How can the Universe expand faster than the speed of light?

Daniel and Jorge blow their own minds talking about the faster-than-light expansion of the Universe 

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Episode Transcript

Speaker 1 (00:08):
Hey, Daniel, what do you think are the goals of
this podcast? You know, the same as they ever were,
blowing everyone's minds by revealing the incredible universe we live in.
But yeah, we've been doing this for a while. You
don't think people's minds are already blown? Can you get
your mind blown only once? Well, I mean, if you
really blow someone's mind, it's it's kind of a once
in a lifetime experience, right, or lifetime ending experience. While

(00:30):
not literally hoping to explode people's heads. Here, Oh, I
see there is another misleading physics metaphor. Yes, today, let's
blow up the phrase blow your mind. Well, let's just
hope we don't blow up the podcast. I actually do
hope the podcast blows up. Lets you mean blow up
like inflating? Then it just expands right exponentially? Did I

(00:50):
just blow up the blowing up? Hi? Am more handed
cartoonists and the co author of the book frequently asked

(01:11):
questions about the universe. Hi, I'm Daniel. I'm a particle
physicist and a professor at U C Irvine, and I'm
the co author of the book We Have No Idea,
A Guide to the Unknown Universe. Oh Man we're both
co authors on different books. We are exactly our fourth
friend by the two of us. By the way, let's
not mislead people here with our authored metaphors. You just

(01:33):
blew everybody's minds. Welcome to our podcast, Daniel and Jorge
Explain the Universe, a production of My Heart Radio in
which we hope to blow your mind by showing you
the incredible wonders of our universe, by diving deep into
the biggest questions about how the universe works, what is
at the edge of it, why can we see as
far as we can, and how is it possible to

(01:54):
see things that are racing away from us. We don't
shy away from asking the hardest, trickiest, deepest questions about
the nature of the universe because we are desperate to understand.
We think that our tiny little brains can somehow metaphorically
expand to understand the entire cosmos that is visible to us,
and we want to share that experience with you. That's right,

(02:15):
because it is a pretty amazing universe. It's a pretty
big universe full of amazing and incredible things to discover
and to puzzle about. And the extra awesome thing is
that it's actually getting bigger. The universe is expanding, and
it's not only expanding, it's expanding faster every day. That's right.
If you love the universe, you should be happy because
you're getting more of it every year for free. You

(02:36):
don't even have to pay extra. It just does it automatically.
It's like built in inflation, right, I mean physically and monetarily,
that's true. But the same amount of dollars buys more
universe every year. Oh? Really? Is the universe for sale?
Is it listed somewhere? You know, real estates the best investment?
And who's selling it? I can sell you andometer right

(02:58):
here today on the podcast aust If you cut me
a check, all right, I'll trade you for Alpha centri
done and done. Mabel Birth the co owners of both things.
That would be confusing, and humanity has long been confused
about how the universe works. We stare up into the
night sky. We try to understand what are those brilliant

(03:19):
little dots of light moving across our vision. We try
to build a model that can explain everything that is
happening out there. And along the way we learned some
pretty interesting things about how the universe works. But what
the rules are for things moving really really fast or
things near very heavy objects like black holes. Yeah, because
through most of human history we sort of like the
diners and thought, hey, this is a pretty big place.

(03:41):
But it wasn't until recently in which humans realize that
the place is actually getting bigger and getting bigger by
the day, faster and faster. And one thing we encourage
you to do on this podcast all the time is
to apply your understanding too new questions of physics. And
it's one thing to hear us blah blah blah about
some situation and ex in it to you, But if
you want to really understand a rule of physics, you

(04:04):
have to apply it in some new situation to see
if it really clicks together for you. Are you saying
people should jump into a black hole just for just
for their own curiosity? Yes, please do jump in a
black hole and then send me an email from within
the black hole to tell me what you see. That's impossible,
isn't it. Well figure out a way, right, Bring an
engineer with you and figure it out, and a physicist too,

(04:26):
so then they can be co authors on your book.
That's right. You can write multiple books and I'll be
co authors on all of the books, or you can
just stay at home and do thought experiments. A great
way to test your understanding of our ideas of physics
is to bang them against each other in extreme situations
to see you, do I really understand what's happening at
the edge of the universe or near the edge of

(04:47):
a black hole? Or if I fire a laser beam
into a black hole, why does it not get hot?
All these kind of questions are great ways to test
the boundaries of your own understanding. Yeah, that's right. You
can expand your own mind just sitting there and thinking
about the things, and also by listening to this podcast
and a bunch of folks right in because they are
confused about two ideas they hear us talk about. One

(05:07):
is that the universe is really strange in a particular
way that nothing in the universe can travel faster than
the speed of light. There's this really weird limit on
how fast things can travel. And the other is that
the universe is expanding faster and faster, and the further
you go out, the faster that expansion seems. So things
that are super far away seem to be expanding faster

(05:28):
than the speed of light. A lot of folks want
to understand these two ideas in their head at the
same time. So today on the podcast, we'll be asking
the question, how can the universe expand faster than the
speed of light? Pretty fascinating that the universe, as you say,

(05:48):
is expanding faster than the speed of light. I mean
we when we only figured this out kind of recently, right,
that's right. We've known the universe has been expanding for
about a hundred years, but it's been only twenty five
years since we discovered that that expansion is accelerating. Right.
We learned that it's accelerating, and that it's excelerating faster
and faster every year by looking at how fast the

(06:08):
galaxies are moving. Right, Yes, we found type one a
supernova which let us measure the distance to super duper
far away objects and look through the past and discovered
that the expansion the universe is larger than it once was,
and it's larger every year. So it's accelerating the expansion
of the universe. But even without that accelerating expansion, there's
something really fascinating about the expansion of the universe, which

(06:31):
is that the velocity of far away things correlates with
their distance, So it means that the further away in
space you look, the faster things are moving away from us,
which means if you look far enough, you look, if
you look deep enough into the universe, you can find
some things that are moving away from us faster than
the speed of light. It seems to be an apparent
contradiction with Einstein's relativity that says nothing can be moving

