 All right. Well, everyone is here and we've got the voice working. Should we just, without further ado, go ahead and get started here? We're just about at the top of the hour. So let me just make some introductory remarks. Welcome to the Science Circle. This is part of the Science Circle continuing series of panel discussions on science topics. And today our topic is gravity. Want to remind everyone that the Science Circle is a grant funded nonprofit based in the Netherlands. And as such, we do have to keep in mind our grant funding. So I'd like to ask everyone to please be on your best behavior, be polite, no griefing or trolling, please. We'd like to keep things, you know, civilized. And for our topic today on gravity, I have with us Phil Youngblood and Dr. William Wall, who are going to help us elucidate topics of gravity. This was inspired a little bit by a series of videos commissioned by Wired Magazine, where they have an expert discuss a topic in five levels of complexity. And so we're going to try to do something like that here. We're going to discuss gravity in three levels of complexity. Sort of the logical way to break that down is that I'm going to talk a little bit about Isaac Newton and Newtonian gravity, sort of his vision of gravity. Then Phil is going to discuss gravity as envisioned by Einstein. And then Dr. Wall is going to discuss sort of theoretical Einsteinian gravity. And kind of one of the overarching perhaps themes of this presentation, I think, is to kind of give, I want to give our students some sort of appreciation for why gravity is such an outlier, so weird. Because as many of you know, in particle physics, we have developed a standard model which integrates essentially all of the quantum, sort of the quantum mechanics of particles in nature. But we have been unable really to integrate gravity into the standard model. And that's the big bug boo. The quest for the theory of everything, a unified standard model, has still eluded us. And gravity is the reason why. And so I kind of hope by the end of this discussion, you'll have an appreciation for why gravity is kind of the big bug boo for the theory of everything. Before we get started, I want to give also a little bit of biographical information about our panelists, really for the benefit of people who don't know our panelists and might see this later on video or something. It also occurred to me that I've never really given much biographical information about myself, so I'm going to do that too. So just quickly here, I have a degree in biology from UCSD, University of California, San Diego, which is actually in La Jolla. Before that, while I was at the University of Oklahoma, I was one of two freshmen allowed to attend a seminar class by Stanford visiting professor and the Nobel Laureate, Paul Berg, who won the Nobel Prize for the discovery of recombinant DNA back in the 70s. I also spent a summer as a lab intern at MIT where my brother was doing a postdoc. And I ended up presenting that lab's paper on an early identification of an oncogene product at a national conference. But after some graduate work in biology, I left science to go to law school and I've been an IP attorney for about 30 years now. So that's patents and trademarks, copyrights, things like that. Another panelist is Phil Youngblood, who has a degree in chemistry in which field he co-authored a peer-reviewed papers. He then switched to computer information systems during a teaching stint in the US military and Phil ran a computer information system cybersecurity program for a major university until retiring in 2019. And Dr. Wall was born in Canada, received his PhD, attended an undergraduate in Canada and received his PhD from University of Texas at Austin, which is right down the street from where I live now. He did his postdoctoral work at NASA, GSFC in Maryland. He was a researcher at the National Institute of Astrophysics, Optics and Electronics in Puebla, Mexico, and his research involved observational studies of interstellar medium using radio telescopes, including the LMT. And Bill, I believe you are retired too now, is that right? Okay, so with our introductions completed, I'm going to go right into... Oh, very interesting. Phil also says he did some recombinant DNA and bacteria. So that's very cool. Yeah, recombinant DNA was really controversial in the 70s. It's one of the reasons that modern biology programs have ethics committees and have all sorts of containment requirements for doing genetic research because of the freak out about recombinant DNA. Anyway, back to our topic at hand. So, so gravity. So Isaac Newton was the discoverer of gravity. He was an English mathematician and physicist who lived from 1642 to 1727. The legend is that Newton discovered gravity when he saw a falling apple while thinking about the forces of nature. Although I believe that story is apocryphal. Regardless of what really happened, the main point is that Newton realized that some force must be acting on falling objects like apples because otherwise they would not start moving from rest. Right. Remember Newton's laws of motion that an object at rest will remain at rest unless acted on by a force. So when an apple is released from its stem, why doesn't it just float in the air? What makes it fall to the ground, right? It shouldn't move at all unless a force is acting on it. Newton also realized that the moon would fly off away from the earth in a straight line tangent to its orbit unless some force was causing it to fall toward the earth. The moon is just a projectile circling the earth under the attraction of gravity. Newton called this force gravity. I was kind of thinking about why he used the term gravity, which I think of as being related to gravitas, maybe sort of someone who has weight, you know? So kind of interesting to choose the word gravity. And using the idea of gravity, Newton was able to explain the astronomical observations of Kepler. And the work of Galileo, Brachy, and Kepler and Newton proved once and for all that the earth wasn't the center of the solar system. The earth, along with all other planets, orbit around the sun. And two astronomers, J.C. Adams and Laverier, later used the concept of gravity to predict that the planet Neptune would be discovered. They realized that there must be another planet exerting a gravitational force on Uranus because Uranus had an odd perturbation in its orbit. Perturbations are deviations in orbits. So a couple of things to keep in mind about this. One is the concept of attraction that bodies attract each other. So the earth and the moon attract each other. The earth, the sun and the earth attract each other. And that the strength of the attraction is related to the amount of mass in the object. Stars have so much mass, for example, that we could not even stand up on them. Newton also discovered that objects of different quote unquote weights fall at the same rate hitting the ground at the same time. This is because the force of gravity acts equally on every sort of unit in an object. It doesn't really so much act on the object itself, but on each sort of particle of that object. And they all accelerate under that force at the same rate. Gravity is the same force that keeps the moon in orbit. And so, which kind of makes you think about, well, what causes something to go into orbit, right? We all know the expression that what goes up must come down, but that's not necessarily true if something is moving fast enough. So if you throw an object across your backyard, it's going to travel in an arc and then come down and hit the ground. But you can imagine, you know, the faster you throw it right, the farther away it goes from you. So just imagine you can throw it so far and so fast, you know, that it leaves the atmosphere. It travels up into a space. It's still traveling in an arc. But at a certain kind of a sweet spot, sort of the Goldilocks speed at which it's traveling, it's not going to escape the gravitational pull of the Earth, but it's going too fast to ever fall back down to the Earth. So what happens when you kind of get hit that Goldilocks spot is that the object ends up just orbiting around the Earth. It's constantly falling down to Earth, but it's going too fast to ever actually fall down to Earth. And that's basically what an orbit is. So when things