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NICHOLAS DIBELLA: So last time, at the end of last class,
I began to talk to you about quantum tunneling, which
allows for a lots of crazy events to occur.
It allows me to walk through chalkboards.
It allows me to fly.
It allows for various types of magic to be true.
And it's just so wonderful that quantum mechanics
allows for these really strange things to occur.
It kind of gives us hope-- it gives possibility--
that pretty much whatever you can imagine can occur.
And today, I'd like to expand on this theme of possibility,
and talk to you all about parallel universes.
So you're all here today in this room at MIT,
watching me talk about some stuff.
But would you believe that in a far,
far away galaxy there is an exact copy of this classroom
with ab exact copy of each one of you-- each person--
with each person having every single characteristic of you,
having the exact DNA, the exact memories, the exact preference
of ice cream, the exact everything,
and an exact copy of me talking to you about stuff?
Well, according to some parallel universe theories,
this actually is the case.
Whereas, in this universe, I simply mention that fact
and continue to talk about some other things,
in another universe I could mention that fact
and just leave the room.
[DOOR CREAKING]
[MURMURS]
Hi.
We're not in that universe, however.
OK.
Now, what do I mean by parallel universes?
Well, first I need to be a little bit more precise on what
I mean by universe, because it's used in a few different ways.
Now, usually when we think about the universe,
we think about "the universe"-- the everything
that's out there.
We think of that as being the universe.
Well, in this phrase, parallel universes,
the type of universe that I'm referring to
is a little bit different.
And there's one type of parallel universe
that I'd like to talk about first,
and that has a very specific meaning of universe.
And that's the observable universe,
which I'll write down here.
So as you all know, the universe is pretty big--
pretty big.
But there's only a certain fraction of it that we can see.
And that's because of the big bang.
And let me tell you briefly about the big bang.
You'll get a lot more about this in a couple of weeks,
but let me just briefly go over the big bang.
So a long time ago, all the galaxies, and all the stars,
and all the matter were a lot closer than they were today--
extremely close.
Infinitely close, in fact.
And it's speculated that about 14 billion years ago, all
of the matter and all of the energy in the universe
was concentrated at a single point.
And for some reason, these bits of matter
just started to expand away from each other.
And the reason for the expansion was that space itself expanded.
And as a result, everything sitting on space
would get farther apart from each other.
And that might sound kind of weird,
so let me give you an analogy.
Suppose you're an ant and you're living on top of a volleyball.
So this is you.
And according to you, your universe
consists only of two dimensions.
You can either walk one way or you
can walk another way, similar to how we move around
on the surface of the Earth.
Relative to the ground there's only, essentially,
two directions we can move.
Well, that's what the universe is like for this ant living
on a volleyball.
Of course, we, the omniscient observers,
see the whole volleyball, and so we
recognize that the ant's actually
living on the surface of a three dimensional object.
But the ant doesn't know that.
Well, what would happen if we expanded this ant's universe?
What would happen if we expanded this volleyball?
We still want to see it of course.
Let's say this is before, and this is after.
Of course, the ant is still the same size,
it's just that the volleyball has gotten much bigger.
So the ant's still lower here, but something
has changed for the ant.
On this universe there could be, for instance,
lots of other ants just specked all around,
just sitting around various points.
We didn't completely raise erase perfectly,
so let me make this a little bit better.
So there are these points on the volleyball
that the ant observes, and they're all
separated at certain distances from each other.
And once you expand this volleyball,
these points, as a result of the expansion of the volleyball,
get farther apart from each other.
So I drew five dots there.
Now there are still five dots, but they are farther apart
from each other.
And then that's something that the ant would observe.
Well, suppose right at the expansion,
one of these other ants-- suppose these dots are ants--
sent a signal-- send some light beam to our friendly ant,
the ant that we started off with.
So right before the expansion, some ant sent a signal.
So the signal travels from this ant to that ant.
Well, suppose the ant sends right
when the expansion starts.
Well, it's going to take some time for that signal
to reach the original ant, because light travels
at a certain speed, and it takes a certain time to get there.
Similarly, in our universe, and our universe's very early
history, light from other stars and other galaxies
has taken time to reach us since the big bang.
And there are some stars that have since
moved very far away from us--
extremely far away from us--
and the light from those stars simply
hasn't had enough time to reach us yet.
And so, there's a certain distance away from us
that is the maximum distance that we can observe.
And this distance defines a whole sphere
called the Hubble sphere, which we refer
to as the observable universe.
So there's only a small section of the whole universe
that we can observe, and we call that the observable universe.
AUDIENCE: What's the radius of--
NICHOLAS DIBELLA: What's the radius of the Hubble sphere?
The radius of the observable universe?
I think it's 40 billion light years.
And that's and that's different from the age of the universe,
because actually the space between us
has actually expanded.
And there are some effects that give rise
to that increased distance.
And in terms of meters, I have that for you.
In terms of meters, it's about 10
to the 27th meters, which is pretty big.
It would take it would take lights about 40 billion years
to reach from here until the end of the Hubble volume--
to the end of the observable universe.
Now, as each year passes by, light
has an extra year to travel.
And so, for each year that passes by,
the observable universe increases by one light year.
So the observable universe is getting bigger and bigger.
Now, strictly speaking, we don't really
know if there's anything outside of the observable universe,
because we just can't observe it.
And so, you might say that anything that's
outside of the observable universe
is just subject to mystical speculations
or metaphysical speculations, and science can't do anything
about those places.
Well, actually, surprisingly, we can say some things
about what's outside of the observable universe,
although the things that we say are more indirect.
Now, there's the question that space might be finite
or it might be infinite.
And we now have a kind of good answer to that question.
But first, what does it mean for space to be finite or space
to be infinite?
Well, if space were finite, you might imagine that you take off
from a rocket ship on earth, and then you travel
and you keep traveling farther and farther away.
