Speaker 1: Hey, Daniel, have you heard of the Zenos paradox? Yeah?
Speaker 1: Is that the one where you can't get to where
Speaker 1: because you keep going half the distance and then half
Speaker 1: that distance and half that distance. Yeah. It's kind of
Speaker 1: like this thought experiment where you say, all right, I'm
Speaker 1: trying to get home, so I'm gonna get to half
Speaker 1: of the distance to my home, and then you stop
Speaker 1: and you say, all right, now I'm gonna get half
Speaker 1: of the distance to my home. And so you go
Speaker 1: another half of that and you say, now I'm going
Speaker 1: to go half of the distance to my home, and
Speaker 1: you do that half, and so the question is will
Speaker 1: you ever get home? I mean, it sounds like you
Speaker 1: would always get there because you're always going half of
Speaker 1: what's left, but you might never get there, right, And
Speaker 1: it raises an interesting question, right, because if you can
Speaker 1: cut a mile and a half and then cut that
Speaker 1: in a half to a quarter mile, and cut that
Speaker 1: in half to an eighth of a mile, can you
Speaker 1: keep cutting it to infinitely small distances? Like are those
Speaker 1: distances even meaningful on a physics point of view? Or
Speaker 1: is there a shortest possible distance in the universe? Afterwards,
Speaker 1: Zeno has to actually take that step right, So physics
Speaker 1: could be like Zeno's paradox, more like Zeno's paradk Not,
Speaker 1: that's right, Zino's paradox unraveled. I am and I'm Daniel,
Speaker 1: and welcome to our podcast. Daniel and Jorge explain the Universe,
Speaker 1: where we take the universe, cut it in half, and
Speaker 1: then cut it in half again, and cut it in
Speaker 1: half again and again until it's small enough for everybody
Speaker 1: to understand and happily digest. This is Daniel Jorges podcast paradox.
Speaker 1: And unlike that paradox, this will actually end at some
Speaker 1: point in about thirty thirty five minutes, that's right. Not
Speaker 1: if you listen to half the podcast and then half
Speaker 1: was left, and then half of what's left right, infinitely
Speaker 1: slicing the podcast, you can enjoy it forever. Yeah, at
Speaker 1: some point you'll be like, but that's right, we'll be
Speaker 1: listening to one unit of laughter. But that's sort of
Speaker 1: the question we want to talk about today. Can you
Speaker 1: slice up space into smaller and smaller pieces? Can you
Speaker 1: divide it into short and short distances? Or is space
Speaker 1: pixelated like a video game? That's right? Or your latest iPhone.
Speaker 1: You look around you and it seems like the universe
Speaker 1: is continuous and smooth, right, But it might be that
Speaker 1: the universe is actually pixelated. That you can be here,
Speaker 1: or then Jason pixelby, you can't be in between, that
Speaker 1: there's the shortest possible distance to the universe. So not
Speaker 1: the stuff is pixelated, but the actual like the universe itself,
Speaker 1: the space in it is like a video game. It's pixelated.
Speaker 1: It's not continuous and infinite resolution exactly. And it's a
Speaker 1: perfect analogy to the stuff. Right. In particle physics, we
Speaker 1: love to take things apart. We say your body is
Speaker 1: made of molecules, and those molecules are made of atoms,
Speaker 1: and those atoms are made of smaller particles, and those
Speaker 1: little particles get down to corks and leptons. We're looking
Speaker 1: for the tiniest particle, the base particle out of which
Speaker 1: everything is built. But in a completely parallel track, we
Speaker 1: can ask the same questions about space. Is a mile
Speaker 1: built out of half miles, which just built out of
Speaker 1: quarter miles, which eventually is built out of the smallest unit,
Speaker 1: or can you infinitely divide it? So this is a
Speaker 1: mind blowing question, And so we were curious what you
Speaker 1: thought the answer was, do you think the universe is pixelated? Yeah?
Speaker 1: So I went around. I asked a random selection of
Speaker 1: UC Irvine undergraduates who were not put off by a
Speaker 1: weird physics professor holding a mic in their face, and
Speaker 1: ask them this question, do you think the universe is pixelated?
Speaker 1: Here's what they had to say. This quantized basically as
Speaker 1: the atoms cannot be. I mean, of course they're made
Speaker 1: by subatomic particles. But I think after that, like it
Speaker 1: can be continuous. I think this spread to do it.
Speaker 1: I think it's like I can ask him to like,
Speaker 1: you reach smaller and smaller and smaller and smaller and smaller,
Speaker 1: but you never get to like a finite like this
Speaker 1: is the smallest thing. Um. I think it would probably
Speaker 1: get smaller and smaller forever. I really don't know about this.
Speaker 1: This is a tough lue. It's a topic. What's your
Speaker 1: best guess? What do you think the job cuts say? Really?
Speaker 1: You know this one is really beyond my understanding of
Speaker 1: this whole ward right now? Yeah, all right to People
Speaker 1: were kind of skeptical about this. There's a whole spectrum
Speaker 1: of answers. I mean some people are like, no, you
Speaker 1: can chop things down infinitely far. Other people like no,
Speaker 1: quantum mechanics says everything is quantized and therefore there must
Speaker 1: be pixels. And other people are like, wow, I have
Speaker 1: no idea, what are you talking about? And I totally
Speaker 1: regret agreeing to answer your questions. It's like, I've never
Speaker 1: heard these two words at the same time, universe and pixels.
