This document discusses several topics related to cosmology and the search for extraterrestrial life, including: 1) Dimensionless numbers and ratios in physics and cosmology like the fine structure constant and ratios involving cosmological and atomic quantities. 2) Estimates of the number of atoms in the observable universe and other cosmological values. 3) The Drake equation and Fermi paradox regarding the search for extraterrestrial intelligence. 4) Coincidences between values that seem finely-tuned to allow for life like nuclear resonance energies.

1. The Anthropic principle, Cosmological
number coincidences & the Fermi Paradox…
Jim Kelly FRAS ©jfK April 2015
The Allen Telescope Array Berkeley California
The Drake Equation N = R* fp ne fl fi fc L

2. http://rsta.royalsocietypublishing.org/content/369/1936.toc?etoc
Phil Trans Royal Soc 2011 Vol 13 p 499-699
Audio 2010 The detection of extra-terrestrial life - Discussion Meetings - The Royal Society.mht

3. Why are the values of certain numbers linked to Life…?
Numbers in the Cosmos
• The Hubble constant: Age, size & mass of the Observable Universe
(Big Bang Cosmology)
• The fine structure constant α ~ 1 /137 (electromagnetic coupling)
(The Constants of Nature: π = 3.14159... φ = 1.161803... e = 2.71828)
• The Anthropic principle and Large numbers 1040
, 1080
, 10120
(Dimensionless ratios of Atomic & Cosmological Quantities )
• Big Bang Nucleosynthesis and the 7.65MeV Carbon resonance
(The work of Fred Hoyle explained as Anthropic reasoning)
• The Drake equation & the search for extraterrestrial intelligence
(Overcoming the hurdles to communicating with the Cosmos)
• The Fermi paradox and Life in the Galaxy...
(The eerie silence.... ET phone Home ! Where is everybody ? )

4. Nuclear masses & Energy
equivalents
Statistical Thermodynamics,
Quantum Mechanics & Atomic
Physics
Gravitation, Electromagnetism
Name symbol value
Tera T x 1012
Trillion
Giga G x 109
Billion
Mega M x 106
Million
kilo k x 103
milli m x 10-3
micro µ x 10-6
nano n x 10-9
pico p x 10-12
SI Units
Mass
(Kg)
Length
(m)
Time
(s)

5. The 4 Pillars of Big Bang Cosmology
Our current understanding of the Universe
1. Hubble expansion: distance-redshift relation
Age of Universe (1929)
2. Cosmic Microwave Background (CMB)
Temperature (COBE) ~ 2.7K (1989)
3. Interstellar H / He Abundance
Stellar Nucleosynthesis B2
F H (1957)
4. Distribution & evolution of Galaxies (Timeline)
Lambda (Λ) Cold Dark Matter Model (WMAP)
Wilkinson Microwave Anisotropy Probe 2001
Doppler Effect

6. Pillars of Creation….
Evidence for the Big Bang
• Expanding universe – Hubble’s Law (H = v / d)
Edwin Hubble 1929 spectroscopically measured the redshifts of distant galaxies with the 100” Hooker telescope at the
Mount Wilson Observatory, the rest as they say is history…
• Cosmic Microwave Background – CMB radiation
Penzias & Wilson received the 1978 Physics Nobel Prize for their discovery of the relic radiation left over from the
Big Bang – microwaves at a temperature of ~ 2.7K
2006 Nobel Prize Smoot & Mather–Blackbody/Anisotropy of the CMB-seeds of large scale structure
• Elemental abundances 4
He/H, Deuterium, 3
He, 7
Li
Burbidge, Burbidge, Fowler & Hoyle (the Classic 1957 B2
FH paper) predicted the “Synthesis of elements in the
stars”. Primordial ratios predicted by Alpher, Gamow 1948 (Famous α β γ paper)
• Olbers’ paradox – Why is the night sky so dark ?
Problem – If the Universe is infinite, eternal & filled with stars we ought to see a bright night sky
Solution – One of the 3 assumptions must be wrong: Starlight hasn’t had the time to brighten the whole sky. Edgar
Allan Poe first recognised this. By looking at the night sky is the simplest & clearest evidence that the Universe
had a beginning….
Eagle Nebula M61Eagle Nebula M61

