Well, thank you very much. I should warn you that I have other talks which I might go back to.
I've had projectors. You see, I had all these pictures from the book so I can show them, but it's not always like that.
In fact, I should explain a bit about the title.
I think it's the Princeton University Press is publishing the book, and it was based on three lectures that I gave about 13 years ago.
You can see how quick I am about the write up, and I think they woke me up too early in the morning and I.
I just gave them this title, which was a bit rash because well, you'll see why.
But in fact, I do think that the words are appropriate to.
I'm going to talk specifically about three different major topics in physics.
And, one, I'm using the word fashion, four, and the other, an excellent faith.
And the third one, fantasy, the fashion one has to do with, well, let me give you an old fashion.
Islington doesn't have to be modern fashion if I can get this thing to work.
There we go. This is a really old fashioned the time of Plato.
So there were four elements, and then the dodecahedron was discovered.
So they had to think of another element, which was the the the aether or something.
It's the planets seem to obey different laws from those on on the earth.
So they had to think of another element to figure out that the another regular polyhedron had been discovered.
It's not just the beauty of these things, which is certainly clear.
And I think we regard physical theories as likely to be if the deep fundamental theories, they're likely to be beautiful theories.
And so you see these beautiful polyhedra which satisfy that particular criterion.
The other thing is they've got to explain things in the world.
And actually I didn't know this originally, but there is and it does explain certain things.
For example, you can take. I'm going to get this thing pointing to cubes and that represents Earth.
You see, the accused represent Earth. The tetrahedron far air was the octahedron and water, the icosahedron, and then the aether was the dodecahedron.
But if you take two cubes, you can cut them up. And create two tetrahedra and one octahedron.
And that expands if you take two sticks. That's made of sort of solid things.
So they're obviously the cubes and you rub them together, you can get well, you see,
you take two cubes, you cut them up and you can produce far two sticks, produce fire and smoke.
So that's an explanation in terms of this whole theory, and I'm not going to say much about that, although fire, of course,
had many different explanations which were fashionable at the times that they were thought of phlogiston theory,
which was disproved basically by Lavoisier.
And then he had a different theory, which is caloric theory, which was disproved a little bit later by Lord Rutherford and so on.
We have better ideas now having to do with molecules running around in oxygen and things like that.
And I'm not going to say anything about that really, but I do want to talk about there is a certain fashionable theory.
This. This is not it yet. These are fine man diagrams.
I should explain what they are, basically. You have to think of the time as going upwards.
Particle physicists think of time going from left to right.
But since I'm more relevant to relativistic the particle physics first, I think my time goes upwards.
And so you think here of this, these lines representing particles, the first one,
two particles come together, together, make another one, and then they split up to make two more and so on.
All these things are possible, things that particles can do.
Each one of them stands for a particular mathematical expression.
And then you're supposed to add all these things up in complicated ways to see what really happens.
The trouble arises when you have these ones with closed loops, because the answers tend to be infinity, and infinity isn't much good as an answer.
Now there are all sorts of clever ways of getting around the infinities, but it was thought of originally,
I think by the Japanese American physicist Nambu that a good idea was to think of.
You see, these are particles were thought of as points you see.
And so when you think of the time progressing, they trace out lines.
And that's what these lines are basically is a little bit more than that, but that's basically what they are.
But if you think of the basic ingredients, not as points, but as loops.
And that was the idea of string theory. Then you can have things which don't have those awkward corners and so on,
and the things can loop around and produce these things with holes in them instead of loops.
And the answers turn out to be fine art. So this was a wonderful idea and I think an extremely impressive and beautiful idea.
They relate to very attractive mathematical ideas called Riemann Surfaces, which are one of the most beautiful things in mathematics.
So, yes, incredible ideas. I was very taken by this when I first heard about them,
but then they people working in these theories found that it didn't really work unless space had 25 dimensions.
When I heard about that, I thought, Well, that's the end of it. That just shows how wrong I was because people thought, well, these idea,
these extra dimensions are kind of hidden and maybe you can make sense of it.
And then the theory works and all sorts of wonderful ideas, I may say, but the mathematics is extremely beautiful attached to these things.
Whether it makes a sense of a physical theory is, to my mind, more questionable.
Now, you might say, surely space doesn't have 25 dimensions, which it doesn't 26 altogether, because time gives you another dimension.
But then what was the point? Well, let me before I go into that, I want to explain a little bit of mathematics.
This is really the only serious mathematics I'm going to do here.
It's very basic elementary mathematics that's a little bit unusual.
First of all, I want to talk about a come back to the string thing in a minute, but this is a sort of interlude which is needed.
What I want to say later, if you want to raise a number to a par at the top, we have eight to the B, except time is the wrong thing to the B.
My press there again. There you go. Hmm.
That means multiplying a batch of B times. Now you can do this again.
H is the C. And by that I mean A to the base, the C to the B to C, because as we did see, it could be written as H of the VC.
So we won't worry about that. But age of the base of the C means a magpies but a base of the C times.
In other words, B multiplied by C times. Times.
So that's a pretty big number. Usually if these numbers are sizeable, in fact, there's a thing called a Google,
which was, I believe, a name introduced by the nephew of a mathematician, Kastner.
And this is he was just trying to think of big numbers.
He was nine years old at the time.
And he invented this name as well, that if you multiplied ten by itself 100 times, in other words, it's one zero 0 to 100 zeros.
That's a pretty big number. And that's ten to the hundred.
Well, it's the sort of number you might think. Well, what's that going to come into?
Physics? Well, it comes in to physics in one particular respect, because it's about the length of time that the biggest black hole will last for.
