1 00:00:02,310 --> 00:00:05,520 Okay. Well, thank you once again for that. 2 00:00:05,760 --> 00:00:14,969 I think everybody's coming in. So that's that's just going it's great pleasure to see you all here today from Sydney. 3 00:00:14,970 --> 00:00:18,420 Nice to see some old friends and also some faces as I don't really know. 4 00:00:18,930 --> 00:00:26,069 My own associations with theoretical physics go back to 1979, which is a scary long time ago of some of you. 5 00:00:26,070 --> 00:00:33,450 I guess it must be Hungary. And I think that's it's it's great. 6 00:00:33,450 --> 00:00:42,630 It's great to see you back. I know this is a new idea. And so we will look forward to hearing your views about how it works. 7 00:00:43,530 --> 00:00:50,429 One of the things that's changed about the American political season times is the slide is that these days it's called Rudolph Pile Centre. 8 00:00:50,430 --> 00:00:54,839 That that was done when I went to technology was still alive was one of Dick's 9 00:00:54,840 --> 00:01:02,370 determinations to get Rudy recognised in a very public way and eventually also, 10 00:01:02,370 --> 00:01:11,730 you know, many years of campaigning and arguing with you as the state's Department of Humanities to get a name shouted the name Paul on the dole. 11 00:01:12,210 --> 00:01:19,170 So the Rudolph passing through physics, but of course the Wilson era in physics, in the building, I mean, it's a set of people. 12 00:01:19,260 --> 00:01:24,149 That's not what happens, of course, and that's it, which many of us that we all know over the years. 13 00:01:24,150 --> 00:01:26,610 And it will always be a set of people rather than the building. 14 00:01:26,910 --> 00:01:34,590 And even if we succeeds in changing the building, you know, the people will be what matters, the people who are what makes the almost the sense of it. 15 00:01:35,490 --> 00:01:38,700 So I think it's great that we commemorate Rudy in this way. 16 00:01:38,710 --> 00:01:43,780 Rudy, of course, was really the person who was responsible for founding theoretical physics as a real entity. 17 00:01:43,780 --> 00:01:50,880 And also and, you know, I think he was certainly one of the greatest witnesses and never to win a Nobel Prize. 18 00:01:51,300 --> 00:01:58,100 So I think that, you know, at least in a small way, can keep his name alive over the years by naming a, 19 00:01:58,170 --> 00:02:02,080 you know, a vibrant utilisation of cosmology by science, all that. 20 00:02:02,170 --> 00:02:10,650 That's that's a fitting, although sufficient to use an instance of anyway, I won't hold up any longer. 21 00:02:11,640 --> 00:02:17,180 As I said, this is an experiment. We haven't done something like this. The goal in physics is that success will do it today. 22 00:02:17,640 --> 00:02:24,660 And of course, it's a lot of things, other things that you would liable for ideas that you have about what we might might do. 23 00:02:24,660 --> 00:02:29,129 Be sure interested in hearing more about theoretical physics today than please just do that. 24 00:02:29,130 --> 00:02:36,840 It's not, you know, either in either person or why you might want to be, but if you feel like it anyway, so, so welcome. 25 00:02:36,840 --> 00:02:43,230 And Margaret and James, this will be game of just let's see. 26 00:02:43,350 --> 00:02:47,280 Okay, etc. So yeah, 27 00:02:47,910 --> 00:02:59,580 my general idea is that we're doing what we want to do this morning is give some sense of how of the extent to which we understand material reality, 28 00:03:00,120 --> 00:03:04,139 the wall of material reality through the concept of field. 29 00:03:04,140 --> 00:03:08,000 And I'm going to start with I'm going to talk principally about classical fields 30 00:03:08,040 --> 00:03:15,929 and Joe will talk about optimisation of fields and maybe we'll talk about fields, 31 00:03:15,930 --> 00:03:23,340 you know, in a context where we know that they're merely an approximation to a more interesting underlying reality, which we suspect is the case. 32 00:03:23,790 --> 00:03:32,429 These are the full fields. And so those we don't claim to understand the true reality, but we understand it through this this idea of a field. 33 00:03:32,430 --> 00:03:37,079 And I'm going to start by just going over the historical background, 34 00:03:37,080 --> 00:03:41,430 how we arrived at the conception of the field, which is a totally nontrivial concept. 35 00:03:42,420 --> 00:03:51,299 And so they started with Newton. Newton and had this great insight that any two bodies attracted each other with. 36 00:03:51,300 --> 00:03:56,070 This force that goes like the product of the masses in inverse square of distances is big. 37 00:03:56,070 --> 00:04:03,210 Inside was that the moon falls towards the earth in exactly the same way as the apple is will still matter. 38 00:04:03,420 --> 00:04:06,569 Feltham Brown. He didn't offer an explanation for how this happened. 