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Need Intuition Behind Expansion of Smaller Structures in the Universe

  1. May 19, 2013 #1
    I am trying to understand what is meant when people say space itself is expanding.

    When I hear that, I imagine a 3-d Cartesian coordinate system in which every axis gets scaled at a given rate (like in an animation).

    What I don't understand is, if everything gets scaled, then how can anyone even tell that scaling is occurring?

    Let's say I looked at a meter stick.
    Then let's double all lengths in all 3 dimensions.
    If I look at the meter stick again, I would think that I wouldn't be able to physically tell any difference between this case and the first...
    Not only has the meter stick doubled length in all directions, but so have all my sense organs (and anything else) which I use to measure it (funny since the meter stick itself is a measuring device).

    This tells me that not everything gets scaled...
    Or at least... not scaled equally.
    So the next natural question is, what determines scaling differences for larger structures (whole universe) vs. smaller structures (single galaxies, solar systems, meter sticks, variance (RMS) of the probability density of the position of an electron, ...etc)

    Looking at this example:

    The smaller structures in that example expanding universe don't seem to themselves be expanding that much... so why are they not getting scaled?
    And if smaller structures are not getting scaled, is it really valid to say space itself is expanding, or is it more valid to say that things are just flying away from one another? - I know the answer that will be given to me here, but not the intuition.

    Here's a quote from a wikipedia page: https://en.wikipedia.org/wiki/Metric_expansion_of_space

    "In principle, the expansion of the universe can be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again."

    So my question is, why doesn't the "standard ruler" itself talked about here also expand, such that the same measurement will be made over and over again.

  2. jcsd
  3. May 19, 2013 #2


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    Everything doesn't get scaled. Small-scale bound systems, like a meter stick, or a planet, or the solar system, or even a galaxy, don't expand. Viewing the expansion of the universe as scaling the space coordinates only works on very large distance scales, like tens to hundreds of millions of light years and larger--distance scales large enough that the density of matter and energy in the universe can be taken to be uniform.
  4. May 19, 2013 #3
    Metre sticks are made out of matter which is held together by electromagnetic and strong nuclear forces—which are much stronger than gravity. The fact that expanding space-time causes distant objects to move apart is just geodesic deviation; that is, precisely the same effect as gravitational attraction due to matter in GR. In either case, the geometry of space-time means that initially parallel free-falling trajectories (geodesics) don't stay parallel. In the case of matter attracting matter, the geodesics get closer to one another. In space-time expansion, they get further apart.

    Now, the gravitational attraction of the earth pulls you towards its centre. Of course, you don't do so because you're not in free fall. The earth's surface is pushing up on you, preventing you from following a geodesic towards the centre of the earth. Or, you can get on an airplane or a rocket ship. By applying forces, you can push yourself off of geodesics through curved spacetime.

    Likewise for space-time expansion. Other forces can overcome the tendency to move apart due to the geometry of space-time. Gravity is by far the weakest force, so it is easily overcome. In fact, the force of space-time expansion is so weak over short distances that it can be overcome even by other gravity (like that which binds the earth to the sun). Hence, only very distantly separated matter is affected by space-time expansion.
    Last edited: May 19, 2013
  5. May 19, 2013 #4
    Ok thank you.

    So I don't understand why people say that space itself is expanding then...
    Based on what you said above, that does not seem to be case to me.
    The balloon analogy in the simulation I linked to above almost seems more like an initial velocity type of thing rather than "space itself expanding".

    I guess maybe the use of the phrase "space itself is expanding" is merely a way of characterizing the overall effect of "initial velocities" of all the parts of the universe at super large scales - but not an actual assertion that space itself is expanding...