You see, black holes will eventually radiate away by hawking evaporation.
If you wait long enough and the universe cools down enough that you have to wait for about a Google years before the biggest one disappears.
So there is a number which has relevance to the sorts of things I talk about in my book.
Now, that number, I think the nephew of Karsner wasn't happy with the size of that number.
He thought of even bigger numbers. And Karsner settled on the idea of a number which was has one and Google Zeros.
So you see that's a double exponent thing, ten to the 10 to 100.
That also comes in in what I will say in a minute. So these numbers are the huge.
They are, though. They are. They have some relevance to the things that I talk about in my book.
Now, I want to say one thing here is this.
You have aged agency and these are fairly large numbers.
It doesn't matter much what A is at all. C is the all important number.
And just to illustrate that, I'm going to write down a number ten to the power, ten to the power 124.
And the reason I'm thinking about that number here is it represents how unlikely the Big Bang was.
Now, what I mean by that is they're all possible different big banks that could have taken place.
So the thing about the Big Bang is it was what's called a singular initial state.
It's something where everything went to infinity, curvatures densities, everything went to infinity.
And all your equations then break down.
So it's called a singularity for that kind of reason. And you might say, well,
they're all possible different versions of the singularity and the very particular one that we seem to have had we so improbable.
The improbability is about one in ten to the ten to the 124.
Well, I say a little bit more about that later,
but the point I just want to make here is if you change that bottom ten to a two, it makes hardly any difference.
The number at the top is now 124.52 or something like that.
And since we don't really know how big that 124 is to that kind of accuracy,
it doesn't really matter whether you put a ten or a two down at the bottom.
So it's quite striking how irrelevant that number at the bottom is and how all important the one at the top is.
So that's the point I want to make.
Now, the real thing I want to say about these large numbers, I want to talk about them when they're actually infinite.
Now, you might say, can we talk about infinite numbers where you certainly can.
And there's a theory. There's a cantor. Perhaps I'll skip to that first, which tells you that you can talk about different sized infinities.
And this is a way you can talk in a number of.
Discrete points on the plane, if you like, is no bigger than the number on the line.
And maybe some of you are familiar with that. I'm only showing you the slide, really, to show that's not what I'm talking about,
because many of you may have seen Qantas theory and how you can talk about infinite numbers and some are bigger than others.
This is just to show that if you have numbers and it's in a lattice in a plane, it's no bigger than the number of points on the line.
And you can win the line backwards and forwards and count all the points on the plane, the lattice points.
But the trouble here is it's not continuous because right o keep pointing to first pressing the wrong number.
Then you can see that that when the numbers get fairly large, they can be very close on the on the grid,
on the lattice, but very far away on the actual counting scheme.
So it's not what's called continuous.
If you want now you want to count in a continuous way, then this Cantor idea isn't quite powerful enough for what I want to say.
So let's now go back and talk about these numbers.
I'm going to call them infinity to a power, infinity to the one that will be basically the number of points on the line.
Infinity squared will be the number of points in the plane,
and infinity cubed will be the number of points in a solid space or curve, could be a curved line or whatever.
And for an end space it's infinity to the end.
So these numbers, you can make mathematical sense of them and.
The great French mathematician educator who sort of early in the 20th century analysed all sorts of things and understood these things very well.
Uh. Okay? No. Now I'm going to talk about functions.
Now you see the top left hand picture here. Sorry.
Top left hand picture here,
you might say how many functions where the number of values they can take a that's goes up the y axis and the x axis goes horizontally.
It's discrete in each case, and you want to know how many different functions that is.
How many graphs can you have altogether when you see the first value could be a different possibilities.
The second could be a different third a different sense eight times, eight times, eight times, a B times.
So that age of the B, different graphs. Now suppose.
These were not discrete. But you had a.
At the bottom some space which had a B dimensions and which went up, we would have a dimensions.
Then the number of these. The functions that you could have is a to the.
Age of the sorry infinity to infinity to va to the infinity to the B because infinity va is the number of things going horizontally.
Infinity the B is going horizontally. Infinity va is going vertically.
And so it is infinity to which the infinity to be. In other words, infinity to a infinity to the B, if you can.
See, I should get pointed, pressing the wrong thing again. Sorry about that.
Here we go. Trying to fit down the vintage that introduces me now.
The bottom line here is an example. So an example would be so as you have electric fields in three space.
So that's meant to be a picture of an electric field. At every point you've got the field points in some direction with a certain strength,
and there's three dimensions worth of different possible electric fields, and the space is three dimensions.
So the number of possible electric fields would be infinity.
The bottom line here. Infinity to the A, infinity to the B, which is now infinity the three.
Infinity to the three. But what I want to say is that it's the three at the top, which is the number of dimensions.
The three at the bottom fortuitously happens to be three as well.
But it could have been, say, the number of possible temperatures, temperatures just one parameters,
then it would be infinity to the infinity to the three and it would be only one.
So this is just showing you how this notation works.
If I want to talk about fields, that's the idea. Okay.
So that's counting the electric fields.
The point I want to make is, well, infinity is a lot bigger than finishes would be if a is bigger than infinity would be.
But as I said before, with the finite numbers, it's really the top exponent.
When you got double exponents, it's the top number, which is important, and that's the dimension of the space.
So infinity edge to the A, infinity to the B is much, much, much greater than infinity to the C, infinity to the D.
If P is greater than D, and it doesn't matter a hoot whether A and see which one is bigger there.
The point is that if you have fields in space of a certain number of dimensions, if that dimension is larger than three,
then the number of fields will completely swamp those in in the ordinary in the ordinary ones we're used to.
