August 24, 2023 • 50 mins
Daniel and Jorge talk about what it means for space to be curved, how we measure it and why the answer is a puzzle.
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Speaker 1 (00:08):
Hey, Orge, I'm going to say a word, and I
want you to tell me if you think it sounds
like a positive or a negative idea.
Speaker 2 (00:15):
All right, go for it.
Speaker 1 (00:16):
The word is flat.
Speaker 2 (00:19):
I guess it could go either way. You know, nobody
likes their soda flat or they are jokes to fall flat.
Speaker 1 (00:26):
But I sure do like my bed to be flat.
Speaker 2 (00:29):
But do you like your tires to be flat?
Speaker 1 (00:32):
No? But I do like my roads to be flat.
Speaker 2 (00:34):
Does that mean you want the earth to be flat?
Speaker 1 (00:38):
I like it spherical, But I also like mountains, so
I guess I'm anti flat earth.
Speaker 2 (00:43):
Do you like falling flat from a mountain?
Speaker 1 (00:47):
I like landing flat on my feet.
Speaker 2 (00:48):
I think this discussion has run out of air.
Speaker 3 (01:05):
Hi.
Speaker 2 (01:05):
I'm Hoorhey, mccartoonist and the author of the book Oliver's
Great Big Universe.
Speaker 1 (01:09):
Hi, I'm Daniel. I'm a particle physicist and a professor
at UC Irvine, and I'm also flat footed.
Speaker 2 (01:15):
Are you saying metaphorically or you know, physiologically?
Speaker 1 (01:20):
Well, your questions often catch me flat footed, so that's metaphorical,
but also literally and physiologically, I have flat feet, so yeah,
I wear inserts.
Speaker 2 (01:27):
Does that have to make you taller you like Tom Cruise,
I don't wear heels.
Speaker 1 (01:34):
No, I wear inserts to avoid crippling pain when running.
Speaker 2 (01:39):
Sounds like the solution is just not to run life
flat on your back.
Speaker 1 (01:43):
Yeah. I'm working on a floating recliner I can live
in for the rest of my life and float around.
Speaker 2 (01:47):
There you go. You can attach like a bicycle pedal
and maybe get your workouts that way.
Speaker 1 (01:53):
Yeah, that's great for going upstairs.
Speaker 2 (01:55):
Yeah exactly. But anyways, welcome to our podcast. Daniel and
Jorge Explained the Universe, a productive of iHeartRadio.
Speaker 1 (02:01):
Where we take all the twists and turns and curves
of this crazy universe and try to flatten it all
out for you. We try to untangle all of the
mysteries of the nature of matter, the forces, the energy,
the geometry of space time, the size and shape and
history of the universe and make a nice, smooth story
for you to understand.
Speaker 2 (02:21):
That's right, because it is an amazing universe full of
stuff inflated with amazing and incredible physics and stars and
galaxies and planets and particles for us to wonder at
and for us to I guess poke it.
Speaker 1 (02:35):
There's so much that's amazing about the universe. And sometimes
you can have two amazing facts that seem to be
in conflict, Like, on one hand, it's amazing that we
still don't really know so many basic things about the
nature of the universe. How big is it? What is
its shape? How did it all come to be? We're
so ignorant about the environment in which we live. And
(02:55):
on the other hand, it's kind of amazing that we
know anything about the universe, and then we've only lived
on one tiny little dot and one random little corner
of the universe and never really left.
Speaker 2 (03:06):
Yeah, it's amazing what we can learn just from this
little corner of the universe. And as you said, how
we can ask these big questions about how everything is
the way it is and why it is the way
it is, Like, for example, we don't know if the
universe is flat footed or not.
Speaker 1 (03:20):
Does the universe even like to run? Or does just
want to sit on the couch and eat snacks all day?
Speaker 2 (03:24):
Yeah, just sit around and spin.
Speaker 1 (03:27):
It has big consequences for the curvature of the universe.
Speaker 2 (03:30):
It is getting bigger and bigger, so you know, maybe
it could use a little bit of exercise. It's getting
wider and wider per second.
Speaker 1 (03:37):
I think we should be universe positive on this podcast.
You know, universe just be whatever shape you are, We
love you.
Speaker 2 (03:43):
Yeah, yeah, true, true, true. I guess we should love
the universe the way it is.
Speaker 1 (03:47):
It's the only universe we got, so might as well
love it.
Speaker 2 (03:50):
Even if we don't understand it. I guess all the
time we should, you know, take it for what it is.
That's kind of what science is, right, taking things for
what they are.
Speaker 1 (03:59):
Taking things for what they are are, absolutely, but then
always asking why are they this way? Why couldn't they
be some other way? Why do we live in this universe?
Do we live in the only universe that's possible? Or
are there many possible universes and we just happen to
be in this one. So often we look around as
we try to tell the story of the universe, and
(04:19):
we ask those kinds of questions like does this make sense?
This seems weird? Is it random? Or is there a
reason for it?
Speaker 2 (04:25):
Yeah, because it is pretty perplexing out there the way
things are. You know, there are amazing things like black
holes that seem unexplainable, and there's sort of really weird
things like quantum mechanics out there that kind of keep
you guessing about what the universe is going to do.
Speaker 1 (04:38):
And as we put together this story of physics that
tells us how the universe operates, what machinery is going
on behind the scenes, that controls like what happens when
two particles bump into each other, or house space curves
and twists in the presence of mass. We start to
tell a story about the universe, we notice, like, hm,
the universe seems to do this kind of thing or
do that kind of thing. And sometimes the story tells
(05:00):
is very weird. It's very surprising. It's not one that
makes sense to us or seems intuitive. It makes us
wonder if maybe we're missing part of the story or
if we're all just very very lucky.
Speaker 2 (05:10):
Yeah, and as you said, there are big questions about
the universe that we still don't know about, like its size,
its shape, and what it's going to do in the future,
and also a very interesting question about its curvature.
Speaker 1 (05:24):
Yeah. As we develop our understanding of gravity and general
relativity and we understand that space is weird and twisted
and curved and that affects how things move, it also
affects how the universe itself expands or contracts. So we
have a lot of really fun questions to ask about
why the universe looks this particular way, especially about the
curvature of space.
Speaker 2 (05:44):
So today on the podcast, we'll be tackling the question
why is space so flat? You mean as opposed to bumpy? Like,
what would be the opposite of flat overinflated under pressure?
Speaker 1 (06:00):
Just like my arches, the opposite of flat would be curved, right,
everybody likes nice curved arches for their feet, and the
opposite of flat in the case of space or the
universe would be curved.
Speaker 2 (06:11):
Well, it could also be well bumpy. I guess bumpy
is also kind of curvy. It means you have a
lot of little curves. You could have bumpy feet.
Speaker 1 (06:19):
Yeah, exactly, that's true. You got to sand those down
a little bit. But in this case, yeah, we're talking
about like the nature of space is space the way
Euclid thought about it, You know, two parallel lines will
never touch, or a space more complicated twisting and curving
on a global sense. We're talking here about the curvature
of the entire universe itself.
Speaker 2 (06:39):
Yeah, and this is I guess a pretty mind bending
and space bending topic, because you know, I think we're
all used to thinking of space, or at least empty
space is being kind of like flat, right, not weird
and curved.
Speaker 1 (06:51):
It's really hard to think about this in the three
dimensions of our universe, and even the word flat is
kind of confusing there. It comes really from thinking about
a two dimensional version of the picture instead of thinking
about space like I can move in three different directions,
it's easier to think about it in two different directions
because then we can like draw it on a piece
of paper. So if you imagine like a sheet of
(07:13):
graph paper, that's a flat sheet of paper, and two
parallel lines on that piece of paper are never going
to meet each other. When we talk about whether space
is flat, we're asking a similar kind of question, but
about three dimensional space, though it's harder to understand, like
what curvature means in three dimensions than it is in
two dimensions.
Speaker 2 (07:31):
Are you saying we're going to use a term that
doesn't quite work or describe things or is counterintuitive to
actually what is actually happening. Are we going to do
that again?
Speaker 1 (07:40):
Yeah, that's exactly right. That's the story of.
Speaker 2 (07:41):
Physics being inadequate.
Speaker 1 (07:44):
We think we understand the universe, and then it surprises
us and it sort of outgrows even like our ideas
and forces us to like generalize these concepts like, oh wait,
flattness can apply in three dimensions, not just two.
Speaker 2 (07:55):
Well, as usual, we were wondering how many people out
there had thought about this question whether space and why
space is so flat, and so Daniel went out into
the internet to ask people this question.
Speaker 1 (08:06):
Thanks very much to everybody who participates. If you'd like
to hear your voice answering these questions for this segment
of the podcast, please don't be shy. Write to me
two questions at Danielandjorge dot com. You'll have a good time,
I promise.
Speaker 2 (08:18):
So think about it for a second. Why do you
think space is flat? Here's what people had to say.
Speaker 4 (08:25):
I think space is flat because I think at the
beginning there wasn't any room for stuff to be clumpy
or lumped together or have little dips or gaps. And
I assume that everything was shot out from the big
Bang in every direction in equal measure, and therefore it
stayed flat to this day.
Speaker 3 (08:45):
I think that we're not one hundred percent certain that
space is flat. It just seems like it's flat because
space has been inflated so much from our perspective. The
analogy that I've heard before is kind of like standing
on the surface of the Earth, where the curvature of
the Earth is so large relative to us that it
seems like it's flat.
Speaker 1 (09:03):
I'm not sure. I thought it was three dimensional.
Speaker 5 (09:05):
Plant has to do with two D.
Speaker 6 (09:07):
I think the flat space is somehow stable equilibrium points,
so the space will eventually evolve into the flat version.
Speaker 7 (09:19):
I was sneaking suspicion it's not so flat, but it
just looks that way to us. I know there's some
bits of like string theory that posit there are dimensions
we simply can't perceive, and so I'm wondering if space
just looks flat to us because we just don't have
a capacity to see the other dimensions.
Speaker 5 (09:40):
I don't think it is very flat. I think it
is pretty multi dimensional. I don't know what really is
meant by that. Maybe like stuff forms discs, like the
Solar System or our galaxy, maybe that is meant by flat.
I think that is due to so that things tend
(10:01):
to take the shape of discs when there's rotation.
Speaker 2 (10:05):
Involved, all right, and not a lot of flat universes.
Speaker 1 (10:11):
Yeah. Here, I think you really are scoring some points
because a lot of people think flat implies two dimensional.
Speaker 2 (10:17):
Yeah, that makes sense, right, like if something if the
universe was flat, it would be the width of a
sheet of paper kind of right.
Speaker 1 (10:24):
Mm hmm. Yeah. If somebody like bakes your birthday cake
and then a truck drives over it and flattens it,
then you think of it as like thinner, right, squeeze
down to two.
Speaker 2 (10:32):
Dimensions two dimensional? Yeah, although two dimensional cake would be
pretty low calorie.
Speaker 1 (10:40):
I don't think the calorie squeeze out of it when
the truck drives over it, unless there's like fusion that happens,
but that would be a pretty heavy truck.
Speaker 2 (10:48):
As if a truck runs over it, I don't think
you want to eat it off the road. It seems
like it will make you sick.
Speaker 1 (10:53):
I think we need to have a highly controlled experiment,
one of those like roads smootheners they have in cartoons
all the time that's crushing white the coyote. Squeeze a
cake and see if it still makes people fat.
Speaker 2 (11:04):
I'm pretty sure that if you ask YouTube, somebody out
there has made a video of a cake being flatted
by multiple things.
Speaker 1 (11:11):
Thank you.
Speaker 2 (11:12):
YouTube sounds like the kind of thing the Internet likes.
Speaker 1 (11:15):
If it doesn't exist on the Internet before this podcast,
it certainly will after.
Speaker 2 (11:19):
But yeah, it's an interesting question why is space flat?
And I guess also is space flat? I guess is
maybe the first question we should be asking, or maybe
the question before that should be what does it mean
for space to be flat?
Speaker 1 (11:30):
Yeah, it's a really fascinating question to even think about,
like what it means for space to be flat, and
to talk about how we measure it's flat and why
we're surprised to find that it is flat. But you're right,
first we should make sure we're clear about what we
mean by flat. And there's sort of two different concepts
to there, of course connected that we need to think about.
We can think about locally being flat, like is the
(11:52):
universe bumpy? And we can think about globally like is
the universe curved? On some big scale. Thinking about locally
is a little bit easy, though of course still twists
your brain a little bit. This is just the idea
that matter bends space, that the reason things don't seem
to move in straight lines but seem to be bent
by gravity. Is not because gravity is a force, but
that space itself is curved. So things are moving through
(12:15):
that curved space. The Sun bends the space around it,
so the Earth moves in that circle, which is the
natural inertial motion for an object in that curved space.
