Light elements abundance in a static toy universe

  1. As an exercise in cosmology-fiction (I actually got curious about this from an actual cosmology textbook problem), taking into account the stellar nuclear reactions that involve the fusion of hydrogen into helium, what would (roughly) be the proportion (in mass) between Hydrogen and He-4 in a static universe?
    Would it resemble the proportions of primordial nucleosynthesis given that these are produced close to thermodynamic equilibrium?
    Last edited: Feb 21, 2012
  2. jcsd
  3. Chronos

    Chronos 10,348
    Science Advisor
    Gold Member

    Chemical abundances in 'pristine' [primordial] gas clouds would be very difficult to explain if the universe was significantly more ancient than we suspect. It is not uncommon that what you don't see tells you as much or more than what you do see.
  4. A static universe can't be more or less "ancient", it is symply time-invariant as a whole.
    It is totally discarded by science so I'm not sure what your comment means. My question is purely theoretical.
  5. BillSaltLake

    BillSaltLake 184
    Gold Member

    Are you assuming that one begins with nothing but pure hydrogen, and that any transmutation was stellar in origin ?
  6. Yes, just the stellar nuclear reactions, only in a static universe makes little sense to say what one begins with, since time is invariant.
  7. BillSaltLake

    BillSaltLake 184
    Gold Member

    Then 4He, 3He, and 2H would be much rarer than observed. Most of these isotopes would be inside active stars and would be consumed during the stars' lives. The initial collapse into stars would be different (I'm not sure of the details) because the initial gas would not be composed of a quarter 4He. I assume there would still be supernovae and metal enrichment, though. There would be probably 1/100 or less 4He than 1H, and most of that locked up in stars. Lower-mass stars (< ~1.5 solar masses) will usually become composed for a limited period of mostly 4He in later life, but this He will eventually fuse to heavier elements.
    Last edited: Feb 21, 2012
  8. I guess you are ignoring that there is no global evolution in the kind of scenario I'm talking about. There can only be a permanent equilibrium distribution. I'm asking what would that distribution be according to the stellar nuclear reactions and core temperature conditions. Maybe it's easier to think in terms of proportion of neutrons and protons in thermodynamical equilibrium at the stars core temperatures.
  9. BillSaltLake

    BillSaltLake 184
    Gold Member

    The meaning of steady state might be a problem. After a very long time, everything might be photons and neutrinos (after black hole evaporation, and after any possible proton decay with the resulting positrons annihilating the existing electrons). I still doubt that the He could ever be over 1% of the H.
    I'm assuming that H was distributed (with some density fluctuations) uniformly at the same density as baryonic matter now, and then it interacted, while the expansion factor remained constant. However, in a true steady state model, nothing would change, and the He:H ratio wouldn't change. There is no a priori equlibrium ratio unless there is a high-temp period or perhaps proton decay.
    Last edited: Feb 21, 2012
  10. Steady state and static spacetime are different notions, the most known steady state universe , that of Gold, Bondi and Hoyle was an expanding spacetime, it wasn't static.
    In static spacetimes there is no global change wrt time (although there may be locally).
    There can be no periods nor "after a very long time"s. No expansion factor either and if you bother to look up some GR text no possibility for the existence of black holes, so no bh evaporation either. As anyone can see it is a completely unrealistic cosmology.

    I'm only trying to learn something about stellar nuclear reactions in equilibrium and in a time invariant situation to contrast it with the factual primordial nucleosynthesis context and have a better understanding of it.
  11. Being more specific how much would the Nn/Np ratio in the time invariant situation in star's cores differ from the neutron freeze-out ratio in primordial nucleosynthesis (of around 1/6-1/7)?
  12. In any sort of time invariant universe, everything would end up as iron. The difficulty is that with light elements, there isn't a chemical equilibrium. Everything wants to be iron, and there are no cosmologically significant reverse reactions to break down iron into lighter elements.

