Well, good evening, ladies and gentlemen, and welcome to the Science Museum.
I'm Roger Highfield.
I'm one of the directors of the museum and we're thrilled to host this event for the University of Oxford's Mathematical Institute.
It's a huge honour to welcome Sir Roger Penrose, Emeritus Transport Professor of Mathematics.
He's used a combination of maths, art and bestselling books to reveal the unity between mathematics and the physical world.
Sir Roger will be joined by Hannah Fry, Associate Professor in the Mathematics of Cities at University College London,
who's actually best known as a broadcaster and writer and has just released her latest book, Hello World.
A good friend of the museum, Hannah, is also among our latest crop of trustees.
In fact, she's been taking selfies in front of her name for half the evening.
Mathematics provides the fabric of modern society, and it's really important to the museum and appears in all sorts of guises.
We've got our patent pod aimed at younger children, which is inspired in part by Sir Roger's ideas.
The equations of aerodynamics were crystallised by Dame Zaha Hadid into the sensuous physical forms of our mathematics gallery.
We're doing a citizen science experiment with Redding University, which aims to improve space weather predictions.
And that's for our new exhibition About the Sun. And of course, there are lots of events like this one,
and mathematics shows that we've developed for hundreds of thousands of schoolchildren each year.
So when it comes to our future projects, you'll find mathematics in an exhibition that we're developing with HQ and all sorts of guises
in our new or our forthcoming medicine galleries such as epidemiology and in a new gallery,
our forthcoming gallery, Science City, which is going to tell the story of how London became a global scientific and technological hub.
And now I'd like to introduce Mike Giles, professor of Scientific Computing and the Oxford Mathematical Institute.
Over to you, Mike. Thank you, Roger.
It's a real pleasure to introduce the second Oxford Mathematics London Public Lecture following last year's successful lecture with Andrew Wiles.
I would like to thank the Science Museum for generously hosting the lecture and a special thanks to execs markets.
Sponsors of the Oxford Mathematics Public Lecture Series and X Markets are a
leading quantitative driven electronic market maker with offices in London,
Singapore and New York. And it's a real pleasure to have so many of their team here tonight.
It's very important for us in Oxford Mathematics to get out of Oxford and spread the word about our subject to as wide an audience as possible.
And our public lectures are our flagship vehicle for doing this.
If for future events, you're not able to come in person, they are all broadcast live and they're also available subsequently on our YouTube channel.
And so to our speakers, as Roger Highfield says, Roger Penrose needs no introduction, a true mathematical polymath.
But is he really a mathematician or a physicist?
Tonight we'll find out. And Hannah Fry also needs no introduction.
All I will add to what Roger has said is that her latest TV series, Magic Numbers,
is also available on iPlayer, and she will be signing copies of her book after the lecture.
So without more ado, let me please present Sir Roger Penrose.
Well, thank you very much for that introduction. I suppose you want to know the answer to the question about whether a mathematician or a physicist.
One of my physicist friends keeps worrying me about that, and sometimes people ask me.
So I think the answer to it is that mathematics I find absolutely wonderful and huge pleasure, and that's what I do.
But it's the physics which drives what I do.
So I'm interested in physics as and what's what are the answers to the way the world works and that sort of thing.
So I say the big drives come from physics, but what I actually do in detail is usually mathematics.
So I'm both, I suppose. I hope I'm both anyway. Anyway, I want to give a little talk, which is to do with things I've been doing extremely recently.
In fact, some of these things are really just about last week or so, so it's really up to date.
So let me explain. I'm going to talk about cosmology.
And so perhaps we could have the first picture. No, that's.
That's the first picture. Thank you. Now, you see this. I like when my mathematics.
I very much like geometry, although I can do a bit of algebra too, but geometry.
And I like to draw pictures of things. So these are pictures of mine, which I'll show you.
I often show them on a an overhead projector or something, but this is a nice way of doing it.
You get nice big pictures here, and this is a picture of the universe.
I should explain various things about it. Time is going up.
So you think of any one moment, if you like, of the section through this.
And one thing I should point out, if you look right at the top, you see look a little bit strange and there's that frilly part of the back.
That's because I want not to be prejudiced as to whether the universe especially open or closed in my goes all the way round,
or it might decide to do something else in the very great distance.
So that's really what that's for.
So I have a fairly bit at the back, just so I don't care this from the point of this talk whether the universe especially open or closed.
Now right at the bottom you have this thing called the Big Bang, and that expanded out, the universe expanded out from that.
And this expansion, I should say, is very much in accordance with Einstein's general theory of relativity,
which you introduce in whatever it was, 1915. And there is this exponential expansion that you see.
If you go up, it's it expands out a bit, slows down a bit, and then starts to do this what's called an exponential or self similar expansion,
which has been observed for looking at distant supernovae, stars and so on.
But I'd saied's equations require what's called the cosmological constant.
It's usually called lambda. These days people call it dark energy.
I don't like the term very much because it's neither dark nor energy in the sense it's pushes rather than pulls energy and gravity pulls things in,
says a strange the terminology, never mind. Anyway, that's the dark energy, and it causes the universe to expand and expand and expand.
And this behaviour is in all the cosmology books.
If you put in this lambda the cosmological constant and when it's positive that's what it does.
So that's pretty well a picture of the universe as we now believe it to be,
except people usually think right at the beginning there is something called inflation.
And I might be asked, why haven't I put inflation in the picture?
Well, there are two reasons. One is maybe I have, because inflation would be right tucked in at the little black spot at the bottom.
You wouldn't even see it in the picture.
This inflation was supposed to have taken part in the universe's activities in the first about ten to the -30 2 seconds.
So think of one followed by 32 zeroes, one over that.
That fraction of a second, in fact, is supposed to have been within the time that the inflation took place.
Now, if you wanted to see what inflation is supposed to look like, we need a pretty good magnifying glass to look at that little point at the bottom.
So let's have the next slide, please. And there's the magnifying glass.
When I use overheads, I put that one on top of the previous picture, but I'm not doing that here.