That's sort of local curvature.
Speaker 2 (12:26):
Right, right, although I think we always have to give
the caveat that. You mean space time, right, Like space
time is what's curved.
Speaker 1 (12:33):
Well, space is a part of space time, and the
curvature of space time is a little bit different from
the curvature of space. But in this case, space is
also curved.
Speaker 2 (12:41):
But I guess I mean like curved space makes me
think of like a road. Like a road is curved,
and so anything that tries to follow a straight line
on that road is going to follow the same path.
But maybe in real life it would kind of depend, right,
I don't know how fast you're going or what your
mass is or right, isn't it?
Speaker 1 (12:58):
Yeah, A curved road is a helpful analogy. Things that
are moving through space are basically following an invisible road
that we can't see. You know, space is curved, but
in this way that we can't directly observe it. Like
you can look at a road and say, oh, there's
a curve coming up ahead, but you can't look at
space and see the curvature directly. But it does affect
the way things move through it. So you try to
(13:18):
drive your car on the curve road of space, and
space moves your car forward. You sort of like guides
it along the curvature of space and fundamensional space time.
It's really fascinating because time and space bend together to
make space. Time itself have these invariants, these things that
don't actually change, but space curves and time curves due
(13:39):
to the presence of mass. Right.
Speaker 2 (13:41):
But like if I throw a bowling ball at a
low speed and a high speed, and I threw a
feather at a low speed and as high speed, they
would sort of curve through space, or I would see
them curve in a different way, or would they all
curve the same way.
Speaker 1 (13:53):
We know that because, for example, you throw a baseball
at different speeds, it's going to go a different path, right,
So it definitely depends on the velocity of the object
as it moves through curve space. So that's all inertial motion.
That's motion under no forces, just the curvature of space.
Speaker 2 (14:09):
So I wonder if it's more accurate to say that
space has curvature and not that space is curved.
Speaker 1 (14:14):
What's the distinction in your mind?
Speaker 2 (14:16):
Well, space like if you say that space is curved,
make me think of it like a tunnel. Like, if
a tunnel is curved, then no matter how fast you're
going or what you throw, you're going to bend the
same way. You can follow the same path. But that's
not sort of how space really works, right, Not everything
is stuck in the same kind of path.
Speaker 1 (14:33):
Yeah, you're right, there aren't rigid tunnels that things have
to go through. It's not like if you enter a
pipe and you get flushed out the bottom or something.
The curvature of space does affect how you move, So yeah,
that distinction makes sense to me.
Speaker 2 (14:44):
Okay, So then there's local curvature of space. What you're
talking about is sort of like how things go around
the Sun, for example, or how the moon goes around.
Speaker 1 (14:52):
The Earth m or how we stay on the Earth,
all that kind of stuff. Things being gravitationally bound, even
like the galaxy holding itself together. That's all local curvature
in comparison to the global curvature, which is a question
about the whole universe and its shape.
Speaker 2 (15:07):
So there's local and global, and I guess what's the difference,
just like the size of it the scale, Like are
you saying that? Like if I'm orbiting around the center
of the galaxy, it's a different kind of curvature of
doue to gravity than the Moon orpening around the Earth.
Speaker 1 (15:21):
It's not fundamentally different. It's all described by general relativity
in Einstein's equations. It's sort of like the difference between
the Earth being a sphere and the Earth having mountains.
Like the Earth could be flat and it could be
a sphere, but it could still have mountains in either case. Right,
the Earth could be bumpy locally, it could have valleys
and mountains even if it's flat, or even if it's
a sphere. So global curvature is more about the question
(15:43):
of like is the Earth a sphere or is the
Earth flat? Local curvature is about like is the Earth
bumpy or is it all perfectly smooth everywhere you go?
Speaker 2 (15:52):
So we are asking if the universe is bumping.
Speaker 1 (15:54):
We're asking if the universe is sort of bent Right,
is three D space more like the surface of a
three sphere? Right? Or is it flat? And morn analogy
to like a sheet of paper. So the global curvature
space is asking about like the big picture, whereas the
local curvature is asking about the little picture right right.
Speaker 2 (16:12):
But I guess my question was, or is you know
where do you draw when do you draw this distinction
between local and global, like at the galaxy level, at
the galaxy cluster level, or it's only global if it's everything.
Speaker 1 (16:23):
It's only global if it's everything. And you know, when
we solve these equations in general relativity, and by we,
I mean those guys who knows all equations in general relativity.
Speaker 5 (16:32):
Not me.
Speaker 1 (16:33):
They can only solve those in certain situations, in situations
where they assume, like the universe is empty, or the
universe is filled with matter, but that matter is perfectly smooth, like.
Nobody can solve the general relativity equations for our universe,
which has like clumps of matter in it. So when
we talk about the whole universe and its curvature, basically
we're talking about a simplification of our universe where all
(16:55):
the matter is spread out evenly. There are no lumps
at all, because that's all they can. And in that case,
there's still this question of the global curvature. Is the
universe curved on some large scale and how is it curved?
Is it flat? Is it open? Is it closed? These
are the questions of the global curvature of space time,
which are irrelevant to the little details because they still
(17:17):
exist even if you smooth all the matter and energy
out everywhere like peanut butter.
Speaker 2 (17:21):
Mmm, but I guess, you know, if it's everything, we
don't really know what everything is, right, Like the whole
entire observable universe might be just a little bump in
a ginormous infinite universe.
Speaker 1 (17:32):
Well, you're totally right, But the curvature around here is
dependent on the energy density, doesn't depend on what's happening
out there. And then we assume that what's happening here
is what's happening everywhere else, And that's an assumption we
don't know. It could be that what we're calling global
curvature is actually local on a much larger scale, that
if you zoom out from the observable universe to the
(17:52):
actual full universe, that we could never see that the
curvature is different, right, and that what we were talking
about the whole time is quote unquote global curvature is
actually the local curvature of the observable universe.
Speaker 2 (18:03):
I guess it's sort of like how before we used
to think that the Earth was flat because we only
knew sort of the local area here around this and
looks pretty flat. But actually if you sort of keep
going or you're taken to account the whole planet, then
you see that the whole planet is curved and round.
Speaker 1 (18:18):
Yeah, exactly. And if you lived on a part of
the Earth that was literally flat, like maybe you were
really precise about it, and you took out a bunch
of tools and you try to measure the curvature of
the Earth. Imagine you lived on like a truly flat
part of the Earth and you measured it to be flat,
and then you left that and you realized, oh, actually
the rest of the Earth is curved. And so what
I got was a misunderstanding of the bigger picture. So
(18:39):
you're right, we can only see the observable universe, and
we can measure the global curvature of this part of
the universe and then assume that the rest of it
is the same. But we'll never know, all.
Speaker 2 (18:49):
Right, So then a local curvature of space sort of
is kind of about how mass spans space, and how
the Moon goes around the Earth and the Earth goes
around the Sun through curve space time. Now, when you're
talking about the global picture, I guess you're not just
talking about how things move, but it's more sort of
a fundamental property of space about what it contains.
Speaker 1 (19:10):
Yeah, and it's really hard to think about it in
three D. So we do this thing where we talk
about two dimensional versions. Sometimes that's helpful and sometimes it's misleading.
So you always have to keep in mind, like how
those things translate from a two dimensional analogy that's easier
for us to think about to the reality of three
D space. And it's easier to think about two dimensional
analogies because we basically live on a two dimensional surface,
(19:31):
the surface of the Earth, right, So it's easy to
imagine like living on a flat sheet of paper versus
living on the surface of a sphere versus living in
like a hyperbola, And so those three shapes have different curvature.
An infinite plane is totally flat. If you drew a
triangle on the ground, the angles would add up to
one hundred and eighty degrees. The surface of a sphere,
(19:53):
we say it has positive curvature. You try a triangle
that follows the surface of that sphere, its angles are
going to add up to more than a hund You
live on the surface of a hyperboloid, and you draw
a triangle on that surface, the angles are going to
add up to less than one eighty. So those are
two D examples of curved surfaces. Then you have to
extrapolate those two three D space, and it's very similar
(20:14):
to a lot of the ideas carry over.
Speaker 2 (20:16):
I feel like this is getting a little bit technical,
So when don't we stretch these thoughts out and try
to get them down flat and talk about what it
actually means for three D universal space to be flat.
But first, let's take a quick break.
Speaker 1 (20:43):
All right.
Speaker 2 (20:43):
We're asking the question why is space so flat? And
I guess the preceding question is is space flat? And
the preceding preceding question is what does it mean for
the for space to be flat? Because I guess base
sort of seems flat to us, you know, it doesn't
seem curve or bent to us, at least our immediate surroundings.
But we know that if you expand your your surroundings
(21:04):
a little bit, you see that space time is flat.
That's how gravity works, and that's what makes the Moon
go around the Earth and the Earth around go around
the Sun. But we're talking now about global curvature of space,
which really means universal curvature of space, which actually sort
of means observable universe curvature of space, right yeah.
Speaker 1 (21:22):
And we're trying to use our understanding of two D
space to sort of bootstrap our way to understand the
curvature of three D space. So if you're like on
a flat surface and you shoot two parallel lines out
like two laser beams, then they'll never cross each other.
This is Euclid's famous geometry, and that's why we call
it Euclidean geometry. These two parallel lines will never meet.
(21:43):
And you can also do that in three dimensional space.
Right now, just imagine the universe is having three directions
shoot two parallel lines, but in any direction in xyz
they will never meet. In flat space, the extension of
flat space from two D three D is pretty straightforward.
Speaker 2 (21:58):
I wonder if, like we even have to go to
a two D analogy, why can't we just talk about
the curvature space in three D.
Speaker 1 (22:03):
Yeah, I think three D flat space is pretty straightforward,
but it can help us understand the curved space to
start in two D or at least let's give it
a shot. In two dimensional curved space, if you fire
two laser beams in the same direction, they will eventually cross.
Like if you're on the surface of the Earth and
you fire two laser beams in the direction in the
north pole, they'll cross when they hit the north pole.
Speaker 2 (22:24):
Right What I think this is why it's confusing, and
I wonder if we can just stick with three D
like three D flat space. If I shoot two lasers
out in space, they're never going to meet. These two
laser beams, they're never going to meet. Right now, let's
talk about curve three D space. I shoot two lasers,
and the lasers are going to do one of two things, right,
They're either going to come towards each other or bend
(22:45):
away from each other.
Speaker 1 (22:46):
That's right. And whether they come towards each other and
away from each other tells you the sign of the curvature.
Positive curvature, they'll come towards each other. Negative curvature, they'll
veer away from each other, never meet.
Speaker 2 (22:58):
Now this is super weird because what's bending the path
of the lasers just the curvingness of space.
Speaker 1 (23:05):
Lasers and light follow the curvature of space. They're like
tracers that tell you how space is curved. So light
moves in straight lines through curved space time, right, But
that leads to curved motion in space.
Speaker 2 (23:20):
So you're saying that space might have a property to
it called curvature, which would to us make the light
beams not go in a straight line.
Speaker 1 (23:28):
That's right. If you assume space is flat, then light
appears to be moving in a curve. If, however, space
itself is curved, those grid lines themselves are curving, then
light is moving along those grid lines. It's just the
gridlines themselves are curved.
Speaker 2 (23:41):
Okay, So now I feel like there's a third possibility.
So like, if I have a laser shooter on my
right hand and a laser shooter on my left hand,
and I shoot them perfectly parallel to each other. If
space is flat, they're just going to keep going straight
parallel forever. But if space is curved, there's some things
that can do. They can bend towards each other away
from each other. But I feel like they could also
(24:03):
like bend perpendicular to each other, like maybe my right
laser beam drifts up and my left laser being drifts down.
What does what would that mean?
Speaker 1 (24:13):
Isn't that the same as bending away from each other?
Speaker 2 (24:15):
I guess if I just turn my head sideways, what
if they spiral around each other? Can space be twisty?
Speaker 1 (24:22):
Space can have all sorts of weird combinations. I mean,
in general relativity, space can doesn't even have to be
totally connected. So a laser beam can like disappear and
appear somewhere else, right, That's basically what a wormhole would be.
We're trying to talk about pretty simple constructions of space
where all you have is a single overall curvature.
