Listener Questions 35: Exomoons, black holes and math!

Daniel and Jorge answer questions from listeners like you! Write to us at [e-mail] 

See omnystudio.com/listener for privacy information.

Episode Transcript

Speaker 1 (00:08):
Hey, Daniel, do people still write us with questions? You know,
the inboxes overflowing like usual, overflowing? Don't you answer them?
I do, but every time I send a response, it
just seems to generate more questions. You're not giving them
a good answer. Maybe, but even when they say, oh,
now I get it, they always come back with but
that makes me wonder about something else. You should try

(00:29):
asking them a question you stopped them that might give
them something to think about, A question like would you
fund my research? Oh? Nobody will ride you back? Then
the question to end all questions? Literally, Hi am or

(00:59):
handmad cartoonist and the creator of PhD comments. Hi, I'm Daniel.
I'm a particle physicist and a professor at U c Irvine,
and I refuse to limit my chuckles. Are people trying
to limit your chuckles? Are you under the oppressive rule
of an anti chuckler? Well, we did have one person
who wrote in and complain about how much time I
spent chuckling on the podcast, and then we talked about
it on a recent episode, and then I got an

(01:20):
avalanche of emails from people who say, never stopped chuckling.
All right, there you go. You got some support from
the internet to keep chuckling. Somebody literally wrote to me
this morning and said, chuckle to your heart's content, sir.
So here I am chuckling away. It seems like a
bit of an overreaction over one comment from the internet.
It's suddenly turned into a social cause. Here free Daniel's chuckles. Now,

(01:43):
I'm self conscious about it. I don't know if I'm
chuckling on purpose, or chuckling to chuckle, or what's going on.
I got to get out of my own head. Oh man,
So they are being limited, they are shackled. Now. I
think maybe it's like a quantum thing. We just shouldn't
look at it so much and just let it be itself.
Let it be both annoying and endearing at this same time.
Stop trying to measure the chuckle and let it be
uncertain but welcome. For a podcast, Daniel and Jorge Explain

(02:06):
the Universe, a production of I Heart Radio in which
we do try to measure the universe, or at least
our understanding of it. Our goal is to use our
minds to try to nail down everything that's happening out
there in the universe from the tiniest little vibrating strings
that might make up the very fabric of reality, all
the way up to cosmic black holes that are swallowing

(02:27):
the centers of galaxies. We think it's a worthwhile way
to spend your time to try to understand the universe,
and we exult in the joy of our curiosity and
the chuckles that we find along the way. Yeah, because
it is a wonderful universe. It's huge, it's amazing, it's fascinating.
It gives us a lot to think about, and, as
you said, sometimes a lot to chuckle about. It's kind

(02:48):
of a funny universe. Funny smelling, funny looking, or funny weird.
It's got all the funnies. It's quantum in that way
as well. It's both funny ha ha and funny uh
at the same time. It's a superposition of funnies. It
is pretty funny weird, that's for sure. So many things
we have discovered about the universe that make us go,
what that can't possibly be true, And then we do

(03:11):
the experiment and the universe says, oh, yeah, that's exactly
what's going on, and it makes us reformulate the way
we think about the whole universe. For me, those are
the best moments in science, when the universe tells us
that we've been thinking about things the wrong way the
whole time. And science is how we explore the universe
and find out how things work and why they are
the way they are. And the way we do that

(03:33):
is with questions, right. Science is all based on questions.
Science is basically just people asking questions. You might imagine
that science is like some big building with columns where
information gets turned out on like a ticker tape or something,
But it's just a bunch of people being curious about
the universe. Every time you spend like nineteen seconds reading

(03:53):
about the life cycle of some guinea pig, it's because
some person has decided to devote their life to studying
that mee pig and how it spends its time. But
what you mean every time I spend nineteen seconds reading
about a guinea pig? Often do you spend nineteen seconds
reading about guinea pigs? Do I need to answer that question?
That's a question I don't want to answer to. I'm
not sure we want to go there. It's just a

(04:14):
hypothetical example. I want people to appreciate the time and
devotion that goes into every single scientific bit of knowledge
we have. Each one comes from some individual needing to
know the answer to that question. So science is in
the end, just a bunch of people asking questions and
deciding they got to know the answer, and then Daniel

(04:35):
deciding he's only going to spend nineteen seconds reading about
their lives work. Well, there is this amazing asymmetry right
in the same way you can spend decades doing research
and somebody can just like skim it on their phone
while they're in the bathroom and they go, oh, that's cool,
and then they move on with their lives. Right, But
think about the millions of people that could be reading
this on their phones. If you multiply I guess those
nineteen seconds of bathroom reading, you get, you know, millions

(04:58):
of seconds of bathroom reading. It's my goal as a
scientist is just to get maximum number of seconds of
bathroom or aim low, you know, just aim somewhere. Who
cares about Nobel prizes or citation counts or fancy awards
seconds of bathroom phone scrolling. That's my new metric. All right,

(05:19):
do you think academis should be based on that? Just
forget about you know, impact factors and h Indices and
Nobel Prices have a new award called the Toilets to Release.
I do think it's important that we reach everybody out there.
It's not important that they're on their toilet while we
reach them, But I do think it's vital that science

(05:40):
communicates outside of just academia and the rest of us scientists,
to everybody out there who's curious about the world and
who's helping to pay for our studies and pay our salaries.
This knowledge and this curiosity belongs to everyone, which is
why we did these episodes where we talk about questions
from not just from cutting edge scientists, but from people
out there like you. That's right, because science effects everybody,

(06:02):
and in fact, everybody has questions about the universe, maybe
not necessarily about guinea pigs or I'm sure people don't
think they have questions about guinea pig, but maybe they do,
and maybe they do have an ultimately question about how
life on nurse is here, why we're here, why is
the earth here, or what would it be like to
live in other planets? Are you saying there are people
out there who don't have questions about guinea pigs? Are
you serious? How many people do you know? Have you

(06:25):
met people outside of your little bubble there? It's just
so easy for your brain to generate guinea pig questions,
for example, how long would a guinea pig last on
the surface of the moon, or on guinea meat or
in outer space? Now you're sounding like a super villain.
I'm not suggesting we do these experiments, but I would
like to know the answer that people do have questions,
and sometimes we answer them here on the podcast. That's right.