7. • The Hubble Deep Field
• ~ 10 days Dec 1995
The age (s), size (m) and mass (kg) of the
Observable Universe

8. Expansion of the Universe
Radiation era dominated by
Dark ages

9. 1010-43-43
ss
QuantumQuantum
Gravity eraGravity era
Cosmic microwave backgroundCosmic microwave background
Surface of last scatterSurface of last scatter
LightLight
13.7 billion13.7 billion
yearsyears
Gravitational wavesGravitational waves
NowNow
The Big Picture….The Big Picture….
SpaceSpace
TimeTime
PlanckPlanck
scalescale
GrandGrand
UnificationUnification
EpochEpoch
ElectroweaElectrowea
kk
1010-10-10
ssLeptonLepton
EpochEpoch
1010 22
ss
1010 1313
ss
Photon EpochPhoton Epoch
1 Billion years1 Billion years
Confinement of quarksConfinement of quarks
p,np,n
Nucleosynthesis of HeNucleosynthesis of He
Decoupling of Matter-RadiationDecoupling of Matter-Radiation
AtomsAtoms
Galaxy Star formationGalaxy Star formation
MatterMatter
DominatedDominated
Era > 10Era > 10 22
ss
RadiationRadiation
DominatedDominated
Era < 10Era < 10 22
ss
The Universe becomes transparentThe Universe becomes transparent
1010-35-35
s Cosmic Inflations Cosmic Inflation
380,000 years380,000 years
≡≡ 1010 1313
ss

10. M104 Sombrero Galaxy ~29M Lyr Messier 49 ~55M Lyr M31 Andromeda Galaxy ~2M Lyr
Hubble constant Ho = ? (km/s) / Mparsec [ slope of Graph ]
1 parsec ~ 3.26 light years = 3.08568025 × 1016
metres Ho ~ ( ? ) s-1

11. Cosmological distance ladder I (Earth-Moon-Sun)
1.
2.3.
1. Earth’s circumference – Eratosthenes noticed that a well in Syene (modern day Aswan on the Tropic of Cancer),
Egypt was light directly from above (12pm) on the Summer solstice while a stick at Alexandria cast a shadow of 7.2°
due to the Earth’s curvature. Knowing the distance between these two places (~ 500 stadia, Olympia) enabled an
estimate of the Earth’s circumference. Taking a stadia as 185m can you calculate the Earth’s Circumference ? s = r
.Ɵ
Knowing a circular distance of 500x185 m corresponds to 7.2° it is easy to find the distance that corresponds to 360°.
2. Relative diameter Earth / Moon – During a lunar eclipse the time it takes for the shadow of the earth to cover the
moon is ~ 50 mins, about ¼ of the time it takes for the moon to re-emerge into light again ~ 200 mins. Therefore the
Earth is ~ 4 x larger than the moon.
3. Lunar distance – Using similar triangles an extended thumb of known distance subtends the same angle as the
larger lunar triangle (when obscured) where the lunar size in 2. can be used to estimate the distance Earth - Moon.
s
r

