ICACGA 2022:The Supergeometric Algebra as the Language of Physics

Transcript

foreign [Music] welcome to those of you who just joined us we're approaching the singularity so it's a bit late for you anyway the last the blue person sees of the purple person is at the boundary of this invisible region this gray region which Guardian shaped yes it's an exact mathematical cardioid and yes I have as usual calculated it correctly so you could believe what you see so the blue person and the purple person far from meeting each other at the singularity lose causal contact with each other already well away from the singularity the purple person watching the blue person sees the blue person no further than than this so when you fall to the singularity you do not meet other people who fail along different radial positions you lose causal contact with them now you might object to this argument say oh look I can tell that this spatial distance between the purple person and the blue person goes to zero I look at the metric and measure the spatial distance along an arc collecting those two people and that goes to zero well there's a problem with that which is there's no actual Observer who can make a measurement on a circular Arc close to the singularity the different parts of the of a circular Arc close to the circular to the singularity are causally disconnected from each other and no Observer can actually make any possible measurement the shortest causal distance between the blue person and the purple person is indicated by this red line you can imagine a pair of photons maybe Hawking photons which are created right here one sends off with maximum angular velocity in One Direction accent angular momentum in One Direction the other goes off with a maximum angular momentum in the opposite direction and they just hit the blue person and the purple person at at the singularity so the singular Singularity is not a point it is a Surface I can take you on a little trip around there we go let's have a trip around the singularity and you can see from a practical perspective it appears to act as a surface you may think spatially close is close no no it's not in general relativity it always gets my intuition it always always against my intuition causally close is what is close if you think about it if I can't affect something it doesn't matter if I'm spatially close to it if I can't affect it I'm far away from it causal separation is the important thing once you realize that you realize that there's a whole different way of thinking about quantum gravity inside black holes I think this is profound I'm going to move on remind those of you who know about black hole says I know her theorem which says that an isolated black hole rapidly evolves to a stated characterized by just three quantities Mass electric charge and spin I've been showing you a black hole with just mass and no Spin and no electric charge this is what a care black hole looks like this is what I call the waterfall model or river model of a care black hole it's like the short Shield waterfall but much more complicated here's space falling in at less than the speed of light outside the Horizon hits the speed of light and then goes faster than the speed of light inside the horizon The Horizon in this case is not a sphere it's not circular it's an exact ellipsoid it's a beautiful piece of mathematics discovered by Roy care in 1966 and you see that there's also an inner Horizon there's no inner Horizon to a short chill black hole but there is for a rotating black hole what happens there well as you fall deeper inside the black hole the centrifugal force gets relatively stronger and stronger and stronger and slows down the inflow of space back to the speed of light the inner Horizon is where the inflow space has slowed back to the inner to to the speed of light if that sounds mysterious how can the centrifugal force do that remember the Earth in its orbit around the sun that's very something very similar when the earth is far from the Sun the Earth on its elliptical orbit goes closer to the Sun and then as you get closer to the Sun the centrifugal force gets relatively stronger and sends the Earth back out again on its elliptical orbit same thing happens in a black hole the centrifugal force gets relatively stronger and slows down the inflow of space if you continue that inflow through the inner Horizon you go into what I call a wormhole space then turns around accelerates back up to the speed of light goes back through a white hole which is not the same as the black hole it's another piece of space-time separated in time I'm just showing the spatial Dimensions here and then exits into a new universe well that doesn't happen in physical reality you stop this and I'm going to exit from the black hole I just pressed a little button to go far away from it and I'm going to I'm going to add an electric charge now ideally I would show you a rotating black hole but I have not yet implemented rotating black holes in the black hole flight simulator and I really really really really really really really really really like to do so maybe in the near future in the meantime we're stuck with a ryzen Nordstrom black hole which is a spherical charge black hole which shares the property of having an inner Horizon you may have noticed that I've added a charge and that added an inner Horizon into the black hole so I'm now going to put myself that's go into one of these unstable circular orbits again slow it down oops and then I'm going to fall into the black hole by doing a retrofire on my Thruster as before and let's see what happens if you can see from the chart on the left hand side that we have come out of our unstable circular orbit because it's unstable we can either fall in or go off to Infinity but this time we fall in and for a while it looks very similar to the schwartshell case The Horizon appears to split into two again the blue thing whitest thing is the Event Horizon that we've fallen through and this red grid isn't a horizon at all it's actually the redshifting