(06:53):
away from most faster than the speed of light. Right,
but do we know that for sure? Because it kind
of depends on how far out into the universe we
can look. Right, Well, we definitely can't see everything out
there in the universe. Is also a horizon beyond which
we just cannot see, but things within the horizon are
moving away from us faster than the speed of light. Although,
as I'm sure you won't appreciate, there are some asterisks

(07:16):
and caveats about exactly what it means for things far
away from us to have very higher velocities. SHO make
that the title of the podcast Asterisks and Caveats. I mean,
who doesn't love this? True crime and comedy and also
asterixtent caveats come here. Physicists form out of contradictions by
invoking cosmic loopholes. Right, But I think what you mean

(07:37):
is that, you know, the universe is expanding, and it's
a bit, but it's expanding like everywhere, like between me
and you, even here in southern California. The space between
us is expanding, right Like the space itself, not the
stuff in it is is expanding between you and me,
but just a little tiny, little bit. But if you
sort of added up over long distances, that expansion gets
bigger and bigger. Like between here and Jupiter, the expansion

(07:58):
is much bigger than between here and Orange County, and
between here and the next Galucia, it's even bigger and bigger.
And so if you go out far enough, that expansion
is huge. It's expanding, you know, thousands or millions of
kilometers per second exactly. And there's two different ways to
look at that. You can look at it as the
expansion of space, or you can look at it as
things moving through space. There are two sort of alternative

(08:20):
ways to view the same situation. But we'll dig into
that in a minute, all right. So then the question
is here is sort of like if the universe, parts
of the universe are expanding away from us faster than
the speed of light. How can that be right? Because
one of the rules of the universe is that you
can move faster than the speed of light. Exactly. That's
the puzzle, and it requires graduating our understanding of the

(08:41):
cosmic expansion from special relativity to general relativity. Sounds special,
and so, as usual, we were wondering how many people
out there had thought about this question or wondered how
the universe can expand faster than the speed of light.
So thank you very much to everybody who is willing
to answer these questions for the podcast. If this sounds
like fun to you, don't be sid Please write to

(09:02):
me two questions at Daniel and Jorge dot com and
I'll set you up to answer these questions for future episodes.
I think about it for a second. How do you
think the universe can expand faster than the speed of light.
Here's what people had to say. I have a heard
it said that because its expansion of space instead of
expansion in space, the universe can expand faster than the

(09:23):
speed of light. Nevertheless, that seems to me to imply
that things are moving at the hypervelocities that should be impossible.
I've heard it, but I don't understand it. You explained
on a previous episode how the universe can expand faster
than the speed of light. It's basically because the speed
of light in a vacuum is the speed limit for

(09:45):
anything to move through space. However, with the expansion of
the universe, nothing is moving through space, new spaces being
created between things. The universe expanding fashion light really makes
the eyes roll back in my head. So I'm thinking
it is light bread baking in the oven, and everything

(10:07):
expands together, and that expansion happens faster than the speed
of light, which is impossible, And now my eyes are
rolled back in my head. Now, I have heard this
question before and I've never really understood it. And I
understand the universe is expanding fast on the light, and
I think it's got something to do with inflation and
the fact that the overall space is expanding similar to

(10:27):
how a balloon expands, and that it's a different scale
or a different measuring technique to that of the speed
of light. Speed of lights finite within the universe, but
the universe is able to expand into other stuff. Perhaps
it's not the universe that is expanding faster than the
speed of light, but it's the empty spaces in between

(10:47):
the particles that is perhaps not limited by the universal
speed limit. Just a thought. I believe that the universe
can expand faster than light because the speed limit of
the universe, which is the speed of light, only applies
to something that is traveling through space, and that speed
limit does not apply to space itself when it expands,

(11:11):
because it's not expanding in space, it is space. All right,
some interesting answers here. Some people are relating it to baking.
It's a great analogy raising than a cosmic bread. But
the major point people seem to be making is that
there's no limit in the speed of expansion, even if
there's limit of motion through space. Yeah, that's kind of

(11:31):
the big caveat in this statement, right, like the rules
that you can move through space faster than the speed
of light, but there's no limit to what you can
do with that space. You can squish it, you can
expand it technically faster than the speed of light. Yeah,
And that's a nice shorthand for thinking about expansion, But
there are some issues with that if you want to
be precise about it, because what does it mean to
be moving through space? Space itself doesn't have a frame.

(11:53):
You can't measure your velocity with respect to space. You
can only measure your velocity with respect to other things
in space. And so special relativity would seem to be
in contradiction with that anyway, because it says, how can
somebody be measuring a distant galaxy moving away from us
at two times the speed of light. We're not measuring
its velocity through space, We're measuring its velocity relative to us.

(12:16):
Sounds confusing. Going back to thing he said earlier, he said,
there's no limit to how fast this space can expand?
Is that really true? Like can I expand space from
zero to infinity in no time? Or even the opposite,
like can I take some space and collapse it in
an instant in zero time? There's no limit to the
rate of which space can expand, but it does need
to be continuous, right, so you can put in any number,

(12:39):
And in fact, we've seen very dramatic expansions of space
in our history of the universe. Right. Inflation is nothing
more than expansion of the universe. And that was a
factor of like ten to the thirty in ten to
the minus thirty seconds. So as far as we understand,
there are no bounds there except that it does need
to be continuous. You can't have an instantaneous transformation of space,

(13:00):
so you can have any number except for infinity essentially interesting,
so literally almost instantly instantaneously, then you can collapse and
expand space. Because that's kind of what happens in the
Big Bang. We don't understand it, but general relativity can
describe it, and we've seen it happening in the universe.
We don't know what can cause it, Like we know
inflation happened and it stretched the universe dramatically. We know

(13:21):
dark energy is accelerating the expansion of the universe. We
don't understand the mechanism for that, like what makes that
happen and what the limits are to that mechanism. But
in principle, the framework of general relativity does allow for
very very dramatic expansions. Yes, all right, well let's dive
into it, and let's maybe start talking first about the
just the general expansion of the universe. Why do we
know about that and how do we find out? So

