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Apparently the distance between galaxies used to be smaller in the distant past. That means it used to take fewer units of time to get from one galaxy to the next. So either the distance really was smaller in the past or the units of time used to be bigger in the past. Which of the following is true?:

  1. The spatial dimensions of the universe are expanding
  2. The time dimension of the universe is contracting
  3. The distinction between #1 and #2 is meaningless
  4. The question illustrates my complete ignorance of general relativity.

    (I fear the answer is #4, so some intuitive guidance would be helpful)
Roger Wood
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2 Answers2

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They say the universe is expanding. Is that the same as saying that time is contracting?

No.

  • First, to measure time we employ means that are independent of the large scale behavior of the universe. In particular, the second, SI unit of time, is defined via the transition frequency of caesium atom and not through e.g. the duration of light-speed trip to Caelum Supercluster.

  • Second, the expansion of the universe is not homogeneous on smaller distance scales. Small scale objects such as atoms or even planets and even larger gravitationally bound systems such as galaxies and galactic clusters keep their size. It is the space between galactic clusters that is expanding. See e.g. this question for the discussion.

So OP's list item 1 is true, list item 2 is false, and list item 3 is also false precisely because there are scales of time and distance that are independent of large scale cosmological behavior. As for item 4, asking questions is how we learn.

A.V.S.
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  • @ A.V.S. That is helpful. I see your comment about gravitationally bound systems. The reference is good and offers a protracted discussion of this point, but does not seem to reach a clear conclusion. One point that keeps getting repeated is that the effects are small, but that is not the case because the timescales are often huge. Two isolated, dead, rocky, tidally-locked planets will continue orbiting each other almost unchanged for many billions of years. Meanwhile the fabric of space underneath them may have expanded by a factor of two or more! – Roger Wood Nov 04 '20 at 18:50
  • @RogerWood clear conclusion is stated in that question itself: bound systems do not expand, the rest are references to mathematical facts of GR as well as metaphors and analogies, some of which may not be too precise. If the evolution of gravitationally bound systems is described by GR (maybe with cosmological constant) then this expansion of bound planetary system would not happen, just like it would not happen if Newtonian gravity is used. This may be the case of pushing the metaphor of stretchy fabric too far. – A.V.S. Nov 04 '20 at 20:45
  • @ A.V.S. Is a bound system one where the objects are moving more slowly than escape speed? – Roger Wood Nov 05 '20 at 04:02
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1-3 are all true.

  1. If you use the most common cosmological coordinates, in which position is scaled by a factor $a(t)$ that increases with time, then the coordinate distance between galaxies is constant but the measured distance increases because of the scaling.

  2. If you use conformal coordinates, in which both position and time are scaled by $a$, then the coordinate distance is constant and the coordinate speed limit (speed of light) is constant, but clocks tick faster at later times so it takes more real time to get to other galaxies.

  3. Coordinates are meaningless. It takes longer, in actual measured time, to get between the galaxies at later times because they're getting farther apart, in actual measured distance. How you model this with coordinates and "scaling" has no bearing on those physical facts.

I guess 4 is also true, but you've gotta start somewhere. Understanding that coordinates are meaningless is the first step to understanding GR.

benrg
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  • coordinates are meaningless

     – Ryan Parikh Nov 03 '20 at 22:49
  • spatial dimensions which the OP is asking about are computed not as a differences in coordinates, but as $\int ds$ over a spacelike curve. And in cosmological context the choice of spatial slice and said curve is pretty much fixed. Likewise, “cosmic time” has also meaning, independent of coordinate choice. Coordinates are meaningless Also not true. While a local coordinate system chosen at random may not carry much of a meaning, a specific choice of coordinates for a given situation can convey a lot about symmetries, spacetime properties and even tools likely to be used. So, -1. – A.V.S. Nov 04 '20 at 07:39
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    "coordinates are labels" is perhaps a better way of putting it than "coordinates are meaningless" – Andrew Steane Nov 04 '20 at 09:12
  • ... you can always choose to write meaningful things on a label, as is done when using proper time in comoving coordinates, for example – Andrew Steane Nov 04 '20 at 09:13