Today's lecture covered the following points:

What is the fastest clock we can possibly imagine?  Consider a light
clock of length l, with a light beam bouncing back and forth.  To put
a photon in it, it has to have a wavelength of l or less, and thus a
frequency of c/l or greater.  It therefore has an energy E = hc/l
(energy of a photon is proportional to its frequency).  But energy is
equivalent to mass; the corresponding mass is m = E/c^2 = h/lc.  But
if we make this too small, it will turn into a black hole, in
particular, the Schwarzschild radius is 2Gm/c^2.  Equating this to l
gives us: l = Gm/c^2 = 2Gh/lc^3.  Solving for l gives us: 
l = (2Gh/c^3)^{1/2}, which, when you plug in the numbers, is something like
10^{-33} cm.  This length is what's called a 'Planck length'.  A
photon of such short wavelength would instantly collapse into a black
hole.  The corresponding time is 
l/c =  (2Gh/c^5)^{1/2} = 5 X 10^{-44} sec. (Strictly speaking, there is
another factor of 4 pi in these expressions; that is, the Planck time
is (Gh/2 pi c^5)^{1/2}.)  You see what's happened here; we've combined
notions from General Relativity (the concept of the Schwarzschild
radius) and quantum mechanics (relation between energy and frequency
of a photon).  We don't really know what happens on spatial scales
smaller where both of these effects are important, because we don't
yet know how to reconcile these two theories.  

As we saw last time, we now know the universe will expand forever; in
fact, the expansion appears to be accelerating.  Let's trace out the full
history of the universe, into the future, measuring from the big bang
itself:

10^{-32} sec:  Inflation ends. 
10^{-6} sec:  Protons and neutrons form out of quarks (we didn't really talk
about this before). 
3 minutes:  Helium nuclei form, as does deuterium (see Lecture 21). 
380,000 years: The universe cools to the point that neutral atoms can
form (hydrogen atoms, mostly).  This period is sometimes called
'recombination', as protons and electrons combine to make neutral
atoms.  The CMB is the radiation left over from this epoch.  
1.2 billion years: Approximately when galaxies formed.
10^10 years: Today (approximately).  
10^14 years: Even the least massive stars burn up all their hydrogen, and
fade into white dwarfs.   No more stars!
10^17 years: Planets are torn away from their parent (burned-out) stars, by
chance encounters with other stars.
10^21 years: Most stars fall into huge black holes into the centers of
galaxies.  
10^44 years: Protons decay.  In most modern particle physics models, the
protons are not stable, but will eventually decay (although this has yet to be
demonstrated experimentally); this is the epoch at which this happens.  All
that's left are electrons, positrons, photons, and black holes. 
10^100 years: Even the biggest black holes will finally
evaporate via Hawking radiation (see the end of Lecture 19).

Perhaps sometime after this, a random quantum fluctuation could start
a new epoch of inflation, and start a new universe... 

Gott's variant on the Copernican Principle: We are not living at a
special time.

  Gott visited the Berlin Wall in 1969: assuming that this was not a
special time in the history of the wall, he argued thusly: there is a
50% chance that this visit fell between 1/4 and 3/4 of the eventual
age of the wall.  Therefore with 50% confidence, the future age of the
wall would be between 1/3 and 3 times its age at the time (8 years),
or 3-24 years.  It indeed came down 20 years later.  Gott applied this
same argument to the human race (now 200,000 years old); with 95%
confidence, it will last between (present lifetime)*1/39 and (present
lifetime)*39, or between 5000 and 8 million more years, in
rough agreement with typical longevity of mammal species.  (Where is
that 39 from?  With 95% confidence, our current longevity is > 2.5%,
and < 97.5% of the total lifetime of the species.  In the former case,
the future longevity is 97.5/2.5 = 39 times as long.  In the latter,
it is 2.5/97.5 = 1/39 as long.)

  A series of similar arguments followed, based on Broadway plays,
world leaders, lifetime of the Conservative government in Britain, the
total number of people to be born in the future, etc.  The average
person on the planet lives in one of the most populated countries.
Similarly, we can guess that we're likely to live on one of the more
populated planets in the galaxy.

  Finally, wouldn't it be cool to colonize space, and Mars in
particular?  This could give us an insurance policy against extinction
due to planetary catastrophes.  However, the manned space program is
not that old (40-someodd years), and isn't in great shape.... Indeed,
the goal of the human spaceflight program should be to improve our
survival prospects by colonizing space, and other planets.  

  This is the end of the course; we hope that you all leave with a deeper
understanding of the universe and our position in it, and a curiosity to learn
more. 

© Copyright 2009, J. Richard Gott III and Michael A. Strauss