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Simple universe model

  1. Sep 2, 2003 #1
    Imagine a very simple "model" for the universe:
    the universe is infinitely large, and contains only hydrogen atoms.
    Now all hydrogen atoms are placed in a perfect metric, each atom is placed at a cubic grid of some known metric proportions.

    What happens to this universe in the course of time?
  2. jcsd
  3. Sep 2, 2003 #2


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    spontaneous symmetry breaking

    what you have described is an unstable equilibrium
    like a pencil balanced on its point (this is the image
    of unstable equilibrium that for some reason people always seem to use) which any random fluctuation will make fall over

    any random imperfection or momentary fluctuation in
    the cubical lattice spacing will cause the matter to
    start clumping

    or so I think anyway
  4. Sep 2, 2003 #3
    That is what I would expect to occur indeed.

    But does there occur overal contraction?

    Would the average density increase?

    BTW. We assume in the model that all atoms are aranged almost perfectly and are not in motion relative to each other..
    Last edited: Sep 2, 2003
  5. Sep 2, 2003 #4


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    To be fair I should get to ask you a question. I am not familiar with the pictures of famous people in the Victorian era. Is that a picture of Hegel perhaps? Or of the political philosopher Marx?

    The cubical lattice is not exactly isotropic but let us apply the Friedmann equations (for homogeneous, isotropic universe) anyway.

    You get to choose the energy density and the cosmological constant and the initial value of the Hubble parameter.

    It is important that you specify the initial value of the Hubble parameter. If you like it can be zero (!) but it has to be something.

    What system of units do you imagine Hegel would have preferred?
  6. Sep 2, 2003 #5


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    Well, if take a volume with atoms evenly distributed, and an overall density that would put omega at 1, the universe should be expanding. Clumping shouldn't increase the overall density, since the overall volume of space is still increasing, right?
  7. Sep 2, 2003 #6


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    I think we are all assuming spatial flatness (as suggested by
    heusden's image of the infinite cubical lattice) so we can assume Ω = 1.

    But I do not understand why you assume the universe is expanding. Could it not also be contracting?

    the Big Friedmann equation is about the square of H, and so it has both a positive and a negative solution
  8. Sep 2, 2003 #7


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    (flat case) Big Friedmann:

    3 (a'/a)2 = 3 H2 = (8piG/c2) rho

    Little Friedmann:

    3 (a''/a) = - (4piG/c2) (rho + 3pressure)

    rho is the energy density
    heusdens gets to say what fraction of it is dark energy (the Lambda fraction is a critical part of the picture)

    I think the Lambda fraction of rho and the initial value of H
    are really critical inputs which will be key factors in determining
    what happens so perhaps we should wait for heusdens to specify

    edit: forgot minus sign in second eqn earlier
    Last edited: Sep 3, 2003
  9. Sep 2, 2003 #8


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    The assumption I'm making is that where omega=1, the universe can only be expanding at a slower and slower rate. Is it not true that only a closed universe can contract?
  10. Sep 2, 2003 #9


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    Ω = 1 is the condition for spatial flatness

    A spatially flat universe can be expanding at a slower and slower rate (as you say) or it can be expanding at an accelerating rate (as cosmologists now believe our universe is)
    or it can be contracting

    It used to be (back in the Nineties) that cosmologists assumed Lambda was zero (no cosmo constant, no dark energy term)
    and then what you say is partly right-----an Ω = 1 universe could either be expanding or contracting and if it was expanding then it would continue expanding forever at a slower and slower rate.
    Even in the Nineties there was the possibility that a flat universe might have been contracting since forever and would eventually crunch, but it was not talked about much because ours is expanding so that picture did not apply.

    But Heusdens could decide he wants to start off with his flat universe in a contraction mode----he is free to pick the intitial values
  11. Sep 2, 2003 #10


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    No fair. Assuming this is to be a simple model of the universe, a cosmological constant should be disallowed.
  12. Sep 2, 2003 #11


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    I know, it does seem hard that Nature plays such roguish tricks on us as to have a non-zero cosmological constant.

    Maybe you can convince heusdens to be more serious than nature and eliminate this frivolity in his version of the world.

