Is time pixelated?

Daniel and Jorge talk about how finely sliced time can get.

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Episode Transcript

Speaker 1 (00:01):
Hey, Jorhan Daniel here, and we want to tell you
about our new book. It's called Frequently Asked Questions about
the Universe because you have questions about the universe, and
so we decided to write a book all about them.
We talk about your questions, we give some answers, we
make a bunch of silly jokes as usual, and we
tackle all kinds of questions, including what happens if I
fall into a black hole? Or is there another version

(00:22):
of you out there that's right? Like usual, we tackle
the deepest, darkest, biggest, craziest questions about this incredible cosmos.
If you want to support the podcast, please get the
book and get a copy, not just for yourself, but
you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters,
and for the aliens. So get your copy of Frequently
Asked Questions about the Universe is available for pre order now,

(00:46):
coming out November two. You can find more details at
the book's website, Universe f a Q dot com. Thanks
for your support, and if you have a hamster that
can read, please let us know. We'd love to have
them on the podcast. Hey Daniel, I have a question

(01:09):
for you about time? All right? I got time for that,
all right. So you do a lot of things, right,
you're a professor, you have a podcast, and you're always
switching between them. That's true. It's a lot of different
things to manage, all right. So then what do you
think is the shortest useful unit of time? Like, can
you get something done in five minutes? Or do you

(01:30):
need like an hour just to dig into something? Well,
you know, sort of depends on what it is. Is
it serious research or just like writing bad jokes for
the podcast? What do you mean? All right? Well, which
one takes more time? Oh? Bad jokes for sure? I
mean at some point you just can't scrape that barrel
any deeper. What if you just give you more time?
As long as you're writing jokes about time, they basically

(01:50):
just right themselves. Hi, I'm Jorge. I'm a cartoonist and
the creator of PhD comics. I'm Daniel. I'm a particle

(02:11):
physicist and a professor, and I never seem to have
enough time. Really, can't you just make time in your
particle collider? I mean, right, it's called space time. Can
you just transform some space into time? You know? What
I need to do is to speed up the rest
of the world near the speed of light, so it
runs slowly, and then I can just get all my
work done while everybody else is frozen. Oh that's a

(02:33):
good idea. But then you'd be left behind. Everyone would
be really far away, you'd be light years away, but
you would catch up and work. I would made all
my deadlines even though I'd be in the neighboring star system. Yeah,
there you go. And then how do you turn your
work in? You can't. I knew there was a flaw
on this plan. Yeah, you paradox yourself into unemployment. The

(02:55):
twin professor paradox. But welcome to our podcast. Daniel and
Jorge explained the Universe say production of I Heart Radio,
in which we take that mental journey around the universe,
speeding your brain up to near the speed of light,
so that we can try to understand the very nature
of the universe that we find ourselves in, this incredible,
glittering cosmos with all of its wonderful questions that it inspires,

(03:18):
the things that make us go, huh, why is it
like that? Why couldn't it be like this other thing?
We dig into all of that on this podcast. We
stare right into the abyss of our ignorance, and we
ask why, and we do our best to explain what
we do and don't know to you. Yeah, because it
is a pretty wonderful universe, but it's also kind of
a weird universe. We grow up thinking that space is

(03:40):
fixed and firm and never changes, but actually it sort
of does. It's it's squishy and also kind of ripley.
I'm glad it's a weird universe, though, What would it
be like if we were doing physics and discovering Yeah,
the universe is basically exactly as you thought it was
and kind of boring. After all, you would have to
switch careers to just writing joke. I don't think I

(04:02):
could have that as a career. But I wonder sometimes
about how, you know, we find the universe beautiful, We
find nature beautiful, and we also find it mysterious and interesting,
And I wonder if that's an accident or a product
of the way the human mind works, that we just
find beauty and mystery everywhere around us. Yeah, or even
like the word weird, like why is it weird to us? Right? Like?

(04:24):
What makes us the overall judges of what is weird,
and what is not? Like, maybe the universe is offended
by us calling it weird. Yeah, and then the word
weird itself is weird? Mean you say it enough times,
it sounds pretty weird. It's got an E and I
in it, like weird, weird, weird, it's a pretty weird word. Yeah. Yeah,
but that's the English people's fault. Blame it on the Brits.

(04:44):
So yeah, it is a pretty, let's say, interesting universe.
You think the universe would be offended if we called
it interesting, sort of like living in interesting times. No,
I think it's good. I think we are lucky. It's
one of the things that makes life worth living. You know.
People sometimes ask me this question, like why should we
fund particle physics? What good is it? And I hear
my colleagues making arguments like, well, you know, we might

(05:05):
have spinoff technologies or we invented the Worldwide Web. But
for me, the true answer is that it explores the universe.
It explores the nature of the human existence, sort of
the same way like art does you ask an artist like,
and why should we pay for art? Why should people
write books? Well, it's you know, just part of the
joy of life. Is unraveling the mystery of the universe
we find ourselves in. That's it, and that's enough. Well,

(05:27):
I'm not sure you want to be in the same
position that the arts are in trying to get funding
using that argument, So I would stick with the Worldwide
Web and useful technology for now. To be honest, I
think you just haven't asked big enough, Like why don't
you pitch your ten billion dollar cartoon to the government.
You know, the more you ask for, the more you get.
I'm not sure the time is right for that crazy idea,

(05:48):
the large hay drawing cartoon. Yeah, there you go. It
will break open the universe probably and create imaginary black
holes of ink that will swallow up the Earth. That's right,
that sounds good. I'd read that my pitching my tax
dollars for that. Anyway, we love for the universe is mysterious,
and it presents us with really fun, interesting, basic questions,
things that we don't understand about, you know, the very

