Daniel and Jorge Explain the UniverseDaniel and Jorge talk about how finely sliced time can get.
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Hey, it's Horehan 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 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. It's available for pre order now, coming out November two. You can find more details at the book's website, universe faq 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 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 need like an hour just to dig into something?
Well, you know, it 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 just write themselves.
I am Jorgem, a cartoonist and the creator of PhD comics.
Hi, I'm Daniel. I'm a particle 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 from space into time?
Now, what I need to do is to speed up the rest of the world near the speed of light. So that it runs slowly, and then I can just get all my work done while everybody else is frozen.
Whoh, that's a 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.
That's right.
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 twin professor paradox.
But welcome to our podcast Daniel and Jorge Explain the Universe, a production of I 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, 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 fixed and firm and never change it, but actually it sort of does. It's a squishy eh 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'd have to switch careers to just writing jokes.
I don't think I 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 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. When 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.
So yeah, it is a pretty, let's say, interesting universe. Do you think the universe would be offended if we call 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 it is it? And I hear my colleagues making arguments like, well, you know, we might have spinoff technologies or we invented the World Wide 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 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, 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 World Wide Web and useful technology right 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.
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. I'd pitch in my tax dollars for that. Anyway, we love the universe is sies and that presents us with really fun, interesting, basic questions, things that we don't understand about, you know, the very 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 this 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 as sort of like a ladder. You know, if you look at it at one distance scale and one time scale, it works a certain way. If you look at it 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 does it all just depend 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 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 Henrik's question.
Hi, Danielle Rogez. I'm Hendrik from Sweden and I have been wondering if time could be pixelated? Is there any minimum unit of time? Or could it be infinitely short? And when I listen 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 pretty interesting question from Henrik. 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. You know, he is absorbing what we were 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 one of the consequences of it? How can I test and explore this. So that's exactly doing physics. So kudos to you, Henrich, for 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 going to email you some Swedish fish, my favorite Swedish candy.
All right. So then it's a pretty interesting question. And Henrik 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 it's like a grid or something, or it's discreet at the very small as 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 that 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 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, 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 you can do. 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'll be were wondering how many people out there had 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 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. Write to me too. Questions at Danielandjorge 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 have to say.
I guess if you 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 be moving sort of in frames, as if like a movie kind of thing.
Tom, pixelation, haven't heard of it?
Tell me about it?
Sounds crazy, that is, it's a usual thing. So do you think it's pixelated or continuous?
Okay, I'm.
Continuous, It's continuous.
Okay.
Wow, man, I don't 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 nanosecond is a pixel?
I have no idea how to answer this question. I really don't know what that question means.
Maybe like is time quantized in some form? Honest, I have no idea. Time is very strange that 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 to units 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 probably not.
I have no idea from a physics standpoint, but from a perception standpoint, I feel like it is, and I think deja vous 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, 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 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 spent ten or.
Well, yeah, it's a tough question. It seems to have puzzled people. Most people just threw 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 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 were stepping forward instead of sliding forward, that seems to be a little bit more alien.
Yeah, so let's maybe tackle this one kind of idea of the 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.
Mm hmm. There's sort of two very different but closely related ways for time to be discrete, for there 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 would be that things step forwards in time that you could be at 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 tics.
Like you can't have a half of a second or something like that.
Yeah, and you know, obviously seconds aren't the minimum unit of time. You can 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 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. 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, 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 grid 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 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 in simulations.
Right, You use simulations with time steps. But simulations are not perfect, right, And 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, discret 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 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.
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 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 can't measure differences in time that are smaller than a certain number, Like if you measure something twice, you can't get two menasurements 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 timescale and land wherever.
Okay, I think I know what you're saying. You're saying that maybe like every possible timestep exists or is possible, Like you can have one point oh three seconds and 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, 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 inside of it. And that's same way. Time 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 it it doesn't fit our idea of a pixel, right, It's more like there is no pixel, but it's sort of fuzzy at a certain scale.
Yeah, exactly. It sets a scale which I think to the physicist is interesting because it means you can't infinitely divide time.
Right.
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 ten to the minus one thousand seconds later, Like does the 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 us.
It's known and it's undetermined, right in the same way that like not all the information about an electron is knowable, not just because we can't measure it, but because it's not specified, is 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 pixelated and whether or not we'll ever know if it is or not. But first, let's take a quick break.
