Download 15. Magic Numbers that Make the Universe

Magic Numbers Make the Universe or
The Miracle of Stars and Why We Are
Michael Bass, Professor Emeritus
CREOL, The College of Optics and Photonics
University of Central Florida
Orlando, FL 32816
© M. Bass
Cosmologies are how we
understand the universe
Biblical and Mythical. Then God said “let
there be light” and there was light
Aristotle’s universe of spheres
with the earth at the center.
Copernicus’ sun centered universe.
Newton’s universe of absolute motion.
© M. Bass
Einstein, relativity and the Big
Bang –Today’s Cosmology
Einstein’s universe of relative motion.
Einstein plus quantum mechanics and the Big
Bang Universe.
© M. Bass
Hubble Telescope Ultra Deep Field Image – all spots are galaxies
and all galaxies have many, many stars!
Just in case
you didn’t
believe me
this image
shows a
few of the
100s of
billions of
galaxies in
the
universe.
A
cosmology
has to
account
for all of
this and
more.
© M. Bass
A scientific cosmology
must explain
The night sky is dark.
The universe can not be static.
Hubble’s law of galaxies rushing apart.
The 2.7 K (loosely called the 3 degree)
black body radiation that fills the
universe.
The fact that there is 1 helium atom
for every 10 hydrogen atoms in the
universe.
© M. Bass
More Facts to Explain
 There are stars, galaxies,
clusters of galaxies, clusters of
clusters, and other structures
in the universe.
 Dark matter and dark energy.
 There are novas and super
novas and places in galaxies
where stars are continually
formed.
There are planets
and on at least
one there is US!
© M. Bass
The Big Bang
The outward rush of the galaxies from
one another can be run backwards to an
initial beginning.
About 13.7 billion years ago the universe
was no bigger that a sub atomic particle,
it was very, very hot and it started to
expand.
Everything that we see around us was
determined in this moment of creation.
Thanks to George LeMaitre a Catholic priest who saw
this solution in Einstein’s general relativity.
© M. Bass
Big Bang Nucleosynthesis
This is a big name for the cooking of
atoms during creation.
The Big Bang model explains many
observed features of the universe - the
He:H ratio, the 2.7 K black body
radiation, the Hubble law and so on - but
it only explains atoms of H, He, D and Li
These were formed in the first 3 minutes.
For all the other atoms we need stars!!
 Thank you Fred Hoyle even though you distracted us with the
steady state universe you got star evolution right.
© M. Bass
The formation of stars
 As the universe expanded
turbulences formed as they must.
 These gave rise to stars and
galaxies of stars.
The first stars were probably
supermassive, lived fast, died young
and seeded the next generation.
 The question we want to address
is what does it take to get the kind
of stars we need to cook the other
atoms that we need to get us.
 To do so requires a universe with
some very special properties.
Stars forming in small
protrusions from the Eagle
Nebula
© M. Bass
How do stars cook up
elements?
 The first stars were formed by
the hydrogen (plus a little
helium) gas produced in the Big
Bang.
 Gravity pulled the gas in on
itself and collisions heated up
the gas.
 When a certain temperature
was reached nuclear fusion
began and so called stellar
burning got going.
 The end products of nuclear
fusion reactions were higher
atomic number elements.
© M. Bass
Star burning
The rate with which a star burns its
hydrogen fuel increases with its mass.
Massive stars burn up fuel much faster
than smaller stars - makes you glad the
sun is a very average star, not a giant.
In such burning stars can produce all
the elements through iron
that includes carbon, oxygen, nitrogen,
calcium ...
© M. Bass
The next step
 To get past iron you must have
temperatures much higher than
just stellar burning nuclear fusion
allows.
 Thus, to get higher atomic
number atoms you must have
super novas.
 So, stars burn, crash, spew out
their remains into the galaxy and
seed the formation of newer
stars.
 WITH DIFFERENT COMPOSITIONS
© M. Bass
The next generations
 So one generation of stars
seeds the next and produces
new stars containing more
than just Big Bang elements.
 So too does the residue of new
star formation.
 Therefore, so do the planets
that form around the stars, and
 therefore so do we.
We are star stuff.
Spinning cloud
flattening into a disk and
condensing into a star
and planets
© M. Bass
What is required?
 We have pronounced the sequence of events
but haven’t explained why it occurs exactly
as it must for us to exist.
 To do this we will employ our knowledge of
modern physics - particularly the Standard
Model of Modern Physics
The current versions of the theories of Quantum
Mechanics and Gravitation
 (You do not have to know quantum
mechanics or general relativity to follow this
discussion.)
© M. Bass
Fundamental Constants
The Standard Model demands that certain
constants be just what they are.
We have theories that agree with observation if
the constants have certain values.
About 20 numbers giving such things as the
gravitational constant, the charge on the
electron, the speed of light, and etc.
If they aren’t, things don’t happen the way
we observe that they do.
 We don’t know why these constants are what they
are, just that they have to be what they are.
© M. Bass
A needle standing upright
on its point
 Why these constants must be exactly what
they are is asking why our universe is like a
needle standing upright on its point.
 The random probability that the several of the
20 constants that must have the precise
values needed to explain us is unbelievably
small.
About one chance in 10234
 The anthropic view, the one that says ours is a
universe designed for our existence, assumes
that a God set the values of the constants just
exactly right and then let things go.
© M. Bass
We must have stars so what
constants are needed?
 Stars are made of - protons, neutrons,
electrons and neutrinos. They also need
photons to balance their energy.