(06:08):
like ABC's of reality. Yeah, because I guess you know,
we grow up experiencing the universe in one way and
we think it works in a certain way in our brains.
But really, when you sort of drill down into it,
or you scale up to bigger things. There are big
surprises and it doesn't work the way we think it does. Yeah,
I think of the universe is sort of like a ladder.
You know, if you look at it at one distance

(06:29):
scale and one time scale, it works a certain way.
If you look at another distance scale, like if you're
looking at particles or if you're looking at water droplets
or galaxies, there seem to be different rules that apply
at these different distance scales, and that's fascinating. It makes
you wonder, like, are any of these fundamental Are we
learning anything really deep and true about the universe? Or

(06:49):
does it all just depends on the questions you're asking?
And so it's not just scientists who have questions about
the universe and about the nature of the universe. It's
also our listeners and everyday people just like you. That's right,
because remember that science is just people asking questions, and
the investigations we do are motivated by the individual questions
of individual scientists wondering things about the universe, and that

(07:11):
includes you, because we are all out there wondering about
the universe and trying to figure it out. So today
we are tackling a question that we got from a
listener who comes from Sweden. It's Henrik, and Henrik is
a pretty interesting question about time. So here is Henrick's question. Hi,
I'm Henrik from Sweden and I have been wondering if

(07:32):
time could be pixelated? Is there any minimum unit of time?
Or could it be infinitely short? And when I listened
to your episode about space being pixelated or not, I
started wondering if time could be pixelated while space isn't,
or vice versa. Thank you guys. All right, it's a

(07:52):
pretty interesting question from Henry. So today on the podcast
will be tackling is time pixelated? That's a pretty strange question,
Is time pixelated? I don't usually associate pixels with time. Yeah,
it's a wonderful question, and I love hearing Henrik do physics.

(08:14):
You know, he is absorbing what we're talking about and
he's taking it to the next natural consequence. And that's
what you got to do with the theory. You say,
all right, well, this describes what I'm thinking about or
describes what I've seen. Can I extrapolate from it to
the rest of the universe or what are the consequences
of it? How can I test and explore this? So
that's exactly doing physics. So kudos to you, Henrick, for

(08:35):
doing some physics in your mind. Yeah, Daniel will be
sending you a check in the mill right now, right
after this podcast. I'm gonna email you some Swedish fish,
my favorite Swedish candy. All right. So then it's a
pretty interesting question. And Henrick was saying that he listened
to an episode that we had about whether or not
space is pixelated. So there's this idea that space could
be pixelated, meaning like it's not smooth and continuous, maybe

(08:57):
it's like a grid or something, or it's disc rate
at the very smallest level. And his question is whether
or not it applies to time as well. That's right,
because we often talk on the podcast about how space
and time are related, and then in relativity at least
we see them as parts of space time a four
dimensional object. So it's a very natural question. Yeah, and

(09:18):
so what did we conclude in that podcast episode about
space being pixelated? We concluded that we don't know, and
we might never know, but there are good reasons to
think that space might be pixelated, right, due to like
quantum physics and they're being like a theoretical plank scale
to the universe as well. Right, exactly, we don't know
how small the pixels of space are if they exist,

(09:39):
and we have a very simple, kind of bad estimate
for how small they might be, just by multiplying constants
of the universe together. And it's very very small number,
like ten to the minus thirty five meters. That's not
a measurement of how small the space pixels are or
proof that space pixels exist. But if you have no
other information about how to estimate it, this is all

(10:00):
you can do. It gives you a sense for like
what the neighborhood of the size might be, all right,
So then if you're curious, you can look up that
episode in our archive. But today we're talking about time
and whether it's pixelated, and so, as usually, we were
wondering how many people out there have thought about this
question or had had time to think about this question
at least a pixel of time and maybe had an
answer for it. So Daniel went out there into the

(10:22):
internet to ask listeners is time pixelated? And so if
you have time to donate your thoughts on random physics
questions for future podcast episodes. Please don't be shy, right
to me. Two questions at Daniel and Jorge dot com.
So think about it for a second. Do you think
there is a minimum amount of time in the universe?
Here's what people had to say. I guess if you

(10:44):
zoomed in far enough, time might be pixelated, like if
you imagined it as a film strip, if you zoomed
in just millions and millions and millions of times, that
it would beam moving sort of in frames, as if
like a movie kind of thing. Tom, pixelation, haven't heard

(11:06):
of it? Um, tell me about it. Sounds crazy, Yes,
it's a usual thing. So do you think it's pixelated
or continuous? Okay, it's continuous? Okay? Wow? Man, I don't

(11:26):
even know how to wrap my head around this question.
Is time pixelated? What does that even mean? Is it
just like if a second is a pixel or even
nano second is a pixel. I have no idea how
to answer this question. I really don't know what that
question means. Maybe like, is is time quantized in some form? Honest?

