How can we measure the curvature of space?

Daniel and Jorge bend their minds (and yours) around the curvy topic of bent space.

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Episode Transcript

Speaker 1 (00:08):
Hey, Daniel, what concept in physics twist your brain more
than anything else? I think it would have to be
general relativity because it's super beautiful and gorgeous, but it's
also really hard to actually wrap your mind around. Isn't
that all relative? Though? But I guess what makes it
hard all the math. There's a lot of math, but
fundamentally it's the concepts. You know. It's just such a

(00:29):
different view of how to see the universe. It says
that space is like a thing and it's invisibly doing
stuff that we're blind to. Yes, pretty well, and now
we got like neutrinos, dark energy, dark matter. Seems like
most of the universe is invisible to us. We're definitely
more clueless than clued in when it comes to the universe.
It's all a giant game of clue. You know. It

(00:51):
was the dark energy that killed the dark matter in
the space library within lutrinos. That might be the first
time neutrinos ever killed anybody. Hi am Orhammy cartoonists and

(01:15):
the creator of PhD comics. Hi, I'm Daniel. I'm a
particle physicist and a professor. You see Irvine, And if
I could choose the way I go out, I'd like
it to be with neutrinos. Oh yeah, why is that?
Because it sounds unique. You know, I'd like to be
the first person ever killed by neutrinos. I don't even
know if that's possible. Like, imagine the crazy intense neutrino
beam necessary to even heat you up a little bit,

(01:35):
not to mention kill you. Sounds like you thought about
this a lot about how to use neutrinos to kill someone. Yeah,
for about ten seconds so far. I guess it is hard,
but I guess with enough of them that they could
be deadly, right, Yeah, if you have a powerful enough beam,
they could actually deposit enough energy and you had to
fry you just like a laser. Oh, neutrino lasers. Would

(01:55):
it be like a neutral tan? It'd be like a
little neutral tan. Right, because this newtrie No, maybe our
next product idea should be neutrinos blocking pree. Now there's
a science scam. Add the word quantum to it and
it'll sell cell cell good of a reading of NPF
one thousand lutrino protection factor. But anyways, welcome to our podcast.

(02:16):
Daniel and Jorge explain the Universe, a production of iHeartRadio,
in which we try to beam into your brain all
of the incredible mysteries and knowledge about the universe without
toasting it. We try to protect that precious little blob
of matter while also injecting ideas and questions and curiosity
into it. We hope to stimulate your brain to think

(02:36):
about the nature of the entire universe, what it looks like,
what it seems like, what it's actually doing behind our backs,
without toasting it aggressively, or at least neutraally toasting it.
Because it is a fascinating universe full of amazing things
out there, and it's an ever changing universe. It's a
universe that's expanding and growing and shifting and moving and

(02:57):
rotating space doing all kinds of things. Is doing a
whole lot of things, and as you mentioned, is doing
a lot of things that we can't see. Our senses
are like tiny little portals into the vast and complex
workings of the universe. Most of what's out there is
really invisible to us. Yeah, and that's one of the
wonderful things about the universe. So that it doesn't reveal
itself right away, we need to probe it. We need

(03:19):
to think about it. We need to find clever ways
to figure out what's going on out there, and so
the history of physics is filled with people noticing something weird,
something they can't quite explain, something that doesn't quite fit.
Usually that's a thread we can pull on to unravel
an entire story about something going on in the universe.
We weren't even aware of the discovery of neutrinos being

(03:42):
pumped out from the Sun, the discovery of vast quantities
of dark matter floating out there in space and changing
the way that galaxies spin and the entire universe is formed.
And that's not the end of the invisible things that
the universe is doing right under our noses. Yeah. Maybe
one of the most mind blowing revelations about the universe
that humans have discovered in the last hundred or so

(04:03):
years is this idea that space is not fixed. It's
not this kind of emptiness that we are used to
in our everyday lives. As we move around in space,
space is actually bending and curved. Yeah, space has a
lot more properties then Isaac Newton might have imagined. It
can do stuff. It's not just there. It's not just

(04:24):
the emptiness, the lack of stuff. It is actually a physical,
dynamical thing that has properties and can affect things in
all sorts of important ways. Yeah, and so one of
the most interesting facts about that is this idea that
space can curve, that space is not just straight up
emptiness with nothing in it. It can actually kind of bend.
This idea that space can be described geometrically is having

(04:47):
curvature is of course one of the great insights that
underpinn Einstein's theory of general relativity. We've had this idea
for about one hundred years and it completely reshapes the
way we think about the universe. But still going to
be pretty tricky to understand what it means. What are
we talking about here? If you have a chunk of
space in front of you, what does it mean for

(05:08):
it to be curved? And is it possible to actually
see it? This is literally a mind bending topic. If
your mind is part of space, then yes, bending of
space will also bend your mind. I do feel like
my head is in outer space a lot of the time,
or outer space or outer space both. We want to
blow your mind into outer space when neutrino lasers, is

(05:31):
that where all this is going neutrino lasers are not
really very useful for anything except for joking about how
Daniel wants to go out. Well, and technically would they
be called lasers or lasers? M yeah, good question. I
guess it depends on the frequency, right, But it'd be
pretty tricky to build an apparatus that could resonate or
focus neutrinos. Neutrino optics would be quite challenging to design.

