Sean Carroll on the Biggest Ideas in the Universe | Closer To Truth Chats

I'm all in favor of asking why questions my point is only that we can't demand that there be an answer that satisfies us right the universe is not set up for our Amusement there might be answers to any particular why question or there might not be so I think we need to sort of look at the kind of question we're asking for example the early Universe has low entropy that's where the arrow of time comes from I would like to know why and the answer might just be it just is that way it's a brute fact foreign [Music] I'm speaking with Sean Carroll about his terrific new book the biggest ideas in the universe space time and motion what I love are the equations no I'm serious and readers will love them too I promise Sean it's great to see you thank you very much for having me back Robert and you've had many years at Caltech but you're now in Baltimore a Johns Hopkins University the Homewood professor of natural philosophy a joint appointment between physics and philosophy perfect position as soon as I read that congratulations was it was it a big decision well it was a big decision in the sense that it affects my life a lot but it was not a hard decision this really is the perfect uh position for me and they like really crafted it to be exactly what I wanted it's the first time in my life that the things that I want to do are exactly the same as the things my employer wants me to do so that's a very good feeling well Johns Hopkins is my alma mater so I'm all thumbs up go Blue Jays let me uh let me give a uh Sean's quick bio in terms of his research because he has focused on cosmology field Theory and gravitation shifting more recently to foundational questions in quantum mechanics such as origin of probability emergence of space and time and statistical mechanics entropy in the arrow of time complexity emergence and causation he's the author of several best-selling books including the big picture and for maternity to here he is the host of the popular mindscape podcast Sean we have lots to cover on the biggest ideas in the universe but let's start with those equations Stephen Hawking said that the reason he did not include equations and his popular books is that someone told them that for every equation it reduced book sales by one half so I did a little calculation I'm going to assume your book has about a hundred uh equations I think there are a lot more but 100 is easy to use so 0.5 to the 100th power is about 10 to the minus 31st and by this metric assuming every Star and every galaxy has a planet with 100 million or a billion people no one in the visible Universe could buy your book but I'm betting that you will prove the equation Skeptics wrong in fact I just checked and even though the biggest ideas in the universe has not yet been released it is already among the best sellers in several physics categories so you have falsified a Stephen Hawking conjecture uh why did you include equations when nobody else does well you know there's different reasons why you might write a popular trade physics book right and typically you're trying to get people up to speed on some of the most fun speculative enticing research ideas out there and that's usually what I do when I write these books but the other thing is you might want to teach people things that we know things that we are pretty sure are on the right track people have done that a lot I haven't really done a lot of it myself but I realized I could do it in a different way by Bridging the Gap between the sort of metaphorical allegorical word based explanations and really becoming a physics student so the equations are there but we don't assume that you go into the book with any mathematical knowledge or even love for the equations yeah and you make a really important distinction between understanding equations and solving equations basically you say that understanding equations if you do some work you can get in your book solving equations you might need eight years in in physics foreign that is exactly right and that's sort of the secret sauce to how we can do this it's not just that I teach you Newtonian mechanics and incline planes and things like that those are mentioned in there but very soon we're getting to what are considered Advanced topics to physics undergraduates many of the things we talk about in the book aren't ever talked about or taught to physics students because we can go faster because we're just giving you the ideas right terrific well what I want to do is go through the book and just give a flavor for uh the kinds of topics that you talk about and I'm going to be selective and ask you the kinds of questions that I was interested in um because the the the my physics background was was was fairly minimal or from a a formal point of view I did my doctorate in Neuroscience um so and I've been following these things but the book gave me this sense of bringing the ideas with the equations I've read a lot of physics books and I've missed the equations I've tried to read a few fully equations books and not really able to follow it so your book really was was terrific so I want to go through each of the chapters quickly and a couple of the ideas and You Know It please try to keep your answers short so we can get through a a lot of ideas I want to throw a lot of ideas so first chapter was on conservation and the question is why begin with conservation why is conservation fundamental and if it were not the case what would be the implications I was trying to get across the idea that there are these things called the laws of physics which are patterns that nature obeys if one thing happens and another thing happens right away the simplest possible kind of pattern is something just stays constant the total energy of the universe or the total electric charge of the universe so the idea of conservation took hundreds and hundreds of years to sink into the minds of physicists that once it did to me that was really the birth of modern physics you talk about it being the first step in the transition between pre-modern to modern science yeah exactly you know before we had modern physics and by modern now we don't mean Quantum field Theory we mean Isaac Newton as modern physics right before then it was a story of natures and purposes you know we tend to anthropomorphize the physical world a little bit and it was really took a long time for people to realize that things would just keep moving if we didn't prevent them from moving there's not a natural state where the rock sits at the bottom of a hill it wants to keep moving its friction and dissipation that get in the way and that really opened up a whole new way of thinking about the world what are the kinds of conservation that we talk about I know is energy momentum angular momentum so or organize that for us briefly yeah exactly and I think that momentum is the first one I talk about was really the first one to be understood because if momentum is conserved then like I said an object moving in a straight line will keep moving in a straight line unless a fork Force acts upon it so it's not trying it's not wanting to move in the straight line that's just its natural thing and then once you have that you realize there's something called Energy which is kind of like momentum but it's a number it doesn't have a direction like the momentum does there's angular momentum the amount of spin we have and then at a higher level of abstraction there are things like electric charge which is not really something that was known to Galileo and Newton but today is really at the heart of all of modern Quantum field Theory you also talk about the conservation of information did I get that right you did you did that's a different kind of thing but absolutely crucially important and again a huge break from pre-modern physics because what it's saying is the information in the universe is preserved from moment to moment in the sense that in principle and by the way this is an idea they had in the 1800s it's not necessarily true because we don't know what the fundamental laws of physics are but the idea is if you knew everything in the universe in principle that determines the entire past and the entire future of the universe the amount of information is conserved from moment to moment now you did I read this right that you say that in an expanding Universe energy is not conserved yeah the slightly more elaborate version of that is once you have general relativity Einstein's theory of curved space time it becomes hard or at least ambiguous to Define what you mean by energy if you just do the straightforward thing take the energy of the individual things in the unit universe and add them all up that's something that would be conserved if you are not in an expanding Universe