What I'm going to do is show you what you would see with this very powerful magnifying glass.
And I have the next picture, please. And well, the thing at the top, I should say, is just the handle, the magnifying glass.
So that's not something funny about the universe. Forget about that.
But the you see, this expansion looks very much like what we see now as this exponential expansion of the universe,
which is observed now from the observation of distant supernova stars and all sorts of other things which fit together to get the picture,
that that's probably what the universe is doing now. But this view is that within these first elements, 32 seconds,
it did this other exponential expansion and expanded by some huge amount in that tiny little point.
Now, I never like this partly because it doesn't fit in with Einstein's equations very happily,
partly because, well, it didn't do half the things they're supposed to do.
It's supposed to smooth out the universe, and it doesn't do that. However, it does do something.
It does a couple of things which are important in cosmology.
I'm not going to say much about that, except that they are important and that if we don't have inflation, you've got to have something a bit like it.
So I'll come to that shortly before that.
Let me describe something about infinity.
You see, the universe does is expansion, and then it's going to go expanding and expanding and expanding right to infinity.
At least that's what Einstein's equations tell us. So infinity is a nice thing to talk about in mathematics, and it's very important in mathematics.
People say you can't really understand infinity, can you? Well, you can in mathematics.
That's just what you can understand. So let me have the next picture.
Now, that's a very nice illustration of infinity, and it's also a very nice piece of geometry.
I am very attracted by this picture. It's an Escher picture.
If he was told about this kind of geometry by Cocteau, who is a very distinguished mathematical geometry,
and he said to Escher, Why don't you use this representation of what's called the hyperbolic geometry?
So you have to imagine that these fish, I think they're fish, are all really the same size and shape.
But when you get round the edge, they're squashed down. And the way they're squashed down is according to what's called a conformal map.
Conformal means where small shapes are preserved, they might be bigger or smaller, but they're not squashed one way or the other.
If they're squashed, they're squashed always in the same way, to the same degree.
So it's what's called conformal. That means angles. So you take the angles on the fins or the wings or whatever they are of these fish.
And those angles are exactly the same, no matter how close to the edge you are.
So according to the universe that these fish inhabit, which is called, as I say,
hyperbolic geometry, but this is what's called the it's called the Poincaré disk,
which is, of course, in mathematics, you often find that the name attached to something is not always the first the right one.
I mean, it's really Beltrami who is in Italian geometry who for this representation before Poincaré?
Well, Poincaré made a lot of very important use of it, so it's all right to attach his name.
Except Beltrami got a rather bad deal out of it.
There's another well-trod is called The Kline Representation.
Again, he doesn't get the credit for it, but it's very beautiful.
And the straight lines in this geometry are really circles. Well, they look like circles in the picture which meet the boundary right angles.
And if you follow the the fish, the noses of them, and they go nose to tail all the way around, you'll see the circles all over the place.
Very nice representation. Now, the point I really want to make about this is using this conformal idea.
So the geometry we don't know about distances, you just know about angles you can represent often, if you're lucky, infinity.
So this boundary around the edge, you can look at it and you say, well, you could step outside that,
but these fish think that that's infinity as far as they're concerned.
So that's the kind of representation which I've been very keen on.
I've played around with these conformal geometries for a long time before I started doing research in mathematics,
or at least official research I was supposed to be doing. And my interest in general relativity,
I found my interest in these things were important and I learned how you could study things asymptotic, things like radiation.
I mean, what is if you have something radiating and the radiation goes way out to infinity and describe it.
If you have infinity just sitting there, it's. Very helpful. So I was playing around with these things in the 1970s and so on.
Okay, now let's think about our cosmological picture.
I think I want the next slide, please, if I've got it right.
See here, what I've done is the same trick as we have in the picture applied to the remote future.
So the remote future goes on and on and on and on.
And one of my reasons for thinking about this in this conformal way was it seemed to me that the universe.
Well, I mean, it gets pretty boring for a while when black holes have swallowed pretty well, everything of interest.
I come to the black holes in a minute and then as we can see, that's I go to the next picture quickly and then I'll go back again if I can do that.
This is a picture of, again, a space time picture.
So time is going up and we have some collapsing material at the bottom and then we have the black hole.
You need a few more dimensions to picture it properly, but the black hole is represent.
The horizon is where you see that line, the singularities in the middle and the horizon just outside that.
And then, according to Stephen Hawking, after a while, these black holes disappear.
Well, I'm pulling with a pop because whatever kind of an explosion it is, it's very,
very tiny on astrophysical by comparison with other kinds of astrophysical events.
So this black hole, it can be. Well, you see, our galaxy has a black hole, which is about 4 million times the mass of the sun.
There are lots of smaller ones undoubtedly going around, but the one at the middle is extremely big.
And you can see it's quite amazing because the pictures like a movie of these stars going around this thing in the middle,
you can't see a thing in the middle because the black hole you can't see directly,
but you can see the stars going around it and this you can see and speeding it up a bit, but it's quite impressive.
So it's there. Now, what happens to the black holes eventually?
Well, you see, they evaporate away by hawking evaporation.
And then when they've all gone. How long does that take? Well, for the really big ones, you have to think of something like a Google.
Yes. What's a Google? Well, that's one followed by a hundred zeros.
Not a very scientific term, perhaps, but it was invented by the nephew of, I think, a mathematician.
And it was a nice name to say if you mean a really big number.
Now, Google is, I say, 10 to 100 years.
And that's the sort of time you're going to have to wait before all the black holes have gone.
The really big ones take the longest to go away, and the smaller ones go much more quickly.
But after they've all gone now, I thought it was pretty boring before sitting around watching for a black hole to evaporate.
Whether that's dead boring when they're all gone, that's very boring.
But then I began to think, who's going to be bored by this?
Well, photons, probably mainly photons. And it's really hard to borrow a photon.
It's hard probably for two reasons. One is it probably doesn't experience anything, but the other is from relativity effects.
Photons. If I could say experience, don't experience time at all.