Speaker 2 (24:40):
I guess if I shoot my laser beams and they
they go past a large massive object in space, like
the Sun, they're gonna curve, and if they're maybe on
opposite or different sides of the Sun, they're gonna curve
in a different way. And as they go through a galaxy,
they're gonna get pushed this way and that way. The
laser beams. But I think you're talking about like if
(25:01):
I shoot them maybe really far apart from each other,
and let them go for a really really long time
on average, Are they going to be moving towards each
other or away from each other? That's what you mean
by global curvature.
Speaker 1 (25:13):
Yeah, And your analogy is great because it lets us
make a connection between local curvature and global curvature. Local curvature,
as you say, is like, is there a star there
that's going to bend the path of my life? And
we sort of got our minds around a little bit
the general relativity that light is bent by masses. Even
though light has no mass, it follows the curvature of space,
and it's bent right now. Instead of having a local
(25:35):
mass like a star with a single point of really
high density, take that star and spread it out throughout
the whole universe instead. So now the universe is filled
with constant density of matter or energy that creates a
curvature of space that's constant. It's not like, oh, there's
a lot of curvature near that star. Let's have a
little curvature everywhere instead of a lot of curvature in
just one spot. And that's one way to think about
(25:57):
the global curvature of space. Think about a universe unit
formally filled with a certain matter and energy density.
Speaker 2 (26:02):
So like if the universe was infinite and was filled
with like evenly spread out gas or an evenly spread
out star, I guess what would happen to a laser beam.
Would it still curve or would it go straight?
Speaker 1 (26:15):
It depends on the density of that stuff. Right, there's
a certain critical density of energy in the universe. Below
a certain level, the universe will be negatively curved. If
it has exactly the right critical energy at this knife's edge,
the universe will be flat. If it's more than that
critical energy, the universe will be curved. So the curvature
(26:35):
of the universe itself of space is connected to the
energy density of stuff in the universe relative to this
critical threshold.
Speaker 2 (26:44):
I guess that's a little counterintuitive, because I would think
that if the universe is filled evenly with the same
energy or gas or matter or energy, then the laser
beam would just go straight because it's being pulled the
same way in all directions.
Speaker 1 (26:58):
Yeah. Unfortunately, general relativity isn't intuitive, and if you add
enough stuff to the universe, it curves up. It makes
the universe effectively like a sphere. That's only consistent with
universes that have a positive curvature, because imagine you take
every bit of space and you make it bend y. Now,
think about, like, what shapes can you build with that?
(27:19):
If you only have curvy pieces, all you can do
is build the surface of a sphere, or all you
can do is build a three dimensional version of the
surface of a four dimensional sphere if all you have
are bendy pieces.
Speaker 2 (27:31):
Yeah, I guess I'm still confused because I'm imagine this
scenario where the whole universe is filled with the same
gas or evenly distributed star. If I shoot a laser beam,
which way does it curve? If the universe is positively curve,
so curve up, down, left right.
Speaker 1 (27:45):
In a universe with positive curvature, if you shoot a
laser beam, it looks to you like it's going straight,
but then it hits you in the back of the head.
Speaker 2 (27:53):
What it wouldn't necessarily hit mean in the back of
my head.
Speaker 1 (27:55):
In a universe that's uniformly filled with matter that's positive curvature,
it will loop back around. It's like being on the
two dimensional surface of a three dimensional sphere.
Speaker 2 (28:04):
But I guess it maybe it might loop around a
few times before it hits me in the back of
the head.
Speaker 1 (28:08):
Any point on a sphere is the same, so it
doesn't really matter where you are, which direction you shoot it.
You always get the same results. From that point of view.
Speaker 2 (28:15):
I feel like then, now it's getting a little bit
into this idea of the how space is connected to itself,
which is at the case, is a curvature of space
necessarily the same as how space is connected to itself,
whether it loops around itself.
Speaker 1 (28:27):
It's definitely connected. Right, It's not the same, but it's
definitely connected. If space is flat, then the universe can
be infinite. If space is positive curvature, then the universe
can't be infinite. It can be finite but also have
no boundary, just the way like the two dimensional surface
of a three D sphere can be finite but unbounded
because it has positive curvature. So these two ideas are
(28:50):
definitely connected. The topology of space, the large scale shape
of space, and the curvature of space. The two things
are definitely closely linked. The curvature of space you can
deduce from the density of matter in that space. Because
general relativity connects those two things.
Speaker 2 (29:05):
Now, that was one laser beam. Now I take two
laser beams and I shoot it off into three D space.
And let's say that the universe has positive curvature. What's
going to happen to these two laser beams. They're eventually
going to hit each other.
Speaker 1 (29:18):
They will eventually cross. Yeah.
Speaker 2 (29:19):
Mmm. And if the universe is not positively curved, if
it's negatively curved, then they'll never hit each other.
Speaker 1 (29:27):
They won't hit each other, they'll veer apart.
Speaker 2 (29:29):
M all right. I think that gives us as good
of an explanation of what the curvature space is in
the universe, right, m hm.
Speaker 1 (29:37):
And all of these things together control the future of
the universe, like the curvature and the topology, the matter
density of the universe. That plus like the dark energy
of the universe, all these things work together to determine
how fast the universe is expanding. Is it expanding or
is it collapsing or is it steady state with no expansion.
(29:57):
All of these things play a role in determining the
future of the universe. Cool.
Speaker 2 (30:02):
Well, maybe talk about how you might measure the flatness
of the universe in like, how do we know whether
the universe is flat or not.
Speaker 1 (30:10):
So what we do is we measure this energy density.
And of course the caveat is we can only measure
it in the observable universe. We can't measure outside, and
so when we say the universe here, we always really
just mean the observable universe. All we can do is
measure the energy density, and we can say, is there
enough stuff in the universe to make it curved positively
so it wraps up on itself. Is there the critical
(30:30):
density so the space is flat? Or is there less
than the critical density so that the universe is open
with negative curvature. So the way we do that is
by measuring the amount of stuff, the energy density of
stuff in the universe.
Speaker 2 (30:42):
Oh, I see you measure the density of stuff. But
I guess we never covered why the density of stuff
determines the curvature of space, Like why is there a
critical amount that makes it negative or positive? Like wouldn't
any amount of stuff in the universe make deniverse positively curve?
Speaker 1 (30:57):
Yeah, that is a little counterintuitive, But a totally empty
un one with no matter or energy in it at all,
would not have flat space. It would have negatively curved space.
So you need a little bit of stuff in the
universe to counteract that.
Speaker 2 (31:11):
Whoa wait, So if I had an empty universe, like
no stars, no planets, no galaxies in it, and I
shoot to laser beams, they're going to diverse from each other.
They're not just going to stay parallel to each other forever.
Speaker 1 (31:22):
Yeah, that's right. This is one of the situations we
can actually solve in Einstein, the general relativity situation with
nothing in the universe, totally empty, no matter, no energy,
no dark energy. And in that case, the universe has
negative curvature, so you have to add stuff to the
universe to make it have no curvature or positive curvature.
Speaker 2 (31:41):
Oh so even no dark energy like this sort of
necessary amount of stuff in it is not related to
the expansion of the universe either, or do you assume
the expansion of the universe or not.
Speaker 1 (31:53):
This does not determine the expansion of the universe. All
these pieces together, the curvature, the density, the dark energy,
all these things together determine whether the universe is expanding,
whether that expansion is accelerating. It's a whole complex dance,
but just the curvature of the universe is determined by
the matter and energy density. If you have a certain amount,
then you sort of counteract the natural negative curvature of
(32:15):
space and you get a flat universe. If you have
more than that, you get a positive curvature. If you're
less than that, you get negative curvature. So a flat
universe is sort of balanced on a knife's edge. You
have to have like exactly the right amount of stuff,
and it's not a big number, Like the critical density
right now is about five protons per cubic meter.
Speaker 2 (32:33):
I guess that's weird that space by itself has negative curvature,
like pure space OG space. If you shoose laser beams,
they would diverge. Isn't that weird because shouldn't space be
like neutral or totally empty.
Speaker 1 (32:47):
Well, intuitive concept of space doesn't even allow it to
be bent, right, So you have to already let go
of those intuitive ideas and think that space is something
quite different from what we imagined as these weird properties.
It's a little bit more complicated than what we've described
because the amount of stuff you have to add to
space to avoid this negative curvature actually changes over time.
(33:08):
It depends also on the expansion of the universe. So
there's a lot of complex moving parts here that we're
trying to distill down.
Speaker 2 (33:14):
But I guess the main takeaway is that space by
itself has negative curvature, but because we have stuff in it,
matter and energy, then it's possible for space to be
flat because that's what the effect of energy and mass
does to space, is it makes it more positively curvy.
Speaker 1 (33:31):
Yeah, and we can measure the curvature of space by
measuring the matter and energy density of the universe. So
we go out we measure that, and that tells us
what curvature we have in our universe. The magnitude of
that curvature can also change the sign can't. If you
have positively curved space, it's always going to be positively curved,
but it can get more positively curved or less positively curved,
(33:53):
like the universe has positive curvature, can collapse on itself,
making itself more and more positively curved, or universe it's
open can expand really really rapidly and get less and
less curved. But they can't flip over. You can't start
from the universe as positively curves and end up with
the universe.
Speaker 2 (34:07):
That's negatively curved unless maybe the density of energy and
matter decreases enough. Isn't that possible? No, As like you said,
it depends on that density. What if the density changes.
Speaker 1 (34:17):
The density definitely does change, right, and we'll talk a
little bit about how that density is changing and how
we understand how it's changing. But you can't change the
curvature of the universe. You can't go from positively curved
space to negatively curve space. That would correspond to like
changing from a finite universe to an infinite universe, which
you can't do right. You can't take the service of
(34:38):
a sphere and snap it out to an infinite plane.
Speaker 2 (34:40):
You can pop a balloon, you can flat a birthday cake.
Speaker 1 (34:44):
That's one of the confusing things about these two D analogies, right,
is that you're imagining it in a three D space.
You're thinking about really a two D service on a
three D sphere. But in those analogies, the two D
surface is all there is, so you can't really flatten
it all.
Speaker 2 (34:59):
Right, Well, into what would happen if you change the
density of matter and energy in the universe, And then
let's ask the big question, why is the universe flat?
But first, let's take another quick break. All right, we're
(35:25):
asking the question why is space flat? Or I guess
why space so flat? Because it's maybe flatter than what
you expected.
Speaker 1 (35:31):
Yeah, when we go out to measure the curvage of
the universe, we find something kind of surprising. We find
that it's really pretty flat. Like there's this critical density
five protons per cubic meter, And we go out to
measure the amount of stuff in the universe. We add
up all the mass, the stars, the galaxies, the dark matter,
and also the dark energy. All of that stuff. It
(35:52):
adds up to like very very close to exactly the
critical density. It's within one percent, which is about our
uncertainty of the critical density, which tells us that space
is either flat or very very close to flat. And
that's kind of a surprise because we don't think the
universe likes to be flat.
Speaker 2 (36:11):
I guess before we go, I have more questions about
what you just said. Well, first of all, how do
we measure the mass and energy density of the universe?
And second of all, how do we know what amount
you need for the universe to be flat?
Speaker 1 (36:24):
So how we measure it is several different ways. We
can use like the cosmic microwave background radiation. This is
radiation from about three hundred thousand years after the Big Bang,
where the universe was very hot and dense with its
bright plasma, and then it cooled off and formed neutral
atoms and light could propagate. We can still see that light.
That light was made everywhere in the universe, and it's
(36:44):
flying around everywhere, and some of it has just reached
Earth from places that used to be very very far away,
and we can use it to sort of look at
what the universe looked like at that time, and there
were little bumps and wiggles in it. It's not completely smooth.
It's like a little bit of a frothing quantum plasma.
And from the size of those wiggles, we can tell
how much energy density there was in the early.
Speaker 2 (37:05):
Universe based on some theory that you have about how
the universe formed and how these things balance out with space.
Speaker 1 (37:11):
Relying basically just on general relativity. I mean, we assume
some model of the universe, but it's based in general relativity.
Doesn't depend on how the universe formed or what came before.
It just depends on the size of those fluctuations in
the early universe and then how those propagate through an
expanding universe to us.
Speaker 2 (37:28):
Okay, so that's one way to measure it.
Speaker 1 (37:30):
So that measures the total energy density like the dark
energy plus the dark matter plus the normal matter density
in the early universe. We can also measure it by
looking at the acceleration of the universe, like looking at
supernova seeing how fast they're moving away from us, or
looking at cephids. This expansion rate of the universe also
helps us measure these various components. So the components of
(37:51):
the energy density of the universe are the dark energy,
the normal matter, and the dark matter, and the super
nova measurements the acceleration of the universe help us measure
the dark energy component minus the matter component, because that
determines the expansion of the universe. So there's like a
bunch of different components here, and we have different ways
to measure each one's or combinations of each one, to
(38:11):
help us in down exactly what those contributions are. Dark
energy is of like seventy percent of the critical density.