And then, you eventually reach a sign that says,
this is the end of the universe.
Dead end.
You might reach a sign that says that.
Well, that's not what I mean by space being finite.
What I mean by space being finite,
is something like this volleyball universe of the ant.
It's finite for--
I mean, we, the omniscient observer,
look at this volleyball and we see that it has a finite size.
Of course, this is an analogy.
It's an analogy to the real world, where our universe might
possibly be some four dimensional hypersphere
that we're living on top of.
So it's a four dimensional extension to this volleyball.
In that sense, the universe might be finite.
And one consequence of this is actually
that if you started at some point in the universe--
supposed you started here.
If you started at this point in the universe and you traveled,
say, this direction, and just kept traveling straight
forward, eventually you would return
to where you started off.
And that seems kind of weird, right?
If I keep traveling this way, then ordinarily I
wouldn't think that eventually I'd return here,
but actually we know that the earth is earth is round,
so eventually we're going to reach back
at our original point.
And that's similar to what would happen in a finite universe.
Well, it looks like this actually isn't the case.
There are some very interesting measurements
that people have done about some radiation
that we observe in the sky called the cosmic microwave
background radiation.
People have done measurements of the stuff.
I'm not going to get into exactly what that stuff is,
but in a couple of weeks you'll know more about it.
But there is this radiation that we just
see when we look out-- when we point our telescopes
and look at the sky.
There's this radiation.
And the way that this radiation looks actually
gives us an indication to the geometry of the universe.
There are these spots, for instance,
in the radiation that would indicate
whether the universe is spherical,
or it might be hyperbolic, or it might be flat.
It might just be one big line--
one hyperplane we would have to say.
And it looks like the universe actually is infinite.
And it looks like the universe is flat,
which is probably the least interesting case that's
conceivable.
But that's what it looks like.
So it looks like the whole universe is infinite and flat.
So let's assume that's the case.
It's supported by observations.
And I think it's actually seems--
it's kind of hard to reason from intuition
that the universe should be infinite,
so I would try to reason from intuition that the universe
should be infinite.
But maybe it seems natural to some of you
that the universe should be infinite rather than finite.
In that case, you'd probably like this.
You'd probably like this fact.
Question?
AUDIENCE: What do you mean the universe is flat?
NICHOLAS DIBELLA: Oh, what do I mean the universe is flat?
Well, this is what I mean by the universe being curved.
For these ants, their universe is curved.
AUDIENCE: Oh, so it's not like it's a flat plane,
just it doesn't curve?
NICHOLAS DIBELLA: Yeah, it doesn't curve.
If it went one direction, you wouldn't return
to where you started off.
That's what I mean by the universe being flat.
And it looks like the universe is flat and infinite.
AUDIENCE: In all geometries, would you
be turned toward where you started though?
NICHOLAS DIBELLA: In all geometries, would what?
AUDIENCE: Like, if you're on a hypersphere,
then unless you come back to where you started,
it's not like that some different geometry it
would be possible for it to be curved, but [INAUDIBLE]
NICHOLAS DIBELLA: Oh, yeah.
It could be possible, that the geometry is curved
but we don't return where we started.
You can imagine something like--
I don't know.
Something like this.
So I go from 1D to 2D, and then you
have to use your minds to make a 3D.
And then you have to use your minds to make it 4D.
Yeah, you can imagine something like this.
You travel this way, keep going, keep going, keep going,
and then you never return to where you started.
Yeah, that's possible.
You could have fun thinking about possible geometries
the universe could be.
But that's not going to correspond to reality
unfortunately.
We can fun thinking about it.
And for a long time, this is all that people were able to do,
just think about it.
We didn't have data long time ago.
We don't have measurements that indicated
that the universe is infinite.
Question?
AUDIENCE: How is 4D supposed to look?
NICHOLAS DIBELLA: OK, how is 4D supposed to look.
I can't tell you how 4D is supposed to look.
Nobody can tell you what 4D looks like.
You just have to have to try to visualize
an analogy of what some properties of it would be like.
You can't actually see it, and that's something
that we have to live with unfortunately.
I mean, sorry.
Yeah, question?
AUDIENCE: There are actually diagrams
of what they think it might possibly look like, except not.
They kind of explain--
NICHOLAS DIBELLA: Well, I know there
are some diagrams I've heard of that, once you look at them,
you kind of get an illusion that you're
seeing the fourth dimension.
Is that kind of what you're describing?
AUDIENCE: No, like, diagrams that show hypercubes.
NICHOLAS DIBELLA: Oh, oh, oh.
Well, those diagrams that you're talking about are--
they're four dimensional objects that are embedded
onto a two dimensional surface.
So you're not really seeing it.
AUDIENCE: And how would they think
that it's flat and infinite?
NICHOLAS DIBELLA: How, do they actually do this?
How do they actually infer from the data
that it's flat and infinite?
Well, that's--
AUDIENCE: If you can only see as far as the observable universe,
then that means that no matter what you see,
you can't tell what's beyond that, and it could be.
NICHOLAS DIBELLA: OK.
Well, we can't directly observe what's
outside of the observable universe,
but we can make indirect inferences.
AUDIENCE: But nothing comes from there.
Like, you can't see radiation.
You can't--
NICHOLAS DIBELLA: Nothing comes from there,
but the universe-- the total universe--
has a certain geometrical shape.
And there are clever ways of making these inferences.
I don't have time to get into them now, but we'll talk later.
So for the purpose of the rest of today's class,
assume that the universe is infinite.
This is the assumption we're going to make.
This has so many wonderful consequences, the assumption
that the universe is infinite.
I should say "the universe" is infinite.
there are some theories about the early--
well, pretty much all the theories
about the early universe speculate
that a long time ago after this massive expansion
following the big bang--
well, during this expansion--
all the material that was present
dispersed randomly and formed certain arrangements of matter.