The time from creation of that photon or whatever happens to it is nothing for that photon.
So that it gets right out to infinity. And it's as though this has just happened instantly.
So as far as the photons or other particles which have no mass are concerned, infinity is right there.
So I'm going to show you in the next picture. Next one, please.
No, that's. Is that the next one? I can't remember.
Perhaps it was the next one. That'll do. These are the cones that you perhaps saw in the previous picture.
They're very important. They're what I call light cones or now cones, and they represent what light would do.
So think of the big picture at the bottom.
And here I've got a couple of clocks, the histories of those clocks, and they're supposed to be identical clocks.
And this purple, whatever they are, ball shaped surfaces represent the first tick, the second tick, the third tick.
But the light cone is there. Irrespective of the clocks.
And it's very important they're sort of sitting there at any point is space time.
The main structure of that space time is given by those cones.
It tells you what light would do if there were light there. And you see the photons zipping along like that.
With the speed of light. That means going along with its word line, going along the cones.
And you can see if you look back at the previous picture with the black hole right on the horizon,
the cones are all tipped over so that the light rays are along the horizon.
But anyway, I want to show you this pic, this picture here, because it illustrates something important about relativity.
The thing I want to illustrate is that there's a thing called the metric now that defines the structure of space time at every point.
There's what's called the metric. Now, the metric is a thing which has ten numbers to describe it.
Nine of those numbers, really, it's the ratio of the ten numbers, nine of those numbers.
And that in that sense, tell you where that light cone is.
So that's most of the information. The one other bit of information are the ticking of the clocks.
Now, in relativity, nowadays we have extremely good clocks, very, very, very precise clocks.
They're so good, for example.
But one of the effects that Einstein predicted about clocks is that if you had a clock down here and a clock way up there,
the clock down here would run just a little bit more slowly than one up there.
But nowadays, if you had a clock sitting here and the clock ticking there,
we can now measure the difference between the time rates, very, very precise.
Now, the fact that we have such precise measurements of time is one of the things that underlies the very precision of Einstein's general relativity.
Now. The one important reason for that is the two formulae that I have at the top on the left hand side.
These are the two most important formula of 20th century physics.
One of them, of course, is Einstein's E equals M.C. squared, which tells you, roughly speaking, that energy and mass are equivalent.
Okay, you've got C squared, but that's just a constant energy and mass equivalent.
The other formula is Max Planck equals H new.
I think people call it F. Often these days that's the frequency E is again the energy.
And Planck tells us that energy and frequency are equivalent.
Okay, you've got another constant, which is Planck's constant, but that's a constant.
So we have these two formulae, both telling you energy is something and one tells you it's equal to mass,
the other something, even the frequency apart from constants.
So that tells you that mass and frequency are equivalent.
So if you have a stable, massive particle, that particle is a clock.
It's a clock of incredible precision. It's not something that you could necessarily measure.
You can't use it on your wrist or something. You have to have some way of of.
So scaling it down does extremely high frequency. But that's what these essentially these very, very good clocks depend upon,
is the fundamental fact that energy and frequency are equivalent in physics.
Now, suppose you have no mass.
Photons don't have mass. They aren't any good of being clocks and they zip along the cone.
They never hit the first of these [INAUDIBLE] surfaces so that that first tick never happens.
Those clocks don't experience time at all. So suppose you had a situation in the universe where there weren't any massive things around then.
It's really the geometry of the cones that you're interested in, and that is in relativity and space time structure, the conformal structure.
I said angles. That's the conformal structure. Well, here it's the light cones and that's the same thing.
So if you only have the. If you don't have any mass, you've just got things without mass.
Then they're not really interested in the metric. They're only interested in the conformal structure.
So now you can apply the trick, which I just illustrated in the estimate Escher illustrated,
and the picture I just showed you a moment ago with this infinity of that geometry being represented by a nice boundary, a nice smooth boundary.
That trick can be used for the whole universe. Now, can I have the next picture?
I hope it's the right one. I think the picture has gone missing.
This one. Can we go back to. Back to back.
Another one. Back another one. That's it?
Yes. Did we have that picture? I can't remember.
Anyway, you see the tricks here. Right in the remote future.
That's the trick I'm talking about. We've squashed down infinity to become a nice, smooth future boundary.
And as far as the photons are concerned, they zip along and they get to the boundary.
So if you had nothing left but things of that mass, this is a problem about electrons.
And so you need to do have a scheme which gets rid of that problem, which is probably the mass phase out in the very remote future.
But let's not go into that issue. It is important for this scheme, but let's suppose you have nothing left but photons.
Then you can do that trick. What about the other trick?
This is the opposite trick. You see, we have this nasty big bang at the beginning.
How do we talk about that? Well, again, you can play a trick.
This is the other direction where you stretch it out.
Now, here, the reason you can get away with that is because things get hotter and hotter and hotter than when you get the big bang.
Then the nearer the, the higher the temperature gets.
And when the temperature is extremely high, that means each particle has an extraordinary high energy,
far higher than the mass energy that, according to the Einstein equals M.C. squared is.
So you get an energy, which means that the mass becomes completely irrelevant.
The closer to the Big Bang you get, the more irrelevant the mass gets.
And so therefore, this trick makes physical sense. Now, I should say that the future one applies very, very generally.
There's a theorem due to Helmut Friedrich, which tells you that you can get away with this very big general case of irregular universes.
In the other direction, it's completely the opposite. It's a very, very strong restriction on the world that the Big Bang can be treated in this way.
I kept worrying for a long time because we know there is a very big restriction.
It goes down to a thing called the second law of thermodynamics. I can't spend time talking about all these things.
Then a colleague of mine, Paul Todd, who was a student of mine, and he had a much better way of describing that.
The very, very, very strong restriction that the Big Bang had satisfied is that you can stretch it out that make it something nice and smooth.
So here we have a nice representation. Nothing outrageous with regard to cosmology.
You can squashed an infinity stretched out the big bang. The squashed down infinity looks like the same as the stretch.