Matter is like thirty percent of the critical density, where
most of that is dark matter, and they add up
to basically this critical density.
Speaker 2 (38:25):
This is from this CMB measurement, or from all measurements.
Speaker 1 (38:28):
The CMB measurement tells us the total density. The supernova
tells us the dark energy minus the matter the difference
between those two because they work against each other when
controlling the expansion of the universe. There's another measurement, the
buryon acoustic oscillations, that tells us about like how matter
was sloshing around in the early universe and made these
sound waves back when the universe was super duper dense.
(38:50):
Sound traveled at nearly half the speed of light, and
the speed of that sound depends on the density of
matter in the universe, and we can still sort of
see the universe ringing from those oscillations in the early universe.
That separately measures just the matter portion. So we have
these different pieces of the pie, and they all add
up to make exactly one pie. And the fascinating thing
(39:12):
is that they didn't have to write it could have
added up to anything. It could have added up to
be twice the critical density or half the critical density,
but it adds up to bang on just the critical
density to within one percent.
Speaker 2 (39:23):
I see. So you're saying we've measured the energy density
of the universe, and according to what we think is
the laws of the universe, according to general relativity, we
have just enough mass and density to make the universe flat,
which means if I shoot two lasers out there in space,
they're not going to hit each other, they're not going
to drift the part, they're not going to hit me
in the back of the head. Those two laser beings
are just gonna keep going forever exactly.
Speaker 1 (39:45):
And this is kind of a surprise to physicists because
they think the universe doesn't like to be flat. Like
the flatness of the universe is not a stable thing.
If you're just above the critical density, if you're like
a little bit more in the critical density, then the
universe tends to collapse and become more and more dense,
and you move away from the critical density. If you
have less than the critical density, you're below it, then
(40:07):
the universe is open. It tends to expand and dilute
itself away from the critical density. So either you're exactly
bang on the critical density, in which you're stable like
a pencil balance on its tip, or you're a little
bit above and a little bit below, and then you
very quickly veer away from it. So sort of a
mystery how we're still so close to the critical density
after billions of years.
Speaker 2 (40:28):
What do you mean it's unstable like a pencil. What
does that mean?
Speaker 1 (40:31):
It's unstable, and that if you move away from the
critical density a little bit, the universe moves away even more.
It's like a pencil balance on its tip. Right, it's unstable.
You have it, a tiny little push, a fly lands
on it, air blows by it really gently. It's going
to tend to fall over.
Speaker 2 (40:45):
Wait to Like, if you measure the density of the
universe and it's a little bit more than the critical
amount of density you need for a flat universe, then
the density is going to increase over time, Like the
universe is going to get more and more denser.
Speaker 1 (40:58):
Exactly. If you have more in the critical density, the
universe will contract, right, and things will get denser and denser.
You'll end up with like a big crunch.
Speaker 2 (41:06):
You mean, like the expansion of the universe will reverse.
Speaker 1 (41:08):
Yeah, exactly. In the opposite scenario, where you lessen the
critical density, things expand forever and things get more and
more dilute, So the density drops right as the universe expands,
the density of matter drops. As the universe contracts, the
density of matter increases, and so if you're not at
the critical density you tend to veer away from it
pretty quickly. And we're like billions of years into the
(41:29):
history and we're still super close to the critical density,
which was a big question in cosmology. How can you
stay so closely balanced so long?
Speaker 2 (41:37):
I feel like now we're tying it to the expansion
of the universe. So the critical density is tied to
the expansion, like if the universe is positively curved, then
the universe is going to contract eventually.
Speaker 1 (41:46):
The courage of the universe definitely plays a role. The
critical density and the curvature, together with the amount of
dark energy, determine the expansion. You can have a universe
that's positively curved and expanding if you have enough dark energy,
because dark energy can overcome this critical density, that you
could have a universe which expands. But in the simple
scenario where you take out dark energy for the moment
(42:07):
and just have a universe with only matter and radiation,
which was basically the scenario of our universe for the
first nine billion years when dark energy was negligible, and
then the universe above the critical density will contract and
increase the density, and the universe below the critical density
will expand and decrease the density. So they did this calculation.
They're like, well, in that scenario, how close do the
(42:28):
universe have to start to the critical density to end
up at one percent. The answer is we had to
be within the critical density to within ten to the
minus sixty two. If you're anything above that, then the
universe would have expanded like crazy or contracted like crazy.
So it seems really, really weird that we end up
with a universe so close to flat when the universe
(42:49):
likes to veer away from flatness.
Speaker 2 (42:51):
Well, that's a really tight requirement for this density that
we need at the beginning of the universe. It kind
of seems like too much of a coincidence.
Speaker 1 (42:59):
It does seem like too much of a coincidence, and
physicists don't like coincidences because the density of stuff in
the universe doesn't seem to be determined by anything. It
could have been anything, So for it to be like
exactly close to one complete pie of the critical density,
it seems too neat. Physicists like a reason for these
numbers to line up, and there is an explanation for it,
and the explanation is cosmic inflation. So you know how
(43:21):
the universe is expanding now, and that expansion is accelerating.
We also think that the universe expanded very very early
on in its history. But like a huge factor, this
accelerating expansion we call inflation. It's an expansion of like
ten to the thirty in like ten to the negative
thirty seconds. And this kind of accelerating expansion tends to
push the universe towards flatness. It makes the universe more flat.
Speaker 2 (43:45):
But isn't it still sort of too much of a coincidence,
Like I wonder if maybe our theories are wrong, or
maybe there's some sort of mechanism that keeps the universe flat.
Speaker 1 (43:54):
Well, we don't know if inflation is true, and it's
just one of the possible scenarios, And you know, maybe
it's just a coincidence, and we just happen to in
the universe that was that close to flat that we
ended up in the universe that didn't overexpand or didn't
collapse on itself. But inflation makes it less sensitive. Inflation says,
you know, you could have started with lots of different densities,
and inflation would have made your universe have the critical
(44:15):
density early on, So you could have started with half
the density or one and a half times the critical density,
and inflation would have made your universe super duper close
to the critical density.
Speaker 2 (44:24):
Meaning like you might have started with too much stuff
in the universe, but then some mechanism stretched out the
universe enough so that you had the critical density.
Speaker 1 (44:34):
Exactly the math of inflation. In fact of any accelerating
expansion in the universe tends to push the universe back
towards the critical density. So if you had too much,
inflation would stretch out the universe in just the right
way to make it have the critical density. Just like
if you're standing on the surface of a tiny sphere
like a beach ball, it looks really really curved. But
then if somebody expands it rapidly by a factor of
(44:56):
ten to the thirty, then now you're standing on the
surface of a huge it looks flat. Right, So a
bigger sphere looks flatter and then a small sphere. In
the same way inflation pushes the universe towards less.
Speaker 2 (45:08):
Curvature, does it also work the other way, Like if
the universe had started with too little stuff in it,
the density was too small. Mood inflation have somehow adjusted
or slowed down or compress the universe somehow. Would you
have had deflation in order to keep the universe flat?
Speaker 1 (45:26):
Yeah, that's a great question. It does. It pushes it
towards critical density from either direction, which is pretty cool
how the math works out.
Speaker 2 (45:34):
So it does do deflation.
Speaker 1 (45:35):
Well, they still consider it inflation because you're still stretching
it out.
Speaker 4 (45:38):
You know.
Speaker 1 (45:38):
Imagine like a hyperbolic surface. You stretched it out, so
the negative curvature goes towards zero curvature. So inflation drives
you towards zero curvature from either direction.
Speaker 2 (45:49):
So it's more like stackflation or less flation.
Speaker 1 (45:54):
I don't know enough economics to know if an analogy
is accurate or not.
Speaker 2 (45:57):
Yeah, I mean it sounds like something they say in
the news.
Speaker 1 (46:02):
And one fascinating thing about that is it means that
our universe right now is driving back towards flatness. Like
the brief history of the universe is you have probably inflation,
which makes the universe mostly flat, and then you have
a matter in radiation dominated time when the universe is
then driven by this critical density, and it continues to
expand that that expansion is decelerating because of the matter
(46:24):
dominated nature of the universe. And then like six billion
years ago, dark energy took over, right, because the expanding
universe dilutes out the matter and radiation, while dark energy
grows as a fraction. So now we have an accelerating
expansion again, which does the same thing. Any accelerating expansion
in the universe pushes you back towards zero curvature.
Speaker 2 (46:43):
Mmm. Interesting. I guess what that makes me think is
that maybe the universe is flat, Like it's just flat.
It's infinite and flat, and all these things we're seeing,
all these measurements and all these theoretical concepts, they kind
of have to work out to a flat universe, and
that's what we're seeing. Like maybe it's not sort of
like this mystery or this universe sitting on a nice edge.
It's just that's just the way that the verse is.
(47:04):
And to us, the math and the measurements look like
it could have gone either way, but it could never
had a chance.
Speaker 1 (47:09):
Yeah, it's possible. Right in the equations of general relativity,
this is curvature parameter. It's either plus one zero, or
minus one, and it can't change again. Right, You can't
go from a negative curvature to a positive curvature, and
our universe is just one of those. The interesting thing, though,
is that to have k equals zero, to have zero curvature,
you really have to have the critical density of matter
(47:30):
and energy. So it sort of depends on what question
you ask, Like you could ask, well, which of the
three curvatures is it? Well, maybe it's just zero, like
you say, but if you think about it in terms
of the continuous spectrum of matter and energy density, then
it has to have exactly the right number, which seems
like one option out of an infinite number instead of
one option out of three.
Speaker 2 (47:48):
Or unless the universe sort of like prevents the matter
and energy to be anything else, in case that wouldn't
make sense.
Speaker 1 (47:54):
Right, Yeah, we it'd certainly possible. And these questions are
really basic and also simple, And in a few hundred
years they might look back on this and be like, hah,
how do they imagine they lived in a curved universe?
Speaker 2 (48:04):
What a bunch of idiots, What a bunch of flat
footed idiots?
Speaker 1 (48:08):
But these are the questions we're asking, and we don't
know and the equations of general real too. They allow
for all three kinds of universe negative curvature, flat or
positive curvature. We just don't know which of those we
live in and why we've measured its space to be flat.
And you're right. Either it just is flat and it
started out balanced on that knife's edge and it will
always be there, perfectly balanced, or it has a little
(48:29):
bit of curvature, but then we don't understand why it's
still so flat unless you do something early on, like inflation.
Speaker 2 (48:35):
Well, I think the idea is that maybe the universe
is flat, which means that the pencil is not upside down,
like maybe the pencil is hanging from the tail, and
that it can only sort of be that hanging down
and the universe would push it down if you try
to move the pencil. That's a possibility. Sounds like it's
still a mystery why the universe is flat. We're measuring
(48:55):
it to be flat and it seems to be staying flat,
which means that the universe either is flat or the
universe is not flat, but something is making it suspiciously flat.
Those are the two options, right exactly.
Speaker 1 (49:08):
If it's not exactly flat, then something is keeping it
very very close.
Speaker 2 (49:12):
To flat, which would be the universe, which means the
universe it's flat.
Speaker 1 (49:18):
The universe is either exactly flat or it likes to
stay very close to flat.
Speaker 2 (49:22):
I'm just trying to propagate flat universe theories and say
that it's all just a conspiracy by the universe.
Speaker 1 (49:28):
You're curving my brain.
Speaker 5 (49:29):
Man.
Speaker 2 (49:30):
All right, Well, the next time you look at into space,
think about what happens to those photons that you're seeing.
Did they come straight at you or did they get
bent by space? Are those photons curving their way through
the universe, maybe even a close circular universe, or did
it come straight at you from really far away.
Speaker 1 (49:48):
Either way, we're grateful that photons are arriving here on
Earth and that we're smart enough to figure out the
messages that they send about the nature of this incredible cosmos.
Speaker 2 (49:57):
Or at least we think we're smart enough. It might
just be falling flat on our facebooks.
Speaker 1 (50:01):
We're feeling good about being smart. Whether or not we
are all right.
Speaker 2 (50:04):
We hope you enjoyed that. Thanks for joining us, See
you next time.
Speaker 1 (50:16):
Thanks for listening, and remember that Daniel and Jorge explain
the universe is a production of iHeartRadio. For more podcasts
from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever
you listen to your favorite shows.
