Distant time and the hint of a multiverse Sean Carroll
the universe is really big we live in a
galaxy the Milky Way galaxy there about
a hundred billion stars in the Milky Way
galaxy and if you take a camera and you
point it at a random part of the sky and
you just keep the shutter open as long
as your camera is attached to the Hubble
Space Telescope it will see something
like this every one of these little
blobs is a galaxy roughly the size of
our Milky Way 100 billion stars in each
of those blobs there are approximately
100 billion galaxies in the observable
universe the 100 billion is the only
number you need to know the age of the
universe between now and the Big Bang is
a hundred billion in dog years which
tells you something about our place in
the universe one thing you can do with a
picture like this is simply admire it
it’s extremely beautiful I’ve often
wondered what is the evolutionary
pressure that made our ancestors in
developed adapt and evolve to really
enjoy pictures of galaxies when they
didn’t have any but we also like to
understand it as a cosmologists I want
to ask why is the universe like this one
big clue we have is that the universe is
changing with time if you looked at one
of these galaxies and measured its
velocity it will be moving away from you
and if you look at the galaxy even
further away will be moving away faster
so we say the universe is expanding what
that means of course is that in the past
things were closer together in the past
the universe was more dense and it was
also hotter if you squeeze things
together the temperature goes up that
kind of makes sense to us the thing that
doesn’t make sense to us as much is that
the universe at early times near the Big
Bang was also very very smooth you might
think that that’s not a surprise the air
in this room is very smooth you might
say well maybe things just smooth
themselves out but the conditions near
the Big Bang are very very different
than the conditions of the air in this
room in particular things were a lot
denser the gravitational pull of things
was a lot stronger near the Big Bang
what you have to think about is we have
a universe with a hundred billion
galaxies 100 billion stars each at early
times those hundred billion galaxies
were squeezed into a region about this
big literally at early times and you
have to imagine doing that squeezing
without any imperfections without any
little spots where there were a few more
atoms than somewhere else because if
there had been they would have collapsed
under the gravitational pull into a huge
black hole
keeping the universe very very smooth
that early times is not easy it’s a
delicate arrangement it’s a clue that
the early universe is not chosen
randomly there was something that made
it that way we would like to know what
so part of our understanding of this was
given to us by Ludwig Boltzmann an
Austrian physicist in the 19th century
and Boltzmann’s contribution was that he
helped us understand entropy you’ve
heard of entropy it’s the randomness the
disorder the chaoticness of some system
Boltzmann gave us a formula engraved on
his tombstone now that really quantifies
what entropy is and it’s basically just
saying that entropy is the number of
ways we can rearrange the constituents
of the system so that you don’t notice
so that macroscopically it looks the
same if you have the air in this room
you don’t notice each individual atom a
low entropy configuration is one in
which there’s only a few arrangements
that look that way a high entropy
arrangement is one that there are many
arrangements that look that way this is
a crucially important insight because it
helps us explain the second law of
thermodynamics the law that says that
entropy increases in the universe or in
some isolated bit of the universe the
reason why the entropy increases is
simply because there are many more ways
to be high entropy than to be low
entropy that’s a wonderful insight but
it leaves something out this insight
that entropy increases by the way is
what’s behind what we call the arrow of
time the difference between the past and
the future every difference that there
is between the past in the future is
because entropy is increasing the fact
that you can remember the past but not
the future the fact that you are born
and then you live and then you die
always in that order
that’s because entropy is increasing
Boltzmann explained that if you start
with low entropy it’s very natural for
it to increase because there’s more ways
to be high entropy what he didn’t
explain was why the entropy was ever low
in the first place
the fact that the entropy of the
universe was low is a reflection of the
fact that the early universe was very
very smooth
we’d like to understand that that’s our
job as cosmologists unfortunately it’s
actually not a problem that we’ve been
giving enough attention to it’s not one
of the first things people would say if
you asked a modern cosmologists what are
the problems we’re trying to address one
of the people who did understand that
this was a problem was Richard Fineman
fifty years ago he gave a series of a
bunch of different lectures gave the
popular lectures that became the
character physical law he gave lectures
to Caltech undergrads that became the
firemen lectures on physics he gave
lectures to Caltech graduate students
that became the final edges on
gravitation in every one of these books
every one of these sets of lectures he
emphasized this puzzle why did the early