Speaker 1: That's right, that's right, and it is a weird question,
Speaker 1: you know. But the pixels is a perfect analogy because,
Speaker 1: like if you have a modern iPhone and you look
Speaker 1: at the screen, it seems like the pictures are fluid,
Speaker 1: they're smooth, or you can't see the pixels because they
Speaker 1: have this retin a display. It gives the illusion that
Speaker 1: it's completely smooth. But it's kind of interesting because if
Speaker 1: you look at an old phone, like just from five
Speaker 1: to ten years ago, it looks horribly pixelated, that's right.
Speaker 1: It looks crunchy and chunky, and you're you you think,
Speaker 1: how could I ever have seen this and thought that
Speaker 1: this was anything of quality? That's right. And you know,
Speaker 1: even um old fashioned photographs, the ones that are analoged,
Speaker 1: not digital, ones that use chemistry, those in effect have
Speaker 1: pixels as well. They're just so small that you can't
Speaker 1: see them, because you know, the development process is a
Speaker 1: chemical process and so it's based on you know, molecules
Speaker 1: and drops of fluid and whatever. It's just the pixels
Speaker 1: are so small. So if the pixels are small enough
Speaker 1: that you can't see them, it gives you the illusion
Speaker 1: that it's perfectly continuous and that you could, you know,
Speaker 1: zoom in forever and see more and more details, you know,
Speaker 1: like on that on those cop shows, whether they like
Speaker 1: enhance the image and it can just like zoom in
Speaker 1: forever and read the time on somebody's watch or something
Speaker 1: right right, or get like a face match. Yeah, but
Speaker 1: in a real picture, there's a limit to the information
Speaker 1: that's been captured. And if you look from far away,
Speaker 1: it looks like you could zoom in forever. But at
Speaker 1: some point, as you start zooming in, you notice the pixels.
Speaker 1: And so that's the question we were wondering about today, like, sure,
Speaker 1: space seems continuous around us, but is it possible that
Speaker 1: if we zoomed in far enough, the pixels could appear
Speaker 1: at some point? Yeah, So that's kind of related to
Speaker 1: the question of space itself, Like we know stuff is
Speaker 1: made that a little bit, But is space itself also
Speaker 1: pixelated like an iPhone screen or an old photograph. Yeah,
Speaker 1: and this question is newly fascinating because we're only recently
Speaker 1: learning what space is, right, Like the question of is
Speaker 1: space pixelated is a reasonable question in parallel to is
Speaker 1: matter quantized and made out of the smallest particles, because
Speaker 1: we've recently realized that space really is thing. Also, it's
Speaker 1: not just like emptiness. Those of you are out there
Speaker 1: saying this is silly. Space is nothing and so of
Speaker 1: course you could be anywhere in it and you can
Speaker 1: divide it infinitely. We've recently realized this space is not nothing.
Speaker 1: Before we thought it was nothing, just the absence of anything.
Speaker 1: But actually it's not right. It's almost like a medium,
Speaker 1: or like what the ocean is to fish. Yeah, exactly,
Speaker 1: it's a thing. It has dynamical properties. Right. We know
Speaker 1: that it's not nothing because you can do things that
Speaker 1: nothing can't do. Right. For example, space can expand that's
Speaker 1: what dark energy is. And for those of you whose
Speaker 1: minds were just blown about the meaning of the phrase
Speaker 1: space can expand, go off and listen to our dark
Speaker 1: energy episode where we talk all about that and space
Speaker 1: can wiggle, right, like things in space can expand and
Speaker 1: contract with these wiggles as gravitational waves passed through them.
Speaker 1: And you know, those of you interested in that, go
Speaker 1: off and listen to our gravitational waves episode. And we
Speaker 1: also know that space can bend, right, that's what general
Speaker 1: relativity tells us, and tells us that gravity is not
Speaker 1: a force, but in that it's a bending of space.
Speaker 1: So space definitely is a thing. It has properties, and
Speaker 1: we've only just recently discovered that it's a thing and
Speaker 1: begun to investigate it. And so it's a very reasonable
Speaker 1: question to ask, is space pixelated like we think matter
Speaker 1: might be, Like what is it made out of it?
Speaker 1: Or what's it like? Really? You know, it's not nothing,
Speaker 1: So if it's something, it's like space is some famous celebrity,
Speaker 1: you know, right, what space like? You know on the
Speaker 1: weekend out? Is it egotistical? It seems egotistical, you know,
Speaker 1: it seems so into itself. What spaces favorite color? Black? Black?
Speaker 1: Space color? That one? I think we know that's a
Speaker 1: settled question in science. No, I think it's important to
Speaker 1: think about this question, like what is the smallest unit
Speaker 1: of space? Right? What is space built out of? Um?
Speaker 1: And I think the analogy to you know, understanding what
Speaker 1: matter is built out of? Works? They're like, is space
Speaker 1: built out of the little bits? Right? These pixels? And
Speaker 1: then the next question if you discover space is built
Speaker 1: that it pixels is what are those pixels made out of?