39 00:04:06,570 --> 00:04:09,660 This kind of mechanism is there's no speculation. 40 00:04:09,660 --> 00:04:14,760 It's just this is energy body. Each two bodies act at a distance on each other. 41 00:04:14,760 --> 00:04:24,149 In this way that that looks good on 60 or so years later with very clever experiments with charged objects, 42 00:04:24,150 --> 00:04:29,730 intuition wise convinces himself and everybody that that the there is a force, 43 00:04:29,970 --> 00:04:33,780 a similar force that acts between two electrically charged bodies that depends on the product 44 00:04:33,780 --> 00:04:38,280 of the masses and the inverse square of the distances and the repulsive in that case. 45 00:04:40,020 --> 00:04:47,700 But shortly afterwards, this simple formula, just as a matter of mathematical convenience, it's broken down into two formulae. 46 00:04:48,030 --> 00:04:59,900 First, you say that one of these two charges, it doesn't matter which say B Q generates an electric, quote unquote field at each point on. 47 00:05:00,600 --> 00:05:07,140 By this formula, the field is proportional to the charge and the other is like the inverse square of the distance. 48 00:05:07,410 --> 00:05:10,889 So you have a series of arrows like this pointing out from the charge. 49 00:05:10,890 --> 00:05:14,490 Q And that's the electric field, whatever that is. 50 00:05:14,490 --> 00:05:19,799 It's just a mathematical tool which enables you to calculate the force on level. 51 00:05:19,800 --> 00:05:25,710 Q The other charge, because the force is equal to the product of the charge and the field. 52 00:05:26,520 --> 00:05:36,660 So you you just have a field being a computational intermediary between the two points that you have in fact taken a huge, huge conceptual step. 53 00:05:36,950 --> 00:05:41,550 Of course, we do this in high school mechanics all the time. 54 00:05:41,560 --> 00:05:50,790 We say that the force on a on a body of mass live land is AMG, which is the gravitational field generated by our planet. 55 00:05:52,620 --> 00:05:58,020 Now, these fields, these electric and gravitational fields, are actually rather special. 56 00:05:58,560 --> 00:06:06,000 They have an important property that they can be obtained as the gradients of some simple straight scalar quantity. 57 00:06:06,000 --> 00:06:15,180 So if you define PHI to be psychosis in the depends on your unit system times charge of radius for the electric 58 00:06:15,180 --> 00:06:22,950 potential or you chuck the gravitational potential is some product of the mass of the big body over a radius. 59 00:06:23,370 --> 00:06:30,299 Then you can obtain these electric and gravitational fields as the radius of the these quantities over here. 60 00:06:30,300 --> 00:06:31,560 So what that means, of course, 61 00:06:31,560 --> 00:06:41,940 is that here here are the contours of constant potential and the field runs perpendicular to these cultures and its magnitude is goes inversely. 62 00:06:41,940 --> 00:06:47,010 Is this as these is the spacing of the contours depends on the steepness of the field. 63 00:06:48,480 --> 00:06:55,440 This is an important computational advance because you can obtain the three numbers the X, 64 00:06:55,440 --> 00:07:04,620 Y and Z components of this vector electric fields clearly affected at different directions in different places out of a single number, 65 00:07:04,800 --> 00:07:08,190 the potential electric light, static potential. 66 00:07:08,940 --> 00:07:14,010 But we're still talking about mathematical fictions with no claim to reality. 67 00:07:16,830 --> 00:07:23,730 The next important element in this paper, this line came from verses the beginning of the 19th century. 68 00:07:24,090 --> 00:07:30,180 So he demonstrated that if you have a wire carrying a currents, then a compass needle. 69 00:07:30,770 --> 00:07:35,610 If you put it in this plane of indigenous, the wire always points tangential to the black. 70 00:07:36,000 --> 00:07:41,700 And if you scatter iron filings on a piece of paper and give them a bit of a shake, they will align themselves. 71 00:07:41,700 --> 00:07:46,860 So you can see in your mind's eye you can see lines of force wrapping around the wire. 72 00:07:49,470 --> 00:07:53,880 So you have the idea that the currents in the wire is generating the magnetic fields. 73 00:07:56,100 --> 00:08:03,690 Again, the magnetic field is just a is just an imaginary fiction which enables you to understand 74 00:08:03,690 --> 00:08:09,930 why it is that the iron filings align the way they do or the Compass Needle aligns the way, 75 00:08:09,990 --> 00:08:14,640 way it does. I think the field really becomes concrete. 76 00:08:15,380 --> 00:08:20,400 It becomes more than a mathematical entity with like the Faraday and the myth in 77 00:08:20,400 --> 00:08:25,290 the early part of the first couple of of the 19th century type of laser people, 78 00:08:25,290 --> 00:08:30,299 he shows that his is most important, his most important discovery. 