dimming surface of the star that collapsed long ago but this one has an inner Horizon and it starts to behave slightly differently from the schwartzell geometry I'm going to slow it down we're approaching the inner Horizon you notice that there's a brightening thing it appears that we're moving towards the black hole but this this is a special relativistic aberration sorry it's a aberration effect we're actually moving very rapidly towards the inner Horizon and then we're getting closely in Horizon boom yikes yeah let's back off again boom you go through the inner Horizon let me get rid of the grids because they kind of confuse things here we are just outside the inner Horizon of a road of a Charged black hole and there at the inner Horizon we see the outside Universe appear and infinitely blue shifted infinitely energetic flash of light this was first pointed out by Roger Penrose in 1968 he pointed out that when you go down to the inner Horizon he talked about a Charged black hole which is what you've seen five more minutes and he suggested that the inner Horizon would be destroyed by this concentration of energy and that destruction would then destroy the Wormhole and the white hole and connections to other universes and he was correct about that but he was unable to complete the mathematics necessary to understand how that works the piece of mathematics that confirmed that there is an exponentially growing instability at the inner Horizon was done by Verna Israel and his student Eric proshorn for his PhD thesis published in 1990. they called it Mass inflation so what happens in Mass inflation is that ingoing and outgoing streams that approach the inner Horizon become go faster and faster and faster if they hit the inner Horizon they hit infinite blue shifter or infinite gamma gamma Factor and if you take into account the back reaction of this proper energy momentum of secreting screams you you find out that it simply exacerbates this instability so inevitably there's an exponentially growing instability this kind of Charmed to me when I first came across this in 2008 and one of my First Reactions was wow you get them you can bang things together make just to make this realistic the way it works in a rotating black hole is you can throw in a a rock Pro grade this green thing is on a pro-grade orbit they have extra centrifugal force because I'm throwing them with the spinner the black hole and even though they're in going at the outer Horizon because of the centrifugal force they turn around and become outgoing at the inner Horizon meanwhile if you later throw on throw a rock in retrograde when it falls through the Horizon it's in going but it remains in-going because it has Set uh less centrifugal force and that results as these in-going and outgoing rocks collide with each other the closer they get to the inner Horizon the the larger the gamma Factor so the net result is in of the order of a few hundred black hole crossing times which is not very long the energy with two rocks which you throw in can easily reach Big Bang density of 10 to the 80 times the density of water that requires a gamma factor of 10 to the 40. you square that to get identity and I wrote an article back in back then to the Gravity Research Foundation pointing this out and it got no honorable mention but I did post it on the archive and I I posed this question if if our universe makes baby universes you know what those baby universes have to look like because the mothers make babies that look like themselves so it has to come out at Big Bang energies at these kind of gut scale energies where in the world where in the universe are these kind of energies being generated the answer is at the inner Horizon of a black hole in particular of supermassive black holes so I posed this question this the string theorists have advocated to us that there are 10 or 11 space-time Dimensions not just the four that we see and there are six or seven hidden Dimensions curled up into a complex manifold and Lenny saskin has suggested that this encodes the DNA of the universe the laws of physics are encoded in the DNA of the universe and if that idea is right it's not my idea but if it's it's right Suppose there exists multiple laws of physics that allow a universe to reproduce reproducing universes would fill the Multiverse with their progeny and finding oneself in a reproducing universe would be common so it wouldn't be unusual to find ourselves in a universe like ours which I think is incredibly fine-tuned one of the features of life is it's fine-tuned if our universe is re is reproducing all the fine-tuning that the physicists worry about it's because we have evolved it's very plain that if this is true then the things that are doing the reproducing the mothers are supermassive black holes this instability is produced by accretion in going and outgoing streams bang two rocks together makes a very effective Bang and the things which are doing are the most decreasing are supermassive black holes my colleagues astrophysical colleagues are challenged to make supermassive black holes as early as we find them in the universe in the first billion years of the universe they're all there are already billion solar mass black holes why is that well it flows of physics are tuned to make effective reproducing universes it's not surprising I'm going to leave with a movie that I believe I did for a Nova documentary over 10 years ago this is a this is the black hole flight simulator you with a supercomputer simulation by John Hawley which at the time was the state of the art showing a disc and jet and we're going to fall through the Horizon in due course and down to the inner Horizon where we will be burned up by this inflationary instability I will stop there and take questions thank you uh Anthony Lazenby here so um if you've got a big bang that forms inside the inner Horizon of a rotating black hole it doesn't sound a very promising place to begin a Universe um what then happens over time to make it possible to see that as a reproducing universe thank