move?

Physics cannot give you the ultimate answer to these questions. All it can do is give you a mathematical model (plus perhaps an intitive interpretation of the model) that successfully predicts how objects move. To some people this is disappointing: "it sucks" as you say in a later post. But, physics - no matter how deep your theories go - is always going to be based on some postulates, which have to be taken as "the laws of physics".

The mathematical basis for GR is (these are the laws of physics):

1) Einstein Field Equations - determines a "metric" for spacetime, based on the distribution of matter.

2) Lagrangian principle - determines the equations of motion for a particle given a spacetime metric.

The "intuitive" explanation is that the metric defines a geometry, hence spacetime has a "shape", and particles follow that shape (in a sense).

A deeper theory might "explain" this further, but it would still be based in its own, perhaps more fundamental, laws of physics.

Finally, in modern physics you cannot entirely escape abstract mathematics. GR has a 4D "curved" spacetime; but, Quantum Mechanics is much worse, to the point where there are multiple, very different interpretations of the mathematics.
 

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