That big bang, you might say, isn't the big bang very, very hot. Yes, it was.
But then you stretch it out, it gets colder again and you squashed an infinity.
It gets hotter. So they look pretty much the same. Okay, now let's have the picture with that.
We I think the last one, if you can rattle along to the last one.
Great. Now, this is what's outrageous. The one I had before.
Okay. It requires maybe people have to agree with me.
It's okay. But now this is outrageous. Our Big Bang, according to what I'm saying, was the conformal continuation of somebody else's infinity.
Now I'm calling these individual things on the left.
I looked up in my dictionary to see how long an Ian was, and I was glad to see there was no definite length of time.
So I'm going to call it the entire history of the universe is one Ian.
Now our remote future then because there's nothing left with any mass, becomes equivalent to a big bang of the next.
Ian And it's nicely smoothed out in just the way you want to have the signal of feminine dynamics and all that stuff in the right form.
So it really works very nicely. Of course, not only in the cosmology community like this idea because they're being brought up with inflation.
And where's inflation in this picture?
Well, actually, you could see it because if you take the one in the middle to be our Ian, then the one before it,
rather than having to have a big magnifying glass to see that exponential expansion, you can see it in the previous Aeon.
Now this is an idea which is a bit like an idea that that was an Italian physicist called Veneziano had his model was a bit different from mine,
but I'm not claiming originality for that particular concept because Veneziano had it in his model.
But okay. Anyway, that's that's the conception I have with consult conformal cyclic cosmology and I find it rather attractive.
It makes nice mathematical sense. So that's why I like it, if you like.
When I'm a mathematician, does it make physical sense? Well,
I gave lectures about this for many years and I was quite happy to give the lectures because
I thought nobody is ever going to be able to do an observation which will prove it's wrong.
So I'm nice and happy. Then I started thinking like. You can find the evidence for it.
And the thing I thought of was the collision between supermassive black holes, which would produce the huge gravitational wave signal.
You see, we have this 4 million solid mass black hole in our centre.
We are on a collision course with the Andromeda Galaxy, which has one inch, about 30 times bigger than or something like that.
And so there will be one walloping explosion when they hit each other and swallow each other up.
We won't be around to see that, but people may be in the aeon beyond us might see the effects.
Now, what I'm saying is that we might see this kind of thing happening in the Aeon prior to us.
Well, I'm not going to talk about that because this is all very controversial.
Do we see these things? I think we do, but we get into all sorts of trouble.
Me and my colleagues, my Armenian colleague and my Polish colleagues who seem to have some decent papers on this,
seem to giving good evidence for that, but nobody's picked up on it.
More recently, we've had another idea. This is very appropriate in a way, because it has to do with Stephen Hawking.
Now, I showed you that evaporation of a black hole.
And Stephen was very worried that his prediction of black hole evaporation was never going to be seen.
He hoped it would be seen by little black holes in the in the big bang.
And and but nobody saw it. But what I'm claiming.
Just think about it for a minute. That black hole, although the radiation coming from it, is very, very weak, extremely low frequency,
all that energy in that black hole is finally dumped into this photon, mainly photons.
So that by the time of the crossover. Let's talk about the previous aeon, though, the one below, the one in the middle.
Think of a black hole in there. It's been sitting around and right tucked up.
I talked about the Google years.
Where is the Google Earth in this picture is you could hardly tell it from the crossover surface to the next one is right up there.
But all the energy in that black hole is contained in that.
And where does it go? Well, it bursts through into the next aeon.
Now, my colleagues, Christoph Meissner, Polish colleague, and Daniel Ann,
who is a Korean who works in New York, have been analysing the cosmic microwave background.
That's the radiation coming from well, is it the Big Bang where it's coming from about 380,000 years after the Big Bang.
But still, it's pretty close to the big bang on the cosmological scale.
And what we claim is happening is that the energy from the black supermassive black hole in the previous aeon burst through to that crossover surface.
And in the 380,000 years, it spreads out to a distance, which is about eight times the diameter of the moon.
That sort of cosmological scale is actually pretty small. The moon looks quite big to us, but that's because I don't know.
From the home sky it's really quite small. And this is the what we call hawking points.
Now, the evidence for these things, the analysis, not all of which has appeared.
Yes, we have an article on the on the archive, but the new one we don't have on the archive yet.
The confidence that we can give, gives to the signal by the usual tests that people use in cosmology would be one part in the well.
In about one of one ones in about 50,000.
Now 5000. Yes. Because you do a lot of tests to see whether they random skies that you construct.
Do you see this feature? So the feature is about confidence levels, about 99.98% confidence.
So it's a pretty impressive thing whether anybody is going to believe it.
After that, I'm not sure. But all they have to do is look.
So thank you very much. Thank you very much.
Actually, first I say so. Okay. I sort of want to make sure that I've understood that in terms of the cyclic cosmology.
So is the idea for our current universe then? Is the idea that will get gobbled up by black holes?
Oh, no, no, we don't get gobbled up. They sit there, I the universe does what I showed in the picture.
It goes expanding out and out and out the black holes as a whole.
I mean that big. But they're totally from the point of view of the universe as a whole.
So. So they're very small in the picture. If I drew a black hole.
Just be a line going up. You wouldn't see the diameter of it's tall.
So how has this gone down in the community? How have cosmologists is that?
Very badly, from my point of view, very badly.
Yes. Well, you see, the the old idea about the.
I think collision and the gravitational waves. Would cause a signal which to independent groups.
I have a person who collaborated with Ms.
Vargas again, who is who's an Armenian, and he initially did a bit of analysis, which people it was a bit unconventional people,
but the paper we finally published on this, we have a way of showing that this is not random,
mainly because you see this sense that you should see circles in the sky.
And these circles are very concentrated in certain regions.
It's clearly not random, but nobody believes it because it goes against the conventional view.
And then Christoph Meissner and this is the first paper they had was to two Poles,
Pavel Neurovascular and Daniel and finally get they published the paper published in the monthly notices of the Royal Astronomical Society.