(11:49):
I have no idea time. It's very strange. A lot
we don't know. I'm not sure. I think that there
are some theories that suggest it might be, but I
don't know that we've measured that definitively. My understanding of
the measuring of time is that it's not infinitely divisible,
that it is hypothesized that ultimately you'll get two units

(12:15):
of time that are so short you can't get any short.
And I think it's referred to as plunk time pixilated
like all the video games. I'm not sure about. The
term doesn't seem right. I'm probably not. I have no

(12:36):
idea from a physics standpoint, but from a perception standpoint,
I feel like it is um and I think deja
vu has something to do with that. It's like it
arrives into my brain in little packets and then my
brain goes and smooths it all out after the fact,

(12:58):
so that it in my memories it seems like it's
all smooth, and I can't actually sense what's going on
in real time. I have no idea what that means.
I guess not because I think it's continuous with the
way that Madam moves in space. All right. Not a

(13:19):
lot of ideas here. Maybe people didn't spend enough time
thinking about it. They only thought one or two units
of time on this and they should have at least
been ten or two. Yeah, it's a tough question. It
seems to have puzzled people. Most people just throw their
hands up in the air and said, I don't know. Yeah,
it seems a little bit more foreign to people than
the idea that space is pixelated, like you're familiar with

(13:39):
looking at a screen, the idea of locations being a
grid that makes some sense. But the idea of time
being pixelated, that you know that there are discrete units
of time as we move forward, that we're stepping forward
instead of sliding forward, that seems to be a little
bit more alien. Yeah, so let's maybe tackle this one

(14:00):
kind of idea at a time. So, first of all,
what would it mean for time to be pixelated? Would
it mean like you can cut up time or you
can step through time in small increments, but at some
point there comes a point where you can take smaller
steps in time. There's sort of two very different but
closely related ways for time to be discreet, for there

(14:20):
to be like a minimal, sensible unit of time. The
first is what you were just talking about. This idea
of pixelization, and pixelization is something we think about for space, right,
like pixels on the screen. You can either be at
x equals seven or x equals eight, but you can't
be at x equals seven and a half. So that's
very natural sense for space and for time. The idea

(14:43):
would be that things step forwards in time, that you
could be like time equals one point seven or time
equals one point eight, but there is no time equals
one point seven and a half. That the universe just
goes from one point seven boom to one point eight.
It's like ticks on a clock, but there's no moment
in between the ticks, Like you can't have a half

(15:03):
of a second or something like that. Yeah, and you know,
obviously seconds aren't the minimum immunity of time. You can't
have half of a second. If time units exist, but
there's a minimum discrete chunk of time, it would be
super duper small. So that to us it seems continuous, right,
and you think it doesn't exist or like what happens
in between those two times? Yeah, well what does it

(15:24):
mean for the universe to be in between those times?
It's like it doesn't have a meaning, Like time is
here and time is there, but in between there isn't anything.
It just doesn't exist. This is something that's sort of
familiar to us from learning quantum mechanics, that not everything
has like a smooth classical path, you know, like an electron.

(15:44):
You measure it here and then you later you measure
it over there. Does that mean that it went from
here to there? No, it just means it was here
and then it was there. It doesn't have to have
a location in between. We think of everything as smooth
and continuous because that's the way it seems to us,
because we're kind of big and slow. But the universe,

(16:05):
as you were saying earlier, could be drastically different from
the way we experience it, all right, So that's one
possibility that time just doesn't exist in between time pixels,
like there's a grade of the time in the universe.
And that's actually something that makes sense to us sort
of numerically, like when we simulate things in the computer.
You want to describe, for example, how a hurricane moves

(16:26):
or how galaxies form, and we want to simulate them.
That's exactly how we do it. We make a grid
in time, and we step our simulated universe forward. We say,
something's happening right now, what's going to happen at the
next time step, and you can decide is it going
to be a nanosecond in the future or ten minutes
in the future. Depends on how much computing time you have.
But it's very natural to step things forward in time

(16:47):
in simulations, right, You do simulations with time steps. But
simulations are not perfect, right, and that that's one of
the main reasons is that they do have sort of
a resolution. It doesn't do it continuously like the universe
sort of seems to be. Yeah, exactly, they're not continuous,
they're discreet. And you're right that you want really small
time steps so that you're extrapolating in a reasonable way.
But it might be that the universe actually does have

(17:09):
the same sort of time steps, and if you did
your simulation with a time step equal to that of
the universe, then it would be perfect. But wow, that
would be weird, right, Like the universe would be operating
at the minimum possible time step because but the computer
is in the universe, so that would blows my mind
a little bit. But all right, So that's the first
kind of time pixelization. What's the second. The second is

(17:31):
that time isn't actually pixelized in the sense that you
could have any value of time. It's not like values
in between one point seven and one point eight are disallowed.
If you try to measure like when did something happen?
You could get any number between one point seven and
one point eight. All those values are real and possible.
In this idea, though, there's a minimum resolution, like you

(17:54):
can't measure differences in time that are smaller than a
certain number, Like if you measure something twice, you can't
get two measurements that are closer than a certain minimum distance,
but you can get any value. So it's sort of
like you have this minimum resolution, but it can slide
up and down the time scale where and land wherever. Okay,
I think I know what you're saying. You're saying that
maybe like every possible time step exists or is possible,

(18:18):
like you can have one point oh three seconds and
up one point two four seven seconds, but maybe at
some point, at some scale of smallness and time, it
just kind of becomes random or fuzzy or sort of unknowable. Yeah, exactly,
And we can think about that because we think about
quantum particles in exactly that way. Like an electron is quantized, right,

(18:41):
it's a single object quantized of the electron field. So
it's got a certain like natural width to it, below
which you can't really probe where its location is, but
it could be anywhere. It can live in continuous space.
If space is continuous, you can still have discrete objects
in side of it. And in that same way, time

(19:01):
might be like fundamentally continuous, but there might be a
minimum basic resolution of time below which the time difference
between two events has no meaning, no meaning, but it exists,
but it's sort of random. And because it's random, you're
saying it doesn't have any meaning. But is that really
pixelated though? Like it's so it doesn't fit our idea
of a pixel, right, It's more like there's no pixel,

