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Author Topic: Geometry and parallel lines.  (Read 10038 times)

Offline yor_on

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Geometry and parallel lines.
« Reply #25 on: 01/07/2011 17:45:01 »
Well, I told you I had a definition of a straight line (in SpaceTime) JP. It doesn't expend energy. And that one is represented by uniform motion and geodesics where we live. But that is from discussing what we see and learn about SpaceTime. It does not, as I see it, discuss 'ideal parallel lines'. Although in reality we have to accept that they, if using some bendable material as all materials I know of are, will form themselves after gravity.
==

Are you defining SpaceTime as a sphere for this? And then assuming some sort of geodesics on the outside, or is it Newtons spheres, in a sphere, in a sphere? If we assume that we come back from where we started and then imagine us driving that cosmic car, using the tires to define our parallel lines then? And when I think of it (gravity) assuming the inside of a sphere I get seriously lost trying to imagine gravity working as described here.
« Last Edit: 01/07/2011 18:02:57 by yor_on »
 

Offline JP

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Geometry and parallel lines.
« Reply #26 on: 01/07/2011 18:16:53 »
I'm defining a curved sphere sitting in in 3D space and a flat plane sitting in 3D space and considering lines you draw on it.  There's no physics going on here, just mathematics. 

There's no time coordinate and no need to go to relativity which will just make things more complicated.
 

Offline yor_on

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Geometry and parallel lines.
« Reply #27 on: 01/07/2011 18:20:50 »
Yes I can see that there would need to be a balance if so, represented by those rubber bands. But that is also assuming that there will be gravitational simultaneous tension, I'm sorry JP, I keep coming back to imagining SpaceTime for it. But using the limitations you set up by using the material, and a sphere, you're right.

But it seems a very restricted definition to me.
 

Offline yor_on

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Geometry and parallel lines.
« Reply #28 on: 01/07/2011 18:30:51 »
The thing is, if we're talking SpaceTime I can imagine gravity's potentials as a fluid, ink sort of, and also getting the shape of a sphere, but as it is in time it will always have a direction. but with the sphere and the rubber bands you can cover the whole sphere simultaneously. And Gravity without a arrow? That one is a hard nut to crack for me.
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But thanks JP. You made me see how it was thought to work, and that was what I wanted too. :)
« Last Edit: 01/07/2011 18:37:27 by yor_on »
 

Offline JP

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Geometry and parallel lines.
« Reply #29 on: 01/07/2011 18:40:44 »
The problem is that to construct geodesics, you have to measure distances so you can compute the minimal distances involved.  It's very intuitive to think of distances in space, since we're used to viewing the world that way--that's how our tape measures work.

If you try to visualize measuring distances in relativistic space-time, it's suddenly way more complicated because the time coordinate behaves in a funny way.  It's not simply a matter of plotting position versus time and picking the shortest lines because time behaves in a funny way.  Points that look separated on the paper actually have zero distance between them.  I can barely visualize things in flat space-time after a fair amount of coursework, and I'm hopeless in curved space-time.  That's why I figured it would be easiest to stick to a simple case of rubber bands on spheres and planes in space.
« Last Edit: 01/07/2011 18:45:49 by JP »
 

Offline yor_on

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Geometry and parallel lines.
« Reply #30 on: 01/07/2011 19:01:08 »
Yes, I agree. It's very tricky. That's why I got me some books on geometry, that I'm planning to either read or use as fuel. Probably both as the mood sets in :)
 

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Geometry and parallel lines.
« Reply #30 on: 01/07/2011 19:01:08 »

 

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