universe have such a small entropy so he
says I’m not going to do the accent he
says for some reason the universe at one
time had a very low entropy for its
energy content and since then the
entropy is increased the arrow of time
cannot be completely understood until
the mystery of the beginnings of the
history of the universe are reduced
still further from speculation to
understanding so that’s our job we want
to know this was 50 years ago surely
you’re thinking we figured it out by now
it’s not true that we figured out by now
the reason the problem has gotten worse
rather than better is because in 1998 we
learned something crucial about the
universe that we didn’t know before we
learned that it’s accelerating the
universe is not only expanding if you
look at that galaxy it’s moving away if
you come back a billion years later and
look at it again it will be moving away
faster individual galaxies are speeding
away from us faster and faster so we say
the universe is accelerating
unlike the low entropy of the early
universe even though we don’t know the
answer for this we at least have a good
theory that can explain it if that
theory is right and that’s the theory of
dark energy it’s just the idea that
empty space itself has energy in every
little cubic centimeter of space whether
or not there’s stuff whether or not
there’s particles matter radiation or
whatever there is still energy even in
the space itself and this energy
according to Einstein exerts a push on
the universe it is a perpetual impulse
that pushes galaxies apart from each
other because dark energy unlike matter
radiation does not dilute away as the
universe expands the amount of energy in
each cubic centimeter remain
the same even as the universe gets
bigger and bigger
this has crucial implications for what
the universe is going to do in the
future for one thing the universe will
expand forever back when I was your age
we didn’t know what the universe was
going to do we thought some people
thought that the universe would wreak
elapsed in the future Einstein was fond
of this idea but if there’s dark energy
and the dark energy does not go away the
universe is just going to keep expanding
forever and ever and ever
14 billion years in the past 100 billion
dog years but an infinite number of
years into the future meanwhile for all
intents and purposes space looks finite
to us space may be finite or infinite
but because the universe is accelerating
there are parts of it we cannot see and
never will see there’s a finite region
of space that we have access to
surrounded by a horizon so even though
time goes on forever space is limited to
us finally empty space has a temperature
in the 1970s Stephen Hawking told us
that a black hole even though you think
it’s black it actually emits radiation
when you take into account quantum
mechanics the curvature of space-time
around the black hole brings to life the
quantum mechanical fluctuation and the
black hole radiates a precisely similar
calculation by Hawking and Gary Gibbons
show that if you have dark energy in
empty space then the whole universe
radiates the energy of empty space
brings to life quantum fluctuations and
so even though the universe will last
forever an ordinary matter and radiation
will dilute away there will always be
some radiation some thermal fluctuations
even in empty space so what this means
is that the universe is like a box of
gas that lasts forever well what is the
implication of that that implication was
studied by Boltzmann back in the 19th
century he said well entropy increases
because there are many many more ways
for the universe to be high entropy
rather than low entropy but that’s a
probabilistic statement it will probably
increase and the probability is enormous
Lee huge it’s not something you have to
worry about the air in this room all
gathering over one part of the room and
suffocating us it’s very very unlikely
except if they lock the doors and
kept us here literally forever that
would happen everything that is allowed
every configuration that is allowed to
be attained by the molecules in this
room would eventually be obtained so
Boltzmann says look you could start with
a universe that was in thermal
equilibrium he didn’t know about the Big
Bang he didn’t know about the expansion
of the universe he thought that space
and time were explained by Isaac Newton
they were absolute they just stuck there
forever
so his idea of a natural universe was
one in which the air molecules were just
spread out evenly everywhere the
everything molecules but if you’re a
Boltzmann you know that if you wait long
enough the random fluctuations of those
molecules will occasionally bring them
in to lower entropy configurations and
then of course in the natural course of
things they will expand back so it’s not
that entropy must always increase you
can get fluctuations into lower entropy
more organized situations well if that’s
true
Boltzmann then goes on to invent two
very modern sounding ideas the
multiverse and the mprofit principle he
says the problem with thermal
equilibrium is that we can’t live there
remember life itself depends on the
arrow of time we would not be able to
process information metabolize
walk-and-talk if we lived in thermal
equilibrium so if you imagine a very
very big universe an infinitely big
universe with randomly bumping into each
other particles there will occasionally
be small fluctuations in the lower