And that's the point I want to make. So if you have a space which has more than three dimensions,
then potentially you're going to have huge numbers of fields which swamp everything else that you might be familiar with.
So that's a real problem. Now, this kind of problem always seemed to me with a problem with these high dimensional theories.
I want to say how people sort of try to deal with it.
Now, the main argument, I think that people who I should say that when I'm objecting to string theory,
I'm not objecting to it as a piece of mathematics is wonderful mathematics, which has implications in all sorts of other fields in mathematics.
I'm not objecting to the idea of a string as a serious prospect for physical theory.
What I am objecting to is that having these extra space dimensions.
Now one of the arguments that people said, well,
there's a good theory that was produced not that long after Einstein produced his general theory of relativity,
a wonderful theory in which the gravity within explained in terms of curvature of space this time, space time.
So four dimensional space time and but it was his theory of gravity a little while later.
Kaluza, who was a German mathematician living in what is now part of Poland.
I don't know what you call it this Polish German mathematician who introduced a beautiful idea where
you could incorporate not just gravity but electromagnetism into the geometry of the space time.
But the space time now had to be a five dimensional space, but it was a very special kind of five dimensional space.
The five dimensional space is one, which is a thing which you can call a bundle.
Now, you see, this is meant to be a picture of a bundle. I'll give you another picture of a bundle in a minute.
Here we go. You see, it's a general idea in mathematics, which is a very fruitful idea that you can have.
Think of the picture on the picture on the left is just showing you how that bundle idea generalises the idea of a graph,
which is what I showed you before, where you can have the the x axis in the initial case on the left there, they're just ordinary axes,
but they could each be high dimensional spaces and the bottom one could be four dimensional space time.
In other words, three dimensional space amount of time. And the vertical axis could be then all sorts of things.
It could be some complicated manifold. And what a bundle is.
Basically, we call B the whole thing F is what's called the fibre.
So that's the space, those little doughnut, little things which you see at the top what the bundle is.
It's an M's worth of S, so you have a whole space, which is a lot of F so stuck together and it's emsworth of them and that's what a bundle is.
Now, the thing is that if Mr. Space Time, that would be well from space is concerned, it's just three dimensional.
And so that would incidentally, why wouldn't I say four dimensional?
The thing is that usually you have in physics you have equations which carry your information away from the initial three space,
and those equations fix what happens in the threes in the four dimensional space once you know what it is on three dimensional space.
So when I'm talking about how much freedom there is, I'm talking about the space.
The temporal evolution is then determined by what happens in space.
So there's no more freedom in the time it's the freedom is in space.
So three dimensions for the ordinary physics, we know. But you could imagine that was larger.
And the thing is that the Kaluza Klein idea, the bundle, it was a bundle of circles.
And these circles were originally it was it didn't have to be circles.
But I think the Klein idea is that that these were circles and they could be imagined to be very small circles.
I'll come back to that in a minute. But the thing is that the the circles up there at the top,
there's no more freedom in there because you're not your functions are supposed to be all down here.
And these things represent a symmetry. The the, the, the in the Kaluza Klein idea.
Klein was a Swedish physicist who came along later and introduced the idea that there should be little loops.
But the thing is that there in the original theory, there is no freedom in those extra dimensions.
The freedom is all in the base space and in the space time.
That's the same thing at the bottom. Now. The idea with string theory was that you did have freedom all over the space.
So they were saying that the whole five dimensional space,
so in this case 25 dimensional space or 26 dimensional space time was meant to be like space time where you have freedom all over the place.
You can wiggle these things all over as much as you like.
And the argument was that you still is, I should say that those extra dimensions don't show themselves because they're very small.
Well, what is small mean? And this is the sort of analogy that people tend to point to.
You could imagine a hosepipe, and if you're a long way away from that hosepipe,
it looks one dimensional, looks like this, this look, it's just this one dimensional line.
And that's the idea, like ordinary three space, that's the analogue, only three space.
But if you look closely, you see this tiny little loop.
Now you see the hosepipe. You're just supposed to think of the surface of a hosepipe.
So that's an extra one, one extra dimension, just the move which gives you two dimensional space time.
And since it's so small, the argument is you don't notice it.
Well, it seems to me that that is a difficult argument to maintain.
Usually the argument is presented in the form. Well, okay, classically classified of classical physics.
Yes, you could with all those extra dimensions and those might wiggle and they would disturb everything else.
And yes, it would be chaos. But because of quantum mechanics, you need a certain energy to excite those extra dimensions.
And that amount of energy has to do with the dimension of that extra little loop that goes round the hosepipe.
And if the hose part is that hosepipe is small enough, then that energy would be ridiculously large.
Energy goes in the opposite direction from the size of the time.
It would take like to go around the little loop. That's the point.
It would take an enormous amount of energy and what they mean by an enormous amount of energy.
They're thinking in terms of, say, an accelerator where you would try and inject that energy into particle creations.
Like in the LHC, where we had this wonderful news last year or whenever it was about the discovery of the Higgs particle and things like that.
You need a lot of energy,
but the amount of energy that the accelerators that we have today would be just totally by comparison what you would seem to need here,
you would need. So the argument goes, an energy is comparable to something like a sizeable artillery shell,
but in one single particle, and that's way beyond what they could do at the particle accelerators that exist.
You need something, say maybe the size of a solar system.
I dunno what the exact figure would be, some huge accelerator in order to get energies up to that scale.
So it's quite safe. They say you couldn't excite these extra dimensions,
but it seems to me that that's the argument is just wrong because you don't need to see just like that, extra dimensions for the entire universe.
