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Okay. Well, thank you once again for that.
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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.
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Nice to see some old friends and also some faces as I don't really know.
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My own associations with theoretical physics go back to 1979, which is a scary long time ago of some of you.
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I guess it must be Hungary. And I think that's it's it's great.
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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.
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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.
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That that was done when I went to technology was still alive was one of Dick's
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determinations to get Rudy recognised in a very public way and eventually also,
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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.
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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.
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That's not what happens, of course, and that's it, which many of us that we all know over the years.
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And it will always be a set of people rather than the building.
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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.
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So I think it's great that we commemorate Rudy in this way.
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Rudy, of course, was really the person who was responsible for founding theoretical physics as a real entity.
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And also and, you know, I think he was certainly one of the greatest witnesses and never to win a Nobel Prize.
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So I think that, you know, at least in a small way, can keep his name alive over the years by naming a,
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you know, a vibrant utilisation of cosmology by science, all that.
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That's that's a fitting, although sufficient to use an instance of anyway, I won't hold up any longer.
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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.
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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.
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Be sure interested in hearing more about theoretical physics today than please just do that.
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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.
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And Margaret and James, this will be game of just let's see.
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Okay, etc. So yeah,
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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,
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the wall of material reality through the concept of field.
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And I'm going to start with I'm going to talk principally about classical fields
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and Joe will talk about optimisation of fields and maybe we'll talk about fields,
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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.
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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.
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And I'm going to start by just going over the historical background,
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how we arrived at the conception of the field, which is a totally nontrivial concept.
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And so they started with Newton. Newton and had this great insight that any two bodies attracted each other with.
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This force that goes like the product of the masses in inverse square of distances is big.
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Inside was that the moon falls towards the earth in exactly the same way as the apple is will still matter.
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Feltham Brown. He didn't offer an explanation for how this happened.
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This kind of mechanism is there's no speculation.
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It's just this is energy body. Each two bodies act at a distance on each other.
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In this way that that looks good on 60 or so years later with very clever experiments with charged objects,
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intuition wise convinces himself and everybody that that the there is a force,
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a similar force that acts between two electrically charged bodies that depends on the product
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of the masses and the inverse square of the distances and the repulsive in that case.
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But shortly afterwards, this simple formula, just as a matter of mathematical convenience, it's broken down into two formulae.
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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.
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By this formula, the field is proportional to the charge and the other is like the inverse square of the distance.
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So you have a series of arrows like this pointing out from the charge.
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Q And that's the electric field, whatever that is.
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It's just a mathematical tool which enables you to calculate the force on level.
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Q The other charge, because the force is equal to the product of the charge and the field.
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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.
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Of course, we do this in high school mechanics all the time.
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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.
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Now, these fields, these electric and gravitational fields, are actually rather special.
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They have an important property that they can be obtained as the gradients of some simple straight scalar quantity.
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So if you define PHI to be psychosis in the depends on your unit system times charge of radius for the electric
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potential or you chuck the gravitational potential is some product of the mass of the big body over a radius.
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Then you can obtain these electric and gravitational fields as the radius of the these quantities over here.
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So what that means, of course,
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is that here here are the contours of constant potential and the field runs perpendicular to these cultures and its magnitude is goes inversely.
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Is this as these is the spacing of the contours depends on the steepness of the field.
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This is an important computational advance because you can obtain the three numbers the X,
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Y and Z components of this vector electric fields clearly affected at different directions in different places out of a single number,
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the potential electric light, static potential.
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But we're still talking about mathematical fictions with no claim to reality.
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The next important element in this paper, this line came from verses the beginning of the 19th century.
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So he demonstrated that if you have a wire carrying a currents, then a compass needle.
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If you put it in this plane of indigenous, the wire always points tangential to the black.
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And if you scatter iron filings on a piece of paper and give them a bit of a shake, they will align themselves.
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So you can see in your mind's eye you can see lines of force wrapping around the wire.
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So you have the idea that the currents in the wire is generating the magnetic fields.
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Again, the magnetic field is just a is just an imaginary fiction which enables you to understand
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why it is that the iron filings align the way they do or the Compass Needle aligns the way,
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way it does. I think the field really becomes concrete.
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It becomes more than a mathematical entity with like the Faraday and the myth in
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the early part of the first couple of of the 19th century type of laser people,
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he shows that his is most important, his most important discovery.
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And it was an evil, evil discovery because our civilisation depends completely on this piece of technology.
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But if you take the magnet and you move it towards the neutral player, you pause the galvanometer connected to the wall to kick.
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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.
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As a matter of fact, this is magic.
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And when this magnetic field cuts through that wire, it generates a swirling electric field, which which rushes around,
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swirls around the wire, pushing the electrons or the charges in the wire from the galvanometer so attached to his magnet.