    Since heusdens doesnt seem to be around maybe you would
    like to choose the initial conditions for his universe and run it?

    I am happy if you (or the original owner heusdens) makes Lambda equal zero because then it will be easy to say what happens.
  13. Sep 2, 2003 #12
    models and their garments of words

    Physics occasionally holds court in the physical world to decide questions posed by theoreticians. Since clumping has been observed in the laboratory(pencil fell) we could go on the ocnsiderations at the time of Hegel which continuued until Einstein died and it was then safe to imagine everything clumping in a point of zero space and other infinities such as a zero of time that Einstein would have embarassed anyone for imagining.
    Though even the the chiefs of the companies who are imagining the order to be imposed on earth can't imagine how to get those atoms evenly spaced (within uncertainty limits) WE CAN. by just imagining that initial state. And it will clump and clumps will clump. Infinite time later(now) we must consider infinite numbers of infinitely massed clumps infinitely distanced from each other. And if "now" is less than an infinite time after the imagined neat spacing our experiment will show our immediate clump to be condensing.
    And we don't have to con congress into funding a giant machine(that will have miitary-ordering use) to do the experiment to determine this.
    So something else brings enough stability for us to exist a while and not perceive condensation.
    Einstein, whose father wound electric armatures spent time considering the electrical forces on the wires. When he drew diagrams he drew slightly curved wires. He imagined a force that kept the electrical charge from clumping to a point.
    When he applied General Relativity to a physical model he chose the most mathmatically complete model at the time--a gas. He assumed a term(Lambda?) to represent the pressure. Pressure(bouncing off each other) keeps all the molecules from being gravitationally attracted to a point--their center of mass. He imagined the force that kept the charge of an electron from collapaing to a point to supply the pressure. When he saw Hubble's red shifts he saw there was experiment to show that some stars were recedeing. He took this evidence gathered from a limited view near earth to see that in this limited "universe" he didn't need the "pressure" to keep it from collapsing to a point. Physcists don't have to consider more than the space available for experiment.
    I can't really say he was embarrassed since he was the first to welcome the experiment--incorporate itto in His Theory.
    He then imagined a limited universe that collapses and expands--on and on. He allowed for the possibility that there isn't enough matter to collapse this local universe. He left it to the experimentalists to decide if there is enough matter and much was spent looking because there didn't appear to be enough. And folks didn't like the idea of getting cold(expand only) and were more comfortable with blowing up occasionally. Some day it will be considered if physicists are influenced by apperception; for instance the desire for earthly eternity and a belief of "In the Beginning".
    He knew that when a mathematical formula became pathological (predicted infinite physical things like density) it was wrong. Only after he died did some folks make their mark claiming such. Would someone please consider taking the UNIVERSE MODEL I posted to a physicist so he can tell me with what experiment it conflicts?
  14. Sep 2, 2003 #13
    ABout the initial conditions for this theoretical universe model:

    The only free parameter is the grid length of the cubes, which determines the density. I assume no motion with respect to each other of the atoms. So initially there is no contraction or expansion.
    I assume nothing about spatial flatness either. The cubic grid is just according to "world lines" (according to rays of light). Wether or not they make up an euclidean grid is to be determined.

    We already agreed that due to small fluctuations (nothing in nature can be perfect) that there would be clustering locally.

    The question thought was wether or not the universe would contract globally.
  15. Sep 2, 2003 #14


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    No cosmological constant, and this simple universe expands forever.
  16. Sep 2, 2003 #15
    Why would it expand globally?
  17. Sep 2, 2003 #16


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    You have the freedom to specify the initial value of H(t) and the solution depends on it.

    In realworld cosmology the value of H(present) is specified and the solution depends on it (one reason they set such great store by accurately measuring H(present), the current Hubble parameter.

    When you say "initially no expansion or contraction", you seem to be making a conscious choice to start YOUR universe with H = 0. Is that what you really want? You could start it off expanding and then it would continue expanding at least for a while----how long and in what manner might depend on some other choice you made like about the density.

    If you choose to start things off with H = 0 then unless you choose positive Lambda your universe is going to immediately start contracting and will eventually crunch.

