Why is there quantum uncertainty?

Daniel and Jorge wrestle with one of the fuzziest concepts in quantum mechanics

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Episode Transcript

Speaker 1 (00:00):
Hey, quick announcement everyone, we have just joined TikTok, So
head over there and follow us to see videos of
Daniel asking and answering science questions. All right, enjoy the pod.

Speaker 2 (00:18):
Hey Daniel, does quantum mechanics really explain reality?

Speaker 1 (00:22):
I mean I think so, even though it's pretty weird.
Are you sure? Well? Lots of experiments we've done over
the last century.

Speaker 2 (00:29):
See yes, Yeah, But like, how can you be certain?

Speaker 3 (00:32):
You know?

Speaker 2 (00:32):
I thought quantum mechanics is everything is uncertain.

Speaker 1 (00:35):
Well, we're very certain that quantum mechanics is uncertain, but
only about certain things.

Speaker 2 (00:41):
I'm pretty certain that makes no sense.

Speaker 1 (00:43):
I think it's curtains for certainty.

Speaker 2 (00:45):
Are you sure about that?

Speaker 1 (00:47):
Now? I'm not sure about anything.

Speaker 2 (00:49):
I'm welcome to being a non physicist.

Speaker 4 (01:06):
Hi.

Speaker 2 (01:06):
I'm poor Hendrick Cartoonis and the author of Oliver's Great
Big Universe.

Speaker 3 (01:10):
Hi.

Speaker 1 (01:10):
I'm Daniel. I'm a particle physicist and a professor at
UC Irvine. Or at least I was certain of that
a moment ago.

Speaker 2 (01:16):
Yeah, Now you're not sure that you have a job,
so he might have said something to get you fired here.

Speaker 1 (01:23):
Yeah, that's one of those questions you shouldn't ask because
it might change the answer.

Speaker 2 (01:27):
I thought ye had tenure that prevented them from firing you.

Speaker 1 (01:31):
There are still limits to what we can do even
if we have tenure.

Speaker 2 (01:34):
But anyways, welcome to our podcast Daniel and Jorge Explain
the Universe, a production of iHeartRadio.

Speaker 1 (01:39):
In which we test the limits of our understanding of
the universe. How certain are we that the universe works
in a different way on a tiny scale, that there
are tiny quantum particles fluctuating in and out of existence,
that when we zoom down to the universe at its
smallest scale, different rules apply. On this podcast, we pushed
all those limits and we try to answer all of

(02:00):
your questions.

Speaker 2 (02:01):
That's right, because it is a wonderful and amazing but
yet also a very mysterious universe that seems kind of
random at times, but also seems like a giant clock
that seems to be working precisely as it's supposed to be.

Speaker 1 (02:14):
And the big goal of physics is not just to
reassure us that the universe works the way our intuition suggests,
but to discover the truth. Science is a knowledge building mechanism, right,
It's a way to figure out how the universe actually works,
even if it's deeply in contradiction with the way we
thought it worked.

Speaker 2 (02:31):
Wait, I thought philosophers thought that you can never uncover
the real truth of things. It's impossible to be completely
certain about the truth.

Speaker 1 (02:38):
Philosophers don't even agree about what you mean by the
real truth.

Speaker 2 (02:42):
Well, I see, it's about I guess vocabulary.

Speaker 4 (02:44):
Man.

Speaker 1 (02:44):
Every philosophy argument in the end comes down to vocabulary. Like,
what do you mean when you say vocabulary? Anyway?

Speaker 2 (02:50):
Oh, you can get a few inception levels deep into
this discussion.

Speaker 1 (02:55):
What do you mean by what do you mean exactly?
What do you mean?

Speaker 2 (02:59):
What is meaning?

Speaker 1 (03:00):
Yes? What is meaning? What is a question?

Speaker 2 (03:02):
Anyway? What is a what?

Speaker 1 (03:05):
And I'd laugh at all these jokes, not to laugh
at philosophy, but out of deep respect for the way
philosophy forces us to figure out what we mean by
our questions? What is it? In the end, we're asking
what kind of answers do we expect? All this kind
of stuff? These are hard questions.

Speaker 2 (03:18):
Wait, does that mean that philosophers don't think you actually
have a job as a physicist?

Speaker 1 (03:22):
I mean, philosophers definitely recognize the physics is building a
set of facts, and those facts like power the world.
There is a reason that technology works, for example, But
exactly what it means about the universe, what is the
real story? What is real depends a little bit on
the questions we're asking, and it's not even clear that
there is an objective truth about it. It might just
be our perception of it answers to the kind of

(03:44):
questions we would ask.

Speaker 2 (03:45):
Well, I guess the elusive quests for the real truth
of the universe is kind of what signs. It's all about,
you know, even if we don't get there, it's all
about trying to get there.

Speaker 1 (03:54):
Exactly, and we can all work together to get there,
even if we're not in agreement about what there is.
Some of us think we are revealing the true underlying
mechanism of reality, something that like alien scientists would also
be revealing. Other folks don't care about that. They say, hey, look,
we're just getting something that works, something that predicts the
outcomes of experiments and lets us build technology. Who even

(04:14):
cares if it's real or what aliens would think about it.
You can totally disagree with the lofty philosophical goals of
science and still work hand in hand and get concrete results.

Speaker 2 (04:23):
I feel like maybe that'sis's favorite part of the job.
It's arguing about the job, you know.

Speaker 1 (04:28):
I think that there's a division early on, and people
who like to argue about it more end up in philosophy,
and the people who just want to like get in
the lab and learn stuff about the world end up
in physics.

Speaker 2 (04:37):
You just want to get in there and blow stuff.

Speaker 1 (04:40):
But there's always this tension, right. The juiciest questions in
physics are the ones that when we get the answer,
we go, hmmm, well, but why is it like that?
What does that mean about the world. The best physics
questions have philosophical implications.

Speaker 2 (04:54):
Yeah, and so there's a lot of uncertainty about what
we do know or what we don't know, or what
we can know about the universe. But even deeper than that,
there seems to be a uncertainty about the universe itself.

Speaker 1 (05:05):
Something shocking, something very difficult to understand about the quantum
picture of the world is that the world itself might
be limited in its precision, not just in our ability
to measure it or to extract that knowledge, but there
could be a fundamental fuzziness to the universe, a lack
of determination about reality.

Speaker 2 (05:23):
It's not just me getting older and needing reading glasses.

Speaker 1 (05:26):
It's that also. Yes, those two effects are combining.