(05:55):
It's even hard to make X ray lasers. So I
think neutrino lasers are pretty far from our technology capability.
So I can safely joke about using them to fry
my brain. Well, they're also pretty far from the topic.
I don't know how we just can I need degree attorney. Here.
We were almost on track there. We're talking about the
curvature space and how space is kind of bendy, and

(06:17):
so today on the program, we'll be asking the question
can we measure the curvature of space? Maybe we should
be measuring the curvature of the podcast, Like can we
actually keep a conversation going in a straight line or
do we constantly bend off the topic into other areas

(06:37):
like neutrino lasers. I think the experimental data says that
we do bend a lot, sometimes in ninety degrees, sometimes
three sixty degrees. Yeah, and sometimes those are the best
moments on the podcast when we talk about something totally
unexpected and discover a fun little corner of physics. Yeah,
but let's maybe stick to the straight and narrow here
and stay on the topic of the curvature space. This

(07:00):
is an interesting topic because, first of all, maybe a
lot of people out there, at least maybe in the
general public, don't know that space can curve. Yes, spatial
curature is really the foundation of general relativity. It's the
idea that gravity is not actually a force, but that
the reason things move as if there was gravity is
because space is invisibly doing this thing. It's bending, it's curving,

(07:21):
it's changing how things move through it. It really requires
complete shift in your understanding of gravity and what the
universe really is all about. Now, technically, Daniel, don't we
need to say that we're talking about the curvature of
space time? Right? Yes, because space by itself doesn't really bend.
It's really more like a bending if you include time
into it. Well, technically I think space does bend, but

(07:43):
you're absolutely right there. The equations and the important like
conservation laws are expressed in terms of space time because
relativity takes time and treats it as the fourth dimension
of space. So really it thinks about a four dimensional object,
not just three D space. So yes, space time is
more accurate description. Right. Wait, are you saying that three
D space bends or it's only that we should really

(08:06):
be using the word space time to mean the four
D concept is what bends? Well, each dimension does bend, Right,
X bends, why bends, Z bends, So space itself as x,
y Z does bend, but time also bends, and they
all sort of bend together. And that's one thing that
Einstein realized is that it makes much more sense to
think of these as four components of one larger mathematical object.

(08:28):
But each individual one does bend the way. For example,
time bends, right, that's time dilation. It certainly does bend,
but it also bends in conjunction with the other dimensions.
That some of the beautiful mathematics of relativities. Seeing how
all four work together cool well as usual, we were
wondering how many people out there had thought about the
question of whether and how you can measure the curvature

(08:49):
of space. So thanks very much to everybody who answers
these questions for us. We'd love to hear your voice
on the podcast as well. Write to me two questions
at Daniel d Jorge dot com and I'll email you
a batch of questions for future episodes. To think about
it for a second, how would you measure the curvature
of space? Here's what people had to say. Yes, we
can measure the curvature of space. I think we did

(09:14):
that gravitational wave detection recently, and I know at least
like the calculations work out, so I'm going to go it. Yeah,
I know we can detect distortions due to gravitational lensing
from massive objects, but I don't think that was what
you mean. I don't know how we would detect the

(09:35):
curvature of space well, being within the space time continuum,
I would think you'd have to be outside of it
to be able to see the curvature. Yes, I don't
know exactly how it works, but probably we can measure
it with a light, with photos something, but I don't
know exactly. Oh this might work. If we can't measure

(09:58):
the curvature of space, why is general relativity all about
all right. Everyone seemed pretty positive about the fact that
you can do it. Yeah, it's definitely something we know
is happening out there, right, which is sort of cool
philosophically and conceptually to accept that this thing is happening
all around you. It's sort of invisible to you, but
it's necessary to understand how things work, right, to accept

(10:22):
that a big fraction of the nature of the universe
itself is invisible to us. Yeah, I guess it's kind
of a weird question because like if space bent and
right here in front of me, I would probably be
able to tell, right, Well, that's the question is how
could you tell, Like, imagine it was just space, no matter,
no particles, everything was totally empty. If you had a
chunk of space in front of you, how would you

(10:42):
measure its curac or could you measure it without its
influence on other things? Like you can't see it bent
the way you can look at a road and say, okay,
I can see that the road is bending ahead of me.
You can't do the same thing with space because it's
bending is not directly visible. What do you mean it's
not directly visible? Like if the space in front of
me curve. Put an i'd be able to see a curve. Well,

(11:02):
imagine an invisible road, right, If you can't see the road,
but you can follow the cars moving along it, then
that's the way you're seeing that the road curves. So
that's a difference between a visible road where you could,
for example, see that it's bendy even when there aren't
any cars on it, and an invisible road like at night,
if you can't tell where the cars are on the mountain,
but you can follow their headlights, so you can infer

(11:23):
where the road must be. In the same way, space
we can't directly see its curvature unless there's matter being
influenced by that space, we can't directly tell what the
curvature is. Well, I see what you're saying. You're saying space,
but itself is invisible. You can't like see space, and
so therefore how do you know if it's bending or not? Yeah, exactly,

(11:43):
And you might think, oh, that's obvious, right, we're talking
about space. Space is invisible because it's space, right, But
remember that we now know that space is a thing.
It has properties. So at each point in space, it
has this property, this amount of curvature that's somehow stored
in it, and yet we can directly see it. So
even though it's invisible, there is something to it. All right, Well,

(12:04):
let's dig into this topic. Daniel steps through the basics
of this, like, what do you mean by curvature? What
does it mean for space to be curved? So first
let's dispense with a sort of common misunderstanding of curvature.
A lot of people have seen this example of like
a rubber sheet with a bowling ball in it, and
have been told that this is an example or an
analogy for the curvature of space. And you know, this

(12:25):
is helpful in some ways because it makes you think
about how space could be bendy, but it's also really
misleading in some important ways. First of all, it treats
our universe as if it was two dimensional, just like
the surface of the rubber sheet, and it suggests the
bending is happening in some third dimension up and down.
So it suggests the bending is extrinsic, that it's like
relative to some fixed external ruler. But in our universe

(12:49):
we think that the bending of space is intrinsic. There
is no external ruler, no fourth dimension where our space
is sort of like bending out towards the bending of
space for us, and in general, relativities intrinsic, which means
it just changes the relative distances between things, like how
far two points are apart. I guess that's weird to
me because I think what you're saying, is it curvatual

(13:12):
is something that happens within space, not relative to anything
outside of it. But if it's not happening to anything
relative outside of it and we're all in space, I mean,
is that still curvature or is it just that's the
way space is? You know what I mean? Like, what's
the difference between a curve space and a man curve space? Well,
you can measure it. And what does it mean? Right? Well,