    I guess that is the answer to your question-----it will start to contract globally.

    The "Little Friedmann" equation guarantees that because it forces a" to be negative (the second deriv. wrt time)
    So if you specify initially a' = 0 (the first deriv. wrt time is zero)
    then a' will immediately go negative and an unstoppable collapse will begin.

    I urge you to start the universe with some Hubble constant besides zero. Zero to my mind is a deplorable Hubble constant for any universe to have to start life with. And it would be nice of you to put in a little Lambda leavening too---a non-zero cosmological constant would brighten the prospect quite a bit although not strictly necessary.
    Last edited: Sep 2, 2003
  18. Sep 3, 2003 #17
    Hee, it's just a "toy" model, not an actual universe...

    I just wish you could explain me why it would contract globally.

    Since the universe is infinite and it has the same overall density, aren't the forces of gravity in each part of the universe exactly balancing?

    For local measures very slight variations occur, so I can at least understand it collapses locally, but globally the situation is near to perfect. Why would it contract?
  19. Sep 3, 2003 #18


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    I have explained why it would contract.
    The two Friedmann equations are basic to cosmology. They are mostly what the field is about.
    I trust them more than verbal explanations.
    You seem not to trust the equations or perhaps not to understand them.
    a(t) is a spatial scale factor built into the metric.
    and when they say expand they mean a' positive and
    when they say contract they mean a' negative
    your initial conditions specified that a' = 0 and that a'' is negative
    (because RHS of one of the Fr. equations was negative)
    that means that a' must immediately go negative----which spells contration

    the metric is a distance between stationary objects and it can increase or decrease, einsteins equation does not allow the distance between two non-moving galaxies to remain constant.
    the friedmann equations are the simplified form of einstein's equation that cosmologists use and they, in turn, do not allow the distance between stationary objects to remain constant--in a solution of the friedmann equations (just like with the orig. einstein one) space must either be expanding or contracting.

    if for some reason you dont like the equations that are used then you must, I fear, either not try to do cosmology or else you must make up your own differential equation
    verbal explanations dont cut it
  20. Sep 3, 2003 #19


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    heusdens, I am worried by an idea you seem to have that it
    matters if the hydrogen atoms (or galaxies, whatever) MOVE
    for the universe to expand or contract

    the atoms or molecules or galaxies do not have to be moving in some fashion for the universe to expand or contract

    that is not what general relativity is about
    since 1915 it never was about the things moving

    it was about the distances between stationary things getting larger or smaller

    this is what "spacetime curvature" is all about

    space can be flat like Euclid thought and yet spaceTIME can be curved, as long as it is expanding or contracting

    1915 Relativity is almost 100 years old. since your grandfather was a boy people have been telling each other "space expands". They never meant that the galaxies were moving in any direction. but only that the distance increases

    What worries me is when you say "the atoms cannot move, except for local clumping, because they are attracted equally in all directions, so therefore the universe cannot contract!"

    This is irrelevant. They do not need to move. Perhaps it is best if they do not move in the space around them at all, so imagine them sitting still without even any local clumping motion. Yet the metric will still either be contracting or expanding depending on how you started it off.
  21. Sep 3, 2003 #20


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    Well, if local flat space expands (assuming we're starting with an expanding universe) and you've got a universe which consists of 99% empty space, you're going to get an overall expansion.
  22. Sep 3, 2003 #21

    I got the idea, in some peculiar way i still think 'classic'.

    The point is though, is space expansion just some extra paramter?

    Or is the expansion or contraction ratio determined by the matter distribution, and the density?

    So it would in fact then be the metric size we choose that either would result in space contraction (omega > 1), space expansion (omega < 1) or flatness of space (omega = 1).

    Is this correct?