(06:48):
If you have a question about something that doesn't make
sense to you, or maybe you heard us talk about
something on the podcast and it doesn't quite click in
your brain, or you were just line in your back
staring up at the stars and wondering what's going on
at the heart of them? Right to us two questions.
At Daniel and Jorge dot com, we answer every single
email and tweet, and we will answer your question as well. Wait, Daniel,

(07:10):
you don't answer all of my emails answer all emails
from listeners. Absolutely, do you listen to our podcast? I
do listen to the podcast. Maybe I just need to
frame it in the form of a physics question. There
you go. But people do send questions to us and
we answer them here. And so today we have three
great questions from listeners about exciting topics like what's it

(07:31):
like to live in a moon of Jupiter? Question about
black holes and whether they have a surface, and also
a question about math, which I guess maybe it's not
as exciting as the first two. What if it's about
guinea pig math? Would that make you more or less interested?
Does that mean like a trial math for the universe? No,
it is an exciting question. Also, it's about the very

(07:52):
nature of reality and whether reality is based on that,
And so it's tackled this first question first, and this
one comes from Billy. Hey, guys, I'm wondering what life
would be like for humans on the moon of a
gas giant. So suppose we find a Jupiter like system
within what we currently understand as the habitable zone of
a star. In this system is a moon that could
sustain human life. What would the day night cycle look

(08:15):
like with the planet or other moons blocking the Sun?
What kind of seasons would you go through with the
passing of more or less massive moons disrupt gravity? And
interesting ways could one of those moons support smaller satellites
like Phobos and demos. M Thanks and I look forward
to hearing your answer. Awesome, Thank you, Billie. That's a
great question, like what's it like? Because we often hear

(08:37):
about how the moons of other planets are maybe habitable,
and there are maybe like the size of the of Earth,
and sometimes they even have water, and so diggussion is like,
what would it be like to live in a moon
of another planet? It's a great question to put yourself
on the surface of one of those moons and think about,
like what would this guy look like? How long would
the day be, what would you see in this sky?

(08:57):
How many eclipses would there be, what would the seasons
be like. It's a really fun question, especially for example,
if you're writing a science fiction novel that's set on
one of those planets, as I suspect Billy might be, Well,
you're really suspicious here. Do you think Billy just has
an ulterior motive here? Can't you be asking out of
cheer curiosity? Absolutely, maybe he is and maybe he isn't.
But after we give our answer, I think he'll be

(09:18):
well set up to write that novel, and I'm looking
forward to reading it him and tens of thousands of
people where you get typing fast billy. But it is
an interesting question. What would it be like to live,
for example, in a moon like Europa, which is a
moon of Jupiter here in our solar system, which has
water and it's it's sort of inhabitable soon, right, Yeah,
and these moons are huge. Remember that Jupiter is much

(09:40):
much bigger than Earth, and so a moon of Jupiter
can be basically the size of a planet. Yeah. And
Europe in particular has liquid water in it, right, Europa
has an icy crust and we think oceans of liquid
water underneath. We're sending probes up there to sample those
oceans because sometimes they crack and shoot geysers of crystallized
water own into space, and we're gonna try to send

(10:02):
something through one of those plumes and see like is
their organic material in there, maybe little frozen microbes. It's
going to be pretty exciting. Yeah, And I think people
have also talked about Titan, right, which is another moon
in here in our solar system that might be livable. Yeah.
A lot of these moons are pretty big and pretty
rocky and might have liquid under the surface, so they
might like naturally have their own life. It's a great

(10:23):
way to ask the question like how likely is life
to evolve? Because it's like an independent way to sample
whether life emerges from similar conditions to what we have
on Earth. And there's another question, which is like, what
would it be like for us if we try to
colonize these places and actually established bases there. What would
your daily life be like on those surfaces? Yeah, and

(10:44):
I guess that's the question Billy had because I guess
if you're in a moon, then you're orbiting another planet,
and then that planet is presumably orbiting the Sun of
its solar system. And so the question is would that
make your days and nights super wonky and unpredictable or
would they make them maybe more predictable, or would you
even have seasons? Things like seasons. Yeah, it wouldn't make

(11:06):
it less predictable, but it would make it very, very
different from our experience. Earth. For example, currently just orbits
the Sun and we have a day night cycle because
of the Earth's spin. If your moon around Jupiter, for example,
then what determines whether you're seeing the Sun or not.
It's not your spin, but how long it takes you
to go around Jupiter. Wait, what do you mean Why
is it determined by your orbit around Jupiter. Wouldn't it

(11:28):
also depend on your inherent spin of the moon. There's
a couple of reasons. One the reason is Jupiter is huge,
and so it's going to eclipse the Sun pretty often.
Right half the time, You're gonna have Jupiter between you
and the Sun, and so because Jupiter is so big
in your sky, you can have like hours long eclipses
every day. Okay, maybe, um, let's get down to specifics,

(11:50):
like if I was in a moon of Jupiter, what
should I expect to see in terms of day and night?
How often would I see the Sun? One key thing
to understand is that these moons tend to be tidally locked,
meaning that one side of them faces Jupiter and one
side of them doesn't, just the way that like our
moon faces the Earth. So there's the near side of
the Moon and the far side of the Moon. We
always see the same side of the Moon from Earth.