Speaker 2 (05:30):
I mean, have quantum vision.

Speaker 5 (05:31):
Now.

Speaker 2 (05:33):
I think we should start that company. Quantum laser surgery. Yeah,
quantum reading glasses. Yeah, I'm parably the only coast of dollars,
so we make a killer profit.

Speaker 1 (05:40):
You can only read one word at a time.

Speaker 2 (05:42):
But anyways, Yeah, there seems to be this interesting nugget
of strangeness to quantum mechanics which tries to explain the
entire universe. And so today on the podcast, we'll be
asking the question why is there quantum uncertainty? I feel
like we're asking a question about uncertainty.

Speaker 1 (06:06):
We are uncertain about why there's uncertainty.

Speaker 2 (06:09):
That's what I mean.

Speaker 1 (06:10):
It's meta uncertainty.

Speaker 2 (06:12):
We get very meta here. Well, if it helps, I'm
pretty sure. I'm a cartoonist, that's one thing I know.

Speaker 1 (06:16):
Yeah, Well, this is exactly the kind of difficult philosophical
question because you know, I even sure like what kind
of answer we're looking for, Like, are we hoping to
reveal that the universe could have only ever been this way?
Or to argue that look, we could be in lots
of different universes. This one happens to have this quantum uncertainty.
You know, there's lots of different ways to attack this
sort of philosophical problem.

Speaker 2 (06:38):
Well, hopefully it's more than just a philosophical problem, right, Eventually,
the hope, the goal is to find kind of physics,
math based answers to these questions, isn't it to me?

Speaker 1 (06:49):
I think the sort of highest level process would be
go out and look at the universe, see what it's like,
boiling that down to like a few essential facts, build
a theory that describes how that works, why that works,
the mathematics to describe it, and then look at that
theory and ask philosophical questions like did it have to
be this way? Could you have a universe that was different?
Could we have built a different theory of the universe

(07:10):
that didn't have this feature or that feature about it?
So in the end, it's mathematical, but it's really rooted
in explaining what we see out there in the universe.

Speaker 2 (07:19):
But couldn't you answer those questions you just asked in
a mathematical way. Maybe in the future. We don't know
for certain they can't be answered, right.

Speaker 1 (07:26):
We don't know for certain they can't be answered. I
think a great analog that's going to help us understand
this question today is the question of like the speed
of light. You know, we live in a universe where
the speed of light is constant for all observers, and
if you start from that, you can build special relativity
and you can explain the whole universe. But you have
to start from that assumption. That's something we've seen in
the universe, something we know is true, we've measured it,

(07:48):
we've done the experiments, we've now coded it into our theory,
but we don't have an answer for why that is true.
And one day maybe people will have a deeper understanding
of the nature of space from which that bubbles up.
You might be able to explain that someday, but currently
we don't have an answer to why. It's just sort
of like the foundational assumption that we need to explain
everything we see in the universe.

Speaker 4 (08:09):
Right.

Speaker 2 (08:09):
Well, as you said, hopefully maybe someday somebody will answer
this deep question, but that person doesn't seem to be
out there, because Daniel went out there and asked this
question of folks and we got some pretty interesting answers back.

Speaker 1 (08:21):
Yeah. Thanks, everybody who answers these questions as wacky and
as crazy as they are, without having any chance to
prepare yourself. Really appreciate your participation, and I'd love to
hear your voice on the podcast. That's right, I'm talking
to you. We haven't heard from you yet, and we
want your voice on the air.

Speaker 2 (08:37):
Well, there's a bunch of people who have heard we
have heard from BOM. Right, you just totally snubbed them,
I feel.

Speaker 1 (08:43):
I said, thanks to all those folks.

Speaker 2 (08:44):
Also, Oh, you meant the other people.

Speaker 1 (08:48):
It's a shockingly small group of people who volunteer for
these which is why you hear the same voices over
and over again.

Speaker 2 (08:53):
Oh, I never noticed. You didn't have to tell me.

Speaker 1 (08:56):
I should have maintained your quantumuncertainty.

Speaker 2 (08:58):
She'd kept that a mystery of the universe. But anyways,
think about it for a second. Why do you think
there is quantum uncertainty in the universe. Here's what people
had to say.

Speaker 5 (09:08):
I guess that both because we can't really have an
accurate measurement on that very timey scale, and because measuring
a quantum process interferes on that process.

Speaker 3 (09:21):
There's quantum uncertainty because when we measure a particle, it
changes what the particle's doing, and when we're not looking
at the particle, we never quite know what it's doing
without measuring it, which changes the state and the particle.
So we can never quite know exactly what a particle's
doing without changing the state.

Speaker 4 (09:35):
I know that if you measure something, it falls into
the wave function collapses, and you fall into one of
the states. I guess is uncertainty, because there's a wave function.

Speaker 2 (09:50):
All right, and pretty deep answers here, I'm pretty certain
of that.

Speaker 1 (09:52):
Yeah, a lot of these folks are developing like a
microphysical picture, like what's happening when you make a measurement?
What prevents you for being able to measure things super
duper precisely? And that's helpful, but I think it's only
really part of the story.

Speaker 2 (10:05):
All right, Well, let's dig into this topic, and let's
start with the basic question, Daniel, what is quantum uncertainty?

Speaker 1 (10:11):
There's so many weird things about quantum mechanics that we
could dig into for hours and hours, but I just
want to zoom in on this one thing, this quantum uncertainty,
which is different from other weird aspects of quantum mechanics,
and quantum uncertainty is a very specific thing. But let's
start off by talking about classical physics, because quantum uncertainty
is basically a rejection of that. So classical physics, the
physics of Newton, and even the physics of Einstein, says

(10:34):
that we live in a universe where you can know
everything about an object, like take a particle or a
banana or whatever. You can know everything about its location,
you can know everything about its velocity, you can know
its entire history that it moves in these smooth paths.
It always has a position, always has a velocity that
to reality, there is no fuzziness that there's an exactness

(10:54):
to this information, and you can know all of it
simultaneously because it's well defined. That's the classic physics picture
of like how things move in the universe. Right.

Speaker 2 (11:03):
That's sort of like maybe a good way to explain
it is basically like up to high school physics, right,
like you know, predicting where the baseball that you throw
is going to land, or you know how things move
you shake him orver you swing them. That's classical physics, right,
Like you can predict where the things are, what things
are going to do. Like you in those exams in
high school, there's no room for uncertainty, Like there's a

(11:25):
right answer, there's a wrong answer.