    What if we would choose the metric so that it comes very close indeed to omega = 1?
  23. Sep 3, 2003 #22
    Finally, the thread is woven into a "model" discussion. Marcus says verbals don't cut it but his Spoken WORD(SWORD) soes a good job of rendering a fit. Though he will likely agree that mathematical formulae are nothing more than condensations(contractions) of words.
    He will likely agree that in the Physics World after 1915 any "observors" will not initially observe any contraction because their rulers will contract at the same rate as the "space". Obviously there are no net gravitational forces or accelerations. One must be kind to allow the concept of an "observor" in this model but "they" are indispensable to the workings of the World of Relativity. ALL THE GR FOLKS ARE TALKING ABOUT IS WHAT AN ONE OBSERVOR OBSERVES ABOUT THE RULERS AND CLOCKS OF ANOTHER OBSERVOR. The only difference between "one" and the "other" is the mass local to one as opposed to the mass local to the other.

    Which is a good time to recommend a quick look at Albert's General Theory. Stop after a few pages when he has to go to Old German for strange symbols to represent math entities. Later you can learn to swallow them without chewing to get the the answers. you can trust lovers of math-chewing to get the right answers. Perhaps Marcus will consider a communal attempt to bring GR to the masses by application of his already sharp sword. I'd certainly appreciate it.

    Albert, working alone, which genius is sentenced to do, imagined the perfectly(infinitely) spaced created for us here in this thread. He noted, as does Marcus, that the math model into which he plugged this initial state demand that the rulers begin to get smaller. But they only get smaller to folks outside this space(sitting here at the keys) "observing" this space. The library is closing so I must.

    Next time I'd like to bring up fact that Einstein used an equation from thermodynamics into which he plugged this metric(ruler contraction and clock slowing). In that equation there aren't any gravitational forces between particles. I hope Marcus can find a moment to glance at the "universe model" I posted.
  24. Sep 3, 2003 #23


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    Heusdens you suggest we look at the spatially flat case
    "....or flatness of space (omega = 1)...

    What if we would choose the metric so that it comes very close indeed to omega = 1?"

    this is good it makes the equations simpler, everything simpler:

    To make it simple (as I think you want) lets make Lamda the cosmological constant equal zero. So the matter density is what matters. Also matter has negligible pressure so we can drop the pressure term from the equation!!!

    Heusden you asked
    "... is the expansion or contraction ratio determined by the matter distribution, and the density?"

    You are right. The rate of expansion or contraction depends on the rate you START WITH and on the average energy density

    Now everything is so simple that all you get to choose is rho
    (the joules of mass energy per cubic kilometer)

    Big Friedmann:

    3 (a'/a)2 = (8piG/c2) rho

    Little Friedmann:

    3 (a''/a) = - (4piG/c2) rho

    If we drop all the 3 and 8piG stuff, which is just constants then
    it gets really simple

    Big Friedmann:

    (a'/a)2 = 2 rho

    Little Friedmann:

    a''/a = - rho

    you can see the change-in-the-change---the second derivative--is proportional to MINUS the density

    (this is what slows expansion down, or if we get in a contraction, speeds the contraction up)

    you can also see that the square of rate of change of the scale---the a prime or first time derivative---is proportional to rho.

    So you get to choose rho----some joules per cubic km----and then you only have two choices left you can have it start with a' positive or negative. Any positive number has two square roots, a positive and a negative.

    In simplifying at the start according to your preference for the flat case without Lambda, we have thown out almost all free choice.
    But maybe that is best, for a toy model.

    So you can start it expanding and it will expand for ever, or you can start it contracting and it will contract faster and faster and eventually crunch.

    Do you mind my calling the two main equations of cosmology by the unserious names of Big and Little Friedmann. Most people would say "First Friedmann equation" and "Second Friedmann equation" but this sounds a bit over solemn. Must go
    my chorus is learning Die Schoepfung by Haydn and we must practice!
    Last edited: Sep 3, 2003
  25. Sep 4, 2003 #24

    Exactly what are you trying to say? That the expansion/contraction of space is only happening for an observer outside of this space?

    Who cares about non-existing observers outside of space or time?

    We only care what obsevers inside space and time can measure.

    How would you explain the fact that we seem to observe galaxies receding from us, from our point of observation?
  26. Sep 4, 2003 #25
    Library closing in three minutes-----I don't have the answer to why they "seem' to be receding but I appreciate communicating with someone who recognizes the importance of the word seem. Photons leaving areas of high mass will be shifted. Looking forward to pursuing your question tomorrow. This is motivation to get connected at home.
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