(13:33):
we know that space can be curved and it can
also be not curved, because we have chunks of space
in our universe that are not curved that are like
far from masses and energy, and chunks of space that
are highly curved near large masses or even so curved
that they become like one directional inside a black hole.
So it's definitely something that space can do, and space
can do differently. They have different amounts of curvature. Well,

(13:55):
I feel like you're now defining it relative to how
it's not curved. Right, You're saying it curves relative to
how it's not curve. But isn't that also used like
an external measure of it or an extremes definition of it. Well,
I think it's still relative, and you can use that definition,
as we will talk about in this episode, to construct
like ways to measure that curvature by, for example, passing

(14:17):
matter through it and seeing the influence on it. Right,
in curvespace, things that are not under acceleration don't appear
to move in straight lines, whereas in flat space they do.
So there's definitely a difference in the behavior of objects
in flat space and in curved space. And it all
comes down to this definition of relative distances. Right. This metric,
which is the solution to Einstein's equations, tells you the

(14:38):
amount of curvature at every point, and that tells you
how things move, and that basically tells you what the
shortest path is between two points in space. And so
it's all about the relative differences, not in reference to
any external ruler, but yeah, it is relative to some
internal ruler, right, which is flat space. That's true. Right,
So you sort of comparing it to like a universe

(14:59):
without any masses or anything energy in it basically, right,
which is yeah, which is kind of like thinking about
it as like the exterior measure of space, like relative
to not space, which is kind of like an outside
point of view. Right. Well, I think it's a nice
way to think about it as a benchmark, compare curved
space to flat space. That's definitely a nice way to
think about it. But that flat space doesn't have to

(15:19):
be an external metric. It's not like our curved space
is sitting inside some larger flat space that's being used
to measure it. We can measure the curvature internally without
referencing anything outside of our universe. Maybe that's what you
mean by intrinsing, is that you can measure this curvature
without knowing what it would be like without any masses
in it. Yeah, exactly. And it's amazing that we can

(15:41):
that we can detect this in our universe, And in
some sense it's kind of obvious to us, like we
notice the effect of curvature all the time because we
grew up experiencing it. Our experience of gravity turns out
not to be due to some mysterious force of gravity,
as Newton described, But it's the effect of curvature changing
how things move through space. So we experienced the curvature

(16:04):
space all the time. It's not subtle, all right. So
curvature is kind of a property of space itself. It's
not relative to some outside space that space sits in.
And so is it related to the force of gravity? Right,
And so Newton's idea was, look, gravity is a force.
I noticed the Earth pulls on things like this apple
or that bowling ball, or my bowl of yogurt or whatever.

(16:26):
And so Newton explained this thing. He observed that masses
tend to attract each other in terms of some force.
And he didn't understand like a mechanism of it. He
didn't understand deep down what's happening. He just described it
and said, here's a mathematical description for what's happening. I
have an equation that describes it. It all seems to work.
So that was Newton's description. But it turns out that

(16:47):
gravity is not actually a force in our universe the
way for example, electromagnetism is, or the strong force or
the weak force. It turns out it's an apparent force,
something that seems to be a force but is actually
caused by something else. But wait, I feel like you're saying,
maybe the electromagnetic force is apparent. It's not a real force.
It's an apparent force. Now I was saying the opposite,

(17:08):
that electromagnetism and the weak force and the strong force,
those are real forces. But that gravity is different. Gravity
is an apparent force. It's not actually a force in
the universe. It's just caused by a curvature. And because
we can't see the curvature, we need to invent this
force in order to explain what we are seeing. Oh right,
I got that backwards. So then the curvature space is

(17:28):
Gravity is your curvaturo space. It's not gravity. So gravity
is our way to explain the effect of the curvature
of space, because we didn't realize that space was curved.
We didn't understand it was happening. Let's take a simple
example of apparent forces we sort of invent to explain things. Say,
for example, you're driving a truck and you've got a
tennis ball in the back. Now, when your truck is

(17:49):
not going anywhere, or it's driving a constant speed. This
tennis ball in your truck is just going to sit
in the back. It's not going to roll forwards or backwards.
But now if you hit the gas and the truck accelerates,
then what happens to the tennis ball. It suddenly rolls
to the back of the truck. Right, But in your frame,
the frame of the truck, why is the tennis ball
rolling backwards? Right? There's no force on the tennis ball.

(18:10):
For somebody sitting in the back of the truck, they
just see it roll backwards. Well, I guess you know,
if you were there in the truck, you would also
feel that force. Right, Yes, you're back. You're saying, maybe,
like if you had a camera inside the truck filming
this ball, someone looking at the footage, would you see
the ball suddenly start to move? Yeah, exactly. Somebody would
see the ball suddenly start to move. And so they
would say, where's this force coming from? Right, there's nothing

(18:31):
touching it. What is pushing on the ball. And we
know the answer is that the truck is accelerating, right,
it's actually how you measure acceleration. But in the frame
of the truck, the camera that's sitting in the back
you can't explain it without adding some external force and saying, well,
there must be some external force on this ball, right,
So you add this apparent force in order to explain

(18:51):
the motion you see. It's the same thing is happening
like on a merry go round. If you're on a
merry go round that's spinning, you feel this apparent force outward. Right.
There's no real force pushing you off the merrygo round.
It's just the fact that it's spinning, which again is
a kind of acceleration, creates this apparent force. So if
you want to do like F equals M and you

(19:11):
want to explain all acceleration in terms of forces, you
have to create this apparent force to explain what's going
on when you accelerate the truck or when you're on
the merrygoround. Those are just examples of other places where
we've had to add apparent forces in order to explain
the dynamics that we're seeing. Well, I guess maybe I'm
a little confused on this subtle point because you know,

(19:32):
in the case of the ball on the truck, there
is a force going on, right, like something is pushing
the truck, but nothing is pushing the ball. Yeah, but
the truck is being pushed by the engine and the
wheels and the friction with the road. What I'm seeing
is the ball not being accelerated with the truck. But
there is a force going on, right there is there
is a regular electromagnetic force pushing the truck. You're exactly right,