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All right, we're asking the question is time pixelated? And 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 the rules of the universe are really pretty different. Of course, when you zoom out to things like our scale, 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, and then maybe step us through, what are some of the 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 discreteness more natural? What would make more sense to us? What's the sort of default position? And I think a lot of people out there would assume, well, continuousness, right, like time should flow smoothly. 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 discrete. Your television is not updating infinitely many times per second. 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 a four K, you know, high resolution television into somebody from the you know, tenth century, they would probably be fooled into thinking like there's actually something magical, real going on inside of the TV. 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 of sub seconds to get there? You know, it feels like at some point you 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 that 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 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 infinity. 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 discrete. Like that chair you're sitting on right now, it seems 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 that beam of light that is shining on your plants, it's actually a bunch of packets of photons. So the world around you, though it seemed continuous, almost everything about it is actually discrete.
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 ist argument, right, And it doesn't really hold that much water. It's just sort of to get you in the mindset of things. Maybe discrete is the more natural outcome instead of continuous, right, So 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 are our opinion of it, So what are some of I guess more of physically robust arguments for or against time pixilation.
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 have very very short time, then you talk 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 pieces or not? Are there gravitons? All these fun questions. They make a lot of arguments about space being discrete, 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 unit to space, a lot of those same arguments you can use to make a 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 in 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 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 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. 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 skip through a few timestips 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 things can be anything at a certain level, and one of those things could be a black hole and 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 you from knowing something very precisely, because if you knew it that precisely, it would turn into a black hole and then censor 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 pixilation of space.
Yeah, although we can't really do this experiment, like, how could you measure a particle with such precision that its 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, the universe sort of counters with a black hole to prevent you from learn about it.
But how do you know those black holes aren't there? Maybe they are there, but they's 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 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 so 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 minus one hundred seconds later, that introduces uncertainty in the particle's energy. So time and energy have the same relationship in quantum mechanics as position and momentum. It's another of the Heisenberg and certainty principles. And so if you measure a particle's 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 it maybe even the same argument, right, because I feel like momentum is sort of related to velocity, and velocity is like distance divided by time. So 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 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 pixelated because space is bixically.
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 for time being pixelated.
Right.
Oh, 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 sense for them to both be pixelated or not. In this case, quantum mechanics suggests 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 but then have a reason of why space and time are pixelated like that.
Yeah, And it all comes down to what happens at these very very small distance scales when 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 minimum unit 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 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 and say maybe gravity is a quantum theory and you're exchanging gravitons, It says take 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 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's maybe continues. But this would sort of 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 loop quantum gravity you could have a theory that is pixelated in space but continuous in time, or if you absolutely had to have discrete time as well, And he said 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. He's very confident about that, and he says you can do something similar with time, but there are some complicated jumps you have to make in the argument, and he wasn't one hundred percent confident in it. But he also said that he would be very surprised if anything that included time and as 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 he would be very surprised if time was any different.
It seems like the theorists don't think time is continuous, that it's maybe more likely or would make more sense, that it's pixelated.
Exactly in luke qantum 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 make sense for time to be pixelated or could it still be continuous.
On one hand, it makes perfect sense for time to be chopped up in a minimum munist because, as we say, quantum mechanics tells us that the universe is discreet, 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, 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 on a spaceship and they're watching our experiment, They see us like length contracted. They see everything shortened because they're moving at 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.
Wait, what do you mean? It doesn't break relativity in a way. It just means that it's al sort a relative, right, Like to someone moving at a certain speed. The minimum distance in the universe would be this much and to someone not moving at that t 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. 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. So you can't 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, 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, save 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 another consequence of having pixels in time. You know, if the universe is not continuous, if it's discrete, right, if you can have like time equals one point five seconds and one point six seconds, but not time equals one point five to 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 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. It 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.
WHOA, that seems like 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 a 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, let's get into our last question, which is how would we even know if time is pixelated? Could we devise an experiment to tell us whether or not it's true or whether it'll be a mystery until the end of time. But first, let's take another quick break.
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I'm David Eagleman from the podcast Inner Cosmos, which recently hit the number one science podcast in America. I mean neuroscientists at Stanford, and I've spent my career exploring the three pound universe.
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All Right is Time Pixelated I guess, Daniel, the biggest question is how would we know, Like, are we trapped in the matrix and we think time smooth and continuous, and are we always going to be trapped in this matrix thinking that it's continuous or we'll be ever to 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 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. There's a possibility that we could always be frustrated. It's 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 it that's so small you can't see it.
But that would be sort of a limitation of our technology, right or is that always going to be true because you know, you 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 a small enough level to be sure that it's not pixelated.