(12:13):
But that doesn't necessarily mean that you're sort of going
around the Earth at the same rate that the Earth
is spinning, Like the Moon has a certain period around
the Earth, but the Earth is also spinning. So it
gets kind of complicated right, that's right. The Moon sees
different parts of the Earth, right, but the Earth always
sees the same side of the Moon. But now put
yourself on the Earth sized moon around Jupiter. It takes

(12:33):
like eighty five hours for Europa, for example, to go
around Jupiter. So now your day night cycle is determined
by how long it takes you to go around Jupiter. Okay,
so like if Jupiter was standing still, Europa would take
eighty five hours to go around to orbit around Jupiter.
That's what you're saying, Yeah, exactly. And so at any
given time, if it's on the side of Jupiter that's

(12:55):
facing the Sun, and the outward facing side of the
moon of Jupiter would see the sun, but the inner
part of this, the part of the moon that's facing Jupiter,
would not see the sun. Yeah, so you have like
two important hemispheres. You have the far side of Europa,
the one that's facing away from Jupiter, and the inner
side of the one that's facing towards Jupiter on the
far side, the outer side, that part never sees Jupiter.

(13:17):
Jupiter never appears in the sky on the far side
of Europa. But you do have eighty five hour long
day night cycles. So you have like forty two hours
of sunlight and then forty two hours of darkness. And
that's a big difference from what we have here. Right,
we have twenty four hour long periods which are determined
by the spin of the Earth. On Europa, the day
night cycles to term by how long it takes to
go around Jupiter. And a longer day night cycle means

(13:39):
higher temperatures during the day and colder temperatures at night. Yeah,
you gotta pack a heavier sweater. I guess, But I
guess if you're on the outside of the outward facing
side of the Moon, then life would be pretty regular, right,
and be sort of like here, except just longer days. Yeah,
it would be here, just longer days. And it depends
on how close in your orbit. For example, gannymed it's

(13:59):
pure it is like a hundred and seventy hours, and
I owe its period is forty two hours. So it
depends how close you are to the gas giant. You
can have a much longer or a shorter day night cycle.
It depends on how long it takes to go around
the gas giant instead of how fast you spin. And
all of those moons are tidally locked to Jupiter, Like
they're all always facing the same way towards Jupiter. Yeah,

(14:22):
they are. Okay, So like half of the world or
half of Europa just sees the regular day night cycle,
and I guess also regular seasons, right, because then the
season is kind of depend on whether Jupiter is farther
or closer to the Sun. Yeah, the seasons depend on
the tilt of the planet, right, And so Earth's axis
of rotation is tilted relative to the Sun's for example,
so part of the year the northern hemisphere is closer

(14:43):
to the Sun, and the other part of the year
the southern hemisphere is closer to the Sun. If you
have no tilt, then you don't have seasons. Every part
of the year is the same. If you're on a
moon of a planet that's tidally locked to that planet,
then the moon's tilt is connected to the planet's tilt.
In the case of Jupiter, for example, the tilt is
actually pretty all It's only three degrees, much less than
Earth's tilt. So on Jupiter the seasons are more mild.

(15:06):
The winter and summer are not as dramatic. So if
you're on the XO moon of a planet that isn't
tilted very much, then you're not going to have seasons.
You could also imagine being on the moon of a
planet that it tilted more. I see, so the seasons,
for example in Europe, at least in our case where
there isn't a lot of tilt, the seasons would be
pretty mild or like not a lot of variations in
the seasons like we have here on Earth. But maybe

(15:28):
that you're saying that day and night cycle would be
pretty dramatic, like the days would be super hot and
the nights would be super cool. And if you're on
the inside surface of the Moon, the one that's always
facing Jupiter, then things are pretty dramatic because Jupiter would
be huge in your sky. For example, you're on Europa,
then Jupiter would be like twenty times as big in
the sky as our moon is here on Earth. It

(15:50):
would be a huge thing. You'd see it all the time.
Would be like a giant thing blocking your your view. Right,
you see Jupiter like a huge thing in the sky. Yeah,
And you would see eclipses basically every day, right, because
Jupiter would get between you and the Sun every single day,
and every time you get that eclipse, it will it
will look like night, right, because Jupiter castle sich a

(16:10):
huge shadow. Yeah, so you have this day night cycle,
but then on the inside surface of the Moon you
also have a daily eclipse, which is like a mini
night in the middle of your day. So like everybody
takes a siesta, sounds great, let's move to open And
if you think about it, also, how much you see
of Jupiter depends on its relationship to the Sun, the

(16:30):
same way that like our moon, either looks full in
the sky if the sun is shining straight on it,
or it can look dark if the sun is shining
on the other side of it. The same thing will
happen to Jupiter. You could have like a crescent Jupiter
or a full Jupiter. Right, it would be pretty dramatic.
And also probably Jupiter would be spinning, so you would
see different sides of it as well, like sometimes you

(16:51):
see the red eye, sometimes you wouldn't. It would be
pretty beautiful actually, because Jupiter is a gorgeous planet. It's
got so much texture on it. It's frankly a lot
better looking than our moon. Well, it depends on your taste,
I guess, But I guess we're saying that if you're
on the side of the Moon and Jupiter that's facing Jupiter.
Then you would basically like your day would be split
into too many days, kind of like you would see

(17:12):
the sunrise above your horizon, but then it would dip
behind Jupiter then when it come out of Jupiter, and
then it would sunset back to the horizon on the
other side, right, and the sunset could be pretty dramatic
as well. Right, you have like light bending around Jupiter.
You have like sunsetting behind Jupiter, which would be pretty
dramatic because then the sun is being filtered through the
Jovian atmosphere, which would be pretty cool. And at night