are so-called weightless in orbit, that doesn't mean that gravity is not acting on them. It just means that those objects are in free fall. The International Space Station is in free fall. Everything in it is in free fall. Free fall gives the illusion of weightlessness, but it does not mean that you have escaped gravity. And weightlessness comes from actually Einstein's equivalency principle, which is this notion of sort of relative motion. And some of you may have experienced this if you ever travel in a train and you see the train next to you moving. And you have this weird moment where you can't tell if your train is the one that's moving or whether the train next to you is the one that's moving. It's just this sense of relative motion is there, but you can't tell which one of you is actually moving. So this notion of absolute motion is the key. It's sort of difficult to show absolute motion, but it's very easy to show relative motion. Furthermore, Newton's sense of gravity is expressed in what's called the inverse square law, which is simply a fancy way of saying that the farther the two objects are away from each other, the weaker the attraction between them, the weaker the force of gravitational attraction. And this notion that gravity is an attraction sort of makes gravity sound like an ordinary force. And nowadays we understand forces as being an exchange of virtual particles that the way the reason you get action at a distance and other spooky things like that. The way the reason the magnet can attract iron, right? In like the invisible through air that's like the magnetic attraction. That is achieved through an exchange of virtual particles. And so you might get the impression that gravity works like through the gravity is a force of attraction kind of like magnetism, right? And magnetism also kind of has an inverse square law. Like if you pull magnets further apart, the attraction between them becomes less, right? So gravity is starting to look a lot like magnetism. So we're going to explain why that's not the case. Gravity is not a classical force like magnetism is. And finally I just want to point out that gravity is a weak phenomenon. I was going to say it's a weak force, but we'll have to find out. We'll have to discuss whether gravity really is a force or not. But it's weak. That is when you pick up an object, like if you pick up a rock in your garden, by picking up that rock, you are resisting the gravitational pull of the entire earth that's pulling down on that rock. But it's such a weak force that you can easily pick it up. That's just a kind of sort of a schoolyard example of why gravity is a weak force. And we'll have more to say about that later. But this is just a little bit of a way to kind of wet your appetite for what I will now let Phil talk about, which is how did Einstein's thinking about gravity alter our conception of it from what we understood for 200 years under Newton? So Phil, why don't you go ahead and tell us a little bit about Einstein? Oh, thank you. Let's see, I make sure this is okay. Great summary there of Newton, and I'll be telling a little bit more about Newtonian mechanics and how Einstein changed it. So my contribution as Matt slash Berrigan mentioned is to give you an idea of what how Einstein contributed to the notion of gravity. First thing then is let's review what Isaac Newton did. He was able to recall, by the way, does anyone recognize what the blue cone looking thing is around the left of this slide? Anyone recognize what that is? That kind of came about at the same time as Einstein was working out the general theory of relativity. It looks like the cone of time. Yeah. If you move back through time, the universe gets smaller. Yeah. And it's used that way too. I'll put on it on its side with the way of the timeline of the universe. In this case, what I'm kind of doing is that it's an analogy for what people thought of gravity at different times. And so essentially before Newton, remember that, yes, okay, Minkowski space, which I'll talk about here in a minute, with the four-dimensional, when we started talking about four dimensions in space time. Okay, so in Newton's day, before Newton's day, remember that it wasn't that long before he came about that the gravity was kind of considered from a geocentric and religious use. In other words, and also from kind of an anthropomorphic thing, which meant that things were attracted to each other the same way people could be attracted to each other. And from religious views, namely that there were heavenly bodies and they certainly weren't made by people, so therefore the planets were being pushed around by angels in perfect circles. And so his theory was quite radical for the time, the same way that Einstein's was, and he was able to describe gravity mathematically, just as Einstein was able to describe his theories mathematically. And down at the bottom, you can see the equation where you've got mass, in other words, it had to do basically with masses and the distance between the objects. But he also was able to explain phenomena, like the tides, and then also uphold the idea of what's called Galilean relativity, that is that physics is the same in any inertial frame of reference. Those are all extremely important ideas that kind of led then to Einstein's continuing view of, or I hate the word use of progressive, but basically enhanced view of gravity. And this was in the 1600s. Okay, if you look then at what came next, then we have to look at Maxwell, because essentially what the same way Newton was trying to reconcile what Kepler and Galilean such people had found is Maxwell then took one of these forces, the electromagnetism which people have been working on for the nearly century. And he was able to describe it mathematically, much like Newton did with gravity, he was able to explain phenomenon having to do with magnetism and electricity, and he was able to then uphold with electricity and magnetism, his idea of uneasy about the idea of gravity being a force at a distance, in other words, he never explained what gravity was, he explained how it worked basically. In other words, it had to do with the inverse relationship with distance and the masses of objects. But he was able to say, okay, there is a field. And so there's just not nothing between the North and the South poles. There is this field that describes the values of electricity and magnetism at any point between them. And that was really important to Einstein, because essentially when he came along, so essentially Maxwell then came between the classic mechanics and theories of gravity and then general relativity and implications, which Bill or Scissigie will explain. So Einstein comes along, and he then is able to describe electrodynamics, that is, particles in electromagnetic field that are moving. And that was essentially, when we talk about the paper for special relativity, we're talking about the title of the paper was essentially on the electrodynamics, the movement of particles in the electromagnetic field. And he was able to describe it mathematically, extending it to light speed, in other words, all the way out to light and then upheld Michelson and Morley's experiment that showed that there was not an ether. In other words, there was no need to invent new and unseen forces or objects just to make things work, which for a long period of time, they thought that space was not empty, but everything had this ether in it, which then led to the idea of an absolute frame of reference because basically, if you were facing one way or another, light would be a different speed because of the ether moving. Well, that might be something that Bill or Scissigie will field, because that's an interesting point. And then so in other words, the idea was relativity referred to the idea that there was no privileged or absolute frame of reference. And it was very important then that it confirmed that physics works at the same for all frames of reference within with the speed of light being constant for all observers. So there was a lot of stuff that the what we call or what was later called the special theory did to up and something. By the way, there is no kind of upending. In other words, if you think about it. And on this slide kind of tells a little bit more there was no upending of stuff in