Anthropic Dimensionless Constants

Informed scientists now univerally recognise that the Universe is exquisitely finely tuned to allow the coming into being of intelligent life. The only reasonable debate is whether this is due to:

a. A Loving Ultimate Creator
b. An extraordinary coincidence
c. The fact that there exists an infinity (or near-infinity) of other 'Universes' in which the constants are different, in an overall 'Multiverse'.

(c) is preferred by eg Martin Rees in his book Just Six Numbers, but only because he "finds [a] incredible" - he offers no arguments against it. Interestingly, just as (a) provides a modern form of the 'argument from design' (c) leads to a modern form of the 'ontological argument'. The most interesting of the advocates of (c) - Max Tegmark (formerly at the IAS, now at UPenn), proposes that any logically possible universe exists in the Multiverse. Since the existence of God is not logically impossible, it follows that God must exist in at least one Universe, but if God exists at all God must exist in all Universes (otherwise God would not be an ultimate creator).

Although inspired by the work of John Polkinghorne the author of this site is Nicholas Beale, who served with him on the committee that advised the CofE on Science, Medicine & Technology.

Two pictures illustrating some of the fineness of the constraints.

aG	Gm2  c	Gravitational Fine Structure constant	~ 10-39
a	e2  c	Fine Structure Constant	~ 1/137
b	me  mN	Ratio of electron to proton mass	~ 1/1836
qW	sin-1(e/gW)	Weinberg angle for weak force	~ 27o
as	gs2  c	Strong fine-structure constant	~ 15
W0	r0  rc	Potential Energy of Universe Kinetic energy of Expansion	~ 1.0000000000
S		Entropy per Baryon	~ 109

We have also got a page on the 1993 Venice Conference on the Anthropic Principle.

Some Known Anthropic Constraints

1. Binding of di-protons. a_s 9% less unbinds the deuteron; 3.4% more binds the diproton. (p322)
2. Carbon Stability (i) 50% decrease in a_s would make Carbon unstable (p327)
3. Carbon Stability (ii) a > 0.1 - Carbon unstable (p326)
4. Enough Mass in Universe Mass of Universe = (4p/3)rl³ so M_u ~ 10⁵ t_u M_Sun so must be ~ 10²³ M_sun
5. Basic Time Constraints t_u > t_N > t_ev > t_star > t_rec [Age of Universe > proton decay time > evolution time > main-sequence stellar lifetime > time after which expanding universe is cool enough for atoms & molecules to form.] Hence:
6. S ~ a/(b a_G) {t_star > t_rec}
7. S ~ a/(/b) a_G^-¼ {t_star > radiation dominated phase of universe}
8. S ~ b^-½ exp(0.25 a^-1) { t_N > t_star}
9. a > b {otherwise no nuclear reactions in the early universe}
10. Enable b decay m_N - m_P - m_e >0 but ~ 0 {else no b decay - since m_N and m_P ~ 1GeV m_N - m_P ~ 1.4MeV this is a one part in a thousand coincidence (p400)}
11. Flatness. There is a known big problem about flatness of the universe, but it seems possible that this is 'solved' by inflation.
12. Helium Formation  the existence of an 'interesting' level of Helium in the Universe (not 0% or 100%) depends on the coincidence G_Fm_e² ~ (Gm_e²)^1/4.  were this not the case we would either have 100% Helium emerging from the Big Bang or 0%. (p399)
13. Carbon Formation depends on a resonance that allows 3He⁴ -> C¹² + 2g resonantly.  This resonance (predicted by Hoyle on Anthropic grounds) occurs at 7.656 +0.008 MeV, whereas there is a level in C¹²  at 7.6549 MeV which lies just above the energy of Be⁸ + He⁴ (=7.3667MeV). (p252)
14. Neutrino-Baryon Cross Section life depends on Carbon and higher elements (formed in 1st Generation stars) being ejected by supernovae.  How does a massive Implosion cause an Explosion? Why doesn't it all disappear down a Black Hole?  It's becasue of Neutrinos, which hardly interact with anything at all, so that you'd have to fire thousands through the earth for one to have a 50:50 chance of hitting anything.  So Life depends, in addition, on having Neutrinos with just the right miniscule cross-sections.
15. Ionisation/Surface Temperature  The typical stellar mass M_Star is just above the border between convective and radiative stars, becasue a¹²(m_e/m_N)⁴ ~ a_G  (p336).
16. Biological Sunlight  The fact that life can develop on a planet suitably positioned in orbit about a stable long-lived star relies on the close proximity of the spectral temperature of starlight to the molecular binding energy.  If it were >> this, living organisms would either be sterilised or destroyed, << the delicate photochemical reactions necessary for biology to flourish would proceed too slowly.  This requires that (m_N/m_e)^1/2 a_G^1/8a^-3/2 ~ 0.9

Basic Problem re Likelihoods

I suppose that we could just ask people to decide what % of the range accounted for 90% of the likelihood, and this would allow them to pick any Normal Distribution (centre the actual value). We could then calculate the likelihood of a randomly chosen set of basic parameters falling in the Anthropic Region.

Does anyone have any better ideas - and would anyone like to help make the necessary software. If so EMail nb@starcourse.org.
 

Some recent papers relevant to Anthropic Principle

• Hawking & al. Some elegant but unproven new ideas.
• A view on some anthropic coincidences in the inflation model.
•  Tegmark & Rees  Why is the CMB fluctuation level 10^-5?
•  Nakamura & al The Minimum Mass of the First Stars and the Anthropic Principle
• Linde & al disputing the Hawking model. Quantum Creation of an Open Inflationary Universe.
• Max Tegmark's papers on dimensionality and on a multiverse.