(17:34):
you might have a really dramatic auroras like the northern
lights and the Southern lights. Cool. So you would have
to sunsets and in two sunrises every day, yeah, exactly,
you'd have one over the horizon of your own moon
and one over the horizon of Jupiter. All right, Now,
this sort of depends a lot on like you said,
the tilt, but it is maybe a pretty typical example

(17:54):
if you have like a big gas giant and with moons, right, like,
if that was somewhere other in another solar system, the
like the probability is that the Moon will be tidally
locked to the giant planet. Right. Yeah, it depends a
little bit on how close it is. The closer moon
gas planet, the stronger this effect is. You can also
have more complex tidal relationships, like, for example, Mercury is

(18:16):
technically tidally locked to the Sun, but the same side
of Mercury doesn't face the Sun all the time. It's
a complicated three to spin orbit resonance where it does
like three flips every two times around the Sun. So
you can get even more complex relationships. But we do
expect in other solar systems to see gas giants near
the habitable zone. Like in our solar system we have

(18:36):
Jupiter and Saturn kind of far out compared to the Earth.
But in many other solar systems we see in telescopes
we see what we call hot Jupiter's big gas giants
much closer to the Sun than our gas giants. So
it's possible they have moons inhabitable zone. Yeah, and those
moons would see a pretty regular day and night pycho,
which might be an ingredient for life. Right, Like it's

(18:58):
things were totally chiotic. If your days and nights were
totally unpredictable. Maybe life wouldn't be able to thrive in
a place like that. Yeah, it would be really amazing
to see life develop in other cycles, Like what would
it be like to have a big night and a
mini night and how would that affect the development of
life and reproductive cycles. Be really amazing to see those
experiments play out in reality. Yeah, everyone would be like

(19:20):
the Spanish were like, what you don't take siesta? Everybody
takes siesta, even the plants, even the guinea pigs or
I guess exo guinea pigs on that planet. Would they
still be called guinea pigs? Well, I think that answer
is a question. For Billy, life on an extra moon
of a gas giant in another solar system would be
most likely pretty regular. Now let's get to our next question,
and this one is about black holes and whether they

(19:43):
have a surface. So we'll get to that question, but
first let's take a quick break. Alright, we were answering
listener questions and we just answered one about what it's

(20:05):
like to live on a moon of a gas giant
in another solar system. This one has asked kind of
a similar question, almost and it comes from Bobby Pelod
annual Horge. My name is Bobby from Arizona. This question
comes to you is kind of a two part Could
a black hole have a surface in that if you
gathered enough materials, let's say iron at a thousand or

(20:25):
billions of times the mass of the sun, and it
became a black hole, would you be able to fall
in that hole hypothetically and stand on the surface of
that solid iron. Additionally, could this same black hole potentially
gather enough materials around it to spark fusion again within
the black hole? All right, A little bit of a

(20:47):
mind bending question here is can a black hole have
a surface inside of its event horizon? And could you
maybe like spark a sun inside of the hole? Man?
I love that image of a sun hidden inside a
black hole, like fusion burning away furiously pumping out photons
which are forever trapped by the black hole. So thank

(21:08):
you Bobby for this question. What do you think Bobby
was thinking? I think Bobby, like many people, is wondering
what's going on inside a black hole? When stuff falls
inside a black hole, what happens to it, what does
it do? What is the structure of matter in there?
What kind of weird stuff does it form. I think
that's sort of the heart of his question, and that's
a question that many people have, including black hole experts

(21:31):
and cosmologists and astronomers. Basically everybody wants to know what's
going on inside a black hole. All right, well, let
maybe let's dig into this and let's be maybe clear,
because black holes do kind of have a surface to them, right,
They have an edge to them, which is kind of
like the where the black starts. Basically, there's definitely like
an edge to a black hole in the sense that
we can say there's a point of no return. If

(21:53):
you get closer to the black hole than this, then
all paths lead towards the center. There's no escape, right.
That's what we call the event horizon. It's like a threshold,
but it's not a surface in the sense that it's
like a physical boundary. If you're falling into the black hole,
you don't necessarily even notice when you pass the event horizon.
There's no like gatekeeper there or force field or anything.

(22:16):
You can't even necessarily know whether you're past the event horizon.
The only way to know if you're past the event
horizon is to do the calculations and see if there's
any path out for any particle, even into the infinite future.
So there is this distance from the center of the
black hole we call the event horizon. That doesn't necessarily
mean that that is a surface. It's a surface only
in sort of a mathematical sense, right. It's it's kind

(22:38):
of like you say, a boundary, but it is a
three dimensional boundary, which kind of makes it a fear. Technically, yes,
and that one that's the mathematical event horizon, but that's
not necessarily what we see when we look at pictures
of a black hole. That's not necessarily like the black
that we see in those pictures, right, That one's bigger
than this event horizon, But that is that does sort

(22:58):
of look like a surface. Yeah, you're used to looking
at something and seeing it the way it is because
your mind is used to reconstructing objects in front of you,
assuming that light travels in straight lines, which is why
your mind gets confused. If you're looking at like a
bendy mirror or through some lenses, things look distorted, right,
in the same way, space itself is distorted even outside

(23:21):
the black hole, and light doesn't travel in straight lines.
It gets all twisted and bent. So what you see
when you look at a black hole is not the
actual physical extent of the black hole, but an image
of the black hole that's been distorted by these weird
paths that light follows. So specifically, you see a black
circle that's actually larger than the event horizon and includes

(23:42):
not just the part of the event horizon that's facing you,
but also the part from behind. Like photons that leave
the event horizon from behind the black hole get bent
around by the gravity and then back towards your eye,
so you can see the entire surface of the black
hole from any side of it, right, So, and that
sort of counts as a surface, right. You said the
word surface in the sense that maybe you wouldn't be