other words Newtonian mechanics and theory of gravity work just fine. Where we are in other words where things are really slow and we've got objects the same size as us primarily and stuff but if you move down into the area of the size of atoms. So if you move to speed switcher closer to the speed of light, then things get weird. And yeah, I thought so too things get weird and essentially Einstein's contribution then was in relativistic mechanics. So there's what happens when you move to speeds closer to the speed of light, whereas he didn't do anything at this time having to do with quantum mechanics or even where quantum field theory which bill or Scissigie will cover. Because those are the objects which are much smaller and they were talked about in detail after Einstein's discovery relativity. Okay, so now you've got basically Newtonian classical physics and mechanics physics and plus electrodynamics. So it's like okay how do you reconcile Newton's theory of gravity and electrodynamics field theory at the same time. And so Einstein attempted to do this now just to see how he did that part of my contribution here in the middle is to kind of give you a look into Einstein's mind how he went from the classic almost doc dogma of Newtonian mechanics to the stuff that bill or Scissigie will talk about with Einstein's field theory or field equations. Okay, so in Newtonian mechanics, if you look at the top, you'll see that basically time is a constant. Whereas down with special relativity, what would be called special relativity. It's very different time actually dilates. In other words, you could say for example you were on a spaceship that was moving near the speed of light or moving faster and faster and faster. You would experience time as being slower than people relative to you that we're going that we're going relatively slow. In other words you were going much faster than than they were. So essentially, and I saw a good article is kind of interesting. It basically said okay, if you're on a spaceship that was accelerating at one G so that essentially it felt like gravity. And you kept accelerating and accelerating. Instead of being able to just go 40 light years say during your lifetime or practical part of your lifetime, you could actually go tens of thousands or hundreds of thousands of light years because time would essentially slow down for your dialogue. The other thing about traveling really quickly and this is the special theory of TV is that length contracts so that actually if you observe an object going really quickly then its length in the direction of movement would seem as if it were shorter even so a cube would kind of look like a kind of a squash cube like that. So these were all very bizarre types of things but it was a consequence of the math. Okay, in special relativity. So, now how did he go from special relativity to gravity because special relativity only work and somebody mentioned Minkowski space basically flat four dimensional space where you have integrated time as a dimension is how do you go from special relativity to thinking about gravity involved there too because special relativity only works in a flat Minkowski space there. Okay, so in 1907 Einstein had kind of a thought experiment that said, okay, if I were in an elevator, he was good at thought experiments, in other words ones that may not have direct evidence associated with them but merely came out of his head. And he thought, well you know if you're in an elevator, and I was accelerating in an elevator, I wouldn't recognize any difference than just being in an elevator on the earth, provided their acceleration was the same as gravity. And that was quite a revelation. And then the other part was essentially that, hey, gravity doesn't move in straight lines. Now there was essentially if you go back to Newton and his mechanics it basically said, okay the only time it's not going to move in a straight line is when you put a force to it. But for gravity, it as Matt slash Berrigan mentioned is for orbits and other objects in free fall, it doesn't necessarily move in a straight line, almost never. Phil, let me interject here for a second on that point, because in the Wired Magazine video, she mentioned a really good illustration of this of how Einstein realized that space was curved, which is because when you throw an object, it travels in a curve. It's just as simple as that, that the object when you throw it, if you throw the apple, and it sort of travels in an arc, then, and it does not travel in a straight line. And it was that sort of simple thought that led him to think that, well, space time itself must be curved. I forgot to put my sound back on. Yeah, uncomfortable sound. Thank you. Okay, I was talking. So basically, yeah, in fact, only going in a straight line would be a special case that is between what like a Newton's apple falling on his head, which, you know, is kind of apocryphal is it would only be between a object and say gravity just going to the earth in other words a straight line. So if you throw the apple, it goes in a curve, which is pretty cool. Okay, like you're mentioning, okay, so the next thing he came up with was that, as you said, is that gravity seemed to work in a curve, which was very different than what Newtonian mechanics or Euclidean geometry suggested. So in 1912, he was working with a former professor of his named Marcel Grossman to describe gravity in curved space time, basically using Riemannian geometry, as opposed to, as mentioned before, flat four dimensional. So this kind of explained, in other words, the mathematical math, then explain how gravity seemed to move. So essentially what Einstein was trying to do was go from relative to mystic mechanics without gravity to trying to explain relativistic mechanics, including gravity. Okay, so then what he did was he and Grossman actually published an outline on the general theory. In fact, that's what it says, outline on that. That's the English version over there on the right, is in 1913, an outline of general relativity, basically just in two parts describing the physics part and then Grossman described the math part. Einstein only said that he wasn't that great in math, but he's far better than any math I've ever tried. And then in 1915, he then gave a series of lectures at the Pressure Academy of Science in Berlin to explain this theory. And so his first theory that was without gravity became the special theory of relativity, in other words, special under the case of gravity or in free fall. And then the general theory of relativity explained how all this worked in the presence of gravity. Oh, by the way, I almost forgot about is that he probably did not give enough credit to his wife. He'd met his first wife in school. And apparently, if you read by others and stuff they used to talk a lot about this, the theories that he then developed. And yeah, he played violin. And yeah, all of all the stuff there in chat, be sure to read chat because there's a lot of good interjections there. And then you had, and then in 1919. Okay, so he puts out this thing. But remember, when you're talking about in Berlin 1915, all that stuff like that. You're talking about basically during World War One. So this theory is not going to get out to everybody. However, in 1919. There were some English scientists under Sartre Eddington that basically used a total total solar eclipse to look at the position of a star that was near the sun and low and behold, it was in a location that suggested that the light was bent around the sun's gravity in the same amount that Einstein had predicted. And it became, whoa, this is good stuff. Because the public not only basically were captivated by the English scientists working with Germans, they're proving a German scientist, correct. Remember this after World War One, but also the strange theory of relativity where light could be strange stuff. Okay, so then after that real quick, and then we'll move on to even stranger stuff that Bill or Silsenji will talk about is that in 1921, Einstein was awarded the Nobel Prize, but it was not for theory of relativity. It was for, well, yeah, actually, also the money from the Nobel went to Malayva Marash, which was his first wife, to help her and the kids after the divorce. Okay, and he didn't attend the Nobel Prize thing