79 00:08:30,300 --> 00:08:38,040 And it was an evil, evil discovery because our civilisation depends completely on this piece of technology. 80 00:08:39,820 --> 00:08:48,100 But if you take the magnet and you move it towards the neutral player, you pause the galvanometer connected to the wall to kick. 81 00:08:49,300 --> 00:08:57,610 And the way he imagined this was that there was a magnetic field which came out of the North Pole, went into the South Pole of the magic. 82 00:08:57,610 --> 00:09:01,450 As a matter of fact, this is magic. 83 00:09:02,770 --> 00:09:12,300 And when this magnetic field cuts through that wire, it generates a swirling electric field, which which rushes around, 84 00:09:12,550 --> 00:09:20,530 swirls around the wire, pushing the electrons or the charges in the wire from the galvanometer so attached to his magnet. 85 00:09:20,800 --> 00:09:28,630 There is a palpable physical thing which which does something to the wire as it sweeps over the wire. 86 00:09:29,080 --> 00:09:34,950 And of course, this mathematically, we represent this by this beautiful, simple formula saying that the colour, 87 00:09:34,990 --> 00:09:42,130 the swirling, the electric fields is proportional to minus the rate of change of the magnetic field. 88 00:09:43,030 --> 00:09:50,380 So for this to make sense, the, the, the, at least the magnetic field has become real and its reality has, 89 00:09:50,500 --> 00:09:54,399 has generated a sort of conviction in the reality of the electric field, 90 00:09:54,400 --> 00:10:01,030 as well as a real physical thing, which is really sweeping those electrons around through that galvanometer. 91 00:10:03,190 --> 00:10:07,149 But reality became an absolute certainty with the work of Maxwell. 92 00:10:07,150 --> 00:10:17,950 Maxwell Miller in the 19th century complimented Faraday's discovery by pure thought, by pure deduction, not experiment this by pure deduction. 93 00:10:17,950 --> 00:10:27,110 This is a classic piece of theoretical physics. He concluded that a time changing electric field would generate a swirling magnetic field. 94 00:10:27,130 --> 00:10:32,080 So Faraday had said at the time that magnetic field would generate a swirling electric field. 95 00:10:33,430 --> 00:10:36,489 Maxwell deduced that the converse must be true at a time. 96 00:10:36,490 --> 00:10:39,700 Changing electric field generated a swirling magnetic field. 97 00:10:40,150 --> 00:10:49,630 And then it follows from this. This. If this was true, then mathematics showed that the electric and magnetic fields could generate each other. 98 00:10:49,960 --> 00:10:57,100 The electric field changing in time, the swirling electric field changing in time could generate a swirling magnetic field, 99 00:10:57,100 --> 00:11:00,159 changing it, trying to generate the swirling electric field and so on. 100 00:11:00,160 --> 00:11:07,090 Even for like a truly I mean, it's clearly too good to be true, you would say. 101 00:11:07,600 --> 00:11:14,490 But so these fields have detached themselves from charges. 102 00:11:14,500 --> 00:11:19,990 The electric field used to be made by charge, the magnetic field used to be made by current. 103 00:11:20,440 --> 00:11:26,500 But now the electric field is making the magnetic field. Magnetic field is making the electric field, and there are no charges present whatsoever. 104 00:11:27,040 --> 00:11:35,910 So these fields clearly absolutely real. And the mathematics showed the ripples of changing electric magnetic fields will propagate with a number. 105 00:11:35,920 --> 00:11:46,510 The speed that close to the speed of the measured speed of light and of of maximum use, that that was what life was. 106 00:11:47,830 --> 00:11:53,350 And therefore this everybody very quickly, that that's what light was. 107 00:11:53,530 --> 00:12:02,980 And therefore, everybody bought into this idea that an electric field chain time changing electric field would generate the swirling magnetic field. 108 00:12:04,540 --> 00:12:16,450 So the visualisation of what's happening here is if I have a charge at this point here, the electric field points towards his negative charge. 109 00:12:19,930 --> 00:12:24,340 The electric field points to where you've got the charge. 110 00:12:27,500 --> 00:12:40,690 If you move the charge, if you move the charge to a new location, the electric field has to stop pointing to that place. 111 00:12:41,380 --> 00:12:47,230 The revelation about your movement troubles out from here only at the speed of light, 112 00:12:47,860 --> 00:12:54,610 so especially far away from your new position in the charge, the electric field is still pointing to the old location. 113 00:12:55,690 --> 00:13:03,940 And the electric field in this is pointing in this near region pointing to the new location has to joins the electric field out here, 114 00:13:03,940 --> 00:13:07,390 pointing to the old location with a kink with a kind of ripple. 