when you are in an expanding Universe it is not conserved we know that just because as the universe expands photons lose energy because they redshift they go from short wavelengths to Long wavelengths their energy goes down deal with it okay you in the first chapter introduce the uh a concept that appears throughout that is an important one it's you call it the spherical cow joke uh tell us the joke and why it's important so a farmer Dairy Farmer wants to optimize the milk output of his dairy cows for some unknown reason he visits the local physics department he asks for the physicists the theoretical physicist to analyze his milk production and the physicist comes back and says okay step one we imagine a spherical cow and the joke that's the whole joke that's it I didn't promise it would be funny it's just illustrative because two reasons number one that is the way physicists work they idealize the situation to make it easier to analyze number two that works in physics it might not work in Dairy farming cows are not spherical and the ways in which they are not spherical might really matter for your milk output but when it comes to planets moving around the Sun you say okay let's think about one planet ignoring the others right we'll put the others back in later as perturbations that's really just the Paradigm for how physics is done these days right and and if you're doing the gravitation of the sun it's it's a point in the middle of the sun rather than analyzing all the Coronas and things like that chapter 2 is on change um so tell me about the transition from a conservation to change what's the difference well conservation is something remaining constant not changing and change is the opposite of that and and look let's be honest change is something that is a vast topic that we talk about in all the chapters of the book but the specific thing I wanted to sneak in there in that chapter is the idea of calculus this was the technological if you want advance that really enabled Isaac Newton to go as far as he did with classical mechanics he understood the mathematics of Change by thinking about how we can zoom in very very close and say that okay change is an accumulation of things over time so you can think of it as one moment to the next to the next to the next but what do you mean by the next moment is that like a second later a plank time later or whatever so he invented the idea of an infinitesimal time later and that opened up the ability to both study the rates of change and the accumulated amounts of change in a rigorous mathematical way and the definition of those two last phrases is the rate of change is the derivative uh and the amount of change is the integral that's exactly right and I I tell you what those mean I give you the symbols for them and we go through some very very simple examples and as I as I emphasize over and over again and you've already exactly pointed out the idea is not that hard right the symbols look a little unfamiliar so they become scary that's one of the reasons why I have a hundred equations a hundred is much better than ten yes if you had 10 equations they're just sort of magical Interlopers that you can ignore but when you have a hundred you get familiar you're like oh yes I know what that means so both derivatives the rates of change and integrals the total amount of change those are things that are completely understandable yeah and those are super important to really understand a physics uh modern physics in all its aspects and others kind of avoid it because if they sound scary it reminds people of the mathematics they either didn't like or didn't take uh but I I love the way you talk about it in fact you have two short phrases I'd like you to explain a little bit because you talk about derivatives as 0 divided by zero and integrals as infinity times zero so I I actually hadn't heard heard those aphorisms before so give me some sense of that well this was the whole advance that Newton and his uh I don't want to say collaborator because that's certainly not true his rival Gottfried Wilhelm Von leibniz who also invented calculus what they both did was invent a systematic way of making sense of the idea that for example for an integral for the total amount of change you could say well how much change is there in this interval than the next interval then the next if you have a finite time interval you can easily divide it into a finite number of sub-intervals and add them all up and then you're taking a finite amount of change multiplying it by a finite number but if you go all the way to a perfect representation not just a crude approximation the intervals get smaller and smaller their length becomes zero and the total amount of change naively is zero but there are an infinite number of them so you're adding up an infinite number of accumulated changes uh each one of which is zero now if that's all you say it's nonsense you can't do that any mathematician will tell you that's not well behaved but what leibnitz and Newton figured out is there is a way to take the limit as we say in calculus to smoothly go from finite reasonable approximations to the exact quantity even though that exact quantity is sort of spiritually or morally zero times infinity yeah I think that's a that's that's a great way to uh to understand it without having to solve anything I did not ask you to solve any integrals do any derivatives nothing like that right so uh in the chapter on change you start with laplacian Paradigm so briefly tell us what that is because I want to trace the paradigms as you go through the book well this is where it really comes to pass that information conservation matters so it was LaPlace in the year 1800 so over a century after Newton but he figured out this really crucial implication of the system of mechanics that Isaac Newton had put forward namely that if you knew the position and the momentum of every little bit of thing in the universe and you knew Newton's Laws then you could figure out what happens in the future in the past so how do you do that that's the laplacian Paradigm and the idea is you take the state of the system right now and you use the laws of physics to say how do we move it forward one infinitesimal moment in time and if you know the answer to that which Newton's equations tell you the answer to it then you can just iterate that you go from one moment to the next the next the next the next and build up as an accumulation the entire past and future history of the system so that's the laplacian Paradigm the idea that we can take information at any one moment of time and use it to move forward and backward and figure out the entirety of the history of the system so that chapter starts with that and then you go back and like to do a little bit of the history because you do it so well uh with Kepler and the uh breakthrough that the ellipse was the planetary orbit and then Newton and why Newton was so important we got to give those guys some credit before we move on absolutely and one of the fun parts of writing these books is always to pull out a little historical anecdote that you don't hear over and over again like I've read a lot of these books and I've heard most of the standard ones but just the idea that you know at that time it was the age of reason it was when coffee shops became really popular for the intellectuals to gather in and people like Robert Hook and Christopher Wren and Edmund Halley would like go to the coffee shop after a meeting of the Royal Society and they would debate like you know what kind of force law would explain Kepler's laws of motion and they finally worked up the courage to ask Isaac Newton who explained it all to them and that it's so much fun but it's also educational and pedagogical because that move from Kepler to Newton is a move from saying the whole orbit of a planet is an ellipse right that's a sort of holistic statement about the entire trajectory Newton doesn't say that he says if the planet's doing this right now I'll tell you what it's doing a moment later and that turns out to be an infinitely more powerful and flexible way of doing things chapter 3 is Dynamics going from change to Dynamics what's the core idea of Dynamics well changes all the different possible ways we can imagine things changing whereas Dynamics is the way they actually do change in the real world and this is going to you know throughout the book be an important theme like we can imagine all sorts of things and what the laws of physics do as patterns is pick out the right ones from all of them and so the phrase the the title Dynamics just means now we're going to tell you Newton's Laws of Motion for classical mechanics so we're going to put it together to understand how things roll around in Landscapes and things like that so A couple of the points