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Specific definition of space in BB

  1. Oct 29, 2005 #1
    I'm sorry if this question is a little basic but I have been unable to find a satisfactory answer looking around on the net.

    When one says "space" itself is expanding (as in the BB model) what is the definition of "space"?

    Thanks in advance
  2. jcsd
  3. Oct 29, 2005 #2


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    Hi David and welcome to these Forums!

    Keep asking the questions, that is how we learn.

    Imagine a 3D volume being filled with a hugh notebook of thousands of pages. The surface of each page is a 2D surface on which you may want to draw diagrams.

    Each surface is separated from its neighbours by a small displacement in a direction orthogonal to the sheet-surface itself.

    If you bend the notebook each sheet-surface will not be flat but still the displacement vector from one sheet to the next will be locally orthogonal to those sheets.

    Use this as an analogy to 3D spaces embedded in a 4D space-time. Each sheet represents the hyper-surface of space marked out at one specific time. The displacement vectors from one sheet to the next being time itself. Slicing space-time up this way is called a foliation.

    Now GR explains gravitation as the effect of space-time being curved by the presence of mass.

    The individual hyper-surfaces of space are curved as well, but remember the curvature of space is different from the curvature of space-time. An example of this is the Milne empty model of the universe in which, because there is no matter in the universe, space-time is 'flat', the components of the Riemannian tensor are all zero. Nevertheless it turns out that each spatial hyper-surface (sheet) is hyperbolic - curved like a pringle crisp or saddle.

    Another point, the way a block of space-time is foliated, sliced up into spatial sheet-surfaces, is dependent on the frame of reference of the observer. Two observers moving relative to each other will foliate space-time differently. In the standard theory of GR, because of its equivalence principle, there is no preferred foliation of space-time. However it seems that we can identify a special foliation, that made by an observer co-moving with the centre of momentum of the matter in the galaxy, in which the CMB is globally isotropic.

    In this special co-moving frame of reference the cosmological solution to Einstein's GR field equation requires the universe to either expand or contract. This means the spatial 3D foliations (surface-sheets of space) expand or contract with a change of time within a static block of space-time. The diagrams we have drawn on one surface-sheet will get bigger or smaller as you go from one sheet to the next.

    I hope this helps.

    Last edited: Oct 29, 2005
  4. Oct 29, 2005 #3
    Thanks for taking the time to reply. Yes that helps for sure, but the explanation seems to indicate that my understanding of this is very limited, and my questions too simple. I understand the analogies of raisins in rising bread etc.. but have trouble understanding what it actually means in context. So let me ask sort of the same thing in another way.

    My understanding is that when I look up at the night sky to a specific star that the distance between myself and the star is increasing. This expansion is not due to the star actually moving away but to the "space" between us expanding. if I lower my gaze from the star overhead to the house across the street is the "space" between myself and it increasing also? (my guess is no it isn't, but this is where my understanding breaks down. Why is this different?). I think it is the word "space" that I don't understand properly.
  5. Oct 29, 2005 #4


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    The mathematical relations that describe the behavior of the universe are independent of implementation. Space as a surface is an awkward perspective, what is important is that the mathematical relations that describe such an analogy coincide with the ones that govern the behavior of that aspect of the universe. For instance, suppose the position of a particle is given by a function of variables a, b, c. Then, any analogy implementing the underlying function f(a, b, c) will successfully predict where the particle will move next. There may be only one such analogy that works for the universe as a whole, but as long as our knowledge is incomplete there is a potentially infinite number of valid explanations of why things happen or of what things are.
    Our current science is a mathematical system that successfully models the behavior of the universe to some degree. But this is similar to saying "my function y perfectly models function x between a and b", we can't be sure that our function y is the same function as x. In fact if x is the function describing the behaviour of the universe, then y is humanity's attempt at approximating x in some interval [a, b]. Our definition of space then is already extremely dependent both on our assumptions and experience, and it could become something entirely different, but as valid, were we to modify some of our basic concepts. (This is my argument as to why space as a surface and not as "nothing", though tough to grip, may be perfectly valid, since whether or not it is "true" is irrelevant.)
    So what the actual definition of space is is not as meaningful as how it relates and works with our other definitions.
    Space is anything you want it to be, as long as it works with what we have, but to generate a good one, knowledge and experience of physical phenomena are key (these are our points in the function x which we can use to generate the approximation y). We are interested in an explanation that works with what we have (no matter how ridiculous it is) not just one that works, we don't want to redo everything. I assume, at some point, it has to get ridiculous.
    Last edited: Oct 29, 2005
  6. Nov 1, 2005 #5
    Thank you for the informative replies above - it leads me to some new questions- and thanks in advance for your time.

    Is all "space" the same? Is the "space" between me and my computer screen the same kind of "space" that one refers to when one says "space" itself is expanding? If not how/why is it different?

    Are there any "credible" (non crack-pot) theories that attempt to refute the notion of expanding space or is it uniformly accepted?

  7. Nov 3, 2005 #6
    I've argued against this way of looking at space on my website:
    If you want something more official then take a look at Don Page's paper:
    I have to say that the 'expanding space' view certainly seems to be the mainstream one, for example in
    and other papers by Davis and Lineweaver.
  8. Nov 3, 2005 #7


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    It depends on which ruler you are using.

    If your ruler is made of atoms - a steel rule for example - then as measured by that ruler the universe is expanding around it. You define the ruler to be of fixed length over cosmological time scales. This means that certain physical constants, the mass of the atom, the charge on the electron and by inference the fine structure constant, are defined to be constant.

    There are reputable theories, the mass field theory of Hoyle and the Variable Light Speed Theory of Albrecht and Magueijo and Barrow Cosmologies with varying light speed as well as the Jordan conformal frame of SCC where one or another of these 'constants' actually varies.

    Rulers will then change length when compared with some other standard and in some of these theories such as the Jordan conformal frame of SCC the universe is then static (non-expanding) and eternal.

    Last edited: Nov 3, 2005
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