because he's over in Japan, teaching and also, you know, it didn't mean as much at that time to him. But essentially he won the Nobel Prize, essentially for the photoelectric effect, which is one of the four papers in 1905, when he was 26, that included not only the basis of special theory of relativity, but also explained Brownian motion, which essentially verified that there were atoms. And then he created energy to mass like as in E equals MC2, even though he didn't use that equation. And then there were a lot of times after this that there were tests of his theory, one of which, more recent one in 2002, the Cassini spacecraft was on the other side of the sun. And so it goes, oh, this is a great time to look at it. And so essentially, it was able to confirm with 50% more accuracy than it had before that, you know, that lo and behold, yep, Einstein's theory does work. Okay, even down to quite a few decimal places. Okay, so let's then hear about some of the ramifications of Einstein's theory. Yeah, very good. Yeah, thanks Phil, fantastic. Yeah, before I introduce a syzygy. I just want to, I guess reinforce the notion that one of Einstein's sort of key contribution was the notion that gravity is the result of objects moving over the surface of curved space time, and that objects with mass distort the space time field the space time continuum to form a gravity well. And that so the this sense that gravity is an attractive force is probably better understood by thinking of it as objects moving along a curved surface. So I mean, just as an example, I mean, if you've ever been to a children's museum, they will have a little toy that usually in the in the four year or something of a gravity well where you can sort of roll a penny, and it circles around a spiral well, and that's supposed to sort of illustrate the sense of what a gravity well is. So, so the key thing I want people to take away from Einstein's vision of gravity is the sense of a curvature of space time. So that removes, in my mind that removes gravity from being a classical force, which is generated by the exchange of particles into sort of a topological phenomenon that is difficult to integrate into classical particle mechanics. And so with that little message. Let's hear what she has to say about what are the theoretical implications of Einstein's conception of gravity so Bill, take it away. Thanks Matt. Am I coming through clearly for everyone. I hope so. Yes, we hear you or I hear you. Okay, great. So it's a great pleasure to be here today and it's always a pleasure to speak with you folks. I thank Matt for inviting me to be on this panel. So, I'm going to be talking about the most complex levels of gravity. General relativity and quantum gravity and here we see pictures of the two luminaries of theoretical physics Albert Einstein and Stephen Hawking. The thing is, quantum gravity is an important part of the theory of everything, maybe even the biggest part of the theory of everything. So, I'm going to be talking about the theory of everything in about 20 minutes. I won't make it it'll have to be longer than 20 minutes and I'm sorry I have to avoid not read your comments or questions just yet because there's just too much to get through and at the end I'll try to address them but feel free to type in the in your chats. I have a much more appropriate title for this part of the of the discussion panel. Let's see I got to type stuff in here. Is a shamefully brief look at both general relativity and the theory of everything, and both are so brief that you can. You can barely see them. And I have to do this like I said within 20 minutes. So again, thanks Matt. Okay, take all the 25 minutes. Yeah, that's okay I look forward to the challenge I look forward to the challenge so let's let's see how this goes. Now I'm overlapping with some of the talks, the other two presentations, and I thank my co presenters for giving the introduction to what I'm going to be talking about and even some overlap. And I also thank Chantel for being the mastermind of this operation. So, I'll start off with some some calculus, and you know I really know how to captivate an audience this is a great way to start any kind of presentation with some calculus. So, we have a function f of x which represents a curve here I see two examples of curves. The first derivative is basically the slope at each point. It's the rate of change of f with respect to x. The second derivative is the rate of change of the slope. So it's basically the curvature. So remember that second derivative is curvature because that's relevant to what's coming next. Yeah, I keep forgetting this is not a regular presentation so I have to do this. Okay, so Phil already mentioned the equivalence principle. So you imagine that you're standing in this rocket with the rocket engines going accelerating at one G right here. You're accelerating upwards at one G so you feel like you're on the surface of the earth you're pressed down the force one G with your regular weight. This is mass but it's close enough. But if you're standing on the surface of the earth in that same rocket, you don't know you can't tell the difference between these two, which isn't quite true but it's close enough. And this is Einstein's genius. He said that they seem to be the same because they are the same and that's what genius is seeing something in as simplest possible terms and the implications of that. So I have to go through this quickly I'm afraid. But if you plot the distance traveled by this rocket as a function of time. So there is function of time you see this nice curve. And it is a curve it's second derivative of distance with respect to time is the acceleration, which is non zero. So there's actual there's curvature this is a space time diagram so to speak, and you see curvature as Matt mentioned earlier. So the curvature here since they're the same, there must be curvature here. And this curvature must be due to the mass of the earth because there's no obvious acceleration here. So what you want is that's what a relativity the general relativity is about is trying to find that relationship between mass and space time curvature, because you want to know how things move. For that you need, let's call what you need. You need the relationship between coordinates and distances. So we have a displacement vector here. And these are the, the coordinate displacements. So you can think of this is you know you're on the corner of Elm and maple and you're going to walk to corner of King and Queen Street. How far have you gone well you can use this formula here. If you know the Pythagorean theorem it's basically a generalization of the Pythagorean theorem three dimensions. This is the shortest distance between two points, a straight line in Euclidean space. In 4D space as mentioned before this is the Minkowski. This has been Kowski space, flat space time generalized to four dimensions. So you're still using the Pythagorean theorem, the minus sign here because space and time are not the same. And as I said a straight line is the shortest distance but that doesn't always apply because we were talking about, we were talking about a flat space time. What if you have a spherical surface? If you have a spherical surface then suddenly it's the great circle, which is the shortest distance depending on the projection you have. You can see which is the shortest distance and that shortest distance is important. This is a two dimensional surface. You can generalize this to four dimensions. I keep hitting the wrong button. Okay. Okay. So you can create a mathematically speaking spaces with coordinates may or may not have a defined distance. If it does have a defined distance, you need what's called a metric that relates coordinates, positional displacements to distances. So there you are in the corner of Maple and Elm. And you want to go to King and Queen. So you have to, what's the distance you're going to be traveling? So you look at the map scale. But then maybe the map scale is a bit complicated. Maybe north-south it's a little different from east-west. And maybe if you go northeast, there's a sort of a combination between those two. So you can imagine your map scale has different components. And that's what this metric is. It's your map scale. And it gives you, because when you go to from Maple