(19:54):
and that's the key insight. There is a force on
the truck and therefore the full frame of reference there
is excel rating. So what you're really seeing there is
that the frame of reference is accelerating, which makes it
a non inertial frame, and the equation F equals MA
only works in inertial frames because there's no force on
the ball. If you want to understand the acceleration of
the ball from the point of view of your camera

(20:16):
in the back of the truck, there is no force
in the ball, like nothing is touching it, nothing is
pushing on it. Something instead is pushing the camera, which
is attached to the truck. It's changing the frame of reference.
So if you want to use F equals m A,
you have to add in a force to compensate for that.
So the acceleration creates this apparent force on the ball,
even though again nothing is actually pushing the ball, but

(20:37):
you see it moving as if there was a force
on it. Right. But I guess that's only because you
don't know that the truck is accelerating. But if you did,
you could figure it out, you could account for it
because of the forces that are there. No exactly right,
there's two different ways to think about this. To think, oh,
I'm in an accelerating frame, so I shouldn't be using
F equals MA, I have to account for the fact
that I'm accelerating. But if you didn't know that the

(20:57):
camera was accelerating, then you have to add a force
to account for it. That would be an apparent force.
And that's exactly our situation when it comes to curvature
and gravity. We can't see curvature. We don't know that
it's out there. In fact, for hundreds or thousands of years,
we didn't even know it was happening, and so in
order to explain the motion of objects as we saw them,
we had to create this apparent force we call gravity

(21:20):
to explain the things that otherwise didn't have an explanation.
Now we know that space is curved, like knowing that
the truck was accelerating, and that can be our explanation
instead of creating this apparent fictitious force. Let's dig it
more into this idea of curvature. And then finally, how
do you even measure something that's invisible out there in space?

(21:40):
But first, let's take a quick break. All right, we
are bending our minds here with the curvature of space,
and I have to say I got a little bit confused.

(22:00):
I feel like we've talked about this for hours and
hours on this podcast, but it's still kind of hard
to process. It's kind of hard to tell the difference
between like, hey, gravity is not really a force, it's
a space that bends, and the alternative point of view,
which is like, hey, maybe if you just look at
it differently, you can see it this way, that it's

(22:22):
a bending us space, you know what I mean? Like,
is it that we can see it as a bending
of space or that it is a bending of space? Oh? Yeah,
great question? Right? Is it just a philosophical distinction or
is it actually a physical distinction? Doesn't matter? The answer
is that it does matter. We know that it is
the bending of space, but most of the time it
doesn't matter. Most of the time, treating it like a

(22:43):
force and treating it like the bending of space give
exactly the same prediction for the Earth going around the Sun,
and for all sorts of things. In some edge cases,
some corner cases, some extreme circumstances, they do give slightly
different predictions. And that's how we know that Einstein's theory
was right and then Newton's is wrong. What are some
of these extreme cases. So there are a couple of examples.

(23:03):
One is like spinning masses. Another is the effect on light.
So Newton's theory predicts that spinning masses have exactly the
same gravity as masses that don't spin. Like if you're
an outer space and the Earth is spinning under you,
the gravity from the Earth is not affected by the
fact that the Earth is spinning. It just depends on
the amount of mass. But Einstein says, actually there's a

(23:23):
little effect there. If the Earth is spinning, it's like
dragging the curvature of space with it, and this causes
a weird, little twisting effect on things out in space.
We talked about a really precise experiment called gravity Probe B,
which actually measured this and confirmed that this is happening.
The other examples the bending of light. Newton's theory says

(23:44):
that masses attract there's a force of gravity between objects
with mass, but photons have no mass, and yet we
see they are bent by massive objects. Einstine's theory was
famously proven when we saw light being bent around the Sun.
This is gravitational insane, and that's light moving through curved space.
So there are some differences between the view that gravity

(24:06):
is just a force like Newton said, and that gravity
is just an apparent force due to the bending of space, right.
I know we talked about both of those cases before
in the podcast, but I guess maybe a question I
wonder if other people have, is that whether we're used
to defining gravity only as like what happens between things
with masses, But if you know mass is also energy,

(24:27):
what if you just expand that definition of gravity to
be what happens between things with energy and so then
you can include things like light and that would also
explain the bending of light, wouldn't it. Or like I
wonder if if you also include energy, then the spinning
of the Earth that could also be sort of like
extra rotational energy. I don't know, I'm just making things up.

(24:48):
I'm just wondering. No, it's really cool. Could you add
these features, these bells and whistles to Newton's theory to
make them work? And there's a whole bunch of people
trying to think about exactly how to abridge Einstein and
Newton's theory to make Newton's theory like a special case
of Einstein's theory, to sort of like put it as
a point in a larger sort of Einsteinian space. And
you can try to do that, but it doesn't quite work.

(25:08):
You know, for example, treating photons as if they have
energy and therefore gravity doesn't work because photons are the
same frequency, bend through space the same amount. It depends
on the curvature of space, not on the energy of
the photon. So it doesn't quite work because I guess
photons can have different energies to them. Yeah, photons of
different frequencies have different energies, but how much they bend

(25:29):
depends on the curvature of space, not on the energy
of the photon. Unless there maybe there's something you're missing. Yeah,
you can add more bells and whistles if you like.
Potentially it's possible for somebody to come up with a
modification to Newtonian gravity to make it work like Einsteins
and think about it as a force. You know, in
some sense, we can never really know what's real out

(25:49):
there and what is just our description of the universe.
But we have a very compelling description of all of
these effects using the concept of space being curved. It's
very susful and so we'd like to think that it's real,
but ultimately we never can know what's actually happening out
there as compared to our mental image of the universe.