Speaker 1: It could be that those pixels are made out of
Speaker 1: something smaller and deeper that's nothing like space, So that
Speaker 1: space itself is an emergent phenomenon, not a fundamental thing
Speaker 1: in our universe. That's something that arises, you know, like
Speaker 1: wetness or economics, you know, so not something that's built
Speaker 1: in at the very beginning of the universe, but something
Speaker 1: that comes out of how things interact. Well, let's take
Speaker 1: this approach. So let's assume that space is pixel ated. Okay,
Speaker 1: what is the space pixel mean or feel like or
Speaker 1: look like? Or what would it do to things? Yeah? Well,
Speaker 1: what would it would mean is that you can't be
Speaker 1: just anywhere you want in space, you know, just like
Speaker 1: Zeno the beginning of this episode. It would mean that
Speaker 1: at some point, if you're small enough or you can
Speaker 1: zoom down enough, it would mean that you have to
Speaker 1: make a choice. Are you at location end or location
Speaker 1: N plus one? Right? It would mean the space is
Speaker 1: discrete the way integers are, instead of being continuous the
Speaker 1: way real numbers are. Right, there's an infant the number
Speaker 1: of numbers. For example, between one and two, there's one,
Speaker 1: one point five, one point two, seven, eight four, and
Speaker 1: you can always squeeze more numbers in there. It's an
Speaker 1: infinite amount of numbers between one and two if you're
Speaker 1: talking about real numbers, a continuous line of numbers. But
Speaker 1: for integers, like there's just one and there's two, there's
Speaker 1: no more integers in between. Space could be like that
Speaker 1: where you're like, I'm at this spot, and if I
Speaker 1: want to take a step, there's the shortest distance I
Speaker 1: can step, and so you have to go to two.
Speaker 1: It's kind of like if you were on your iPhone
Speaker 1: you were animating one pixel dot black dot on a
Speaker 1: white background. This dot can't just be anywhere on the screen.
Speaker 1: It has to move from one box to the next box.
Speaker 1: That's right. It can't like cross over the boundary. You
Speaker 1: can't be halfway between one pixel and another because then
Speaker 1: each pixel would have to be half white and half black,
Speaker 1: which they can't be. Right at pixel is the basic
Speaker 1: unity either on or it's off, So like, if you
Speaker 1: look at the iPhone from a distance, this dot would
Speaker 1: look like it's moving smoothly across the screen, but really
Speaker 1: it's taking a little jumps between squares, right, Like it's
Speaker 1: in square ones at this moment, and then it's suddenly
Speaker 1: in the next ware, and then suddenly it's in the
Speaker 1: next player. You're saying that maybe, like I'm not really
Speaker 1: moving continuously through space. Maybe I'm just kind of like
Speaker 1: jumping from one box to the next exactly. And the
Speaker 1: illusion of smoothness, the way you feel of it that
Speaker 1: you are moving smoothly, is your brain stitching that together.
Speaker 1: And it's easy to do because the pixels, if they exist,
Speaker 1: would be super duper tiny. But they only have to
Speaker 1: be smaller than we can notice. You know. For example,
Speaker 1: if you slow down a movie, it's nothing but a
Speaker 1: bunch of still images, right, and if you watch them
Speaker 1: fast enough the key is faster than your eye can
Speaker 1: register the differences, then it appears to be an infinitely
Speaker 1: smooth sequence. It seems like you're watching something in real life.
Speaker 1: Slow down of course, and you can see, oh, it's
Speaker 1: just a bunch of still images. In the same way
Speaker 1: space might be discreete We just haven't noticed, but that
Speaker 1: if you get small enough, you realize that these nodes.
Speaker 1: You know, it's like you can't get off halfway between
Speaker 1: subway stations, right, might be the space is like that
Speaker 1: that every location in spaces like a subway stop. You
Speaker 1: don't want to get off the train halfway between pasions
Speaker 1: and get stuck in the tunnel. Right. You can't write
Speaker 1: the universe forbids it Right, But if you're the pixel
Speaker 1: like in the in the screen, the pixel isn't really moving.
Speaker 1: You just turn it off in one square and you
Speaker 1: turn it on them the next square, so it sort
Speaker 1: of disappears and it appears. Yes, are you gonna ask
Speaker 1: if that's really like teleportation? Yeah? Right, Like does that
Speaker 1: mean as I'm moving through space, I'm actually like disappearing
Speaker 1: here and appearing in the next spot. Yeah, I guess
Speaker 1: it does, you know? I guess it means that you
Speaker 1: zapp from one spot to the other without going in
Speaker 1: between them, right, And so that really is a kind
Speaker 1: of teleportation. I hadn't thought of that before. It's sort
Speaker 1: of awesome. Um. In the same way, like if time
Speaker 1: is quantized, then you know you're sort of slicing your
Speaker 1: way through time. In the same way. That's fascinating. Yeah,
Speaker 1: so we're if space is pixelated, that we're all teleporting
Speaker 1: right now, all the time, only you move, only if
Speaker 1: you moved. Oh my god, we just invented teleportation right
Speaker 1: here live on the podcast. Amazing. Get the legal team
Speaker 1: on the patent please, will you? And there goes your
Speaker 1: physics professorship right out the door right there. That's right. Boom,
Speaker 1: I'm officially a crackpot. Well, let's take a quick break
Speaker 1: before we go on. Okay, so that's what it means
Speaker 1: for the universe to be pixelated, that we're all just
Speaker 1: kind of trapped in an iPhone screen. Then we can't
Speaker 1: really move anywhere. We have to move within these boxes.