Speaker 1 (11:26):
That's right, and there's an exactness to the answer, and
even well past high school physics, I guess, depending on
your high school you know, Einstein's physics is also classical
in that sense. I mean, Einstein was a huge revolution
compared to Newtonian physics. Relativity is a whole other brain twister.
But Einstein's picture of the universe fundamentally is the same
in that there's no uncertainty. He imagined you could know

(11:47):
where a particle is that had an exact position, and
you could simultaneously know its position and its momentum and
all sorts of other things about.

Speaker 2 (11:54):
It, even like light.

Speaker 1 (11:55):
Yeah, the classical theory of electrodynamics, you know, which comes
from Maxwell and inspired Stein to develop relativity, didn't have
any sort of quantum uncertainty to it. Photons had an
exact position, all.

Speaker 2 (12:07):
Right, So then that's Einstein and newtune. But then around
the beginning of the nineteen hundreds they figured out that
things are kind of strange and weird.

Speaker 1 (12:15):
Yeah, basically, quantum mechanics looks at that and says, yeah, no,
you can't know all of these things simultaneously. And the
history of it's really fascinating. It comes around in the
nineteen twenties when people were trying to understand how the
atom worked and what was the picture of microscopically of
the electron and the nucleus. Was this sort of like
an orbital picture like bor was suggesting, or was there
something funnier and more complicated going on? And it was

(12:37):
really Heisenberg of the famous Heisenberg uncertainty principle, who developed
the sort of first theory of quantum mechanics that describe
how the atom worked in a way different from boor
that had like a fundamental different mathematics underneath it.

Speaker 2 (12:50):
I feel like, or I seem to recall that initially
quantum mechanics didn't have this idea of uncertainty to it, right,
Like didn't it start with people just noticing that like
light case and packets, or that electrons wouldn't you know,
fly off unless you met certain minimum energy requirements and
things like that. There's no uncertain to your fuzziness to
it at the beginning.

Speaker 1 (13:09):
Was there the roots of quantum mechanics are exactly as
you described. You know, there's like the black body radiation problem,
and there's the photoelectric effect that we dug into on
the podcast several times, and you're right, it was actually
Einstein who figured that out.

Speaker 4 (13:20):
Right.

Speaker 1 (13:20):
You connected the ideas of Plank with the experiments that
we were seeing and saw that light had to come
and packet, so it can only interact with a single electron. Absolutely.
So those really those core ideas which then led to
the formulation of quantum mechanics. Those didn't have uncertainty in them.
That wasn't an essential ingredient.

Speaker 2 (13:36):
Right, That's where the word quantum comes from, right, like quanta,
like little quantity, little countable things.

Speaker 1 (13:43):
Right, you can have one electron or two electrons or
nine electrons, but you can't have one point seven photons,
for example. But then as people were trying to apply
these theories and these ideas to describing the atom, they
need to develop mathematics that work, mathematics that explained what
we saw. And Heisenberg developed this theory of quantum mechanics
that he used to make calculations and to understand like

(14:04):
why did the electron have this energy level? Around the
atom and not that energy level. Why did we get
this atomic spectrum from the atom? He developed this whole
theory of quantum mechanics, and you can see inherent in
the mathematics of his theory comes out this basic idea
of the quantum uncertainty sort of falls out of the mathematics.
He needed to describe the world as he saw it.

Speaker 2 (14:24):
Can you describe that a little bit more?

Speaker 1 (14:26):
Like?

Speaker 2 (14:26):
Why did it need to include that uncertainty into these
formulations in order to explain things like the little packets
of light?

Speaker 1 (14:33):
Well, Heisenberg developed his theory of quant mechanics, and it
was based on a certain kind of mathematical object called
matrix's that we don't have to dig into. But what
he noticed about the structure of his theory was that
it seemed to matter the order in which you make measurements.
Like if you measure one thing, it changes the state
of the system, and then if you measure something else
you'll get a different answer. And so quantu uncertainty is

(14:54):
all about this. It's about recognizing that the order of
the measurements you makes matter for some pairs of quantities,
measuring one thing can change something else.

Speaker 2 (15:03):
I feel like maybe that's at the root of quantum uncertainty,
which is like, it's really only uncertainly with regards to
two things at the same time, right, Like, it's not
like something has an inherent fuzziness, but its location you
can know its location sort of very precisely, but then
you lose out in some other quantities, right Exactly.

Speaker 1 (15:21):
It's about simultaneous knowledge of specific pairs of quantities, right,
And it's really very specific. It's not like general and
broad and say you can't ever know the position very well,
or you can't ever know the momentum very well. You
can know the position as well as you like, but
it comes at a cost for one specific other quantity,
the momentum. And there are other things that are paired

(15:41):
in this way. If you dig deeper into this in physics,
you discover that these things are called conjugate variables. And
this came out of the mathematics that Heisenberg was using
to describe his theory of quantum mechanics.

Speaker 2 (15:53):
Well, I'm pretty certain that we're going to get into
this uncertainty and this idea of conjugate pairs, and how
that figures into the uncertainty that we see in quantum
mechanics that tries to explain the universe, and so let's
dig into those details. But first let's take a quick break.

(16:21):
All right, we are uncertainly talking about uncertainty today, specifically
quantum uncertainty, or at least we're trying to understand here
where it comes from and how it manifests itself in
our everyday lives. And so we talked about how quantum
mechanics kind of change things, and there's a certain uncertainty
about it that has to do with two things being

(16:42):
measured at the same time. That's kind of a key
to the concept of quantum uncertainty, right, first of all
measurements and second of all two things at the same
time exactly.

Speaker 1 (16:50):
And there's lots of fuzziness about quantum mechanics, but this
is what we're talking about right now, is this uncertainly
about simultaneous knowledge. There's a whole other issue in quantum
mechanics about indeterminism, you know, laws of quantum mechanics determining
probabilities rather than outcomes. That's a whole separate issue, super fascinating,
but different from quantum uncertainty. Right, So quantum indeterminism is

(17:11):
different from quantum uncertainty, which tells us about like how
much we can know simultaneously about a particle or an object.

Speaker 2 (17:18):
Wait, what that's different. There's two kinds of uncertainties.

Speaker 1 (17:21):
Well, one of them is uncertainty. The other one is indeterminism.

Speaker 2 (17:24):
Well, that's what you call it, but it's basically another
word for uncertainty, Isn't it Like you're not certain of
what the outcome is going to be. So today we're
not talking about like if I throw an electron at
a magnetic field, I don't know if it's going to
be your rider left. That's a different kind of uncertainty.
What are you saying?