(26:09):
All right, well, then we have to sort of accept
them that it's a real curvature, like it really does
ben It seems to be a very accurate description of
what's happening in the universe. So it's very tempting to
say it's real. You know, philosophically, what does it mean
for it to be real? It means that, like it's
happening even if we don't look like, if humans weren't
here to measure the curvature, space would still be bent.
So that's a philosophical claim, not a scientific one. That's

(26:32):
not something we could ever actually test. But yeah, it's
pretty convincing when you have a theory that works this well,
it feels like you've discovered how the universe is working
rather than just describing it. Well. Maybe one thing that's
a little bit also confusing is that in terms of
the curvature space, it's sort of like you can't tell
it's curved if you're in it. You can only tell
its curved if somebody's watching you from the outside. Right, Like,

(26:55):
if you were writing that light being being bent through space,
you wouldn't feel any force, is right, you would think
you were going in a straight line. But to someone
outside of you, you'd be like, oh, that like rain bent. Yeah,
you're exactly right. Anything moving according to curvature feels no acceleration.
Like if you built an accelerometer, and basically that tennis
ball in the back of a truck is an accelerometer,

(27:16):
something that measures whether there is acceleration. Say you have
an accelerometer with you and you're in a spaceship and
you're flying through totally flat space at constant velocity. You're
watching the accelerometer, nothing happens, no surprise there. Now, say
you're flying through curved space. As you say, could you
tell that you were flying through curved space? Just by
looking at stuff inside your ship and your accelerometer. After all,

(27:39):
you are bending, right, you're changing your direction. Well, the
answer is no, you do not feel any acceleration inside
your spaceship. Your accelerometer does not register any acceleration because
you're moving along the curvature of space. The accelerometer only
measures sort of like forces against the curvature of space,
like resisting gravities flow. So, yeah, the only way you

(28:00):
can measure that curvature is by fight, for example, comparing
your position to other objects out there. You mean, as
you were writing the lightbeam. Yeah, as you're writing the lightbeam.
This concept of freefall, of moving through space without any
other forces, just letting gravity control you, it is really
important in general relativity. That's the sort of like concept
of an inertial observer. Somebody who's like skydiving, they jump

(28:23):
out of an airplane. They're in freefall, ignore air resistance.
Newton would say, oh, they're being pulled down by the
force of gravity, right, and Einstein would say, no, they're
just moving along the curvature of space. There's no force
on them. They're just in freefall. And Einstein's right that
if you had like an accelerometer with you after you
jumped out of the plane, it would not measure any acceleration. Right.

(28:45):
Maybe this is where it gets sort of tricky and
you kind of have to include the definition of time
into it, right, because I guess if you jumped out
of an airplane, you would get moved, right, like your
pocisition in space would change. Yeah, exactly, even though there's
no acceleration, right. That's because in curved space time you
have to accelerate just to remain stationary. Right. The airplane,
for example, it's applying a force to stay up. It's

(29:07):
actually accelerating upwards. When you jump out of the airplane,
you are no longer accelerating. You're now in freefall, so
there are no forces on you because remember gravity not
a force. You're just moving according to the curvature space,
just like that space ship out in space moving through
bent space. It's not going to notice anything. You jump
out of the airplane. You're not going to measure any acceleration.

(29:28):
The airplane is staying up hopefully, and so it's accelerating
up right, just like somebody who's standing on the surface
of the Earth in order to avoid moving down towards
the center of the Earth. The Earth is accelerating them upwards.
It's providing a force, the ground is pushing them up.
It's actually accelerating them all upwards. You are in freefall.
You don't measure any acceleration. You measure everybody else accelerating upwards. Right.

(29:52):
I think maybe this is where you kind of have
to say the word space time, right, because I mean
you can't just say like, you're following the curvature of
space because that only works if you also include time
into the word. Absolutely. Yes, time is crucial here because
we're talking about motion. So you do kind of have
to say the word really that it's a curvature of
space time, right, Yeah, curvature of space time absolutely all right.

(30:14):
Like you said, it's kind of hard to know that
spacetime is bending around you if you're in it, if
you're being moved along its curvature, And so I guess
the question is how do you measure then that space
is being bent? What are some of the ways that
people do that? So the most straightforward way to test
weather space is bend is to see its effect on stuff, right,

(30:34):
This famous description of general relativity is that matter tells
space time. How to bend. Spacetime tells matter how to move.
So if you see stuff moving in straight lines, that
tells you that spacetime in front of you is flat.
If you're an inertial observer and you see things moving
in curves, that tells you that space time in front
of you is curved somehow. So you can just watch

(30:56):
the motion of objects, just like looking at those cars
to sending down the mountain at night, look at their headlights,
you can tell if the road they're on is bent.
So basically you have to be kind of like an
outside or observer, or I guess you have to sit
at a distance imagine what that space in front of
you would be like if there wasn't any bending, and

(31:19):
if something moves through there differently than it would through
empty space, then you know it's being a bent. Yeah. Say,
for example, you didn't know the Sun was there, and
you threw a planet into the Solar System and it
didn't fly right through. Instead, it bent and it ended
up in an orbit. Right, that's definitely not the motion
you expect through flat space, And so you can tell
that space is curved because the object is not moving

(31:41):
in a straight line. It's following the curvature of space.
It's on what we call a geodesic them hath a
particle follows if there's no acceleration on it, And so
you can tell, for example, that the space in our
Solar System is curved because the Earth is not moving
in a straight line. Right. I think we've talked about
this before. Like if you took out the Sun and
you replace it with a black hole with the same

(32:02):
mass as the Sun, it would be super tiny, right,
I think maybe around the size of a bowling ball
or something like that, which you would never see from
this distance, right, because it's millions of miles away, But
the planets would still keep orbiting the same way as
they would before. Yeah, I think the Sun would actually
compressed about three kilometers. But you're absolutely right on the
point of gravity. Our Earth would move around it in

(32:24):
the same way, and so space was like invisibly bent
by a black hole. Then you could tell, and that's
exactly what we do. At the heart of our galaxy.
We can tell that there's a black hole there even
though it's largely invisible by the motion of the stars nearby.
They whizz around as if there was some very massive
object there. Curving space. That's what I mean. Like a