Hey, Orge, I'm going to say a word, and I
want you to tell me if you think it sounds
like a positive or a negative idea.
Speaker 2 (00:15):
All right, go for it.
Speaker 1 (00:16):
The word is flat.
Speaker 2 (00:19):
I guess it could go either way. You know, nobody
likes their soda flat or they are jokes to fall flat.
Speaker 1 (00:26):
But I sure do like my bed to be flat.
Speaker 2 (00:29):
But do you like your tires to be flat?
Speaker 1 (00:32):
No? But I do like my roads to be flat.
Speaker 2 (00:34):
Does that mean you want the earth to be flat?
Speaker 1 (00:38):
I like it spherical, But I also like mountains, so
I guess I'm anti flat earth.
Speaker 2 (00:43):
Do you like falling flat from a mountain?
Speaker 1 (00:47):
I like landing flat on my feet.
Speaker 2 (00:48):
I think this discussion has run out of air.
Speaker 3 (01:05):
Hi.
Speaker 2 (01:05):
I'm Hoorhey, mccartoonist and the author of the book Oliver's
Great Big Universe.
Speaker 1 (01:09):
Hi, I'm Daniel. I'm a particle physicist and a professor
at UC Irvine, and I'm also flat footed.
Speaker 2 (01:15):
Are you saying metaphorically or you know, physiologically?
Speaker 1 (01:20):
Well, your questions often catch me flat footed, so that's metaphorical,
but also literally and physiologically, I have flat feet, so yeah,
I wear inserts.
Speaker 2 (01:27):
Does that have to make you taller you like Tom Cruise,
I don't wear heels.
Speaker 1 (01:34):
No, I wear inserts to avoid crippling pain when running.
Speaker 2 (01:39):
Sounds like the solution is just not to run life
flat on your back.
Speaker 1 (01:43):
Yeah. I'm working on a floating recliner I can live
in for the rest of my life and float around.
Speaker 2 (01:47):
There you go. You can attach like a bicycle pedal
and maybe get your workouts that way.
Speaker 1 (01:53):
Yeah, that's great for going upstairs.
Speaker 2 (01:55):
Yeah exactly. But anyways, welcome to our podcast. Daniel and
Jorge Explained the Universe, a productive of iHeartRadio.
Speaker 1 (02:01):
Where we take all the twists and turns and curves
of this crazy universe and try to flatten it all
out for you. We try to untangle all of the
mysteries of the nature of matter, the forces, the energy,
the geometry of space time, the size and shape and
history of the universe and make a nice, smooth story
for you to understand.
Speaker 2 (02:21):
That's right, because it is an amazing universe full of
stuff inflated with amazing and incredible physics and stars and
galaxies and planets and particles for us to wonder at
and for us to I guess poke it.
Speaker 1 (02:35):
There's so much that's amazing about the universe. And sometimes
you can have two amazing facts that seem to be
in conflict, Like, on one hand, it's amazing that we
still don't really know so many basic things about the
nature of the universe. How big is it? What is
its shape? How did it all come to be? We're
so ignorant about the environment in which we live. And
(02:55):
on the other hand, it's kind of amazing that we
know anything about the universe, and then we've only lived
on one tiny little dot and one random little corner
of the universe and never really left.
Speaker 2 (03:06):
Yeah, it's amazing what we can learn just from this
little corner of the universe. And as you said, how
we can ask these big questions about how everything is
the way it is and why it is the way
it is, Like, for example, we don't know if the
universe is flat footed or not.
Speaker 1 (03:20):
Does the universe even like to run? Or does just
want to sit on the couch and eat snacks all day?
Speaker 2 (03:24):
Yeah, just sit around and spin.
Speaker 1 (03:27):
It has big consequences for the curvature of the universe.
Speaker 2 (03:30):
It is getting bigger and bigger, so you know, maybe
it could use a little bit of exercise. It's getting
wider and wider per second.
Speaker 1 (03:37):
I think we should be universe positive on this podcast.
You know, universe just be whatever shape you are, We
love you.
Speaker 2 (03:43):
Yeah, yeah, true, true, true. I guess we should love
the universe the way it is.
Speaker 1 (03:47):
It's the only universe we got, so might as well
love it.
Speaker 2 (03:50):
Even if we don't understand it. I guess all the
time we should, you know, take it for what it is.
That's kind of what science is, right, taking things for
what they are.
Speaker 1 (03:59):
Taking things for what they are are, absolutely, but then
always asking why are they this way? Why couldn't they
be some other way? Why do we live in this universe?
Do we live in the only universe that's possible? Or
are there many possible universes and we just happen to
be in this one. So often we look around as
we try to tell the story of the universe, and
(04:19):
we ask those kinds of questions like does this make sense?
This seems weird? Is it random? Or is there a
reason for it?
Speaker 2 (04:25):
Yeah, because it is pretty perplexing out there the way
things are. You know, there are amazing things like black
holes that seem unexplainable, and there's sort of really weird
things like quantum mechanics out there that kind of keep
you guessing about what the universe is going to do.
Speaker 1 (04:38):
And as we put together this story of physics that
tells us how the universe operates, what machinery is going
on behind the scenes, that controls like what happens when
two particles bump into each other, or house space curves
and twists in the presence of mass. We start to
tell a story about the universe, we notice, like, hm,
the universe seems to do this kind of thing or
do that kind of thing. And sometimes the story tells
(05:00):
is very weird. It's very surprising. It's not one that
makes sense to us or seems intuitive. It makes us
wonder if maybe we're missing part of the story or
if we're all just very very lucky.
Speaker 2 (05:10):
Yeah, and as you said, there are big questions about
the universe that we still don't know about, like its size,
its shape, and what it's going to do in the future,
and also a very interesting question about its curvature.
Speaker 1 (05:24):
Yeah. As we develop our understanding of gravity and general
relativity and we understand that space is weird and twisted
and curved and that affects how things move, it also
affects how the universe itself expands or contracts. So we
have a lot of really fun questions to ask about
why the universe looks this particular way, especially about the
curvature of space.
Speaker 2 (05:44):
So today on the podcast, we'll be tackling the question
why is space so flat? You mean as opposed to bumpy? Like,
what would be the opposite of flat overinflated under pressure?
Speaker 1 (06:00):
Just like my arches, the opposite of flat would be curved, right,
everybody likes nice curved arches for their feet, and the
opposite of flat in the case of space or the
universe would be curved.
Speaker 2 (06:11):
Well, it could also be well bumpy. I guess bumpy
is also kind of curvy. It means you have a
lot of little curves. You could have bumpy feet.
Speaker 1 (06:19):
Yeah, exactly, that's true. You got to sand those down
a little bit. But in this case, yeah, we're talking
about like the nature of space is space the way
Euclid thought about it, You know, two parallel lines will
never touch, or a space more complicated twisting and curving
on a global sense. We're talking here about the curvature
of the entire universe itself.
Speaker 2 (06:39):
Yeah, and this is I guess a pretty mind bending
and space bending topic, because you know, I think we're
all used to thinking of space, or at least empty
space is being kind of like flat, right, not weird
and curved.
Speaker 1 (06:51):
It's really hard to think about this in the three
dimensions of our universe, and even the word flat is
kind of confusing there. It comes really from thinking about
a two dimensional version of the picture instead of thinking
about space like I can move in three different directions,
it's easier to think about it in two different directions
because then we can like draw it on a piece
of paper. So if you imagine like a sheet of
(07:13):
graph paper, that's a flat sheet of paper, and two
parallel lines on that piece of paper are never going
to meet each other. When we talk about whether space
is flat, we're asking a similar kind of question, but
about three dimensional space, though it's harder to understand, like
what curvature means in three dimensions than it is in
two dimensions.
Speaker 2 (07:31):
Are you saying we're going to use a term that
doesn't quite work or describe things or is counterintuitive to
actually what is actually happening. Are we going to do
that again?
Speaker 1 (07:40):
Yeah, that's exactly right. That's the story of.
Speaker 2 (07:41):
Physics being inadequate.
Speaker 1 (07:44):
We think we understand the universe, and then it surprises
us and it sort of outgrows even like our ideas
and forces us to like generalize these concepts like, oh wait,
flattness can apply in three dimensions, not just two.
Speaker 2 (07:55):
Well, as usual, we were wondering how many people out
there had thought about this question whether space and why
space is so flat, and so Daniel went out into
the internet to ask people this question.
Speaker 1 (08:06):
Thanks very much to everybody who participates. If you'd like
to hear your voice answering these questions for this segment
of the podcast, please don't be shy. Write to me
two questions at Danielandjorge dot com. You'll have a good time,
I promise.
Speaker 2 (08:18):
So think about it for a second. Why do you
think space is flat? Here's what people had to say.
Speaker 4 (08:25):
I think space is flat because I think at the
beginning there wasn't any room for stuff to be clumpy
or lumped together or have little dips or gaps. And
I assume that everything was shot out from the big
Bang in every direction in equal measure, and therefore it
stayed flat to this day.
Speaker 3 (08:45):
I think that we're not one hundred percent certain that
space is flat. It just seems like it's flat because
space has been inflated so much from our perspective. The
analogy that I've heard before is kind of like standing
on the surface of the Earth, where the curvature of
the Earth is so large relative to us that it
seems like it's flat.
Speaker 1 (09:03):
I'm not sure. I thought it was three dimensional.
Speaker 5 (09:05):
Plant has to do with two D.
Speaker 6 (09:07):
I think the flat space is somehow stable equilibrium points,
so the space will eventually evolve into the flat version.
Speaker 7 (09:19):
I was sneaking suspicion it's not so flat, but it
just looks that way to us. I know there's some
bits of like string theory that posit there are dimensions
we simply can't perceive, and so I'm wondering if space
just looks flat to us because we just don't have
a capacity to see the other dimensions.
Speaker 5 (09:40):
I don't think it is very flat. I think it
is pretty multi dimensional. I don't know what really is
meant by that. Maybe like stuff forms discs, like the
Solar System or our galaxy, maybe that is meant by flat.
I think that is due to so that things tend
(10:01):
to take the shape of discs when there's rotation.
Speaker 2 (10:05):
Involved, all right, and not a lot of flat universes.
Speaker 1 (10:11):
Yeah. Here, I think you really are scoring some points
because a lot of people think flat implies two dimensional.
Speaker 2 (10:17):
Yeah, that makes sense, right, like if something if the
universe was flat, it would be the width of a
sheet of paper kind of right.
Speaker 1 (10:24):
Mm hmm. Yeah. If somebody like bakes your birthday cake
and then a truck drives over it and flattens it,
then you think of it as like thinner, right, squeeze
down to two.
Speaker 2 (10:32):
Dimensions two dimensional? Yeah, although two dimensional cake would be
pretty low calorie.
Speaker 1 (10:40):
I don't think the calorie squeeze out of it when
the truck drives over it, unless there's like fusion that happens,
but that would be a pretty heavy truck.
Speaker 2 (10:48):
As if a truck runs over it, I don't think
you want to eat it off the road. It seems
like it will make you sick.
Speaker 1 (10:53):
I think we need to have a highly controlled experiment,
one of those like roads smootheners they have in cartoons
all the time that's crushing white the coyote. Squeeze a
cake and see if it still makes people fat.
Speaker 2 (11:04):
I'm pretty sure that if you ask YouTube, somebody out
there has made a video of a cake being flatted
by multiple things.
Speaker 1 (11:11):
Thank you.
Speaker 2 (11:12):
YouTube sounds like the kind of thing the Internet likes.
Speaker 1 (11:15):
If it doesn't exist on the Internet before this podcast,
it certainly will after.
Speaker 2 (11:19):
But yeah, it's an interesting question why is space flat?
And I guess also is space flat? I guess is
maybe the first question we should be asking, or maybe
the question before that should be what does it mean
for space to be flat?
Speaker 1 (11:30):
Yeah, it's a really fascinating question to even think about,
like what it means for space to be flat, and
to talk about how we measure it's flat and why
we're surprised to find that it is flat. But you're right,
first we should make sure we're clear about what we
mean by flat. And there's sort of two different concepts
to there, of course connected that we need to think about.
We can think about locally being flat, like is the
(11:52):
universe bumpy? And we can think about globally like is
the universe curved? On some big scale. Thinking about locally
is a little bit easy, though of course still twists
your brain a little bit. This is just the idea
that matter bends space, that the reason things don't seem
to move in straight lines but seem to be bent
by gravity. Is not because gravity is a force, but
that space itself is curved. So things are moving through
(12:15):
that curved space. The Sun bends the space around it,
so the Earth moves in that circle, which is the
natural inertial motion for an object in that curved space.
