The geometry of the expansion of space

  • #1
benorin
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Main Question or Discussion Point

I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose because I assume it true for the following: suppose that at a given point in time three galaxies taken as points at their centers form a ##1 : 1 : \sqrt{2}## right triangle. What sort of triangle will these galaxies form later? Let the distance between any two points in space be increased by a length h due to the expansion of space at that time we again measure the triangle, then since each side of the triangle is just the distance between two points itself we will have a ## 1+h : 1+h : \sqrt{2}+h ## triangle, some simple algebra reveals that this is an isosceles triangle which is not a right triangle, so the expansion of space does not preserve right triangles? Not knowing even if I have a correct underlying definition, I will stop here and wait for confirmation. Please correct me if need be and feel free to illuminate any thing you think is in the vein of this post.
 

Answers and Replies

  • #2
283
143
I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose because I assume it true for the following: suppose that at a given point in time three galaxies taken as points at their centers form a ##1 : 1 : \sqrt{2}## right triangle. What sort of triangle will these galaxies form later? Let the distance between any two points in space be increased by a length h due to the expansion of space at that time we again measure the triangle, then since each side of the triangle is just the distance between two points itself we will have a ## 1+h : 1+h : \sqrt{2}+h ## triangle, some simple algebra reveals that this is an isosceles triangle which is not a right triangle, so the expansion of space does not preserve right triangles? Not knowing even if I have a correct underlying definition, I will stop here and wait for confirmation. Please correct me if need be and feel free to illuminate any thing you think is in the vein of this post.
Based on the Hubble's law, the recessional velocity of the objects due to the expansion of the universe is proportional to the distance between the objects. Let's label the vertices of the triangle A,B,C. That means, when distance between A and B is doubled during time T, the distance between A and C, and B and C is also doubled during the same time interval T. So the angles will be preserved, just the edges will be scaled. This must be truth becasuse none of the points in the universe is privileged.
 
  • #3
283
143
I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose because I assume it true for the following: suppose that at a given point in time three galaxies taken as points at their centers form a ##1 : 1 : \sqrt{2}## right triangle. What sort of triangle will these galaxies form later? Let the distance between any two points in space be increased by a length h due to the expansion of space at that time we again measure the triangle, then since each side of the triangle is just the distance between two points itself we will have a ## 1+h : 1+h : \sqrt{2}+h ## triangle, some simple algebra reveals that this is an isosceles triangle which is not a right triangle, so the expansion of space does not preserve right triangles? Not knowing even if I have a correct underlying definition, I will stop here and wait for confirmation. Please correct me if need be and feel free to illuminate any thing you think is in the vein of this post.
maybe I could also add, that expansion is observed on the scales where the concerned galaxies are not gravitationally bound, e.g located in different groups or clusters.
Also the reason why you got the different angles is because you incorrectly assumed that during time T, the distance between any two points is increased by constant length h, which cannot work if you think about it a little more.
 
  • #4
benorin
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makes sense, thanks!
 
  • #5
benorin
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How is it that gravity could slow this expansion of space? I've heard that the presence of mass warps spacetime but this sounds like bending it not contracting it's length. I've taken a standard undergrad three semester course of physics which had little bit of modern physics in it. But I don't really get that stuff quite yet, so please make your answer simple so I can understand. Thanks!
 
  • #6
Bandersnatch
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How is it that gravity could slow this expansion of space? I've heard that the presence of mass warps spacetime but this sounds like bending it not contracting it's length. I've taken a standard undergrad three semester course of physics which had little bit of modern physics in it. But I don't really get that stuff quite yet, so please make your answer simple so I can understand. Thanks!
Length contraction has nothing to do with gravity. But you don't need GR to understand this. Expansion is just like Newtonian motion of objects flying away from each and every observer, with some initial velocity proportional to distance from the observer. Enclosed in a sphere of radius equal to that distance is some mass, which decelerates the motion.
 

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