to open the chapter to set the position are no preferred position uh what's the significance Galilean relativity so how do those two concepts set the framework to discuss Dynamics yeah you know we attribute the idea of Relativity to Einstein or at least to the 20th century but it it goes far back it goes all the way back to Galileo Galileo you know is an interesting character because he really enabled all of modern physics even though it was Newton who put it all together Galileo was not as good at math as Newton was but he was a genius he was an Einstein level genius For Thought experiments and insight and figuring out what mattered and what didn't so it was Galileo who really put the finishing touches on this idea that if it weren't for friction things would move in a certain way they would just continue moving on in a straight line and furthermore he realized he was trying to argue that the earth goes around the Sun that was an important debate during the day why do we see the sun move well because the Earth rotates and people said if the Earth rotated we'd feel it wouldn't we like it's pushing on us somehow and Galileo said no because you're rotating along with it you and the surface of the Earth are moving at zero velocity with respect to each other and therefore you feel nothing that's where relativity comes in you're moving at zero velocity relative to the surface of the earth now Einstein Etc put the speed of light in there in a way that Galileo didn't but this idea that there is no absolute measure of where you are or how fast you're moving in the universe that's Galilean relativity and that's exactly the same way of thinking uh the fact that Einstein you know centuries later put the speed of light in there and came up with something that radically affected our intuition more so but still it's exactly the same concept oh absolutely and it goes to the heart of classical mechanics the system that Isaac Newton eventually set up because his famous equation we're allowed to talk about equations here Robert because there's a lot of equations in the book so I love them I love them keep them coming the most famous equation in classical physics is f equals m a force equals math times acceleration my old physics professors used to joke if you had not studied for the test as long as you know f equals m a you can work everything out and the reason behind the joke is very I mean you got to think about what that's saying Force equals mass time acceleration if you know the force force due to gravity or because you're pushing it or whatever you can figure out how fast something's accelerating and the acceleration is the derivative of the Velocity the rate of change of the velocity and the velocity is the rate of change of the position so the idea is there's two things you have to give me position and velocity then Newton automatically gives you the next one the acceleration and from that you can figure out everything you put the total energy equation very simple everybody can understand this as potential energy plus kinetic and I want you to explain that briefly because that will affect some many of the other major principles and equations that we'll later discuss it is and you know it's one of those things that you just blurt out when you're taking physics there's kinetic energy potential energy add them up but there's a lot of subtlety there if you dig into it number one there's this thing called Energy which remains constant and if you're a little bit skeptical you can ask yourself what do you mean there's something energy that remains constant like if I see some energy disappearing you're just going to tell me it went into a different form of energy like is there any content to this but the answer is yes there is content to it because you can attach equations to each of the different parts of the energy the different components and in this simple example we look at in this chapter there's kinetic energy which is the energy associated with moving the energy that depends on your velocity and there's potential energy which is the energy hat you have whether or not you're moving the energy that just depends on your position so your height above ground for example affects your kinetic affects your potential energy sorry you could turn it into kinetic energy by jumping on off the roof but that's not always an advisable thing several of the concepts that you put forth here again are basic principles that will be needed to explain more complex aspects so just briefly describe the importance of oscillations harmonic oscillations perturbation Theory and phase space so three nicely categories for you to jump into and tell us what they are yeah there's a lot going on there they do phase space first because it's kind of simple but again it's one of those simple things that's going to keep turning up and you're gonna have to realize that it was more important than you thought so we think about space right there's lots of definitions to space and we use the word in physics and math books in a kind of haphazard way but the ordinary space where we live three-dimensional space a set of all these locations where things can be okay that's one way of thinking about three-dimensional space but Newton's Laws tell you that in order to know what's going to happen next you need to know both the position of something and its velocity or even better its momentum momentum and velocity as far as Newton is concerned or just interchangeable because P equals MV momentum equals mass times velocity so there's another space we can think about we can think about the space of all positions and velocities so a six-dimensional space for a single particle because there's three dimensions of location three dimensions of momentum okay that's phase space this six dimensional space for one particle what if you have two particles well there's three numbers for one particle for its location three for its momentum three for the other particle for its location and three for its momentum so it's a twelve dimensional space and among other things not only is it a physically important quantity but I'm warming up the reader to get used to bigger dimensional spaces overall okay so so let me ask a specific question about phase space which is my personal question when I was reading through um and that is you use Avogadro's number which is 6 times 10 to the 23rd which is the number of molecules or atoms in a mole a standard unit of of stuff and then you say the phase space is 3.6 times 10 to the 24th so it's just one order of magnitude more than that and that confused me I know no Avogadro's number I know what phase space means but to have them actually so close to one another surprise me well no that's clearly my fault I did a bad job of explaining because the point is simply that each particle in Avogadro's number of particles that's 6 times 10 is 23 particles for each of those particles there's a six-dimensional phase space so the total phase phase is just six times Avogadro's Number okay oh I see a 3.66 times six times six got it okay okay very very good all right so quickly on oscillations and perturbation Theory this was actually secretly my favorite part of the book because it's again hugely important in how physicists actually work but we don't tell you you know we tell you about the simple harmonic oscillator which is this idea that in a potential energy function that looks like a parabola V of X goes like x squared okay so it's like the bottom of a hill you can rock back and forth with a frequency that doesn't depend on your amplitude no matter how fast you're rocking back and forth it takes the same amount of time in a simple harmonic oscillator that's the simple thing that we tell everybody what we don't tell you is if you zoom in close enough to the bottom of any potential energy it always looks like a simple harmonic oscillator there's not one simple non-harmonic things but they can be ignored in the spherical cow spirit so when particle physicists when you take your first class on Quantum field Theory and try to understand why a quantized field looks like particles the answer is because they look like simple harmonic oscillators and we will get to that in book two okay we'll talk talk about that later and then perturbation Theory which you talked about a little bit before simplifying and then adding the complexities at the end exactly so when you go in that potential energy you go zoom in down near the bottom and you realize oh it looks like a simple harmonic oscillator and you solve that exactly and you're very proud of yourself and then someone maybe it's your professor comes along and says okay now what about the fact that it's not exact let's put back in all the things you just ignored when you were zooming in in that potential and perturbation theory is a way of