115 00:13:07,600 --> 00:13:10,179 And that ripple spreads out from there at the speed of light. 116 00:13:10,180 --> 00:13:17,499 And that's why and that's essentially what's happening when you launch an electromagnetic wave, it's actually kind of more complicated than that. 117 00:13:17,500 --> 00:13:23,770 That's the basic idea of why that propagation speed has to lead to radiation. 118 00:13:23,770 --> 00:13:28,659 If you shake the charge to and fro, you're going to be sending out ripples in the electric field, 119 00:13:28,660 --> 00:13:35,320 and that ripples in the magnetic fields through Maxwell and Faraday's principles. 120 00:13:35,800 --> 00:13:40,990 And that's the origin of radiation. So we discovered that the end. Discovered by this time that action isn't in the distance. 121 00:13:41,500 --> 00:13:46,330 It's that the charges generate feels in their immediate vicinity. 122 00:13:46,480 --> 00:13:51,940 And these these fields propagate at a finite rate outwards. 123 00:13:51,940 --> 00:13:59,170 So action is local. This charge affects the nearby space, which affects the device the further away space and so on. 124 00:13:59,530 --> 00:14:02,530 So space communicates with other space. 125 00:14:02,590 --> 00:14:06,490 It isn't actually the distance. It's a local effect. And it isn't instantaneous, like. 126 00:14:11,400 --> 00:14:15,030 So the next part of the story comes with Lorenz and Einstein. 127 00:14:15,540 --> 00:14:24,499 Lorenz. Henrik Lorenz. The Dutchman was studying Maxwell's equations, and he noted to Curiosity that these equations were unchanged. 128 00:14:24,500 --> 00:14:30,239 If you mean it couldn't have changed from position in time X and T to a new position and time, 129 00:14:30,240 --> 00:14:39,389 x primes and t primes could be related by this matrix here where beta is a number less than one in gamma rays obtained out of beta by this formula. 130 00:14:39,390 --> 00:14:43,080 A fifth very simple matrix, very simple to change. 131 00:14:43,380 --> 00:14:51,060 Why the equation unchanged by this change, but it's causing the change of Einstein provided the answer, 132 00:14:51,060 --> 00:14:56,219 Einstein explains, That's again physical interpretation. 133 00:14:56,220 --> 00:15:00,460 He said that this is the position in time, as used by one observer. 134 00:15:00,640 --> 00:15:04,830 This is the position of time, as used by an observer who is moving with respect to the first observer. 135 00:15:06,600 --> 00:15:13,350 So this was came as quite a shock to the community because if the crucial thing 136 00:15:13,360 --> 00:15:17,130 was that the new time of the movement wasn't equal to the old time coordinate 137 00:15:18,120 --> 00:15:23,159 and the time interval between two events of surprise person would not be the 138 00:15:23,160 --> 00:15:27,030 same as the time interval between the same two events to the other time person, 139 00:15:27,030 --> 00:15:34,230 untrained person. So there was destroyed Newtonian sense of absolute time. 140 00:15:35,340 --> 00:15:42,630 However, by the 1920s and it did take from 19 5 to 1924, the Nobel Prize Committee Committee, 141 00:15:42,960 --> 00:15:52,260 Swedish Academy was thinking what prize Einstein should get towards the around 1918 because he was clearly forgetting Nobel Prize. 142 00:15:52,770 --> 00:15:57,270 They didn't really feel it was appropriate to give him the prize for relativity 143 00:15:57,270 --> 00:16:01,890 because it was too speculative and unsupported by proper experimental evidence. 144 00:16:03,060 --> 00:16:17,730 So he took the kinetic theory instead. So and the so the the the interpretation, the physical interpretation of it was not easy to find. 145 00:16:19,320 --> 00:16:24,090 But we, we bought it. And the the significance of, 146 00:16:24,420 --> 00:16:36,860 of Maxwell's equations being invariant under this coordinate transformation is that the is that the physical significance is the 147 00:16:36,870 --> 00:16:45,929 way physics happens in the unframed oratory or the portrait is at rest with respect to the prizes above is exactly the same. 148 00:16:45,930 --> 00:16:49,169 Since the equations are the same, everything will unfold the same, 149 00:16:49,170 --> 00:16:54,000 and you will be able to tell by doing experiments with electromagnetism inside your refrigerator, 150 00:16:54,210 --> 00:17:00,210 whether you're moving with, whether you are moving in any sense. So all motion will be relative rather than absolute. 151 00:17:02,370 --> 00:17:13,799 So the the we ready by the by the acceptance of of special relativity in the 1920s 20th century 152 00:17:13,800 --> 00:17:21,420 physics in some sense also in a large part of what classical 20th century physics was was fixed. 153 00:17:23,100 --> 00:17:30,210 The the aether fall from being hadn't been abolished by by was absolutely established. 154 00:17:30,300 --> 00:17:36,270 So the ethos of space time this that the the space and time are some kind of a medium. 