(19:23):
but it's sort of fuzzy at a certain scale. Yeah, exactly.
It sets a scale which I think that the physicist
is interesting because it means that you can't infinitely divide time.
That was the other part of Hendrick's question, like can
you have infinitely small slices in time? Does it make
sense to think about things happening at one moment and
then tend to the minus one thousand seconds later, Like

(19:44):
does their universe really evolve things step by step at
that granularity. And what this would tell you is not
that things are locked into specific numbers, but that it
makes no sense to think about steps in time that
are that small. You can just make stuff u It's
unknown and it's undetermined, right in the same way that like,

(20:05):
not all the information about an electron is knowable, not
just because we can't measure it, but because it's not
specified as undetermined. In that same way, pieces of time
smaller than like whatever is the minimum resolution and time
are not known or knowable. All right, Well, those are
the two ways in which time could be pixelated, and
so let's get into why we think it might be

(20:26):
pixelated and whether or not we'll ever know if it
is or not. But first let's take a quick break.
All right, we're asking the question is time pixelated? And

(20:48):
so we had a whole episode about whether space was pixelated,
and we had all those reasons there. But now we're
asking if time is pixelated, And so the question is
why do we think time might be pixelated? It seems
pretty continuous and smooth to me. It does seem continuous
and smooth, but you know, our intuition breaks down when
we try to apply it to things that are much
much faster or much much smaller, and they reveal that

(21:12):
the rules of the universe are really pretty different. Of course,
when you zoom out to things like our skill, those
rules do sort of coalesce to recover our experience. So
it's amazing that you can have like one set of
rules for the very tiny particles and it can all
sort of work together to conspire to give a very
different kind of universe at the human scale. Right, So
then maybe step us through. What are some of the

(21:33):
arguments for saying that time is pixelated and what are
maybe some of the arguments against it being pixelated? Well,
I think there's a few elements here. One is, you know,
what is more natural? Like what do we expect to
be the truth? Like, is continuity of time really the
most natural thing? Or in the end, is discreete this
more natural? What would make more sense to us was

(21:56):
the sort of default position. And I think a lot
of people out there would assume, well, continuousness, right, like
time should flow smoothly. It seems to flow smoothly to me,
But you know that doesn't mean that that's the case.
You know, you watch TV and it seems to flow continuously,
but you know deep down that it is actually discreete.
Your television is not updating infinitely many times per second.

(22:18):
And that's the key, is that continuity, having continuous time,
implies a sort of infinity, and we just don't see
infinities in nature very often, right, Yeah, I guess like
if you showed it a four K, you know, high
resolution television to somebody from the you know, a tenth century,
they would probably be fooled into thinking like there's actually
something magical, real going on inside of it to be

(22:40):
but really it's you know, flashing, you know, twenty nine
times a second, and it's really only like two thousand
by two thousand pixels exactly. And continuity is really strange,
Like to imagine an infinite amount of information as the
universe evolves forwards, it's sort of like Zeno's paradox, Like
how do you even get from one second to two
seconds if you have to go through an infinite number

(23:02):
of sub seconds to get there? You know, it feels
like at some point you've got to take an actual
step forward, and to do that, you can imagine a
minimum unit of time where the universe is finally like
ticking over Otherwise, how does it even leave the one
second mark if it's always taking a smaller and smaller
and smaller and infinitely smaller step forwards. So you're saying
that a continuous universe sort of makes sense to us

(23:25):
from our experience, but it starts to break down when
you really drill into it, because you come up with infinities.
You do, you come up into infinities. And what we've
discovered is we look around us in the universe, is
that discreetness is actually much more natural. Like the things
that we see around us that seem continuous are actually discreet.
Like that chair you're sitting on right now. It seems

(23:45):
like it has a smooth surface, right, but it doesn't.
It's actually a lattice. A lattice is a network of
points that are tied together to approximate a smooth surface.
And if you zoom out, of course it looks smooth,
but if you zoom in far enough, it looks like
a chain link fence, you know, and a beam of
light that is shining on your plants, it's actually a

(24:06):
bunch of packets of photons. So the world around you,
though it seemed continuous, almost everything about it is actually discreet.
I see you're saying, because maybe the space and physical
things around this are sort of pixelated in a way
through discrete, then it would sort of make sense for
time to also be pixelated, exactly. And that's sort of
a natural intuitive argument, right, And it doesn't really hold

(24:28):
that much water. It's just sort of to get you
in the mindset of thinking, maybe discreete is the more
natural outcome instead of continuous. Right, then you need to
be persuaded against being discrete instead of being persuaded against
it being continuous. Right. But I guess the universe doesn't
care about what we think are our opinion of it.
So what are sibility I guess more of physically robust

(24:48):
arguments for or against time pixelation. Right. And so it
turns out that when you drill down into the very
small time and the very small space, what you do
is you run into questions about how gravity works. You know,
in very very small spaces. Now you have things like
particles moving around, and you get into questions of like
what are the forces between those particles? And if you

(25:10):
have very very short time, then you're talking about very
very high energy gravity kicks in and in the end
you need to know something about how quantum gravity works,
like what are the gravitational effects for very high energies
and very short distances, And people who are working on
quantum gravity these theories of like, you know, what is
the fundamental nature of space? Is it sliced up into

(25:32):
pieces or not? Are there gravitons? All these fun questions.
They make a lot of arguments about space being discreete
and we can dig into those in a minute. And
almost all of those arguments also apply to time because
space and time are very closely related. So the physical
arguments that there might be a minimum unity to space,
a lot of those same arguments you can use to

(25:54):
make minimum unit of time. Yeah, because I guess in
physics there is this idea that time is just another
dimension maybe or it's like you know the fourth leg
and the table that is space time, and that it's
somehow like the same thing, right, you sort of think
about it that way in physics. Yeah, and it's even
more closely connected. Let me give you an example. You

(26:15):
can make a pretty simple argument that there should be
a minimum unit of space, and then you can take
the same argument and use it for time. So it
goes like this. You say, let's, for example, try to
measure a particle. What happens if you try to measure
a particle really really precisely, so you know it's position,
like basically exactly well. Quantum mechanics says, if you know

(26:36):
something's position really really well, then you don't know it's
momentum very very well. Right that the more precisely you
measure the position, the less you know about the momentum.
That means that this particle now has a huge uncertainty
on its momentum, so much so that it might have
enough momentum basically enough energy to create a black hole.