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There is a palpable physical thing which which does something to the wire as it sweeps over the wire.
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And of course, this mathematically, we represent this by this beautiful, simple formula saying that the colour,
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the swirling, the electric fields is proportional to minus the rate of change of the magnetic field.
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So for this to make sense, the, the, the, at least the magnetic field has become real and its reality has,
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has generated a sort of conviction in the reality of the electric field,
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as well as a real physical thing, which is really sweeping those electrons around through that galvanometer.
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But reality became an absolute certainty with the work of Maxwell.
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Maxwell Miller in the 19th century complimented Faraday's discovery by pure thought, by pure deduction, not experiment this by pure deduction.
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This is a classic piece of theoretical physics. He concluded that a time changing electric field would generate a swirling magnetic field.
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So Faraday had said at the time that magnetic field would generate a swirling electric field.
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Maxwell deduced that the converse must be true at a time.
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Changing electric field generated a swirling magnetic field.
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And then it follows from this. This. If this was true, then mathematics showed that the electric and magnetic fields could generate each other.
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The electric field changing in time, the swirling electric field changing in time could generate a swirling magnetic field,
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changing it, trying to generate the swirling electric field and so on.
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Even for like a truly I mean, it's clearly too good to be true, you would say.
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But so these fields have detached themselves from charges.
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The electric field used to be made by charge, the magnetic field used to be made by current.
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But now the electric field is making the magnetic field. Magnetic field is making the electric field, and there are no charges present whatsoever.
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So these fields clearly absolutely real. And the mathematics showed the ripples of changing electric magnetic fields will propagate with a number.
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The speed that close to the speed of the measured speed of light and of of maximum use, that that was what life was.
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And therefore this everybody very quickly, that that's what light was.
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And therefore, everybody bought into this idea that an electric field chain time changing electric field would generate the swirling magnetic field.
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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.
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The electric field points to where you've got the charge.
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If you move the charge, if you move the charge to a new location, the electric field has to stop pointing to that place.
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The revelation about your movement troubles out from here only at the speed of light,
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so especially far away from your new position in the charge, the electric field is still pointing to the old location.
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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,
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pointing to the old location with a kink with a kind of ripple.
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And that ripple spreads out from there at the speed of light.
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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.
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That's the basic idea of why that propagation speed has to lead to radiation.
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If you shake the charge to and fro, you're going to be sending out ripples in the electric field,
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and that ripples in the magnetic fields through Maxwell and Faraday's principles.
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And that's the origin of radiation. So we discovered that the end. Discovered by this time that action isn't in the distance.
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It's that the charges generate feels in their immediate vicinity.
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And these these fields propagate at a finite rate outwards.
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So action is local. This charge affects the nearby space, which affects the device the further away space and so on.
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So space communicates with other space.
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It isn't actually the distance. It's a local effect. And it isn't instantaneous, like.
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So the next part of the story comes with Lorenz and Einstein.
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Lorenz. Henrik Lorenz. The Dutchman was studying Maxwell's equations, and he noted to Curiosity that these equations were unchanged.
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If you mean it couldn't have changed from position in time X and T to a new position and time,
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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.
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A fifth very simple matrix, very simple to change.
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Why the equation unchanged by this change, but it's causing the change of Einstein provided the answer,
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Einstein explains, That's again physical interpretation.
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He said that this is the position in time, as used by one observer.
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This is the position of time, as used by an observer who is moving with respect to the first observer.
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So this was came as quite a shock to the community because if the crucial thing
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was that the new time of the movement wasn't equal to the old time coordinate
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and the time interval between two events of surprise person would not be the
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same as the time interval between the same two events to the other time person,
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untrained person. So there was destroyed Newtonian sense of absolute time.
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However, by the 1920s and it did take from 19 5 to 1924, the Nobel Prize Committee Committee,
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Swedish Academy was thinking what prize Einstein should get towards the around 1918 because he was clearly forgetting Nobel Prize.
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They didn't really feel it was appropriate to give him the prize for relativity
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because it was too speculative and unsupported by proper experimental evidence.
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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.
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But we, we bought it. And the the significance of,
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of Maxwell's equations being invariant under this coordinate transformation is that the is that the physical significance is the
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way physics happens in the unframed oratory or the portrait is at rest with respect to the prizes above is exactly the same.
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Since the equations are the same, everything will unfold the same,
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and you will be able to tell by doing experiments with electromagnetism inside your refrigerator,
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whether you're moving with, whether you are moving in any sense. So all motion will be relative rather than absolute.
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So the the we ready by the by the acceptance of of special relativity in the 1920s 20th century
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physics in some sense also in a large part of what classical 20th century physics was was fixed.
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The the aether fall from being hadn't been abolished by by was absolutely established.
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So the ethos of space time this that the the space and time are some kind of a medium.
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And in the rest of the 20th century became apparent that you can understand the whole material.