It's that extra dimension extends to the whole universe.
So if you could excite that extra dimension, you would be doing it for the entire universe.
And an artillery shell is absolutely trivial for the entire universe.
In fact, I have a picture in my book which is this one here which I hope I can make sense of.
The top you see the earth going around the sun and the amount of energy that there is in the Earth's motion around the sun is,
I don't know, a million, many. I forget how many millions it is more than the energy that you would need to excite these extra dimensions.
And if that is spread over a distance, which could be, say, the earth, sun orbit, which it would be,
I mean, you've only got to excite that thing just a little bit by disturbing the space time.
Just a bit. It's trivial.
It's a tiny, tiny proportion of an amount of energy.
So if you are going to excite that stretch of the extra dimensions that way, if that little hosepipe thing is going across the middle,
it's supposed to represent that those extra dimensions is the loop being around and the space time is the horizontal lines.
Then you could. Hmm. You would need to have enormous millions and millions and millions of quanta in order to excite it.
And so when you've got lots and lots of quote quanta, people say, well, you must think of it as a classical problem.
So classically, yeah, you could excite these things. So I really don't know why people don't take this argument seriously.
And I say that. I did actually present this argument at a conference which was honouring Stephen Hawking's whatever it was,
birthday, and I think 2002, which was before I gave the lectures at Princeton.
And there were a number of expert string theorists there.
And the thing was published and I never got anybody complaining about this argument.
They just ignored it, which I'm afraid is what seems to happen.
Anyway, let me move on, because that's enough about that particular thing.
That's fashion.
Anyway, so I was a little bit nervous that since it took me 13 years to write the book, that what was fashionable then might not be fashionable here.
I was rather relieved to know that although the fashion in string theory has tapered off a bit, it's still pretty fashionable.
Uh. So anyway. This is quantum mechanics.
Why am I talking about quantum mechanics? Well, you see, that's the faith now is completely different from string theory.
String theory?
See, some people object to string theory because it doesn't have any implications in observed experiments or experiments that one can think of.
That's the trouble. Okay, it may be a wonderful theory, but how do you test it?
That's not my objection. I'm saying that that is a good objection, but it's not the one I'm trying to make.
I'm trying to say that it actually doesn't hang together as a physical theory.
It makes a lot of mathematical sense in many ways, but it doesn't seem to hang together as a plausible theory for the physics of the world.
Quantum mechanics is a completely different kettle of fish,
because quantum mechanics has absolutely enormous numbers of experiments supporting it at it.
Nobody would have thought of it. It weren't for the fact that there were experimental facts which simply do not fit in with our classical picture.
This is one of the examples which is often presented as a.
Sort of a typical archetypical experiment.
You say here we have an electron gun or something which fires particles as a screen behind.
And there are a couple of little slits here. Now, the thing is. Every time a particle goes through, look at the next picture.
This is the B part. One of the slits is now closed and the other slit is open.
And as you follow these electrons through, they make individual points, particle like behaviour on the screen.
But these points are sort of concentrated more or less in the middle where the straight line through the slit would be,
but with a bit of scatter from one way or the other.
If you close that slit and open the other one, you've got a very similar picture slightly shifted to the left,
to the right, but nevertheless very similar particle like behaviour.
If you open both slits, you get magic.
Suddenly the two possible things that the electron might do, each one seems to interfere with the other possibility.
And in some places you find where it's not p. I think I've got the right one.
You find that they sort of cancel out the two different possibilities.
Little places they enhance each other, which is very, very strange.
And so you have to attribute wavelike behaviour to the particles and they now
behave like waves and it's as though they have to pass through both slits at once.
So it's very much part of standard quantum mechanics, it's part of the the Feynman diagrams,
things like playing before you need to add them together because that means all these different things might happen.
It's not just one process, it's all the possible processes have to be considered as somehow coexisting.
So the particles and this is what happens with individual particles, they can be in two places at once.
Ridiculous idea. If you have a, you know, old fashioned Newtonian and so on, way of thinking, classical way of thinking about particles.
They have individual locations, but quantum mechanically, they can cohabit in different well, that's the wrong word.
They can co-exist in different places. And that's certainly the way you understand quantum mechanics.
It works fine for particles. It even works fine for big things like buckyballs.
These are molecules which involved 60 or 70 carbon atoms, but still they're not that big.
You can't see them. But Schrödinger was worried about these things and he introduced his cat and he said,
If you follow my career that's treating this equation, you would have to consider that a cat could be alive and dead, same time.
Well, this is my version of the cat. It's a little bit more humane than Schrödinger's version.
Yeah, the cat. You see, I have a room, and in this room there are some nice tempting food.
And the cat wants to get in and have some food. It's a bit more like John Bell's version, meaning he had the full cat in the empty cat.
But that's a different version. Here. Here. What I've got is up at the top, a thing called a beam splitter that sends individual.
Well, there's a laser at the top that's marked. I think it's a laser.
And then you see, oh, sorry, I still can't get hang of her with pressing the right, but here we go.
That's it. And then there's a mirror here. I think of that as a half silvered mirror.
So every time we've just emits a single photon, single photon,
it hits the beam splitter and the photon now shares its existence between being reflected and transmitted.
That's the way you have to understand quantum mechanics. So this thing goes both ways, and if it goes one way, it opens the door.
If it goes the other way, it opens the door. If it's reflected overspeed or you go straight through, it is open to be a door.
And therefore, because the particle was in superposition of being in those two positions.
Schrodinger's equation if you follow this equation along, you say, yes, the doors have to be one open superimposed with the other open.