doing that systematically there's an x squared potential which is the simple harmonic oscillator then there are contributions that look like X cubed x to the fourth x to the fifth x to the sixth and you can systematically learn how those affect the Motions of the particles using perturbation Theory and perturbation Theory obviously in particle physics and the later development of the standard model became exceedingly important we wouldn't have the standard model of particle physics without that every time you see a Feynman diagram those little squiggly lines of particles bumping into each other that's a perturbation Theory calculation now um the way I see the the the principle towards which this Dynamic chapter um drives is the principle of least action and then you get into the lagrangian so tell me about the lagrangian uh equation that's getting a little bit more complicated but but it's it's we've set we've set the the foundation for it so it should be very easy to to explain based on that principle of least action yeah and this is something where you know I struggled with this one in writing it not because it's hard to write but because I felt like I was undoing some of the good I had done in the previous chapter you know in the previous chapter I rambled on about the laplacian Paradigm you tell me what's happening at a moment and then I tell you what's happening next and then that can accumulate the principle of least action says that's not the only way to do physics there's a whole nother way which says you give me where the system starts and where it ends you don't tell me how fast it's moving I can figure that out by looking at what is called the action which is a quantity that is that happens over the trajectory of the particle I imagine all possible trajectories and what I notice is the real one the one that the laws of physics says actually say actually happens is the one that minimizes that action and again these are words that if you're lucky you might hear in a popular physics book I'm going to give you the equation that tells you what the action is we've already talked about the kinetic energy energy and the potential energy you add them together to get the energy what if you subtracted them what if you took the kinetic energy minus the potential energy that's a quantity we can Define it's called the lagrangian and the action is just the accumulation of the lagrangian over the whole history of the particle so in other words the integral of the lagrangian over time is the action and the minimum value of the action is the real motion of the particle so if you think about that physically the LaGrange Gene is kinetic energy minus potential we're trying to minimize that so that's trying to minimize the kinetic energy and also minimize minus the potential energy which means maximize the potential energy so there's sort of one influence that wants the particle to go up to the top of the hill where the potential energy is maximized the problem is that costs kinetic energy because you have to move up there but you're also trying to keep the kinetic energy low so there's a competition between these two effects and it balances out to give you the real motion Allah Newton's laws of physics so to me this was a a terrific part of the book because it really explained uh the the deep meaning of the equation because on its surface easy to understand where energy is kinetic energy plus potential energy but to get your head around what's the the meaning the the physical meaning of kinetic energy the energy of motion minus the potential energy the energy of position not immediately obvious from that statement that that makes any sense at all no and you know one of the things I gotta apologize for is I just say it in the book I I could if if I wanted to write a book that was twice the length show you derive the fact that starting with this idea of the LaGrange and the action you get out Newton's laws but I'm just hoping that you understand what the idea is without the derivation and it's worth doing both because it's intrinsically cool like once you read it like wow physics is awesome right but then also again once we get to Modern physics it's lagrangian lagrangian lagrangian all the way down that's what all Quantum field theory is from start to finish so you're laying a foundation for future success yeah and the key to understand that is you're not defining energy you're defining this principle of least action and that's why you have as you said this tension between kinetic and potential energy because you're you're seeking this other way of doing physics by finding this this basic principle yeah and you know it's perfectly okay to take a breath at this point in the book because kinetic energy even though there's an equation for it in some sense you can see it you can see the thing moving right and potential energy in some sense you can see it it's on the top of the hill or on the bottom of the hill you can't see the lagrangian kinetic line is potential energy that's just not a tangible immediate thing so it's nevertheless crucially important to physics so the reader has to sort of you know uh put on their big boy pants and say like I'm gonna understand this slightly abstract thing right and as I said to me that was one of the highlights of the book because it really emphasized that um that deeper understanding that becomes the foundation for all modern physics right okay at that at that point you we kind of switch uh from the foundations to the big concepts of space and time so next chapter was on space so I'm going to ask you a very simple question is space a thing in itself or is it just changes in the distance or relationships of other things well that's a very good question as you know since you read the book but that was the big debate between uh one of the big debates between Isaac Newton and leibniz at the time substantialism space is a thing a container where everything else is located versus relationalism Space is just a convenient way of talking about distances between two things and I think that the modern view is much closer to substance than relation we really think of space as a thing in and of itself especially once you get to general relativity and space can have a geometry if it weren't a thing how could it have a shape right but you know again we don't know the the final laws of physics we're still working toward that and one of the reasons why I think it's important to remember these centuries-old debates is because they have a way of coming back and there's a point of view within modern quantum gravity that says we should think relationally once again and since we don't know the final answers it's good to keep all the options in mind now in this chapter we introduce you introduce hamiltonian mechanics and so we had this Newtonian lagrangian now we're at Hamilton hamiltonian mechanics which elevates momentum so give us that sense yeah and this is another tricky one but it's one that I just love because it absolutely does not get explained even to physics students who are learning about hamiltonians the idea is the following maybe if you were reading about the laplacian Paradigm very very carefully so you're given the position and the velocity you predict what happens next right you're given information at One Moment In Time you predict what the next moment will hold but wait a minute the velocity is a rate of change of the particle's position over time to calculate the velocity you kind of have to peek ahead a little bit right if it's at one location one moment is at a different location the next moment so is it cheating to include the velocity as being defined simply at a moment of time and hamiltonian mechanics definitively answers that question but it does so in a way that the nomenclature is not great so it says think of the momentum instead of the Velocity we have a relationship between momentum and velocity momentum is mass times velocity but forget that relation and this is the hard part because once you've learned it it's very hard to forget just imagine there's something called momentum okay there's some Vector that every particle has and there's something called position that every particle has and then the hamiltonian way of doing physics says there are equations of motion one of which says the rate of change of momentum is basically f equals SMA the other is that the rate of change of position is momentum divided by mass in other words momentum equals mass times velocity right so the I hope I got that right I think I might have said that wrongly yeah the rate of change of position is momentum value Mass I got it right good anyway the point is it goes back to change versus Dynamics right changes any way that things could change Dynamics is the real actual thing that things do hamiltonian mechanic