12. Cosmological distance ladder II Greeks
Anaxagoras of Anatolia (c500-428 BC) – explained eclipes (moonshine merely reflected sunshine).
Aristarchus of Samos (c310-230 BC) – measured the angle between the moon when directly
overhead and the sun (hence perpendicular) in order to determine the earth-moon/earth-sun ratio.
Eratosthenes (c276-193 BC) measured the Earth’s circumference (see Fig 1.)
4. Figures due to Aristarhcus. See modern distances right,
Moon–Earth-Sun angle θ ~ 89.85°
5.
4. Solar distance – knowing the Earth-Moon distance (Fig 3) and measuring the angle between the
moon and sun it is a matter of trigonometry to calculate the distance to the Sun.
5. Solar size – Knowing that during a Solar Eclipse the Moon exactly covers the face of the sun it is
possible to determine the Solar diameter by knowing the size of the moon. Check yourself above.
Typical modern day values
Earth’s circumference = 40,100 km
Earth’s diameter = 12,750 km
Moon’s diameter = 3480 km
Sun’s diameter = 1,390,000 km
Earth – Moon distance = 384,000 km
Earth – Sun distance = 150,000,000 km

13. 1 parsec (parallax of 1 arc second) coined 1913
00
00' 01’’ (1/60 x 60 degrees)
Herbert Hall Turner

14. Uncertainty in measurement %e ~ (δx / x) .
100%
Measuring the Hubble constant Ho
• Ho = 71.0 +/-1.4 (km/s) / Mparsec
(WMAP 7 year result 2010)
• Ho = 72 +/-8 (km/s) / Mparsec (HST
2001 Cepheid variable star
measurements)
• Ho = 72.6 +/-3.1 (km/s) / Mparsec
(HST 2010 Gravitational lensing
measurements)
• Ho = 73.8 +/-2.4 (km/s) / Mparsec
(HST 2011 infrared camera redshift
of various astronomical objects)
• Ho = 74.2 +/-3.6 (km/s) / Mparsec
(HST 2009)
• Ho = 77.0 +/-15% (km/s) / Mparsec
(2006 Chandra X-ray Observatory)
Andromeda Galaxy
2 Million light years
Hubble Calculator
INPUT
Ho = 71 km s^-1/Mparsec
Ho = 2.30E-18 s^-1
1 / Ho = 4.35E+17 s
Age 1.38E+10 yr
Universe 13.78117 Gyr

15. Action of the Observable Universe = mass x size2
/ time (Js)
Action of Quantum (Planck’s constant) h = 6.6 x 10 -34
Js
Action of the Universe / Action of Quantum =
A Dimensionless Number ~ 8.51 x 10 86
/ 6.626 x 10 -34
~ 1 x 10 120
Age (Time since Big Bang) (Back of an envelope
calculation !)
Units of Ho = s -1
So therefore 1/ Ho = s
T = 1 / Ho = 1 / 2.30095 × 10-18
s
T = 4.34603 x10 17
s ~ 13.781 Gyr
Size (of the observable universe – distance light has travelled since
the Big Bang)
R ~ c / Ho (not including redshift)
R ~ 3 × 108
/ 2.30095 × 10-18
R ~ 1.30 × 10 26
m
Mass (Not including Dark Matter or Dark Energy)
Estimate based on Critical density ρc = 3 Ho
2
/ 8 π G = 9.9 x 10-27
kg
m-3
ρc = M / V = M / R3
So M = ρc x R3
M = 9.9 x 10-27
x (1.25 × 10 26
) 3
M ~ 2.2 x 10 52
kg
Action
Action = Js = Nms = kg m s-2
m s = mass x size2
/ time = M x R2
/
T
52 26 2 17

16. Number of atoms in the Observable Universe
Approximately 1080
There are 2 methods to estimate the Number of atoms in the Observable Universe
Critical Density
Critical density ρc = 3 Ho
2
/ 8 π G = 9.9 x 10-27
kg m-3
Density = Mass / Volume , ρc = M / V
where V = (4/3) π R3
(R = 1.3 × 1026
m)
Mass = Number of protons (N) x mass of 1 proton (mp )
So ρc = N x mp / (4/3) π R3
= 9.9 x 10-27
N = ρc x (4/3) π R3
/ mp
N = ( 9.9 x 10-27
) x ((4/3) π ) x (2.2 x 1078
) / 1.67 x 10-27
N ~ 5 x 1079
H atoms
Stellar Density
Mass of typical stars ~ 2 x 1030
kg
Equivalent to N ~ 1 x 1057
H atoms per star (mp = 1.67 x 10-27
kg)
N ~ M / mp~ 2 x 1030
/ 1.67 x 10-27
~ 1 x 1057
Galaxy ~ 400 billion stars (4 x 1011
) Each Galaxy has 1 x 1057
x 4 x 1011
H atoms = 4 x 1068
Universe contains ~ 80 billion Galaxies
So there are 4 x 1068
. 8 x 1010
H atoms in the Observable Universe H atoms ~ 3 x 1079
Both methods give approximately the same number ~ 1080
atoms