(26:57):
And once you create a black hole, well, then you
can no longer measure something about this particle because it's
inside a black hole. So, like, these very simple arguments
suggest that there's a minimum distance below which you can't
measure something because if you did, it would turn into
a black hole and prevent you from measuring it. So
that's the argument about space, And you can make a
very similar argument about time. WHOA, you just kind of

(27:22):
skipped through a few time steps there. You're saying the argument,
like one argument for space being pixelated is that you know,
if you don't have a pixel to the universe. Then
basically kind of like um, things can be anything at
a certain level, and one of those things could be
a black hole, and that's that's impossible or is that's
weird or are you saying that we don't see that.
I'm saying that the universe has a mechanism to prevent

(27:43):
you from knowing something very precisely, because if you knew
it that precisely, it would turn into a black hole,
and then censored that information. So it's sort of like
a fundamental limit there, because if you ask questions deeply enough,
basically the universe responds by covering things up with black holes.
And we don't see that, thankfully, which means that the
universe does have sort of like a fundamental maybe a

(28:06):
pixelation of space. Yeah, although we can't really do this experiment,
like how could you measure a particle with such precision
that it's momentum would be so uncertain that it might
turn into like a microscopic black hole. So that's not
an experiment we could do. We'd love to do that
experiment and observe microscopic quantum black holes. Wow, we would
learn so much. It's just really sort of a thought
experiment that demonstrates how if you ask precise enough a question,

(28:28):
the universe sort of counters with a black hole to
prevent you from learning about it. But how do you
know those black holes aren't there? Maybe they are there,
but they're so small you can't see them. Yeah, maybe
they are there, but it still means that you can't
know the position of this particle to a certain resolution
because it turns into a black hole, and you can't
measure what's inside a black hole. Okay, so that's an
argument for space being pixelated. So then how do you

(28:50):
translate that into time? Well, the relationship and quantum mechanics
between position and momentum, there's exactly the same relationship between
energy and time. And if you want to make a
bunch of measurements of a particle at very very small
time steps like now, and then tend to the mind
is one hundred seconds later, that introduces uncertainty in the
particle's energy. So time and energy have the same relationship

(29:14):
and quantum mechanics as position and momentum. It's another of
the Heisenberg and certainty principles. And so if you measure
a particle trajectory in time very very precisely. Then you
create the same uncertainty in its energy, which allows it
to potentially have enough energy to create a black hole,
and boom, cosmic censorship rises again. I see, But isn't

(29:34):
it maybe even the same argument, right, because I feel
like momentum is sort of related to velocity and velocities
like distance divided by time, So it really aren't you
just making the same argument twice, except that you know
you're using the fact that time and space and velocity
are related to each other to carry over the argument, right, Like,
couldn't maybe space be pixelated but time not pixelated. But

(29:58):
because they're related when you're trying to measure velocities, then
it implies that time is pixelated. That's exactly the argument. Yeah,
it says that space and time are very closely connected,
and therefore an argument you can use to pixelate space
is going to also give you pixelization of time. Right,
But maybe time is fundamentally not pixelated. It just appears

(30:18):
pixelated because spaces or maybe space is not fundamentally pixelated,
but time is. Right, Yeah, that's what I mean. I
feel like, Yeah, I feel like that's not really an
argument four time being pixelated, right, I see that's interesting.
That's a philosophical question. I think that it shows you
that the two things have the same relationship, so it
makes the most ends for them to both be pixelated

(30:40):
or not. In this case, quantum mechanics suggests that they
both are. But I see that other interpretation. Yeah, all right,
So there is an argument for time being pixelated, and
it has to do with quantum mechanics, and so that
sort of the uncertainty principle. So then, but do you
have then have a reason of why space and time
are pixelated like that? And it all comes down to
what happens at these very very small distance scales when

(31:02):
you have a lot of energy, and this is the
province of quantum gravity. And unfortunately, we don't have a
strong theory of quantum gravity, Like we don't have a
theory that works that describes what happens when gravity comes
into play with quantum objects and that gravity is strong.
If we did, then it would lay out for us
what is the minimum unit of time, what is the

(31:23):
minimum unity of space if there is one at all,
And the different flavors of quantum gravity that we're considering,
the different ideas people are working on for what's going
on at the very smallest scale and how this all works.
Have sort of different approaches to dealing with minimum distance
and minimum time. But I guess, couldn't you take the
sort of theoretical size of the space pixel and then

(31:47):
convert that to a time pixel because you're saying they're
sort of related or tied together. Yes, exactly, and that's
what's done, for example, in loop quantum gravity. Loop quantum
gravity says maybe the universe is not continuous in space.
It quantizes space itself, right, instead of trying to quantize
gravity is a maybe gravity is a quantum theory and