Yeah, I think there are ways that we could convince ourselves that it probably is pixelated, but it'd be pretty hard to prove that it's not. You know, it'd be pretty hard to prove that it's infinitely continuous. I think you'd 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 discreete than to prove that it's continuous.
But you just gave me some arguments for why space might be pixilated, right with the whole infinitely small black holes. Can then we come up with a theory or some sort of way or some sort of consequence over the theory of the equations 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, 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 in its 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 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, the width of its wave function. A 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 up the energy of your particle colliders, the smaller the particles you can discover because you can like 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 ten to the minus twenty meters wide, you know, quirks 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 than what we think is the Plank scale, which is ten to the minus third five meters, And that's a big ratio.
Right, Yeah, you just need more money, Daniel, Just ask the taxpayers for more money.
Yeah, we should siphon funds out of your ten billion dollar comics project.
Oh no, no, no, no, you can't touch that. Some things are more important than understanding the nature of the universe.
That's right.
That's a limiting distance, right, that's not quite the limit in time? Or is it the equivalent you're saying.
I'm saying they're equivalent because these experiments also happen 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 sort of at the same time. But unfortunately they're like way too weak to probe really the fundamental nature of the universe. And to make them big enough and powerful enough to probe that distance scale, you'd 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 are alternatives to break in the bank here to 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. The first idea was proposed about ten years ago by Beckenstein. 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 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 and 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, 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 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 it just right, they have like just enough energy to move it one like quantum universe step forwards. And so this is an idea that Beckenstein 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 bull crap and would never work.
I see, all right, so that's a no no. What are other ways in which we could maybe figure out if time is pixelated?
Well, really, I think the most promising way to figure out if time is pixelated is to try to get 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 see the universe take forward in time, but they are experiments that might help reveal the very nature of space and time, which would 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 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 gotten pretty good recently at building larger quantum 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 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 break down 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 done so far is made things like those 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. It'd be very easy, where it'd be like on a computer chip kind of thing, and in the basements of research facilities they'll be like having quantum diamonds in superpositions and doing crazy experiments.
But I guess maybe the question is, you know, that might help us figure out if gravity's quantized, but how does that help us know if time is quantized or pixelated.
Yeah, it'll tell us if gravity 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'll 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 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 about the nature of space and time.
Right, But even if you find out the gravity is quantized and space is quantized, you still wouldn't technically right. Maybe possibly now if time itself is also quantized. Like we said earlier, it could be the one of us quantized and 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 is a minimum resolution below which it doesn't make sense to ask questions. Or if you discover, oh no, it looks like loop quantum gravity is correct and Carlo Rebellia is 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 am I show us that none of our ideas are correct and something else totally weird and new is required, and time might not be quantized. It might be something else totally different than we haven't even imagined.
It might be a different time.
It would be time for a new idea.
It'll be a timely discovery.
Yeah, so I would say that in summary, you know, it's not something that we're going to be able to directly probe very easily, but we can get around to it to sort of at the back by trying to build a consistent theory of space and time, which requires understanding quantum gravity.
Because you 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 in purpose?
I would, I totally would sign me up. 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's brain. Well, I guess the question is yet to be the termins there are there are 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, fundamental theories of the universe, maybe it'll come up. Hopefully it'll come up. Is that kind of the plan there, Let's focus on something else and let's procrastinate, and maybe it'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 you want to do. All right. Well again, I think it's an 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 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 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. Maybe we should collide physicists together and just see what happens.
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 Jorge Explain the Universe is a production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. How is us dairy tackling greenhouse gases? Many farms use anaerobic digesters to turn the methane from maneure into renewable energy that can power farms, towns, and electric cars. Visit you as dairy dot COM's Last Sustainability to learn more.
Hi, I'm David Eagleman from the podcast Inner Cosmos, which recently hit the number one science.
Podcast in America.
I mean neuroscientists at Stanford and I've spent my career exploring the three pound universe in our heads.
Join me weekly to explore the relationship.
Between your brain and your life, because the more we know about what's running under the hood, that or we can steer our lives. Listen to Inner Cosmos with David Eagleman on the iHeartRadio app, Apple Podcasts, or wherever you get your podcasts.
I'm doctor Laurie Santos, host of the Happiness Lab podcast.
As the US.
Elections approach, you can feel like we're angrier and more divided than ever. But in a new hopeful season of my podcast, I'll Share with the Science Really shows it was surprisingly more united than most people think.
We all know something is wrong in our culture, in our politics, and that we need to do better, and that we can do better.
Listen on the iHeartRadio app, Apple Podcasts, or wherever you listen to podcasts.
