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Post by abacus9900 on Nov 22, 2010 19:14:15 GMT 1
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Post by speakertoanimals on Nov 22, 2010 21:09:52 GMT 1
I'd just be repeating what its says on Wikipedia, which wouldn't be that useful. Anyway, I don't think these diagrams would be at all useful unless you have already mastered the basics.
Looking at bottom diagram, time is runnig from the small circle on the inside, to the larger one on the outside, hence radial lines represent things fixed in space, sitting there through time. going around a circle is movement in the single spatial dimension. Hence we have brown line on the left as the earth (or matter that would form the earth), running radially outwards. Yellow line os quasar, and the fact that it is radially 'opposite' means it is a long way away (distance you have to travel around a circle to get from earth to quasar.
What light does (red line), if you look closely, is always move along diagionals of the squares marked, which is distance in space traversed (going around distance) in equal units of time ( moving radially is time). Hence the light can do this (move locally always at speed of light, yet get from quasar at early times (bottom of come near small circle), to earth (brown radial line) despite the fact that at present time, we are a very long way away from the quasar (brown arc of circle, representing present distance between us and the quasar).
what this says (not very clearly) is what we said before. Small circles are space when it was still small, larger circles are space after expansion, and what light manages to do is travel from quasar to us, by travelling when we were closer together. Hence light travels 13 billion lightyears and reaches us, even though the quasar is currently 28 billion lightyears away. It effectively travels that 28 billion lightyears when things hadn't expanded so much, which is why it manages to travel 28 billion lightyears in only 13 billion years, whilst still always moving at lightspeed.
Which I don;t expect you to understand, the diagram isn't that useful.
And isometry just means -- we draw it so that distances in space and time are preserved, even if we have to throw away two dimensions, and curl the single dimemsion around to make it fit on the page.
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Post by speakertoanimals on Nov 22, 2010 21:32:29 GMT 1
Just to try and explain further -- the small circle at the bottom is early universe (distance between earth and quasar small), the larger circles at the top are after expansion. So with time running upwards, we have a sort of cone shape, where the fact that we get larger and larger circles as we move up represents space expanding.
The cone isn't complete else we would be saying the universe was closed, we could go off in one direction and come back to where we started without turning round if it was a real cone.
The curve is not curved spacetime, but just for the purposes of the diagram.
So, object at fixed position (earth or quasar) is line that runs vertically, but doesn't move around the cone . Light, on the other handm, constantly moves, hence as it moves vertically (time passes), it must also move around the cone (moving through space). The speed is the angle it makes with the horizontal circles, which is constant.
Distance now between us and quasar is the length of the segment of a circle drawn horizontally near the top. The moving light, moving through the universe as it expands, traces out a complicated path, but we have the usual effect that squares it traverses early on get wider as time goes on -- so the reason it can seemingly travel 28 billion lightyears in less than that time in years, is that that distance was smaller in the past (small arcs of circles near the bottom compared to longer arcs near the top, after expansion).
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Post by speakertoanimals on Nov 23, 2010 16:17:47 GMT 1
And just to reduce it to the simplest level -- imagine a circular cone. We have earth on one side (vertical line, lets take cone pointing upwards),and quasar on other side (another vertical line).
The distance apart NOW is the distance around the cone horizontally at the base.
The fact that it is a cone represent space (distances in horizontal plane) expanding with time (vertical direction is time).
Now take light -- it always follows a slanting path (constant speed of light). So light leaves quasar in early times, and follows a slanting path around the cone until it reaches earth NOW. The point being it can reach earth now, although there hasn't been enough time for it to travel the distance the quasar now is away from us in the time available, since it traverses most of the path at earlier times (near the point of the cone), when all distances were smaller.
In terms of distance travelled in horizontal plane (spatial distance travelled), the light travels less than the distance around the base since it starts at the point!
That is about it for those diagrams, but actually I think my earlier explanations were a lot simpler -- the distance already travels expands as you keep travelling, hence it appears that you have travelled a greater distance than you actually did, because the road has been stretched since you traversed it.
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Post by alanseago on Dec 2, 2010 8:01:50 GMT 1
Very clear, STA, even I can understand that. I admit that I have struggled in silence until now.
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Post by speakertoanimals on Dec 2, 2010 15:10:40 GMT 1
Thanks for that! I do try, and those diagrams took a deal of explaining.............
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