(32:08):
you're exchanging gravitons. It says, takes space itself and imagine
it not to be smooth and continuous, but like a
big foam, like a bunch of tiny little bubbles that
are all linked together as these loops. And so it's
very natural to think about space as having a minimum
distance in loop quantum gravity. It's actually essential because in
loop quantum gravity, if space has no minimum distance, then

(32:31):
a bunch of the calculations they do give nonsense results.
You get like infinities and craziness. So it sort of
saves the whole theory to have these minimum values, so
they rely on that, and the same arguments can be
used in loop quantum gravity to argue for minimum steps
in time, so like maybe space is pixelated or foamy,
but gravity is maybe continuous. But this would sort of

(32:53):
merge quantum mechanics and relativity together exactly. And I actually
asked Carlo Ravelli about this yesterday. He's an expert in
loop quantum gravity, and I asked him if in looke
quantum gravity you could have a theory that is patilated
in space but continuous in time, or if you absolutely
had to have discrete time as well, And he said

(33:15):
that he thinks that the theory is on solid footing
from the point of view of space pixels that you
can represent areas having discrete units. So that's very solid
and very confident about that. And he says that you
can do something similar with time, but there are some
complicated jumps you have to make in the argument, and
he wasn't a confident in it. But he also said

(33:36):
that he would be very surprised if anything that included
time and it's a measurement could really have a continuous
spectrum because from his point of view, the world is quantum,
everything about the universe is discrete, and then he would
be very surprised if time was any different. It seems
like the theorists don't think time is continues, that it's
maybe more likely or would make more sense, that it's

(33:59):
pixelated exactly in loop quantum gravity, it makes most sense
for time to be pixelated in the same way that
space is. Now there are other theories of quantum gravity,
theories like string theory, that have a different approach on
minimum units of time. Well, I guess maybe the question
that a lot of people might be thinking at this
point is that would it makes sense for time to

(34:20):
be pixelated or could it still be continuous? And one hand,
it makes perfect sense for time to be chopped up
in the minimum units, because, as we say, quantum mechanics
tells us that the universe is discrete, right, But there's
a problem when you do that. Introducing like a minimum
time scale or a minimum length scale is tricky because
we know from the other great theory of the universe relativity,

(34:44):
that things like distances and times are not universal. So like,
for example, if we're in the laboratory and we're measuring
the universe down to its minimum distance. We have some
pair of tweezers that can work at the plank length.
For example, what happens if somebody is zooming by the
spaceship and they're watching our experiment, They see us like
length contracted. They see everything shortened because they're moving at

(35:07):
a fast speed relative to us. So then they would
be seeing things at smaller than the minimum distance. So like,
having a minimum distance breaks special relativity in a really
important way. Right, what do you mean It doesn't break
relativity in a way. It just means that it's it's
all sort of relative. Right, Like to someone moving at
a certain speed, the minimum distance in the universe would

(35:29):
be this much, and to someone not moving at that speed,
it would be this much, but it would still have
a minimum distance. Yeah, if you assert the primacy of relativity,
then you're giving up an absolute minimum distance. You're saying
minimum distance is not really minimum, it's relative. But if
you start from the other direction, you say, no, there's
an absolute minimum distance anybody can measure, no matter how
their speed. Then that would break relativity. If you can't

(35:51):
have the two things at the same time, you can
have one, but then it breaks the other one. So
you're saying that a pixelated universe, even a space pixelated universe,
would break relativity or it's not consistent with relativity exactly.
It's inconsistent with special relativity, which we thought until now
was like pretty well established, Like we have measured it
out the wazoo and it works pretty well. But you know,

(36:13):
these directions in quantum gravity really do suggest that there
might be space pixels. But that's fundamentally inconsistent with special relativity.
So that's a big puzzle to work out. I see,
safe relativity is true, as Einstein said, then the universe
is not pixelated, or it can't be pixelated, or it
doesn't make sense for it to be pixelated. Yeah, and
you know we're focusing today on pixels in time. There's

(36:35):
another consequence of having pixels in time. You know, if
the universe is not continuous, if it's discreet, right, if
you can have like time equals one point five seconds
and one point six seconds but not time equals one
point five five seconds, that means the time is not
smooth and the universe sort of cares what time you're
at that you can't like do the same experiment halfway

(36:56):
between time pixels, and that actually has a really important consequence.
As we've talked about once on the podcast before. This
basic concept that energy in the universe is conserved that
relies on an assumption, and that assumption is that space
has a symmetry in time, that space always looks the same,
that the universe doesn't care when you do an experiment.

(37:16):
It's just could happen now or later or yesterday. You know,
it doesn't care about your deadlines. And discrete time breaks
that it says there are special values of time that
makes sense, and so that would throw conservation of energy
out the window. So if you have discrete units of time,
then basically you break conservation of energy. That seems like

(37:37):
an important rule in the universe. Yeah, so we're breaking
all the rules today. All right, Well, I guess what
I'm getting is that it makes sense for time to
be pixelated by some arguments like loop quantum theory and
thinking about space being pixelated, but it doesn't make any
sense for it to be pixelated from other points of
view like relativity or conservation of energy. All right, well,

(37:57):
let's get into our last question, which is how would
we even know if time is pixelated. Could we device
an experiment to tell us whether or not it's true
or whether it will be a mystery until the end
of time? But first, let's take another quick break. All right,

(38:24):
is time pixelated? I guess Daniel, The biggest question is
how would we know? Like, are we trapped in the
matrix and we think times smooth and continuous, and are
we always gonna be trapped in this matrix thinking that
it's continuous or will we ever be able to step
outside of time and see that it's actually you know, discrete. Unfortunately,
we might never know. You know, it might be that