Speaker 1: That's right. But if it is, it's a really fancy,
Speaker 1: super modern iPhone because the pixels would be super duper tiny, right,
Speaker 1: it has an awesome graphics processor. What would you call
Speaker 1: it the iPhone you It would be like a quantum display.
Speaker 1: That's right, iPhone verse, Tim Cook, give us a call.
Speaker 1: That's right. Somebody put a trademark on man. We need
Speaker 1: like a constant legal team standing by just to you know,
Speaker 1: get down all the great ideas we come up with.
Speaker 1: On the fly. So how could we tell if we
Speaker 1: are in a pixelated universe or not? Yeah, well that's
Speaker 1: hard because to see that we are in a pixelated universe,
Speaker 1: and we'd have to see the pixels, right, So we
Speaker 1: have to zoom in somehow far enough to be able
Speaker 1: to see them, and of course so far we haven't.
Speaker 1: So far everything seems continuous. We don't notice discontinuities in
Speaker 1: the way things move um, and we also have no
Speaker 1: idea how big these pixels are. Right, so far, we
Speaker 1: have explored space and matter using high energy particle colliders,
Speaker 1: and that's let us probe down to about ten to
Speaker 1: the minus twenty meters. That's zero point than twenty zeros
Speaker 1: in a one. I mean, that's a tiny little distance.
Speaker 1: I don't even know what the prefixes for that. It's
Speaker 1: some super tiny distance. We've studied space down about that
Speaker 1: distance using particle colliders where we smash these tiny particles
Speaker 1: together and use the probe tons so like look inside
Speaker 1: the other protons, and that lets us study space. So
Speaker 1: we know that if there are space pixels, they have
Speaker 1: to be smaller than that, right, you meaning at the
Speaker 1: large Hadron collider, you can poke things at that distance,
Speaker 1: meaning you can tell if things matched together within that
Speaker 1: small of a distance apart. Right, Yeah, Essentially, our current
Speaker 1: theory assumes a space is continuous, and our current theory
Speaker 1: doesn't break down down to ten of the minus twenty,
Speaker 1: and so we would notice some deviation. Something would be different,
Speaker 1: The calculations would be wrong if space became pixelated and
Speaker 1: at a level let that we didn't expect. And so
Speaker 1: so far we're pretty sure spaces seems continuous down to
Speaker 1: ten to the minus twenty. So the pixels, if they exist,
Speaker 1: have to be really small, right. But I wonder, you know,
Speaker 1: if there's a philosophical limit there, you know, in the
Speaker 1: sense that like, do you think Super Mario, if he's
Speaker 1: in the video game and he's a pixelated character, could
Speaker 1: he tell that the world was pixelated? You know, because
Speaker 1: he's pixelated and he thinks in pixelated thought? Could he
Speaker 1: not things pixelated thoughts? Yeah, you know what I mean.
Speaker 1: I think, in terms of thought units, here's a three
Speaker 1: pixel unit thought. I think that's an interesting question. If
Speaker 1: the pixels they we lived in a universe where the
Speaker 1: pixels were fairly large in comparison to our bodies. Yeah,
Speaker 1: I mean, I think that's hard to imagine that realistically
Speaker 1: because it would mean there's a pretty strong limit on
Speaker 1: how complex our bodies could be. I mean, if your
Speaker 1: body was made out of pixels that were like six
Speaker 1: centimeters across, then you could just couldn't be very complicated
Speaker 1: if you were a meat or tall. In order to
Speaker 1: have enough complication to have an interesting mind, you know,
Speaker 1: you need a huge, complicated brain. So the brain would
Speaker 1: have to be enormous compared to the size of the pixels.
Speaker 1: So I think it's pretty hard to have complex enough
Speaker 1: life to ask that question um and still be small
Speaker 1: compared to the size of the pixels. So if super
Speaker 1: Mario is an idiot, then yeah, he'd probably be pretty
Speaker 1: close to the size of the pixels. But then he's
Speaker 1: not gonna be asking the question why am I pixels? Well,
Speaker 1: his intelligence would be pixelated, so he probably have zero units.
Speaker 1: And then if he takes a mushroom, is that going
Speaker 1: to grow too? That's just you know, I always wondered
Speaker 1: about those mushrooms, you know, does that change the way
Speaker 1: he thinks? Like what is going on with those mustions?
Speaker 1: But where do I get something? He doesn't actually get
Speaker 1: bigger at just his pixels in his mind. That's right.
Speaker 1: Then the other question is, you know, would he even
Speaker 1: think to ask the question if pixels were obviously the universe,
Speaker 1: you wouldn't ask why is the universe pixelated? You would
Speaker 1: just be one of the basic assumptions that you accept
Speaker 1: day to day, you know. And that's one of the
Speaker 1: things I find fascinating about physics is that we keep
Speaker 1: unraveling basic assumptions about the universe that we didn't even
Speaker 1: really think to question, you know, the questions like is
Speaker 1: time the same for everybody? Right? Of course we used
Speaker 1: to think, of course, it was like time is time
Speaker 1: in a clock here and a clock there are the same,
Speaker 1: And now we know it's not. Time is relative and
Speaker 1: depends on your speed and all sorts of weird stuff.