(13:43):
our understanding is that space is stretching everywhere. It's expanding.
It's getting bigger. Between me and you, space is getting larger.
Between us and other galaxies, space is getting larger. This
is an expansion that's happening everywhere at the same time,
not an explosion from a tiny dots some people might

(14:03):
imagine the Big Bang started. Take a very dense universe,
stretch it out to a less dense universe, a colder,
more dilute universe. Right, But when you say that space
is stretching everywhere or getting bigger everywhere, you don't mean
like space itself is getting bigger. Like you actually mean
like there's more space being created out of nothing, right,

(14:23):
Because it's not like a kilometer is suddenly more or
like what we call a kilometer is getting bigger. It's
like there's just more space growing all the time out
of nothingness. Right. I think both of those descriptions are accurate.
I'm not sure exactly what the distinction is between them. Like,
the universe is expanding at a rate we call the
Hubble parameter. It's seventy kilometers per second er mega parsak.

(14:45):
What that means is that every second a mega parsak,
which is a unit of distance and astronomical unit becomes
longer by about seventy kilometers. Right, So every second a
mega parsak does get longer, is it getting stretched or
is the universe creating new space in the middle? Doesn't
really matter either way. We just describe it as an expansion.
We say the universe is scaling up. Well, I guess

(15:06):
what I mean is that, like between here and Jupiter, right,
space is expanding, it's getting bigger. But between here and Jupiter,
like how long it takes light to go there and back?
It's not getting bigger every year, right, Like, that's pretty
much stay in the same. So if you take two
mirrors and you put them a megaparsec away from each other,
what's a megaparsic? So a mega parsk is about three

(15:27):
million light years. It's a really really big distance. So
it's how far light travels in about three million years.
So set up two mirrors three million light years apart,
one megaparsec apart from each other, it would take light
a certain time to go there and back. Right now,
wait for the universe to expand, those mirrors will be
further apart from each other, and so we will take

(15:47):
light longer to get there and back. The space really
is expanding, either by creating new space or by stretching
that space relative to this standard of the speed of
light between here and Jupiter. Is something else going on.
That's because the Sun is holding Jupiter in place. In
the case the two mirrors, there isn't any gravity to
keep the two mirrors at a certain distance. But the

(16:08):
distance between us and Jupiter isn't expanding because the Sun
is holding Jupiter in place, the same way that the
Earth is holding you in place, even though the space
between you and the Earth is expanding. Right. I guess
maybe a more concrete example would be like, let's say
I stretched the cable, a steel cable that doesn't stretch
between here and Jupiter. Right. I measure that the cable
to be a certain length, and as the space expands

(16:29):
between here and Jupiter, the cable is not stretching, right,
It's staying the same the length, right, Or the spa
the distance between its molecules is staying in the same.
So does that mean that the space that it's in
got thinner somehow or stretched, or they're just like more
space grew in it. That's right. The length of the
ruler is determined by the bonds of the stuff inside

(16:50):
the ruler, the atoms holding themselves together with those electrons,
so that doesn't change. You put that ruler out into
space and it's just floating there. The space around it
will expand you can still use that to define a distance.
You can say my ruler is one megaparsec long. But
if you started out with mirrors at either end of
your ruler, and then you waited a second, and the

(17:10):
mirrors would no longer be at either end of the
rulers because there's nothing holding those mirrors together. So space
is expanding between the mirrors, pushing them apart. So you
have this ruler which no longer covers the distance between
your two mirrors. Al right. Maybe an easier way to
ask my question is like, if space doubles in size
as we say it's doing, does that mean there's twice

(17:31):
as much space as there was before or is there
the same amount of space? It's just like stretched out dinner.
I say space doesn't get thinner, right, there's no like
density to space I would require measuring like with respect
to something else. This is an intrinsic expansion, which means
it just changes the relative distance. There's no meaning for
the density of space. So the first answer is the

(17:52):
more accurate description. There's more space between those two points.
Oh I see, So there's just more space popping up
everywhere in the universe, even between like the space of
my fingers. There's more space always popping up all the time.
That's right, And the expansion is actually really quite weak.
We're talking about seventy kilometers per second over three million
light years, so between your fingers that's really really tiny,

(18:14):
and almost anything is powerful enough to overcome it. Gravity,
the bonds in your fingers. It's also basically nothing for
our solar system, even for our galaxy, it's almost negligible.
But as distances get really really large, then it becomes overwhelming,
and between superclusters of galaxies it's the dominant thing, all right,
So maybe let's bring it down for people. Are you

(18:35):
saying over three hundred million kilometers over three million light years,
over three million light years Every second that distance grows
by seventy kilometers, So right now it's three million light years,
and then and now it's three million and seventy kilometers long,
and now it's three million and a hundred and forty kilometers.

(18:56):
Is that what kind of what you mean, yes, exactly,
So every second, each mega parts that grows fractionally by
a tiny, tiny, tiny amount. It's one point zero zero
zero zero zero zero zero zero zero zero zero zero
two megaparsex after a second. That's really tiny, because the
Milky Ways is not even a megaparsic, right, it's like
a hundred thousand light year exactly. It's a tiny fraction

(19:19):
of a megaparsec. Okay, but you're saying that over large
distances like businesses between galaxies and the size of these superclusters,
it starts to get pretty significant, right, It starts to
get pretty significant. And since the universe is really really big,
many many millions and billions of light years wide, and
if you go far enough away, this is really significant.
And the rate at which things are moving away from

(19:41):
us because of this expansion starts to get very very large.
So you can measure this velocity. We call it the
recession velocity. How fast is something moving away from us
because of this expansion and you go to the other
side of the Milky Way, the recession velocity is tiny, right,
if you go to the next galaxy, it's not tiny.
If you go really, really far away then starts to
be large, and if you go far enough away, it