 These interact through four forces - gravity,
electromagnetism, weak nuclear and strong
nuclear (in order of increasing strength)
 Forces are characterized by strength, range
and type of particles they affect.
 Particles participate in forces through coupling
constants
mass for gravity
charge for electromagnetism
© M. Bass
Gravity
It is the only universal interaction.
every particle having mass feels gravity.
Its range is infinite.
Its strength is proportional to the
product of the masses that interact.
The proportionality constant, G, is
incredibly small, in units of proton
masses, it is 10-38.
© M. Bass
The importance of G
If this constant were any larger
stars would
live much shorter times than they do
they would not last long enough for
us to evolve
If this constant were any smaller
stars would
not collapse, ignite, and fuse H into
He and other necessary elements
© M. Bass
You need nuclear reactions
As gravity causes the gases of a star to
collapse nuclear reactions must take place
without nuclear reactions the internal pressure
of the gases can not compete with gravity and
the whole mess would collapse immediately into
a black hole.
For nuclear reactions to proceed as they
must to cook up the elements
the proton and neutron can differ in mass by
only 2 parts in a thousand and the electron must
be ~1800 times less massive than the proton
© M. Bass
n, p, e and n
Any larger differences and protons and
neutrons would not stick together in
atoms under the effects of the weak
nuclear force.
There would be no atoms, no chemistry,
no biology and the universe would be
very boring.
Neutrinos are particles essential to
conserve momentum in nuclear reactions.
It turns out that the neutrino mass can not
exceed ~10-9 of a proton mass.
© M. Bass
The scale of the universe
The universe must be big enough to
accommodate us.
To do so the mass density of the universe,
must be no larger than 10-40 per m3 in
units of proton mass.
If it were any larger the universe’s
expansion would not have happened.
If it were any smaller the universe would
have already expanded out of sight.
© M. Bass
There must be light
Electromagnetism is the force that governs
the radiation of light.
It must be present exactly as it is in order
to carry energy away from stars so that
stars stay in equilibrium long enough to
cook the elements and warm our planet.
This balance of gravitational collapse,
nuclear burning, and electromagnetic
radiation enables stars to last billions of
years.
© M. Bass
e, h and c
The demands for electromagnetic
radiation to maintain the energy balance
of stars requires that
the charge on the electron be no more and no
less than 1.60217657 × 10-19 Coulombs,
 Planck’s constant be exactly
6.62606957×10−34 J-sec., and
 the speed of light be 2.99792458 x 108 m/sec.
Any more or less and stars don’t make it.
Any more or less and there is no biology.
© M. Bass
The probabilities if these
numbers occurred randomly
 For the existence of particles with the necessary
masses:
the proton
=1 part in 1019
the neutron
=1 part in 1022
the electron =1 part in 1022
the neutrino =1 part in 1027
 For the cosmological constant
(density of empty space)
=1 part in 1060
 For the ranges of the forces
=1 part in 1080
 For the strength of the forces =1 part in 104
© M. Bass
Add ‘em up
 The total probability of all of these numbers
randomly being just what they must be to have us
is the product of all the probabilities or
1 part in 10234
 This is so astonishingly small that we are forced to
seek some deeper understanding of how so special
a universe could come about.
 What we have so far is a theory that fixes these
numbers so that it agrees with observed facts.
 What we don’t have is a theory that explains these
numbers.
© M. Bass
Possibilities
Some say it is God’s doing.
Some suggest multiverses with
cosmological natural selection where
universes that generate many universes
generate universes like themselves.
Some suggest simply that in the infinite
multiverse, we exist in one universe in
which we could exist.
Infinity is a big number and in it there are an
infinite number of universes just like this one.
© M. Bass
The Standard Model
This is the model of physics in which the very
small and the very large are taken together.
It has been tested many times and has yet to
fail.
The Higgs Boson was where it was supposed to be.
However, it demands that the numbers be what
they are.
A suggestion of why arises from String Theory.
© M. Bass
String Theory
 In 1984 John Schwarz and Michael Green published a
paper in which they showed that by allowing fundamental
particles to be tiny vibrating strings, not points, some
amazing things could be deduced.
 The differences between particles was determined by the
differences in how the strings vibrated – masses, charge,
spin and so on.
 Most exciting was that one of the vibrating strings had the
properties of the graviton – the force carrier for gravity.
Maybe string theory could unify gravity and quantum mechanics!!!
Before we go on String Theory is just that. No
experiment has been suggested that can test it.
© M. Bass
More work on String Theory
To be mathematically consistent it required 11
dimensions.
Then it required these dimensions had to
have certain shapes that corresponded to the
numerical values of the constants in the universe.
But, then it turns out there can be an innumerable
number of shapes. (In one treatment 10+500.)
So if you believe string theory we exist in one of
the infinity (very large number) of universes that
has the right set of shapes for us to exist in.
© M. Bass
String Theory and the
Multiverse
 The multiverse is the infinity of universes allowed by
string theory.
 If there are an infinity of universes there are an infinity
of universes just like ours.
 So it is not so surprising that we exist in a
universe that allows us to exists.
 Maybe everything is just good luck and the numbers
demanded by the Standard Model or that correspond to
some as yet unknown shapes of hidden dimensions in
String Theory are really not so unlikely as we think.
© M. Bass
Final thoughts
We have only just begun to have a scientific
cosmology based on observation,
experimentation and tested theory.
This universe is the only one we will ever
have so it is the only one we can try to
understand.
Whatever cosmology we come up with has
to include us.
© M. Bass