Speaker 1: So physics is helping us peel back the universe and
Speaker 1: figure out where are perceptions have led to biases in
Speaker 1: the way we view the universe, and so why that's
Speaker 1: why this space pixelization is just like another one on
Speaker 1: the list. It might be eventually, physics shows us that
Speaker 1: space is different than the way we always imagine, you know,
Speaker 1: that's made up of these little units. So I think
Speaker 1: what you're saying is that as far as we know,
Speaker 1: we look at the world around us and the complexity
Speaker 1: of it, it's such that we're pretty sure that it's
Speaker 1: not pixelated up to a certain scale, which is tend
Speaker 1: to the minus twenty. Yeah, we certainly do. And if
Speaker 1: we were close to the pixel scale, it would limit
Speaker 1: how much complexity we could have in our universe. Right
Speaker 1: If if the pixels were a centimeter across, then our
Speaker 1: one meter scale life couldn't be very complex at all. Right, Right,
Speaker 1: Like what kind of interesting thing could you build out
Speaker 1: of actual real sized legos? Right, you can't make a
Speaker 1: machine that's very complicated. You know, you want to see
Speaker 1: these rich effects that you see when you put the
Speaker 1: world around you. Yeah, yeah, Okay. So what makes scientists
Speaker 1: even think that the universe could be pixelated? I think
Speaker 1: they were just hanging out in the sevenies and smoking
Speaker 1: too much weed and they were like, man, though, it's
Speaker 1: it's not like um. Some people might think, Oh, it
Speaker 1: comes from the idea that the universe is a simulation,
Speaker 1: and if it's a simulation, then of course it's pixelated,
Speaker 1: because computers in the outside the universe are pixelated. Now,
Speaker 1: it comes from a deeper place becomes from noticing that
Speaker 1: quantum mechanics seems to work really well. Right, Quantum mechanics
Speaker 1: has described everything we know except for gravity, and it
Speaker 1: seems to be a fundamental description of the universe that
Speaker 1: everything is quantized. You know, packets of light, for example,
Speaker 1: can't have an arbitrary amount of energy, they can only
Speaker 1: have certain units of energy. Matter itself is made out
Speaker 1: of particles, which are little quantized bits of stuff. Right,
Speaker 1: So it seems like, for for a reason we don't understand,
Speaker 1: the universe is quantized, and quantized of course, just means
Speaker 1: little units of stuff, and so it's very natural to
Speaker 1: imagine that space also might be quantized. The space also,
Speaker 1: instead of being infinitely divisible, might also be it out
Speaker 1: of pieces. Because the universe seems to like quantum mechanics.
Speaker 1: So you're saying that, like the stuff that we see
Speaker 1: around us does have smallest bits, like there is a
Speaker 1: lego piece of matter. You can't split an electron really
Speaker 1: like you can have half an electron or a quarter
Speaker 1: of electron. So maybe that says something about the universe
Speaker 1: as a whole, like maybe everything is just kind of blocking.
Speaker 1: That's right, it would make sense, it would it would
Speaker 1: feel natural and it would feel coherent with what we
Speaker 1: think about modern physics if space was also quantized. And
Speaker 1: then there's you know, there's some technical reasons, like there
Speaker 1: are some theories physics which just don't work if you
Speaker 1: get small enough. What do you mean, you know, some
Speaker 1: theories of quantum mechanics and the way it describes interactions
Speaker 1: below a certain distance that you just start to get infinities.
Speaker 1: Like you you know, how does the theory of physics work? Well,
Speaker 1: it's a it's something that predicts an experiment, right, say,
Speaker 1: I think this is going to happen. What is my
Speaker 1: theory of electromagnetism tell me? And so you can do
Speaker 1: some calculation. It tells you the actron is gonna turn
Speaker 1: left and go at this angle. But sometimes the theories
Speaker 1: break and they give you numbers that make no sense,
Speaker 1: like oh, the electron is gonna turn and it's gonna
Speaker 1: go to infinite angle or have infinite energy. So there's
Speaker 1: some theories and it's a bit too technical to get
Speaker 1: into that break down at really really small scales um
Speaker 1: and they just start to give infinities. And so some
Speaker 1: of those problems are solved if you have the smallest distance,
Speaker 1: because then you don't have to go to those smallest scales, right,
Speaker 1: And this especially is a problem when people try to
Speaker 1: describe gravity using quantum mechanics. It comes up with all
Speaker 1: sorts of crazy problems. And one solution to that is
Speaker 1: to say, well, what if there is the shortest distance,
Speaker 1: then we don't have to think about doing these calculations
Speaker 1: down to infinitely small distances. Right, So nothing can happen
Speaker 1: at such a small scale. So in theory, the theory
Speaker 1: doesn't break down. It's just nothing can happen at that scale.
Speaker 1: So why you can worry about it. Yeah, it's like
Speaker 1: a clue. It's saying, oh, this theory doesn't work. It
Speaker 1: can't describe universe where there's infinitely small distances something. Then
Speaker 1: the idea is, well, maybe the theory is wrong, or
Speaker 1: maybe the universe doesn't have infinitely small distances, in which
Speaker 1: case the theory works. There's lots of fun ways to
Speaker 1: make your theory work, and one of them is just
Speaker 1: to imagine that the places where it breaks are the
Speaker 1: places where it's not physical, where it's not actually describing
Speaker 1: what's happening. Well, this is a perfect point to take
Speaker 1: a break. Well, this is interesting. So there's apparently a
Speaker 1: number that physicists think might be the pixel of the universe. Like,
Speaker 1: there's like a concrete number they think might tell you
Speaker 1: what the pixelation the resolution of the universe is, right
Speaker 1: a little bit, I mean I think that's overstating it.