    However, this has been known since the 1940's, and the idea behind the steady state model was that there was a "magic source" of hydrogen to replace anything that got burned to He4. However, if we lived in a universe in which the magic source of hydrogen kept H/He ratios constant, we'd see no deuterium or He3, and a lot more Carbon-12 and heavier elements.

    Very different. He4 to C12 has 1:1 and heavier elements are have more neutrons than proton culminating in neutron stars which are all neutrons.
  13. For some reason you guys keep mixing static with eternal steady state models, even though I tried to clarify the difference in a previous post.
    In steady state models there is time dependency, it is a expanding model. In static spacetimes nothing "ends up", there must be just an equilibrium distribution related to temperature, density and mass difference of protons and neutrons but independent of time.
  14. phyzguy

    phyzguy 2,489
    Science Advisor

    There can be no equlibrium as you envision it unless there is a two-way pathway. So in your hypothetical static universe you need to answer twofish's question about what moves things "uphill" from iron back to hydrogen. Otherwise the equilibrium distribution in the universe you are asking about is a universe filled with black holes and iron. The steady-state universe answers this by postulating continuous creation of hydrogen and expansion.
  15. What moves things "uphill" is the fact that in a static universe both ways of the two-way path have the same probability by definition, or at least that is what time-reversible reactions seem to imply.
  16. Clearly in the model you present there is no entropy and yes theoretically all reactions are time invariant so without entropy there would be no way to discern a 'direction' to time. To answer your question, in such a universe you can have whatever ratio of elements you like since all reactions are matched with their counterpart (or your universe won't remain static).
  17. Thanks for your input mathal, finally someone sees what I mean.
    You are right, that was in fact my initial thought, that in such a universe any ratio would be possible, but I'm trying to introduce some constraints in the form of typical stellar core temperature , pressure and density and supposing the usual stellar nucleosynthesis reactions would also work so that some equilibrium distribution can be given that would make more sense than some other.
  18. Chronos

    Chronos 10,348
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    Gold Member

    An interstellar medium enriched by stellar ejecta would be anything but static. A universe without entropy would be not even wrong, but, I naively suspect it would remain in its original state. A universe without BB nuclosynthesis still needs a source of hydrogen for primordial stars to form. Once the stellar formation process began, the ISM would be continuously enriched by stellar ejecta. I fail to see how that could ever achieve equilibrium. It would merely continue to be enriched until so heavily metallized it could no longer support stellar fusion. The answer seems to be stars would not form in a universe without entropy.
  19. Exactly. This is merely a thought experiment. Objects like stars from our universe are not static- they age, things change, proportions of elements change with time. They couldn't exist in the form they have here. I find it hard to conceive of such a universe, the interrelationship of the laws that govern this universe are not workable without entropy. It is not that it is a physical law, merely that it is a consequence of the laws we operate under (in particular gravity).

    You are thinking of primordial stars- our universe. The static universe TrickyDicky is presenting requires they just be here timelessly. An impossible requirement from my understanding of physics.
  20. Of course it is just a thought experiment, like the many that are used in science to get a better understanding of things, when Einstein imagines he is riding a photon no-one thinks about the practical impossibility of doing that. Many things are explained in physics thru thought experiment or ideal models that are known not to exist in reality.
    Anyway a static universe doesn't imply there is no "local" change, it is just the global cosmological parameters as a whole that don't change wrt time.
    Otherwise it would have been plain silly from Einstein and the physicist of their time to even consider static spacetimes as models for our universe knowing as it is obvious that locally things change.
  21. Ken G

    Ken G 3,614
    Gold Member

    Remember that when Einstein postulated the static universe, he did not even know there was such a thing as nuclear fusion. After the Hubble flow was found and fusion was discovered, both which happened a decade later, it was quickly realized that the Big Bang model explained the H/He ratio in a universe of finite age. It wasn't until later still that all the other nuclei got explained, when the role of stars was appreciated!
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