155 00:17:37,650 --> 00:17:42,299 And in the rest of the 20th century became apparent that you can understand the whole material. 156 00:17:42,300 --> 00:17:45,240 Well, there's nothing but expectations of this medium. 157 00:17:46,320 --> 00:17:52,290 The fundamental, crucial thing is the fundamental equations of physics must be invariance under Lorentz transformation. 158 00:17:53,490 --> 00:17:59,790 And we'll see this as this requirement restricts the dynamics of the aethers just as simple as is an energy by pure thought, 159 00:17:59,790 --> 00:18:05,489 pretty much to say what's going to happen. And a lot more to introduce you to the motion densities, 160 00:18:05,490 --> 00:18:18,629 which are the intellectual tool that we use to exploit this the to to show how the possible dynamics in space time is is restricted by this 161 00:18:18,630 --> 00:18:28,020 requirement that everything he Lorentz invariant of and the process of course go back to the branch who turns out to be as an Italian, 162 00:18:28,020 --> 00:18:33,360 worked most of his career in Saint Petersburg or Berlin, but because it was the 18th century French finance name. 163 00:18:35,700 --> 00:18:47,040 So the graph shows the mechanics of projectiles, bullet paths, which were the paths of action with least all the paths they could take. 164 00:18:47,040 --> 00:18:50,520 So the path is is X as a function of time. 165 00:18:51,240 --> 00:18:54,090 This time the projectile is at some particular position, 166 00:18:54,090 --> 00:19:02,400 X and the X is a T when you integrate them and there's some function of position and possibly the Lagrangian that goes in here, 167 00:19:02,640 --> 00:19:09,410 if you do this integral here, you get a number for each path and the path chosen is the path along which this integral is the. 168 00:19:10,430 --> 00:19:14,450 We now understand that the origin of this lies in quantum mechanics. 169 00:19:14,450 --> 00:19:17,960 But in the 18th century, they they told you that they would have feelings. 170 00:19:17,990 --> 00:19:25,460 This was something to do with live in the best of all possible worlds and the Almighty operates in the most economical way anyway. 171 00:19:25,580 --> 00:19:32,510 So the corrosion, this function of X and T is all of these simple systems, the difference between the connection, the potential energy. 172 00:19:32,510 --> 00:19:36,139 So the energy is the sum of these two things. And everybody is familiar with energy. 173 00:19:36,140 --> 00:19:44,540 Even politicians know about energy that, but they don't know this difference, which actually is what governs the dynamics of the universe. 174 00:19:45,230 --> 00:19:48,560 So given electricity, you can derive equations and motion from. 175 00:19:48,920 --> 00:19:53,150 It's just a mathematical exercise which goes back to Newton himself. 176 00:19:53,480 --> 00:19:57,139 But these equations go by the name of the law, the road equations. 177 00:19:57,140 --> 00:19:58,850 The first exercise of this sort was in fact. 178 00:19:59,510 --> 00:20:06,980 So it's just a mathematical exercise to observe this principle, to extract the ordinary equations of motion. 179 00:20:07,880 --> 00:20:13,700 So fields such as Phi here also evolve so as to minimise an action. 180 00:20:13,940 --> 00:20:18,499 And this actually is a more complicated thing. It's an issue both over space and time. 181 00:20:18,500 --> 00:20:25,010 It has to be over space because the field exists everywhere. It isn't the particles in some particular place that you consider. 182 00:20:25,010 --> 00:20:31,730 It's called in another place. The field is everywhere. If you're going to determine its dynamics, you have to consider expanding everywhere. 183 00:20:31,970 --> 00:20:34,940 So there is a certain function that the motion density, 184 00:20:35,480 --> 00:20:41,180 all of the field and its derivatives and derivatives with respect to space and time distance rule. 185 00:20:41,660 --> 00:20:50,830 So given a field configuration of the field in space and time, you can find these gradients into this function. 186 00:20:50,850 --> 00:20:54,110 Get a number. If you integrate those numbers that rule space and time, 187 00:20:54,110 --> 00:21:04,399 you get the action and the evolution of the field is but over time is one which extreme sizes which makes the smallest possible. 188 00:21:04,400 --> 00:21:11,320 Usually this the single and I'm going to do right this is approaching density it fills up out the field 189 00:21:11,360 --> 00:21:17,720 is great to the point is once you know what this is the growth of this function is a mere function. 190 00:21:18,080 --> 00:21:22,370 You threw them through just a mathematical cancelling. 191 00:21:22,520 --> 00:21:26,540 You have determined the complete dynamics. You specify the complete dynamics of the field. 192 00:21:26,540 --> 00:21:30,080 So everything in the physics is encapsulated in this function. 