(20:03):
actually gets to be larger than the speed of light.
So things are technically moving faster away from us than
the speed of light, which is the big question in
this episode. So let's get into that actually really means
and how we can make sense of it. But first
let's take a quick break. All right, we're talking megaparsex

(20:35):
and inflation and recession, which just a reminder, this is
not a financial podcast, not yet, at least not until
it blows up, until it crashes. We are talking about
bubbles though, right, Yeah, exactly. We are talking about spheres
in the universe. And there's lots of ways that we
like to think about spheres and put ourselves at the

(20:56):
center of them, and we tend to cosmologically to think
that's a mistake there. That's not the center of anything,
but it is at the center of what we can observe,
and so in some senses, it does make sense to
build a universe with us right in the middle of it. Yeah,
and there's also a lot of speculation, uh, in these theories.
So let's get into this idea then, of things moving

(21:17):
away from us faster than the speed of light. So
you're saying that the universe is expanding a little bit
at a time. You each spot everywhere in it, and
so over long distances things are the distance between here
and that thing that's out there is growing faster than
the speed of light. Yeah, this is Hubble's basic discovery.

(21:37):
He was looking at stuff that was further and further
away and measuring its velocity, and he found this linear relationship.
Things that are further away move away from us faster.
If you plot velocity versus distance, you get a straight
line and you can just keep going further and further
distances faster and faster velocities away from us. So this
was Hubble's big discovery, like more than years ago, now

(22:00):
that things are moving away from us at in this
linear relationship. And that's the Hubble parameter. We used to
call it the Hubble constant, except it's not really constant,
so now we call it the Hubble parameter. It's a
relationship between the distance and the speed the slope of
that line. If you go far enough away, those velocities
start to get greater than the speed of light. And
so that's the basic conundament is how can something be

(22:23):
moving away from us faster than the speed of light,
And I guess maybe the isn't the answer there in
that world, like, it's not technically moving away from us, right,
it's just sitting there, but there's more space growing between
us and them? Is it technically moving when you can
measure It all comes down to how you measure velocities. Right,
If you take a really big ruler and you measure
the distance from here to there, and then you do

(22:44):
it again in ten seconds, you can measure velocity, and
that velocity does appear to exceed the speed of light,
and so from that perspective, that does break that rule. Well,
I guess it's where it all gets relative, because I
guess the question is is that thing out there in
space actually moving within this space it's around? Like, gets
it technically moving? Or like, let's say we have something

(23:05):
that is maybe right next to me, and over trillions
of years, the space between me and it expands, and
so it gets further and further out, maybe to the
point where distance is growing fast in the speed of light.
But did that thing ever experience any acceleration? Right? So
let's talk about what special relativity actually allows and what
it doesn't allow. Right. Special relativity says that nobody can

(23:26):
measure a relative velocity to be greater than the speed
of light in their local inertial frame. Okay, and those
are the loopholes. We're going to drive this huge expanding
universe through local inertial frame. Right. What that means is
that you define a frame of reference, you define or
and you say, I'm here at the core of my X,

(23:48):
y Z, and I'm the one making measurements, and I'm
not accelerating with respect to this frame. I'm just sitting
here at the origin and I'm making a bunch of measurements.
The other key thing is the word local. Right. In
special relativity, we can we make measurements of things that
are nearby. We say that the speed of light never
exceeds see when it goes near you. Things that are
much further away are not in your local inertial frame,

(24:10):
and so the rules of special relativity don't apply. That's
when you need to apply general relativity for things that
are not in your inertial frame, like when the universe
is curved or expanding, or when things are really really
far away. What are you saying that the rules are
different depending on where you are in the universe, or
that our theories don't always work the same way in
different parts of the universe. The rules are the same

(24:32):
everywhere in the universe. A special relativity only applies to
the things you can see near you. It can't describe
the whole universe because there is no global inertial frame
for the universe. Like the universe has wiggles and curves
and all sorts of stuff, and that breaks special relativity.
You can't have a global inertial frame for the whole universe.

(24:53):
You have to use general relativity, which gives you another
way to look at the universe and make these measurements
and fitted it all together. You're saying, that's the pull.
What do you mean by that? So, one reason we
can measure these galaxies to be moving away from us
faster than the speed of light is that they are
not in our inertial frame of reference. Right, It doesn't
really make physical sense to measure their velocity relative to

(25:14):
us because we're not in the same frame. It's like
a frame over here near us, and there's a frame
over there where they are. But we can't really compare
velocities in hours to theirs general relativity tells us there's
no global frame. We don't know how to make those comparisons.
In fact, the definition of velocity and general relativity is
a little bit fuzzy for things that are far away

(25:34):
from you. Well, I feel like I'm getting a little
bit confused here because of this difference between things moving
and space expanding. Whether it's something in expanding space is moving,
and I feel like maybe you're saying it's the same thing,
but I guess it's not quite clicking in my mind.
So maybe let's go back to that example of saying, like,
if I start with something next to me, and over
trillions of years, the space between me and it expands

(25:56):
so that to the point where it's now that thing
is super far away from me, and maybe even that
the distance between me and it growing faster than the
speed of light. Is that thing technically moving away from me?
Or is it just sitting in space and the space
is growing around it? You know what I mean? Like,
did anything ever push that thing? Did that thing or
me experience acceleration? And if not, then maybe may it's

(26:17):
not moving. It's maybe it's just sitting there and space
is growing around it. Here's the technically accurate and totally unsatisfying.
Answer is that both pictures are accurate. Right in one picture,
the thing is moving away from you, it has velocity
relative to you, and the other picture, there is no
relative velocities. There's just the expansion of space. Everything is
just floating, motionless, and space between them is expanding. Those

(26:39):
two pictures are actually equivalent. And what I meant a
moment ago when I said that in general relativity we
don't have a well defined meaning of velocity is exactly
that that both of those pictures can describe what we see,
even though physically they sound very different. So let's step
through them one at a time. Right, In one picture,
we talk about the distance between us and some other objects,

(27:00):
and that means it like if we could freeze time
and somehow take a huge ruler and measure the distance
to this distant object, and we could write it down
on our piece of paper, and then we could wait
a minute or a year and do it again. We
could use that to measure the velocities. Now, no, that's
not really physical, right, because you have to freeze the
universe and like trust out your ruler and take this measurement.