And not only did it form some types of arrangements
of matter, but actually this expansion
created all different possible arrangements of matter
to spread out.
So imagine a very long time ago, you've
got all every possible arrangement of matter.
So in this room, for instance, there are air molecules,
there are molecules making up you,
there are atoms and subatomic particles,
and there's a finite number of particles in this room.
And there is a finite number of ways
that you can arrange those particles.
I could, for instance--
I'll make an analogy.
Suppose I've got a rectangular universe.
Before I had a volleyball universe,
now suppose I have a rectangular universe.
Suppose I have a rectangular universe that
has four different types of particles.
No-- let's say there are two different types of particles.
So there's particle 1 and particle 2.
These are all the different types
of particles in our fake universe-- our play universe.
We have 1 and 2.
And suppose there's only space in our universe for four
different particles.
Or yeah, say there's only space for four of them.
Then what can we do?
We can put 1 here.
We can put 2 here.
We can put another 2 here.
And we can put another particle 1 there.
I know it looks like there's more
there's more space for more particles,
but let's say that this is the most
that our universe our fake universe can accommodate.
So this is one possible arrangement of those particles.
Another possible arrangement of those particles
would be to have 1, 2, 1, 1.
Another one would be 1, 2, 1, 2.
In fact, how many different arrangements
are there in this universe?
AUDIENCE: 16.
NICHOLAS DIBELLA: 16.
Yeah, it's 16.
There's two for this one, there's two for this one,
two for this one, and two for this one.
Two, times two, times two, times two, is 16.
So there are 16 different possible arrangements
of these particles.
In this universe.
And so, there are really 16 different types
of realities in this universe.
Reality is defined essentially by how
various particles are arranged.
And somehow the way these particles
are arranged gives rise to how we perceive them and so forth.
So the arrangement of particles gives rise to the reality
that those particles impart to us.
Now, our universe, of course, is not rectangular like this.
Well, that's actually not so important.
But our universe is much bigger than this universe
that we have here.
I'll go here to this board.
Our observable universe is a sphere.
Remember, the whole universe we suspect is flat and infinite,
but our observable universe is some finite sphere.
And our observable universe has a certain radius.
And this radius happens to be--
I have it written down--
8 times 10 to 26th meters.
Now, suppose a particle has a radius of about--
OK, what we want to do now is fit particles
into this universe.
And we're going to ask how many particles can we
fit inside of it.
It's going to be a lot of particles,
because the observable universe is really big
and the particles are really small.
But we can get a rough estimate for how many particles
we can put inside of it.
So a particle-- say this is a little particle--
looks like a TIE fighter.
What am I doing?
OK, say this is a particle, and it's got a length of about 10
to the minus 13 meters, which is significantly
smaller than the length of the observable universe.
Well, now you can ask, how many of these particles
can you fit inside of this universe?
And to do that, you can simply calculate
the volume of this universe and divide
by the volume of a subatomic particle, which
might be a proton, or a neutron, or something like that.
Simply take those two volumes and divide them.
Take the radius, cube it.
Use the formula for the volume of a sphere and then just
divide by that formula applied with this radius.
And you get about 10 to the 118th particles.
AUDIENCE: That's more than a google.
NICHOLAS DIBELLA: That's more than a google, yeah.
But it's not more than a googleplex.
Particles--
AUDIENCE: What's a googleple?
NICHOLAS DIBELLA: A googleplex is 10 to the 10 to 100.
So it's 10 to the google.
So a google is 1 followed by 100 zero's,
but imagine a number of followed by a Google of zeros.
Yeah.
There's not even there's not even
space for that many particles in the observable universe.
That's how big a googleplex is.
Did you guys hear that the term googleplex was actually
proposed by a nine-year-old or something like?
AUDIENCE: Somebody's nephew.
NICHOLAS DIBELLA: Yeah, some mathematician's nephew
or something like that.
AUDIENCE: What's a googleplex again?
NICHOLAS DIBELLA: What's a googleplex again?
It's 10 to the google.
And a google is 10 to the 100.
That's just cool stuff--
cool math terms to know.
Like zenzizenzic and other stuff.
Disregard that.
10 to the 118th particles can fit in our universe.
That's how many particles can fit.
But now we can ask, how many different arrangements
of particles can there be in this universe?
And that's an extremely large number.
Over here in this simple universe,
we had space for four particles, and we
found that the number of different arrangements
was just 2 to the power of 4.
And that was 16.
AUDIENCE: [INAUDIBLE]
NICHOLAS DIBELLA: Oh yeah, you can also have no--
so it would be three.
Yeah, it would be three.
Yeah, you could have no particles there,
so it would be three.
But once we apply that idea to this--
2, 3, raised to a huge number.
It's not going to make a whole lot of difference.
And oh, yeah, and here I'm just thinking about one particle.
So I should have said 3 to the fourth,
because you could have zero particle at a slot.
So 10 to the 118th particles can fit in our universe.
And that means that there are 2 to the 10,
to 118th different arrangements.
And that number is actually greater than a googleplex.
AUDIENCE: Whoa.
NICHOLAS DIBELLA: And that's actually--
I mean, I said 2 versus 10.
That didn't really make a whole lot of difference.
Now, that number's actually about 10 to the 10
to the 118th.
It's approximately that.
That's how huge it is.
Now, I can ask, if the universe started out
with every different possible arrangements of particles--
If we started out with this vastly huge number
of different ranges of particles, then by now
you'd still expect to find every possible arrangement
of particles.
You'd still expect to find that.
The laws of physics will allow that to happen.
So now I can ask--
well, if you do have an infinite universe, then
how far do I have to travel before I
reach an exact copy of our observable universe?
How far do I have to travel to get to that?
Well, there are 10 to the 10 to the--
is that right?
