Light elements abundance in a static toy universe

[phyzguy]

Well, let's say that all the known physics would be the same except that the global entropy of such imaginary universe would be constant. Almost all physical laws are time reversible anyway.

As far as I can see, this is a meaningless statement. Perhaps you should study how the second law of thermodynamics comes about. It is a consequence of the large increase of the volume of phase space available near statistical equilibrium. I think any attempt to modify the laws of physics so that "the global entropy of such imaginary universe would be constant" would result in a universe that is unrecognizable. For example, I could say, "No interactions can occur". Well then, it's obvious the result of your static universe - whatever you start with stays in place forever.

 

[Ken G]

I explained at least twice that my thought experiment was NOT an eternal steady-state universe.

But that's the whole problem, that is precisely what your thought experiment is, since you acted as though the age of the universe is not a parameter in your question. There are only two possibilities-- either univeral age is not a relevant parameter, in which case you are talking about something "eternal", or else time is a dynamical parameter, in which case the answer will depend on the age. You did not say what that parameter was, thus you have to be talking about the former situation, there simply is no other possibility. Now, perhaps you mean that time is a parameter that has some understood value (like the usual 13.7 billion year age), but in addition to that parameter's value, there is also a kind of slowly varying quasi-steady solution that you are interested in. In that case, the problem is that the slowly varying quasi-steady value of H/He is pretty much just what we see, because in 13.7 billion years, stellar nucleosynthesis has not had time to have any real impact on the quasi-steady value of H/He (because not enough of the H is in massive enough stars to have an impact on H/He in that timescale). If you wait much longer, it will, but then H/He will be a function of age, and you have to say what age you have in mind. It will all be standard Big Bang, also.

 

[TrickyDicky]

But that's the whole problem, that is precisely what your thought experiment is, since you acted as though the age of the universe is not a parameter in your question. There are only two possibilities-- either univeral age is not a relevant parameter, in which case you are talking about something "eternal", or else time is a dynamical parameter, in which case the answer will depend on the age. You did not say what that parameter was, thus you have to be talking about the former situation, there simply is no other possibility. Now, perhaps you mean that time is a parameter that has some understood value (like the usual 13.7 billion year age), but in addition to that parameter's value, there is also a kind of slowly varying quasi-steady solution that you are interested in. In that case, the problem is that the slowly varying quasi-steady value of H/He is pretty much just what we see, because in 13.7 billion years, stellar nucleosynthesis has not had time to have any real impact on the quasi-steady value of H/He (because not enough of the H is in massive enough stars to have an impact on H/He in that timescale). If you wait much longer, it will, but then H/He will be a function of age, and you have to say what age you have in mind. It will all be standard Big Bang, also.

Anyone can look up easily in books or in wikipedia that a static spacetime is different than a steady-state universe. My thought experiment refers to a static one.

 

[Ken G]

Anyone can look up easily in books or in wikipedia that a static spacetime is different than a steady-state universe. My thought experiment refers to a static one.

Anyone, looking that up, would discover that all static universes are strict subsets of the class of all steady-state ones. That fact follows quite directly from the meanings of those words. As I said: you never gave an age. Now, is that because it doesn't matter? That is the definition of steady state.

 

[TrickyDicky]

Anyone, looking that up, would discover that all static universes are strict subsets of the class of all steady-state ones. That fact follows quite directly from the meanings of those words. As I said: you never gave an age. Now, is that because it doesn't matter? That is the definition of steady state.

The only explanation I can find to what you are saying is that you might be using the term "steady state" with a different meaning than I am. In fact in wikipedia at least two different meanings can be found: steady state as a kind of equilibrium of a system as used in many disciplines like thermodynamics and economics, and "steady state theory" or cosmology which is the specific model of universe that Hoyle et al. came up with in 1948 and that was seriously considered as alternative to BB universe until the 60's. This latter is the sense I have been giving to the term "steady state universe". It is well known that this model is that of an expanding universe. It is not possible therefore for static universes to be a subset of an expanding universe as I hope you will agree.
A a spacetime is said to be static if it admits a global, non-vanishing, timelike Killing vector field K which is irrotational, this is the standard definition and the one I'm following in my thought experiment as scenario for a putative plausible imaginary equilibrium distribution of chemical elements abundance.
Now, as was pointed out before, in abstract terms every distribution is compatible with such a universe. My question is, is there a way to constrain this with the known nuclear reactions (in reversible form) and the physical conditions of stellar's cores?

I thought this was an interesting exercise, I'm not so sure now.

 

[Ken G]

The only explanation I can find to what you are saying is that you might be using the term "steady state" with a different meaning than I am. In fact in wikipedia at least two different meanings can be found: steady state as a kind of equilibrium of a system as used in many disciplines like thermodynamics and economics, and "steady state theory" or cosmology which is the specific model of universe that Hoyle et al. came up with in 1948 and that was seriously considered as alternative to BB universe until the 60's.

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."

A a spacetime is said to be static if it admits a global, non-vanishing, timelike Killing vector field K which is irrotational, this is the standard definition and the one I'm following in my thought experiment as scenario for a putative plausible imaginary equilibrium distribution of chemical elements abundance.

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:

Yes, just the stellar nuclear reactions, only in a static universe makes little sense to say what one begins with, since time is invariant.

(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.

 

[TrickyDicky]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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.

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]

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]

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.

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]

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.

 

[TrickyDicky]

What I cannot understand is why you won't concede that in a static spacetime there is time symmetry and therefore nuclear reactions would be reversible, so the "all iron" answer can never be the correct answer.

 

[Ken G]

I can't concede it because it's wrong, the physics of that claim is confused. The static character of the spacetime has nothing at all to do with the nuclear reactions possible. The latter depends, not on the spacetime (which simply defines the inertial paths, and asserts that they are always the same), but on the conditions of the matter (temperature, density, and so on), and the physical processes allowed in those conditions. The model would have reached a steady state if the age is effectively infinite, so all processes that can occur must balance their inverse process. That doesn't mean you have some known H/He ratio, it might just mean you don't have any of either H or He. I'm saying that is what you would indeed have, because the conditions one can assume for your static spacetime (given that they are unspecified, yet you asked your question anyway, we can assume you intended conditions of T and density like we find in the universe today), do not have a process for turning He back into H, so we are on a one-way street leading to iron. Hence the answer that you don't like. Now, obviously if you are allowed to invent imaginary physics, you can get any H/He you are more happy with, but then there is also no reason to pose your question here.

 

[TrickyDicky]

I can't concede it because it's wrong, the physics of that claim is confused. The static character of the spacetime has nothing at all to do with the nuclear reactions possible. The latter depends, not on the spacetime (which simply defines the inertial paths, and asserts that they are always the same), but on the conditions of the matter (temperature, density, and so on), and the physical processes allowed in those conditions.

Ok, let's imagine this spacetime was a solution of the EFE, in that case the matter conditions would also be fixed by the RHS of the EFE.

 

[Ken G]

Ok, let's imagine this spacetime was a solution of the EFE, in that case the matter conditions would also be fixed by the RHS of the EFE.

You think the H/He ratio, and the nucleosynthesis physics, shows up on the RHS of the EFE? What is actually there?

 

[twofish-quant]

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.

That's because it's not clear what rules you are imposing. If you can state the rules of the game, we can figure out what goes on.

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.

And once you specify that mechanism then you get whatever answer you want.

 

[TrickyDicky]

You think the H/He ratio, and the nucleosynthesis physics, shows up on the RHS of the EFE? What is actually there?

Stress-energy tensor.