(27:22):
That's not possible because things are expanding as you're doing it.
So in some sense, even the definition of distance there
doesn't really make sense. But that's sort of like our
intuitive idea of distance. So from that perspective, this thing
really is moving away from you faster and faster every year.
That velocity you measure is larger every year, And I
think what you're saying is that, like, maybe initially, if

(27:43):
it's right next to me, I'm going to measure that
it has zero velocity because it's just sitting next to me.
But maybe next year, when it's further away from me,
I'm going to start measuring, like, hey, now it's further
away from me, the distance grew, and I can divide
that by the time that passed and say, oh, now
it has a velocity. So you're saying that that's true,
even though nothing pushed it, even though it didn't feel
any acceleration, it's velocity grew between last year and today,

(28:06):
exactly because the universe is expanding, right, and so it's
moving these things away from each other. It's increasing the
relative velocity of these things, and you can measure that
physically also in the red shift, right, things that have
a relative velocity give you a red shift. The photons
from these things are red shifted. It starts out a
certain frequency. By the time it gets to you, it's redder,

(28:26):
and we use that to infer the velocity of these
things all the time. Right. So that's one picture, right,
But the thing itself didn't never felt any exceleration, right, Like,
if I was sitting in that rock that's moving away
from me, I would never feel like anything happened, right, Like,
I wouldn't feel pressed against the wall, or I wouldn't
feel like somebody pushed me. I would just be sitting there,
and my velocity the relative to me, it's just magically, magically,

(28:48):
it's just growing. It's like free velocity. Yes, it's free velocity.
The universe is just creating this. Right. And the other picture,
which is a bit more physical, though a little harder
to think about, is think about each of these objects
in their own frame, whether each at rest, right, and
now these frames have space expanding in between them. So
from that point of view, right, everything was at rest.
Everything is still at rest, but space is just sort

(29:09):
of like expanded between them. There's no velocity, it's just
that space is expanding. So this is another frame. It's
like it requires you to have a coordinate system that's
growing with the universe, like stretch the ruler as the
universe grows. These are called co moving distances, if you
want to google it and read more about it. And
so in this picture there is no velocity. It's just

(29:31):
that space itself is expanding. I think that's what I
was asking earlier. It's like in this other picture, and
now a kilometer is actually kind of longer, right, technically
a kilometer is now longer. And you can wonder, like
what about the red shift? The red shift is something
I see. It shouldn't depend on like what a physicist
is thinking about, whether they're thinking about two different frames
with the one big frame. It shouldn't depend on that.

(29:54):
And the red shift that these two pictures predict is
the same. And the first one, the red shift comes
from velocity in the set, second one, it comes from
the expansion of the universe, which also lengthens the wavelength
of the light. So in the second picture, where there
are two frames and spaces expanding between them, then the
photon that leaves one galaxy is stretched out by the
expansion of the universe, not by the relative velocity because

(30:16):
there is none in that second picture, and I think,
how could both of these things be true? Well, these
are two different pictures of the universe, and what general
relativity tells us is that there's no unambiguous way to
decide between these two pictures. That's why relative velocity for
very distant objects is not well defined in general relativity. Well,
I guess maybe the maybe the difference. I wonder if
the difference between the two pictures is that in one

(30:38):
of them, the speed of light is technically staying the same,
but in the other one, I feel like the speed
of light is kind of getting diluted, right a little bit,
because if a kilometer grows, but the time it takes
light to grow to that kilometer is no longer than
or shorter than that, somehow the speed of light went down. Well,
the speed of light is the standard, right, there's no

(30:59):
other metric, So the time it takes light to go
between the galaxies definitely increases. And they used to be
a kilometer apart. Now we just say that there are
five kilometers apart, and that's because it takes light longer.
Light is the way that we measure these distances, after all,
there's no other external metric, right, that we can use
to measure the distance between things other than the time

(31:19):
it takes light to go between them. I thought you
said that in the second scenario, a kilometer is now longer.
The kilometer space is now two kilometers of space. It's
not like the kilometer itself is getting diluted in some way. Right,
you have more space. The space and that's out there
is now longer, so it takes longer for light to
go through it. Right, So it would still be a kilometer,
It just takes light longer to go through it, which

(31:40):
means the speed of light technically went down. No, no,
it's not still a kilometer, right, it's more space now.
But I thought we said we stretched the kilometer like
the kilometer stretched. Oh, we don't stretch the definition of
a kilometer, right, that's comes from the speed of light.
We just stretched the space which used to be one
kilometer of space, and now it's a bigger serving of space.
We don't change the definition of the kilometer. Space itself expands,

(32:03):
so the kilometer stace is same now there's just more kilometers.
We define the kilometer in the same way, right, it's
how far light goes in a certain amount of time, right,
so we don't change the definition of the kilometer. I
guess we can go around the circles. But I think
the main point is that the universe is expanding and
the stuff that's really far aways moving faster than the
speed of light. The universe really is expanding, and it

(32:24):
really is creating space between us. And if you try
to think about relative distances in terms of like one
mega ruler where you're gonna measure these distances, then you're
sort of falling into one of the loopholes of special relativity,
which says that that's not a meaningful physical thing. You
could never actually measure that distance. Like if you're looking
at a galaxy that's billions and billions of light years away,
you can never actually make the measurement we're talking about

(32:45):
where you try out a ruler and measure the distance
and then wait and measure the other one. Because space
is expanding at the same time, it requires you to
like artificially freeze the universe. So those things are not
in our local inertial reference frame, so special relativity doesn't
really apply. So it's possible for these recession velocities to
be faster than the speed of light without breaking special
relativity because it doesn't really apply to things that are

(33:07):
not in our inertial frame, right. I think you've always
phrased it as it's not possible to move through space
faster than the speed of light, but it is possible
to make space faster than the speed of light, which
I think usually explains it. But here I feel like
we're trying to be more specific about and say there,
it's basically the same thing. Kind of, It's like it's
the same thing, and so you can go faster than

