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I know this has been asked and here are the links of at least two. The first link below is what I thought was the standard description.

What does it mean for space to expand?

Now by accident while reading a different discussion I noticed this question.

How do we know we're not getting bigger?

One of the answers points to a link by an article by J.A. Peakcock and the other an article by "New Scientist" quoting Steve Weinberg so I thought I would include the link:

https://www.newscientist.com/article/mg13818693-600/

Basically in a nutshell Weinberg I think is saying space in not expanding it is the Copernican Principle and the fact that the universe was smaller in the past. He calls this a "complication". I assume while other people might call it space expanding which he says emphatically is wrong.

I always thought space and time were well sort of tied together. I wonder how something ia getting bigger in the past but not expanding in space? The Copernican Principle is easy to understand and obviously true but that space does not expand according to this article is confusing. Perhaps there is a mathematical reason for this?

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    $\begingroup$ I don't read the "space does not expand" from tne article in NewScientist. Or are you referring to one or the other of the two former links? $\endgroup$ Commented May 28, 2023 at 16:38
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    $\begingroup$ @planetmaker. It's the second link. I cut paste. BEGIN quote: "Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand? ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’ Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept,’ he says. ‘Think of the Universe in a Newtonian way – that is simply..." END of quote $\endgroup$
    – Sedumjoy
    Commented May 28, 2023 at 18:13
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    $\begingroup$ Minor edit: It's the "Copernican Principle", not the "Corpernicum Principle", named after Nicolaus Copernicus. Copernicus proposed that the planets (including the Earth) orbit the Sun. The previous Aristotelian (named after Aristotle) point of view saw the Earth as the center of the universe. $\endgroup$ Commented May 29, 2023 at 13:37
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    $\begingroup$ Thank you David. Sorry I should know better by now and check before posting. ...I hope you give me your opinion. Is space expanding? Me bad now I feel like a politician asking for something. :) $\endgroup$
    – Sedumjoy
    Commented May 29, 2023 at 14:21

2 Answers 2

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Space is not uniquely defined.

Spacetime, not space, is the physical domain in general relativity. Space is just a 3-dimensional surface within the 4-dimensional spacetime. The definition of a spatial surface (or "slice") is that it is a surface on which the time coordinate has a constant value. But there are infinitely many ways to pick a spatial surface and even more ways to pick a time sequence of spatial surfaces. None are objectively correct. So fundamentally we cannot make objective claims about what space is doing.

Positions within space are not uniquely defined.

The spatial slices were the surfaces of constant time. To complete our description, we also need to define the "threads" of constant spatial position. Here is an illustration of slicing and threading (taken from these lecture notes); $\eta$ refers to time, which is vertical in the diagram, while $x^i$ refers to position, which is horizontal in the diagram. slicing and threading As with slicing, there are also infinitely many ways in which we can choose the threading.

Choosing coordinates in cosmology

The Universe is expanding. That means that things are moving apart in a uniform way. For many calculations, it turns out to be really convenient to use this expansion as the basis for our slicing and threading. In particular, we choose

  • Spatial slices on which observers who follow the average motion of their surroundings (i.e., are "comoving with the Hubble flow") agree on how much time has elapsed since the beginning of the Universe.
  • Time threads that follow these "comoving observers", so that they are defined to be at rest. Since the comoving observers are moving apart, these time threads diverge in the future direction.

Indeed, those coordinates are the only ones for which the cosmological principle (that the Universe is the same everywhere and in every direction) is satisfied.

Thus, we often choose to "let space expand" in the senses implied by these choices of slicing and threading -- particularly, the fact that the threads diverge. But that is a choice that we (and not the Universe) make. Other choices are equally valid. For example, when studying systems that do not expand, like galaxies and things inside them, it is much more natural to choose time threads that do not diverge. Then there would be no sense in which space expands.

Thus, expansion of space is not physical.

Since it is a choice that we (and not the Universe) make, it cannot have any physical consequences.

As an analogy, we like to describe locations on the Earth by their latitude (north-south position) and longitude (east-west position). Going north from the South Pole, the lines of constant longitude (meridians) diverge. Does this mean the surface of the Earth expands as you go north? There's no objective answer to that -- it depends on definitions. But if you were to walk north from the South Pole, would the diverging meridians induce (for example) a tendency for your body to stretch? Clearly no.

