- This episode was made possible by Brilliant.
Hi everyone, I'm Jade.
Lovely to meet you or see you again.
In the movie "The Matrix"
people are plugged into a virtual world
without them knowing it.
All of their experiences are completely stimulated
and don't correspond to the real world around them.
It's a classic piece of science fiction or is it?
What if I told you that cosmologists,
the people who study
the large-scale structure of our universe
actually argue over whether our universe
is really just a simulation.
In the cosmologist version
the idea is that all that really exists is a single brain
which stimulates all of the senses
that make up your experiences.
Everything you've ever tasted, smelled, touched,
all of your memories, your entire life
from the day you were born until the day you die.
This all-simulating brain is called a Boltzmann brain.
This sounds insane when I just say it like that.
So before we get into why this is something legit science
even talk about,
we need to cover some basic physics.
Before we start,
this is part one of a collaboration
with Isaac Arthur who makes really cool videos
about space and philosophy.
He'll be popping in and out of this video
and make sure to check out part two
on his channel afterwards.
All right, in any physical system
it's often really useful to quantify
the amount of ordered structure in that system.
We can do this by counting the number
of possible ways we can rearrange the system.
Take this example.
Imagine flipping 10 coins.
There's only one way to flip 10 heads.
That's a pretty ordered system.
But if you wanted to throw five heads and five tails
there are 252 different ways to do that.
This way of looking at the overall order
of a system is called entropy
and physicists love to talk about entropy.
They love it, because they can always rely on it
for one thing, to keep going up.
What do I mean by that?
Okay, well, in our coin case,
you can imagine that the number of possible ways
we can get heads or tails is proportional to the entropy.
Flipping 10 heads can only be done one way
and so has very low entropy,
but flipping five heads and five tails
can be done in many ways and so has high entropy.
So if you started with 10 coin spacing heads
and started flipping them,
you would tend to a state of higher entropy.
- [Isaac] The takeaway is entropy always increases
in a closed system.
You can also think about the entropy
of more realistic systems
like the air in the room around you.
When you open the door to let some cool air in
the cool air doesn't just stay in the corner,
it gradually spreads out and mixes with the warm air
lowering the temperature of the whole room.
It goes from a neat, separated system
to a messy, mingled system,
which is impossible to avoid.
Try as much as you want,
you won't get those cool air particles
back to the corner of the room.
- But hang on,
some of the very astute of you, maybe wondering
but you said entropy always increases,
but it is possible that I can start off with
five heads and five tails and flip them all heads
making the entropy go down.
Explain that Jade.
All right, well spotted.
In fact, you're right.
That is possible.
And it's a key piece of the puzzle
in understanding Boltzmann brains.
Entropy is a concept governed by statistical fluctuations,
the larger the fluctuation the more unlikely
the event is to happen.
But while on average, entropy always increases,
it's very possible to have fluctuations
which lower entropy
given enough time and dumb luck.
So that's entropy.
Now let's leave that for a moment
and talk about cosmologists,
the people concerned with Boltzmann brains
and the whole of your entire existence
may be a simulation thing.
The goal of cosmology is to understand the universe
on the largest scales.
They try to answer questions like:
What is the entire universe made of?
Is it changing over time?
Is the universe the same over here as it is over there?
Arguably, the Holy grail of cosmology
is about the origins of the universe.
The theory is that the universe started off
in a very hot, dense state in the past
a state of very low entropy.
The big question is, why?
This question is still not entirely answered today.
And it's so hard, because we have no way
as far as we know, to measure anything before the big bang
if the concept of before the big bang even means anything.
But that hasn't stopped cosmologists
from coming up with models about how the universe
may have started and evolved.
It's hard to summarize an entire active field of research
but one paper by some of the leading physicists
in the field, summarize it like this.
"The question then is whether the origin of the universe
was a naturally occurring fluctuation
or was it due to an external agent
which started the system out
in a specific low entropy state?"
Now we'll get into what naturally occurring fluctuation
means in a second.
But the phrasing of external agent here
is just meant to describe any other mechanism
of why the universe may have started out the way it did.
So here we can finally tackle head-on
the problem of Boltzmann brains.
- [Isaac] The guy that Boltzmann brains are named after
Ludwig Boltzmann, was a 19th century physicist
whose primary contribution to physics
was our modern understanding
of particle thermodynamics and gases.
Unfortunately, the idea that small particles
like atoms and molecules make up matter
was highly controversial at the time,
due to nobody being able to see them.
He spent much of his life fiercely defending his theories
against constant attacks by the scientific community,
but he was right.
And much of what we know about thermodynamics and entropy
is because of this great man
whose equation is now etched on his tombstone.
- But what does the thermodynamics
have to do with cosmology?
Remember the Holy grail question of cosmology?
Why did the universe start out the way it did
in such a state of low entropy?
Well, one answer to that question is
that the universe is actually much older
than we observe it to be.
And the big bang was a kind of
all coins flip heads type situation.
By that, I mean, it was an astronomical fluctuation
which created a region of space with very low entropy
which was the big bag.