Is that approximation good?
I think it is, right?
Maybe I made a mistake.
[INTERPOSING VOICES]
NICHOLAS DIBELLA: I have things written down.
[INTERPOSING VOICES]
NICHOLAS DIBELLA: Well, actually, I think it's OK.
I think it's OK Yeah, doesn't matter a whole lot.
But now I can ask--
eventually, as I travel from our observable universe
to another universe to another universe to another universe,
eventually, you'd expect these arrangements to repeat.
Because they have to eventually.
If you come across 2 to 10 to 118th arrangements
and then you get to another one, well, you have to repeat it,
because there's only that many different arrangements.
And so, if you travel far enough,
then applying that reason to our own universe,
you'd expect to find an exact copy of our own universe.
And you'd have to travel about--
well, you could take the size of our observable universe
and just multiply it by the number
of different arrangements.
And so, you'd expect to find an exact copy of our universe
at about 10 to 10th to the 118th meters away.
I mean this is a really huge number,
so we don't have to be a whole lot precise about how
we manipulate them.
So you'd expect to not only find a copy of yourself,
but you also expect to find a copy of New York.
You expect to find a copy of the planet Mars.
You expect to find a copy of the Andromeda galaxy.
You'd expect to find an exact copy
of every single piece of matter in the huge observable
universe.
In another you are having this exact same conversation.
OK, OK.
In another-- now, here years where quantum comes in.
Here's where quantum mechanics comes in.
According to quantum mechanics, there's a--
what I'll do next, my next action,
isn't predicted with 100% certainty.
My next action could be that I throw a chalk at you,
or it could be that you use some sort of mental powers
to pull the chalk from me somehow,
through some very complicated contrived quantum tunneling
mechanism.
But the fact is that my future isn't
known with complete certainty.
And so, there are a number of possibilities
of what my future would be.
And there's a number of possibilities
of what your future would be--
and your future, and your future,
and the entire future of the observable universe actually.
And actually, there's an infinite number
of possible futures of every particle
for the observable universe.
And there's a non-zero probability
associated with each one of these possible outcomes.
And that means, that if you travel far enough,
you'd eventually not only reach an exact duplicate of her
of our universe at this instant, but you'd also
find an exact duplicate of our universe
that has the same exact future of 10 minutes from now,
and the same exact history, and same exact everything.
And you'd expect to find infinitely many of those.
It's crazy, but it's true.
And actually, this is the least controversial type
of parallel universe.
This is the least controversial type.
This is only what's called a level I multiverse.
So the multiverse is the whole collection
of all these universes, which we say are parallel-- we call them
parallel universes.
The multiverse is the collection of all of these.
And this is the simplest type of multiverse.
AUDIENCE: So are all the different
really possible though?
Because, don't they have to obey laws of physics and stuff
like that?
NICHOLAS DIBELLA: Yeah, yeah.
OK.
Every arrangement that obeys the laws of physics is possible.
But the laws of physics are pretty flexible.
[LAUGHTER]
No.
I mean, flexible in the sense that if you conceive
of something happening, then if you're smart enough,
then you can figure out a way for it to happen.
And actually, precisely proving that it's possible for me to,
I don't know, as a result of lifting up
my foot I cause one of the students
in the back to think about Harry Potter,
to prove that that's possible is really hard.
And it might actually not be possible.
But I suspect that it's possible,
because you have all these different things that
could happen.
I could somehow affect the air molecules here
and cause them to do something that will propagate,
reaching the students in the back,
and then affecting his neurons in some way.
It would be it would be very complicated,
but it's really hard to prove that.
But I hope it's true.
And I hope I'm not crazy for hoping
that it's true, because I think it
would be so cool if it's true.
Some people object to these ideas
because they find them weird.
But I actually hope they're true because they're weird.
And I think it's really cool.
Yeah, question?
AUDIENCE: Yes.
So all this depends on that that the universe is infinite?
NICHOLAS DIBELLA: Yeah.
This all that depends on the assumption
that the universe is infinite.
OK.
If the universe is big enough however, but not infinite--
if it's really large, but still finite--
then it's still possible to find an exact copy of our universe.
But it wouldn't be guaranteed.
It wouldn't be guaranteed.
Question?
AUDIENCE: Do you mean the universe or the amount
of matter in the universe?
NICHOLAS DIBELLA: Well, necessarily both.
AUDIENCE: Space could be infinite,
but there might not be--
NICHOLAS DIBELLA: Oh, that's true, that's true.
Space could be infinite, but there might not
be an infinite amount of matter.
So you can imagine, for instance, what's
been called an island universe.
You have an infinite universe, but there's
only matter and energy at a very small island in the universe.
And if that's true, then you can make predictions
about what you'd observe with various astronomical
measurements.
You can make definite predictions
with that type of model.
And people have made some predictions
with that type of model.
And it turns out that those models
are ruled out by observation.
The island universe is ruled out by observation.
AUDIENCE: So there has to be enough matter
to fill the entire universe?
NICHOLAS DIBELLA: Yeah.
There has to be--
matter has to persist throughout the whole universe.
And there's good evidence that it does.
AUDIENCE: But how could there ever
have been an infinite amount of matter in one point?
NICHOLAS DIBELLA: How could there ever
have been an infinite amount of matter at one point?
AUDIENCE: [INAUDIBLE] had to create it.
So it must have been all--
NICHOLAS DIBELLA: Well, that's a hard question.
And actually, a process called inflation might explain that.
And I'm going to talk about inflation in a minute.
Where am I on time?
Let me see.
Yeah, we could take a break here.
We'll take a break here.
I'll return talking about inflation
and the level II multi-verse.
I mentioned that the level one multi-verse
is the least controversial, and it's the least weird.
So if you thought that was crazy, well, listen to this.
Now, I'm going to discuss the level II multi-verse.