entropy states and then they relax back
but there will also be large
fluctuations occasionally you will make
a planet or a star or a galaxy or a
hundred billion galaxies so Boltzmann
says we will only live in the part of
the multiverse the part of this
infinitely big set of fluctuating
particles where life is possible that’s
the regions where entropy is low maybe
our universe is just one of those things
that happens from time to time now your
homework assignment is to really think
about this to contemplate what it means
Carl Sagan once famously said that in
order to make an apple pie you must firt
first invent the universe but he was not
right in Boltzmann’s scenario if you
want to make an apple pie you just wait
for the random motion of atoms to make
you an apple pie that will happen much
more frequently than the random
and motions of atoms making you an apple
orchard and some sugar and an oven and
then making you an apple pie
so this scenario makes predictions and
the predictions are that the
fluctuations that make us are minimal
even if you imagine that this room we
are in now exists and is real and here
we are we have not only our memories but
our impressions that outside there’s
something called Caltech in the United
States and the Milky Way galaxy it’s
much easier for all those impressions to
randomly fluctuate into your brain than
for them actually to randomly fluctuate
into Caltech the United States and the
galaxy the good news is that therefore
this scenario does not work it is not
right this scenario predicts that we
should be a minimal fluctuation even if
you get our galaxies out you would not
get a hundred billion other galaxies and
Fineman also understood this Fineman
says from the hypothesis that the world
is a fluctuation all the predictions are
that if we look at a part of the world
we’ve never seen before we will find it
mixed up not like the piece we’ve just
looked at high entropy if our order were
due to a fluctuation we would not expect
order anywhere but where we’ve just
noticed it we therefore conclude the
universe is not a fluctuation so that’s
good the question is then what is the
right answer if the universe is not a
fluctuation why did the early universe
have a low entropy and I would love to
tell you the answer but I’m running out
of time
here is the universe that we tell you
about versus the universe that really
exists I just showed you this picture
the universe is expanding for the last
10 billion years or so it’s cooling off
but we now know enough about the future
of the universe to say a lot more if the
dark energy remains around the stars
around us will use up their nuclear fuel
they will stop burning they will fall
into black holes we will live in a
universe with nothing in it but black
holes that universe will last 10 to the
100 years a lot longer than our little
universe has lived the future is much
longer than the past but even black
holes don’t last forever they will
evaporate and we will be left with
nothing but empty space that empty space
lasts essentially forever however you
notice that since empty space gives off
radiation there’s actually thermal
fluctuations and it cycles around all
the different possible combinations of
the degrees of freedom that exist in
empty space so even though the universe
lasts forever there’s only a finite
number of things that can possibly
happen in the universe they all happen
over a period of time equal to 10 to the
10 to the 120 years so here’s two
questions for you number one if the
universe lasts for ten to the ten to the
hundred twenty years why are we born in
the first fourteen billion years of it
in the warm comfortable afterglow of the
Big Bang why aren’t we in empty space
you might say well there’s nothing there
to be living but that’s not right you
could be a random fluctuation out of the
nothingness why aren’t you more homework
assignment for you so like I said I
don’t actually know the answer I’m going
to give you my favorite scenario either
it’s just like that there is no
explanation this is a brute fact about
the universe that you should learn to
accept and stop asking questions or
maybe the Big Bang is not the beginning
of the universe an egg an unbroken egg
is a low entropy configuration and yet
when we open our refrigerator we do not
go ha how surprising to find this low
entropy configuration in our
refrigerator that’s because an egg is
not a closed system it comes out of a
chicken maybe the universe comes out of
a universal chicken maybe there is
something that naturally through the
expert through the growth of the laws of
physics give
rise to universe like ours in low
entropy configurations if that’s true it
would happen more than once we would be
part of a much bigger multiverse that’s
my favorite scenario so the organizers
asked me to end with a bold speculation
my bold speculation is that I will be
absolutely vindicated by history and 50
years from now all of my current wild
ideas will be accepted as truths by the
scientific and external communities we
will all believe that our little
universe is just a small part of a much
larger multiverse and even better we
will understand what happened at the Big
Bang in terms of a theory that we’ll be
able to compare to observations this is
a prediction I might be wrong but we’ve
been thinking as a human race about what
the universe was like why it came to be
in the way it did for many many years
it’s exciting to think we may finally
know the answer someday thank you