you very much Anthony it's not easy at all to make a baby Universe there's all kinds of things that prevent it from happening where you bang things together you produce not only a high density thing which might well produce a gut vacuum but you also produce a lot of particles and a lot of radiation and entropy and that is gravitationally attractive so getting a big bang a big bounce which is what some parts of the community talk about is actually extremely difficult but if you think about it for a moment when you get two rocks which bang together you have a huge volume you have a very large number of gut scale volumes and all that you require is that one of them managed to turn around and make itself in into a baby Universe now maybe part of your question is what happens to this baby you've got to get a bounce and it has to start creating its own space time it has to it's it's not gonna swallow up the the space time that it it it's come from it's got to blow its own space-time we know that because that's what our universe has been doing it has been creating its own space time the question of is that possible is a mathematical and physics question and yes I think it's a very interesting one that I'm working hard on yeah well that was my question so the further evolution of this uh something that is being created at this high energy then it's got to go forward in time and end up looking like some sort of useful Universe yes and it's doing all that somehow inside the inner Horizon of a supermassive black hole that all sounds surprising that that can work well you may be surprised but nature can outwit you whatever you do what you have is a situation where you've you you can get high density there's there's no question of that but what you have to do if you want to make that into a baby universe but dominated by vacuum energy which would seed and an inflationary phase you've basically got to shed the entropy and the entropy needs to fall into other things there's black little mini black holes all over the place and it's going to be a complicated thing but all you want is for one little baby to win the lottery remember how trees and fish reproduce they produce enormous number of seeds this is what happens when you bang two rocks together all that needs to happen is one or two succeed okay so but sorry too um keep going but you do need then to calculate what happens to this space-time yes over time and that is a calculable thing which would establish if you could end up with an environment which is large-scale enough to function as a universe but that calculation has not been done yet that calculation has not been done yeah okay what's one question for me chat yeah one question from your chat where they ask how is it related to space-time algebra and geometric algebra how does the black hole flight simulator use the geometric algebra I'm Christopher it uses the geometric algebra to do all of the lorentz transformations and it does it does it over the whole screen each frame so uh there are tens of thousands there's a lot of rent Transformations and all of those done are done using the geometric algebra in parallel and when I follow g86 of course I I use the geometric algebra to change my frame of reference accordingly using the geometric algebra thanks that's really interesting um can you just say a little bit about the the red lines you've made some Choice there for how your sort of visualizing The Horizon in terms of the the remnants of the collapsed star and you you've put those kind of red um that red pattern over it how are you forming that that pattern it's just uh lines of latitude and longitude on the oops so we you actually do see the the pollen antipole kind of wrap around yes you do okay okay let's just just see what what Chris is talking about let's go yes because light bends around a black hole you can see that's that's the North Pole yeah and the South Pole okay and you wouldn't be able to do that if you were in the Newtonian thing looking at the Earth either that or your eyes are too far apart but yes you do see that with a black hole I can ask a question about that you you're talking about the The Singularity being a surface yes you get a cardioid shape but that surface is different for different observers if you do your blue ones or a particular cardioid but that purple Observer would see a different cardioid well they would find themselves on the on the same point on this singular surface so it does look like it has the Drone it has the topology of a sphere so your land again don't think of it as a point it's a spherical thing it has the appearance of a spherical thing and classically the boundary of this four-dimensional Short Hills space time is a three-dimensional space it's a three-dimensional space-like surface because the dimension that comes to an end classically is the time dimension however if you believe in quantum gravity and quantum mechanics Evolution con mechanically must be unitary and that must link the states of the singular surface at one time to those at another time so really it is from a quantum mechanical point of view a two-dimensional surface thanks any more questions from here any more from the chat yes questions does it use gosh Theory gravity whose theory no I'm not using a game I'm just using plain old general relativity here I am not sure what part of gauge gravity that you're you're thinking about uh general relativity is a gauge Theory based on two two symmetries the Lorenz group and the translation group but I'm using plain general relativity here if baby universes are made I have to say it must involve some change in the DNA of the universe and if the string theories are right that means visiting 10 or 11 dimensions and there's some challenging physics that is associated with that and there you definitely have to worry about other forces gauge forces and all that kind of thing but it gets real yeah there's complexities okay so I think uh the last question so far so thank you for always very existential application of geometric algebra [Applause]