And the evolution of the universe ever since then
has just been a consistent increase in entropy
like what we would expect.
Now, that all sounds plausible.
But if we stop and think about it for a second,
smaller fluctuations in entropy
are much more likely than larger ones, would you agree?
So it should seem intuitive
to think there would have been a smaller fluctuation
in entropy and hence be more likely
to have created only half the universe
as opposed to the entire universe that we observe.
Scratch that, it would be even more likely
to simply produce our own galaxy,
even more likely to just produce our own solar system,
our planet, a single human body, or even a single brain.
The Boltzmann brain argument states
that it's astronomically more likely for a single brain
to spontaneously and briefly fluctuate into existence
complete with false memories of our universe
than it is for the entire universe to have fluctuated
into such a low entropy state as the big bang.
So statistically speaking
you are most likely a Boltzmann brain.
I can imagine this doesn't sit well with a lot of you
neither does it sit well with a lot of cosmologists.
Of course, in principle
if our theories tell us
that we're most likely to be Boltzmann brains,
we shouldn't believe our theories, right?
Well, not necessarily.
There have been many arguments
that try to come to grips with the problems that arise
if we take this view,
because it points to a broader issue
about how we construct and interpret cosmological theories.
I'll try to give the intuition
for a couple of the counter arguments here,
but the subtleties for each of them
will depend on the particulars
of the cosmological model we're analyzing.
An interesting argument against Boltzmann brains
comes from cosmologist
and all-round cool dude, Sean Carroll.
And it's that the very idea of thinking
that we might be Boltzmann brains is in his words,
"Cognitively unstable."
This idea is a bit confusing
but this is the best way I know how to sum it up.
So what cognitively unstable means is that
if our theories tell us that we are Boltzmann brains
the only way that could be the case
is that if we are Boltzmann brains
simulating everything in the world that we experience.
So then, because we're Boltzmann brains
simulating the real world
we can't really trust any of our observations
about the world.
So this means that we can't trust our observations
that came up with the theories that we are Boltzmann brains.
(Jade sighs)
Does that makes sense?
It's a self-contradicting situation.
And it's what Carroll means by unstable.
It doesn't settle on a conclusion.
It flip-flops between, well, we might be Boltzmann brains
but then if we are, then we can't trust our observations
that tell us that we are,
but we still might be, but then if we are, we might not be.
What's interesting about this argument
is that it doesn't rely on empirical data.
It's arguing for a particular way of doing science
in a consistent way.
What are some other more digestible arguments
against Boltzmann brains?
- [Isaac] Many cosmologists
say that all cosmological theories
ought to be able to predict
that we should be likely to exist.
However, in assessing this likelihood,
we should take into account the fact that we do exist.
Let's break that down.
This is an example of what is called the anthropic principle
and in its simplest form, it says,
"That the environment we observe around us
is the kind of environment that would allow
observers like us, to exist."
This is a powerful idea when used to its full extent
and it's particularly useful in fields like cosmology
where the data is limited
and you can't really do controlled experiments
with the entire universe.
However, talking about probability gets complicated
and a little precarious in situations
where the infinity is like potential size and age
of the universe come in.
So the details of the analysis
start to become very important but suffice to say,
that with different bases and arguments
and taking into account that we exist
as a key part of your empirical evidence
then humans in a big bang universe come out
over and above these pesky Boltzmann brains.
Of course, there is an alternative way of looking at that
which goes back to a more elemental assumption
of the observer being able to trust what they see
and assume it is real, accurate and normal.
And we'll examine this and some alternative approaches
such as the anthropic principle
and some of its consequences in part two.
- The take home message of this video
is the fact that cosmologists try to avoid the idea
that we are Boltzmann brains,
isn't because they have a fear
that we might actually be one of them,
it's more of an interesting thought experiment
that points out subtle issues
about how we deal with probabilities in our theories
when we're asking these big Holy grail questions about
why the universe is the way it is?
As we saw in this video,
big ideas like is the universe a simulation?
Seem like nothing more than science fiction
if we don't have the basic physical principles
to back them up.
You can't really understand the idea of Boltzmann brains
without first understanding entropy.
I like to cover big ideas in my videos,
but to do that I need to nail the basics first.
One way I do this is by practicing with Brilliant.org.
If you'd like an extensive overview of fundamental physics
I highly recommend their course on classical mechanics.
It includes quizzes about motion, energy,
reference frames, oscillations, and more.
Their interactive quiz style really forces you
to think about what you're learning.
And as any physics professor will tell you
to get any kind of intuition about a topic
you need to work through problems.
And this couldn't be more true.
Every time I look into a quiz, I either learn something new
or gain a fresh insight.
When you are ready to tackle those big ideas,
Brilliant has more advanced courses too,
like this one on quantum computing
or this one on gravitational physics
where you can learn about black holes.
Brilliant has more than 50 courses
on topics in math, physics, and computer science.
The first 200 people to click the link below and sign up
we'll get a 20% discount
just go to brilliant.org/UpAndAtom.
So what do you think?
Are you a Boltzmann brain?
Let me know your thoughts in the comments below.
(upbeat music)