(33:28):
the speed of light. There are two different ways to
look at it in general relativity, yeah, and I think
the more intuitive way is the second with co moving
way to say, the universe is expanding. Everything is at
rest in its local frame, and the universe is expanding
between those two things, and there's no limit to how
fast the universe can expand. And interestingly, that means that
there are things out there that are moving away from us,

(33:50):
apparently faster than the speed of light. Means that a
photon leaving that galaxy is not getting closer to us, right,
It's moving through its local space, but that local space
is expanding away from us faster than the speed of light.
So as time goes on, the photon is not getting
closer to us, even though it's moving through its local
space at the speed of light. Right, the distance between

(34:12):
us and that photon is not decreasing. What do you
mean the distance is not changing because it is changing,
isn't it. So the photon is emitted by that very
distant galaxy which is moving away from us faster than
the speed of light. Right or equivalently, the space between
us and it's local spaces expanding faster than the speed
of light. Right now, those photons are moving towards us
in their local space, but the distance between us and

(34:34):
those photons is not decreasing because space is expanding between
us and that photon. So if a photon is moving
through space which is super luminately receding, then it's not
making progress towards us. So some things that are super
far away that are moving away from us faster than
the speed of light, their photons will never reach us
no matter how long you give them, because space between

(34:55):
us and them is expanding faster than the speed of light. Right, Yeah,
I remember we talked about the before. It's sort of
like if someone is zooming away from you on a
spaceship and they, you know, shoot a nerf gun at you,
that nerve bullet is never going to get to you
because it's not being shot at you faster than then
the rocket is moving away from you. That's right, And
that's for like a Galilean transformation. Right, we're just linearly

(35:16):
adding the velocities. Light is weird and different though, and
light always moves at the speed of light. So somebody
in our local frame who's moving away from you, if
they shine a flashlight at you, that light still moves
towards you at the speed of light. Doesn't matter how
fast they are going, so it's not their relative velocity. There.
Here's the expansion of space, right, And interestingly, there's some

(35:36):
things that are so far away from us that their
light will never reach us. There are other things that
have always been moving away from us faster than the
speed of light, but their photons do eventually reach us.
All right, Well, let's get into that mystery and how
that's possible. But first let's take another quick break. All right,

(36:06):
we are expanding our minds here, trying to learn things
faster than the speed of light. And trying to understand
these concepts. I think I sort of understand what you're
saying about this contradiction between the two things. I mean,
we've always explained it as you know, nothing can move
through space faster than the speed of light, but space
can grow. You can make new space at a rate
that's faster than the speed of light. That's how things

(36:28):
that are really far away from us in an expanding universe,
the distance between us is growing faster than the speed
of light. But nothing in that spacing between us can
move faster than the speed of light in their sort
of local space. Right. But I think what you're saying
is that for a physicist, there's really no distinction between
space being created between us and using the word that
it's moving away from us at a certain rate. Right,

(36:49):
like it. It sort of makes into the sense if
you make that distinction. But I think what you're telling
us here today is that to a physicist, the fact
that there's more space growing between us is the same
thing as if it was moving away of us. Yeah,
that's exactly right, And in your local inertial frame, there
really is no difference. You try to extend that to
the whole universe, and to say I'm going to talk
about the velocity of things that are really really far away,

(37:12):
you end up with this weird calculation that gives you,
like the velocity of these things is two times a
speed of light or three times the speed of light.
And the reason that's strange is that you're using this
concept of a distance and velocity and how you measure velocity,
which doesn't really work over super duper long distances because
you could never actually measure those things. You can't really
measure those velocities of things. There's an apparent velocity if

(37:33):
you make simple assumptions and just like translate redshift into velocity,
but that velocity doesn't have a physical meaning. It makes
just much more sense to talk physically about the expansion
of space between us and them. I wonder if another
way to look at it is to say that this
expansion of the universe, this like free velocity, basically breaks
all the rules that we thought were true, right because technically,

(37:55):
because of this expansion, as you're saying, things are gaining
velocity are free, you know, nothing's pushing it, No energy
is actually causing this change in velocity. If it's not
equals m a in this case, right, it doesn't break
all the rules. It just breaks the rules that we're
used to applying even the things in our cosmic neighborhood.
It definitely doesn't break general relativity. General relativity can definitely

(38:16):
describe it, but it requires a very different picture of
the universities and when that we're not used to, and
very specifically, you can't have a whole frame of reference
for the universe and talk about like velocity of things
across the universe. General relativity says you can only really
make local observations, and the things that are really far away,
you can't even really talk about what their velocity means.
They're in their own frame over there, and we're in

(38:38):
our frame over here. So you a tempted to like
put your mind at the center of the universe and
expand that picture out to include everything out there. But there,
it really is no unified picture like that that makes sense,
because you can never actually make those measurements. Well, I
guess maybe I'm confused about what you mean that you
can't talk about it. I mean, we're talking about it.
We've just spent fifty minutes talking about I guess it's

(38:59):
really we can't talk about it. Are you saying that
the laws don't apply to the laws note work? Are
you saying that it doesn't make sense in our current
kind of way of thinking about things. It definitely works
and the laws makes sense, right, But there's no unique
way to picture it. Like in special relativity, you can
pick a unique frame and you can say, I'm gonna
put myself in the origin, I'm at rest, I'm gonna
measure everything relative to me. But you can't do that

(39:22):
for the universe, right. You can't say, here's how I'm
gonna define everything, and this is the right way to
do it. You can't have a single frame with everybody
in it. In order to talk about the velocities of
things that are really really far away, when space is
curved between us and them, or when the space is
expanding between us and them, you have to make some
arbitrary choices. You have to choose your coordinates, and different

(39:43):
people could choose different coordinates and they get different velocities.
Like we said earlier, one person could say, I'm gonna
put the Earth at the center, and I'm gonna measure
velocities using an unphysically long stick. I'm gonna get crazy
velocities two times of speed of light. Another person you
could say, now I'm gonna choose coordinate that grow with
the universe, so everything is at rest, so nothing has