(32:45):
three kilometer wide bowling ball, I want to see the pins.
Yeah yeah, but you still wouldn't see that from here, probably, right,
something an object three kilometers, why you probably wouldn't see
that from here, would you, Especially if it's a black
in a black backdrop. I don't know, if it's one
of those like swirly galaxy. Bowling balls might also bend
into the background. Oh yeah, they do have those glow

(33:05):
in the dark bowling balls. Yeah, exactly. And so that
seems sort of obvious, and maybe that sounds like a cheat,
like we're just saying, oh, gravity is actually the curvature space.
So anywhere you see the effective gravity, you're seeing the
curvature space, and therefore you know that space is curved.
But remember we also talked about the curvature space doing
things that just Newton's gravity can't do, like bending light

(33:27):
around the Sun. And this was Einstein's famous test of
general relativity. He predicted that in an eclipse, we would
be able to see the bending of light from distant
stars as it goes around the Sun. Right Like, during
an eclipse, right actisse, you can see the light race
kind of bend around the eclipsing moon. Actually, the bending
is of distant stars well behind the Sun, around the Sun,

(33:50):
and the reason we use the eclipse it is not
because we're looking for the light being bent around the Moon,
but just that then the Moon mostly blocks out the
Sun's light, so it's easier to see these stars are
very close to the Sun. In principle, you could see
this at any time. Stars that are sort of just
behind the Sun are having their light bent by it,
but it's pretty hard to do when the Sun is on.
So basically we use the eclipse to turn the Sun

(34:12):
off to block it, and then we can see the
stuff around it more easily. But also technically the sun
rays are probably being bent by the Moon in front
of the Sun. Oh right. Also, yeah, absolutely a little bit,
but maybe not noticeably. Yeah, for sure, you put your
hand up to block the Sun, and your hand is
bending the light rays of the Sun, right because your
hand curves space. Everything with mass curve space. It's a

(34:36):
pretty subtle effect. I mean, even the Sun bends this
light by like a thousands of a degree, so it's
pretty hard to see. All right. Well, I think what
you're saying is that one way to know if curvature
of space caused by a mass is to see if
things that fly near it, including light bed Yeah, exactly.

(34:56):
And one time on the podcast you made a really
cool point that the best way to see this actually
use like two beams of light, you like, shine a
laser through space and see if they stay parallel, right,
because if space is flat, then they will stay parallel forever.
But if space is curved, then they will bend and
they may even cross. Okay, So that's one way to
measure how a space can bend is if you see things,

(35:18):
the trajectory of things, even including light bending around something.
You know that bending relative to what you're looking at.
That means that there's something there and it's bending space.
What are some other ways that we can measure the
bending of space? Time? Yes, space time exactly, very good point.
And time is also bent with space, as you've said, right,
and so the curvature is not just in space but

(35:38):
in space time, which means that time is also curved.
And that's this feature we call gravitational time dilation. The
curvature of space makes clocks slow down. And this is
really super fascinating and different from the kind of time
dilation we're used to thinking about from velocity. Like if
you see somebody in a spaceship traveling really really fast,

(35:59):
we know that your view of their clocks sees their
clocks slow down. Moving clocks run slow. That's one really
cool effect, but it's actually totally separate from this kind
of time dilation. This is time dilation just caused by
the curvature of space. So if you're in a part
of space that has a lot of curvature, your clock
will run more slowly. And so if you look out

(36:20):
into the universe and everybody else has clocks and you
see their clocks running faster, that means that you are
in curved space. You looked at your clock and it
seems to be running normally. Everybody else's clocks are running faster.
They see your clock as running more slowly. So that's
one way to detect the curvature of space. M I
think you mean like the example of like you know,

(36:42):
you can measure the curvature of space by seeing how
they bend, how their trajectory bends in space. That tells
you there's something there, But like there might be a
situation where you can't tell that space is bent even
though there's something there. Like for example, if I shoot
a laser straight at a black hole, I'm not going
to see the path of the laser move were changed, right,
just gonna keep going in a straight line, I guess,

(37:03):
until it hits the black hole. But before that you
wouldn't be able to tell that space with bending unless
you use something else like time. Yeah, good point. If
you shoot a laser being directly at the heart of
a black hole, like pointed bang on to the singularity,
then its path wouldn't bend right because it's sort of
moving along that curvature, but it's time would bend right,

(37:23):
and so anything falling towards the black hole, it's time
gets dilated. And this is something we've actually measured. But
what would that mean for a laser though, Like would
you see the lasers slow down? So this gets into
very tricky territory and general relativity about measuring velocity of
distant things. If you are near those photons as they
pass you, you measure them as having the velocity of

(37:43):
the speed of light. If you are far away from
them and they're moving to curved space, then the rule
that light always travels at the speed of light no
longer applies. That only applies to flat space near inertial observers,
so you could actually see light travel are all sorts
of different weird velocities. You would see it's slow down, Yes,
it is pretty weird. You sort of have to need

(38:04):
to like plant the clock in that light laser beam
in order to know that the space was curved. Otherwise
would you know? I suppose by measuring its velocity as
a distant observer you could measure the curvature of space there.
But your right time is a really cool way to
measure the curvature as well. And this I think is
really cool because these are experiments we have done. We
shot a laser into the heart of a black hole.