(24:02):
able to tell us you're falling in, but maybe somebody
from the outside would see you sort of fall into
that surface, right where they would see a surface relative
to somebody falling in. Yeah, it's definitely a boundary. It's
a surface mathematically, it's not a surface in the sense
that you could like stand on it. There's nothing there
to support you. You can't like walk around on the
event horizon. Right. So, I think Bobby's question now here

(24:23):
is whether or not a black hole has a surface
in the sense of like having a physical hard surface
on which you can actually like stand or into which
you would crash if you fell into a black hole.
Because I imagine maybe he's thinking, like a regular hole
here on the ground on Earth. It's a hole, and
you would fall in, but eventually you would hit something.
And if there's a whole bunch of stuff in the
hole you or like like a trash or something, you

(24:44):
would eventually fall into the hole, but then you would
hit the pile of trash. And so I think maybe
Bobby is wondering, like, you know, the black holes have
all this stuff inside of him. If you fell into
the black hole, wouldn't you eventually hit this stuff? Yeah,
And it's a great question when you think about this
is in terms of the forces. So gravity is very
powerful when things get very massive and things get very close,

(25:04):
but it's not all powerful, right, Like think about the
huge ball of iron in the center of the Earth.
Why isn't that a black hole. It's not a black
hole because iron has internal structure, has enough internal structure
to resist the gravitational collapse, like the atoms pushing against
each other that form this ball of iron, they resist gravity.
But inside a black hole, gravity is much much more powerful.

(25:28):
It's more powerful than the structure of iron. It's more
powerful than any sort of bond that we are aware of.
We don't think there's anything that can overcome the power
of gravity once you are inside the black hole. So
if you take a big blob of iron, as he said,
a huge mass of iron, like millions of times the
mass of the Sun, and collapse it to a black hole.
Once all that iron is inside the black hole, it

(25:49):
doesn't have the strength to resist the gravitational collapse. And
that's why general relativity predicts a singularity. It says that
things just keep compressing and compressing and compressing until you
get dot of infinite density. M hmmm. I think you're saying,
like here on Earth and there's a bunch of stuff
at the center, but it's not collapsing because other forces
are keeping gravity from collapsing further, you know, like the

(26:12):
electromagnetic force between all of the electrons and the protons
and the corks inside of the atoms in Earth's core.
But in a black hole, like we've sort of done
something different. We've like accumulated so much stuff that gravity
is so powerful it squishes even the electromagnetic force, like
it just squeezes everything down theoretically into an infinite point. Exactly.

(26:32):
You can have a certain mass of iron and you
can hold itself up, but if you make it too massive,
gravity gets too strong and then it collapses. And that's
how black holes form. Right. Black holes form from stars
that made too much heavy stuff at their core, so
they're no longer able to resist gravity's collapse, and then
it turns into a black hole. So all that iron,

(26:52):
according to general relativity, forms a singularity, a dot at
the center of the black hole where all of that
mass has accumulated. And so unless you can walk around
on an infinitesimal point, according to general relativity, there's not
really a surface inside the black hole, and there's no
chemistry going on and no fusion or no anything else. Right,
are you saying, at the center of a black hole,
there's no surface, there's no pile of trash or iron,

(27:14):
there's just an infinite dot. But what about the stuff
getting to the dot? Isn't that stuff accumulated? Maybe? Yeah,
that's a good point. It takes a finite amount of
time once you pass the event horizon to reach the singularity.
And so if the black hole is actively feeding, then
you have singularity surrounded by stuff that's still falling in,
you know, sort of like a toilet bowl of stuff

(27:36):
swirling around it. And remember this is according to general relativity.
Einstein's equations predict this runaway effect that leads to a collapse,
that leads to a point because in Einstein's theory, space
is smooth and continuous, it can be chopped up into
infinitely small slices, and you can also know where everything
is at all times. These assumptions are in total contradiction

(27:57):
to what we know about the universe being quantum mechanical,
and so physicists don't take this prediction of singularity seriously.
We don't see it as like an actual prediction of
what's happening inside. It's sort of like an indication that
the theory itself is breaking down because it predicts something
kind of crazy, right, physicist, something that maybe general relativity
is wrong, and you wouldn't get a singularity at the

(28:18):
center of a black hole. You would maybe get like
a quantum blob. Yeah, we think that something will prevent
the singularity from happening, because you can't confine particles to
an infinitely solved space without giving them effectively infinite energy
because of the quantum uncertainty principle, and so there's a
minimum quantum fuzz to the universe always. So when you
try to compress matter really, really far, there must be

(28:39):
some quantum mechanical way that they resist becoming a singularity,
you know. I think of them as sort of like
layers of defense. Matter has many ways to protect itself
from collapsing. First, there's like the chemical internal structure like
the Earth, or if you have a star, then it's fusion,
which is pushing out and pumping out energy to prevent collapse.
If you're like a neutron star, then there's like the
neutron degeneracy. We don't know what's going on inside a

(29:01):
black hole. There might be something else quantum mechanical that
matter can do to resist being compressed into a singularity.
To know how that works, we'd have to have a
theory of quantum gravity, which we just don't have that.
There's lots of fun ideas about what might be going
on inside. Yeah, and so inside of a black hole
there might not actually be a hole. I think it's
what you're saying, or it would still be a hole.

(29:23):
There just wouldn't be a pinpoint singularity in the middle.
And it might be that the stuff inside of the
hole is still holding together or you know, making a pile,
due to some other quantum force. Yeah, and it's very
unlikely that if you throw a bunch of iron into
a black hole that it's going to stay iron. It's
going to turn into some other completely different state of

(29:44):
matter because the iron molecules are not going to be
able to survive that intense experience. They're gonna get shredded
apart to their basic constituents. Maybe even the protons will
get pulled apart into their quarks. Maybe those quarks we
have pulled apart into whatever they are made out of.
We just don't know. From outside, it still just looks
like a black hole. You can't see beyond the event horizon.

