Okay. Good morning. Hi, Kelly. It's been a pleasure meeting some of you already at conferences.
I look forward to meeting you one again for coffee and at lunch.
I'd like to carry on from Jane to stop. And so James talked to you about Tesco sales.
I want to talk to you about closing sales. And in particular, there's one thing I'd like to convey,
which is question of what is a possible what to have the rights to resist is a possible how do you strike?
Also, if income tax I chose to say at the beginning that my general preference is for interactive talks.
There would certainly be question introduction to all questions.
At the end. I would encourage you the usual to ask it in between.
Just interrupt me. Sit your hand up and ask.
So it's like I say, I first of all, once describe how you go from classical fields to giant strides to hospitals.
So the story is going to be by decomposed fields in two sizes and then focus on the logical selectors to counterpoint.
Just once I say it's not a pleasant place.
I don't want to discuss the status of the fields.
And so I discussed vacuum, which is much more interesting than the vacuum of classical fields and the expectations fields.
I finally decided this debate about it's rational,
so let's just explain the postulates and then we're going to explain what interactions between particles.
So this is a total fails. It's also a choke hold.
Some subjects. It's a talk on public places.
And in this I am in very good company for a very distinguished and all that because this set the career of a young professional
business consists of treating the public oscillator in ever increasing levels of abstraction with the confidence.
So this is going to be a talk all the latest long ago takes us to the pendulum.
But the small change oscillations or the pendulum and Haskell transform lots of
classical theory lots of the very hopefully just produces to physics of all sizes.
So since I want to go status also host I wanted to start by just reviewing the basics of the classical colonial science.
The simple, of course, later is what he calls the most important system in physics has a kinetic energy James
call settings or squares and a potential energy half including the squared x squared.
Here omega is the angular frequency of the oscillations.
It's customary questions, emotions and makes a lot more modest.
And I would describe x and these classical equations.
The motion also spike oscillating solutions. But what's interest solutions?
A course I'm going to see the side a is the amplitude and classically the amplitude I can take any value and the larger I is,
the more energy the offsets has. Using the more sophisticated language of classical mechanics.
There is an accordion Hamiltonian for the whole sector.
The project describes is the kinetic energy protection energy and the Hamiltonian right because it looks I must use it.
This is gives a more direct connection to composition.
It is something that the total energy piece greater to end forces off and omega squared.
Excellent. So how many sources?
I've reviewed clinical sites up unable to build the link between classical fields and harmonic oscillators,
and then that some of those chips get quantum fields.
And I just. Joins us to talk about this.
I want to expand abstracts to those other points from Jeff from James talk of okay, so we see no idea where Haskell fails.
Haskell deals his values at all points in space and time.
Examples of these are the electromagnetic spectrum potential UV and the gravitational potential field for both of these potentials.
From the best potential, you could drive the electric fields from the gravitational potential.
By taking the grating surveys, you can you can derive the the actual gravitational field.
These equations for these tables have have a very simple kind of classical vacuum solution, which is magnetism.
So if the electron is exponential, the simple case, the vacuum solution that's essential is zero everywhere.
No electric fields, no next fails, nothing propagation, no particles.
All of this is the same as possible classical solution.
And it's very boring. And these fields, the electromagnetic field potential, the gravitation potential, both satisfy the wave equation sources.
The way of equation is that translation that describes the configurations of fields.
I describe it as describes propagation waves of sexual waves.
But this is the dynamics of classical, of the classical.
That's magnetism or the gravitational spectrum. What's the significance of this?
Okay. So if you say some fields after they sit by falling here, so to speak,
we will be this is the next magnetic potential, for example, by just these type of a general fields.
So you have some fields fully satisfies the question, then what does that tell us?
How so what the kind of solution for this?
So the. This is a linear regression, so we're going to be able to decompose it into some of those.
So let's just focus on one loaf of salt. So one note of this operation is you can right click it t easily.
I can do x. So hey k is the way number four actually the momentum of this note.
So all this is describing is a load of this field that's propagating with the direction table, the message type.
And this note is so meant to locate.