and Elm to King and Queen, you want to go the shortest possible distance because you don't have much time, which is sort of my situation right now. But okay, everyone's being generous. Give me time. Okay, great. The shortest distance in general is called a geodesic and a general space. In Minkowski spacetime, the geodesic element given here, which I've written this equation before, I use the numerical coefficients explicitly here. These are the coefficients of that Minkowski metric, at least four of them are along the diagonal. And for the spacetime, it's a little different using what's called the Robertson-Walker metric. So like I said, you want that relationship between coordinates and distances. You need the exact form of the coefficients of the metric. As I said, the metric has a number of components in general. And the values of those coordinates and how they vary in spacetime depends on the choice of your coordinate system, but also on the geometry of spacetime itself. And that's what you're trying to get to. You're trying to get to that geometry of spacetime. Because once you have that, you can get the geodesics. And once you get the geodesics, they give the paths followed by mass energy and gravitational fields. So they're moving naturally on these paths of shortest distance. And Einstein had to learn a whole new math in order to do this differential geometry. So in order to get that, in order to determine what that geodesic is for a given spacetime, he developed his Einstein field equations, which I'll try to simplify as much as possible. Maybe not quite as much as in this drawing, but I'll simplify it a bit if I can. So here are the Einstein field equations. This actually represents like 10 different equations because these indices here vary depending on the dimension you're talking about. So what I suggest is these are beautiful equations. Let us all bask in the glory of the beauty of these equations for a moment. Okay, that's enough basking. Let's talk about what these components are. I found this figure on Facebook is in little places. So physicist group on Facebook, which I should have looked for before. Anyway, so what are all these different components of the equation or different parts of the equation? So here is the Ritchie curvature tensor and the scalar curvature. I'll talk about what those mean in a moment. But this is the metric that you're trying to find. You're trying to find this metric. This is the cosmological constant. And you can leave this out because we're not going to talk about cosmology today. There's just too much to talk about. And the stress energy tensor, stress energy momentum tensor. These are all the parts of the equation. So what is this equation telling you? Archibald Wheeler physicist in the 50s and 60s says it best. So on this time, we have the space time part of the equation, space time side of the equation. And we have the matter side of the equation. So space time tells matter how to move and matter tells space time how to curve. That's a great quote. OK, so when you write these out completely, as I said before, these are 10 coupled nonlinear second order partial differential equations. You can reduce them to six independent equations. What are differential equations? Now remember, I told you about first and second derivatives. Well, differential equations have on one side, you have the derivatives, first and second derivatives, or higher order derivatives sometimes, and the function itself equaling something else. So you have to try to solve that for the function that you're looking for, which is not straightforward. If it's linear, then it's easier. But if it's nonlinear, there is usually no simple way to solve the differential equations. They're differential equations, which are not that easy to solve always anyway, but nonlinear and it's a system of those equations. So it takes a while to find solutions. And you have to have a guess of what a possible solution looks like before you can determine the solution. OK, so these parts of the equation, what they mean, this is the Ricci curvature tensor, which I mentioned before, which is a reduced form of the Riemannian curvature tensor. Tagline mentioned that earlier in the chat. The Ricci tensor has 10 independent components. And this curvature scalar is a reduced form of the Ricci tensor. For those of you who know what that means, it's a trace of the matrix representing the tensor. They are calculated from the first and second derivatives of the metric with respect to spacetime coordinates. Remember, second derivative means curvature. So curvature is important here. So the curvature of that metric and the curvature means how it varies in space and time. You take the second derivative of that and you can see the curvature of that metric. It's not the actual curvature of spacetime itself because, as I said before, well, I'm about to say I think I haven't said it yet, but the metric actually depends on the coordinate system you're using as well as the curvature of spacetime itself. You want to get to the intrinsic curvature of spacetime because that's going to give you your geodesics. And I mentioned the stress energy of momentum tensor. Here are all its components. I don't have time to talk about all this, but you put your mass in here or your energy. And these represent momentum flux and momentum flows in your spacetime. This represents your momentum vector, momentum density. Don't really have time to talk about this in detail. So here are the equations again, Einstein field equations. You start with a stress energy momentum tensor. You have an idea of what your system of mass and energy looks like and how they're moving. And you put them into your stress energy tensor. Then you have to make a guess at your metric. And then once you make a guess at your metric, you have to create the curvature tensors and the curvature and curvature scaler. And then you try to solve for this metric. Or you try to make sure that they match up on both sides. And this is a major effort. This is a very reduced form of these equations. But there are actual solutions. And you're solving for the metric, as I said, because that'll give you your geodesics. And the first one was by Carl Schwarzschild. The Schwarzschild metric for spherically symmetric. Actually, he made a very simple assumption in calculating this metric. It's like one of the simplest assumptions you can make. And what he did was he assumed that the universe is empty. So the metric, the tensor, I should say, the stress energy momentum tensor, was zero everywhere except for at r equals zero in the coordinate system at the origin of the coordinate system. There's a point mass there. And there's no size to this mass, which doesn't really matter. Because you can still assume it's a spherically symmetric mass. And you have this interesting, you have these components of the metric here, these parenthetic quantities. This rs is a Schwarzschild radius, which is important significance. We're going to talk about that in a little while. But for r, this is a coordinate r. It's not the size of the mass. This tells you where the field is that you're trying to, or the curvature is that you're trying to measure. So when r is much larger than rs, then you can get an orbit, which is very much like a Newtonian orbit. Not perfect though. The orbit is no longer closed. And this correctly accounts for the procession of a parahelion of mercaries orbit. There was a part of that procession that they couldn't understand. And this fixes that problem. If you've ever had a spirograph kit when you're a kid, and I certainly did, you know what it's like to make ellipses with it. And sometimes the ellipses don't quite close, and you find that you're creating a new ellipse that's slightly rotated from the first one and so on. It's quite educational, playing with spirograph. And I'm not compensated by a company that makes spirograph. Okay, but now what happens when you have r that's close to this rs or less than this rs? What happens to these parenthetic quantities? Well, you can have the parenthetic quantities like if r is zero, for example. This thing becomes infinite. And this goes to zero. This part goes to zero because this is infinite. Dividing by infinity is zero, which is an oversimplified way of looking at things. But also if rs equals