(38:46):
time is continuous and we are hunting forever for the
minimum unit and not finding it, but not finding it
doesn't mean it doesn't exist. So there's a possibility that
we could always be frustrated, sort of like you know,
finding the smallest particle. You never really know if it's
the smallest particle or if there's a smaller particle inside
that that's so small you can't see it. But that

(39:07):
would be sort of a limitation of our technology, right
or is that always gonna be true because you know,
you're sort of like you can't prove a negative kind
of or you know, since infinity is forever, there's no
way we can never get down to the small enough
level to be sure that it's not pixelated. You know,
I think there are ways that we could like convince
ourselves that it probably is pixelated, but it'd be pretty

(39:30):
hard to prove that it's not, you know, pretty hard
to prove that it's infinitely continuous. I think you need
some pretty elaborate theory of physics that requires that that
has some other consequences somehow that I can't even imagine
that you could then confirm. So I think it's easier
to prove that it is discrete than to prove that
it's continuous. But you just gave me some arguments for
why space might be pixelated, right with the whole infinitely

(39:53):
small black holes. Couldn't we come up with a theory
or some sort of way or some sort of consequence
over the theory of the equation to say that, look it,
time has to be pixelated. Yeah, exactly. I think that's
the best way forward. If we come up with a
rigorous theory of quantum gravity and it requires, because of
its very nature, you know, for time to be pixelated,

(40:13):
and then that theory holds together and makes a bunch
of predictions. You know, maybe not directly showing us the
clock ticks of the universe, but having other consequences of
that it's inherent nature. Then we can be pretty confident
that the universe is pixelated when it comes to time.
All right, Well, then how could we hope to prove
that it is pixelated? Then? What kinds of experiments can

(40:34):
we make or what experiments have been made so so far?
The edge of our knowledge is basically particle colliders. Particle
colliders smash particles together at very very high energy, which
is the same thing as saying that they're studying things
at very very small distance scales. Remember that the energy
of an object controls its effective wave function right at

(40:56):
the width of its wave function, and really really high
energy object is one with very high frequency, which means
that you can localize it to very specific place. And
so with very high energy particles you can probe things
really small distances. Or think about it another way, the
more you crank of the energy of your particle colliders,
the smaller the particles you can discover, because you can

(41:17):
break them open and see small things inside them. So
we've made a lot of progress there, and we are
studying things that are like tend the minus twenty meters wide,
you know, quarks that are inside the proton. So that
sounds pretty small, right, It's like ten to the minus
twenty meters is a very small slice of the universe.
But you know it's ten to the fifteen times bigger

(41:39):
than what we think is the Plank scale, which is
tend of the minus thirty five meters. And that's a
big ratio, right, Yeah, you just need more money, tenie,
just as the taxpayers for more money. Yeah, we should
siphon funds out of your ten billion dollar comics project.
You can't touch that. Some some things are more important
than understanding the nature of the universe, that's right. But

(42:00):
that's a limited distance, right, that's not quite the limited
time or is it the equivalent you're saying. I'm saying
their equivalent because these experiments also happened really really fast,
and to be really really fast you have to have
really really high energy also, and so fundamentally, these high
energy experiments are probing short times and small distances at
the same time. But unfortunately they're like way too weak

(42:24):
to probe really the fundamental nature of the universe and
to make them big enough and powerful enough to probe
that distance scale you need like a collider the size
of the Solar System or maybe even the galaxy. So
it's not even something we even imagine asking for a
little too expensive to make a collider of the size
of the Solar system. So then what can we do? What?
What are alternatives to break in the bank here to

(42:46):
find the answer? So people are trying to come up
with tabletop experiments, things you can do in a single
laboratory to probe either directly, like the discrete nature of
space and time, or to try to like do really
subtle experiments to understand quantum gravity. There's some really cool
ideas developing experiments that might really work and could actually
help us understand how things work at the smallest scale.

(43:09):
The first idea was proposed about ten years ago by Bekenstein.
He's a guy who worked closely with Stephen Hawking to
develop the understanding of black holes that we have today,
so definitely a smart person. And he had this crazy
idea of shooting a single photon at a crystal. And
the idea is that what happens when you shoot a
photon at a crystal. It's a quantum object. Either it

(43:30):
gets absorbed or it doesn't. And if it gets absorbed,
then you know where does its momentum go like pushes
the crystal a little bit, the same way we talk about,
you know, like solar sales, shooting photons from the sun
and hitting a sale of pushing a spacecraft forward. This
is like a mini version of that, where you shoot
a single photon at a crystal and if it gets absorbed,

(43:51):
it needs to like move forward a little bit. And
so the idea is to like tune the energy of
the photon so it matches like the basic minimum distance
of the universe, so you can measure somehow if this
crystal like slides forward a tiny bit. All right, So
you're shooting a photon, and I guess you make the

(44:11):
photon small enough that maybe you'll see that jump between
like oh it hit the crystal and oh it didn't
hit the crystal, which would sort of tell you that
the universe is not continuous. Is that kind of what
the experiment would be doing. Yeah, that's the idea that
you have like lots of these little photons and they're
interacting with elements of the crystal. If you tune in
just right, they have like just enough energy to move

(44:33):
it one like quantum universe step forwards. And so this
is an idea that beckn Seem proposed about ten years ago,
and some people thought it was very exciting, like, oh wow,
maybe we could measure quantum gravity on a tabletop. Other
folks I've asked have frankly said it's probably bullcrap and
would never work. I see, all right, so that's a
no no. What are other ways in which we could