This is a single low sales. The most is apertures and equations of motion for this planet.
To reduce this as a function of all space and time, just signal the motive, the absolute largest single time and the equation.
This note reduces to the public sector equation.
I substitute into the white question and this is the official version for a holiday cost later with such frequency.
See? So what's the significance of this?
The significance of this is you look at the classical fields,
what equation you take one of these moves most this virus is destroyed by the local state.
The question. Because this is a linear equation.
This means that we can get the general solution to it by decomposing the thought fields as the sum of all possible buckets.
So this is essentially a theoretical position, right, for solution as a linear combination of all the individual lives.
And because we could do this decomposition, this means that the dynamics of the fulfils reduces to the dynamics of all the individual lives.
And we can really see that each individual load satisfies the local sex characteristics.
What's the importance of this mossy thing we take the thing we take away from this is that if you have a continuous capital fails,
the dynamics of the continuous classical fails is the dynamics of an infinite number of classical political crises.
You can say we're trying to think about how this thing behaves, how this thing evolves.
You can, instead of thinking it just feels effective, more productive.
Think of it as an infinite number of classical point points.
And this point is also subject to re-emphasise it.
The dynamics of continuous classical fields is the dynamics of infinite number of possible expenses.
So, for example, with your in this community, we thank you for breaking sounds, lots of electromagnetic waves here.
You've got electronics quite propagating along here.
Let's get latest on electric feels this way.
I mean, yes, feels addicted to it. And if you look at objects of ease, you can see that lovely and sinusoidal down, up and down.
So these are precisely what you get for all of the decisions of the polymers.
So the dynamics of the fields reduces to the homologous oscillators, the explosive harmonic oscillator and goals.
You have these sites of like, let's build them in the transverse direction because this is an electron in this way.
This describes one polarisation of the life. There's another polarisation where somebody is in this direction and the makes this direction.
There's an electric field in this direction. In this direction.
So having reduced classical fields to an infinite number of oscillators.
To understand, it got seven quantum treatments of magnetism.
For example, we want to be able to go from classical fields in classical Hellenic oscillators to quantum fields.
What's normal science? Let me just pause. Two questions now for before I make a position.
Yes. Got sick the polarisation as well as our position of the two extreme positions.
It's a. So we're going to now move to concentrate on the post-colonial stages.
So let's just go back to the hotel sector. The only place up has a gradation to minus you.
Hamiltonian 68 plus for the patient version x doubles up as minus omega squared
x and it's got plus play and also oscillating solution like right now a
classically A's continuous and the larger is more energy of your states as
they can take any value and the energy harmonic oscillator as I mentioned so.
Now the world is not has helped. The world is quantum all the through laws of nature.
Of course, the laws of nature in that classical physics symmetry.
So yeah, the truth is an approximation. So what we should be thinking of instead of the cosmological states goes into the quantum.
Political nature is by finding basic systems of quantum mechanics, and the quantum is just characterised by its discrete tensions.
So because of the multiple states as a section of the cosmological states, there is this the puzzle.
And now strength is a greater state of an inch, half a smaller and bigger first size of the states and three hall effects for America.
Well, I think for him, get set in context. All right. We got each energy level moves up by a quantum of a smaller omega.
That all is necessarily involved because this is supposed to be nice.
And this also the lowest possible level.
The grass level has a nonzero and she has a nonzero energy of one of H four.
So notice is all this is different from the classical system in the classical system
where you all states in solution that I respect which has the energy I have no any value.
So the ancients I think call them and she's all distressed.
Okay. So what's the post picture saying?
Of course, politics. That's just part grass energy, climate change.
And then all the subsequent levels go up by a factor of 85.
So they're all well to report what's in there.
The banking states, the ground state, which is a zero point energy of one half h bar omega.
So there's always an energy even in the back. And then they're also excited states the ethics of the states has an influx of I farming.
So this is what this individual calls points to looks like.
What we said earlier was this feels decomposition phenomenological scientist.
So most things said about one of them, Michael Slater, thinking about lots of sketches.