(30:04):
So gravitationally speaking, a singularity or a quantum blob with
the same mass all acts the same from the outside,
So as you say, it still looks like a hole. Yeah,
But to Bobby's question, then if there is a quantum
flows ball in the middle, that means that the inside
of a black hole there would be a surface, right,
like a physical surface that you could maybe stand on,
if you could somehow survive or even think inside of

(30:27):
a black hole, right, Yeah, perhaps it depends a lot
on that theory of quantum gravity. So what's going on
inside it? You know, we talked to the podcast once
about the dark star theory that black holes are not
actually black holes. They're just very slowly collapsing stars that
will reach a minimum point from quantum mechanics and then
bounce back out and turn into like white holes eventually.

(30:49):
And so that's also not the kind of thing you'll
necessarily be able to walk around on a collapsing star
unless you have like really good boots. Yeah you have
dark Star shoes. But achnically it would have a surface, right,
It would answer Bobby's question, And the answer would be yes,
there would be like a physical blob inside of a
black hole, and that has a surface that you could

(31:09):
stand on or throw things at, and that they would
splat you stand on in sense that you could like
be there on top of it. I don't know if
he would absorb you or pull you apart or melt
you instantly, So I certainly wouldn't recommend it to anybody
out there who's considering it, It It sounds like people maybe
want to test it first, you know, by throwing like
an animal at it. What what kind of animal the
people usually do experiments with first? Is it bananas? Hamsters?

(31:34):
I can't remember bananas animals on other planets. Maybe exo
bananas might be in the animal category. Oh my goodness,
he'll bring up all kinds of ethical issues for me there.
Did I tell you, by the way, what my kids
dressed up as for Halloween? Well, my son has become
very long and lean, and so he dressed up as
a banana. All right, He's aspiring to the greatest fruit

(31:56):
on the planet. So we had a banana in the family.
But I'm not throwing him into any black holes no
matter what he wears on Halloween. Yeah, I might get
a little slippery, but I think that answers Bobby's question.
Could a black hole have a surface? The answer is yes.
I mean it has kind of a threshold surface. It
has a visual surface, which is the part that looks black,
and it may if general relativity is wrong, and we

(32:19):
think it most probably is, it does have maybe a
physical surface inside of the hole. It certainly might It
could be a dark star, it could be a fuzzball
made of strings, it could be something else entirely we
haven't yet imagined. If we could see inside a black hole,
we could know what happens when you compress matter in
these extreme circumstances, and we could learn something about the
fundamental nature of reality. All right, well, thank you Bobby

(32:41):
for that question, and now let's get to our last question.
This one's about the very nature of the universe and
whether or not it all adds up. So we'll tackle
that question. But first let's take another quick break. All right,

(33:05):
we were answering the listener questions, and our last question
is about the nature of reality. It comes from Matthew. Hello, Daniel,
and ho. I have a question about the math of
the universe. What is it? Trigonometry, algebra, calculus, the math
of space exploration. I was thinking about the James Web

(33:27):
space telescope out there in Lagrange too. How the heck
that was math? Right, Like somebody was like, oh, look,
here's the math. We can put this thing there and
it'll stay put because it's like circling the Sun with
the Earth and the Moon. But then it's like doing
little loop de loops in addition to the circling the sun.

(33:51):
And another thing, how do they get it to stay
focused on something a billion trillion miles away when it's
doing all that motion? Are they kind like firing thrusters? Anyways?
Tell me about the math of the universe, like from
the olden days to now? What the heck trigonometry? What
is it? Like that scene in Apollo thirteen where they'll

(34:13):
check their math and oh, my gosh, I gotta know more.
All right, thank you Matthew for that awesome question. Also,
I think, uh, I think that's my reaction to a
lot of these things about the universe. What the heck?
I can't? I can't anymore. It is amazing how the
universe works and how it seems to be so describable
by math. It really is incredible. Yeah, And so that's

(34:35):
Matthew's question, is that he's asking what is the math
up the universe? Is it trigonometry, algebra, calculus, long division?
It is really interesting to wonder which parts of math
describe the universe, because you can imagine that we could
invent a whole bunch of math that doesn't describe the universe,
that isn't relevant necessarily. What do you mean, Like, you

(34:56):
can have mathods as one plus one equals two of it,
but but maybe you could have a neverse where one
plus one doesn't equal to no. I mean that you
can invent kinds of math that don't have to reflect
the physical universe. For example, you can invent weird kinds
of geometry, you know, surfaces that live in eight dimensions,
but the universe might not be eight dimensionals. So you
can spend your whole life thinking about the mathematics of

(35:17):
eight dimensional objects, but that's not actually relevant to our
universe if our universe is just three dimensional. But you know,
we don't know how people spend, for example, decades developing
ideas called group theory about how things relate to each other,
then later it turns out to be totally relevant to
particle physics. So you never know what math is going
to be relevant. But it's definitely possible that there's kinds

(35:39):
of math which are not relevant to the universe, right.
But I guess it's kind of a tricky philosophical question
because like, if you can come up with math that
makes sense, doesn't technically mean that it exists in the universe.
Even if you can find like a you know, a
law of particles that follows that math. The maths is
still there and it makes sense in this universe. Doesn't

(35:59):
mean it it's part of the universe. Yeah, It's one
of the deepest questions in the philosophy of math, like
are those numbers real and the part of the universe?
And then you get into weird things like well, what
does it mean to be real? Because like those numbers,
the number two, where is the number two? Right? Everything
else that's real has like a location, it has behavior,
can participate in experiments. You can talk about whether protons

(36:22):
are real and you can do tests on them. You
can't do that for the number two. There's no way
the number two can like participate in experiments, can cause effects.
So if it's real, it's real in a different way
than other things that are real. But I think maybe
Matthew's question is not so much about these big philosophical questions.
I think maybe he's coming at it from a more
intuitive point of view, which is like, you know, does

(36:44):
the universe have a mathematical description? Can you describe the
universe with math? And if you can, what kind of
math is it? Is it trigonometry, algebra or is it
just all addition all the way down. Um. I would
say there's two parts of that answer. One is what
kind of math do we use to describe the universe?