193 00:21:31,100 --> 00:21:35,659 So there are well-known equations to go from this principle to the field equations. 194 00:21:35,660 --> 00:21:40,310 Just get all the equations to go from this principle to the only Newtonian motion. 195 00:21:41,060 --> 00:21:48,180 So to see how this works, it's really the way equation here is the simplest possible way of equation, such as the pressure, 196 00:21:48,180 --> 00:21:58,760 etc. In this role of a communicate between us and this equation derives from this the proportion density. 197 00:21:59,000 --> 00:22:02,930 So this is the time derivative of the field, this is the space through in the field. 198 00:22:03,230 --> 00:22:07,100 This you can think all this causes kinetic energy. The same thing goes potential energy. 199 00:22:07,340 --> 00:22:17,930 So in this case, the simple way of making across you just broadly density works fine things to note, this is a linear equation. 200 00:22:18,750 --> 00:22:24,470 Therefore the linearity here derives from the fact that this is quadratic in the gradients. 201 00:22:24,800 --> 00:22:28,550 This quadratic it field it is gradients. In fact it only contains gradients. 202 00:22:28,550 --> 00:22:35,330 It doesn't contain the field. And that's because the equations of global differentiation with respect to these things. 203 00:22:35,330 --> 00:22:42,500 So you lose a power. So when you get here's how you lose power of the field and quadratic equations generate linear weight equations. 204 00:22:43,250 --> 00:22:48,530 And the other thing to notice is that this equation is unchanged by other in this transformation. 205 00:22:48,770 --> 00:22:51,950 That's normal, but you may well know that slightly. 206 00:22:52,250 --> 00:22:56,270 There's one finding the obvious, and this thing is also unchanged. 207 00:22:56,570 --> 00:23:03,320 So if you go from 60 x four, I'm trying these gradients here change, but the motion does not change. 208 00:23:04,490 --> 00:23:10,250 So there's two very important two very different parties, more complicated example, 209 00:23:11,030 --> 00:23:14,240 significantly more complicated example than is given by electromagnetism. 210 00:23:14,840 --> 00:23:21,590 Now we think of the field as the four components of the electromagnetic potential. 211 00:23:22,310 --> 00:23:26,330 So previously we were talking about the electric and magnetic fields. 212 00:23:27,680 --> 00:23:33,020 They indeed are called fields, but for a theoretical physicist that means the gradient of the field. 213 00:23:33,200 --> 00:23:39,640 The field is this job, is this object up here, and you extract this object up here, 214 00:23:39,650 --> 00:23:43,700 the magnetic field, by taking the curl of the three spatial components. 215 00:23:44,120 --> 00:23:51,019 And you would you get the electric field as a combination of, of the gradient of the time component, which is essentially, 216 00:23:51,020 --> 00:23:59,340 which is the electrostatic potential in the sign and the, the time derivative of the spatial components. 217 00:23:59,510 --> 00:24:09,020 So this one is encoding electric statics that is minus graphite and this one is encoding Faraday's swirling electric field associated with the. 218 00:24:09,140 --> 00:24:18,630 Time changing magnetic field because we take the curve of this that rocks away but the is minus the great curl a which is minus the gradient. 219 00:24:19,250 --> 00:24:26,469 Can take place here see. So okay, so we have the so this is the field up here. 220 00:24:26,470 --> 00:24:29,830 It's now a four component object, number one component object. 221 00:24:30,370 --> 00:24:39,700 And here if we just have the electromagnetic fields in empty space, if the every component of that is the wave equation, 222 00:24:40,600 --> 00:24:45,650 and that comes from an erosion density which consists of E squared minus B squared. 223 00:24:46,000 --> 00:24:52,710 Unfortunately, some committee in Paris decided that electric fields will be measured in different units of magnetic fields. 224 00:24:52,720 --> 00:24:54,850 You have to put a factor of C underneath there. 225 00:24:55,300 --> 00:25:01,870 But the electric and magnetic fields are two halves of one dominant, and they should consider we have the same units. 226 00:25:02,980 --> 00:25:07,240 So ELC is essentially the same speed of electricity. 227 00:25:07,750 --> 00:25:11,620 So this you can think of this kinetic energy, this will think of this potential energy. 228 00:25:12,010 --> 00:25:18,820 The justification doing this is kinetic energy is is built into ABC and this is the laboratory testing. 229 00:25:20,080 --> 00:25:23,500 Again, this is quadratic in field gradients. 230 00:25:23,650 --> 00:25:28,780 So we have and so this is really defined by something defined by some these gradients 231 00:25:28,780 --> 00:25:32,980 just as we have for the primary density correction gradients radius before. 