They're both. It's sort of both at once happening. What does a cat do?
Well, the cat becomes superimposed between going through one door and the other door, and it goes and gets its food.
It's like the particle going through the two slits, and you have to consider that both alternatives are coexist,
even if the cat gets happily eating its food at the other end as one single cat is
free is its history would have been shared between those two doors and shutting.
We say that's a load of nonsense. That's the implication of his equation.
And well, he said he complained about say what he complained about in the minute.
And I wanted to explain a little bit more about quantum mechanics.
You might ask what on earth this has got to do with it? Well, you see, I was invited to give a lecture by the Hans Christian Andersen Society.
It was coming up to Hans Christian Andersen's 100th 200th anniversary, and they had various people giving lectures.
And they asked me to give a lecture, and I wondered why on earth they'd asked me to give a lecture on fairy tales or something.
And then I thought, Well, I've had used the title The Emperor's New Mind, which was a play on the Emperor's New Clothes.
And I thought maybe that was what they wanted to hear about,
but I didn't think I would talk about that because I was more interested in foundations of quantum mechanics at the time.
And I went through and thought about all different Hans Christian Andersen stories.
And occurred to me that the story of The Little Mermaid in various different respects would illustrate very well what I meant.
So this is what this is. It's The Little Mermaid. And what's she doing?
Well, I did talk about this in this lecture, but then I had to give another picture, which is what it's about.
So the bottom part of the picture is the quantum world, in a sense.
This is where Schrodinger's equation holds. Well, it's an interesting question.
Does it hold always or not? You see, Schrodinger's equation is describes how the quantum world behaves.
And I use the word letter U for that. It stands for unitary evolution.
This writing equation is an unitary evolution of more or less interchangeable for our purposes.
So unitary evolution is the way in which the state, the quantum state evolves.
It evolves in this very particular way, deterministic way.
The state, which describes the quantum world, evolves in this way.
And that is a mysterious way with things all sort of entangled up with each other and things that we don't understand.
So I've illustrated that with strange sea creatures and all tangled up in various ways, and that's the quantum world.
At the top we have the classical world. I use the word sea for classical world classical equations, and that includes Newton's equations.
Einstein's equations. Max was the wonderful equations for electromagnetism.
And that's the classical world at the top. The mermaid.
She shares both worlds. She's the magic part.
And that is what the letter R is being used for. That's the reduction of the states.
And I want to explain what the reduction of the state means.
There is also a feature of this picture, which is slightly oddly drawn deliberately,
that the not only is the mermaid sharing these two worlds, but somehow she if you look at the top part,
she's looking down on on the classical world from a new height, which is the experience she gains from the quantum world,
which sheds light on the classical world that people didn't appreciate before.
But anyway, let me explain how we do quantum mechanics.
You see, this is the way quantum mechanics is used in practice.
The letter U. Or Quantum States is the thing, the upward line on the left.
That's the quantum state. And this is time, not horizontal in the particle physics way of writing.
Fine.
And here we have the state represented by this graph, and it evolves in this deterministic way, according to you, according to this writing equation.
And then every now and again, you do what's called, well, making a measurement or something,
which is the reduction of the quantum state or the collapse of the wave function.
And suddenly we reinterpret the state as a set of alternatives, depending on what measurement you're doing a very crazy thing to do,
but nevertheless, that's what you have to do in quantum mechanics.
And one of these alternatives seems to be what comes out, and that's probabilistically you have this deterministic evolution,
and then suddenly a probabilistic, probabilistic decision is made by the universe.
It chooses one or the other or the other, and that now evolves according to you.
And then again, one of these is chosen and then evolves according to you.
And so I'm like, that very strange.
And Schrödinger made this comment, went to Niels Bohr, and I think he was staying with Bjorn Heisenberg was there and he said,
well, if, if it weren't for if this dam jumping, if we catch the jumping with it suddenly jumps to one of these individual states.
If this random jumping is here to stay. I'd wish I'd had never had anything to do with quantum mechanics.
Well, the other to try to encourage him and get him out of his misery state.
Nevertheless, he appreciated that there's something very strange about what this going on.
It's not the way the world that we perceive behaves.
Some people say, well, you know, the world really does behave according to you.
And all these two alternatives coexist. I'm not taking that view.
Well, that's quite popular here in Oxford. And I'm not saying that's called the many worlds or many universes view or something.
I'm not taking that view. I'm just I want to describe the world we actually see about us.
And that does behave according to this strange thing. And that is not explained by the unity.
Many people try to get this picture as a sort of approximation thing, but I don't think any of it works.
If the unitary evolution is all that happens, you don't get this picture that we seem to observe.
See, this is the faith, if you like. Quantum mechanics works so well, does works extraordinarily well for small things.
And you have problems when you have large things like cats or black holes.
You have bad things there, too. But people, they build up this quantum faith.
And faith is that you must hold at all levels. And I'm arguing, no, that can't be true.
There must be a bigger theory. And it certainly. Is that not the truth?
Just writing a thought this. Einstein certainly thought this.
Debray thought this. Who introduced the idea of particles having a having behaving like ways and so on.
And even more surprisingly, Dirac, who is the person who really introduced the formalism that all quantum mechanics experts use pretty well.
And there's a nice quote in my book which shows that Dirac also thought that this quantum mechanics is provisional theory.
Someday there will have to be a better theory in which this picture is made sense of.
Now, my view is that it will only be made sense of when we bring general relativity into the picture.
You have to combine quantum mechanics with general relativity.
And by that I don't mean what people call quantum gravity,
because quantum gravity means the rules of quantum mechanics applied to gravitational theory, in particular general relativity.