(38:26):
Did I miss that headline? Unfortunately, nothing's so cool because
we don't have laser beams orbiting black holes. To do
these experiments. We have to make do with measuring the
curvature of space around our Earth. And so we've done
is built really really precise clocks and see that they
run differently at different altitudes for example. And again this
is not velocity based time dilation. This has not put

(38:47):
a clock up in a spaceship and orbit the Earth.
Really really fast. They have, for example, a super precise
atomic clock that they can raise and lower by like
a foot, and they can see a difference in how
fast it runs if they raise and low or just
buy one foot, because the curvature is different as you
move further away from the surface of the Earth. All right, well,
let's get into some of the other ways that you
can measure the curvature of space, and then let's talk

(39:10):
about what this all means. Man, But first let's take
another a quick break. All right, we're talking about the
curvature of space. It's bending my mind a bit. And

(39:31):
how you might measure this bending of space If you
didn't know, I guess if space was being bent, I
guess if it's not obvious, the space is invisible technically, yeah,
if you can't see the curvature directly, how can you
tell that it's there? And I love this philosophical question
of even if you measure it, do you really know
that it's there? Or if it's just some weird effect,
Like could somebody come up with another theory of physics

(39:51):
it doesn't require the curvature of space, but requires some
other weird change in our understanding of reality. That can
also explain everything we see, possibly, and then you might
be forced to believe that that's how reality actually is,
That space doesn't curve, it's actually this other thing that's happening. Yeah,
so we're sort of along from the ride as physics
is figuring it out. Is this shifting of the clocks

(40:12):
in relativity, like this idea that time slows down maybe
also another way to show that gravity is not like
Newton imagined it, right, because there's nothing in Newton's laws
that account for like time slowing down. Right, Yeah, great,
point is there? I don't know, No, there is not.
Newton thinks of space and time as absolute and universal, right,

(40:33):
So this is another feature of relativities, connecting space and
time together, tying it all up into one four D
mathematical object, and accepting that they're related to each other
and in special relativity, space and time are all twisted
up together. How you measure clocks depends on where you
are and how fast you're going, so they're definitely tied
together in a way that Newton never anticipated. Right. All right, Well,

(40:53):
we're talking about how to measure this invisible thing of
an invisible thing, and so what are some of the
other ways that you might measure the bend of space.
One really cool way to measure the bending of space
is to look at the geometry of objects. Like you
can tell if space is curved by building triangles or
by measuring the circumference of circles. And this is easiest
to understand if you think about like what happens on

(41:15):
the surface of a sphere versus like what happens out
in space. If you're like out in space and you
build a triangle and you measure its angles, you get
one hundred and eighty degrees. Now, if you're on the
surface of the Earth and you build like a really
big triangle, then you measure all of its angles and
add them up, you'll discover that they don't actually add
up to one hundred and eighty degrees. To add up
to a little bit more, because the angles of a

(41:35):
triangle add up to one hundred and eighty degrees only
on a flat surface, not on a curved surface. Well,
I guess only if you kind of project that shape
onto the surface of the Earth, right, you can still
have a perfect triangle. It's just sitting on top of
the Earth in a weird way, isn't it. Yes, if
you follow the curvature of the Earth, then that triangle

(41:56):
has an angle greater than one hundred and eighty degrees.
If you don't follow the curvature of the Earth in
your triangles like sort of awkwardly sitting on top of
the Earth, then yeah, it can still be flat, but
if it follows the curvature, it won't have angles that
add up to one hundred and eighty m. That's the
one way that you can tell if that the surface
of the Earth is curved, right, Yeah, exactly. You can
measure the curvature of the Earth. And that's sort of

(42:17):
a famous example, but it applies to other objects too,
and I think maybe people haven't heard about this, and
I think it's really cool. You can also measure the
curvature by measuring pie right like draw circle, measure the
diameter and the circumference. The ratio is pie, and on
a flat surface, pie is three point one, four, one, five, nine, etc. Etc.
But on a curved surface it's not right. On a

(42:38):
curved surface, the diameter gets longer. Instead of just being
like straight across the circle, it's now like rising above
the circle and coming back down. So pie changes as
space gets curved. I think what you mean is that
if you drew a circle across the equator, or if
you thought of the equator as a circle, and then
you try to measure its radius from the north pole,

(43:00):
you wouldn't get pie. You would get something else because
you're measuring the radius along the surface of the Earth. Right,
You're measuring this basically the curvature, the longitude basically line
which are longer than if you just do a line
through the center of the Earth on that circle exactly.
And so if you were like not aware that the
Earth was curved, you try this huge circle and you
walk from one part of the equator across the north

(43:23):
bold and then back down to your circle and measure that.
Then you would get an answer that's much longer than
just drilling a hole through the center of the Earth.
And so basically that's a measurement of pie. And so
pie is a measurement of curvature. And so if you
go out in space and make a really big circle
and then measure its diameter using a laser beam, you
can measure the curvature of that space by comparing what

(43:45):
you get to pie. But what if you make a
giant pie the size of the equator, wouldn't you still
be measuring pie and fill it with neutrinos? I can't
tell if you're joking. Are you talking to giant pie pie? Yeah,
I mean a giant apple pie to say, ride with
the diameter of the equator. But then you still measure pie. Well,

(44:07):
that's a good question. If you build a flat pie
out in space that's ignoring the curvature of space, it's
being held together by electromagnetic bonds which are really strong,
then it could still be flat, right, But if you're
following the curvature of space, you're using like a laser
beam to follow the curvature of space, then you would
not get pie measured across your giant apple pie, which
would have to cut I guess, with a neutrino laser

(44:29):
beam because it'd be so big. What kind of ice
cream do you serve with neutrino apple pie? I don't
even know. Obviously a dark ice all right. So that's
another way to measure the curvature space is using geometry,
which is like a sixth grade subject just measuring angles
between things, and they don't come out to be what

(44:50):
you would expect in flat space, then you know your
space is what are some other ways that we can
measure the vending space? So I think one of the
coolest ways is this experiment we talked about much earlier,
which measures frame dragging. This is an effect that doesn't
happen in Newtonian gravity at all. So, as we said before,
the Earth is spinning, and as it spins, it's sort
of like drags space time with it a little bit.