That's sort of local curvature.
Speaker 2 (12:26):
Right, right, although I think we always have to give
the caveat that. You mean space time, right, Like space
time is what's curved.
Speaker 1 (12:33):
Well, space is a part of space time, and the
curvature of space time is a little bit different from
the curvature of space. But in this case, space is
also curved.
Speaker 2 (12:41):
But I guess I mean like curved space makes me
think of like a road. Like a road is curved,
and so anything that tries to follow a straight line
on that road is going to follow the same path.
But maybe in real life it would kind of depend, right,
I don't know how fast you're going or what your
mass is or right, isn't it?
Speaker 1 (12:58):
Yeah, A curved road is a helpful analogy. Things that
are moving through space are basically following an invisible road
that we can't see. You know, space is curved, but
in this way that we can't directly observe it. Like
you can look at a road and say, oh, there's
a curve coming up ahead, but you can't look at
space and see the curvature directly. But it does affect
the way things move through it. So you try to
(13:18):
drive your car on the curve road of space, and
space moves your car forward. You sort of like guides
it along the curvature of space and fundamensional space time.
It's really fascinating because time and space bend together to
make space. Time itself have these invariants, these things that
don't actually change, but space curves and time curves due
(13:39):
to the presence of mass. Right.
Speaker 2 (13:41):
But like if I throw a bowling ball at a
low speed and a high speed, and I threw a
feather at a low speed and as high speed, they
would sort of curve through space, or I would see
them curve in a different way, or would they all
curve the same way.
Speaker 1 (13:53):
We know that because, for example, you throw a baseball
at different speeds, it's going to go a different path, right,
So it definitely depends on the velocity of the object
as it moves through curve space. So that's all inertial motion.
That's motion under no forces, just the curvature of space.
Speaker 2 (14:09):
So I wonder if it's more accurate to say that
space has curvature and not that space is curved.
Speaker 1 (14:14):
What's the distinction in your mind?
Speaker 2 (14:16):
Well, space like if you say that space is curved,
make me think of it like a tunnel. Like, if
a tunnel is curved, then no matter how fast you're
going or what you throw, you're going to bend the
same way. You can follow the same path. But that's
not sort of how space really works, right, Not everything
is stuck in the same kind of path.
Speaker 1 (14:33):
Yeah, you're right, there aren't rigid tunnels that things have
to go through. It's not like if you enter a
pipe and you get flushed out the bottom or something.
The curvature of space does affect how you move, So yeah,
that distinction makes sense to me.
Speaker 2 (14:44):
Okay, So then there's local curvature of space. What you're
talking about is sort of like how things go around
the Sun, for example, or how the moon goes around.
Speaker 1 (14:52):
The Earth m or how we stay on the Earth,
all that kind of stuff. Things being gravitationally bound, even
like the galaxy holding itself together. That's all local curvature
in comparison to the global curvature, which is a question
about the whole universe and its shape.
Speaker 2 (15:07):
So there's local and global, and I guess what's the difference,
just like the size of it the scale, Like are
you saying that? Like if I'm orbiting around the center
of the galaxy, it's a different kind of curvature of
doue to gravity than the Moon orpening around the Earth.
Speaker 1 (15:21):
It's not fundamentally different. It's all described by general relativity
in Einstein's equations. It's sort of like the difference between
the Earth being a sphere and the Earth having mountains.
Like the Earth could be flat and it could be
a sphere, but it could still have mountains in either case. Right,
the Earth could be bumpy locally, it could have valleys
and mountains even if it's flat, or even if it's
a sphere. So global curvature is more about the question
(15:43):
of like is the Earth a sphere or is the
Earth flat? Local curvature is about like is the Earth
bumpy or is it all perfectly smooth everywhere you go?
Speaker 2 (15:52):
So we are asking if the universe is bumping.
Speaker 1 (15:54):
We're asking if the universe is sort of bent Right,
is three D space more like the surface of a
three sphere? Right? Or is it flat? And morn analogy
to like a sheet of paper. So the global curvature
space is asking about like the big picture, whereas the
local curvature is asking about the little picture right right.
Speaker 2 (16:12):
But I guess my question was, or is you know
where do you draw when do you draw this distinction
between local and global, like at the galaxy level, at
the galaxy cluster level, or it's only global if it's everything.
Speaker 1 (16:23):
It's only global if it's everything. And you know, when
we solve these equations in general relativity, and by we,
I mean those guys who knows all equations in general relativity.
Speaker 5 (16:32):
Not me.
Speaker 1 (16:33):
They can only solve those in certain situations, in situations
where they assume, like the universe is empty, or the
universe is filled with matter, but that matter is perfectly smooth, like.
Nobody can solve the general relativity equations for our universe,
which has like clumps of matter in it. So when
we talk about the whole universe and its curvature, basically
we're talking about a simplification of our universe where all
(16:55):
the matter is spread out evenly. There are no lumps
at all, because that's all they can. And in that case,
there's still this question of the global curvature. Is the
universe curved on some large scale and how is it curved?
Is it flat? Is it open? Is it closed? These
are the questions of the global curvature of space time,
which are irrelevant to the little details because they still
(17:17):
exist even if you smooth all the matter and energy
out everywhere like peanut butter.
Speaker 2 (17:21):
Mmm, but I guess, you know, if it's everything, we
don't really know what everything is, right, Like the whole
entire observable universe might be just a little bump in
a ginormous infinite universe.
Speaker 1 (17:32):
Well, you're totally right, But the curvature around here is
dependent on the energy density, doesn't depend on what's happening
out there. And then we assume that what's happening here
is what's happening everywhere else, And that's an assumption we
don't know. It could be that what we're calling global
curvature is actually local on a much larger scale, that
if you zoom out from the observable universe to the
(17:52):
actual full universe, that we could never see that the
curvature is different, right, and that what we were talking
about the whole time is quote unquote global curvature is
actually the local curvature of the observable universe.
Speaker 2 (18:03):
I guess it's sort of like how before we used
to think that the Earth was flat because we only
knew sort of the local area here around this and
looks pretty flat. But actually if you sort of keep
going or you're taken to account the whole planet, then
you see that the whole planet is curved and round.
Speaker 1 (18:18):
Yeah, exactly. And if you lived on a part of
the Earth that was literally flat, like maybe you were
really precise about it, and you took out a bunch
of tools and you try to measure the curvature of
the Earth. Imagine you lived on like a truly flat
part of the Earth and you measured it to be flat,
and then you left that and you realized, oh, actually
the rest of the Earth is curved. And so what
I got was a misunderstanding of the bigger picture. So
(18:39):
you're right, we can only see the observable universe, and
we can measure the global curvature of this part of
the universe and then assume that the rest of it
is the same. But we'll never know, all.
Speaker 2 (18:49):
Right, So then a local curvature of space sort of
is kind of about how mass spans space, and how
the Moon goes around the Earth and the Earth goes
around the Sun through curve space time. Now, when you're
talking about the global picture, I guess you're not just
talking about how things move, but it's more sort of
a fundamental property of space about what it contains.
Speaker 1 (19:10):
Yeah, and it's really hard to think about it in
three D. So we do this thing where we talk
about two dimensional versions. Sometimes that's helpful and sometimes it's misleading.
So you always have to keep in mind, like how
those things translate from a two dimensional analogy that's easier
for us to think about to the reality of three
D space. And it's easier to think about two dimensional
analogies because we basically live on a two dimensional surface,
(19:31):
the surface of the Earth, right, So it's easy to
imagine like living on a flat sheet of paper versus
living on the surface of a sphere versus living in
like a hyperbola, And so those three shapes have different curvature.
An infinite plane is totally flat. If you drew a
triangle on the ground, the angles would add up to
one hundred and eighty degrees. The surface of a sphere,
(19:53):
we say it has positive curvature. You try a triangle
that follows the surface of that sphere, its angles are
going to add up to more than a hund You
live on the surface of a hyperboloid, and you draw
a triangle on that surface, the angles are going to
add up to less than one eighty. So those are
two D examples of curved surfaces. Then you have to
extrapolate those two three D space, and it's very similar
(20:14):
to a lot of the ideas carry over.
Speaker 2 (20:16):
I feel like this is getting a little bit technical,
So when don't we stretch these thoughts out and try
to get them down flat and talk about what it
actually means for three D universal space to be flat.
But first, let's take a quick break.
Speaker 1 (20:43):
All right.
Speaker 2 (20:43):
We're asking the question why is space so flat? And
I guess the preceding question is is space flat? And
the preceding preceding question is what does it mean for
the for space to be flat? Because I guess base
sort of seems flat to us, you know, it doesn't
seem curve or bent to us, at least our immediate surroundings.
But we know that if you expand your your surroundings
(21:04):
a little bit, you see that space time is flat.
That's how gravity works, and that's what makes the Moon
go around the Earth and the Earth around go around
the Sun. But we're talking now about global curvature of space,
which really means universal curvature of space, which actually sort
of means observable universe curvature of space, right yeah.
Speaker 1 (21:22):
And we're trying to use our understanding of two D
space to sort of bootstrap our way to understand the
curvature of three D space. So if you're like on
a flat surface and you shoot two parallel lines out
like two laser beams, then they'll never cross each other.
This is Euclid's famous geometry, and that's why we call
it Euclidean geometry. These two parallel lines will never meet.
(21:43):
And you can also do that in three dimensional space.
Right now, just imagine the universe is having three directions
shoot two parallel lines, but in any direction in xyz
they will never meet. In flat space, the extension of
flat space from two D three D is pretty straightforward.
Speaker 2 (21:58):
I wonder if, like we even have to go to
a two D analogy, why can't we just talk about
the curvature space in three D.
Speaker 1 (22:03):
Yeah, I think three D flat space is pretty straightforward,
but it can help us understand the curved space to
start in two D or at least let's give it
a shot. In two dimensional curved space, if you fire
two laser beams in the same direction, they will eventually cross.
Like if you're on the surface of the Earth and
you fire two laser beams in the direction in the
north pole, they'll cross when they hit the north pole.
Speaker 2 (22:24):
Right What I think this is why it's confusing, and
I wonder if we can just stick with three D
like three D flat space. If I shoot two lasers
out in space, they're never going to meet. These two
laser beams, they're never going to meet. Right now, let's
talk about curve three D space. I shoot two lasers,
and the lasers are going to do one of two things, right,
They're either going to come towards each other or bend
(22:45):
away from each other.
Speaker 1 (22:46):
That's right. And whether they come towards each other and
away from each other tells you the sign of the curvature.
Positive curvature, they'll come towards each other. Negative curvature, they'll
veer away from each other, never meet.
Speaker 2 (22:58):
Now this is super weird because what's bending the path
of the lasers just the curvingness of space.
Speaker 1 (23:05):
Lasers and light follow the curvature of space. They're like
tracers that tell you how space is curved. So light
moves in straight lines through curved space time, right, But
that leads to curved motion in space.
Speaker 2 (23:20):
So you're saying that space might have a property to
it called curvature, which would to us make the light
beams not go in a straight line.
Speaker 1 (23:28):
That's right. If you assume space is flat, then light
appears to be moving in a curve. If, however, space
itself is curved, those grid lines themselves are curving, then
light is moving along those grid lines. It's just the
gridlines themselves are curved.
Speaker 2 (23:41):
Okay, So now I feel like there's a third possibility.
So like, if I have a laser shooter on my
right hand and a laser shooter on my left hand,
and I shoot them perfectly parallel to each other. If
space is flat, they're just going to keep going straight
parallel forever. But if space is curved, there's some things
that can do. They can bend towards each other away
from each other. But I feel like they could also
(24:03):
like bend perpendicular to each other, like maybe my right
laser beam drifts up and my left laser being drifts down.
What does what would that mean?
Speaker 1 (24:13):
Isn't that the same as bending away from each other?
Speaker 2 (24:15):
I guess if I just turn my head sideways, what
if they spiral around each other? Can space be twisty?
Speaker 1 (24:22):
Space can have all sorts of weird combinations. I mean,
in general relativity, space can doesn't even have to be
totally connected. So a laser beam can like disappear and
appear somewhere else, right, That's basically what a wormhole would be.
We're trying to talk about pretty simple constructions of space
where all you have is a single overall curvature.