After having many, many referees coming back say, look, this is no good, you must do this test and must do this.
They did. The more they did, absolutely everything reversed. And finally, the editor wrote to them to say more or less, well,
I suppose we're going to have to accept your paper wasn't quite in those words, but it was more or less death.
And they said, we'll accept it on condition that in the first paragraph you say this might be a chance effect,
but it could be a chance if they're like anything and they give a chance.
The chance is about 124 to 1, that it's a real effect.
Nobody pays any attention. I asked Christoph what responses you have.
Zero. And so we've had zero. And so it's not like, you know, all sorts of angry people saying that on this wrong and that's wrong.
And how can you do this? And sure, it contradicts this deathless silence.
That's what we had. And now we have the thing on the archive.
We had a paper rejected already big from somebody complaining that this thing says this this this result is unbelievable.
They haven't checked to see that. It's really they're just unbelievable.
It is unbelievable if you believe these effects come in from inflation, because for inflation it would have to be the very last point of inflation.
Otherwise you wouldn't see a thing like this. And that's what they call a graceful exit.
They have a problem of getting rid of the how do you turn it off? How do you sell off?
Everywhere all at once? Pretty well all at once. That's a big challenge.
That was one of the reasons I had trouble believing it from the start.
So it contradicts that view. So that's why they say, I suppose this is unbelievable.
It's unbelievable on the basis of current cosmology.
But I guess picking up on that point more generally,
there are there have been times in the past where there was sort of conventional wisdom in physics that eventually,
as David said, do you think more generally there are other areas of physics that are currently being misconceived?
Yeah. I would say the main man is quantum mechanics.
Now, quantum mechanics, people say, is the most well-tested theory in physics.
I'm not sure if that's quite true.
You have to compare it with general relativity, the two big revolutions of 20th century physics, quantum mechanics, general relativity.
They're both extremely precisely tested with, you know, let's not make a comparison.
It's a bit different in each case. Extremely well tested.
Now, people normally think I think I'm just guessing, but they think, well, quantum mechanics is the physics of the small.
Big things are made of small things. Therefore, the physics of the small rules.
And therefore, if you have conflict between the two areas, you've got to get into quantum mechanics.
That would be fine if it weren't for the fact that quantum mechanics is self inconsistent.
Now I'm putting this in a rather strong way.
I mean, Einstein said it's incomplete. That was he was much more polite, as I say, was incomplete.
Schrödinger agreed with him. People may be familiar with the Schrödinger cat.
Schrödinger's cat was given by running as a demonstration.
Of what's wrong with quantum mechanics is more or less saying, look, an absurd thing like this is what my that's Schrödinger's equation predicts.
His own equation predicts that you could have a dead and alive cat, which is dead or alive at the same time.
Now, you never see such things. And people would say, Well, it's hard to make the coherence and environmental decoherence,
all that kind of stuff, but it never really solves the problem.
So where people are led correctly is that to what these rather many worlds kind of interpretation?
Okay, the cat is the dead one and the live one coexists in two separate worlds.
And we are led to believe that that's what quantum mechanics tell us.
Well, it is what quantum mechanics tells us. If you believe that this linear Schrödinger equation, evolution or unitary.
Yes, people call. Is absolutely universal.
Now, when I when I had my phase of going through many works myself, but I, I came to the conclusion that that's probably wrong and that the,
the unitary evolution which says the superpositions of these is quantum mechanics,
says that that you can have a particle which is here and here at the same time and you get.
That's true. I mean, you get two slits and it seems to go through with at once very strange.
And then I say, well, what's the limit to that? Could cricket balls me here, in here at the same time?
Well, according to quantum mechanics, yes. But you never see that.
So why don't you see that? Well, there's all sorts of things.
Well, they can't mess up with the decoherence and the atmosphere and all sorts of stuff, but that doesn't really explain it.
So I never was happy with that. I say never. That's wrong because I did have one time in my life and I believe the other thing.
But the thing is that when you start thinking about general relativity, you realise that there is a serious conflict between these superpositions,
that there's a problem with the very fundamental basis of general relativity,
which is principle of equivalence, the things that fall into that big, big mass and the small mass of all together,
Galileo, whoever it was, the astronaut who dropped these things on on the moon that fell together.
People expect that fundamental principle, which drove Einstein to his amazing theory, is inconsistent with quantum mechanics.
And so I was developing that idea, and that gives you a limit to when these quantum superpositions will persist.
And these are experiments which are. Being trying.
Well, some of them have been going on for several decades, I would say, and not yet with an answer.
So they've kind of borderline, but one can actually do with current technology.
But I guess this is something that you have done quite a number of times in your career.
It really is in terms of challenging conventional understanding of various areas of physics.
What sort of a frame of mind do you have to have to sort of the bravery to be able to do that?
Because in this program, I don't know if some.
Partly, I think, not worrying about what people are going to think about it,
which is public and not realising what people are going to think and thinking, okay, it's alright too and not realising what people's reactions are.
And I feel a little bit of happy about this. Quantum mechanics one because Einstein.
Yeah, I've got Einstein on my side.
Well, he was there a long time before me and Schrodinger, the boy, a little more surprisingly, Dirac was a to find a quote from there.
I can say yes, he. If you find the right quote, you can see he thought the same thing.
Quantum mechanics is a provisional theory. Hmm. Because of problems like this and other problems.
Okay. It works beautifully. Brilliantly. It must be pretty correct.
You have these experiments now, which it used to be, that quantum entanglements, this things happening here and here,
really know about each other, in a sense, and quantum entanglements, whether I think the record a few years ago was 173 kilometres or something.
Now it's, I don't know, thousands of kilometres.
It's experiments with satellites and so on. So quantum effects stretch over those distances.
I'm really glad they do because not that's not where I think things go wrong.
If they went wrong, they're my ideas would be wrong to say.
So it's it's it's got to be mass displacement.
You see, when you have a bit of mass doesn't have to be much a bit of mass displaced.
And it's here and here at the same time, but there's too much mass doing that. Then you're in trouble with general relativity.