(44:53):
maybe figure out if time is pixelated? Well, the really,
I think the most promising way to figure out if
time is pixelated is to try to get it these
theories of quantum gravity, to understand, you know, basically the
nature of space and time itself, and to do it
all at once. So these aren't experiments where you can
like see the universe take forward in time, but they
are experiments that might help reveal the very nature of

(45:15):
space and time, which we give us clues about whether
space and time are pixelated. And the way to make
progress there is to try to see gravity having influence
on individual particles, because we don't know how gravity works
when it comes to little particles like we know how
gravity works when it comes to the Earth and the Moon,
or the Earth and the Sun for example, or even

(45:36):
black holes. But we don't know what happens between two particles.
Are they like passing little gravitons back and forth? Are
they bending space? Is space discrete? There? Like? What we
need to do is see really strong gravitational effects on particles.
The problem, of course, is that particles have almost no
mass and so they have almost no gravity. But we've

(45:56):
gotten pretty good recently at building larger quantum of objects,
like getting a whole bunch of particles and getting them
like in sync together into one quantum state like a
Bose Einstein condensate or something similar, where you can make
like larger and larger objects that have quantum properties, and
maybe we can make them large enough that we can

(46:17):
start to see the gravitational effects between like clumps of
quantum objects. I see, like if you make a big
enough quantum object, you would see how anything quantum interacts
with gravity. Because right now we don't really know, right
like our theories breakdown when you try to make quantum
particles interact with gravity. We just don't know what happens
when quantum particles are feeling gravity. And so what we've

(46:40):
done so far is made things like Bose Einstein condensates
that have like, you know, maybe up to a thousand
atoms in them, these tiny little blobs of stuff. And
that's really not big enough to observe any gravity, because remember,
gravity is the weakest force out there. But we're making progress,
and it's the kind of thing where like in ten
years undergrads will be doing that in their freshman physics lab.

(47:02):
It'll be very easy or be like on a computer
chip kind of thing, And in the basements of research
facilities they will be like having quantum diamonds and superpositions
and doing crazy experiments. But I guess maybe the question is,
you know, that might help us figure out if gravities quantized,
but how does that help us know if time is
quantized or pixelated. Yeah, it will tell us if gravity

(47:22):
is a quantum theory or not, you know, or if
space is quantized or not. So it will sort of
help us get direction theoretically for how to tackle this
very question about the nature of space and time. So
it won't directly tell us if time is pixelated, it
will give us a lot of clues about how to
build a theory of quantum gravity, and gravity of course
very closely connected to space and time, so it'll sort

(47:45):
of like help us lay the foundations to maybe eventually
get there. But it's you know, it's nice to know
that we might be able to do some experiments that
can help us figure out if gravity is quantum or not,
so that we can try to get our heads around
these basic questions. Is about the nature of space and time, right,
But even if you find out the gravity is quantized
and spaces quantized, you still wouldn't technically right. Maybe possibly

(48:07):
now if time itself is also quantized, like we said earlier,
it could be the one of the is quantized on
the other one is not. But it depends on the
details of your quantum theory. Right, So if you discover,
for example, string theory is right, then string theory says, well,
time is sort of continuous, but there are is a
minimum resolution below which it doesn't make sense to ask questions.
Or if you discover oh no, it looks like loop.

(48:28):
Quantum gravity is correct and Carlo Revelli was right and
time is also quantized, So it might help you because
it would reveal the quantum theory that describes space and time,
which might require time to be continuous or smooth, or
it might show us that none of our ideas are
correct in something else totally weird and new is required,
and time might not be quantized. It might be something

(48:49):
else totally different than we haven't even imagined. It might
be a different time. It would be time for a
new idea. It will be a timely discovery. Yeah, so
I would say that in summary. You know, it's not
something that we're gonna be able to directly probe very easily,
but we can get around to it's sort of at
the back by trying to build a consistent theory of
space and time, which requires understanding quantum gravity. Because you

(49:11):
don't think there is there could ever be an experiment
that could test it directly. I think those experiments require
such enormous energy they're effectively like creating black holes, and
so it's hard to imagine you ever doing experiments at
that scale, right, Who would ever make a black hole
on purpose? I would. I totally would sign me up.

(49:32):
I'm not saying I wouldn't want to. I'm just saying
I don't think it's possible. I think maybe it's time
to cut short this episode now before we introduce too
many bad ideas into a physicist brain. All right, well,
I guess the question is yet to be determines. There
are their arguments for time being pixelated and arguments against
time being pixelated. It sounds like we might never know.
But if we make enough progress just in basic, you know,

(49:54):
fundamental theories of the universe, maybe it'll come up. Hopefully
it will come up. Is that kind of the planned there,
Let's focus on something else and let's procrastinate, and maybe
we'll come up on its own. Let's figure out the
foundations of everything, and maybe along the way we'll solve
this other problem. All right, and maybe we'll find more
time for you, Daniel, to do all the things we
wanted to all right, Well again, I think it's an

(50:16):
interesting reminder of how much we don't know about the universe,
about basic things like space and time, and it's time
that we figure them out. It's always a good time
for for physics, right, It's always a good time, and
there's always a good time for physics, and physicists are
always a good time and that's the But that's a
theoretical conjecture there, Daniel that's never been proven in the lab.
No experiments have proven that. I think unfortunately that's true.

(50:40):
Maybe we should collige physicist together and just see what
happens that. Now, that sounds like fun. That sounds like
a good time to you. All right, Well, we hope
you enjoyed that. Thanks for giving us your time, See
you next time. Thanks for listening, and remember that Daniel
and or Hey Explain the Universe is a production of

(51:02):
I Heart Radio or more podcast from my heart Radio.
Visit the I heart Radio app, Apple Podcasts, or wherever
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