232 00:25:33,730 --> 00:25:44,260 And again this is the notion this number change when you go to a prime to a to the frame of reference of a moving observer. 233 00:25:44,260 --> 00:25:54,610 It's provided it's provided the these things since this thing transforms according to this rule that the the time 234 00:25:54,610 --> 00:26:01,299 components and space components of the unframed person are related to the frames persons components by multiplication, 235 00:26:01,300 --> 00:26:03,840 by this by this Lorenz transformation matrix. 236 00:26:03,840 --> 00:26:11,090 So as this thing has to transform like a format, given that this thing doesn't change the numerical value, 237 00:26:11,120 --> 00:26:18,700 this stays the same as a given event, and that makes this equation valid in every format system. 238 00:26:20,930 --> 00:26:28,190 Let's give another example because of the of of how we feel very direct. 239 00:26:28,550 --> 00:26:33,650 Who is the third and great series of the series of British theoretical physicists? 240 00:26:34,280 --> 00:26:39,889 He was trying in the late twenties, he was trying to find the risk of generalisation of the Schrodinger equation. 241 00:26:39,890 --> 00:26:46,880 But what he actually discovered was a new aspect of the aether. A fork for component field came up in a field, 242 00:26:47,240 --> 00:26:52,670 except now each of these each of these numbers is a complex number, not a real number, but a complex number. 243 00:26:52,670 --> 00:26:56,960 So it's a complex full value, a complex full component field. 244 00:26:57,500 --> 00:27:01,700 And under rest transformation, this thing transforms in a new way. 245 00:27:01,880 --> 00:27:08,180 It doesn't transform the way not not previously known to physicists and previously those mathematicians. 246 00:27:08,570 --> 00:27:13,970 It transforms like a direct spin. We don't need to worry about what exactly this rule is. 247 00:27:14,300 --> 00:27:16,340 It's just that there is some matrix. 248 00:27:16,340 --> 00:27:25,399 And depending on the speed, the relationship between between your observers from one frame of reference to another frame of reference, 249 00:27:25,400 --> 00:27:33,450 so simple as that by betas, the ABC operates between the two things, so there is some matrix that you get. 250 00:27:33,470 --> 00:27:37,400 You must play for every change, for every hour observed. 251 00:27:37,400 --> 00:27:43,070 Is this a matrix of which you multiply all these four components together for comparison? 252 00:27:43,070 --> 00:27:52,670 The other thing and he pulls it, the track field is the electrons and protons excitations in this field, as Joe will talk about later. 253 00:27:53,630 --> 00:27:57,709 So so let's just have a look how this mathematically works out. 254 00:27:57,710 --> 00:28:04,100 This is a somewhat different this is a slightly different looking wave equation and this is slightly different in intensity. 255 00:28:04,730 --> 00:28:10,670 What's basically happening is we now have a first order differential equation or a second differential equation. 256 00:28:11,090 --> 00:28:16,310 We have the up side by the X is equal to sort of a multiple of upside. 257 00:28:17,240 --> 00:28:21,320 And if you just left, if the coefficients here were real, 258 00:28:21,680 --> 00:28:28,639 you would have a you wouldn't get you get exponential growth or exponential decline in the 259 00:28:28,640 --> 00:28:32,900 field's value would be the solution to the equation and you want to play this behaviour. 260 00:28:32,900 --> 00:28:38,660 So we have a square root of minus one over here which ensures that we have this first order equation. 261 00:28:38,660 --> 00:28:42,260 We need that little to get lady behaviour. What else is there to revolve? 262 00:28:42,500 --> 00:28:46,879 This is the other complication is that this is a this is a set of four numbers, 263 00:28:46,880 --> 00:28:52,610 this is a set of four numbers and here is a matrix which depends on which coordinate we're dealing with. 264 00:28:53,900 --> 00:29:01,520 And here are a couple of these matrices. Okay. So so this is a linear differential equation. 265 00:29:01,520 --> 00:29:09,160 Partial differential equation is at this time in first order. And this is the approach in density that generates it here is basically a sort of dot 266 00:29:09,180 --> 00:29:16,520 products that kind of the price of the vector on itself here is a dot product for of growth, 267 00:29:16,520 --> 00:29:26,090 a row vector matrix of a column vector. And now we have the Russian is traffic in the field and it's grey like that. 268 00:29:29,360 --> 00:29:33,559 I think that's over. And crucially, this stays the same. 269 00:29:33,560 --> 00:29:38,930 If you make a rental transformation with including the property transformation, the four numbers are going to reside. 270 00:29:40,160 --> 00:29:44,330 So what about the coupling between fields? 