And so that's where I think you're liable to see a difference.
But people say, Oh, we're quantum mechanics so beautifully tested, but they've never tested it this level.
Mm hmm. But you ask me, why do I. I think it's because it didn't.
Don't necessarily. I don't know. I think my father was a bit like that.
So he certainly had you know, he just thought what he thought.
And if it was against the current beliefs, that was all right.
So you sort of joked there about being big headed, but you're not afraid to change your mind either.
I mean, there's been several times where you've you've you've gone against what you've said in the past.
You were one of them. Was the the big bang thing?
Yeah. No, it was it was strange because I was quite early on Stephen Sacco but I don't know what he got wind of it.
And somewhere I went and was interviewed by him and this is Hardtalk.
BBC Hardtalk. Yeah, that's right. Absolutely. And so, you know, I went into the cinema and he went to the beginning.
He said to talk to me quietly. He said, Well, look, it's my job to be rude about people.
You see, usually I talk to politicians, but I'm afraid I'm going to have to be a bit rude.
Is that all right? So that's a person right by me. So at one point you said you said, why did you change your mind?
Say, because I used to believe the big bang was the beginning. And I'm saying it's not the beginning.
I had these theorems with Stephen Hawking, these theorems about singularities, and they had the same very general circumstances.
If you believe Einstein's theory, you've got to run in the singular state where things, things go wrong.
So that's the beginning. So, well, you have to have your way around that.
And I thought the reasons against it were, I mean,
against it just being the beginning were much stronger and the previous reasons I had for believing in it.
So yes, changing your mind is path. I think I said in the interview.
Well, I think being a scientist, I'm allowed to change my mind if the evidence starts to point the other way.
Hmm. Very true. I mean, you do have these quite bold ideas, I think it's fair to say.
I mean, I think you've you've described them as crazy ideas, actually, yourself.
How can you tell the difference between a good crazy idea and just a crazy idea?
Which is true with the thing I conformal cyclic cosmology.
See if you see that scheme. When I talked about, I used to call it outrageous or crazy.
Mainly because I wanted to get in there first because before other people started saying It's crazy, but it is a crazy idea.
But then so is inflation, you see. So, so. Okay, one crazy idea, I guess.
Another crazy idea. But there's something pretty crazy about the big bang.
And Einstein already at the early stages. He thought it was pretty crazy already.
He thought that and. Uh.
All these people who will later, I guess, and other people who'd got some of the equations Freedman and Lamantia solved in science equations said,
Look, there's this singularity at the end. And I said, Look, that's bad physics.
Then eventually had to be convinced that this made sense in the equations.
So he had to change his mind there. There's also a funny thing about the cosmological constant, you see,
because as I introduced it for the wrong reason, he wanted the universe static to expand.
And then people said, well, Hubble shows the universe expanding.
Woops. So I signed, retracted and said, Oh, it's the worst mistake I've ever made.
You see that cosmology. But it turns out to be true. See? Sorry, I going to say something else.
Yeah, I don't know.
I think. I think it probably was my father because he he he had the same sort of attitude,
and he didn't mind whether things were unconventional or what other people did.
As long as he had good reason for thinking what he thought. So do you think you can you can teach someone to challenge the status quo.
You have to be careful at the same time when there's a huge amount of evidence.
I get letters from people mails these days, from all sorts of people who put forward and they think,
you know, I be very sympathetic with them because I've done this sort of things.
You say that I would be sympathetic with their ideas, which are just about as crazy as mine.
But the trouble is that so often they come into conflict with well-established things.
And so it's all right to be crazy, but you got to be careful that they're not in conflict with well-established physical facts.
And I think that's a lot of people don't take that part of it into into consideration.
A difficult line to tread. It's yeah, it is difficult.
Now, we've spoken so far about mainly your ideas in physics.
Basically, you've had quite a big impact in a number of different fields.
I mean, computer science, artificial intelligence, but also in the art world.
So tell us, if you would, a little bit about your your collaboration or your work with Escher.
Yeah, well, this went back to,
I think in my second year as a graduate student when I was at Cambridge and the International Congress of Mathematicians was being held in Amsterdam.
And so I decided with some friends of mine, Oh, that'd be fun.
So I went to Amsterdam here, the great German violin, great figures there talking about mathematics.
And I remember seeing getting onto a bus at the point where Sean Wylie, who is a lecturer in topology,
told me when I was at Cambridge and he holding in his hand was this catalogue with this very strange looking picture.
You open it up. And there were these. It was just night and day with the birds flying one way, and they'd become birds flying the other way.
And one is night and the other day. And the spaces between the birds and the birds going the other way.
Oh, my God. What's that? And he said, Well, there's this exhibition going on in the Van Gogh Museum, and you I'm sure you'd be interested in that.
So I went to see this and I was absolutely blown off my feet.
And about these amazing pictures, particularly I remember the one called relativity,
where the people got staircases pointing at right angles to each other and so on on the other side of the stairs.
And I thought that was incredible. So I went away and I thought, Can I do something a little bit different?
What I've seen, which is impossible. So I started drawing pictures of bridges and rivers and all of that,
which went over each other in an impossible way and finally came up with this Triborough Bridge.
So I think we have a picture of this sort of pictures. I think navigate. This is your original drawing, I think.
Is it? Yes, I think that's the one. This in our article.
Yes. You see, I showed that to my father and he showed it to all his colleagues and they all got made the paper thought they made them feel.
You know, it's interesting, when chimpanzees apparently shown this, they also feel ill.
Really? Apparently, yes. I was told about this.
Yes. It's not just humans. How can you tell if a chimpanzee feels it?
I'm not sure. But I was told there were experiments that showed this.
Wow. Yeah, that's interesting. Apparently, they felt very uncomfortable saying these things, but I think.
Yeah, anyway, you see. So then my father started drawing buildings, which were impossible, and then he produced a staircase going round and round.
Neither of us were aware of Oscar rides.
His father had played with these things earlier, or in fact, people the bright bridle pictures and things which use these impossible structures.