(45:13):
And so if you're an object out orbiting the Earth,
you feel a different force because the Earth is spinning
than you would if it wasn't spinning. Would you feel
is a little torque, like a little twist, not just
a force inwards towards the center of the Earth, but
like a little twist that spins you a little bit,
because how space is sort of flowing over you. So
there's these awesome experiments called gravity Probe B that built

(45:34):
like the most spherical objects known to man, these super
precise gyroscopes out in space that were like mind in
Brazil and then polished by like German grandmothers for years
and years and years, and these were able to measure
this very very small effect. But it's real, you know,
we have a whole episode about this. But this sort
of related to tidal forces too, right, Like, if you
have an object down in space near Earth spinning, some

(45:57):
things are sort of closer to it than others, and
so there's some delay in how the gravity kind of
goes from one end to the other. Yeah, exactly, this
only happens on objects that are not points, that objects
that have an extent, because as you say, they're experiencing
space differently, and so it's that relative effect across the
object that ends up causing the torque. So you're right. Conceptually,

(46:17):
it is similar to tidal forces in that way. The
effect is larger for bigger objects and zero for point
like objects. But this frame dragging is a way to
confirm that space can curve, but you sort of need
as guidance spinning object to cause that kind of effect. Yeah,
you don't get frame dragging around objects that are not spinning.
So in one way, it's really a test of Einstein's

(46:39):
theory to say, is this effect that Einstein predicts but
Newton doesn't, is it real in our universe? And the
answer is yes, And that's a consequence of all of
Einstein's math and his concept that space is curved. This
is a direct result of space being curved and how
space reacts and how that curvature reacts to mass, especially
spinning masses, and so in that sense, it's an indirect

(47:02):
confirmation that space is actually curved. The scientists who work
on this project, they think of this is like one
of the most direct measurements of the curvature of space.
Because so many other measurements could be explained by Newton's theory,
this one only can be explained by Einstein's theory. So
they take it as really proof that Einstein was right
and therefore space is curved or space can curve right, Yes,

(47:25):
can curve, are more likely space time can curry. Spacetime
has the ability to have curvature, which is really still
bongles my mind. Yeah, so I guess maybe to wrap
it all up, like, let's say I wanted to tell
if the space around our Solar System or even the
space around our galaxy was curved, maybe not due to

(47:47):
the mass of the galaxy, but just like overall, like
are we living in a spherical universe or are we
living in a cube universe? Or are we living in
a donut universe? Like how do you tell that you're
space around is curve Would you be able to tell
with any of these methods, or do would some of
these methods work, and other thoughts. So, so, to measure
the curvature is space on like a cosmological scale, you

(48:10):
could use this if you could construct a giant triangle
bigger than galaxies, or shoot laser beams between galaxies in
a big triangle, then you could use these methods to
measure them. But that's not really practical, right, But what
we can do instead is see the effect of space
on things that are already out there. For example, we've
looked at the cosmic microwave background radiation, this light left

(48:34):
over from just after the Big Bang, and that light
has like wiggles in it has like hot spots and
cold spots, and we know something about how big those
hot spots should be because of how much time things
had to like even out and cool off. And then
the curvature of space affects the size of those hot
spots as we see them. If space is curved in

(48:54):
one way, then the spots get bigger, they get like
blown up by lensing. If space is curved in another way,
they get shrunk. So we can actually measure like the
overall curvature of space near us by looking at the
size of hot spots in the cosmic microwave background radiation,
because I guess that light comes from really really really
far away kind of and all around us. Yeah, and

(49:15):
all around us. It's been traveling from billions and billions
of years, and so it's probing a really really big space.
It's like the oldest light that we can see. So
it comes from like the very edge of the observable universe.
What does that light say? Is the universe bending right
or left? That light says that, to within our accuracy
to measure it, the universe is flat. Like there are

(49:36):
little bendy spots here and there near galaxies, but that
overall there is no curvature to the universe. That the
universe seems to be mostly flat. That's sort of a
weird result, though, I would maybe say maybe you're just wrong,
And it's sort of like when you're trying to see
if something is right or let and you say, oh,
it's neither. I'm like, well, how do you know you

(49:59):
got it right? Yeah, it's a good question. And lots
of people have done these experiments with lots of different
technologies and look at lots of different aspects of it.
So we're pretty confident. But you know, there's also statistical
uncertainty there. It's like flat to within about one percent,
and so there's a possibility that space is a little
bit bent one way or the other sort of overall,

(50:20):
but we know that space is bent near us, right
effect of all, the mass of the galaxy in the
Solar System is definitely a curving space in our neighborhood.
What if we build a giant pie the size of
the galaxy. I'm in, I don't need to hear anymore.
I mean, well, technically you could do also do that
right that thing. That's what you meant earlier by giant lasers.

(50:41):
Like if you build a giant circle the size of
the galaxy and measure pie by measuring the conference and radius,
then you would be able to tell right that things
are bent. Hm. Yes, galaxy sized pie is a good
experiment in any case, because even if it turns out
to be inconclusive, it might still be delicious fun fun

(51:02):
fund all right, Well, it sounds like there are many
ways to measure the curvature of space, some of them
more delicious and or dangerous than others. But the amazing
fact is that is space time does bend. It's been confirmed,
and there are experiments you can do to measure it.
That's right, and it is possible to get a grasp

(51:22):
on what's going on with our universe understanding it's otherwise
invisible doings if we are clever enough, and if we
follow the threads of all those weird little things we
can't otherwise explain. I wonder what people who think that
the Earth is flat think about this concept, like it's
it's just too much for them, or do you think
there are people out there who say, yes, the Earth
is flat, but the universe is cur I don't know.

(51:45):
I'm a flat universe er. All right. Another exploration of
how mind bending and also space time bending the universe is,
I guess a good reminder that sometimes we think the
universe is one way from our local experience, but if
you go out there into the universe or to explore
extreme situations, it turns out that the universe is different.

(52:06):
Hope you enjoyed that. Thanks for joining us, see you
next time. Thanks for listening, and remember that Daniel and
Jorge explain the universe is a production of iHeartRadio. For
more podcast from my heart Radio, visit the iHeartRadio app,

(52:26):
Apple Podcasts, or wherever you listen to your favorite shows.