(40:03):
any velocity. Actually, and both of those things can be true, right,
and there's no way to pick between them in general relativity.
So that's what we mean when we say it's not
meaningful to talk about those velocities because they're a little
bit arbitrary. They depend on the coordinates that you pick,
and you're free to pick any coordinates you like. In
general relativity, maybe what you're saying, it's a general relativity
allows you to use non inertial frames kind of or

(40:26):
frames that are growing. Absolutely, general relativity can describe non
inertial motion, things that are accelerating, things that are expanding,
even if that expansion is accelerating, and you can use
non inertial frames, and in general relativity, absolutely, yes, general
relativity you can describe all sorts of things like that.
All right, Well, let's get into that mystery. You said
earlier that there are things that are growing away from

(40:47):
us faster than the speed of light, but that maybe
and you would think you can never see them because
if they're moving away from as fast in the speed
of light, we will never see their light. But you're
saying that it is possible for us to see their
light on some things. Yes, it's possible to see things
that are moving away from us faster than the speed
of light, which seems a little strange, but it's because
this recession velocity we're talking about is not constant. The

(41:09):
expansion of the universe is not happening at a constant rate.
It's changing with time, So that changes over time which
parts of the universe are moving away from us fast
in the speed of light and slower than the speed
of light. So some things were moving away from us
faster than the speed of light. Always other things were
moving away from us faster than the speed of light,
but then no longer were, and then might be again

(41:29):
in the future because of the acceleration. There's a whole
sort of different outcomes based on how far away from
us you are. Wait, I thought that the universe has
I mean, the universe started expanding at the Big Bang,
and it's always been expanding. That hasn't been contracting in
any point, right, It hasn't been contracting, but it was
decelerating right. Expansion the universe has a few different phases.

(41:50):
There's inflation, which is a very very rapid expansion in
the very beginning, and then this sort of a quiet
period where things are expanding slower and it's actually decelerating.
The expansion are is just driven by like the density
of the universe. Solve the Einstein equations, you get a
certain expansion based on how much stuff there is in
the universe. But because the density of the universe decreases
as it expands, then that expansion changes. So the expansion

(42:13):
was actually slow in the universe, was decelerating until recently
when dark energy took over and it kicked it back
up in the gear again, and the expansion has been
accelerating since. So you have these sort of three different
phases in the history of the universe, and that change
is like sort of what's been moving away from us
fast in the speed of light and the fate of
all of those photons. Okay, you're saying that before dark

(42:34):
energy kind of pressed the accelerator and made the universe
really start expanding faster and faster as we see it today.
Before that happened, maybe there are things that we're moving
the universe is sort of decelerating at some point, right,
because it wasn't growing as fast, which means that there's
kind of a window there for us to see things
that we're once moving faster than the speed of light,

(42:54):
but then at some point we're not. So maybe we
can see those photos for a little bit, but then
eventually we won't be able to see them again exactly.
And the key thing to understand is this concept of
the hubble sphere. Inside the hubble sphere, things are moving
away from us less than the speed of light. Outside
the hubble sphere, the apparent recession velocity is greater than
the speed of light. So it's just a definition. It says,
let's draw boundary where things are moving away from us

(43:16):
at the speed of light, and everything further away from
that is outside the hubble sphere. That's what the hubble
sphere is. That's how you define it. Yeah, that's the
definition of the hubble sphere, the bubble of space where
things are expanding away from us the less than the
speed of light. And that's different than the observable universe, right,
It's very different from the observable universe. And this hubble
sphere depends on the Hubble constant. Right, The Hubble constant

(43:37):
tells you how fast things are moving away based on
how far away they are. So for a given Hubble constant,
that defines a Hubble sphere. But the Hubble constant is changing,
it's not really a constant. As we said earlier, the
universe was decelerating for a long time because it was expanding.
That changes the energy density, which then changes the expansion.
So the Hubble constant was actually decreasing, right, which grows

(43:59):
the hubble sphere. Means you have to go further away
to find objects that are now moving away from you
at the speed of light. So this hubble sphere, the
portion of the universe inside of it, which is moving
away from us at less than the speed of light,
is expanding as time goes on. And is it is
that growing with the expansion of the universe or is
it that it does it have its own kind of

(44:19):
like growth rate as its own growth rate, that it
is linked to the expansion of the universe because it's
the expansion of the universe that changes a density, which
then changes the Hubble parameter. So it's a bit of
a complicated relationships like nasty differential equations in there, but
they don't exactly track each other, which is why the
hubble sphere can grow to encompass things that we're once
moving away from us faster than the speed of light,

(44:40):
including and here's the key. You can find photons which
were once in superluminately receding regions and put them inside
the hubble sphere so that we can now see them. Right.
I think what you're saying is that if the universe
is expanding faster and faster, the hubble sphere shrinks. And
if the universe slows down and and starts to not

(45:01):
grows fast, and the hubble sphere grows. So it depends
a little bit on the coordinates. Right in physical units
where you're like trotting out a ruler to measure things,
the hubble sphere always just grows. It just grows faster
or slower. It's growing because the universe is expanding. It's
growing because the Hubble parameter is decreasing right as the
universe expands and the density drops because the universe is expanding. Yes,

(45:23):
the universe expansion is driving it. But what I say
was still true right Well, in physical units, the hubble
sphere never shrinks. It only grows. It does shrink in
the co moving units, so it's always growing. The whole sphere.
It's always growing, but sometimes it grows faster and sometimes
it grows slower. Okay, And meantime the universe is expanding,
but sometimes it grows faster or slower. And so you're saying,
there's this kind of like this relationship between the two spheres,

(45:46):
the observable universe fear and the hubble sphere, and there
they have this kind of dance like sometimes one is
bigger than the other and sometimes when it's smaller than
the other. So if you think about what happens for
objects at various distances, you can get an idea for
how these interplays determine the fate of a photon which
is shot at us from those distances. Right, So I
think the end result then is that there are photons

