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