17. Dimensionless ratios of Atomic & Cosmological
Quantities
Summary
• Fine Structure constant 1/137
7.297362 x 10-3
No Units !
• Electromagnetic : Gravitation
coupling constant ~ 1039
• Age of Universe : Atomic light
crossing time ~ 1040
• No of H atoms in the
Observable Universe ~ 1080
≡ Number of protons
• Action of the Universe : Action
of Quantum ~ 10120
(1040
) 2
~ 1080
(1040
) 3
~ 10120
N = Age of Universe / Atomic light crossing time
Time for light to cross the universe / time for light to cross an
atom
Age of Universe = 4.346 x 1017
s
Time = distance / velocity = electron radius / speed of light
Classic electron radius (Lorentz radius ) Thomson scattering
length = e2
/ 4πεo me c2
Atomic light crossing time = e2
/ 4πεo me c3
(time for light to cross an atom)
= (1.6 x 10-19
)2
/ (4 x 3.14159 x 8.85 x 10-12
) . (9.1 x 10-31
)
. ( 3 x 108
)3
= 9.36875 x 10-24
s
N = 4.346 x 1017
/ 9.36875 x 10-24
= 4.6 x 1040
~ 1040
Ratios of the same Quantity have no
No Units !!!
Spooky Or what ?

18. mp = 1.67262E-27 kg Fine structure constant α = e
2
/ (4π ε0) hc 1 / α
mn = 1.67493E-27 kg Electromagnetic coupling constant 0.007297362 137.035819
me = 9.10938E-31 kg Nuclear Atomic
mp / me = 1836.152663 Gravitational coupling constant αG = G mp
2
/ h c G mpme / h c
(Gmp
2
/h c) /(mp /me) = 3.21596E-42 5.905E-39 3.21596E-42
G = 6.673E-11 N kg-2
m2
Electromagnetic : Gravitational coupling constant α / αG = 2.26911E+39
e = 1.60218E-19 C Strength of Coulomb Electrostatic : Newtonian Gravitational Force
c = 299792458 m s-1
h = 6.62606E-34 Js Planck units G h c
h =h/(2π) = 1.05457E-34 Js Planck mass √ (h c /G) = 2.17665E-08 kg
Planck length √ (G h /c
3
) = 1.6161E-35 m
ε 0 = 8.85419E-12 F m-1
Planck time √ (G h /c
5
) = 5.39072E-44 s
µ0 = 1.25664E-06 H m-1
Planck Temperature √ (h c
5
/G k
2
) = 1.41692E+32 K
k = 1.38065E-23 J K-1
Classic electron radius Lorentz radius (Thomson scattering length)
(mp/me) x α = re = e
2
/ (4π ε0) mec
2
= 2.81743E-15 m
13.40145985
Physics coupling constants,
Planck units Calculator

19. The fine structure constant
α re-calculated
π = 3.14159...
Circumference / Diameter of a circle
φ = (1 + √5) / 2 = 1.61803...
Golden ratio (extreme to mean ratio of a line)
A x C 1 B
----------------------------------------------------------------
Geometrically Algebraically
x / 1 = (x + 1) / x Solve x2
= x + 1
e = Lt n →∞ (1 + 1/n)n
= 2.71828...
Exponential function Base of Natural Logarithms
φ^(π) ^(-1/e)
= 1.61803^ ((3.14159) ^(- 1/2.71828))
= 1.61803^ ((3.14159) ^(-0.3678796)
= 1.61803^ 0.6563095
=1.37...
α In Quantum Electrodynamics the
strength of the interaction between
electrons & photons

20. The fine structure constant explained
α = 7.2973525698(24)×10−3
= 1/137.035999074(44)

21. Eddington Numbers
Fundamental Theory
I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425
076 185 631 031 296 protons in the universe and the same number of electrons NEdd .