Speaker 2 (24:40):
I guess if I shoot my laser beams and they
they go past a large massive object in space, like
the Sun, they're gonna curve, and if they're maybe on
opposite or different sides of the Sun, they're gonna curve
in a different way. And as they go through a galaxy,
they're gonna get pushed this way and that way. The
laser beams. But I think you're talking about like if
(25:01):
I shoot them maybe really far apart from each other,
and let them go for a really really long time
on average, Are they going to be moving towards each
other or away from each other? That's what you mean
by global curvature.
Speaker 1 (25:13):
Yeah, And your analogy is great because it lets us
make a connection between local curvature and global curvature. Local curvature,
as you say, is like, is there a star there
that's going to bend the path of my life? And
we sort of got our minds around a little bit
the general relativity that light is bent by masses. Even
though light has no mass, it follows the curvature of space,
and it's bent right now. Instead of having a local
(25:35):
mass like a star with a single point of really
high density, take that star and spread it out throughout
the whole universe instead. So now the universe is filled
with constant density of matter or energy that creates a
curvature of space that's constant. It's not like, oh, there's
a lot of curvature near that star. Let's have a
little curvature everywhere instead of a lot of curvature in
just one spot. And that's one way to think about
(25:57):
the global curvature of space. Think about a universe unit
formally filled with a certain matter and energy density.
Speaker 2 (26:02):
So like if the universe was infinite and was filled
with like evenly spread out gas or an evenly spread
out star, I guess what would happen to a laser beam.
Would it still curve or would it go straight?
Speaker 1 (26:15):
It depends on the density of that stuff. Right, there's
a certain critical density of energy in the universe. Below
a certain level, the universe will be negatively curved. If
it has exactly the right critical energy at this knife's edge,
the universe will be flat. If it's more than that
critical energy, the universe will be curved. So the curvature
(26:35):
of the universe itself of space is connected to the
energy density of stuff in the universe relative to this
critical threshold.
Speaker 2 (26:44):
I guess that's a little counterintuitive, because I would think
that if the universe is filled evenly with the same
energy or gas or matter or energy, then the laser
beam would just go straight because it's being pulled the
same way in all directions.
Speaker 1 (26:58):
Yeah. Unfortunately, general relativity isn't intuitive, and if you add
enough stuff to the universe, it curves up. It makes
the universe effectively like a sphere. That's only consistent with
universes that have a positive curvature, because imagine you take
every bit of space and you make it bend y. Now,
think about, like, what shapes can you build with that?
(27:19):
If you only have curvy pieces, all you can do
is build the surface of a sphere, or all you
can do is build a three dimensional version of the
surface of a four dimensional sphere if all you have
are bendy pieces.
Speaker 2 (27:31):
Yeah, I guess I'm still confused because I'm imagine this
scenario where the whole universe is filled with the same
gas or evenly distributed star. If I shoot a laser beam,
which way does it curve? If the universe is positively curve,
so curve up, down, left right.
Speaker 1 (27:45):
In a universe with positive curvature, if you shoot a
laser beam, it looks to you like it's going straight,
but then it hits you in the back of the head.
Speaker 2 (27:53):
What it wouldn't necessarily hit mean in the back of
my head.
Speaker 1 (27:55):
In a universe that's uniformly filled with matter that's positive curvature,
it will loop back around. It's like being on the
two dimensional surface of a three dimensional sphere.
Speaker 2 (28:04):
But I guess it maybe it might loop around a
few times before it hits me in the back of
the head.
Speaker 1 (28:08):
Any point on a sphere is the same, so it
doesn't really matter where you are, which direction you shoot it.
You always get the same results. From that point of view.
Speaker 2 (28:15):
I feel like then, now it's getting a little bit
into this idea of the how space is connected to itself,
which is at the case, is a curvature of space
necessarily the same as how space is connected to itself,
whether it loops around itself.
Speaker 1 (28:27):
It's definitely connected. Right, It's not the same, but it's
definitely connected. If space is flat, then the universe can
be infinite. If space is positive curvature, then the universe
can't be infinite. It can be finite but also have
no boundary, just the way like the two dimensional surface
of a three D sphere can be finite but unbounded
because it has positive curvature. So these two ideas are
(28:50):
definitely connected. The topology of space, the large scale shape
of space, and the curvature of space. The two things
are definitely closely linked. The curvature of space you can
deduce from the density of matter in that space. Because
general relativity connects those two things.
Speaker 2 (29:05):
Now, that was one laser beam. Now I take two
laser beams and I shoot it off into three D space.
And let's say that the universe has positive curvature. What's
going to happen to these two laser beams. They're eventually
going to hit each other.
Speaker 1 (29:18):
They will eventually cross. Yeah.
Speaker 2 (29:19):
Mmm. And if the universe is not positively curved, if
it's negatively curved, then they'll never hit each other.
Speaker 1 (29:27):
They won't hit each other, they'll veer apart.
Speaker 2 (29:29):
M all right. I think that gives us as good
of an explanation of what the curvature space is in
the universe, right, m hm.
Speaker 1 (29:37):
And all of these things together control the future of
the universe, like the curvature and the topology, the matter
density of the universe. That plus like the dark energy
of the universe, all these things work together to determine
how fast the universe is expanding. Is it expanding or
is it collapsing or is it steady state with no expansion.
(29:57):
All of these things play a role in determining the
future of the universe. Cool.
Speaker 2 (30:02):
Well, maybe talk about how you might measure the flatness
of the universe in like, how do we know whether
the universe is flat or not.
Speaker 1 (30:10):
So what we do is we measure this energy density.
And of course the caveat is we can only measure
it in the observable universe. We can't measure outside, and
so when we say the universe here, we always really
just mean the observable universe. All we can do is
measure the energy density, and we can say, is there
enough stuff in the universe to make it curved positively
so it wraps up on itself. Is there the critical
(30:30):
density so the space is flat? Or is there less
than the critical density so that the universe is open
with negative curvature. So the way we do that is
by measuring the amount of stuff, the energy density of
stuff in the universe.
Speaker 2 (30:42):
Oh, I see you measure the density of stuff. But
I guess we never covered why the density of stuff
determines the curvature of space, Like why is there a
critical amount that makes it negative or positive? Like wouldn't
any amount of stuff in the universe make deniverse positively curve?
Speaker 1 (30:57):
Yeah, that is a little counterintuitive, But a totally empty
un one with no matter or energy in it at all,
would not have flat space. It would have negatively curved space.
So you need a little bit of stuff in the
universe to counteract that.
Speaker 2 (31:11):
Whoa wait, So if I had an empty universe, like
no stars, no planets, no galaxies in it, and I
shoot to laser beams, they're going to diverse from each other.
They're not just going to stay parallel to each other forever.
Speaker 1 (31:22):
Yeah, that's right. This is one of the situations we
can actually solve in Einstein, the general relativity situation with
nothing in the universe, totally empty, no matter, no energy,
no dark energy. And in that case, the universe has
negative curvature, so you have to add stuff to the
universe to make it have no curvature or positive curvature.
Speaker 2 (31:41):
Oh so even no dark energy like this sort of
necessary amount of stuff in it is not related to
the expansion of the universe either, or do you assume
the expansion of the universe or not.
Speaker 1 (31:53):
This does not determine the expansion of the universe. All
these pieces together, the curvature, the density, the dark energy,
all these things together determine whether the universe is expanding,
whether that expansion is accelerating. It's a whole complex dance,
but just the curvature of the universe is determined by
the matter and energy density. If you have a certain amount,
then you sort of counteract the natural negative curvature of
(32:15):
space and you get a flat universe. If you have
more than that, you get a positive curvature. If you're
less than that, you get negative curvature. So a flat
universe is sort of balanced on a knife's edge. You
have to have like exactly the right amount of stuff,
and it's not a big number, Like the critical density
right now is about five protons per cubic meter.
Speaker 2 (32:33):
I guess that's weird that space by itself has negative curvature,
like pure space OG space. If you shoose laser beams,
they would diverge. Isn't that weird because shouldn't space be
like neutral or totally empty.
Speaker 1 (32:47):
Well, intuitive concept of space doesn't even allow it to
be bent, right, So you have to already let go
of those intuitive ideas and think that space is something
quite different from what we imagined as these weird properties.
It's a little bit more complicated than what we've described
because the amount of stuff you have to add to
space to avoid this negative curvature actually changes over time.
(33:08):
It depends also on the expansion of the universe. So
there's a lot of complex moving parts here that we're
trying to distill down.
Speaker 2 (33:14):
But I guess the main takeaway is that space by
itself has negative curvature, but because we have stuff in it,
matter and energy, then it's possible for space to be
flat because that's what the effect of energy and mass
does to space, is it makes it more positively curvy.
Speaker 1 (33:31):
Yeah, and we can measure the curvature of space by
measuring the matter and energy density of the universe. So
we go out we measure that, and that tells us
what curvature we have in our universe. The magnitude of
that curvature can also change the sign can't. If you
have positively curved space, it's always going to be positively curved,
but it can get more positively curved or less positively curved,
(33:53):
like the universe has positive curvature, can collapse on itself,
making itself more and more positively curved, or universe it's
open can expand really really rapidly and get less and
less curved. But they can't flip over. You can't start
from the universe as positively curves and end up with
the universe.
Speaker 2 (34:07):
That's negatively curved unless maybe the density of energy and
matter decreases enough. Isn't that possible? No, As like you said,
it depends on that density. What if the density changes.
Speaker 1 (34:17):
The density definitely does change, right, and we'll talk a
little bit about how that density is changing and how
we understand how it's changing. But you can't change the
curvature of the universe. You can't go from positively curved
space to negatively curve space. That would correspond to like
changing from a finite universe to an infinite universe, which
you can't do right. You can't take the service of
(34:38):
a sphere and snap it out to an infinite plane.
Speaker 2 (34:40):
You can pop a balloon, you can flat a birthday cake.
Speaker 1 (34:44):
That's one of the confusing things about these two D analogies, right,
is that you're imagining it in a three D space.
You're thinking about really a two D service on a
three D sphere. But in those analogies, the two D
surface is all there is, so you can't really flatten
it all.
Speaker 2 (34:59):
Right, Well, into what would happen if you change the
density of matter and energy in the universe, And then
let's ask the big question, why is the universe flat?
But first, let's take another quick break. All right, we're
(35:25):
asking the question why is space flat? Or I guess
why space so flat? Because it's maybe flatter than what
you expected.
Speaker 1 (35:31):
Yeah, when we go out to measure the curvage of
the universe, we find something kind of surprising. We find
that it's really pretty flat. Like there's this critical density
five protons per cubic meter, And we go out to
measure the amount of stuff in the universe. We add
up all the mass, the stars, the galaxies, the dark matter,
and also the dark energy. All of that stuff. It
(35:52):
adds up to like very very close to exactly the
critical density. It's within one percent, which is about our
uncertainty of the critical density, which tells us that space
is either flat or very very close to flat. And
that's kind of a surprise because we don't think the
universe likes to be flat.
Speaker 2 (36:11):
I guess before we go, I have more questions about
what you just said. Well, first of all, how do
we measure the mass and energy density of the universe?
And second of all, how do we know what amount
you need for the universe to be flat?
Speaker 1 (36:24):
So how we measure it is several different ways. We
can use like the cosmic microwave background radiation. This is
radiation from about three hundred thousand years after the Big Bang,
where the universe was very hot and dense with its
bright plasma, and then it cooled off and formed neutral
atoms and light could propagate. We can still see that light.
That light was made everywhere in the universe, and it's
(36:44):
flying around everywhere, and some of it has just reached
Earth from places that used to be very very far away,
and we can use it to sort of look at
what the universe looked like at that time, and there
were little bumps and wiggles in it. It's not completely smooth.
It's like a little bit of a frothing quantum plasma.
And from the size of those wiggles, we can tell
how much energy density there was in the early.
Speaker 2 (37:05):
Universe based on some theory that you have about how
the universe formed and how these things balance out with space.
Speaker 1 (37:11):
Relying basically just on general relativity. I mean, we assume
some model of the universe, but it's based in general relativity.
Doesn't depend on how the universe formed or what came before.
It just depends on the size of those fluctuations in
the early universe and then how those propagate through an
expanding universe to us.
Speaker 2 (37:28):
Okay, so that's one way to measure it.
Speaker 1 (37:30):
So that measures the total energy density like the dark
energy plus the dark matter plus the normal matter density
in the early universe. We can also measure it by
looking at the acceleration of the universe, like looking at
supernova seeing how fast they're moving away from us, or
looking at cephids. This expansion rate of the universe also
helps us measure these various components. So the components of
(37:51):
the energy density of the universe are the dark energy,
the normal matter, and the dark matter, and the super
nova measurements the acceleration of the universe help us measure
the dark energy component minus the matter component, because that
determines the expansion of the universe. So there's like a
bunch of different components here, and we have different ways
to measure each one's or combinations of each one, to
(38:11):
help us in down exactly what those contributions are. Dark
energy is of like seventy percent of the critical density.