says momentum is in conceptually Independent Idea from velocity but they are proportional to each other in the real trajectories that physical systems actually do okay so if that's the case then what is the fundamental difference between the lagrangian and the hamiltonian you know the lagrangian the hamiltonian and even the original Newtonian version of classical mechanics these are all almost exactly mathematically identical there's some nitpicks and footnotes we don't need to worry about there but they're equivalent both in terms of what you need to make a prediction and what those predictions are but I have this wonderful quote from Richard Feynman in there I'm going to mangle the exact thing but to paraphrase it he says theories can be exactly identical in their predictions but be psychologically different in how you would move Beyond them so hamiltonian lagrangian Newtonian ways of thinking about classical mechanics give the same predictions but they have different concepts in them and again as I keep saying over and over again we don't know the final answers so one of the reasons to let people in on all these Alternatives is to prepare them for what might come next the other is that they're put to use in even in things we already do understand those lagrangians and actions are all over Quantum field Theory the hamiltonian is all over ordinary quantum mechanics the Schrodinger equation which we're going to get to eventually is absolutely centrally dependent on the idea of the hamiltonian yeah and and the that was my next uh question and the importance of hamiltonians in in modern quantum mechanics is is foundational well that's exactly right and you know again the hamiltonian is one of these conceptually slippery things what is it it's just the energy that's what it is but it's very specifically the energy as a function of positions And momenta So when you say in ordinary Newtonian mechanics the kinetic energy is one half MV squared one half the mass times the velocity squared that's equivalent to saying it's one half p squared over M because P the momentum is M times V right but in the hamiltonian point of view you have to say it's one half p squared over M you're not allowed to say one-half MV squared because the hamiltonian is a function of the momentum not of the velocity you end the chapter on space with uh a a a discussion or a presentation of fields and you call feels the fundamental building blocks of reality so give us some color of that yeah again as far as we know currently but it crept up on us you know LaPlace had this idea of a gravitational potential field the idea there is he was trying to address this mystery that Newton had worried about action at a distance right Newton says the gravitational force depends on the inverse of the square of the distance between two objects and people including Newton himself said how does it know how does the planet know how far away the sun is to know what its gravitational force is supposed to be and Newton is like that's a really good question I hope someday people figure it out I don't know the answer LaPlace said imagine there is a field pervading all of space in between the Sun and the planets and a field just means it has a value at every position then he comes up with an equation which again gives you exactly the same predictions as Newtonian gravity does but it's conceptually different because now there's a field filling space which seems to fit our into tuition a little bit better and indeed we get Maxwell coming up with electrodynamics in the mid 19th century Einstein putting general relativity his theory of curved space time is a theory of a metric tensor field and all of modern particle physics is based on Quantum field Theory so LaPlace had the right intuition that imagining a field is a really really useful way of thinking about the fundamental nature of stuff next chapter naturally following from space is time I'm going to ask you the same question is time a thing in itself or is time just changes in the sequence and duration of other things well of course soon enough namely the chapter after this we'll learn that the modern point of view is that time is part of space-time and I think that it's right to think of space-time as a thing in and of itself at least provisionally that's the best we know right now so yeah time is a thing no worries um compare space and time before we combine before we unify them if you compare them them how are they alike and how are they not alike yeah I go a lot in the book in comparing how time and space are similar and also how they're different they're similar because we can measure them right their distances they help us locate ourselves in the universe when you meet somebody you tell them where you're going to meet them and when you're going to meet them they're different obviously because unlike space time has a direction and I wrote a whole book on this that was from eternity to here people can read that so we give the ultra condensed version of The Arrow of time the fact that entropy is increasing from the past to the Future if there were no change could there still be time well you wouldn't have invented it but then again you wouldn't exist because without change there's no such thing as people okay um let's talk about reversibility um compare reversibility versus time reversal invariance you do that nicely in the book yeah it's something that doesn't get enough attention I think again I'm sort of like doing all my own favorite things you know trying to correct the misimpressions that I see uh lying around there in the literature so reversibility which doesn't get a lot of press but is the most important thing is the foundation of that laplacian Paradigm the conservation of information if you know the state of the system now you use the laws of physics to predict what will be in the future and if you know the state of the system in the future you can say what it was now that's reversibility you can go backward and forward time reversal invariance is supposed to be a symmetry where you simply reverse the direction of time okay so in the definition of reversibility that I gave you there is no past involved right but time reversal says let T the time variable go to minus t and what I argue is that we we make a big deal in modern particle physics about time reversal being violated but I say that has nothing to do with the arrow of time because you've just chosen a particularly contentious definition of what you mean by time reversal invariance that are better definitions in which it is perfectly well conserved I can see people uh kind of getting ready to argue with you a little bit it's a controversial area to be sure as long as they buy the book that's the point of the book you mentioning the arrow of time you deal with this a lot you dealt with it in the previous book on entropy in the arrow of time but I noticed you call the arrow of time and Epi phenomenon which means it's like the foam on a wave it's not the wave itself it looks like it's something but it really ain't foreign well it's obviously crucial and crucially important to how we experience time the fact that the past and future are different is the most obvious fact about anything in the world and it's kind of a mystery that it's nowhere to be found in the fundamental laws of physics and the resolution to that mystery which is perfectly resolvable is that the arrow of time doesn't depend on the fundamental laws it depends on the specific state of our universe in particular the fact that near the Big Bang 14 billion years ago the entropy the disorderliness of the universe was very very very low and it's increasing ever since and that's where the difference between past and future comes from so it depends on the stuff in the universe not on the underlying laws so I'm trying to wrap my head around that and is that worthy enough or is it minimalized enough to call it an Epi phenomena and and the foam on the wave sort of uh sort of uh uh uh analogizes with that's all right I'll I'll go along with that for a while I'll think about it distinguish between presentism where only the present is real eternalism where the past present and future is real which is Einstein's block Universe versus possibilism if I pronounce that right where the past and present are real but the future is still open yeah these are different philosophical stances one can have one reality of different moments of time presentism says only now is real like you said block universe or eternalism treats every moment as real and people always trip up on this because they we're so stuck in the arrow of time in the present moment that they say you're saying that the future exists right now no I'm saying the future exists it doesn't exist right now it exists in the future but all moments are supposed