Speaker 1 (17:39):
So in quantum mechanics, we talk about randomness to describe
predictions that are probabilistic. If you put a particle in
a box and you ask where is it, you don't
get a specific prediction the way you do for classical mechanics.
You get predictions for where it's likely to be. You
get predictions for the probability distribution, so that if you
do it like a thousand times and measure its location,

(18:00):
you then get a distribution of measurements that follow the
predicted probability distribution. That's inherent in most of the quantum
mechanics we're used to thinking about due to the story
it tells us about how the universe works. It's not
a particle that's following equations of motion that are fundamental.
It's the wave function or the quantum field, which is
inherently probabilistic about the measurements you'll make of it. Now,

(18:21):
quantum uncertainty is related but actually quite distinct. You can
think of it as another source of randomness, but it
says that specific pairs of measurements are linked that if
you measure one, it makes the other one have a
wider spread of probabilities. So it's like it induces more indeterminacy,
but it's linked to specific pairs of variables rather than

(18:43):
the probabilistic nature of the wave function.

Speaker 2 (18:47):
I see. So today we're not talking about quantum randomness
at all. We're just talking about our ability to know
where things are and where they're going.

Speaker 1 (18:55):
Yeah, we're not talking about quantum randomness except for talking
about how we're not talking about it, which is the
first rule of quantum randomness.

Speaker 2 (19:02):
That's right. Firstrule of physics club is talk about what
it means to be in a physics club and what
a club is. But I guess the question is, like,
are those two things related or are they totally separate
ideas In quantum mechanics, the randomness and the inability to
be certain about precision and velocity and things like that,
you can have one without the other.

Speaker 1 (19:21):
So indeterminacy and uncertainty are different ideas because remember that
there are some theories of quantum mechanics which don't have
randomness and indeterminacy as inherent features, for example Bomian mechanics,
where the spread of outcomes isn't due to some randomness,
but it's due to slide variations in the initial conditions

(19:42):
of how you set up your experiment, of how exactly
you put that particle in a box, and so in
those theories like Boemian mechanics, uncertainty doesn't come from randomness.
It actually comes from the measuring device being part of
the experiment that's being measured, which keeps it out of
total quantum equilibrium, which causes uncertain So you don't actually
need randomness to have uncertainty in your quantum theory. Overall,

(20:04):
though there's a connection between uncertainty and indeterminacy in most
of the theories of quantum mechanics, though not at all,
and even to the one where there is a connection.
Uncertainty is a special kind of randomness because it relates
to specific pairs of quantities, not a general randomness.

Speaker 2 (20:20):
Oh interesting, I don't think I ever knew that.

Speaker 1 (20:23):
And the history of this is really fascinating, like how
it developed. And Heisenberg really was a pioneer, and he
developed this calculational tool that allowed him to predict you know,
energy levels, et cetera. But it was a little bit opaque,
like he had these matrices and he was operating on
vectors with them, and people were like, all right, but
what does that mean? Like what are you talking about?
What's happening inside? What is the electron doing? And Heisenberg

(20:46):
was really kind of annoyed by this question, and he
wrote a whole paper about like what it means and
what is real? And the title that paper I can't
translate for you because nobody agrees about how to translate
this one German word in the title, there's like a
quantum uncertainty about one of the earth. The papers of
quantum mechanics.

Speaker 2 (21:01):
What do you mean? What is this title?

Speaker 1 (21:03):
So the title of The paper is on the aich
content of quantum theoretical kinematics and mechanics, and German speakers
say that word means either like the visualization, which word anschulich,
which I'm sure I'm mispronouncing, thank you, and it might
mean like on the physical meaning of it or the

(21:24):
intelligibility of it or the visualization of it. There's this
concept in German which we don't have an exact word
for in English, but basically it's trying to get it like,
what does this mean? What is quantum mechanics saying about
what's happening?

Speaker 2 (21:37):
It's like the zeitgeist of quantum mechanics.

Speaker 1 (21:40):
Yeah, and Eisenberg's attitude is like, who cares? You know?
I have this mathematical tool and it makes predictions. I
can predict how your measurements are going to come out,
and so we're all good. People didn't really like that,
And at the same time, Schrodinger developed a completely alternative
view of quantum mechanics which is now more famous and
well known, you know, the Schrodinger equation. And because he
was you like a wave equation, it sort of allowed

(22:02):
people to more easily visualize what's going on. You know,
people have this like concept of a blob of probability
around the atom, et cetera, et cetera, And this really
kind of pissed Heisenberg off.

Speaker 2 (22:13):
You mean he was annoyed to philosophers.

Speaker 1 (22:15):
And yeah, he actually wrote in a letter once to
another physicist, Polly, he said, quote, the more I think
about the physical part of Schrodinger's theory, the more disgusting
I find it.

Speaker 2 (22:26):
Whoa yaouch?

Speaker 1 (22:29):
And then he said I consider it, And then he
used this German word must. And I try to look
up some translations to this German word, and again there's
a lot of uncertainties. Some people say it means junk.
Some people say it means poppy cock, some people say
it means rubbish, and the other less safe for work
translations of this word as.

Speaker 2 (22:46):
Well, I think it means that Heisenberg had some saucy
words for Schroder.

Speaker 1 (22:51):
But the point is that in Heisenberg's view, this question
of like where is the electron was the wrong question.
In Heisenberg's quant mechanics, there is like no true position
of a particle. There's only the outcome of a measurement,
and there's only if you measure something what's going to happen.
And inherent in Heisenberg's quantum mechanics was this idea that
if you measure one thing and then measure another thing,

(23:14):
the order matters that like reversing the order will change
the outcome, which is sort of confusing. Like imagine measuring
the width and the height of a table. You don't
think about measuring them in a certain order because you figure, like, well,
but with and the height are things, I can measure
them in what order I want. But in this case,
in Heisenberg's quantum mechanics, for some things the order does matter.

Speaker 2 (23:34):
Well, let maybe let's break it down into a concrete example,
Like let's say that this table had quantum uncertainty about
its width and its length. Now what would that mean.
It means I can measure one but not the other,
or I can sort of measure one and sort of
measure the other, or what does that mean?

Speaker 1 (23:49):
So it would mean that measuring its width would change
its length, right, and measuring its length would change its width,
which would mean the outcome of those measurements depended on
the order you make them. That measuring it's with then
it's length, or measuring its length and it's with would
give you different answers.