r, then you have this is zero. And this term blows up. So the point is there are two singularities here at the event horizon. What's called the event horizon and when it r equals zero. And if you have all the mass contained within this rs, then you have what's called a black hole, which of course I've found a nice picture of here. So it has its own accretion disk with a jet coming out of it. And if you have r less than rs, then this becomes negative. So suddenly time acts like distance and this distance coordinate acts like time because they change signs. So interesting things happen when you have, when matter is compressed into this radius. You have what's called an event horizon. And what happens is mass falls into this, that gets too close to this event horizon can't escape because it have to go near the speed of light to escape. Of course time slows down from the perspective of an outside observer. So from an outside observer, it never goes inside. And I wonder if there really is an inside. Supposedly someone who actually goes inside and observer wouldn't notice anything unless they were torn apart by the tidal forces. But for the moment, let's move on to other solutions of the Einstein field equation. Other metrics. The care metric is for rotating bodies. So you have a phenomenon known as frame dragging. So you have space time that's actually being dragged around. Now this one is particularly interesting. This is okay. So it's been dragged around here. So yeah, but the cubiary metric is particularly interesting. It's done differently because the metric was specified first and then you solve for the stress energy momentum tensor. And what he was creating here was basically a bubble in space time, a space time bubble that could move through the outer space time at more than the speed of light. And of course I had to put the USS Enterprise in the middle here just to make it complete. So this is talking about warp drive. Would it actually work because you need something called negative mass or maybe there are other ways of doing it. This could be invalidated by quantum effects. Maybe you'd have time travel. I wanted to spend a long time talking about the warp drive, but there just isn't enough time. So I have to talk about quantum gravity. Nevertheless, I can do some warp related jokes. Yeah. I mean, it's box right here. I mean, when the Romulans are around, you have to be very wary of free Wi-Fi. And then I do like driving the snow blizzards at night. Sometimes. That's on my mood. Other solutions. These are particularly interesting solutions here. This is the, this is a worm. There are wormhole solutions, different wormhole solutions. The idea is you have two black holes are connected through space time, a shortcut through space time. So it's supposed to be shorter than going all the way around here. So, but the problem is that these wormholes are not necessarily traversable. As I said, there are event horizons on both sides. So I mean, can you even get through the event horizon? You can't before the end of the universe. For the end of time. But there's one that could be stabilized by exotic matter. You can't get a mass and maybe other recent ways to do it. Quantum foam. The idea is the space time has all these virtual particles popping in and out of existence. And there could be wormholes that are joining them on this very tiny scale. And it could be an intrinsic part of space time. And color blue here because this is a foreshadowing of events to come. This should put you on the edge of your seats. I'm sure. Okay, now I'm going to talk about quantum gravity. And Matt and Phil and I were emailing each other to coordinate our talks. I expressed my reluctance to do quantum gravity because I'm not really an expert on quantum gravity. And while there are other problems. But Matt, well, he said despite your concerns that quantum gravity is too hypothetical, I think it is necessary to discuss because it illuminates the struggle of the last century to integrate gravity into the standard model. Well argued Matt. I can't refuse. Can't refute it. All right, damn it. I'll do it. It's a challenge. Bring it on. Okay, so quantum gravity. We'll talk about how that was applied to black holes. The idea is when you're near the surface of a black hole or the event horizon, or degenerate stars like neutron stars and maybe even white dwarfs. The conditions are so extreme that you might have to use quantum mechanics must be important. So Hawking applied, well, a version of quantum field theory to black holes and I'll talk about why it's difficult to use quantum field theory with gravity. And he found that they emit the radiation, which means that they actually evaporate over time. You have virtual particles forming just outside the event horizon and some virtual particles falling and some go out. This is a very weak radiation. But if they eventually evaporate, that's something called the information paradox. As I said before, you have all the materials sort of piled up on the event horizon, at least from outside observer's perspective. So when they evaporate, is the information in that surface, that area of black hole, is it lost when everything evaporates? Apparently it's not, but I think that's still a subject of some debate. So the classical black hole only increases in time. I like entropy, entropy increases with time and that's the measure of disorder of a system. It's also sort of like the information capacity of a system. So the entropy of a black hole is proportional to its area. This is an idea by Hawking and Beckenstein. Not its volume, which is really strange. And this came to physicists to Hooft and Suskind proposed a holographic principle that everything in the universe, you could compress it into a black hole and it'd be sitting on the surface of this event horizon like in two dimensions. And yet it's a three-dimensional universe that can be represented in two dimensions. So it's almost like a hologram. This has implications for doing calculations on quantum gravity because you can reduce dimensions or you can use different dimensions to see if that'll help you solve the problem of quantum gravity, which I haven't really gotten into what the problem is yet. So there are four fundamental forces that we know about and all of them have been very successfully characterized with quantum field theory. Can we do that with gravity too? Is it even possible? It seems unlikely that gravity would not be amenable to quantum field theory eventually. And Blaner Suskind is a theoretical physicist that stands for it, I believe, argues that gravity provides hints that it's quantum too and yeah, we're gonna talk about that soon. Gravity is more difficult to include in this QFT framework, quantum field theory. It's framed in a given space-time coordinate system, a background space-time coordinate system. And that's not what GR is about, it's about variable space-time. So QFT doesn't work in curved space-time, although I should point out that there is actually a QFT for curved space-time. And you can look at this picture, this article here that mentions it and actually does a treatment for it. It's been around for like 20, 30 years or something apparently. But it suffers the shortcomings of it needs a fixed space-time for the coordinate grid and what you really want for a proper quantum gravity theory is a wave function of possible space-times, not a QFT incur space-time but of space-time. Now everything we've discussed up to now has been theoretical and this is basically my objection to talking about quantum gravity or at least it was my objection. My objection was, I mean, you need some kind of experimental verification or all these beautiful ideas or nothing but fairy tales. These quantum gravitational effects occur at space scales of 10 to the minus 35 meters, pretty tiny. And to probe anything on that scale, you'd need energies from a particle accelerator. 