But I think what one needs is a more evenhanded marriage, where there is a back reaction onto quantum mechanics itself.
So it must be that there's give on both sides.
Quantum mechanics has to give, as well as no doubt general relativity will give at some stage that quantum mechanics,
in fact, is the more important, given my view is that quantum mechanics will have to change.
This picture here is a space time picture. So that is my time going upwards.
Oh, except happened. I've got jumped again. I really can't master this thing, I'm afraid.
Here we go. At the bottom, you see two sizeable lumps of material which are put into a superposition of two places at once.
You can do that with a beam. Splitters and things wouldn't be hard to do so that it would be here and here at the same time.
Now, the question is, that's what the unitary evolution.
The other thing would tell us, the Schrödinger equation that tells us, yes, it could be like that.
I'm agreeing with that. But that wouldn't last.
It would be unstable. And the thing is, the picture top here is the distortion of the space time.
So if it's in one place, you can see the space time, a little wrinkle and it goes up.
If it's in the other place, it's got a different little wrinkle which goes up.
And these little curves at the side represent how the acceleration of freefall goes.
And once you try to superimpose these ideas, you run into inconsistency with quantum mechanics,
which is not normally recognised, but there is an inconsistency which begins to show up after a certain time.
So there's a time scale that relates to how much mass is displaced.
If it's more mass displaced, the timescale would be much shorter.
If this there's a cat, it would be ridiculous. It would be instantaneous.
If it's a very tiny thing, like protons, neutrons or something, then it would last a long time, probably longer than the age of the universe.
So it's a huge difference depending on how big those things are.
And here's the picture.
I have probably a bit hard to see what's going on here, but basically it's a bit like the picture we just had, but it's evolving.
So the bottom you have the to the the lamp is in one location.
That's the thing at the bottom distorting the space time.
You can see a little bit of a wrinkle in it and then it gets moved apart and you see the two space times then get different from each other.
And when the whole difference, the region of difference becomes an order unity in what's called absolute units,
absolute units of the units, when you take Planck's constant, basically equal to one speed of light one and the.
Newton's gravitational constant equal to one, then that's the size, the units that you use, the crazy units to use in practice.
But it does give you the sort of picture that in that sort of scale of time, a choice has to be made one or the other.
So that's the way the world seems to behave. And you don't get the coexistence of different alternatives.
You just get one or the other. In fact, they're one of the nice things about this sort of scheme is that it is open to potential experiment.
You don't have to have accelerators bigger than the solar system, which you might have to to test the effect of quantum mechanics on gravity.
But if it's gravity and quantum mechanics, this sort of thing might give an answer to it.
And this is a sort of cartoon of an experiment which is being explored for, oh,
couple of decades by now by Dirk Baumeister and his colleagues in Santa Barbara in the US and in Leiden in the Netherlands.
And this is the cartoon, this picture of what how this is done.
You have a laser at the left beam splitter in the middle, and the photon coming from the laser is split into two possible existences.
One is caught in the in a in a cavity, which is up at the right here.
That one. The other one is in another kind of cavity, a funny one which reflects backwards and forwards about a million.
This goes a million times to about a million times. It hits this little tiny mirror, which is about a 10th of the thickness of a human hair.
You just can't see it. And it hits it bangs about a million times.
That's about enough to displace it by about the diameter of a nucleus.
That's just about big enough that in seconds or minutes, the thing should,
according to the scheme I just told you, become one or the other, and this would be detectable.
And as I say, it's likely within within the next decade, maybe within the next five years,
this experiment will determine whether or not this is correct.
So watch this space. Okay. What about fantasy?
When I talk about fantasy, I was aiming the thing at one particular thing.
I'll tell you about that in a minute. The picture here is not the fantasy.
This is more or less what we believe and what I believe also about the history of the universe.
According to current theory and observation,
what we seem to have the time is now going upwards as in that previous few pictures and this is the history of the universe.
They think of sections through it, giving the space lectures. They can't draw the three dimensions.
You just think of space as one dimension of this picture. You might ask what all this really stuff is at the back.
That's just because I'm not trying to say the universe is open or closed.
It might be closed up. It might be open. It doesn't matter for what I want to say here.
We don't know. It's pretty close to being open, but that's not good enough.
Might possibly be closed up. Now this you see there's an expansion which takes place.
That's the big bang right at the bottom. It's fairly sedate expansion and then it starts accelerating.
This is the accelerated expansion that seems to be observed.
It's referred to as the mysterious dark energy. Sometimes it's in all the cosmology books.
Since 1917, Einstein introduced an extra term into his equations for what actually turned out to be the wrong reason.
Never mind, he did introduce it, and it is, as far as I know, in all cosmology books, all serious ones since that time.
It's called The Cosmological Constant.
And this does give this accelerated expansion, which was observed remarkable observations made at the end of the 20th century.
And fine, that seems to be what's going on.
And this expansion will presumably, according to Einstein's equations, will continue indefinitely.
I'll come back to that later, which is a bit of a worry in some respects, but that's the picture that we get.
But I want to worry about something slightly different here, namely that right at the very bottom,
at the Big Bang itself, current cosmology says tucked into that little black spot which represents the Big Bang.
Here is another version of this whole universe.
Imagine this expansion going on far more than in this picture.
I don't know how many more times, 60 times or something, and squashed into that little tiny point.
And that's what's called inflation. And inflation was introduced for various reasons.
Most of them, in my view, are not correct, although subsequently some of the reason, some new reasons came out which are supportive of inflation.
Just show you how good my predictions are here. When I first heard of inflation, I thought it wouldn't last a week.