271 00:29:44,810 --> 00:29:47,980 If you want to generate electromagnetic waves, you need an antenna. 272 00:29:47,990 --> 00:29:53,629 In the antenna, you need to have you need to have some currents so that so the full equation, 273 00:29:53,630 --> 00:29:58,250 which we had a zero we had before because we'll be discussing event waves in space. 274 00:29:58,550 --> 00:30:04,790 If you have an antenna, you have to put this there's a term here which is some city constant times the 275 00:30:04,790 --> 00:30:08,270 current density this is the current density which is of course the vector. 276 00:30:08,510 --> 00:30:11,660 So that's the that's the wave equation, including the sources. 277 00:30:12,320 --> 00:30:18,020 If you have electrons and they are moving in an electric field, of course the motion is different. 278 00:30:19,010 --> 00:30:19,990 So sorry. 279 00:30:20,000 --> 00:30:27,470 So this is the degradation density, this is the noisier density generates this differential equation since the green dot as we discussed before. 280 00:30:27,740 --> 00:30:30,860 And here is the extra tone that generates this thing. 281 00:30:30,860 --> 00:30:39,499 Yeah, but electrons are going to be the source that this current is actually made by moving electrons in the way they look. 282 00:30:39,500 --> 00:30:44,989 The formula that deals with that is the charge on the electron ploughs side of slap sign, 283 00:30:44,990 --> 00:30:52,069 which is sort of the density is something that's the quantity density electrons we have at least have one of these delta matrices, 284 00:30:52,070 --> 00:30:55,340 drag matrices inside here to provide the Victorians. 285 00:30:55,340 --> 00:30:58,520 So the current density associated with the Dirac field is this. 286 00:30:59,360 --> 00:31:08,960 So what we want to do is replace that with this and replace that with this and 287 00:31:09,440 --> 00:31:13,580 write out what the so what is the technology density of the whole thing look like? 288 00:31:14,090 --> 00:31:17,370 Here is the laboratory density for the electromagnetic waves alone. 289 00:31:17,370 --> 00:31:23,660 That around here is the drawing. See for the for the electrons all on their own. 290 00:31:23,870 --> 00:31:27,979 And here is the coupling term. That's this term. 291 00:31:27,980 --> 00:31:42,860 Here is this system here. Here is the coupling term that joins the two together and expresses both how the electrons generate electromagnetic waves, 292 00:31:43,220 --> 00:31:53,540 but also this term explains how or forces the way that the electromagnetic field changes the dynamics of the charged particles, the electrons. 293 00:31:54,680 --> 00:31:58,490 So the coupling. So this is quadratic in the fields gradients. 294 00:31:58,880 --> 00:32:01,460 This is quadratic in the field and it's gradients. 295 00:32:01,730 --> 00:32:08,990 And this mixed term here is cubits has it has one representative in one field in two representatives of another field. 296 00:32:10,490 --> 00:32:16,160 So you can you can put so this this encodes a huge prodigious amount. 297 00:32:16,200 --> 00:32:18,680 Physics is that a very simple expression. 298 00:32:18,980 --> 00:32:27,290 And there isn't much choice in what expressions to write down here because the requirement for the rates in various the of these things remain 299 00:32:27,710 --> 00:32:36,770 unchanged when you make every one of these terms remains unchanged for each of the events transformation is is enormously prescriptive. 300 00:32:38,480 --> 00:32:41,570 So here's my here's my summary is space time. 301 00:32:41,960 --> 00:32:48,350 The aether vacuum in school by various things is a complex system and it carries several. 302 00:32:48,350 --> 00:32:56,750 We've only talked about too many component fields thinking that it carries a great many, many from the fields. 303 00:32:57,260 --> 00:33:02,719 We derive the way equations to describe this system from a single laboratory density. 304 00:33:02,720 --> 00:33:06,680 So I've only written down the beginning of electrons in density is given more fields. 305 00:33:06,980 --> 00:33:08,930 We will need more, more terms, 306 00:33:08,930 --> 00:33:17,360 but they'll be made in the same way by a block describing how the field works on its own and coupling terms explaining how it connects to the other 307 00:33:17,360 --> 00:33:26,240 fields present and the requirements are the rents and variance of the nitrogen density enormously strongly restricts the possible field equations, 308 00:33:26,540 --> 00:33:37,610 so make it possible to speculate very to to almost exhaustively consider all logically possible of this types of physics. 309 00:33:38,060 --> 00:33:41,209 And this notion density comprises a block for each mode. 310 00:33:41,210 --> 00:33:45,770 Yeah, for free dextrose, free particles plus company terms between the blocks. 311 00:33:46,370 --> 00:33:50,960 So that's all that I wanted to say. We're just.