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Well, there's nothing but expectations of this medium.
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The fundamental, crucial thing is the fundamental equations of physics must be invariance under Lorentz transformation.
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And we'll see this as this requirement restricts the dynamics of the aethers just as simple as is an energy by pure thought,
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pretty much to say what's going to happen. And a lot more to introduce you to the motion densities,
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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
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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,
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worked most of his career in Saint Petersburg or Berlin, but because it was the 18th century French finance name.
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So the graph shows the mechanics of projectiles, bullet paths, which were the paths of action with least all the paths they could take.
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So the path is is X as a function of time.
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This time the projectile is at some particular position,
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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,
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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.
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We now understand that the origin of this lies in quantum mechanics.
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But in the 18th century, they they told you that they would have feelings.
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This was something to do with live in the best of all possible worlds and the Almighty operates in the most economical way anyway.
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So the corrosion, this function of X and T is all of these simple systems, the difference between the connection, the potential energy.
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So the energy is the sum of these two things. And everybody is familiar with energy.
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Even politicians know about energy that, but they don't know this difference, which actually is what governs the dynamics of the universe.
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So given electricity, you can derive equations and motion from.
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It's just a mathematical exercise which goes back to Newton himself.
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But these equations go by the name of the law, the road equations.
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The first exercise of this sort was in fact.
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So it's just a mathematical exercise to observe this principle, to extract the ordinary equations of motion.
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So fields such as Phi here also evolve so as to minimise an action.
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And this actually is a more complicated thing. It's an issue both over space and time.
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It has to be over space because the field exists everywhere. It isn't the particles in some particular place that you consider.
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It's called in another place. The field is everywhere. If you're going to determine its dynamics, you have to consider expanding everywhere.
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So there is a certain function that the motion density,
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all of the field and its derivatives and derivatives with respect to space and time distance rule.
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So given a field configuration of the field in space and time, you can find these gradients into this function.
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Get a number. If you integrate those numbers that rule space and time,
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you get the action and the evolution of the field is but over time is one which extreme sizes which makes the smallest possible.
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Usually this the single and I'm going to do right this is approaching density it fills up out the field
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is great to the point is once you know what this is the growth of this function is a mere function.
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You threw them through just a mathematical cancelling.
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You have determined the complete dynamics. You specify the complete dynamics of the field.
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So everything in the physics is encapsulated in this function.
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So there are well-known equations to go from this principle to the field equations.
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Just get all the equations to go from this principle to the only Newtonian motion.
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So to see how this works, it's really the way equation here is the simplest possible way of equation, such as the pressure,
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etc. In this role of a communicate between us and this equation derives from this the proportion density.
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So this is the time derivative of the field, this is the space through in the field.
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This you can think all this causes kinetic energy. The same thing goes potential energy.
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So in this case, the simple way of making across you just broadly density works fine things to note, this is a linear equation.
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Therefore the linearity here derives from the fact that this is quadratic in the gradients.
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This quadratic it field it is gradients. In fact it only contains gradients.
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It doesn't contain the field. And that's because the equations of global differentiation with respect to these things.
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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.
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And the other thing to notice is that this equation is unchanged by other in this transformation.
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That's normal, but you may well know that slightly.
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There's one finding the obvious, and this thing is also unchanged.
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So if you go from 60 x four, I'm trying these gradients here change, but the motion does not change.
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So there's two very important two very different parties, more complicated example,
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significantly more complicated example than is given by electromagnetism.
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Now we think of the field as the four components of the electromagnetic potential.
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So previously we were talking about the electric and magnetic fields.
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They indeed are called fields, but for a theoretical physicist that means the gradient of the field.
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The field is this job, is this object up here, and you extract this object up here,
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the magnetic field, by taking the curl of the three spatial components.
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And you would you get the electric field as a combination of, of the gradient of the time component, which is essentially,
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which is the electrostatic potential in the sign and the, the time derivative of the spatial components.
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So this one is encoding electric statics that is minus graphite and this one is encoding Faraday's swirling electric field associated with the.
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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.
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Can take place here see. So okay, so we have the so this is the field up here.
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It's now a four component object, number one component object.
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And here if we just have the electromagnetic fields in empty space, if the every component of that is the wave equation,
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and that comes from an erosion density which consists of E squared minus B squared.
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Unfortunately, some committee in Paris decided that electric fields will be measured in different units of magnetic fields.
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You have to put a factor of C underneath there.
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But the electric and magnetic fields are two halves of one dominant, and they should consider we have the same units.
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So ELC is essentially the same speed of electricity.
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So this you can think of this kinetic energy, this will think of this potential energy.
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The justification doing this is kinetic energy is is built into ABC and this is the laboratory testing.
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Again, this is quadratic in field gradients.
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So we have and so this is really defined by something defined by some these gradients
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just as we have for the primary density correction gradients radius before.