In fact, she knew about some of them, too, but we decided we'd write an article on this, which we did with the triangle in the staircase.
And then we thought, Well, what journal will accept this? What's what's that subject?
So my father said, Well, I happened to know the editor of the British Journal of Psychology.
I'm pretty sure he would take it in. So we decided it was psychology.
So we decided this psychology. In fact, he did get it accepted for British Journal of Psychology and it's become psychology.
I've seen this in psychology books, but we sent a copy to ESA and gave credit to the Escher exhibition.
And then my father had a correspondence with Escher and then somewhat later I actually visited Escher
and he got I had some these puzzle pieces which I left with him and he gave me one of his prints,
which was a great honour to get one of these from him. But he eventually started including the triangle in his own words.
Yes. Where he from our article, the first thing he put in was the staircase and he had this one called ascending and he said,
I think we've got that as well. Actually, I've got that. Yes. That's the one. Yes.
That's this one of the monks going around in two directions. That's right. Now, that's an amazing picture.
Yeah. And then this one came later.
The worst of the waterfall came a bit later. Yes, that's based on the triangle.
But he, in the meantime had produced over dairy, which uses the same type of idea so that he goes was stimulated by these things and
I got stimulated by him also with sort of some of his repeating pictures and so on.
Hmm. And talking of repeating, it's like that link those two things.
Yeah. So this isn't a one off.
You're sort of, you know, playing around with these kind of shapes because, of course, many people will know about Penrose tiling.
Well, I used to fiddle around with just periodic ones a lot.
And as we have a picture as well as lots of. Oh, well, this is yes this is the come to that missing.
Okay. But the I just I used to draw in my notebooks, little complicated ones which have more and more complicated ways of repeating.
But they were repeating one. And these so these are shapes that have shapes that tile a plane with.
Yeah. And you're trying to make it so that you never repeat yourself. Well that came.
Yes. You see? Yes, that came a bit later, you see.
Unfortunately, it came just after Aysha died and my father died, both of whom would be very fascinated by these things.
It was a great shame. I mean, Aysha, I was a bit slow off the mark, I'm afraid, because she would appreciate it if she had.
First of all, I don't a pattern. I think it was I was trying to answer a letter and I couldn't bring myself to but there was a logo in the corner,
which was Pentagram with six pentagons inside.
And I thought, Well, suppose you repeat that several times.
And I thought of a rule for doing this, and I made a big picture and I sent that to a friend of mine who was in hospital just to cheer up a bit.
And then a little bit later I looked at this thing and I thought, Is there some way of forcing this picture with a jigsaw puzzle arrangement?
I don't know why I had that thought, but I suppose that's one of these things you might say a gas or something,
which I was giving it about 50% chance that that was.
And then I tried those things. I'm sure you could. So I needed about six different shapes there with four shapes.
And I needed three of the Pentagon's and one of the promises system and of the other shapes.
And, and then I could do it with six shapes.
And then I had a conversation with, with an American mathematician son in Cochin who was visiting in Oxford,
and he was talking about Rafael Robinson had six shapes, which would only tile the plane, no repeating way.
And he said, Rafa Robinson, somebody likes to get down to the smallest number possible.
So I said, Well, I can do it with five because I knew I had the six and I could.
I knew there was a way I could glued to the pieces together and I could do with five.
So I thought I could do with five. So I went home and I started thinking about it for a bit and I thought I got it down to four.
That's nice. Then I thought a bit more and I thought, Oh, I can do with two.
And I'll tell you my reaction to that. People ask me what was my reaction? I tell you what my reaction was.
Disappointment because this is just ridiculous.
It's it's suit. It's so simple. It must be, you know, Islamic designs or something.
They must have it. I mean, purely surely that's not new, but apparently it was new.
I mean, nobody has found it in Islamic designs. So you can see here what you have to do is have the two shapes that you can see.
They're both rhombus damaged shapes and they're slightly different.
There's a dark one and a light one. The light one is the thin rhombus and the fat rhombus is the dark one.
Now, each one has two stainless steel arcs on it.
And the thing is, you have to match the arcs. I was done with the arcs that nobody else has done this yet anywhere else, as far as I know.
But the originally I just put little arrows on the shape.
So you had to match the arrows and they would be non periodic.
The only way you can tile the entire plane right up to infinity is with a non-repeating pattern.
And each of these that one nice feature about it is if you go out to infinity and you take any finite subset of it,
that appears infinitely many times in all the others. So this is true here.
And instead of putting little arrows, you have to match the arcs.
And I like that because it brings out these circular features and nice things to look at.
So we have this low in the front of our building and and people might say, is this a special picture?
Well, any way of tiling with these patterns right out to infinity, we'll have that exact pattern in front of our building infinitely many times.
I quite like that you came up with this idea when you were looking at a stamp on a letter.
Were you essentially procrastinating, which I this I was definitely procrastinating, I tell you.
Yes. So do you make a distinction then between the the sort of the math that you do when
you're playing around procrastinating and the math that you do very seriously?
No. I mean, it's a good question because as you say, I would be doing some problem,
like when I was doing my Ph.D. and beating my head against the problem, which I'd never properly solved, and I'd keep coming back to that.
But then, you know, I say, Well, let's fiddle around with something else, which is fun, you see.
And then I go back to that problem. So I give you like that's that's the difference between procrastinating and doing what I'm supposed to be doing.
And maybe the procrastinating was in some ways more fruitful.
I don't know. That's an interesting question. I'm not sure the answer to that, but it certainly has been fruitful.
Yes, that's true. I think I think it probably was more.
I don't know. I'd have to go back through my old notebooks and see how many with the results of procrastination and how many were deliberate thought.
But I think you see, you can think along the route, you see you have a clear kind of route to say, well, that's the obvious thing follows.
Let's follow. And then you say about, well, let's try something else.
It's not something that comes back into the same old thing that's trying before I betray that already.