It's now, of course, fundamental to cosmology, and I was wrong again.
But nevertheless, I don't have a great deal of faith talking about faith in the inflationary scheme.
And one of the reasons, one of the big reasons is that I don't believe that it explains one of the early things.
It was therefore see one of the strange things about the universe is its very, very great uniformity in many respects.
It's very, very uniform and the idea of inflation was that somehow it could have been very irregular to begin with,
but it kind of got stretched out by this inflationary phase and produced this very uniform universe.
Now, I want to explain a bit why I don't believe that. But first of all, let me just give you some hint.
You see, you have to introduce an extra field, which is called the inflation field.
This is some funny particle which is not part of current particle physics.
But nevertheless, people need to introduce this.
And these curves here are taken from various books and articles which are just to show that this curve,
which represents the sort of potential function, the important thing that this field has and they are drawn just to make it have the right properties.
And you see the different people have different ideas for the shape of the curve.
The good reason being that there is no good theory which gives you a shape that they want, so you more or less draw it by hand.
So that's just to show you that there is. No real acceptance of exactly what's going on.
But if it has these various things, the claim is it does produce this expansion over these pictures.
These pictures are just to indicate one of my problems with inflation actually earning the universe out.
I should say that the inflation field is like other fields in physics in that it's symmetrical in time.
If you run the clock backwards, it works just as well as running the clock forwards.
So what's happened if you run it backwards? Well, let's imagine the first two pictures represent a collapsing universe, but it collapses at the end.
It might start by expanding the first one and then expand and then starts to collapse.
Or it might be collapsing all the time. Doesn't make any difference. And all the possible things which might happen are that great mess at the end.
That great mess at the end is really a congealing of all sorts of black holes and things.
And when I gave you this number ten to the 10th of 124 at the beginning,
that is how improbable it is that you get something which is nice and smooth at the end of a collapse.
Now, that would apply just as much at the beginning. This shows you how improbable this very smooth thing beginning would be.
And because the information field doesn't smooth out, that meant a great mess at the end.
We're running the clock backwards. You get you could start off with something very irregular and you would still get this messes.
It doesn't it explains that you can't answer all those irregularities.
Basically, it's like if you have a fractal picture, you probably see as you expand them out.
It still stays fractional no matter how much you expand it. And that's the sort of thing you've got to expect.
That's the most likely thing in something like that.
We had a very, very special initial stage, which was very smooth indeed, but not because of inflation.
Inflation does not do that. However, it does do other things.
Let me see where I am here. There's this is just explaining.
Yes, inflation does do other things. And it's the reason it didn't die in a week.
I think it's because of the other things it does and it does do things which let me not get into them now, I should say.
But there are three good reasons two or three, and there are about four or five bad reasons, which I don't.
Anyway, the two or three good reasons are good. So if you don't have inflation and I say I don't want inflation, if you don't have it,
you've got to have another theory which gives the same explanations as inflation does.
Now, I told you that this is the fantasy chapter, and I was regarding inflation and very many other more fantastical theories.
And by the time between giving this title to the Princeton University Press and starting to write my book, I had my own fantastical theory.
So I have a different point of view about fantasies. Now you say fantasy.
We need fantasy. The world is so extraordinary.
And it is when you think about quantum mechanics, so extraordinary that we need a fantastical theory, it's just got to be the right fantasy.
So I'm trying to say inflation is a fantastical theory.
It's not quite the right fantastical theory, but maybe it is in a certain sense.
And what I'm trying to say, this is a picture of a black hole, which I'll come back to in a minute.
Let me go back first. So what I am trying to say is that instead of tucked in right at the beginning,
which is where inflation is, there is a sort of inflation, but it was before the big bang.
Now, that's a very fantastical idea. I didn't think of that.
That idea was, well, way back into the old cosmology models that were pretty big bang theories, but more recently,
a theory due to veneziano, which also had an inflationary phase which was before the Big Bang.
So I'm going to give you a scheme of that nature, but it's little different from any of those.
And to explain the idea, let me first go back to the black hole.
Well, I don't really want the black hole except to explain what all those little cones are.
Those cones are to tell you causal behaviour.
So this is a spacetime. And the first thing in order to get the spacetime to look like general relativity, you've got to put these cones on it.
And what do the cones represent? Were they represent how light would behave?
Think of the middle picture here. Light flash at the bottom.
This is time going up the picture in the middle one. So that is time going up again.
The flash of light spreads out. Here we have a three dimensional picture flash here.
And the next moment is the sphere around the next moment, a sphere bigger than that.
That's the flash coming out. These are different sections of this car. And of course, you have to add another dimension to get that picture.
Now, I hope you're used to that manner. You have the passcode, which is a flash coming in.
And what does this represent? It represents the speed of light. At any point, ordinary particles have got to have world lives.
That's histories which are within the cone. And at every point you've got to have one of these cones.
So that's what the pictures that I've been showing you here represent and a little bit more you see here is a a particle.
And you can see its world line. Its history must be within the cone now.
The picture that we have here. I'm sorry. I'm in the wrong way of having that minute.
That is not quite the full kind of geometry you need.
You want to have a scale as well. Now a scale is given by clocks.
We know that there are extraordinary precise clocks now that, well, your GPS wouldn't work with if it weren't for extraordinary, precise clocks.
But even a general relativity, you know, clocks more slowly if they're down there than if they're up there.
But it doesn't have to be that much. It can be only a few. Only about a centimetre, maybe less than that.
That people can measure the difference in clock rates that tiny distance.
