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Light elements abundance in a static toy universe

by TrickyDicky
Tags: abundance, elements, light, static, universe
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TrickyDicky
#37
Feb28-12, 03:27 PM
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Quote Quote by Ken G View Post
The term "steady state" is used in a very wide array of physics models, and it always means one thing: no explicit dependence on time or age. Including, no time dependence of H/He. That's quite a bit more than just a "static spacetime."
Did you specify an age in your question? Then you don't just mean a static spacetime, you mean a static everything (including a non-varying H/He). Indeed, you said:
(my bold). If you didn't actually mean that time was invariant, only that the spacetime didn't depend on it, then ask your question again, but this time specify the age of the universe, rather than referring to a "steady-state" H/He ratio. It sounds like what you meant was, "what would the H/He ratio be, at age 13.7 billion years, in a static spacetime." The answer to that is the same as I said: stellar nucleosynthesis has not had a significant impact on H/He in 13.7 billion years, so H/He is whatever value you assume "at the beginning." The static spacetime, unlike the Big Bang, gives us no constraint on H/He at all. So yes, put like that, it is an interesting point to make-- but it was already made.
In a static spacetime there is no age of the universe concept.
Ken G
#38
Feb28-12, 05:52 PM
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Quote Quote by TrickyDicky View Post
In a static spacetime there is no age of the universe concept.
No, that is wrong. Of course there is still an age of the universe concept, it would just have to do with how old the matter is, not anything about the spacetime. For one thing, it would eventually all be iron, as was pointed out.
TrickyDicky
#39
Feb29-12, 03:21 AM
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Quote Quote by Ken G View Post
No, that is wrong. Of course there is still an age of the universe concept, it would just have to do with how old the matter is, not anything about the spacetime. For one thing, it would eventually all be iron, as was pointed out.
What is the age of a universe that has no beginning in time?
Chronos
#40
Feb29-12, 04:59 AM
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TD, it appears you are implying the universe is infinitely old and all the evidence accumulated to date strongly suggests we do not reside in such a universe.
TrickyDicky
#41
Feb29-12, 05:17 AM
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Quote Quote by Chronos View Post
TD, it appears you are implying the universe is infinitely old and all the evidence accumulated to date strongly suggests we do not reside in such a universe.
We all know for sure we do not live in such universe, I thought words and expressions such as "imaginary","hypothetical", "cosmology-fiction", "thought experiment" in my posts would make that clear enough.
Also note that the words infinitely and old can't be logically put together.
Ken G
#42
Feb29-12, 02:32 PM
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Quote Quote by TrickyDicky View Post
What is the age of a universe that has no beginning in time?
Infinite. So what? This doesn't tell us what H/He will be. For that, you need an age, or a timestamp of some kind (perhaps time since the last periodic event). Or, if you don't, then you have a steady-state value of H/He (which is just what we said you will not get). That exhausts the possibilities, so there is no sense in a question that asks for a static H/He but not a steady-state H/He, and gives no age or time stamp of any kind. The question has no meaning.
TrickyDicky
#43
Feb29-12, 04:40 PM
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Quote Quote by Ken G View Post
then you have a steady-state value of H/He (which is just what we said you will not get).
why?
This is the condition of the exercise.
Ken G
#44
Mar1-12, 08:29 AM
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And this is the answer to the exercise: if you do not give an age, then it makes no difference what the spacetime is (static or expanding), you can never get an H/He unless the latter has reached a steady-state value. I'm sorry, that's just perfectly obvious. So you have two choices, even within a static spacetime:
1) specify the age of the universe, and derive H/He from that. If the age is short (along the lines of our current age), you cannot answer it because it depends on the initial value assumed, since stellar nucleosynthesis hasn't had enough time to do much. If the age is very long, you'll have all iron. If the age is somewhere in between, stellar nucleosynthesis rates, and the age given, will determine H/He.
2) use an effectively infinite age, which is tantamount to the last possibility of #1.
That is the answer to your exercise, and it's all been given above. I'm afraid I don't know what else you are looking for.
TrickyDicky
#45
Mar1-12, 12:15 PM
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Quote Quote by Ken G View Post
And this is the answer to the exercise: if you do not give an age, then it makes no difference what the spacetime is (static or expanding), you can never get an H/He unless the latter has reached a steady-state value. I'm sorry, that's just perfectly obvious. So you have two choices, even within a static spacetime:
1) specify the age of the universe, and derive H/He from that. If the age is short (along the lines of our current age), you cannot answer it because it depends on the initial value assumed, since stellar nucleosynthesis hasn't had enough time to do much. If the age is very long, you'll have all iron. If the age is somewhere in between, stellar nucleosynthesis rates, and the age given, will determine H/He.
2) use an effectively infinite age, which is tantamount to the last possibility of #1.
That is the answer to your exercise, and it's all been given above. I'm afraid I don't know what else you are looking for.
when you say 2) is equivalent to an age somewhere in between (last possibility of 1)) I cannot see how you reach that conclusion:infinite age=age somewhere in between?
Ken G
#46
Mar1-12, 02:39 PM
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Ah, typo-- I meant the second case in #1, not the last case. If the age is long enough to reach a steady state, then age doesn't matter, and that is equivalent to an infinite age, in regard to the question you are asking. The bottom line is, if a question is posed that does not specify the age, one must assume the age doesn't matter, which is always equivalent to assuming a steady state, which is always equivalent to an infinite age, which means the answer is "all iron."
TrickyDicky
#47
Mar2-12, 03:21 AM
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Quote Quote by Ken G View Post
Ah, typo-- I meant the second case in #1, not the last case. If the age is long enough to reach a steady state, then age doesn't matter, and that is equivalent to an infinite age, in regard to the question you are asking. The bottom line is, if a question is posed that does not specify the age, one must assume the age doesn't matter, which is always equivalent to assuming a steady state, which is always equivalent to an infinite age, which means the answer is "all iron."
Ok, so the answer is "all iron", how come we get the same answer for a static "infinite age" universe and a for expanding "arbitrarily old (very old) age" universe?
Ken G
#48
Mar3-12, 04:20 PM
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We don't necessarily-- the "all iron" is not guaranteed in an expanding scenario, the density might eventually drop too low to make stars, and the H/He at that point would be "frozen in" for all time following, much as the H/He ratio was "frozen in" in the original Big Bang nucleosynthesis. So "all iron" is only the static no-age-given answer, whereas "maybe all iron, maybe some frozen-in value of H/He" is the expanding answer. Some even think expansion might get so severe as to rip matter apart. So it's not clear what the asymptotic behavior of the expanding scenario actually is, because of the changes in the background spacetime.
TrickyDicky
#49
Mar4-12, 04:52 AM
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It turns out the answer "all iron" is wrong for a static spacetime because that would require time evolution of the universe which is a feature static spacetimes don't have globally. Thanks Ken G anyway, at least you tried.
Ken G
#50
Mar4-12, 10:17 AM
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Quote Quote by TrickyDicky View Post
It turns out the answer "all iron" is wrong for a static spacetime because that would require time evolution of the universe which is a feature static spacetimes don't have globally. Thanks Ken G anyway, at least you tried.
Simple logic indicates there are only two possibilities here:
1) You are wrong. You are saying that because the spacetime is static, no time evolution in any physical variable is possible. Which theory does that come from?
2) Your original question is meaningless. You asked for the static H/He ratio, and now you are saying that no evolution of that ratio is possible. If you believe that, then obviously the H/He ratio in a static universe is set by the initial condition, which you did not specify.
So take your pick-- your question has no answer, or has a simple answer that you don't believe. What a waste of time.
TrickyDicky
#51
Mar4-12, 02:54 PM
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Quote Quote by Ken G View Post
Simple logic indicates there are only two possibilities here:
1) You are wrong. You are saying that because the spacetime is static, no time evolution in any physical variable is possible. Which theory does that come from?
Not exactly, no time evolution of the H/He ratio would be possible, because it is considered a global time-dependent feature of the static spacetime.