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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.
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It's provided it's provided the these things since this thing transforms according to this rule that the the time
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components and space components of the unframed person are related to the frames persons components by multiplication,
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by this by this Lorenz transformation matrix.
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So as this thing has to transform like a format, given that this thing doesn't change the numerical value,
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this stays the same as a given event, and that makes this equation valid in every format system.
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Let's give another example because of the of of how we feel very direct.
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Who is the third and great series of the series of British theoretical physicists?
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He was trying in the late twenties, he was trying to find the risk of generalisation of the Schrodinger equation.
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But what he actually discovered was a new aspect of the aether. A fork for component field came up in a field,
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except now each of these each of these numbers is a complex number, not a real number, but a complex number.
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So it's a complex full value, a complex full component field.
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And under rest transformation, this thing transforms in a new way.
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It doesn't transform the way not not previously known to physicists and previously those mathematicians.
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It transforms like a direct spin. We don't need to worry about what exactly this rule is.
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It's just that there is some matrix.
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And depending on the speed, the relationship between between your observers from one frame of reference to another frame of reference,
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so simple as that by betas, the ABC operates between the two things, so there is some matrix that you get.
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You must play for every change, for every hour observed.
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Is this a matrix of which you multiply all these four components together for comparison?
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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.
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So so let's just have a look how this mathematically works out.
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This is a somewhat different this is a slightly different looking wave equation and this is slightly different in intensity.
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What's basically happening is we now have a first order differential equation or a second differential equation.
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We have the up side by the X is equal to sort of a multiple of upside.
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And if you just left, if the coefficients here were real,
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you would have a you wouldn't get you get exponential growth or exponential decline in the
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field's value would be the solution to the equation and you want to play this behaviour.
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So we have a square root of minus one over here which ensures that we have this first order equation.
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We need that little to get lady behaviour. What else is there to revolve?
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This is the other complication is that this is a this is a set of four numbers,
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this is a set of four numbers and here is a matrix which depends on which coordinate we're dealing with.
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And here are a couple of these matrices. Okay. So so this is a linear differential equation.
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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
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products that kind of the price of the vector on itself here is a dot product for of growth,
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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.
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I think that's over. And crucially, this stays the same.
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If you make a rental transformation with including the property transformation, the four numbers are going to reside.
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So what about the coupling between fields?
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If you want to generate electromagnetic waves, you need an antenna.
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In the antenna, you need to have you need to have some currents so that so the full equation,
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which we had a zero we had before because we'll be discussing event waves in space.
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If you have an antenna, you have to put this there's a term here which is some city constant times the
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current density this is the current density which is of course the vector.
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So that's the that's the wave equation, including the sources.
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If you have electrons and they are moving in an electric field, of course the motion is different.
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So sorry.
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So this is the degradation density, this is the noisier density generates this differential equation since the green dot as we discussed before.
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And here is the extra tone that generates this thing.
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Yeah, but electrons are going to be the source that this current is actually made by moving electrons in the way they look.
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The formula that deals with that is the charge on the electron ploughs side of slap sign,
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which is sort of the density is something that's the quantity density electrons we have at least have one of these delta matrices,
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drag matrices inside here to provide the Victorians.
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So the current density associated with the Dirac field is this.
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So what we want to do is replace that with this and replace that with this and
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write out what the so what is the technology density of the whole thing look like?
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Here is the laboratory density for the electromagnetic waves alone.
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That around here is the drawing. See for the for the electrons all on their own.
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And here is the coupling term. That's this term.
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Here is this system here. Here is the coupling term that joins the two together and expresses both how the electrons generate electromagnetic waves,
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but also this term explains how or forces the way that the electromagnetic field changes the dynamics of the charged particles, the electrons.
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So the coupling. So this is quadratic in the fields gradients.
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This is quadratic in the field and it's gradients.
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And this mixed term here is cubits has it has one representative in one field in two representatives of another field.
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So you can you can put so this this encodes a huge prodigious amount.
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Physics is that a very simple expression.
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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
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unchanged when you make every one of these terms remains unchanged for each of the events transformation is is enormously prescriptive.
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So here's my here's my summary is space time.
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The aether vacuum in school by various things is a complex system and it carries several.
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We've only talked about too many component fields thinking that it carries a great many, many from the fields.
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We derive the way equations to describe this system from a single laboratory density.
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So I've only written down the beginning of electrons in density is given more fields.
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We will need more, more terms,
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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
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fields present and the requirements are the rents and variance of the nitrogen density enormously strongly restricts the possible field equations,
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so make it possible to speculate very to to almost exhaustively consider all logically possible of this types of physics.
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And this notion density comprises a block for each mode.
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Yeah, for free dextrose, free particles plus company terms between the blocks.
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So that's all that I wanted to say. We're just.