22. Large number coincidences & the Anthropic
Principle in Cosmology Brandon Carter 1974
“What we can expect to observe must be restricted by the
conditions necessary for our presence as observers”
• The 1st
use of this argument has been argued to
have been used by Fred Hoyle in the prediction
of the 7.656 MeV Carbon resonance although
there is some dispute here on the matter.
• See for example “When is a prediction
anthropic? Fred Hoyle and the 7.65 MeV
carbon resonance”
by Helge Kragh
Reference http://philsci-archive.pitt.edu/5332/
• Coincidences based on:
• Traditional kind – Stars of varying
sizes & colours (Red Giants to white
dwarfs) have masses ~ 104040
(1 /
Gravitational coupling constant).
Conventional Stellar theory.
• Weak Anthropic reasoning
• The age of the Universe must be
consistent with Observers
• Strong Anthropic reasoning
• We must be here to observe the
Universe

23. Nucleosynthesis
H : He ~ 73% : 25% (by mass)
The first 33 minutes
Only the Isotopes shown on the left
were created in the Big Bang
All other elements were forged in the
hot interiors of Carbon rich Red
Giant stars or in Supernovae of
massive stars
Proton – Proton Chain
H burning into He
1
1H
1
0n
4
2He
2
1H
3
1H
3
2He
1.1. 11
H+H+11
HH ⇒⇒ 22
H +H + 00
e+e+νν
1 1 1 11 1 1 1
2.2. 22
H +H + 11
HH ⇒⇒ 33
HeHe
1 1 21 1 2
3.3. 33
He+He+33
HeHe ⇒⇒ 44
He+He+11
H +H +11
HH
2 2 2 12 2 2 1
11

24. The Cosmic Onion
The CNO Cycle
Hans Bethe – proposed CNO Fusion cycle “Energy production in stars” Phys Rev 55, 434-456Hans Bethe – proposed CNO Fusion cycle “Energy production in stars” Phys Rev 55, 434-456
(1939)(1939)
1.1. 1212
C+C+11
pp ⇒⇒ 1313
N +N +γ (γ (1.95MeV)1.95MeV) ⇒⇒ 1313
C+C+ 00
e +e +νν (2.22MeV) 2.(2.22MeV) 2. 1313
C +C + 11
pp ⇒⇒ 1414
N+N+
γ∗γ∗
6 1 7 6 1 e 6 1 76 1 7 6 1 e 6 1 7
3.3. 1414
N +N + 11
pp ⇒⇒ 1515
O +O + γ (γ (7.35MeV)7.35MeV) ⇒⇒ 1515
N +N + 00
e +e + νν (2.75MeV)(2.75MeV)
77 1 8 7 1 e1 8 7 1 e
4.4. 1515
N +N + 11
pp ⇒⇒ 1212
C +C + 44
He + 4.96MeVHe + 4.96MeV
7 1 6 27 1 6 2
1
23
4