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    $\begingroup$ Thank you for your gracious response. I am still mulling it over. It take me a while to think about it.But as I am mulling let me ask. Can we all agree the universe is bigger now than in the past as described by Steven Weinberg? What is it that is getting bigger? Maybe that may be confusing me. You say "expanding space cannot have consequences" Does "getting bigger" as claimed by Steve Weinberg have physical consequences? Thank you $\endgroup$
    – Sedumjoy
    Commented May 28, 2023 at 22:06
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    $\begingroup$ By the way the analogy is insightful but the earth is not getting larger like the universe however I do see your point and although very interesting we must ask if the analogy is valid. $\endgroup$
    – Sedumjoy
    Commented May 28, 2023 at 23:22
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    $\begingroup$ @Sedumjoy If the Universe is closed, then its conventional spatial surfaces are getting larger in the same way that the Earth's lines of constant latitude grow longer as you move north from the South Pole. Space is expanding in this sense, but again the choice of spatial surface matters. $\endgroup$
    – Sten
    Commented May 29, 2023 at 0:18
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    $\begingroup$ @Sedumjoy In the analogy, the Earth's surface is to represent the full 4D spacetime of the Universe, not just space. The Universe's spacetime doesn't get larger (or evolve in any way, since there's no external time parameter with respect to which to evolve). So the analogy is fair in this sense. $\endgroup$
    – Sten
    Commented May 29, 2023 at 0:21
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    $\begingroup$ Sten, how can you explain cosmological red-shifting using your analogy? If space wasn't really expanding but just our choice coordinates makes it look as is, how does this choice cause the fact that when I measure a CMB photon here on earth, I measure low-energy microwave photons and not a high-energy photon? $\endgroup$ Commented Jun 14, 2023 at 11:28
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The short answer is that spacetime is changing in such a way that, to put it clumsily, the amount of space between objects is increasing at a rate proportional to the distance between them.

One can't explain this by saying that those objects are moving away from one another because for objects sufficiently distant from one another the space between them increases faster than the speed of light. (This distance is called the "cosmological horizon".)

While this may not be "expansion" in the strictest sense, we don't really have a better, widely-understood term for it.

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    $\begingroup$ Faster-than-light recession is often cited as evidence that cosmic expansion can't just be objects moving away from each other, but it's not. You can literally make a cosmological model in which objects are flying apart within the flat, clearly-not-expanding spacetime of special relativity, and that model nevertheless exhibits faster-than-light recession. This page has some nice pictures illustrating why this happens, but the basic point is that recession rates are not relative velocities. See also physics.stackexchange.com/q/400457/180843 $\endgroup$
    – Sten
    Commented May 30, 2023 at 13:22
  • $\begingroup$ @RLWatkins. I am glad you included this link because it has additional links that are all related to this topic in one form or fashion for the reader in general. You found an elegant solution for the layman like myself. You describe what is happening without having to use the word "expand". And it is perfectly consistant with Stan's answer and "The New Scientist Article". $\endgroup$
    – Sedumjoy
    Commented May 30, 2023 at 16:55
  • $\begingroup$ @Sten Do you have a link for the "objects are flying apart within the flat, clearly-not-expanding spacetime of special relativity"? (This clearly isn't our universe; the FLRW metric is not the same thing as the Minkowski metric.) $\endgroup$ Commented May 30, 2023 at 20:48
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    $\begingroup$ @PeterErwin I'm referring to the special case of FLRW with negligible energy density (also known as the Milne model). That metric is just a reparametrization of a portion of Minkowski space. The point is not that this is an accurate model for our universe but rather that it's a counterexample to the claim that faster-than-light recession means there is some fundamental sense in which space is expanding. (In that model, faster-than-light recession is attributable to time dilation. See also the cosmology tutorial linked in the earlier comment.) $\endgroup$
    – Sten
    Commented May 31, 2023 at 4:43
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    $\begingroup$ Another, less obvious counterexample is the dark energy-dominated universe -- de Sitter space -- patches of which can also be written in a manifestly static form. By the way, these examples also illustrate that cosmic expansion fundamentally relies on the motion of material within the universe. If the universe is empty (Milne) or filled with a Lorentz-invariant fluid (de Sitter), then there is no objective sense in which it expands. $\endgroup$
    – Sten
    Commented May 31, 2023 at 5:02

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