to be equal in eternalism and then possibilism is supposed to split the difference by saying that because the past is in the books because we can't change it whereas the future is something we can affect we're going to call real both the present and the past but not the future I'm an eternalist myself but I want to again lay out all the possibilities for people to decide good good I I'm uh um I would skew until it's possibilism but uh you know it's worth the exercise of comparing the three gives you a deeper sense of of what of what your own feeling would be in your own intuition would be and and gives you appreciation for the the other possibility because this is the type of question where you feel your intuition is obviously correct and everyone else is obviously wrong until you understand it so we could use that same um uh humility in politics but that's that's a different topic uh what can physics say about a a philosophical approach to time which is the differentiation between uh per durantism and enduranceism perderintism where all objects are considered to be four-dimensional objects or worms that worms its way through four-dimensional time and objects have temporal Parts you can't define an object without defining its temporal part you have to define a period a a a part of it that stem that's part of the object where enduranceism says that all objects are three-dimensional objects you don't have to have the time as as an inherent part of the object itself but the object is present in whole at each individual time is is that a difference without a distinction is it and what can physics say about it if anything you know I actually think that it matters I don't talk about that distinction in the book but it is an important one and one of the reasons why it matters is because again we're constantly trying to push beyond what we currently know what physics has to say to philosophy is here's what happens in the world and then philosophers had the job of sort of conceptually making sense of it all so this is a great question because you might think oh it doesn't matter you know objects persist over time whether I call them each moment a different object or what I call the whole four-dimensional thing an object who cares but then you have the many worlds interpretation of quantum mechanics where the thing can persist in time and then now become two things in two different worlds what do you do then and I think that being ready to attack all those issues philosophically is something that you can absolutely help yourself toward by understanding the physics as best you can we'll talk about the many worlds interpretation which I think will probably disagree on when you have book two book two yes space time is the next next chapter and um uh we've talked about space and time the unification many people know that but you talk about a difference between a flip between the shortest distance to the longest time so I thought that was a very short way to to get some deep understanding yeah and you know I'm just sharing with everybody the little epiphanies I had along the road to understanding this stuff uh that's a great part of the book by the way to to have your insights what what are the kinds of things that that made a difference to you uh that's a great part of the book a real value thank you thank you very much and when it comes to space time which is just the topic of special relativity basically uh the thing that Einstein put a Capstone on in 1905. my feeling is that a lot of people get confused because the Deep lesson of space-time is talk about space-time don't talk about space and time separately those are human conveniences the real thing is space time but when we learn about special relativity in a typical popularization of it we learn about time dilation and length contraction and these are all things that are hanging on to the ideas of space and time as fundamental if you think of space-time as fundamental and you you're told that there is something called the interval in space-time and just like a distance in space there's a formula for it just a distance in space on an XY grid is given by Pythagoras's Theorem right x squared plus y squared equals the distance between two points there's a formula just like that in space time the big difference is there's a minus sign that separates the spatial contribution from the time contribution so you have an interval that you measure on your clock the proper time from one moment to another and it's the amount of time coordinate that gets elapsed minus the amount of spatial distance you do and that's the whole difference between space and space time give some more color to that what what what what is what does that mean well think about the famous twin paradox thought experiment which is not a paradox at all but you have two twins which is convenient because they're the same age one stays home on Earth Alice the other one Bob goes out on a spaceship at 99 the speed of light and comes back and what happens is when they come back Alice is now a lot older than Bob even though they were born at the same time what happened oh my goodness how can we ever understand this the answer is they moved on different paths through space-time so Alice's age what she actually measured on her calendar wristwatch or whatever time keeping device she had is just the number of years that we sort of have on our Universal calendars that we all use whereas Bob has that amount of time squared because it's like Pythagoras Theorem minus all the spatial distance he went out and came back squared so you know just from that kind of formula that the prediction is whoever moves out and comes back will be younger when they come back they will experience less time because it's time squared minus space squared so that always makes you experience less time and that absolutely confirms that space and time are a single thing well it confirms that it's a useful way of thinking about it the other amusing historical story is Einstein put all this together in 1905 in 1907 it was Herman minkowski who had previously been one of Einstein's professors at University and it was minkowski who said you know this all becomes simpler if you think of your theory as unifying space and time together and Einstein said ah that seems like sort of a mathematical distraction from the real physical importance it took him a little while but he eventually realized you know you had the space-time point of view was really helpful what are some common fallacies when you one thinks about special relativity general relativity Laurentian contractions oh you know I think that it depends on who's doing the thinking but uh I I think that the I don't think it's a matter of fallacies so much as a matter of ways of thinking that in some construal are okay but Lead You astray in other places and and my favorite one is just the idea that clocks move more slowly when you're traveling faster when you're traveling close to the speed of light uh so Bob went out there in his ship he came back right near the speed of light he is now younger so you say well clearly his clock was moving more slowly but remember the word relativity in the theory of relativity you have to say relative to what was his clock moving more slowly for him everything was perfectly normal the number of heartbeats per wristwatch tick of the clock is exactly the same as it always would have been so I don't like to say the time moves more slowly I think the time moves at one second per second no matter what you're doing the next chapter on Geometry and why it's uh important we know certainly in general relativity I'm going to only ask you one question from this chapter and that is give me a simple way to understand the metric tensor good I mean and this is you know there's a lot of conceptual abstract leaps we make in the book and I hope to sort of make them as gentle as possible this is a mathematical leap into the world of tensors and in some sense they're not that hard you know you can think of a vector pointing in some direction in space or you can think of it as a list of components there's the amount of Vector in the X Direction in the y direction the Z Direction so a little column of three numbers the X component the Y component the Z component a tensor is just rather than a column of three numbers maybe a square Matrix a three by three array or a four by four array once we get into space time and why do you have to make that extra leap of complication well because you're trying to conceptualize all of the different ways that a mathematical entity like space-time can be curved you know there's only one way to be flat being flat is being flat to be that has no curvature anywhere but then you say I have some curvature there's a million different ways in which you could have curvature