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In Issues related to expansion of the universe while space-time itself is moving how it is possible to calculate the speed of an moving object? In other words how object's movement is separated from the space-time movement?

Qmechanic
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Alberto
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2 Answers2

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The best way to think about this question is to view space expansion as a global phenomenon while relative movement of objects is a local phenomenon. The only reason we are aware of space expansion is the distance related red shift of radiation received from very distant objects. By very distant objects I mean objects in galactic superclusters that are not part of our own local supercluster. A supercluster is defined as the largest collection of galaxies that are bound by their gravitational attraction.

Measurements of relative speed of objects in our local supercluster are not significantly influenced by the expansion of the universe because at this local scale the expansion during any small interval of time is very small compared to the dynamics associated movement between objects.

Lewis Miller
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  • My question is a fundamental question. I know about redshift and supercluster and I know about accelerated movement of distant galaxies. My question is on what basis we can attribute redshift to expansion of space-time rather than the movement of the galaxies themselves? What's the difference between the two? – Alberto Mar 15 '16 at 20:08
  • Okay, I have a better understanding of your question now. Redshift is always due to the movement of galaxies. For nearby galaxies, it can be either a redshift or a blueshift since the relative motion of nearby galaxies is dominated by their gravitational interactions. As the galaxies become more distant it is primarily redshift because the relative motion begins to be more and more dominated by the scale factor $a(t)$ that describes the expansion of the universe. The scale factor depends on your favorite solution to the equations of general relativity and your model of the big bang. – Lewis Miller Mar 19 '16 at 16:53
  • So if i understood your comment there is no reason to attribute the redshift to space expansion and we can attribute it to space expansion or to galaxies velocity. If this is true there is a problem here: if redshift happens because of galaxy movement (not space expansion) , the speed of galaxy can not be more than the speed of light but vice versa the space itself can travel faster than the speed of light. So the future of universe depend of sulution of this problem. Am I right? – Alberto Mar 19 '16 at 20:19
  • The reason we attribute RS to space expansion is because it increases with distance. We are still seeing the effect of relative motion. Space expansion can exceed the speed of light if we look at sufficiently large distances. But we never see RS exceeding speed of light, because galaxies at those distances are not part of our observable universe. – Lewis Miller Mar 20 '16 at 01:57
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Does it matter? Let's say you make a manifold and you friend makes a manifold. And you each put some worldlines on your manifold. And you each put a metric tensor on your manifold. And you each use the metric to compute proper time along the worldlines.

And you mark equally spaced portions of the worldlines (equal according to proper time, using the metric along the curve) and you send out null geodesics from those marks to the other worldline.

And you compare how many null curves hit the one world line from the other worldline compared to how many of the worldline's own markings are along the worldline. You can call that a kinematic redshift or a gravitational redshift because you that's just name calling. The science happened when you numerically compared how many null curves hit the curve compare to the proper time markings along the curve.

You could do it in your manifold. Your friend could do it in their manifold. If you get the same numbers you make the same predictions so what does it matter what you call it.

This isn't me being facetious because you literally asked how to tell something that didn't affect the calculations, didn't affect the predictions. So it doesn't have an observational answer. There is no empirical answer, which says something about the question.

Basically, coordinates are like a gauge. If you pick one, then that picking doesn't make it physical. And the predictions end up not depending on the gauge or the coordinates, so you don't want to get too excited about the coordinates or the gauge.

So maybe in one coordinate system it looks like a kinematical redshift. Maybe in another coordinate system it doesn't look kinematic in origin. Don't get overly excited by things that don't affect your predictions. Don't shy away either if it helps you get stuff done. But it just is what it is.

Timaeus
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  • Thanks. I asked this question because I read that space itself can travel faster than the speed of light. So it important to know the answer of question. Because if redshift happens because of galaxy movement (not space expansion) , the speed of galaxy can not be more than the speed of light. – Alberto Mar 16 '16 at 06:36