Speaker 1: There is a number which we think might have something
Speaker 1: to do with the pixelization of the universe. But the
Speaker 1: argument is pretty weak. All right, I'll walk you through it,
Speaker 1: but you'll be unimpressed with how strong argument is. Alright,
Speaker 1: just trying to manage your expectations a little bit, right,
Speaker 1: all right, I'll make them pixel size. There you go, Yeah,
Speaker 1: I go from one unit of expectation. Here's the argument.
Speaker 1: The argument is, we've noticed there are some fundamental constants
Speaker 1: in the universe, like the speed of light, and that
Speaker 1: has units meters per second, right, And that's just a number,
Speaker 1: and we measure it, and it's a parameter of the universe.
Speaker 1: We don't know why it's this and why it's that,
Speaker 1: and of course we have a whole podcast episode about that,
Speaker 1: but it is a number. And there are other units
Speaker 1: we've noticed, like the strength of gravity, right, it's called
Speaker 1: big G. The gravitational constant appears in Newton's formula, and uh,
Speaker 1: you know, and the plank constant, the one that appears
Speaker 1: in quantum mechanics. It tells you how um, well, you
Speaker 1: can know two numbers at the same time. So there's
Speaker 1: all these basic units that we've measured and we've discovered,
Speaker 1: and we think they reveal something about the universe. We
Speaker 1: think they tell us something about why the universe is
Speaker 1: this way not that way, and we don't know where
Speaker 1: they come from. They're kind of like the pie or
Speaker 1: you know, just the number that exists in the universe. Yeah, well,
Speaker 1: pies an especially fascinating one because it's unit lists, right,
Speaker 1: so it's pure in some sense. But these numbers have units,
Speaker 1: you know, they're like jewels per second or meters per
Speaker 1: second or whatever. And so we think they tell us
Speaker 1: something about why the universe is this size or has
Speaker 1: this or you can go this fast, or you know,
Speaker 1: it's some sort of like ratio between two things. Yes, exactly.
Speaker 1: They fix the relationship between things like the speed of
Speaker 1: light fixes the relationship between distance and time. Right, it's
Speaker 1: meters per second, So I see that the speed of
Speaker 1: light is like a universal physics number. Yes exactly, And
Speaker 1: so there's other numbers like these in physics theories. Yeah,
Speaker 1: there's a few that we've discovered along the way, and
Speaker 1: we think they're deep and fundamental, and you know, some
Speaker 1: future theory of physics might reveal why they are the
Speaker 1: way they are, but currently they're just numbers, and we
Speaker 1: imagine that they could have been set to something else,
Speaker 1: and that's a whole other discussion. Here's the thing you
Speaker 1: can do, though, is that you can manipulate these numbers.
Speaker 1: You can multiply them by each other until you get
Speaker 1: a number that has units of distance. So you multiply
Speaker 1: um planks constant and you have the gravitational constant the
Speaker 1: speed of light squared. You can cancel out all the
Speaker 1: units until you get a number that has just units
Speaker 1: of distance. Okay, so what is that number. Well, they
Speaker 1: call it the plank length because it has planks constant
Speaker 1: in it, and it's a number. And the number is
Speaker 1: ten to the minus thirty five meters. That's zero point
Speaker 1: thirty five zeros and then a one. So that's a tiny,
Speaker 1: tiny number. And because it comes from these simple basic units,
Speaker 1: we imagine it has special meaning. We imagine that it's
Speaker 1: a clue that it tells us something about the way
Speaker 1: the universe works. And because it's just units of distance,
Speaker 1: we like to think that it tells us something about
Speaker 1: the fundamental nature of distance in the universe, that does it?
Speaker 1: I mean, who knows. It's just a bunch of numbers
Speaker 1: we multiplied together, you know, and we thought those numbers
Speaker 1: were important, but maybe they're not. It's kind of like
Speaker 1: if you take the smallest things and the fastest things,
Speaker 1: you know, and you know, like the the smallest bit
Speaker 1: of matter and the going up the fastest possible speed,
Speaker 1: and you know, what would be the smallest distance that
Speaker 1: it could go. That's kind of what it is to
Speaker 1: mix all of these numbers together. Right, Yeah, it's it's
Speaker 1: not that much smarter an argument than that great I
Speaker 1: feelt like that was an insult. I don't say that
Speaker 1: to insult physics, right, Like, it's not a great argument.
Speaker 1: But it's the first thing you do, right, it's unit analysis.
Speaker 1: Say well, if we have no clue, what can we do. Well,
Speaker 1: let's command these numbers and maybe that will give us
Speaker 1: a clue. So it's not no physicist are out there
Speaker 1: saying this is definitely the fundamental unit of the distance.