Speaker 2 (24:05):
Wait, it would change, like if I measured the width,
it would change the length of it, like physically, or
it would maybe make me less able to measure the length.

Speaker 1 (24:15):
It would change the uncertainty, the fundamental uncertainty of that quantity,
which would affect what you measure later.

Speaker 2 (24:20):
Yeah, what do you mean the uncertainty? What would be
the uncertainty of its length? Like I can't predict what
its length it's going to be, or it can actually
measure it.

Speaker 1 (24:28):
You can still make a measurement of its length, but
the outcome that measurement depends on the fundamental uncertainty of
that object. That quantity is not well known, that quantity
is not like defined. It depends on the inherent uncertainty
of the object itself. And so if you affect that
uncertainty affects your measurement.

Speaker 2 (24:45):
Right, So let's say I measure the table and I
measure that it's thirty six inches wide. What does it
mean to the change is its length? That I'm going
to measure it and I can't measure it, or I'm
going to measure it and it's going to sometimes it's
going to be twenty somethings twenty forty or it's like
I'm going to measure it and it's gonna be fifty
when I thought it was forty. What does it mean
that it changes? You know what I mean? Like, what
are you trying to say?

Speaker 1 (25:04):
Well, what I'm saying is that it changes the distribution
of possible measurements you're going to make for the length.
If you measure the width first, it changes the quantum
state of the particle. So now when you go to
measure the length, you're measuring like a different system than
you were measuring before you measured the width. You've perturbed it.

Speaker 2 (25:20):
You're saying, it's changing the randomness of the length.

Speaker 1 (25:22):
There is a random element there because the possible outcomes
of the length are now determined by a probability distribution,
and that is wider. You can think about it that way.

Speaker 2 (25:32):
Yeah, Oh, I see, So it's like more random. Like
if I measured the width of the table, then the
length gets more random, like before it could maybe be
you know, between five and six feet. But now and
that I measured the width, now suddenly like this magical table,
it's like whoa, Now, now the length of it can
be one inchry it can be a million inches.

Speaker 1 (25:50):
Yeah, And it's very counterintuitive when you think about a table,
because first of all, the table is a classical object,
doesn't have any these properties, and because we think of
a table as having like specific length and width, and
that's also true of quantum objects. Right. This uncertainty only
applies to very specific pairs of things that you can measure,
not to everything. So for a particle, for example, it
applies to position and momentum, not to like its ex

(26:12):
position and its why position. You can measure something in
X really precisely and then measure and why really precisely
with no problem, and the order doesn't matter. But if
you measure its position in X really precisely, it messes
up your potential knowledge of its momentum in X.

Speaker 2 (26:26):
I see, but I guess for our magical table, I
can still measure the length, right, Like if I measured
the width, that doesn't mean I can't measure the length.
I can still measure the length. It's just going to
be exper random, so that if I had like a
million of these magical tables, I'm going to think the
length is all over the place.

Speaker 1 (26:40):
M Yeah, that's exactly right.

Speaker 2 (26:42):
That means that there is an element of randomness to
the idea of uncertainty, Like, how could you have uncertainty
without randomness?

Speaker 1 (26:48):
Yeah, that's a good point.

Speaker 2 (26:49):
Okay, So that's the magical table, and if quantum uncertainty
applied to that table, that's how it would be for
the table. But now let's maybe take a more physical example.
You were talking about precision and momentum.

Speaker 1 (27:00):
Yeah, because it's important to understand quantumuncertainty doesn't just apply
willing nearly to everything. It doesn't say the whole universe
is flascting no matter what it says. Specific pairs of
things can't be known at the same time. So you
can know the X and the why of a particle,
but you can't know it's X and it's momentum also
in X.

Speaker 2 (27:17):
Wait, I can know it or I can measure it,
because like the table, I can measure the with and
the length, right, Or are you saying that if I
measure the width, I can measure the length.

Speaker 1 (27:27):
You can always measure it. But in the case of
the table, if you measure the width, you get a number.
You measure the length, you get a number. But now
you no longer know the width because you messed up
the width when you measure the length. These two things
are connected.

Speaker 2 (27:38):
I see. I think maybe what you mean by no
is you actually mean predict, Like if I measure the width,
then it makes it harder for me to predict what
the length is going to be of this table. Because
I can know what the length of the table is.
I can measure it, right, That's how we know it.
But it's more about like being able to know it
before you measure it.

Speaker 1 (27:53):
Well, I'd say, when you measure it, you measure it
with some uncertainty. Even if you know it, you know,
with some uncertainty. There's like error bars on it.

Speaker 2 (28:00):
Oh, it's about error bars. That's different, though, isn't it.

Speaker 1 (28:03):
Well, you know, it depends on how you interpret the
air bars and the randomness. But like repeated measurements which
probe that probability distribution will give different outcomes. It doesn't
fundamentally have a specific length. It has a distribution, and
if you measure it multiple times, you'll get different answers
according to the width of that distribution.

Speaker 2 (28:20):
Oh, I see, I feel like you're saying kind of
like the table has the length and with but then
there's our measurement of the length and with which might
not be what it's real length.

Speaker 1 (28:28):
And with this in the case of the magical table,
which follows this quantum uncertainty though obviously tables don't really right.
If we say that it has this quantum uncertainty attached
to the length and the with, then the length and
the width are not determined simultaneously. It's not that it
exists and it's written in a gold tablet by God somewhere.
We just don't have access to seeing it. It's just
that it's not defined.

Speaker 2 (28:49):
Oh, I think I see what like you're saying. I
think that if I measure this table with like a
super precise ruler, and I measured the with and I
get that it's three feet wide and I'm super certain
about that, that means that no matter what I do
to measure the length, I have to assign a certain
uncertainty or a certain error to it. I might measure
the length of the table, I might say, oh, I

(29:11):
measure it to be six feet, but in the back
of my head I have to be like, well, that's
probably not actually six feet. Is that kind of what
you mean by uncertainty?

Speaker 1 (29:19):
Yeah? And then if you go back to measure the width,
you're going to get a different answer than you did
before because measuring the length has now changed the width.

Speaker 2 (29:27):
But no, i'm it's still the same table.

Speaker 1 (29:28):
No, it's not still the same table, right, because you've
made a measurement to it and measuring things changes them.

Speaker 2 (29:33):
Oh, but what if I mentioned it at the same time.