So in the level I multi-verse, the only kind
of weird thing that happened was that there
were universes outside of our own
that had different arrangements of matter.
And there's only a finite number of arrangers of matter
and a finite amount of space that are possible.
So if you travel far enough, then eventually you
reach a copy of our arrangement of matter,
and you'd find a copy of our history and our future.
And that's pretty much all there is to a level I multiverse.
Question?
AUDIENCE: There's no way anything
could get more complicated than what we just did.
NICHOLAS DIBELLA: There's no way that anything
could get more complicated?
AUDIENCE: It's not possible
NICHOLAS DIBELLA: It's not possible.
OK.
Well, in a level II multiverse, not only
are there different arrangements of matter in finite Hubble
volumes, but we also have different dimensionalities
of space and time.
We also have different properties of particles.
For instance, the mass of the electron
is different in a parallel level II universe than it is here.
Different properties of particles,
and different physical constants.
I'm going to talk more about this in the second, what
each one of these means.
But first, let me tell you how this could happen.
So there's a-- hi.
There's a popular theory that's proven enormously
successful to explain the early universe,
and this theory goes by the name of inflation.
And inflation refers to an extremely, extremely rapid
expansion of space in the early universe.
So you can imagine, a very long time ago,
you had the universe, for instance.
Say this is the whole universe, and it expands very rapidly.
It's hard to visualize that, but just try to think in your heads
that the distance between points expands, and expands
really rapidly.
That's what I mean by space expanding.
So space expands everywhere.
Space everywhere expands.
However, there are some regions in the universe
where space stops expanding.
And it stops expanding just because of what are
called quantum fluctuations.
There is a quantum probability that space here
will stop expanding, and there there's a possibility here
that space will stop expanding.
And so, there are lots of regions
that pop up around the universe where
space has stopped expanding.
And we call these regions bubbles.
So the universe has expanded, and there
are some bubbles where space has stopped expanding.
And there are some other regions where space continues
to expand really fast.
Well, it turns out that when this happens a very mysterious
process called symmetry breaking--
spontaneous symmetry breaking--
occurs.
And it occurs in each one of these bubble universes.
So this is a bubble.
It occurs in each one of these bubbles.
And as a result, the symmetry breaking, what happens
is that these values become fixed--
the dimension of space becomes fixed, the dimension of time
becomes fixed.
I mean, the number of dimensions of space
and the number of dimensions of time become fixed.
So in our universe, for instance,
there are probably three dimensions of space
and just one dimension of time.
And that's exactly what we observe.
I can walk forward, backwards, upwards, downwards, sidewards,
rightwards, whatever.
So there are three different directions we can travel,
and those are the three dimensions of space.
And there also appears just to be one dimension of time
that we travel, and we travel into the future.
So there's one dimension of time.
And that's what's symmetry breaking did for our bubble.
It fixed the dimensionality of space and time to be 3 and 1.
Symmetry breaking also fixed--
by fixed, I mean it determined-- determined
the different properties of particles.
For example, it fixed the value of the electron mass, which
is, as you know, about 9.1 times 10 to the minus 31 kilograms.
It fixed the mass of the proton, which is about 1.67 times 10
to the minus 27 kilograms.
It's fixed the mass of--
those only the two ones that are the mass I know.
It fixed the mass of lots of other different particles,
and it also fixed things like charges-- like,
electric charge.
Why?
Well, I'll get to why in a minute.
But it's also fixed electric charge.
It also fixed some property called
spin, which is a type of intrinsic angular momentum.
Don't worry about it if you haven't heard of it.
It also fixed-- well, it fixed a whole bunch
of properties of particles.
There are certain properties that particles have,
and they have these properties because a type of symmetry
breaking occurred in the early universe
as a result of inflation.
Let me write this down-- inflation.
And so, different properties of particles were determined,
and different dimensionalities space and time
would determined.
And also, different physical constants are determined.
I mean, the speed of light is about 2.99792458 times 10
to the 8 meters per second, for example.
And that value was determined by symmetry breaking.
It's also conceivable that our bubble universe
could have been--
what's the word I'm looking for--
given, or could have been imparted with a different set
of these numbers.
Our universe could have had a dimensionality of space
being four.
There could be four dimensions of space
and one dimension of time.
And if that were the case, then our world
would be quite different.
And actually, we probably wouldn't exist in this world.
First, it's easy to visualize what four dimensions of space
would mean in terms of how we can move.
We would have four different independent directions
that we can move.
That's what it would mean for there
to be four dimensions of space.
But actually, you can make some predictions
about how atoms would behave if the laws of physics
are the same but the dimensionalities
of space and time are different.
And you can make these predictions by simply fixing up
the equations of the laws of physics
in an appropriate manner, and then get at some results.
By the way, all of these bubble universes
have the same laws of physics.
They have the same laws of physics.
The only things that are different
are the dimensionalities of space and time,
the properties of matter, and the physical constants,
like the speed of light.
Also what could differ--
Well, within each one of these universes
there could be a whole slew of type I universes.
So type I is kind of contained in type II.
So you have infinite number of type I,
an infinite number of type I there, and so forth.
But they all have the same laws of physics.
Now, you can make certain predictions
about what the world would be like in a universe
with different dimensionalities from that of our own.
For example, if the dimension of space--
let's say there are four space dimensions and five time
dimensions.
Which is conceivable.
Its hard to imagine, but it's conceivable.
And you can fix the equations of physics
to include for this number of dimensions.
Let's say there are five time dimensions.
Well, such a world would be very different from our own.
Because it turns out that if our universe were like this, then
it would be absolutely impossible to make a prediction
about any event with a non infinite uncertainty.
So we couldn't make any prediction.
We're able to make pretty good predictions
in our own universe, right?
I mean, I predict that this chalk, once I drop it,
will fall on this paper with an uncertainty of say 1 mile.