Matter is like thirty percent of the critical density, where
most of that is dark matter, and they add up
to basically this critical density.
Speaker 2 (38:25):
This is from this CMB measurement, or from all measurements.
Speaker 1 (38:28):
The CMB measurement tells us the total density. The supernova
tells us the dark energy minus the matter the difference
between those two because they work against each other when
controlling the expansion of the universe. There's another measurement, the
buryon acoustic oscillations, that tells us about like how matter
was sloshing around in the early universe and made these
sound waves back when the universe was super duper dense.
(38:50):
Sound traveled at nearly half the speed of light, and
the speed of that sound depends on the density of
matter in the universe, and we can still sort of
see the universe ringing from those oscillations in the early universe.
That separately measures just the matter portion. So we have
these different pieces of the pie, and they all add
up to make exactly one pie. And the fascinating thing
(39:12):
is that they didn't have to write it could have
added up to anything. It could have added up to
be twice the critical density or half the critical density,
but it adds up to bang on just the critical
density to within one percent.
Speaker 2 (39:23):
I see. So you're saying we've measured the energy density
of the universe, and according to what we think is
the laws of the universe, according to general relativity, we
have just enough mass and density to make the universe flat,
which means if I shoot two lasers out there in space,
they're not going to hit each other, they're not going
to drift the part, they're not going to hit me
in the back of the head. Those two laser beings
are just gonna keep going forever exactly.
Speaker 1 (39:45):
And this is kind of a surprise to physicists because
they think the universe doesn't like to be flat. Like
the flatness of the universe is not a stable thing.
If you're just above the critical density, if you're like
a little bit more in the critical density, then the
universe tends to collapse and become more and more dense,
and you move away from the critical density. If you
have less than the critical density, you're below it, then
(40:07):
the universe is open. It tends to expand and dilute
itself away from the critical density. So either you're exactly
bang on the critical density, in which you're stable like
a pencil balance on its tip, or you're a little
bit above and a little bit below, and then you
very quickly veer away from it. So sort of a
mystery how we're still so close to the critical density
after billions of years.
Speaker 2 (40:28):
What do you mean it's unstable like a pencil. What
does that mean?
Speaker 1 (40:31):
It's unstable, and that if you move away from the
critical density a little bit, the universe moves away even more.
It's like a pencil balance on its tip. Right, it's unstable.
You have it, a tiny little push, a fly lands
on it, air blows by it really gently. It's going
to tend to fall over.
Speaker 2 (40:45):
Wait to Like, if you measure the density of the
universe and it's a little bit more than the critical
amount of density you need for a flat universe, then
the density is going to increase over time, Like the
universe is going to get more and more denser.
Speaker 1 (40:58):
Exactly. If you have more in the critical density, the
universe will contract, right, and things will get denser and denser.
You'll end up with like a big crunch.
Speaker 2 (41:06):
You mean, like the expansion of the universe will reverse.
Speaker 1 (41:08):
Yeah, exactly. In the opposite scenario, where you lessen the
critical density, things expand forever and things get more and
more dilute, So the density drops right as the universe expands,
the density of matter drops. As the universe contracts, the
density of matter increases, and so if you're not at
the critical density you tend to veer away from it
pretty quickly. And we're like billions of years into the
(41:29):
history and we're still super close to the critical density,
which was a big question in cosmology. How can you
stay so closely balanced so long?
Speaker 2 (41:37):
I feel like now we're tying it to the expansion
of the universe. So the critical density is tied to
the expansion, like if the universe is positively curved, then
the universe is going to contract eventually.
Speaker 1 (41:46):
The courage of the universe definitely plays a role. The
critical density and the curvature, together with the amount of
dark energy, determine the expansion. You can have a universe
that's positively curved and expanding if you have enough dark energy,
because dark energy can overcome this critical density, that you
could have a universe which expands. But in the simple
scenario where you take out dark energy for the moment
(42:07):
and just have a universe with only matter and radiation,
which was basically the scenario of our universe for the
first nine billion years when dark energy was negligible, and
then the universe above the critical density will contract and
increase the density, and the universe below the critical density
will expand and decrease the density. So they did this calculation.
They're like, well, in that scenario, how close do the
(42:28):
universe have to start to the critical density to end
up at one percent. The answer is we had to
be within the critical density to within ten to the
minus sixty two. If you're anything above that, then the
universe would have expanded like crazy or contracted like crazy.
So it seems really, really weird that we end up
with a universe so close to flat when the universe
(42:49):
likes to veer away from flatness.
Speaker 2 (42:51):
Well, that's a really tight requirement for this density that
we need at the beginning of the universe. It kind
of seems like too much of a coincidence.
Speaker 1 (42:59):
It does seem like too much of a coincidence, and
physicists don't like coincidences because the density of stuff in
the universe doesn't seem to be determined by anything. It
could have been anything, So for it to be like
exactly close to one complete pie of the critical density,
it seems too neat. Physicists like a reason for these
numbers to line up, and there is an explanation for it,
and the explanation is cosmic inflation. So you know how
(43:21):
the universe is expanding now, and that expansion is accelerating.
We also think that the universe expanded very very early
on in its history. But like a huge factor, this
accelerating expansion we call inflation. It's an expansion of like
ten to the thirty in like ten to the negative
thirty seconds. And this kind of accelerating expansion tends to
push the universe towards flatness. It makes the universe more flat.
Speaker 2 (43:45):
But isn't it still sort of too much of a coincidence,
Like I wonder if maybe our theories are wrong, or
maybe there's some sort of mechanism that keeps the universe flat.
Speaker 1 (43:54):
Well, we don't know if inflation is true, and it's
just one of the possible scenarios, And you know, maybe
it's just a coincidence, and we just happen to in
the universe that was that close to flat that we
ended up in the universe that didn't overexpand or didn't
collapse on itself. But inflation makes it less sensitive. Inflation says,
you know, you could have started with lots of different densities,
and inflation would have made your universe have the critical
(44:15):
density early on, So you could have started with half
the density or one and a half times the critical density,
and inflation would have made your universe super duper close
to the critical density.
Speaker 2 (44:24):
Meaning like you might have started with too much stuff
in the universe, but then some mechanism stretched out the
universe enough so that you had the critical density.
Speaker 1 (44:34):
Exactly the math of inflation. In fact of any accelerating
expansion in the universe tends to push the universe back
towards the critical density. So if you had too much,
inflation would stretch out the universe in just the right
way to make it have the critical density. Just like
if you're standing on the surface of a tiny sphere
like a beach ball, it looks really really curved. But
then if somebody expands it rapidly by a factor of
(44:56):
ten to the thirty, then now you're standing on the
surface of a huge it looks flat. Right, So a
bigger sphere looks flatter and then a small sphere. In
the same way inflation pushes the universe towards less.
Speaker 2 (45:08):
Curvature, does it also work the other way, Like if
the universe had started with too little stuff in it,
the density was too small. Mood inflation have somehow adjusted
or slowed down or compress the universe somehow. Would you
have had deflation in order to keep the universe flat?
Speaker 1 (45:26):
Yeah, that's a great question. It does. It pushes it
towards critical density from either direction, which is pretty cool
how the math works out.
Speaker 2 (45:34):
So it does do deflation.
Speaker 1 (45:35):
Well, they still consider it inflation because you're still stretching
it out.
Speaker 4 (45:38):
You know.
Speaker 1 (45:38):
Imagine like a hyperbolic surface. You stretched it out, so
the negative curvature goes towards zero curvature. So inflation drives
you towards zero curvature from either direction.
Speaker 2 (45:49):
So it's more like stackflation or less flation.
Speaker 1 (45:54):
I don't know enough economics to know if an analogy
is accurate or not.
Speaker 2 (45:57):
Yeah, I mean it sounds like something they say in
the news.
Speaker 1 (46:02):
And one fascinating thing about that is it means that
our universe right now is driving back towards flatness. Like
the brief history of the universe is you have probably inflation,
which makes the universe mostly flat, and then you have
a matter in radiation dominated time when the universe is
then driven by this critical density, and it continues to
expand that that expansion is decelerating because of the matter
(46:24):
dominated nature of the universe. And then like six billion
years ago, dark energy took over, right, because the expanding
universe dilutes out the matter and radiation, while dark energy
grows as a fraction. So now we have an accelerating
expansion again, which does the same thing. Any accelerating expansion
in the universe pushes you back towards zero curvature.
Speaker 2 (46:43):
Mmm. Interesting. I guess what that makes me think is
that maybe the universe is flat, Like it's just flat.
It's infinite and flat, and all these things we're seeing,
all these measurements and all these theoretical concepts, they kind
of have to work out to a flat universe, and
that's what we're seeing. Like maybe it's not sort of
like this mystery or this universe sitting on a nice edge.
It's just that's just the way that the verse is.
(47:04):
And to us, the math and the measurements look like
it could have gone either way, but it could never
had a chance.
Speaker 1 (47:09):
Yeah, it's possible. Right in the equations of general relativity,
this is curvature parameter. It's either plus one zero, or
minus one, and it can't change again. Right, You can't
go from a negative curvature to a positive curvature, and
our universe is just one of those. The interesting thing, though,
is that to have k equals zero, to have zero curvature,
you really have to have the critical density of matter
(47:30):
and energy. So it sort of depends on what question
you ask, Like you could ask, well, which of the
three curvatures is it? Well, maybe it's just zero, like
you say, but if you think about it in terms
of the continuous spectrum of matter and energy density, then
it has to have exactly the right number, which seems
like one option out of an infinite number instead of
one option out of three.
Speaker 2 (47:48):
Or unless the universe sort of like prevents the matter
and energy to be anything else, in case that wouldn't
make sense.
Speaker 1 (47:54):
Right, Yeah, we it'd certainly possible. And these questions are
really basic and also simple, And in a few hundred
years they might look back on this and be like, hah,
how do they imagine they lived in a curved universe?
Speaker 2 (48:04):
What a bunch of idiots, What a bunch of flat
footed idiots?
Speaker 1 (48:08):
But these are the questions we're asking, and we don't
know and the equations of general real too. They allow
for all three kinds of universe negative curvature, flat or
positive curvature. We just don't know which of those we
live in and why we've measured its space to be flat.
And you're right. Either it just is flat and it
started out balanced on that knife's edge and it will
always be there, perfectly balanced, or it has a little
(48:29):
bit of curvature, but then we don't understand why it's
still so flat unless you do something early on, like inflation.
Speaker 2 (48:35):
Well, I think the idea is that maybe the universe
is flat, which means that the pencil is not upside down,
like maybe the pencil is hanging from the tail, and
that it can only sort of be that hanging down
and the universe would push it down if you try
to move the pencil. That's a possibility. Sounds like it's
still a mystery why the universe is flat. We're measuring
(48:55):
it to be flat and it seems to be staying flat,
which means that the universe either is flat or the
universe is not flat, but something is making it suspiciously flat.
Those are the two options, right exactly.
Speaker 1 (49:08):
If it's not exactly flat, then something is keeping it
very very close.
Speaker 2 (49:12):
To flat, which would be the universe, which means the
universe it's flat.
Speaker 1 (49:18):
The universe is either exactly flat or it likes to
stay very close to flat.
Speaker 2 (49:22):
I'm just trying to propagate flat universe theories and say
that it's all just a conspiracy by the universe.
Speaker 1 (49:28):
You're curving my brain.
Speaker 5 (49:29):
Man.
Speaker 2 (49:30):
All right, Well, the next time you look at into space,
think about what happens to those photons that you're seeing.
Did they come straight at you or did they get
bent by space? Are those photons curving their way through
the universe, maybe even a close circular universe, or did
it come straight at you from really far away.
Speaker 1 (49:48):
Either way, we're grateful that photons are arriving here on
Earth and that we're smart enough to figure out the
messages that they send about the nature of this incredible cosmos.
Speaker 2 (49:57):
Or at least we think we're smart enough. It might
just be falling flat on our facebooks.
Speaker 1 (50:01):
We're feeling good about being smart. Whether or not we
are all right.
Speaker 2 (50:04):
We hope you enjoyed that. Thanks for joining us, See
you next time.
Speaker 1 (50:16):
Thanks for listening, and remember that Daniel and Jorge explain
the universe is a production of iHeartRadio. For more podcasts
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Hosts And Creators
Daniel Whiteson
Kelly Weinersmith
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