Speaker 1 (29:35):
Yeah, great question, But you can't do that, right. You
make a measurement of a quantum system. You can measure
a thing, right, and these two things you can't measure simultaneously.

Speaker 2 (29:43):
Oh see, that's I feel like that's another concept. Then
in quantum mechanics, why can't I measure this table at
the same time.

Speaker 1 (29:49):
In Heisimber's quantum mechanics, the way you make a measurement
is that you operate on that quantum state. Operating on
the quantum state will change it, and you can't do
two operations simultaneously.

Speaker 2 (29:59):
Maybe for those us that are not familiar with quantum states,
what does that mean? That means that, like in a system,
there are some variables that you just can't measure at
the same time.

Speaker 1 (30:07):
I'll try. All measurements have to be made in a
certain order because potentially measurements could mess up later measurements.
In some cases they don't, right, Like you can measure
the X and then you can measure the Y, and
the answer you get for why doesn't depend on whether
you already measured x. But if you measure x and
then you measure momentum and X, then you will get
a different answer. And the order does matter, like measuring
x and then momentum or measuring momentum and then position

(30:31):
in X will change the answers that you get.

Speaker 2 (30:34):
I see, it's kind of part of the magical properties
of my table. Like a regular table, I can definitely
get two people to measure it within the length at
the same time, but a quantum uncertain table you just can't.
You can only do one at a time.

Speaker 1 (30:45):
Yeah, And it's sort of hard to understand that about
a table because it doesn't seem to make any sense.
And X and Y seem to be orthogonal, right, And
that's why I suggested it as a ridiculous example, because
it's very counterintuitive, and quantum mechanics is counterintuitive in that way,
but not quite as counterintuitive. I mean, you can't get
some understanding of why measuring one thing messes up another
if you think more specifically about, for example, momentum and

(31:08):
position instead of like table lengths and widths.

Speaker 2 (31:11):
Right, I just think that, you know, for more less
of us saying that's what the mass says, and it's magic.
It's pretty much the same thing. It's magicmagical, mathemagical.

Speaker 1 (31:20):
There you go. I mean you can think about it
in terms of like measuring a particle, right, say you
want to know its location, how would you actually make
that measurement? Well, in order to measure the location of
a particle, you got to like bounce something else off
of it. There's no passive observing of the universe. You
got to like bounce a photon off of it, for example,
to see where it is. And if you want to

(31:43):
know its precision really, really precisely, then you need a
really high energy photon because high energy photons have short
wavelengths and so they can tell you information about really
small distances. But if you bounce a really high energy
photon off of your electron, then you're going to totally
mess up its momentum. It'sent is going to be very
different now than before you measured it. So if you

(32:03):
go off to measure its momentum, you're going to get
a different answer than if you hadn't measured the position.

Speaker 2 (32:08):
That's if you try to do it one after the other.
But I'm just throwing out an idea. What if you, like,
throw a photon at it and you measure how the
photeland bounces, and then that tells you both things at
the same time. Maybe right, Like if I catch a baseball,
I know its position and how fast it was going.

Speaker 1 (32:26):
Yeah, and you can do that for a classical object,
and you can know simultaneously multiple things about quantum objects,
just not some things right, just in this case, like
not position and momentum simultaneously. And the reason that you
can't has to do with how this information is encoded
in the particle, which I think we can understand without
getting too mathematical.

Speaker 2 (32:45):
All right, well, let's dig into some of this mathemagic
or not mathe physics, I guess, and the idea of
wave and the wave function, which is I think where
we're going with this, dig into that waving is. But
first let's take another quick break. All right, we're talking

(33:11):
about the hairy topic of quantum uncertainty and all the
uncertain details about it. Down to the nittigree to hear. Now, Daniel,
you think that maybe a good way to explain this
is using waves, and specifically sound waves, right as maybe
they relate to the wave function of quantum particles.

Speaker 1 (33:27):
Yeah, if you're trying to think about position and momentum
of particles and how they're like encoded in the mathematical
description of the particle in quantum mechanics, truly helpful to
think about analogies we have in the classical world that
are a little bit more intuitive. And there actually is
one that a lot of people are familiar with, and
that's sound waves and songs and how words and music
can be broken up into very specific frequencies.

Speaker 2 (33:49):
All right, let's dig into it. How is a quantum
uncertainty like a song?

Speaker 1 (33:54):
Well, think about like your equalizer on your stereo when
you hear songs that has like a bass and a
trouble and whatever, and the high frequencies and low frequencies,
and your equalizer is telling you like how much bass
is there, or how many low frequency sounds are there,
or how many high frequency sounds are there.

Speaker 2 (34:09):
Or more like how strong the song is in this
frequency range?

Speaker 1 (34:13):
Right exactly, So we're going to think about the relationship
between frequencies, pure notes of specific frequencies and how you
can use them to build up different kinds of sound.
That's going to give you a feeling for the physical
reason why there are some specific quantities that you can't
know at the same time how they're linked by quantum uncertainty.
So start with a pure note, like an opera singer

(34:34):
singing a high seed. That's just one frequency on your
equalizer or on a spectrograph. It's going to give you
a single spike at that frequency, and there's very little
uncertainty in the frequency. Right you hear the sound, you
know the frequency. There's only one frequency to the sound.
Now think about the corresponding quantity, the shape. If she
hits the high sea, then where is that sindwave? That

(34:55):
sinwave is everywhere in the room. It goes up and down.
It doesn't really have a shape. It's a sine wave everywhere.
It fills the room or the opera house or whatever
it is. So you know a lot about the frequency
of her note. The spectrograph is a spike, but the
soundwave itself is very spread out in position. It's filled
the whole room. It's everywhere. Well, what if we wanted
our opera singer to create a sound that you could

(35:18):
only hear in part of the room. And you know
that you can get different sounds in different parts of
the room if you take advantage of how they can interfere.
That's why they very carefully designed acoustics in opera houses,
et cetera. But we can get our singer to make
a sound that you can only hear in one part
of the room, like in only one spot can you
hear it, and the other spots it'll be totally silent.
She can do this if she adds more frequencies, right,

(35:40):
So if she has just one frequency, just the high
seats everywhere, Now add another singer singing a different frequency,
and those two sine waves have different frequencies, and so
they'll cancel out in some places of the room and
add up in others. That's constructive and destructive interference at
a third singer with another frequency, and you can shape
the total effect further. The more frequencies you add, the