I don't know.
So there's an uncertainty of one mile
of where this chalk will fall.
OK, It worked.
My uncertainty was non-infinite.
It was pretty big, but it was non infinite.
And it turned out to correspond to what we observed.
Well, if these were the dimensionalities
of space and time, you wouldn't be
able to get any better than infinite uncertainty.
You can also can imagine there being just one space dimension,
and there being like four time dimensions.
So let say one space and four time.
Well, in this universe with these dimensionalities,
it turns out that all atoms are unstable.
They're immediately unstable.
If I had an atom it would just exist for a split second
and then that would be the end it.
It would be impossible for molecules to form.
It would be impossible for atoms just
to sit there, much less than stick together to other atoms.
And it would be impossible for macromolecules to form.
It would be impossible for simple cells to form--
What's that?
AUDIENCE: No sentient life there.
NICHOLAS DIBELLA: Yeah, no.
No life there.
This type of universe would be completely
devoid of intelligent people like us.
[LAUGHTER]
Yeah?
AUDIENCE: What would it be like outside of these bubbles?
NICHOLAS DIBELLA: Outside of these bubbles?
AUDIENCE: Would the amount of dimensions
and all properties of physical constant
be changing all the time?
They would never be the same?
NICHOLAS DIBELLA: You mean--
AUDIENCE: If you left the bubble,
and you were just in the rest of space,
I guess continuing to expand.
NICHOLAS DIBELLA: I'm not exactly sure.
I think-- Yeah, I'm not sure what
it's like outside the bubbles.
I don't completely understand this.
I'm telling you the stuff that I do know.
AUDIENCE: Do you know if it would
be like just one moment they're inside the bubble
and everything is normal, and the next minute they're
outside the bubble and it's completely different?
NICHOLAS DIBELLA: Oh, oh, oh, oh.
OK.
Well, I can kind of answer that.
I can kind of answer that.
These bubbles are infinite in size.
So once you're in one of these bubbles you can't get out.
You're not going to be able to get out.
And you can't interact with the other bubbles unfortunately.
AUDIENCE: How are they infinite in size
if there's more than one of them?
NICHOLAS DIBELLA: That's kind hard to imagine
how they can be infinite in size and with more than one of them.
But that's simply--
I know it's hard to visualize.
But infinity is a really weird concept,
and it does weird things to you when you think about it.
AUDIENCE: But the entire universe in its entirety
is infinitely larger than infinitely large things.
NICHOLAS DIBELLA: Yeah.
You have to be pretty careful when you use the word infinity.
You might have heard about different types of infinity,
like countable infinity, uncountable infinity.
For instance, there are more irrational numbers
than there are rational numbers.
And I'll let you all wonder about that.
The point is, the way you deal with infinity is kind of weird,
and it's kind of confusing, and it does weird things to you.
AUDIENCE: [INAUDIBLE] any amount of any number--
any combination of sounds has to be a number.
NICHOLAS DIBELLA: Any combination of what?
AUDIENCE: Any combination of sounds ever
has to be [INAUDIBLE] of a number.
But there are infinite numbers.
And there are less--
you have to have--
NICHOLAS DIBELLA: I don't know what you're talking about.
What?
Talk to me after class.
I don't know.
OK.
Well, getting back to this.
In this universe with these dimensionalities,
atoms would cease to exist.
They'd just be completely unstable.
Now, this level of multiverse actually provides
a nice explanation for the question,
why is there one dimension of time
and why are there three dimensions of space?
Why is the mass of an electron this number?
Why is the speed of light this number?
Why is Newton's gravitational constant this number?
It provides a nice explanation for that.
Because there are infinitely many bubbles.
And there are infinitely many different types of symmetry
breakings that can occur.
So you'd expect to find some probability
distribution of various dimensionalities of space
and time.
You'd expect to find a probability distribution
of various properties of particles
and various values of physical constants.
And so, it just kind of occurred by chance
that our universe has these certain values.
If it were the case that these other bubbles didn't exist.
If it were the case that they were just one universe with one
set of numbers for physical constants,
one set of numbers for properties
of particles, one set of dimensionalities
for space and time.
If there were just one universe with those very specific sets
of numbers, then it's very hard to explain why those numbers
and why not other numbers.
Well, the level II multiverse provides a very elegant
explanation--
it just occurred by probability.
It's just a result of symmetry breaking occurring
in the early universe.
That's a wonderful explanation.
Another explanation that's been traditionally proposed
is that something fine-tuned those values.
Well, that's a kind of controversial view
that I think is less elegant than this multiverse theory.
Question?
AUDIENCE: Well, you were saying that all this
is happening from our universe.
So from our big bang all this happened?
NICHOLAS DIBELLA: Yeah.
From our big bang, this all happened.
OK.
So there's one huge universe, which is "the universe."
Which you could say is "the multiverse."
And inside the multiverse there are various infinite bubbles
that arised as a result of this process
called inflation occurring.
And a result of this symmetry breaking occurring,
fixed these various numbers.
AUDIENCE: But does that mean that all this happening now,
is that-- if space is infinite, could there
be another big bang?
NICHOLAS DIBELLA: Oh, could there be another big bang?
Yeah, there there could be.
There could be another big bang.
This whole subject of talking about the universe
as a whole, this is the subject of cosmology.
And there are a lot of really cool ideas in cosmology.
You can talk about multiple big bangs.
You could talk about the universe expanding
and then contracting, and then being a cyclic universe.
There are lots of cool ideas.
It's possible that there could be multiple big bangs.
And I think it might be possible within this theory.
And that might even--
there are various versions of inflation,
and there are probably lots of versions where
multiple big bangs do occur.
But I'm not an expert on it, and so I'm just
feeding you what I know.
Was there another question?
Yeah.
AUDIENCE: How many meters is on kilometer?