so the metric tensor tells you the distance along every possible curve you can draw in a curved space or space time and that's enough to fully fix the geometry of it so this was Einstein's great realization that by manipulating and thinking about that metric tensor he could figure out an equation that said how space and time are curved and that of course is general relativity which leads us to the next chapter a very important one on on gravity and I want to start by asking this question this is not original I've heard it I've heard it uh uh said before that is it and I don't know if this is right I'm asking you is it true that if Einstein had not put forth special relativity in 1905 someone else would have done it very soon but if Einstein had not put forth general relativity 1915 it might have been a very long time before someone else would I think the first part of that is certainly true um special relativity was really a group project very much Einstein was the final person to put the finishing touches on it and in fact in some sense the hard mathematical work had been done we understood what are called Lorenz Transformations and the ways that lengths and times might change and what Einstein really added to it was the idea that you can get rid of this thing lurking in the background called The Ether people thought that light waves propagated through a medium called The Ether and it was Einstein who realized you didn't need that you get all the answers all you had to do was change your Notions of space and time which is a lot you know it admittedly but people like Ponca Ray and Lorenz and so forth were on the track of that kind of understanding I think that someone would have come up with it if Einstein hadn't now it took 10 years for Einstein to turn that into general relativity and it was certainly his you know Capstone achievement and it wouldn't have happened in 10 years if Einstein died been around it would have been longer than that but how much longer I don't know you know David Hilbert came up with Einstein's equation almost the same time as Einstein did now admittedly he was good friends with Einstein Einstein told him everything he had done but there were other people uh Gunner Nordstrom was another physicist working on the same kind of problem it was really really hard and Einstein was smarter than everybody else but I I don't think it would have taken decades it would have taken years okay uh you make the point that inertial mass and gravitational Mass are different but it's significant that that they they're two different definitions but they're the same thing what's the significance of that yeah I'd like to analogize it analogize it rather with uh electromagnetism where you have the force on an electrically charged particle depends on its charge and then you have the inertia on that particle depends on its mass so it's acceleration by f equals m a forces mass times acceleration depends on both its charge and its mass and the charge can be positive or negative right in a single electric field electrically charged positive particles will move One Direction and negatively charged particles move the other direction but in Gravity the same quantity the mass is both the measure of inertia and what you might think of as the charge right the amount of gravity we produce depends on your mass the response we have to gravity depends on your mass so the mass just cancels out of all the equations and this is Galileo's Insight two objects with different masses will fall at the same rate if we ignore air resistance and all those things one of the great um visions of uh general relativity and gravity in putting the whole story together is the the total mass energy of the universe and how it came about and the idea that the Universe could have come about out of nothing however we Define nothing that's a that's another closer to truth subject that you and I have talked a lot about um the the fundamental idea enabling that is that gravity is considered negative energy and somehow balances the mass energy of the universe so that if the total mass uh Zero Energy Universe model if it's a flat model euclidean model that's not hyperbolic and it's not curved the total amount of energy in the universe is exactly zero in that the amount of positive energy in the form of matter energy is exactly canceled out by the negative energy you in the form of gravity now I can understand that but then I think that energy gravity is a something and how how does that how does that I mean it's a force so how is it negative how is gravity considered negative energy it sounds like a cheat that you physicists do no no it's actually quite common in physics remember if you if you have a ball on a hill and you say I can Define the energy of that ball right like the zero point of energy doesn't matter all that matters is how energy changes so if I have a ball right here and I assign it a certain amount of energy down here it has a negative amount of energy there's nothing weird about that the zero point doesn't matter so for Gravity what happens is simply if I have two objects that are orbiting each other let's say right well I can extract energy from that system by letting them spiral closer together this literally happens when black holes give off gravitational radiation so the gravity Invitational force between them is larger when they're nearby but the energy of the system is lower because it's given away energy to the rest of the universe so it has increased the amount of negative energy in the gravitational field and that balances out by the gravitational waves that have been detected that's the exactly that's going out okay that's a very very fundamental point the last chapter of this fabulous book uh is on black holes and it's very natural it's the ultimate test bed of uh of theoretical physics um and I I know this to be a fact but I still hard to get my brain around it that crossing the Event Horizon Beyond which you can't return like can't come out of that we know what the Event Horizon is for black holes is a moment in time not a location in space so then it becomes impossible to avoid the singularity to which you're pulled uh but the reason it is you can't avoid the singularity is is that it's a a point in your future and it's like trying to avoid tomorrow accepting that it's true sure and this is sort of the payoff chapter I mean you've worked really hard okay you've read all these chapters all these equations and in the previous two chapters on Geometry and gravitation it's really been a different kind of math than you've probably been exposed to with the tensors and all that but what it allows us to do is to talk about something like black holes in a way that you just couldn't do without the equation so this is your reward for making it this far and also it drives home a very important lesson because the equations are smarter than we are you know Albert Einstein put forward general relativity in 1915 he lived for another 40 years or so he never knew what a black hole was yeah the idea would have been alien to him because it was really hard to get our brains around but the equations knew it was there yeah the idea of a black hole was implicit in Einstein's equation and in the solution to Einstein's equation written down by Carl schwarziel just two years later so this idea that the center what we think of the center of the black hole R equals zero The Singularity is a moment in time in the future no one would have guessed that it is something that you just get out of the equation and so you can write down the equation you can point to it and go look right here it's telling you the singularity is in your future and you're going to hit it and you can draw pictures to understand it after the fact but you have to be led to that conclusion by trusting the equations the the alternative is that there's something wrong with the equation something's missing this something's more fundamental we're not getting how can we just how can we falsify that alternative it's always possible you know uh many people have tried to out Einstein Einstein and come up with a better Theory than general relativity I am actually personally responsible for a few efforts in those directions and what you want to do is not just propose a theory but then propose predictions that can go out and be tested and general relativity is tested to Exquisite Precision in many different ways I'm responsible for some of those also I'm a big believer in it so you can look here in the solar system at the motion of the planets you can look at the deflection of light you can look at the gravitational waves and the black holes and you can look at cosmology and the big bang and they all fit general relativity you can look at the GPS on your iPhone it all it's all there and you know again