25. The “mass gap” problem
at A = 5, A = 8
A crevasse exists at Atomic mass
number A = 5 and no bridge can
be found at A = 8.
Is the 1952 prediction by Fred
Hoyle of a 7.65 MeV resonance
in Carbon Anthropic ?
Stable Isotope Z A Disint. (T½ ) Atomic weight
1
1H (99.985%)
2
1H (0.015%)
1
1
1
2
Stable
Stable
1.00794
2.014102
3
2He (1.4 x10-4
%)
4
2He (~ 100%)
2
2
3
4
Trace %
Stable
3.016030
4.002604
1
1H + 4
2He
2
1H + 3
2He
1+2
1+2
1+4
2+3
p emission
0.01514%
5.010544
5.030132
6
3Li (7.42%)
7
3Li (~ 92.58%)
3
3
6
7
Low %
Stable
6.01512
7.016
2
1H + 6
3Li
3
1H + 5
3Li
4
2He + 4
2He
5
2He + 3
2He
1+3
1+3
2+2
2+2
2+6
3+5
4+4
5+3
7.435%
β−
(12.3a) + p
2α (3x10-16
s)
n emission + %
8.029222
8.028549
8.003204
8.02833
9
4Be (100%) 4 9 Stable 9.01218
10
5B (80.4%) 5 11 Stable 10.811
12
6C (98.89%) 6 12 Stable 12.000

26. Fred Hoyle and the 7.656 MeV resonance in 12
C
B2
F H “Synthesis of the Elements in Stars” Rev Mod Phys 1957 vol 29 p547,
The Triple α process
• Energy equivalents of 4
2He (α particle),8
4Be and 12
6C
• 1 u = 1.660538921 x10-27
kg
• E (eV) = m (c2
/ e) = m (kg) x (5.609534842 x 1035
)
• 4
2He = 4.002604 u = 6.646479727 x10-27
kg
= 3 .728365960 GeV
• 2 α 's = 7.456731921 GeV, 3 α 's = 11.18509788 GeV
• 8
4Be = 8.00530 u = 1.329311222 x10-26
kg
= 7.456817618 GeV
• 12
6C = 12 u = 1.992646705 x10-26
kg = 11.17782112 GeV
• 4
2He + 8
4Be - 12
6C = + 7.362458 MeV
∆E ~ 293.542 keV (7.656 – 7.362458) MeV
• 2 (4
2He) - 8
4Be = - 85.697 keV
• 3 (4
2He) - 12
6C = + 7.275759 MeV
∆E ~ 380.241 keV (7.656 – 7.275759) MeV

27. The Drake Equation and SETI
Is anybody out there ?
The original SETI search at the Greenbank radio telescope
looked in one channel at 1402.5 MHz the 21 cm line in
the Hydrogen spectrum reminescent of the red glow from
interstellar gas, like here in the Horsehead Nebula in the
constellation of Orion.
Civilisation Calculator
R*= 10
fp = 0.5
ne = 2
fl = 1
fi = 0.5
fc = 1
L = 10000
N = 50000
R* - rate of star formation
fp - fraction of stars with
planets
ne - number of earth like
planets
fL - fraction where life occurs
fi - fraction where intelligent
evolves
fc - fraction that are
communicable with universe
L - Lifetime of civilisation
N - Number

28. Is Life a Cosmic Imperative ?
Three Hurdles need to be overcome for us to communicate with the Cosmos
No Biology only Physics /
Inorganic
Chemistry
Organic Chemistry Biogenesis The origins of
Life... Self replicating molecules
................................
Bacteria/viruses single cell microbes
Life on Earth The Tree of Life
Darwinan evolution
Complex multicellular photosynthetic organisms
6CO2+6H2O + LIGHT = C6H12O6+6O2
Carbon dioxide + Water + Light = SUGARS +
Oxygen
...........
Is Intelligent Life an evolutionary imperative ?
Does this lead to a desire to communicate...

29. The Fermi Paradox 1950
Where is ET ?
They must have colonized the
Galaxy by now...
So where are they ?
The Eagle Nebula M16
“The Pillars of Creation”

30. Bibliography &Further reading
8 Books that tell the Lecture in more detail
700 pages of equations Easier to read story The nuts & bolts Story of the Hubble
constant
Easy to read Best Intro The complete story so far... SETI/Are we Alone ? Simple Anthropic
arguments