(46:08):
coming towards us, which at some point we're like, oh,
I'm never gonna get to horrid. He's never going to
see me. But now then then the universe kind of
shifted gears and it's like, oh, oh, now I'm gonna
make it too hori after all. Kind of exactly because
the radius of the hubble sphere is increasing. Some photons
that were initially in a super illuminally receding region and
a portion of space that was expanding away from us
faster than the speed of light, can now find themselves

(46:30):
in a sub speed of light receding region, right, And
not because they make it there, but because the hubble
sphere expands to sort of engulf them, and the objects
that admitted those photons have now moved to larger distances,
and so they're still receding superluminally. So something that has
always been moving away from us faster than the speed
of light, we do have a window to see it,

(46:51):
because it's photons cross into the hubble sphere and make
it into this portion of the universe that they can
then zip through and actually make progress towards us. Right.
I guess maybe the part that it's hard to grasp
because we don't have the math in front of us
is that, you know, the hubble sphere is not a thing, right,
It's just something you were using to describe it. I
think the point is that there are regions of space

(47:12):
that are stretching faster than other regions, and so sometimes
the photon might be in a region that is stretching
faster than the speed of light. But if it gets
into a region where it's threatened not stretching as much,
then maybe it has a chance to catch up to
that stretching and get to us. Yeah. Well, the stretching
is having at the same rate everywhere in space. It's
just not the same rate everywhere in time. And then
remember the recession velocity is a function of distance from us.

(47:35):
So as the phoneton is moving to the universe and
time is passing, this hubble sphere can sort of sweep
across it. You say, the hubble sphere is not a thing.
It's just like where things are traveling away from us
faster or slower than the speed of light. And so
then you can find itself in a portion of space
that's within our hubble sphere, then you can make it
to us because space between us and it is no
longer expanding faster than the speed of light. Well, you

(47:56):
just said something that raised something with me here. He
said that the expansion of the universe is the same
everywhere in space. Is that really true? I mean, aren't
there spots in space that are denser than others wouldn't
the maybe the expansion be a little uneven. Well, that's
a great point. We think that the contribution to the
expansion is the same everywhere, and that's accurate only in
the picture of the universe is like totally homogeneous right
where there are no like lumpy bits. Of course, once

(48:19):
you add in lumpy bits, things are different, and we
mostly ignore those when we talk about like big cosmological things.
We don't think about like the gravitational impact of Jupiter
or even a galaxy or a black hole, and most
of those things we can only solve in flat space,
assuming that the universe is not expanding, So we mostly
just ignore those little bits when we talk about like

(48:39):
really big cosmological questions. Right, but that there are clusters
and walls and bubbles of superclusters. Right, are you saying
the expansion of the universe is the same in the
big empty spaces between clusters of galaxies and it is
in the within the clusters. That's our theory, and we
think that it's the same everywhere. We think it's totally homogeneous.
It doesn't vary with space, does vary with time, because

(49:00):
it depends on the overall density of matter and radiation
in the universe, and that does evolve, but we don't
think it varies with space. So the Hubble constant, we
think is constant across space, but not across time, or
at least you assume it's clossant across space. Yes, we're
assuming that, and all of our observations are consistent with that,
but you know, we don't really know, and again we
don't really understand the expansion of space or its acceleration.

(49:23):
So certainly possible that dark energy could be doing different
things in different parts of the universe. We don't see
any evidence of that, but it's certainly possible. Well, it's
kind of hard to measure what's going on in empty space,
isn't it. Well, we can measure what happens in some
of those voids by looking at photons that passed through them.
We see photons from the very early universe, and we
can sort of measure the density of space between us
and where they were generated and the expansion of that

(49:46):
space by seeing how they're red shifted and blue shifted
as they go through like denser and less dense regions.
So we have one way to probe that space because
photons do pass through them, and we talked once about
really cosmic voids. If you remember, we talked once about
hotspots and could spots in the universe as those photons
passed through those big voids, so we do have one
handle on them. Cool. Well, my mind is definitely expanded

(50:07):
and um, but I'm not quite sure my understanding. You're
caught up to the speed of light here. But I
think the main interesting picture here is that the universe
is almost like a living thing, like it's growing. It
has phases of fast growth and phases of slow growth,
and you know, and we don't know how what's going
to happen in the future, which means that it's sort
of unpredictable how much of the universe will be able

(50:27):
to see right, It is a little bit unpredictable. In
our current models. We have some ideas for what those
numbers are, and they're sort of mind boggling. We think
the things that are now forty six billion light years away,
if they emitted light at the very very beginning of
the universe, that light is just reaching us now. And
we think that things sixty two billion light years away
if it admitted light at the very beginning of the

(50:49):
universe it will eventually reach us at the very very
end of the universe, but anything further than that will
never enter the hubble sphere, will never reach us. Will
always be moving through space that's expanding faster than the
speed of light. So even though locally those photons are
pumping away at a crazy speed, they're not actually making

(51:09):
any progress towards us. Right, although never say never, right?
Didn't you say earlier in another episode, And haven't you
always said that dark energy is kind of unpredictable. It
might you know, reverse course or shift gears or something
like that might make the universe crunched down again. Yeah,
great point. This is all assuming our current understanding of
the universe and the blend of dark energy and dark

(51:30):
matter is correct. We could learn one day that dark
energy is something totally different, and you could flip around
and compress the universe, and then we could see much
much more of it one day before we eventually get
squished too much of it, seem Yeah, the universe crunches
down into a tiny dot again. Will all be very
familiar with every light that's ever been admitted, right exactly
just before it fries us to a crisp All right, Well, um,

(51:52):
stay tuned. I guess as we learned more about the
universe and what dark energy is, and we'll know more
about how the universe is changing. Well, thanks for joining us.
Hope you enjoyed that. See you next time. Thanks for listening,

(52:12):
and remember that Daniel and Jorge explained the universe is
a production of I Heart Radio. For more podcast for
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