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Could chance and the anthropic principle explain baryon asymmetry?
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Could chance and the anthropic principle explain baryon asymmetry?
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Kryptid
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Could chance and the anthropic principle explain baryon asymmetry?
«
on:
06/05/2018 03:30:45 »
If the Universe was infinitely large (or at least
sufficiently
large), wouldn't we expect to see regions within it the size of the observable universe that are almost entirely dominated by matter due to chance alone?
In all areas of the Universe, we would expect the initial quantities of matter and antimatter to be equal. In almost all regions of the Universe, we would then expect that matter and antimatter to annihilate each other and result in large quantities of radiation. However, there should still be a very tiny, but finite, probability that a volume of particles and antiparticles would spontaneously segregate themselves into separate regions dominated by matter or antimatter.
This would be akin to air in a jar spontaneously separating itself into pure oxygen at the top and pure nitrogen at the bottom. Although it would take much, much longer than the age of the Universe for such a thing to happen in one jar, you could potentially (mathematically-speaking) have a large enough number of jars of air such that we can expect at least one of those jars to have spontaneously separated in such a manner within the current age of the Universe.
Since a civilization of life forms like ours could only develop in certain environments, we would necessarily find ourselves in a matter-dominated region of the Universe. With too much antimatter, large, complex structures like stars and planets could not form. Even with antimatter levels small enough to allow for the formation of stars and planets, we would still need antimatter levels much smaller than even that because too many gamma rays would sterilize planets. We need to live in a region of the Universe sufficiently dominated by matter such that gamma rays from substantial antimatter annihilation could not have reached us within the period of time needed for our development up to the present day.
I know this sounds like a last-ditch model, but it might actually be possible to falsify it. Small regions dominated by matter should be significantly more common than larger regions (since larger spontaneous matter-antimatter segregation events would be correspondingly less likely to occur). So any intelligent civilization would be much more likely to find itself inside a region of the Universe that was
just barely
radiation-free enough to support their existence than one that is excessively large. Is there any evidence for such a fine balance in our visible universe in terms of gamma ray levels? Is there any evidence for unusually large levels of gamma rays existing just at the boundary of the visible universe? Interesting, this might also work as a partial solution to the Fermi Paradox: only planets near the center of the visible universe are sufficiently-distant from gamma rays coming from the visible universe's border to allow for the development of complex life.
Even if I'm wrong, it might help eliminate chance as an explanation for baryon asymmetry.
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Last Edit: 06/05/2018 03:40:55 by
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Kryptid
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Re: Could chance and the anthropic principle explain baryon asymmetry?
«
Reply #1 on:
09/05/2018 00:07:59 »
Does anyone think they could help me with some calculations? I would like to figure out just how large the Universe would need to be in order for an observable universe like ours to occur via chance sorting of matter and antimatter. In particular, I'm wanting to know if one of the proposed sizes of Universe through the No-Boundary Proposal (which is 10
10
10
122
megaparsecs in diameter) is sufficient.
I suppose we would have to start by knowing how many different possible configurations of matter could exist within the volume of the visible universe, yes? I recall reading a calculation in a science magazine once about Tegmark's multiverse that used the maximum possible number of protons that the universe could contain as a basis for the calculation. The conclusion was that, in a sufficiently large Universe with a random distribution of matter, we could expect to find a Hubble volume identical to ours about 10
10
115
meters away from us.
In this calculation, I suppose we could take the total number of protons that could be squeezed into our Hubble volume and assume that each proton-sized volume could take the form of a matter particle, an antimatter particle, or be empty. I know the number of possible configurations must be truly enormous. Does anyone know how I might begin to do such a calculation?
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chiralSPO
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Re: Could chance and the anthropic principle explain baryon asymmetry?
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Reply #2 on:
09/05/2018 16:08:48 »
Well, I'll kick this off:
X is the existence of 1 observable universe sized volume containing no antiprotons
Probability of X is (# of outcomes in which X is true)/(# outcomes possible)
Using these parameters:
• cubic universe with side length of 10
10
10
122
parsecs. Let's call this length "L"
• which is a cubic array of cubes of side length <10
–12
meters. Let's call this length "S"
• 3 possible states for each small box, proton, antiproton or nothing.
• Recall that there are 24 equivalent orientations a cube can have (think of it as each of 6 faces can be "down" and then there are 4 choices for which face is "North").
Thus the # of possible states = 3
(L/S)
3
/24
To address the # of outcomes in which X is true we need to take account of a few more parameters:
• probability of small cube containing proton is "p" and is the same as the probability of containing an antiproton, but the cases are mutually exclusive. so we are looking for "not p" or 1–p. (you don't care whether this space contains protons are not, just as long as no matter. Choice of value for p will play a huge role in what the final probability of X is, and can be anywhere between 0 and 0.5.)
• the observable universe is a cubic region of space with side length M (S << M << L) (choice of M will also have a very significant role in the final probability of X)
For X to be true, there has to be at least 1 contiguous cubic volume of M
3
that has 0 antiprotons in it.
We need to know the expression for the probability of a cubic volume of M
3
having 0 antiprotons in it, which is:
(1–p)
(M/S)
3
/24
and we need to know the expression for how many cubic volumes of M
3
fit in the cubic volume of L
3
, which is:
((L–M)/S)
3
Putting these together, # outcomes in which at least one (not none) of the M
3
sized cubes has no antiprotons in it:
(1–((1–p)
(M/S)
3
/24))
((L–M)/S)
3
Now, putting this all together:
(1–((1–p)
(M/S)
3
/24))
((L–M)/S)
3
P(X) = ————————————
3
(L/S)
3
/24
I leave the reader to experiment with values of L, M, S and p
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Last Edit: 09/05/2018 22:13:28 by
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Re: Could chance and the anthropic principle explain baryon asymmetry?
«
Reply #3 on:
09/05/2018 18:59:38 »
Thanks for all of that help, ChiralSPO. Unfortunately, I don't know how to go about actually using your provided equation, because none of the calculators that I have tried to use can work with numbers that large. Does anyone know a workaround?
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chiralSPO
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Re: Could chance and the anthropic principle explain baryon asymmetry?
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Reply #4 on:
09/05/2018 19:07:32 »
Indeed. That's why I stopped where I did.
We are calculating the ratio of two cosmically enormous numbers.
I think with some effort one could effectively cancel out some of the terms from denominator and numerator, successively making them more reasonable terms... One might also have luck taking the log of the ratio (at any point along the simplification process), and then doing more straightforward algebra to simplify it further, and then put it back into exponential notation.
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Kryptid
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Re: Could chance and the anthropic principle explain baryon asymmetry?
«
Reply #5 on:
09/05/2018 23:21:17 »
Maybe there's a simpler way to do this. I just read in this article that the number of protons in the observable universe is on the order of 10
80
:
http://space.mit.edu/home/tegmark/multiverse.pdf
. Presumably, there would be a similar number of electrons in the observable universe as well. If we assume that this is a typical number of baryons for any given Hubble volume, can we use that to calculate the odds of those 10
80
particles being made up completely of matter particles instead of a mix of matter and antimatter? Naively, I think the odds should be about 1 in 2
10
80
. A Universe that is 10
10
10
122
megaparsecs across would no doubt contain
far
more than 2
10
80
Hubble volumes. It seems that aspect of it is at least plausible then.
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Last Edit: 10/05/2018 03:03:14 by
Kryptid
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