(36:02):
more you can shape that sound. And if you add
an infinite number of singers crowded onto that stage, you
can make any sound shape you want. In the room,
including a very very narrow spike, so that the sound
can only be heard at one spot in the room.
So in this scenario, the sound has a huge spread
of frequencies but a single very well determined location. All

(36:24):
the sound is in one place. So maybe now you
see the tradeoff. Either you can have a single frequency
the one high scene note, but the position is very
broad it's anywhere in the room. Or you can have
a broad range of frequencies lots of singers on the stage,
but the position is now very very narrow. So because
of the wavelike nature of sound, you can't have narrowness

(36:48):
in both frequency and in location. Those two things are
inherently linked by the nature of the physical process of sound.
You can't use a single frequency to create a narrow spike,
a sound that exists only one location in space. It's
either narrow frequency in broad position or broad frequency range

(37:08):
and narrow position. Frequency and position are conjugate variables, they're
linked in that very special way, and that also applies
to quantum waves. For a particle in a box, the
frequency of the wave function tells you its momentum. So
if you want your particle to have little uncertainty, in position,
you have to use lots of frequencies, lots of possible

(37:29):
momenta which add up to give you that spike. And
because you have lots of possible momentum now in your
wave function, that means a large momentum uncertainty, So small
uncertainty position requires a large momentum uncertainty. And in the
other direction, if you want your particle to have little
uncertainty in momentum, then you can only use a narrow

(37:49):
range of frequencies, which means you'll get a very broad
blob in position. You can't build a quantum wave function
out of just a few frequencies that also localize in position,
for the same reason that the opera singer can't sing
a single note and have it be localized in the room.

Speaker 2 (38:06):
Yeah, I think that maybe a way that I've seen
it explain is a little bit talking about like the
with of things are you saying they can be described
by wave functions? Right, Like something that has like a
really wide wave means that it's it's really fuzzy and
you don't know where quite where it is, whereas something
that is really narrow you can sort of know its position,

(38:27):
but it's also going really fast.

Speaker 1 (38:29):
Maybe exactly for something you know really really well, and
it's wave function is going to be super duper narrow,
like a spike. But to build a spike in terms
of frequencies, in terms of like various possible momenta requires
a very large number of them. You need like lots
of them to add up and cancel out in just
the right way to give you that spike. Whereas you
want something really big and fat as a blob, then
you need fewer different frequencies to add up to give

(38:52):
you that big, fat blob. Something that's very uncertain. So
a wave function that's really narrow needs lots of different
frequencies to add up, which means different possible momentum because
frequency and momentum are the same for a particle, which
means a lot of uncertainty in its momentum, Whereas if
you have a lot of uncertainty in its position, you
only need a few frequencies, which means less uncertainty in

(39:12):
its momentum. That gives you a little bit of the
flavor of why position and momentum have this special relationship.
Quantum manternity is all about very specific pairs of things
you can measure that have this relationships, not just like
any two things that you measure, right, And so.

Speaker 2 (39:26):
Maybe it might help to get into some of these
other things. So you're saying that position of momentum are
linked together in this quantum uncertainty because of its wave nature. Right.
For example, if you take to measure the velocity of
a wave, somehow it's related also to its frequency, which
that's where the fuzziness maybe it comes from. So maybe
talk about some of these other variables in quantum mechanics

(39:46):
that are also linked together by uncertainty.

Speaker 1 (39:48):
Yeah, And a tiny little quibble there is that it
can be explained in terms of like shirting or wave mechanics,
but Heisenberg can also explain it without any waves at all.
He has a completely different formulation quant mechanics that uses matrices.
And for those of you who like know matrix mechanics,
you know, like multiplication of matrices doesn't commute that you like,
it matters what you order you multiply things by with

(40:11):
your matrices, So like it comes out of quantum mechanics.
No matter what mathematical formulation you use, matrices or waves
or whatever. It's like really deep in there. But you're right,
it's not just position and momentum that this affects. There's
lots of other things that are paired. Another famous example
is energy and time of what like of a particle. So,
for example, a particle might have a specific mass, and

(40:33):
that affects how long it lasts. So, for example, an
electron which lasts forever has a very specific mass. Every
electron out there has the same mass exactly, because electrons
live for an infinite number of years. But if you
have particles whose lifetime is shorter and there's a quant
mechanical uncertainty to how long they're going to live, then
their mass is more uncertain. So for example, a top quark,

(40:56):
it might be one hundred and seventy three GV might
be one hundred and sixty five one hundred and eighty one.
There's a huge variation there in the possible masses a
top quark would have because it doesn't live for very long.

Speaker 2 (41:08):
So when you say like it lasts, meaning like it
it might at any point break down into other things, right,
lower energy things, and so it has a lifespan and
you're saying, like, how long we expect it to be around?
Hole is tied to its mass exactly.

Speaker 1 (41:22):
Electrons, we think their lifetime is basically infinity. You could
wait infinite number of years the electron just sitting out
there in space would still be an electron. Top quark
lasts for like ten to the minus twenty three seconds,
So there's a lot less uncertainty about how long a
top quark is going to be in the universe just
because its lifetime is shorter, which means there's more uncertainty
about its energy, and that comes down to uncertainty about

(41:43):
its mass. So there's like a whole distribution of possible
masses you could measure for a top quark of masses
that it actually has. It's like a fundamental uncertainty and
like how much energy there is in this thing, because
there's very little uncertainty about how long it's going to last.
It's not going to last very long at all.

Speaker 2 (42:00):
It's not just like uncertainty about where it is and
where it's going. It's like concertainty about it's actual like
being right, like what it is, how much of it.

Speaker 1 (42:08):
Is there exactly. And there's a really deep connection between
these two variables energy and time, position and momentum. We
talked about this philosophical connection in another episode. It all
comes out of this theorem No Other's theorem, which tells
us like relationships between symmetries and conservation laws. We know
the fact that space is the same everywhere in the
universe means momentum is conserved. It's another connection there between

(42:30):
position and momentum. No Other's law also tells us that
energy is conserved if space is the same across time.
There's a connection between energy and time. And so you
see that there's really a deep connection between these variables.
Some of these things are just sort of fundamentally paired physically,
position and momentum, energy and time. There's also weird properties

(42:51):
of the spins of particles that have these kind of relationships.

Speaker 2 (42:54):
What do you mean by spin?