15 orders of magnitude higher than the large Hadron collider can attain. And I can make a number of assumptions to say what kind of collider would we need? If we had a circular collider here, it would have to be about the size of the solar system with these particular assumptions I made. Although some have said the size of a galaxy or whatever. So we need a radically different approach. And here we see that foreshadowing again. The suspense is mounting. I know you can feel it. I sure can. So I have to talk a bit about quantum mechanics and its weirdness. There's so many examples of its weirdness but I only have time to examine one particular one. And this is quantum entanglement. It's the most relevant to what I'm going to be talking about. So you have a pair or group of particles that share a quantum state that does not exist for all of them. And one example of that is you have a laser beam shining through a crystal and that the photons can split into two photons that are entangled. And we're going to see what that means in a moment. It gives a specific example. We have to talk about what spin is. Particles act like they're spinning. Of course, if they're fundamental particles with zero size it doesn't make sense they'd have spin but it's some kind of intrinsic property of them. One of the quirks of quantum mechanics is that you can only measure one component of the angular momentum at one particular time. And whenever you measure it along a particular axis it's always spin up or spin down. It doesn't matter what the original spin was. That becomes the new spin after you measure it. Again, this is kind of weird. That's quantum mechanics. Okay, so entanglement. Let's say you have a couple of particles and theoretical physicists for some reason like to use Alice and Bob. So one particle's Alice, one's Bob. These are electrons that are entangled. This represents the initial state. There's some kind of superposition of up and down. You don't know which it is until you actually measure it. And when you do measure it you find, oh, this one's up. Bob is down. But sometimes you'll find Alice is down and Bob is up but they're always opposite to each other. So they start out close together but they move apart very great distances. And you can measure their spins simultaneously and one is always up and the other is always down despite the fact that you're doing this at a time that is shorter than the light travel time. So this happens instantaneously. You're communicating to each other that one is up and one is down. And this is something that Einstein calls spooky action at a distance. And Einstein and Podolski and Rosen wrote a paper saying, oh, there's some hidden information here that the particles have. And they start out in their distance apart before they fly apart from each other. But no, John Bell designed some experiments and did some experiments to prove that quantum mechanics is right. There is actually some kind of communication, very fast communication between these two. It seems to be instantaneous communication that no one understands. And now you can't use this for communication, at least not as far as we know because as soon as you measure, as soon as you measure the spin of either one, you destroy the entanglement. If one is up and one is down, then after that they're liberated from each other, no longer entangled. Now we get to quantum field theory. So obviously this is an extension of quantum mechanics, but it includes special relativity, classical field theory. It doesn't include GR because it's incompatible with curved space-time, which is not quite true. But as I said before, the one for curved space-time is incomplete. So the particles are considered to be, or the particles are excited states of the field. And the field can be thought of as virtual particles popping in and out of existence. For gravity, this would be the hypothetical graviton. This predicted the existence of antimatter gives us the standard model of particles, which Matt has mentioned earlier, which is given here in this diagram. Wikipedia is great. You get so much stuff that you can use, which I've given credit for. The problem is that with regular quantum field theory, gravity is non-renormalizable. And what that means is there are a bunch of infinities, which often have to do with the self-energy of the particles that cannot be removed unless you do something different. One approach is to use what's called string theory. So instead of point particles, you have these one-dimensional objects, strings that are open or closed, and they vibrate in multiple dimensions. The graviton appears very naturally here, which is great. It requires a large number of dimensions, sometimes 11 dimensions, or other numbers. This has implications. It predicts another bunch of particles called the supersymmetric particles. But the problem is it assumes a background space-time coordinate grid, and again, you want that coordinate grid to be flexible. It's not confirmed by the Large Hadron Collider Experiments. There are no mini black holes, no supersymmetric particles. And here's an example of a multi-dimensional manifold surface cross-section through it, a 2D cross-section through it. Then there's loop quantum gravity. This is interesting. Space and time are like little grains of sand almost, except they're in forms of loops. This is independent of the space-time background. The problem is it doesn't treat the other forces. Can you get a smooth space-time out of it? And are there enough dimensions in this theory? I think there's some question as to whether that's the case or not. So this is the putting everything into context. So we start with classical mechanics, Newtonian gravity. Classical mechanics led to special relativity, led to quantum mechanics. Newtonian gravity led to general relativity, along with special relativity. They both contributed to general relativity. Quantum mechanics led to quantum field theory. And there are other forces in here which aren't mentioned. You have nuclear forces, for example. There should be a line going from here to here, because this QFT in curved space-time does come from here. But you combine these two, perhaps they'll lead to a final theory of quantum gravity, which as I said is a problem for the reasons that I've given. And there is an interesting way around this. So this is called the ER equals EPR conjecture, put forward by Leonard Susskind and Juan Maldesena. The idea is that if you have a wormhole, it connects to black holes that they're entangled, like fundamental particles. So when you have pairs of virtual particles in the vacuum, they are naturally entangled, but they're connected by wormholes, and that would explain how the entanglement occurs, because you're having instantaneous communication between them. Which means wormholes are a fundamental part of space-time. So as you can see, the suspense is being resolved here. So I'm sure you're all relaxing now, feeling relieved. I know I am. So entangled particles are like black holes connected by a wormhole. So we can talk about a quantum computer. You have entangled qubits in a quantum computer, which there aren't any real quantum computers yet, or ones that work particularly well as I understand it. They're like proto-black holes, according to Susskind. So here is the final resolution here. Quantum computers can supposedly directly simulate black holes and provide insights into quantum gravity. So we don't need these powerful particle accelerators to do this. And yeah, I've represented a qubit here, classical bit 01. A qubit is more complicated than that, and there are a bunch of them that are entangled. This looked like an interesting article. I couldn't read it though, it was in Dutch. I mean, who reads Dutch? Sorry, Chantel, I couldn't resist. So maybe someday, maybe in 10 years, who knows, we'll have quantum computing laptops. They're filled with all these nano black holes, and we can actually do some serious work on quantum gravity, even in our own homes with our own quantum laptops. Who knows? So if you think you understood any of that, then you weren't paying attention. I'm not sure who said that. I'm pretty sure I didn't say that. And Alan Greenspan is great. He's got a number of great quotations. I know you think you understand what you thought I said, but I'm not sure you realize that what you heard is not what I meant. I'm sure that's very clear. So both of these apply to the presentation I've just given, and they apply to each other, actually. I kind of feel like a Rumsfeld quote would be suitable here. Like, we have known unknowns, we have known unknowns, and we have unknown unknowns. Yeah, that seems appropriate. So I have a bunch of recommended reading. What I'm going to do is