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Why is space-time curved?

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organon1973

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If the universe is a 4-dimensional hypersphere (a hypersphere, any sphere of greater than 4 dimensions -- our universe, of 4 dimensions), why is it curved? And why do objects move toward one another, in a straight line, by virtue of gravity?

Thoughts:

If the universe is indeed a sphere -- what is the shortest path between two points on a sphere? A curve. Do objects move toward one another, by virtue of gravity, along the shortest possible path? Yes, they do -- we do not see two objects taking detours during that course of motion and stopping at celestial Starbuck's.

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If the universe is a 4-dimensional hypersphere (a hypersphere, any sphere of greater than 4 dimensions -- our universe, of 4 dimensions), why is it curved? And why do objects move toward one another, in a straight line, by virtue of gravity?

Thoughts:

If the universe is indeed a sphere -- what is the shortest path between two points on a sphere? A curve. Do objects move toward one another, by virtue of gravity, along the shortest possible path? Yes, they do -- we do not see two objects taking detours during that course of motion and stopping at celestial Starbuck's.

What you are really asking is what is the cause of gravitation. Even Isaac Newton punted on that one. He wrote in -Principia Mathematica- Hypothesis non fingo. I frame no hypothesis. Newton had no idea what caused gravitation and Einstein had no idea why mass causes space time to bend. My guess is that it is implicit in the symmetry of the metric tensor g\sub i\sub j. Why is that the metric tensor. Quien sabe?

Bob Kolker

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?????

Who ever said the universe had a shape?

If we take the universe to mean everything, all that is, i.e. existence, then it cannot have a shape because that implies existence has limits. That's a self-contradictory statement. What would exist beyond existence? Beyond the edge of that "shape"?

The universe is infinite in that you can keep going and not find the edge. But no matter how far you go, that distance is still finite. You understand? It's like numbers: the number line is infinite, but each number is finite.

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I don't see a way around reading all about this in books about general relativity. There's no explaining it with analogies about spheres and coffee shops, just as there's no way around reading Rand if you want to understand Objectivism. You're asking questions and asnwering them with less than well informed speculation at an alarming rate here. You should slow down, and try to read up on and fully understand one thing at a time.

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Just as the universe itself is not in time or space because those concepts refer to the arrangement of existents within the universe, it also cannot have a "shape" because it does not possess any boundaries that would allow such a concept to exist. Don't confuse the mathematics (GR) describing the approximate effects of gravity on the universe as the universe itself. A map describes a place it is not the place itself. GR is a close approximation of how matter and energy interact within the universe. It can not describe the universe as a whole.

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Don't confuse the mathematics (GR) describing the approximate effects of gravity on the universe as the universe itself. A map describes a place it is not the place itself. GR is a close approximation of how matter and energy interact within the universe. It can not describe the universe as a whole.

I'm not aware of any experimental results that indicate GR is not an exact description of gravitational effects. What aspect of GR do you think is only an approximation?

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I'm not aware of any experimental results that indicate GR is not an exact description of gravitational effects. What aspect of GR do you think is only an approximation?

What he's saying is while it might accurately make the predictions, it is not necessarily representative of reality. String theory, for example, accurately makes fundamental predictions. These theories are all incoherent in their own ways, though, and that is where the breakdown in understanding occurs. Space and time can only be understood in relation to the motion of objects, so to talk about them as real entities makes no sense and needs further clarification.

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I happen to know a little bit about gravity. To start off, its only a hypothesis that the universe is a hypersphere, there are a few other geometries that I don't remember off the top of my head that would also satisfy the conditions of our 'local space'. You may come close to imagining spacetime by picturing a cloth (this represents one dimension of space and one dimension of time). We understand this cloth to have an associated metric or distance between points. Curvature is the change in metric or distance between points. You may also understand curvature as the 'curviness' of this cloth. To relate this to high school math, curvature in an area of cloth implies that the pythagorean theorem for distance between points changes on that patch of cloth. Also, this cloth has the property that if you zoom in really far, far enough that we may call it the 'local space' of a point on the cloth, it should be approximately the old flat space that you're used to from algebra.

As far as we've been able to tell CURVATURE IS GRAVITY. Particles moving along your cloth will follow the shortest path/distance according to the changing metric. These lines of shortest distance are called 'geodesics'. Further, mass or energy create the curvature necessary for altering the geodesics along which particles travel. A particle entering a region of curvature might leave at a different angle or be bound in orbit. You can look up all sorts of visual examples of curvature. Of course, all of this refers to curvature in a single region of local space, or in a single patch of cloth.

You can't tell from one piece of cloth the exact structure of the rest of the cloth. However, physicists may consider what they consider to be the average curvature of space (which is very little curvature) and then try to find different global geometries which would allow for that large scale average curvature. A hypothetical but ridiculously expensive test to identify the global average curvature in a region of space would be to fly in a very large circle in space and then to find the difference between your starting point and your ending point.

Also, Quantum Physics isn't incompatible in principle with the concepts of general relativity I described so far. The difficult arises in that unlike the quantization of Electrodynamics, the quantization of gravity doesn't have spacetime as a background for the particles to move around in. Quantum Gravity must describe both the dynamics of particles and of the spacetime dependent on those particles. There are a lot of difficulties that pop up, just as there were difficulties in Quantum Electrodynamics that people like Richard Feynman resolved with some tricks. So gravity is a lot more complicated and might require a couple of genuises to figure out how to get rid of all the infinities other mathematical difficulties.

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