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