Speaker 1 (42:55):
So particles can have quantum spin right, spin up or
spin down depends on how you measure it. Like if
you try to measure the spin of a particle, you
can do so by putting it in a magnetic field.
Then it will align one way or the other way. Well,
that's a spin along one axis the axis of that
magnetic field. You could also try to measure its spin
like at we're using a perpendicular setup. Like take another

(43:17):
magnet and rotated ninety degrees. Try to measure it spin
in another way, so you like spin in X and
spin and y. It turns out these two things are related.
You can't know the spin of a particle in two
directions simultaneously. Like you measure it spin in X, that
will mess up its spin and y. If you measure
it spin and why, that will mess up its spin
in X. These two things are linked the same way

(43:38):
position and momentum are linked. Right.

Speaker 2 (43:41):
Well, by mess up, you mean like it changes its probability, right,
like what it can be.

Speaker 1 (43:45):
Yeah, there's this famous experiment where they take a bunch
of atoms and they put them into a magnetic field
so they're either spin up or spin down. Then use
a fancy device to filter all them out so they
like only take the spin up ones. Then they send
this through the experiment again, but rotate it so now
they're measuring it like along another axis. And when they
send it back through the first device again, they're now
both spin up and spin down. So you've taken a

(44:06):
beam that are only spin up. You measure it in
an orthogonal way, that messes up your original distribution in
the first direction. So measuring in one direction messes up
the measurement in the other direction. Because these two things
are linked fundamentally, you can't know them simultaneously.

Speaker 2 (44:21):
It kind of feels like maybe these things are paired
together by kind of the constraints that measuring those things have.
It's impossible to measure the spin of a particle in
the up and down direction and in the site to
side direction at the same time, and therefore those two
things are linked.

Speaker 1 (44:40):
Yeah, those two things are definitely linked. You know, why
these two things are linked and not other two things
is a really interesting and deep question. I think that's
fundamentally a question of the episode, like why is there
any quantum uncertainty in classical physics? All these things are
totally separate and independent, and quant mechanics has like linked
some certain pairs of quantities together and said, is a
limited information in these things? And you know, the philosophical

(45:03):
answer to that question is a little bit slippery, you know,
like we have this mathematical description that we can use
to predict all these wonderful quantumic experiments, and those mathematics
have this uncertainty built into them inherently, So you can
then look at that theory and say like, well, why
you know, and no, it's matrix mechanics or here's a
frequency analysis of a wave function. Fundamentally, that's not really
a satisfying answer because it doesn't tell us like why

(45:26):
we don't live in the universe without this uncertainty. Why
couldn't you have built a classical universe without them? Why
did the designers of the universe, whoever they are, give
us the universe with this property instead of other properties?

Speaker 2 (45:37):
These things are not They're tied to each other, but
they're not tied across different categories. Like, for example, you
can know the position of a particle and its mass
and it's been along the up and down direction right perfectly,
those three things.

Speaker 1 (45:50):
Pick one in each category and you can know it
as well as you like.

Speaker 2 (45:52):
All right, So then it sounds like we haven't answered
the question of the episode.

Speaker 1 (45:58):
The answer to the question of the episode is we
don't know, right. It's a feature of our universe the
way like the speed of light is a feature of
our universe. We observe it, we can build mathematical theories
to describe it. We can then scratch our heads and say, hm,
does it have to be this way, and we don't
have an answer to that. We don't know if it
would have been possible to build a universe that was classical.
We actually talked about that on a recent episode. Philosophically

(46:20):
and fundamentally, theoretically, you might have been able to build
a classical universe without any quantum uncertainty, but ours seems
to have this feature.

Speaker 2 (46:27):
But I think, as you said, you know, it's a process, right,
We're in the middle of this process, and it might
be that in the future we do know why the
speed of light had to be a certain velocity, right.

Speaker 1 (46:37):
Yeah, and in the future and we understand quantum gravity
and string theory, there might be a simple reason like, oh,
the universe has this property and therefore you have quantum uncertainty,
or the universe is this way and therefore the speed
of light is what it is. But you know that's
just going to generate more questions, right, whatever property that
is that gives rise to quantum uncertainty, we're then going
to ask, well, why that property?

Speaker 2 (46:58):
So basically it's a never ending story, I hope.

Speaker 1 (47:03):
So then I'll keep having a job.

Speaker 2 (47:05):
Well, assuming people want you to do it, or I
guess you could do it you can pay yourself. I
guess it's still a job. If you pay yourself yourself,
you can be a self employed physicists.

Speaker 1 (47:14):
Yeah, there's lots of great self employed physicists out there.

Speaker 2 (47:16):
What if I just say that the answer is forty two?
Is there a universe out there where the answer is
forty two?

Speaker 1 (47:23):
The answer to what question?

Speaker 2 (47:24):
I don't know the answer of why the speed of
light is the way it is, it's because the number
forty two, I don't know.

Speaker 1 (47:32):
I'd love to live in a universe where that answer
made sense for that question, but I don't think that's
this universe.

Speaker 2 (47:37):
I wonder if them that universe they have the Hitchhiker's
Guide to the Galaxy. Or I guess in an infinite
multiverse there is a universe for the answer is forty two.
And also Douglas.

Speaker 1 (47:48):
Adams was right, yes, and it all makes sense.

Speaker 2 (47:52):
Yes, And then that one you'd be out of a job,
but not cartoonist, because we can always draw cartoons of
the number forty two.

Speaker 1 (47:58):
That's right, and cartoonists can always be self employed.

Speaker 2 (48:00):
All right, Well, I hopefully that gives you a sense
of how this universe still has a lot that can't
be explained. You know, there's these fundamental uncertainties in it
and what we can and cannot measure. At the same time,
it is sort of a magical table kind of for now,
right it is.

Speaker 1 (48:18):
We can describe it mathematically, and we can give answers
to like why the mathematics works this way and why
these things bubble up from the mathematics, but we don't
fundamentally know why we live in a universe with quantum uncertainty.

Speaker 2 (48:29):
Yeah, and if you eat out of a magical table,
is that a good way to control your diet?

Speaker 1 (48:36):
If you don't know the lengthen with of your table,
it's a good way to make a big mess on
the floor.

Speaker 2 (48:40):
Yeah, there you go. You might be sitting down your
food in empty space. All right, Well, we hope you
enjoyed that. Thanks for joining us. See you next time.

Speaker 1 (48:53):
For more science and curiosity, come find us on social
media where we answer questions and post videos on Twitter, Discord, Instant,
and now TikTok. And remember that Daniel and Jorge Explain
the Universe is a production of iHeartRadio. For more podcasts
from iHeartRadio, visit the iHeartRadio app Apple Podcasts or wherever
you listen to your favorite shows,