It's extraordinary. Why are clocks so precise? Well, there's a good reason why they're so precise.
And that is that they the ordinary particles, massive particle stable, massive particles are clocks.
This comes basically from the two most fundamental laws of physics or equations of physics of 20th century Einstein equals.
And C squared, of course, is one of them. That's one of these two here.
The other one is max planck's equals h new news.
The frequency. Frequency is equivalent to mass.
H is just a constant. Energy is equivalent to mass according to Einstein.
So therefore, electric energy could. It's equivalent to Mars.
So therefore, Mars sort of cancelling mass up between those two frequency.
Is it? Sorry. Cancelling energy out between those two.
Frequency is equivalent to mass.
So any massive particle which is a stable, massive particle is a clock by these fundamental laws, very, very precise laws.
Of course, the clocks that you actually have in practice aren't single particles.
You've got to you've got to magnify that somewhere to make a clock that you can actually read the time off.
But basically, it's because of this very fundamental nature of time which comes from these two basic equations.
So clocks basically the mass of particles.
Okay. So this is what I want to say. And the final thing here that okay, that is the picture.
If you don't have clocks, if you have the clocks, then you have the full scheme that Einstein has.
But you don't need the clock part for most of physics.
Maxwell's beautiful equations electromagnetic equations describe electricity, magnetic magnetism and light doesn't need it.
In fact, all it needs is the cones. You don't need the scaling given by the clocks.
I should say that distances and times are equivalent because of the speed of light.
The metre rule in Paris used to be the definition of metre.
Now the definition of metre is just in terms of light seconds because that thing isn't good enough for current you.
Just time measurements of what you use and speed of light gets you distances.
So it's the time measurements which give you the scaling that you need in addition to these cones.
But certain things in physics don't need that. Maxwell's equations don't.
In fact, the strong and weak forces. Of particle physics don't need either, so they don't require the scaling.
This geometry with the light cones is good enough. Now, when I say that.
That's what's called conformal geometry. Now, if you didn't have any massive particles and in the very remote future, mostly it'll be photons.
I remember you had this picture of the universe expanding, and it does expands and expands.
And I was worried about this one time. It's an emotional argument.
I admit that I was there thinking, goodness, if this universe is going to go on and on and on and on, and it's going to be incredibly boring.
It's already pretty boring by the time there's nothing left but black holes.
It's even more boring when the black holes finally evaporate after a Google years and there's nothing left.
That's the very boring era. And then I thought, Well, who's going to be bored by that?
Not us. But mainly it's going to be photons around.
It's very hard to borrow a photon, partly, of course, because photons probably feel anything, but never mind.
The real reason is because photons don't measure time if they travel along the light cone.
The time between the creation of a photon and its reception somewhere else is zero as far as that photon is concerned.
So right out to infinity is zero. So the end of the universe comes zapped like that if you're a photon.
Well, you see, this ties in with something else, which I illustrate here.
Those are the different clocks going on. And if they get up to lose the light cone, they don't experience any time.
This is a wonderful picture by the Dutch artist M.C. Escher, and it illustrates a kind of geometry.
Called hyperbolic geometry. Don't worry about that too much. But you see, this is what's called a conformal picture.
These fish, I think they're fish. As you get closer and closer to the edge, they get smaller and smaller.
But they are. It's a conformal picture. So you see the eyes of a fish that exact circles.
They remain exact circles right up to the edge.
So although that is infinity as far as the fish are concerned, if you look at it from this picture where large and small and equivalent,
but as long as you squash uniformly in each direction, that's what's going to conformal in space time.
It means you keep your light cones, you squash the space in the time by the same amount.
Then the most of physics doesn't notice the difference. The only in physics which does notice the difference is where mass comes into it.
Remote future photons. They don't care about mass. What about the Big Bang?
That doesn't care about mass either? Because the energies get so big that mass becomes irrelevant.
You may have heard people talking about the Higgs particle and when temperatures get higher than the fact of mass of the Higgs particle,
then particles become massless. So they're massless at both ends.
If they're masses at both ends, the physics which is relevant is the physics of this conformal geometry.
So think about this Escher picture. Infinity is a nice, finite place.
So if you were a conformal person, somebody who didn't have mass, then that would just be a boundary like everywhere else.
Well, it's just a boundary. So here is the picture I have and you see the line across the middle if you're below it.
That is. Their remote future. That line represents your remote future.
If you are above it, that represents somebody else's big bang and you see it,
the squashing down of infinity gives you a finite boundary and the stretching out of the Big Bang gives you a finite boundary.
And the idea is that that would give you a cosmology, which is my crazy cosmology.
You see here on the left, we see a picture more as I had before, which is.
I think that's meant to be. Ah. Ian, I'm calling. That's Ari on a picture of the universe before it.
Which instead of being tapped into its big bang before it was this entire aeon, before that was another aeon.
After I's will be another one and so on. And these are stuck together.
If you stretch out the big bang and squish down infinity, then they all fit nice and smoothly.
And so this is the crazy scheme. I call it conformal cyclic cosmology, which I think explains the thing for inflation.
It does also explain the smoothness of the Big Bang.
It's a nice way of looking at how to describe the smooth as the Big Bang, which is due to Paul Todd, my colleague here in Oxford.
And this was a way of characterising the way in which the Big Bang was special.
That's the ten to the ten 224. I told you the one.
Thing or the one the few which are the one out of that 110 to 104 will be the smooth ones that we seem to have.
And to have those ones you get automatically with this scheme because it's got to fit smoothly onto the remote future of the previous one.
Well, I think I probably mystified you enough in calling an end to this.
Thank you very much. Thank you.