NICHOLAS DIBELLA: How many meters is one kilometer?
1,000.
AUDIENCE: OK, that's it.
NICHOLAS DIBELLA: Very deep, philosophical question.
OK.
Does anybody have the time?
I'm not going to look at my--
AUDIENCE: 2:39
NICHOLAS DIBELLA: 2:39 OK.
Let's see.
So this is the level II multiverse.
I think I'm going to skip level III and going to just go to IV.
I don't think we have time to do all of them.
But level III would actually take a long time to explain,
because, well, level III has to do with the many worlds
interpretation of quantum mechanics,
and I would have to explain that first
and then talk about crazy consequences.
But actually, the level III multiverse
doesn't add any qualitatively new features.
Like, you we still have these different sets of numbers.
You still have different arrangements of matter.
So I'm just going to push forward
to level IV, which is the highest level multiverse.
You guys ready?
AUDIENCE: No.
AUDIENCE: Always.
AUDIENCE: Never.
AUDIENCE: It's scary.
NICHOLAS DIBELLA: It's scary?
AUDIENCE: Yeah.
It's [INAUDIBLE].
How did they even come to this?
NICHOLAS DIBELLA: How did they come to this?
Well, inflation was discovered by--
AUDIENCE: We're still discovering things on Earth
that we don't know.
How do we figure out--
NICHOLAS DIBELLA: There are a lot of really smart people
that have thought of these things,
and inflation was actually discovered by physicists
here at MIT, Alan Guth.
He discovered this inflation mechanism.
And it actually it explains a whole lot of phenomena
that are really hard to explain, and impossible to explain
with other mechanisms.
It explains why, for example, the universe
is roughly uniform.
Why the universe roughly looks the same
no matter where you go.
It looks roughly the same.
It explains lots of things like that.
Question?
AUDIENCE: Is he still here?
NICHOLAS DIBELLA: Yeah, yeah.
I have his book [INAUDIBLE].
Oh, good.
Cool, cool.
AUDIENCE: So you must ask him--
NICHOLAS DIBELLA: Yeah.
AUDIENCE: Is he a teacher.
NICHOLAS DIBELLA: Yeah, actually next semester
I'm taking a class that he's teaching,
called The Early Universe.
And that's really cool that we students
get to take classes taught by the absolute experts
on these fields.
So yeah, come to MIT.
[LAUGHTER]
OK.
So now level IV multi-verse.
I looking doing that too.
Now, level II multi-verse, we had different dimensionalities
of space and time, different properties of particles,
different physical constants, but the same laws of physics.
Well guess what's going to be different in the level IV
universe?
Different laws of physics, yeah.
AUDIENCE: That's weird.
NICHOLAS DIBELLA: It's been noticed for a long time that--
well, the universe is explained very well
by mathematical models.
A lot of you probably haven't taken any mathematical classes
on physics, but there are lots of equations
in physics that give rise to these various predictions
that I'm talking about.
And I gave you some equations in the second class.
Maybe I shouldn't have--
but somebody influenced me.
But there are various equations in physics.
And there are various equations that
are very specific to a particular set of laws
of physics.
And we say that these laws of physics
have a particular mathematical structure.
And it's been a view for a long time
that these mathematical structures merely
approximate the universe.
Maybe the universe is impossible to describe with math.
Our models predict very well what
we should observe in the universe,
but they're not perfect.
In fact, we know for a fact that we don't have the precise--
we don't have the absolute correct model for our universe.
Well, because, actually, quantum mechanics
and general relativity don't work with each other.
They contradict each other.
And this is a problem in modern physics
that people are working on solving.
String theory is one hope for--
what's that?
AUDIENCE: So only one is right?
NICHOLAS DIBELLA: Well--
AUDIENCE: Or is it mixable?
[INAUDIBLE]
NICHOLAS DIBELLA: The question is, is there
only one mathematical structure that can model the universe?
Well, you could probably think of different sets of equations
to give the same results.
But if that's the case, then it might
have to be that they're all really manifestations
of the same thing.
AUDIENCE: OK.
NICHOLAS DIBELLA: They might all be isomorphic,
is the technical term--
the term the mathematicians use.
AUDIENCE: So how would they decide which model
is the right or wrong one?
NICHOLAS DIBELLA: How would they decide which model
is right for our universe?
Well, first of all, you to have a consistent model.
You have to have a consistent theory.
It has to be consistent.
General relativity plus quantum mechanics is not consistent.
When you try to talk about the quantum mechanics
inside of black holes for instance,
you get at results like infinite probabilities.
And what does an infinite probability mean?
It's meaningless.
It doesn't really mean anything.
And so, the theory we have right now is inconsistent.
And people are searching for a consistent theory.
And so far, string theory looks like it's our best hope.
But that's not worked out yet.
But it's doing better than other theories,
and so, it receives a lot more attention.
But it's still the fundamental problem.
AUDIENCE: How do they determine consistency then?
NICHOLAS DIBELLA: How do you determine consistency?
Well, you check to see, here are two things,
do they agree with each other?
If this is true and this is true,
it implies that this is true.
AUDIENCE: Is it consistency with experiments
of what we already know?
NICHOLAS DIBELLA: OK.
Various types of consistency--
OK.
First and foremost, it has to be consistent in itself.
If it's not consistent in itself--
AUDIENCE: That's bad.
NICHOLAS DIBELLA: Then it gets bad.
And secondly, we hope that it models the actual universe.
I can think of a theory right now that's consistent,
but it doesn't model the universe.
I could propose a theory that the whole universe
is determined by how I move this pen.
I can think of various rules of how it works.
But it doesn't agree with experiment.
So we need something that agrees with experiment.
But it's been asked, why--
well, actually, it's been remarked by Einstein,
that perhaps the most incomprehensible
thing about the universe is that it is comprehensible.
And it's comprehensible with the aid of mathematics.