(37:06):
And the other is whether we could boil that down
to one sort of like basic kind of math. So
on the first one, we tend to use calculus a lot.
Like calculus is often described as the language of physics,
it's really a very very powerful tool to describe what
we see about the universe. That's because calculus is like
the mathematics of change. If you have something flying through

(37:27):
the air with a certain velocity, that's fine. But now
if you want to change that's velocity and you want
to understand where it's gonna go, you have to accumulate
all those changes and figure out where it's going to land.
That requires calculus. So the mathematics of change is really
the mathematics of motion in our universe. So calculus is
really fundamental, right because we have you saying because we

(37:49):
have time and universe and time kind of implies change
and we need calculus. But it's also I think a
little bit maybe more fundamental, I wonder, because it calcula
is also about how the rates of change the pend
on each other, right, Like we seem to have found laws,
for example, like F equals m A that says that,
you know, the rate of change depends on this force

(38:09):
or that force or this situation, and so it seems
like the universe has laws that govern over the rate
of changes of things, and that's why calculus is useful. Yeah,
Calculus is useful because he gives us these tools, and
we can express the laws of the universe that we
discover in terms of those So you're right, almost all
the laws of physics, like F equals m A, that's

(38:31):
an expression in calculus, because a is a derivative. Acceleration
is the rate of change of velocity. That's a differential
that's part of calculus. Force is really change in momentum
with respect to time, right, and so that's a differential.
So you're absolutely right that most of the laws of
physics can be expressed in terms of objects that were

(38:51):
invented for calculus. But calculus also handles things that are
not rate of change with time. You know, calculus lets
you integrate over space. Also, if you have an object
that has like a varying density and you want to
know it's total mass. You can integrate over the object
over space in order to get the total mass if
the density is varying. So calculus is the math of
change of time or of space. Yeah, and then what

(39:14):
happens when you go down to the quantum level? First
of all, does calculus still apply or does it get
more into like quantum of waves and and functions and fields.
Is calculus still useful there and maybe even appropriate because
the world is quantized. It's absolutely still useful there. Like
the shorting your equation, that's a differential equation. Absolutely, it's
a wave equation which tells you how the wave changes

(39:36):
in space and how that relates to how it changes
in time. So calculus super fundamental, and the basic theory
of the standard model, which we call quantum field theory,
is full of calculus because calculus involves integrals, and integrals
allow you to add up over many, many different things.
You can add up slices in time or slices in
space a quantum mechanically, it also leads you add up

(39:57):
different probabilities. So, for example, one important formulation of quantum
mechanics by Feinneman says, if you want to understand how
a particle moves from A to B. You have to
integrate over all possible paths of the particle. So calculus
lest you consider multiple different possibilities simultaneously. So it's crucial
to quantum field theory. Right, So calculus is pretty useful,

(40:19):
So kids pay attention to that class when you when
you get to calculus. But I guess maybe a question
here is is calculus the theory to use for the university?
Like it's useful and you definitely seem to be able
to use it to describe a lot of the universe
and even predict a lot of what happens in the universe.
But maybe we're just kind of lucky, Like maybe calculus
just sort of works most of the time, and so

(40:39):
we think it's the way to go. But maybe there's
a different math the here that would describe the universe
in more detailed The more we learn about it, is
that possible? It certainly is possible, and we're constantly improving
on and developing new techniques in calculus. It's not like
calculus is a finished thing. It's not like Newton enliven.
It's invented a few and years ago and now it's done.
People are still working on it, like today, figuring out

(41:00):
ways to do complicated integrals and whole new techniques that
that makes previously unsolvable problems now solvable. So it's definitely
a developing field and it's improving, and so that means
that in the future we will have more powerful math
that describes the universe even better, because there's lots of
things that we still don't know how to do, problems
we can't solve, probably because we just don't have the

(41:22):
mathematical tools for them. Yet you're saying is pretty good
and we're going to stick with it, But maybe less
you were saying, the deeper question is whether or not
this is just in general, using math to describe the universe,
if that is something fundamental about the universe, or it's
just our way of understanding it. This is the question
the philosophers of math debate and have been debating for

(41:43):
thousands of years and probably will keep debating for thousands
more years. I'm not sure it's something they can really
make progress on that Really at the heart of it,
we're asking whether math describes the universe or whether it
controls the universe, Like is the universe itself mathematical. Is
math part of the universe itself or is it just
our description of it is the way that we organize

(42:05):
our thoughts. Is it like a convenient way to think,
or is it really the source code of the universe itself?
And telling the difference between those things is pretty tricky.
You mean, like the difference is kind of like whether
the universe actually cares about math, right, because maybe, like
in one scenario, the universe just does its thing and
the universe doesn't even care about math or know what

(42:25):
math is. The other scenario is that the universe is
kind of beholden to math or somehow the universe is
math at its core. That's the difference, right, Yeah, that's
a good way to think about it. Sometimes the way
I think about it is in terms of like a
computer program. Say somebody writes a computer program and then
you use it Microsoft Word for example, and you could
try to like figure out how word works, and you