So if we have lots of oscillators, then give us your spectrum of quantum system just to the ends up in each oscillator.
So if you go in only like this, then the overall energy,
there's always a crash site where you add up the energies of each of the individual ground space.
So the ground state system and oscillators.
So some of the ground sites each of engineers attention, potentially each oscillator and each oscillates can also be excitation.
Yes. You can pull sacred sites at your place inside. No place excited.
Lots of excitations, a lot of expectation for each oscillator for energy, AGL, energies of each individual place.
And there's also there's always a Graham site energy from the some of the greatest energy of each of those.
Without a position in a position to say what a quantum field is.
So a capital fails.
Plus, the field decomposes in dreams, the number of classical canonical oscillators each associated to a characteristic wave of momentum and a phrase.
A continuous quantum fails that we want to promote the classical helical slide just quantum holding
oscillate just so continuous quantum fields decomposes to an infinite number of quantum global slices each.
So thanks to a particular right number, it frees. So if you say in quantum mechanics, well, this quantum field, which is still very well sensical,
still theory states of an infinite number of quantum particles.
So these states, all the ground states for nothing.
So I take this back to you states and sorry to the states, but there is of these little slices of extensions.
There's one point I just want to mention here, Mrs. Sykes.
This is a soy comic, but I just want to kind of say it is that the answers tabulate is more concrete of the thing so infinite.
And generally you think in physics that you do a calculation and you get to infinity,
something is probably go wrong or you should be suspicious of what you get.
So the reason you have an infinite number of little sites here, so this is precisely tied to the word continuous.
Okay. So this is if you assume that your fields has all pre-draft granularity that
you could you could just description works down to distances all true small.
Then what you end up getting is you get this infinite number of points.
Now if you think that probably at some level this language of quantum field theory will break down because maybe you will get vaccinated.
I something up some help that there's some sufficient small scale.
This language of quantum field theory is going to break that the continuous break here and the
continuous and the infinite break and infinite replace replaced by a number which is very,
very, very large but is still finite and a little level.
That is all the difference in the world between something that is large, fully nice and something is actually.
Okay. So this is then what a course of bills is.
It's an infinite number of possibilities. Next, I want to discuss the stakes of this theory.
So you choose to discuss the vacuum space where nothing is excited and excites the sights.
Again, much like a false economic conflict, questions is asked for.
You know, is there any concept of a sort of a containment box able to see this field that they all of, you know, space time, as it were?
So here we think that this pervades all the space forms. It is something like electromagnetic fields.
We think electromagnetism applies everywhere.
Get that confused by the concept of how many places, each with its own medium, vast energy supply, infinite energy has.
That's really the question. I loved coming to them for three or four, so I slept through it somewhere.
Okay. So now talk about the sex. So the first synthesiser, if you like, is the is the vacuum space.
So the vacuum site, all these articles, scientists are in their reticence.
Now, I would like states, George. I have got an infinite number of books, lectures in this will be able businesses.
So I set out to document 600 sites in the mines you can promote to 60 but so here.
Yeah. So this is lightweight is what it looks like to me.
One, two, three, four, five, six, six.
And this is and each of these I to go sites through the graph sites here you see the end
channels a little behind those oscillators going up and this is the conceptual direction back.
All oscillators are in their graph size. There are no ball skills anywhere.
This is the quantum analogue of the classical thing.
Just eight to equals zero. Midfield zero.
However, however, the quantum vacuum is a lot more interesting than the explanation.
And the reason the call of action is much more interesting. Classical vacuum is the because of zero.
Okay. So as has already been alluded to, the serious energy situation.
I think what's going on is there's two questions.
First of all, is the zero four energy physical jersey?
Yes. And the second answer is, if it's difficult, why it's you said that you should push a halt.
Okay. The first question is the zero point energy physical.
So this is decisively altered in the affirmative by something called the Casimir Effect or the test.
So what is this? Well, if you place two perpendicular metal plates back into it, just you just cut it down yet again.
You don't put anything between it. So let's say just focusing one does one by here, one doesn't apply here.
And so classically what happened? Classically like.