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Light elements abundance in a static toy universe 
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#55
Mar512, 09:52 AM

P: 3,060

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.



#56
Mar612, 02:05 AM

PF Gold
P: 3,136

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 oneway 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.



#57
Mar612, 03:14 AM

P: 3,060




#58
Mar612, 09:38 AM

PF Gold
P: 3,136




#59
Mar612, 10:27 AM

P: 6,863




#60
Mar612, 10:43 AM

P: 3,060




#61
Mar612, 11:17 AM

PF Gold
P: 3,136

Yes... no physics about nucleosynthesis at all. You can kind of tell this, actually Einstein did have a cosmological model with a static spacetime. So why didn't he go ahead and try to answer the question from your OP? Because he knew it would not be possible to do, there's not enough information without additional assumptions. Now, of course Einstein didn't know squat about nucleosynthesis, but what we do know about it now is what gives the answer "all iron", so Einstein would have then known his static solution was wrong in the absence of some new physics (which is what we are telling you, also). So the bottom line is, as has often been repeated, there are only two possible answers to your question:
1) if no new physics: all iron 2) if new physics: anything you want I wish I had just said that from the start, but then again, I think I basically did. 


#62
Mar612, 11:24 AM

P: 3,060

And in the simplified case of a static universe with a fluid in thermodynamical equilibrium the stressenergy tensor is proportional to the hydrostatic pressure and the inverse of the metric tensor.



#63
Mar612, 11:44 AM

P: 3,060




#64
Mar612, 01:54 PM

PF Gold
P: 3,136

The stressenergy tensor is what it is there are many different things that can lead to the same stressenergy tensor. You seem to imagine that tensor completely describes everything that is happening, but this is incorrect. Consider this analogy. As I write this, everything happening in my head can be influencing in some way the words that appear, yet you cannot take those words and infer everything happening in my head. So it is for the stressenergy tensor, and so it was for Einstein and his static spacetime cosmology, and that is also why he knew he could not use that cosmology to infer H/He. Why else do you think Einstein could design a theory around the stressenergy tensor without even knowing that nucleosynthesis existed?
To repeat: Einstein could make a static cosmology. He could not infer H/He from that cosmology, because he did not know the physics of nucleosynthesis. We do, so we can get H/He, and it's all iron, unless you want to put in some additional unknown physics, in which case you can get any answer you like. 


#65
Mar612, 03:20 PM

P: 3,060

No, I don't think the stress tensor describes what you are thinking. Thanks for your valuable help. 


#66
Mar612, 11:53 PM

PF Gold
P: 3,136




#67
Mar712, 04:21 AM

P: 3,060

So that the ratio of protons and neutrons when they are allowed to freely and reversibly transform into each other (this particular equilibrium), I understand, is determined just by their relative masses. This seems to be the only stipulating that is needed to calculate a H/He ratio under the postulated conditions. But please correct me if this is not so. Sorry for not making this stipulations clear in the OP. 


#68
Mar712, 07:16 PM

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P: 3,136




#69
Mar812, 04:23 AM

P: 3,060

You are correct also that I should have specified that it should be a stable homogeneous universe, which is as you very well point out an impossibility as there are no static and homogeneous cosmologies that are stable. In fact the only static homogeneous model is Einstein's universe and it is a well known fact that it is not stable . I realize I left out a lot of important data in my OP and I apologyze again for it (I see now that could be frustrating from the answering POV). Regarding temperature, I realize that it is a key component to compute a freezeout neutron/proton ratio (and from that a H/He) with the Boltzmann statistics formula that includes the temperature and the mass of protons and neutrons in the BBN model. But I'm wondering if the concept of temperature would even make any sense in such a bizarre scenario as the one I'm imagining. It would seem temperature is very related to time asymmetry, and here we would have time symmetry. So I guess by pure logic a H/He ratio could be simply obtained in this imaginary setting from the fact that He4 has four nucleons and hydrogen has one, and by chance it is also 4. But this leads nowhere so at this point I'm ready to wrap this up unless someone has any further comment to make. 


#70
Mar812, 08:23 AM

PF Gold
P: 3,136

I think a lot has been cleared up. I don't think the temperature concept requires time asymmetry, because it has meaning in equilibrium, but I agree that a static cosmology has a lot of paradoxes associated with it, and I'm a little surprised neither Newton nor Einstein recognized that. Perhaps it was simply that their imaginations didn't grasp the alternative, and needed a little nudge from observations.



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