Quote Quote by Ken G View Post
2) Your original question is meaningless. You asked for the static H/He ratio, and now you are saying that no evolution of that ratio is possible. If you believe that, then obviously the H/He ratio in a static universe is set by the initial condition, which you did not specify.
I tried to specify it by considering the nuclear reactions in reversible form.
Ken G
#52
Mar5-12, 01:04 AM
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Quote Quote by TrickyDicky View Post
Not exactly, no time evolution of the H/He ratio would be possible, because it is considered a global time-dependent feature of the static spacetime.
I have no idea why you think it is considered that. It certainly isn't considered that by cosmologists.
I tried to specify it by considering the nuclear reactions in reversible form.
As someone else said, if you change the physics, you can get any answer you want. But in this universe, H-->He is only reversible in the early minutes of the Big Bang, conditions that did not exist in your question. That's why the Big Bang model answers the H/He ratio-- it represents exactly the ratio of neutrons to protons one would expect to be "frozen in" from the reversible process p<-->n in the early minutes of the Big Bang, assuming expansion. The cores of stars tend to only result in p-->n.
TrickyDicky
#53
Mar5-12, 03:36 AM
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Quote Quote by Ken G View Post
It certainly isn't considered that by cosmologists.
You are right, that is because cosmologists generally deal with physically realistic scenarios, I'm having problems getting you people into the "thought experiment mode" here.

Quote Quote by Ken G View Post
As someone else said, if you change the physics, you can get any answer you want. But in this universe, H-->He is only reversible in the early minutes of the Big Bang, conditions that did not exist in your question. That's why the Big Bang model answers the H/He ratio-- it represents exactly the ratio of neutrons to protons one would expect to be "frozen in" from the reversible process p<-->n in the early minutes of the Big Bang, assuming expansion. The cores of stars tend to only result in p-->n.
Again, "this" universe (ours) is not the one I'm talking about.
Yes, the cores of stars as isolated systems tend to p-->n, so in the hypothetical static spacetime some mechanism should be compensating this, I guess.
Ken G
#54
Mar5-12, 08:09 AM
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Quote Quote by TrickyDicky View Post
You are right, that is because cosmologists generally deal with physically realistic scenarios, I'm having problems getting you people into the "thought experiment mode" here.
Not true, we have no issue with thought experiments. We like thought experiments, we think they are a nice way to learn real physics. Not make believe physics, though. You just didn't like the correct answer for some reason.
Again, "this" universe (ours) is not the one I'm talking about.
Yes, the cores of stars as isolated systems tend to p-->n, so in the hypothetical static spacetime some mechanism should be compensating this, I guess.
That's not a thought experiment, that's make believe. There's a difference.


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