    "Initial velocities" seems like an explosion, and I have read other things that say that the expansion of the universe is fundamentally different than an explosion.
  6. May 19, 2013 #5
    Thank you as well.
    I'll need to spend some more time reading the material you linked to, but the main thing I'm getting out of your response is expansion has basically the same underlying phenomenon as gravity (geodesic curvature) and that smaller-scale structures in the universe have forces on them that can overcome the geodesic curvature due to expansion. So expansion is still present for these smaller structures, it is just a smaller component of an overall super-position of stronger forces.
  7. May 19, 2013 #6


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    Not quite; there's more to it than just "initial velocities". On large distance scales, the universe is (at least to a good approximation) homogeneous and isotropic; that means that, spatially, one part is just like any other and it looks the same in all directions. But this is only true for a particular family of observers, called "comoving" observers; in the balloon analogy, these are observers who are at rest at some particular point on the surface of the balloon. As the balloon expands, the distance between any given pair of such observers increases; the same is true for any pair of comoving observers in our universe. Since the comoving observers themselves are at rest (at least, they are with respect to the standard cosmological coordinates, which correspond more or less to something latitude and longitude on the surface of the balloon), the only way they can be getting further and further apart is for space itself to be expanding.

    As the above makes clear, saying that "space is expanding" requires you to pick a particular definition of what "space" means: it means space at a given instant of time for the family of "comoving" observers. In other words, it depends on adopting a particular set of coordinates to describe the universe. This set of coordinates is very natural to adopt, but it's still a choice of coordinates.
  8. May 19, 2013 #7
    More or less. Peter's point was that the model of universe we use to look at space-time expansion requires a pretty "zoomed out" viewpoint where the distribution of matter can be taken as uniform. Hence, the metric expansion doesn't even have such a tidy expression at the length scale of every day matter. At that scale, the gravitational attraction of every day matter dominates. That was my point when I said that "the force of space-time expansion is so weak over short distances that it can be overcome even by other gravity".
  9. May 19, 2013 #8
    I think you misspoke, Peter. There is no space-time expansion if you adopt the coordinates of co-moving observers, by definition. It is the proper distance that increases with metric expansion, not co-moving distance.
  10. May 19, 2013 #9


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    Huh? The increase in proper distance *is* what is called the "expansion of the universe". (It's a spatial expansion, btw, not a spacetime expansion.) In comoving coordinates, the increase in proper distance is seen in the increase of the scale factor with comoving time.
  11. May 19, 2013 #10
    Sorry, yes, spatial expansion. Yes, that's my point. You said that saying, "space is expanding" requires a definition of space (i.e. a choice of coordinates) and that choice is defined by a set of co-moving observers. My point is that space does not expand in the coordinates of co-moving observers. That's what co-moving observers are for.

    Edit: Oh, I see: you meant co-moving observers for the purpose of defining co-moving time. Gotcha. I had thought you were saying that spatial expansion was defined by the spatial coordinates of co-moving observers.
  12. May 19, 2013 #11
    Interesting stuff. I'll have some good material to read into based on your replies. Thank you both!
  13. May 19, 2013 #12


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    Right. Co-moving observers are at fixed spatial coordinates in comoving coordinates, but spatial coordinates don't define distance, they're just coordinates. You have to look at the metric to see how to determine spatial distance as a function of the coordinates.
  14. May 20, 2013 #13


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    The idea behind "expanding space" is supposed to make things easier to understand. I personally don't see the appeal, either. But it's undeniable that a lot of people like to talk about it.

    For a guide to the literature (which is more enthusiastic about the expanding space idea than I am personally), a good place to start would be:

    http://arxiv.org/abs/0707.0380 Expanding Space: the Root of all Evil?
    http://arxiv.org/abs/astro-ph/0310808 Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe

    I'll quote part of the first paper that I agree with:

    If you view "expanding space" as something that you can measure by looking at how observers who observe the universe as isotropic move relative to each other, the idea is useful.

    It often leads to a lot of confused questions, though, such as "if space is expanding, why isn't Brooklyn expanding" of Woody Allen fame. Such questions are obviously taking "expanding space" idea to be something much more fundamental than the defintion offered above.

    I think part of the problem is that the "expanding space" idea is frequently (mis) used to make people who are trying to learn GR without having an inkling of SR to "shut up". It sort of works at this, in that it doesn't hurt anyones feelings, but - it leaves something to be desired in terms of incalculating a truly correct understanding.
  15. May 20, 2013 #14
    Thanks pervect, much appreciated!
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