Speaker 1: It just says, if there is one, it might be
Speaker 1: around this number. I mean, within a factor of a
Speaker 1: hundred or a thousand would be a pretty still a
Speaker 1: pretty good clue, right, tend to the negative thirty five,
Speaker 1: which sounds really small. It is really small. It is
Speaker 1: really small, but it's kind of it's not small comparative infinity,
Speaker 1: do you know what I mean? Like the number Pi,
Speaker 1: you can take decimals out to thirty five thirty five
Speaker 1: million decimals. Yeah, but you're saying maybe the universe only
Speaker 1: goes up to thirty five decimals. Yeah, that's right. It's
Speaker 1: a lot bigger than you know, ten to the minus
Speaker 1: one hundred, or ten of the minus one thousand, or
Speaker 1: ten of the minus ten thousand, Right, these are much
Speaker 1: much smaller numbers. Um. The thing is, it's also much
Speaker 1: smaller than the thing we've seen. Remember we studied space
Speaker 1: down about ten to the minus twenty, So that means
Speaker 1: that we are a factor ten to the fifteen away
Speaker 1: from seeing these pixels, if in fact they exist, and
Speaker 1: if they're at that scale. Yeah, I mean, just for
Speaker 1: a sense of scale, like the solar system is ten
Speaker 1: to the fifteen meters across, I believe, so if you
Speaker 1: could only see things, you know, down to ten to
Speaker 1: the fifteen meters, you'd be missing a lot of interesting detail,
Speaker 1: Like you'd miss Earth and life and planets and stuff
Speaker 1: and us. What a tragedy, I know. How could you
Speaker 1: study the universe without seeing the most important and best
Speaker 1: looking two dudes in it? Right? Like if you were
Speaker 1: a giant decisive a galaxy and you had an iPhone
Speaker 1: the size of you know, the Milky Way, and the
Speaker 1: biggest pixel in it was the sizeable solar system, there
Speaker 1: would be a lot you'd be missing exactly. So between
Speaker 1: where we've seen at tend of the minus twenty meters
Speaker 1: and how far things might go attend to the minus
Speaker 1: thirty five ms, they would be a huge amount of
Speaker 1: complexity and richness down there that we're totally ignorant of.
Speaker 1: Little tiny pixel people think asking these same questions, it
Speaker 1: could be a little pixelated alien going Mario, hold on,
Speaker 1: I don't think I've ever heard your time. That's pretty good,
Speaker 1: and we just lost all of our Italian listeners. Um,
Speaker 1: the Italian listeners please write in and comment at Jorge's
Speaker 1: accent at Daniel and Jorge dot comn Jorgel fans, the
Speaker 1: whole Country dot Com. Okay, well, um, let's get some
Speaker 1: perspective here. What what do you think would mean for
Speaker 1: us and our understanding of ourselves or universe if we
Speaker 1: found out that the universe is pixelated? It would be
Speaker 1: a really deep inside just into the very nature of
Speaker 1: the universe. You know, to know that number tells you
Speaker 1: something about the scale at which the universe was built. Right,
Speaker 1: Everything in the universe happens from its basic elements. So
Speaker 1: we have fascinating structure, you know, galaxies and superclusters and
Speaker 1: all that stuff, but all that arises from the interactions
Speaker 1: of smaller pieces, you know, particles and electrons. Everything is
Speaker 1: determined by what happens at the smallest scale, right, So
Speaker 1: everything in the universe comes out of these basic elements.
Speaker 1: So to learn how big the smallest unit is tells
Speaker 1: you how the universe was constructed. And in the end,
Speaker 1: what is science and physics about other than this goal
Speaker 1: of trying to deprogram the universe or look at the
Speaker 1: source code or figure out how this thing is organized.
Speaker 1: And so that would be pretty pretty awesome, but you
Speaker 1: know it would actually just be a first step. Yeah, no,
Speaker 1: it's it's you just made me realize it would really
Speaker 1: kind of blow your mind to just have this sense
Speaker 1: that the universe has a structure, right, that it's somehow
Speaker 1: feels built, you know, like there's a scaffolding to the universe. Yeah,
Speaker 1: like a graph paper, right, And then you have to
Speaker 1: ask questions like who made the graph paper and why
Speaker 1: that size? Right? Why is it ten of THEUS and
Speaker 1: not ten of the minus five or ten of the
Speaker 1: mines thirty meters? Right? What does that mean? There's like
Speaker 1: a clue there about the very structure of the universe.
Speaker 1: Is it a random number and it generated arbitrarily when
Speaker 1: all the multiverses were created? Or does it give you
Speaker 1: a clue somehow about something deep about the universe. On
Speaker 1: the other hand, you know, we talked about like galaxy
Speaker 1: is just being emergent phenomenon, right, there a really cool thing,
Speaker 1: but they're just formed out of smaller bits and their
Speaker 1: complex behavior arises into this thing called a galaxy. A
Speaker 1: lot of people think these days that space itself could
Speaker 1: be an emergent phenomenon, Okay, that these pixels of space
Speaker 1: could be built out of something smaller that are not
Speaker 1: that's not space. So space is not space, is what
Speaker 1: you're saying space is actually you know, A and B
Speaker 1: or a combination of Yeah, yeah, the way like you know,
Speaker 1: cookies are not their ingredients, right, you mix them together,
Speaker 1: you bake them, you get a cookie. But if you
Speaker 1: start with flour and utter and sugar and none of
Speaker 1: those things are cookies, right, So cookies an emergent phenomena
Speaker 1: in your kitchen. They're not a fundament you know what
Speaker 1: I mean, unless you buy a lot of cookies and
Speaker 1: that's all you buy, in which case they are the
Speaker 1: fundamental pixel of your kitchen. Like, there's even some hidden
Speaker 1: forces inside of space, is what you're saying, right, Like
Speaker 1: there's something yes, yeah, And there's some pretty cool theories
Speaker 1: about that. Like there's one that's called them quantum loop theory,
Speaker 1: and it builds space out of these tiny little loops.