it's it's a another Testament to the fact that the theories are smarter than we are Einstein didn't know about the Big Bang either when he wrote down the equations but his equations correctly tell us what happens then you talk about a white hole and we we know what that is is a black hole run backwards in time but then make the interesting comment that the universe as a whole which came out of the Big Bang which was this Singularity at the beginning looks something like what a white hole would be a white hole is a very theoretical thing nobody thinks they really exist but the universe kind of looks like that yeah absolutely and a lot of people wonder about the fact that there's so much matter and energy in the universe why doesn't it collapse to be a black hole after all Roger Penrose and Stephen Hawking became famous proving theorems that say if you get enough matter and energy in the same place they will always make a black hole but there is a little hidden assumption in those theorems though they don't actually say you will always make a black hole they say that either there will be a singularity in your future as there is in a black hole or there will be a singularity in your past as there is in a white hole and we have a singularity in our past that's the big bang now we have to say here of course when we use the phrase the Big Bang to talk about the singularity that's a little bit sloppy because the singularity probably doesn't exist that's the place where the theory breaks down not an actual part of the history of the universe it's a signpost saying we need to understand the fundamental nature of space and time better under exactly those conditions great book uh Sean I really enjoyed it um and learned a lot and uh recommended to everyone very very much so um some some final some final thoughts um you talk about why questions we're we're all answering why questions and pushing it further and further but then you talk about why questioning bottoming out without some Ultimate answers with nowhere further to go you have a great phrase that's just the way it is I I've known you've used that with me on closer to truth in the past when I've pushed you on certain things you look me in the eye and say that's just the way it is you know take it or leave it um but you do it politely though you do it very politely of the brute fact what what's in that category well of course we don't know and and this is why it is something where we have to be careful and subtle rather than just bludgeoning our way into our favorite answer I'm all in favor of asking why questions my point is only that we can't demand that there be an answer that satisfies us right the universe is not set up for our Amusement there might be answers to any particular why question or there might not be so I think we need to sort of look at the kind of question we're asking for example the early Universe has low entropy that's where the arrow of time comes from I would like to know why and the answer might just be it just is that way it's a brute fact but it doesn't smell that way to me because I can think of many other ways the universe could have been at Early times that don't look anything like that so it's not just there is a single fact there is a condition picked out among many different possibilities and I want to know why this possibility rather than the others for other questions like why is something is there or something rather than nothing why is there a universe at all there I don't I don't think the question has the same character I don't think there could be a very good answer to that question in the terms that the question is being asked so there I suspect that the answer is that's just the way it is but I'm not certain about any of that so I'm happy to have my uh priors overturned by better evidence and the the fundamentals of why the laws of physics the way they are I mean that's sort of one level up from why is there something rather than nothing but those two I would put in that category at least at least right now I see that the biggest ideas in the universe is a three-part series space-time in motion the first book that is just being released which I say is is fantastic uh is classical physics but it's the it's the foundation of what you need to understand all physics the second uh will be quanta and fields which is on quantum physics and the third complexity and emergence so I just want you to give us a tease about the future books so what what are some of the the motivating uh energies that you feel to to write each of those and why are they organized as they do and why do you end with complexity and emergence well a couple of things going on there one is again I'm focusing on things we think are pretty solidly understood and established within physics so it's not about string theory in the Multiverse and black hole information or anything like that but modern physics is based on this idea of quantum field Theory you take Fields Allah LaPlace and Maxwell and Faraday and so forth you quantize them it's a simple idea there's some puzzles with it some you know things we don't yet understand but it's giving us spectacularly successful predictions for what we see at experiments and so I really try to explain what quantum mechanics is what Quantum field theory is what different kinds of fields are where the forces of nature comes from the Higgs boson on the fermions versus the boson bosons all of that stuff and then build it up into matter atoms why atoms have the size they do Etc then in volume three we go on to admit that sometimes there are interesting systems with more than just a handful of atoms right they're Collective phenomena that have sort of an autonomous way of talking about them you can talk about fluid mechanics without knowing your fluid is made of atoms so I talk about cosmology which is a simple example but then more interesting examples about thermodynamics and statistical mechanics and complex phenomena which physicists are still struggling to get a handle on but we see some patterns amongst the noise power laws and scaling relations and networks and that's something that we do understand a little bit about now but it's also going to be a growth area going forward and for everyone who's looking forward to quanta and feels and complexity and emergence you had better get the the fur first volume on space-time in motion because you won't be able to understand fully the second and third volume without the first volume I have a one question about emergence give me a really short answer but it's one of the questions uh that we focus on a lot and that is is there such a thing as what's called strong emergence where it is impossible even in principle to account for certain emergent Properties by reduction in terms of fundamental laws well I think that reduction is always a bad way of talking about it I never use the word reduction myself I do think that there is a fundamental description of reality and I think that we have part of that in hand in our best current theory of the standard model of particle physics plus gravity I don't think that there is any phenomenon in nature that we can observe in our everyday lives that is incompatible with that theory of course so there's no strong emergence from that low level but you can always talk about strong emergence between other levels like if you're if you're quote unquote microscopic theory is human beings and your macroscopic theory is Societies or economies then I can't make the same promises right our understanding of human beings is far far weaker than our understanding of electrons and photons and so forth so it's possible in my mind that the best theory we have of human beings is not enough to predict what we happen in a society you need to add some extra ingredients in some interesting way I don't know if that's true or not but I can at least contemplate it well we'll talk a lot more about that when book three and book two come out but everybody needs to get book one in order to understand the future you have a standing invitation to come back for each one I say to everyone the biggest ideas in the universe has my highest recommendation viewers can watch 26 of Sean's videos and ATV episodes in which he appears on the closer to truth website and closer to truth YouTube channel thanks Sean thanks everyone for watching thanks Robert thank you for watching if you like this video please like and comment below you can support closer to Truth by subscribing

Channel: Closer To Truth

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Keywords: closer to truth, robert lawrence kuhn, Sean Carroll, biggest ideas in the universe, physics, space time motion, sean carroll mindscape, sean carroll quantum mechanics

Id: TY4Tkx9BrXI

Length: 72min 57sec (4377 seconds)

Published: Tue Sep 20 2022