And many people have wondered, why does math work so well?
Why does it work so well?
Maybe it's the case that the universe actually
is mathematical.
Math isn't merely an approximation,
but the universe is mathematical.
And that's the main idea behind this level IV multiverse.
So in our universe there is--
well, if it's true that the universe is mathematical,
then in our universe there's a mathematical structure
that is the universe.
So the main assumption here is that the universe
is mathematical.
Well, what kind of mathematical models?
Well general relativity is, for instance,
some sub branch of differential geometry
and spacetime is a pseudo-Riemannian manifold.
It's very complicated math.
They're very complicated mathematical structures.
But the fact is that they are mathematical structures.
And the assumption behind the level IV multiverse
is that the universe is mathematical.
Now, we can ask, why this mathematical structure and not
other mathematical structures?
And a nice answer to that question,
similar to the answer to the question, why
these dimensionalities, why these concepts and not others,
is that there are many other universes with different laws
of physics, which correspond to different mathematical
structures.
So I just proposed one before with the
had to do with this pen.
If I could formulate that into a mathematical theory that's
consistent, then according to level for multiple IV
multiverse theories there exist universes
that obey the laws of physics as dictated by this pen.
In our universe--
AUDIENCE: And when you say there exists,
would that mean that if you travelled far enough
or something, or if you search the whole physical universe,
you say, "there exists"--
NICHOLAS DIBELLA: "There exists," yeah, yeah.
AUDIENCE: You're going to find it somewhere?
NICHOLAS DIBELLA: You're going to find it somewhere.
Yeah.
But you probably won't be able to get to it
because it's so far away.
AUDIENCE: Yeah.
NICHOLAS DIBELLA: And because it's moving away from a--
AUDIENCE: A different bubble or something.
NICHOLAS DIBELLA: Yeah, a different bubble.
You probably won't be able to reach these.
AUDIENCE: Kind of like, existence
is a iffy sort of a thing.
NICHOLAS DIBELLA: Existence is an iffy sort of thing.
This is the most controversial level of multiverse.
The first one that I described you seemed crazy at the time,
but now we have different laws of physics,
different constants.
And level I we're at home with.
question?
AUDIENCE: In the multiverse, is it
possible for universes to overlap?
NICHOLAS DIBELLA: Is it possible for universes to overlap?
Well, it depends on how you define universe.
Is it possible-- are you asking for there
to be two different level IV universes overlapping?
Because if that's the case, then that
would require the overlapped universe to obey--
well, it might require it to obey
two different mathematical laws at the same time,
or might just be an amalgam of the two.
AUDIENCE: Well if you have the two
different mathematical structures though, right,
sometimes mathematical structures do overlap.
NICHOLAS DIBELLA: Yeah.
Yeah-- so, it's-- yeah.
Yeah.
Question?
AUDIENCE: Two things-- one, how fast or far
can a modern rocket go?
NICHOLAS DIBELLA: How far what?
AUDIENCE: How far or fast can a modern rocket go?
NICHOLAS DIBELLA: I don't know how fast
a modern rocket can go.
AUDIENCE: How far can it go?
NICHOLAS DIBELLA: How far can it--
well, if you just leave it, if you wait long enough,
it'll go arbitrarily far--
a rocket.
AUDIENCE: OK.
AUDIENCE: It can go fast enough to cause the Doppler--
I know that things [INAUDIBLE] that had
the Doppler effect [INAUDIBLE].
NICHOLAS DIBELLA: OK, yeah, yeah.
Yeah.
Yeah, rockets can go pretty fast.
Let me get back to multiverses though.
OK.
What time is it?
AUDIENCE: 2:52
NICHOLAS DIBELLA: 2:52.
OK.
I have few more minutes.
OK.
So in this level IV multi-verse you
have different laws of physics.
Our universe has one specific type
that what we hope to one day find.
We might not find it, but we hope we will find it.
If we do find it, then that would be evidence
for this level IV multiverse.
It would be evidence for the assumption
that the universe is mathematical.
It we have evidence because we then
would have a mathematical structure for our universe.
And if other universes exist with different laws of physics,
then than that would be a rather nice explanation
for why these laws not others.
Well, it's because, every conceivable set
of physical laws would exist.
Every conceivable set of laws would exist would,
and there's some probability distribution
that your universe is equipped with these laws and not
some others.
AUDIENCE: How would you ever determine--
NICHOLAS DIBELLA: How did you ever determine
those probabilities?
I don't know.
And I don't know how you would actually
figure out if the level IV multiverse theories are true.
Other than that they answered some questions rather nicely,
like why these laws and not others.
It might actually be completely impossible the answer.
It might be forever in the realm of metaphysics.
But it provides a nice sense of closure
to all of these universes.
We can explain everything so nicely
with the aid of parallel universes.
Things it seems the things that seem once to be so mysterious,
now they just fall under the rug or something.
Is that a--
I don't know.
Am I using the phrase right?
Fall under the rug?
Swept under the rug?
Is swept under the rug a bad phrase?
Like, a mean phrase?
OK.
Well, these questions are answered so nicely
is what I'm trying to say with parallel universes.
And they seem crazy, and they are crazy.
But there is lots of evidence for them,
particularly the lower level type multiverses.
And so, we should take them seriously.
And even if you don't take them seriously,
you should at least appreciate them,
that they give us nice things to talk about,
nice things to think about.
And they give us lots of more opportunities to make jokes.
That's always one of my favorites.
AUDIENCE: Do you have any joke?
NICHOLAS DIBELLA: Do I have any jokes?
Well, sure.
I have lots of jokes.
I had one joke--
I was planning on saying, one other type
of conceivable universe that's level IV.
In our universe, gravitation is not
responsible for people falling in love,
but it's conceivable that in another universe gravitation
is responsible for people falling in love.
[LAUGHTER]