Speaker 1: It says, maybe the fundamental unit of location in the
Speaker 1: universe is not space, it's something else. It's these little
Speaker 1: tiny loops, and those would be quantized of course, quantum
Speaker 1: loop gravity. And out of those the way those things
Speaker 1: are connected, space is formed. And that can tell you
Speaker 1: all sorts of things, like well, maybe that tells you
Speaker 1: why there's a maximum speed to how fast information can
Speaker 1: travel through space because it's how fast these loops can
Speaker 1: talk to each other. Like space is not like a space,
Speaker 1: is not like a jelly or like a space. It's
Speaker 1: more like a mesh or like a weed. Yeah, yeah, exactly,
Speaker 1: or a really complicated subway system and connected by these
Speaker 1: other forces. And so you hear people eminent um science
Speaker 1: communicated saying things like maybe space emerges from the quantum foam, right,
Speaker 1: and like I was to hear that, and I think,
Speaker 1: what does that even mean? Man um And that's what
Speaker 1: it means. It means that it's not a basic element
Speaker 1: of the universe, but that it comes out of the
Speaker 1: interaction of smaller stuff, right the way cookies come out
Speaker 1: of ingredients. Because I'm walking down the street, what's actually
Speaker 1: happened is that all of my electrons and protons and
Speaker 1: cords are actually like moving around in this mesh, this
Speaker 1: invisible mesh that is the universe. No, no, no, I
Speaker 1: think it's even it's a trickier to think about than that,
Speaker 1: because you can't think of these elements of this mesh
Speaker 1: as bits of space. They're not right, You can't move
Speaker 1: from one to the other. Somehow space arises from that
Speaker 1: This whole concept of location and motion through it could
Speaker 1: be an emergent phenomenon, right, and the one that doesn't
Speaker 1: have any meaning below that distance. So you're not moving
Speaker 1: through the mesh somehow, you know, information is propagating through
Speaker 1: the measure, the mess is interacting with itself in some way.
Speaker 1: But this notion of moving comes out of your assumption that,
Speaker 1: like space is fundamental, and we have to rethink that
Speaker 1: if space is not fundamental, meaning like a super Mario
Speaker 1: moving around the screen in your TV, it's not actually moving.
Speaker 1: He's just like a table of data in some program
Speaker 1: that doesn't doesn't look like space. It's just numbers related
Speaker 1: to each other exactly. That's the perfect way to think
Speaker 1: about it. What makes those pixels right, not smaller pixels? Right?
Speaker 1: It's some calculation inside the iPhone and is a little
Speaker 1: bit of technology there that lights that up, and you
Speaker 1: know it's not motion, So it's something totally different underneath.
Speaker 1: And so it could be the universe is made out
Speaker 1: of things that this gradation is granularity of space. These
Speaker 1: grains are made out of something totally new and alien
Speaker 1: to us, and discovering them could peel back a layer
Speaker 1: and reveal something really deep about the universe and so
Speaker 1: you know, past the joint man, because we're we're getting
Speaker 1: pretty deep here. So what do you think or hey,
Speaker 1: do you think space is pixelated? Or you think this
Speaker 1: is just a crazy idea? You know, intuitively, it seems implausible, right,
Speaker 1: Like space seems so smooth, and like we said before,
Speaker 1: it would mean that we're always sort of teleporting from
Speaker 1: one spot to the other. But you know, like you said,
Speaker 1: who knows, right, we used to think matter was perfectly smooth,
Speaker 1: but it turned out not to be. So it sounds
Speaker 1: like modern physics has uprooted you from all of your
Speaker 1: beliefs about the way the world works. Huh. You know
Speaker 1: you now have skepticism about everything. Yeah, are you even there, Daniel?
Speaker 1: Um No. I think that's a healthy attitude, you know,
Speaker 1: um And I think it's hard to hold that in
Speaker 1: your head. I mean, on one hand, you go around
Speaker 1: your daily life, you drive your car, you buy coffee,
Speaker 1: you do all these things without thinking about the way
Speaker 1: the world is working underneath you. And then sometimes I'm
Speaker 1: just struck breathless by realizing the credible complexity of things
Speaker 1: that are happening invisibly around us. Um And you know,
Speaker 1: that things might be totally different from the way we imagined.
Speaker 1: It's hard to hold that in your head a lot,
Speaker 1: which is why it's nice sometimes to just read a
Speaker 1: magazine and you a cup of coffee because it's breathtaking.
Speaker 1: You know. It's disorienting the way learning that we're tiny
Speaker 1: specs on a little mode of dust and a huge
Speaker 1: universe is um but it's also fun. Well, I hope
Speaker 1: that you guys out there listening also maybe see the
Speaker 1: world a little bit differently. All right, thanks very much
Speaker 1: for listening, and enjoy the rest of your day. If
Speaker 1: you still have a question after listening to all these explanations,
Speaker 1: please drop us a line. We'd love to hear from you.
Speaker 1: You can find us at Facebook, Twitter, and Instagram at
Speaker 1: Daniel and Jorge that's one word, or email us at
Speaker 1: Feedback at Daniel and Jorge dot com. Nine