I'm going to make this PDF file. I'm going to make a PDF file of this, and I'll make it available to everyone. Fantastic. There's a lot of things here, a number of pages of recommended reading and viewing. I did a lot of this myself, because of course I had to come up to speed, because I hate to admit I'm not really an expert on this stuff. But I did my best. You did fantastic for a non-expert, I'll say. Thanks. What I recommend is that you do at least some of this, because we're going to have a fireside chat, apparently, on Wednesday. Well, when you show up, there's going to be a quiz. So I mean, you really should study. Yeah, I shouldn't make it clear. I'm just joking. Nothing like that. I probably won't be able to address all of this. So hold on to your questions and thoughts for the fireside chat. But before we go, I just wanted to raise another theoretical question that I think would be a little bit fun to talk about before we close out. So in the video that inspired this format about gravity on five levels of complexity, the last most complex level discussed talked about the hawking radiation around black holes and the implication that because of this, the universe could slowly sort of evaporate off all of its information and sort of lose all of its information in any kind of coherent way and sort of leaving the universe sort of dead. And the professor mentioned that a couple of things about this. First, that one solution to this dilemma is the multiverse, the many worlds theory, which is that we don't really know whether an event horizon even really exists and or where the event horizon is. And so it may be possible that in one universe an event horizon might evaporate off, but in another universe it doesn't. So that was one sort of little straw of hope that the professor was offering to us that the hawking radiation may not be inevitable in every universe, I guess. And then the other idea was that the surface of a black hole is essentially two-dimensional. It's flat, but it contains all of the information of the three-dimensional universe that it has gathered and therefore the surface of a black hole could be used as a holographic projector to project its information into a 3D universe. And here you get into the idea of a holographic universe. And I'd kind of like to get the thoughts of both Phil and Bill about what they think of both of those. First of all, is the multiverse really that much comfort? And secondly, is this notion of two-dimensional information containing everything that can all the information of a 3D universe be represented on a 2D surface and therefore implying that the universe is holographic? So maybe just like maybe five minutes for each of you on that or just whatever you want to do, but just want to get your sort of quick takes on both of those. Well, one thing I can say is it's not certain that information is lost when the black hole evaporates. It might be encoded in the hawking radiation. As far as can we encode the entire universe into a 2D surface, we have holograms, for example. You shine a light through a holographic plate and form a three-dimensional object. So you can indeed encode three dimensions into two dimensions. So presumably you could do that with the entire universe. It would be one big black hole, though. And maybe the whole universe is a black hole. Yeah. I'm going to go straight to Bill on that. So fair enough, I'm not going to press that too hard. But one other thing that I find really intriguing, kind of a stoner thought. Bill mentioned this in one of our emails that black holes have very simple properties. They sort of have spin and momentum and things like that. Very, very simple properties, pretty much identical to the properties we used to describe fundamental particles. And it does make me wonder whether, I mean, maybe if the universe is just littered with black holes, maybe those black holes are the fundamental particles of a bigger universe. And we are just kind of living in the flotsam and gentsam sort of the interstitial space between fundamental particles, i.e. black holes, of a larger universe that engulfs us. So let's all fill our bongs and contemplate that while we bring this to a close. Yeah, I was trying to go through the comments here, see if I could find something I should mention or talk about. But I mean, during the fireside chat, I'm happy to answer whatever questions I can. Let's see. SR has some comments, but they're pretty technical. SR maybe hang on to those questions and we can address them with more time during the fireside chat. Oh, so Sire had to leave, so that's too bad. Yeah, that was too bad. Is an empty universe possible? Tagline asks, and I don't know if an empty universe is even possible that the point that Schwarzschild was doing, the point of his calculation was to do something simple. You want to start with the simplest possible solution. And having an empty universe with one point mass in it is very simple compared to other possibilities. So I want to address Brioni's question about why is gravity so weak? And my understanding, the way I like to think of that, gravity is weak because space-time is extremely stiff and it's very hard to bend. So it takes a lot of mass to bend space-time even a little bit. But it doesn't take very much bending of space-time to even form a solar system. But it does take the gigantic mass of the sun just to bend space-time a little bit so that planets begin to orbit it and the planets begin to coalesce from interstellar matter and so forth. But basically gravity is weak because space-time is very stiff. It's hard to bend. Yeah, that's one way of looking at it. There's another explanation which is string theory it provides, but it's not backed up by the Large Hadron Collider, which is unfortunate because it's actually kind of a beautiful idea is that we do live in like an 11-dimensional universe and only perceive four dimensions of space and time, but the other dimensions are compactified. Yeah, yeah, yeah. So the idea then is that gravity, unlike the other fundamental forces, actually can permeate those other dimensions. So it's diluted by those other dimensions, whereas the other forces are not. I like that explanation, but it may be just plain wrong. It's another case of a beautiful theory slain by an ugly fact. Right, and maybe just before we close, I do want to mention that one reason string theory gained traction so quickly and dramatically is because it is one of the few models of reality from which gravity simply falls out naturally from the equations. And so when mathematicians realize this, that by thinking about string theory, gravity appears to be simply a natural part of the universe. That is why string theory really caught on as a field of study, which is quite different from the way the standard model was essentially just compiled by observation. So for those of you who are curious about why string theory is a big deal, that's why. Because string theory predicts gravity, whereas the standard model does not. So that's the deal with that. Yeah, I mean that's a great thing about string theory is that you get the graviton falling out of it very naturally, but it doesn't seem to be correct. I did want to look a bit more at some of the comments here. One is, let's see, SR says, do not ignore polarity of matter. That's the idea that there will be positive mass except that there is no negative mass that we know of. It might actually exist. It might not. And we might be able to achieve things like warp drive or stable wormholes by other ways, by negative energy and the vacuum fluctuations. It's still possible. All right, very good. Well, I'm afraid, I mean, we're really running out of time here. So I know there are not a problem at all, but that's why we have the fireside chats. So I know we didn't get to everyone's questions. So I want to encourage everyone to join us on Wednesday for the fireside chat. But for now, I'm afraid we have to gavel this to a close. Thanks to my panelists, Phil and Bill, and their fantastic presentations. And I want to thank Sean Tall and the Science Circle for hosting this event. And I hope you all have a very good rest of your weekend. And we are hereby closed. And I'm going to turn off my microphone. Good night, everyone. Good night, everyone. Thanks. Thanks, everyone. Thanks for showing up.