(42:46):
could reverse engineering using some other programming language. Maybe it
was written in Python and you figured out how to
write it in C. Right now you have a description
of this computer program in your own language. That doesn't
necessarily mean that that's the per brand that's actually running
inside of word. You might just have a description of it,
or it might be that you've discovered the actual source

(43:06):
code ForWord itself. In the same way, the math that
we are building might be the actual code that the
universe is following. Or it could just be a good
description of it. And there might be other possible descriptions
that are equally valid. We just don't know, all right, Well,
which is it? Then? I guess I wish we knew.
One of my favorite philosophical attempts to answer this question

(43:26):
came from hartree Field. He said, let's see if it's
possible to do science and physics specifically without any math,
without any numbers at all, Like, can you devise laws
of physics that don't have numbers in them? Wait, numbers
or even like variables and symbols or none of that,
none of that at all, he writes in his book,

(43:48):
like I denied that numbers exist. He wrote this whole
book called Science Without Numbers where he was admitting that
math is useful, but he was trying to prove that
it's not necessary by building up a new version of
these theories that didn't use any numbers. What what would
that even look like if you wrote it down, that
you have to write down something. While on page forty

(44:10):
seven of his book without Numbers, for example, he talks
about how to do this. It's pretty philosophically intricate. He
like abuse points of space with certain kind of properties
so that you don't ever have to do any calculations.
Like most specifically he thinks about gravity and how gravity work,
and when we do gravitational calculations, we create all sort

(44:31):
of abstract intermediate ideas, like the gravitational field that we
say that the Earth is pulled on the Sun because
of the gravitational field of the Sun. And he's like,
you need numbers to describe that field, but what if
that field wasn't there. You don't ever observe the field directly,
You just observe the Sun pulling on the Earth. What
if that's just something that space does and there is
no field at all. That's an example of how he's

(44:53):
trying trying to rid the calculation of intermediate steps that
need numbers to describe them, but all tim redly would
and you have to write it down, And what do
you eventually have to you know, have an equation or
something you know in his formulation of Newton's gravity, there
are new equations, there are no numbers, there is no mathematics.

(45:13):
It's hard to imagine because we think that math is
the answer, right, Like you do a calculation, you get
a result, it says, oh, the force on the earth.
Is this for us? Math is the language itself. But
he developed a way to perform these calculations to think
about it that doesn't have math as the internal steps
or either as the answer. And is this credible? Does
this seem suspect or is this like an actual valid

(45:35):
possibility for the universe. I think that most philosophers see
its like a heroic effort to make the point that
maybe math isn't necessary. But there's a lot of steps
he took along the way which people quipple with. And
people don't think that this effort could be applied to
like everything in physics. And so it's like, hey, cool point, man,
But it doesn't really work. It doesn't really convince anybody

(45:56):
that you don't need math to do science. I see
people are like, hey, there are a number of errors
in your theory, and then he's like, wait, but there
are no numbers exactly. I think that most people, most
mathematicians and most physicists think that math is an inherent
part of the universe, right, But then I guess the
larger question I was kind of alluding to is whether
the universe cares if there's math or not, or like

(46:17):
which came first, math or physics. I don't know what
it means for the universe to care about something, but
I think there is another interesting aspect to Matthew's question,
which is, like which math is essential? Trigonometry, algebra, calculus.
And that's interesting because you're like slicing up math now
into different categories which are a little bit arbitrary, right,

(46:37):
Like calculus uses trigonometry and algebra and all of these things.
But there actually is a really interesting effort inside of
math to try to like boil all of math down
into the shortest list of rules you would need to
build up all the rest of math, like to find
the core axioms at the heart of it all. Oh, yeah,
where is that coming from? From the math fields or

(46:57):
from the physics fields? That comes from mathematics? Like a
hundred fifty years ago, people have been doing math for
thousands of years. About a hundred and fifty years ago,
people were like, hold on a second, what are the
basic rules of math? Anyway? And so there was a
guy named Piano who showed that almost all of arithmetic
can be boiled down to just a basic fuel rules,
and then people who came after him showed that most

(47:18):
of math could be boiled down to arithmetic, and then
later people showed that most arithmetic can be boiled down
to something called set theory, which is math about like
groups and what's in a group, what's out of a group?
How do you combine groups? How do you overlap groups?
So the current like idea about the very foundation of
math is that in the end, it's all about sets.
It's all about like what's in a group, what's out

(47:38):
of group? From that you can build arithmetic, and from
that you can build calculus. So fundamentally, we think that
the description of the universe is mathematical and it's all
set theory all the way down. That's kind of what
I was saying, Right, there's addition. Basically, it's just a
group exactly. It's addition and its popularity. It's all clicks

(48:00):
versus very elitist or it's all about clickbait. All right, Well,
I think that answers Matthew's question, what is the math
of the universe? Well, the answer is, so far calculus
has been really useful in describing the universe, but um
physicists are not sure if maybe even calculus is the
fundamental way to describe the universe, or even the most
fundamental um way to describe math itself. That's right, but

(48:22):
that doesn't mean we don't like thinking about these questions
and wondering about what's going on in the heart of
the universe and why it is even possible to describe
it mathematically or to make sense of it with our
little primate brains. So you're gonna keep going until it
all adds up, or until you ask what the heck?
I can't even until we're part of the in group
that actually knows some answers, until we're all guinea pigs,

(48:43):
we're all test subjects in this universe living on the
surface of some crazy exo moon or black hole. All right, Well,
thank you to everyone who sent in their questions. We
love answering questions. We hope you enjoyed that. Thanks for
joining us. See you next time. Ye, thanks for listening,

(49:07):
and remember that Daniel and Jorge Explain the Universe is
a production of I Heart Radio. For more podcast for
my heart Radio, visit the I heart Radio app, Apple Podcasts,
or wherever you listen to your favorite shows. Yeah.