How about this though? It comes back against the same old thing, so it's not often you think something which is really different and that does
usually require a bit of maybe not thinking deliberately about the problem,
something else which suggests a connection. Oh, that's a little bit like that.
Oh, maybe it is something like that.
And it may be a little bit of thinking outside the box is that's what people say play I guess as well, just sort of playing with things.
Yeah, yeah. I'm okay. I'm going to come to the audience in just a second.
So if you have questions that you'd like to ask to Roger, then please think of them.
But I wanted to ask you just in the last couple of minutes I have with you,
I just wanted to ask you about your experience of maths at school, because I heard that you were moved down a class.
Roger I was moved down to class. Yes, I was a I think it's when I was eight years old.
I miss it a little while back.
This bit is a class in Canada, was school in Canada and the teacher there was one teacher who had what was called high grade,
high grade two and low grade three. I was in low grade three and she used to have us do sort of mental arithmetic.
You had to add multiple things and she was too quick for me. I just couldn't keep up with it.
So I was considered to be pretty stupid. I wasn't very good at arithmetic anyway.
I was very slow at it. So I always got lost and I don't know if it was that or not, but she considers I was too stupid.
And she moved me down to high grades to. After a few days, she thought maybe it was a little easier for me and I agreed to.
So she we we never got on.
I may say at one point there was a moment much later when a number of people, not just me, got moved up to Hybrid three instead.
I think she's just getting rid of me. I think she just thought I was too stupid to be able to be dealt with.
So she's very to get rid of me by moving into hybrid theory instead, which I found that I got on with the teacher better.
But then there was a I think it was a bit later there was a teacher who I thought
was pretty insightful because I didn't do all that well in the maths tests.
But he said, Look, I'm going to let you have as long as you like.
It was supposed to take the period at the end of the period people to have the papers.
It says, take you so long as you like. Don't consider that's the end of the test.
People go out and it was the play period after that looking longingly out of the window to see them playing around.
But I would keep going. I would keep going. Sometimes even the period after that, I was still going strong.
Then I'd do well. I'd get into the high nineties, you see, on 99, 100 or something on the, on these tests.
So I thought that was pretty good of him because he realised I was just too slow and it was partly because I wasn't very good at remembering things,
you know, times, tables, maybe I had to work it out each time.
So that was pretty slow. Obviously I had the idea.
But I didn't know how to do it quickly. And this this was with me for quite a long time.
I speeded up a bit after the years, but I was always pretty slow.
Yes. So in terms of if you could have a chat with your 17 year old self then or well,
I guess maybe more a message to people who are 17 now and kind of coming through the school system.
Yeah, but they do have to sit these times exams and more generally, what advice would you would you give them?
It has to be now, I think, rather than me then other people at that time, because maybe I've given them the same advice.
I'm not sure what advice. Spin off. Ask me that and I really don't know what advice to get people.
I think it's much more difficult now because of the horrendously competitive.
The way that schools are and schools and universities are tremendously competitive and you have this horrible conflict because on the one hand,
you've got to be objective. And how do you how are you objective?
Where do you make a test? Which is objective?
And then people, you know, they then they, you know, you can make up things which are new and which people have seen before, but that's pretty hard.
He's trying to make up a test. It's the right level and it's extremely hard to test without favouring those who've learnt by rote.
And so I think that the rote learning as opposed to the free thinking, unfortunately, I don't know,
is that whether it necessarily wins out at the level of exams for university, but it's it certainly gives people a great advantage.
So I think it's much harder now for people who just like to think on their own and not worry about exams too much and so on,
because it's become much more competitive. I don't know how to do with that question.
So maybe the answer is just to procrastinate more. Yeah, that's the well, that is when they have this need, give people extra time.
Let me say my 18 year old son benefits from that.
He also suffers from a big bit slow, too, but having a bit of extra time to do it was this was to his advantage in that.
Yeah. Okay. I think we'll come to the audience, though. We have got I'm going to say about 10 minutes or so.
Who would like to. Oh I've lots has going up. So anyway so we have microphones going round.
He may just have to. Oh there's a case on that. Any other microphones request.
First of all are you and I do. Oh, is that the question?
Yeah, I think so. I call myself an atheist, although some people worry about that.
Yes, you're right. Good question.
Is. Would you sign your book for me?
If you can find me? Yeah. Okay, let's.
Let's get a microphone. One just down here on the front verification.
We'll go one and then we'll come to you straight after. And then we'll go over the other side afterwards.
Go and shout, shout for us. So Jim Archuleta gave a very interesting.
Talk to us a lot about the idea of. Potentially.
I am saying quantum entanglement is wormholes. Do you have any thoughts on that?
Wormholes. You mean quantum entanglement?
I don't think wormholes are going to be any use, I'm afraid. Despite the film.
What was it? Interstellar. Yeah.
No, I. You see, if you really think about general relativity and you try to.
I think I'm partly responsible for wormholes. I'm afraid so.
Because I had a theorem which I proved that black holes produce singularities under very general circumstances.
And one of the conditions I had is that universe suddenly didn't.
Well, is that technically that you had what's called a quasi surface.
And if you want to put that in the ordinary language, you somehow the universe doesn't join on to another universe or something like that.
And so what had to settle that rather loose form?
And then some people picked up on that said, Oh, Penrose says, you might join under another universe.
And that's the answer. I disown it, so I don't think it makes much sense.
These things are not stable. And how on earth can you make a wormhole which is aimed where you want to go to?
I don't understand that at all. But it's quantum entanglement.
No, I don't think there's some nonlocality.
No, I mean, fascinating feature of quantum mechanics that you have separated objects which somehow know something about each other,
not enough that they can communicate with each other.
It's a very subtle thing, but more than them being independent, it's between that sort of gap of being independent.
They're not independent the slightly to do with each other,
but just not enough that they can send each other a signal, which is a pretty subtle thing.
But quantum mechanics exhibits this phenomenon. I think it tells you something quite different, and that is that space, time structure.
There's something much deeper going on in the physics,
which is a non-local description which gives you space time as a sort of approximation at a certain level.
But we don't have that yet. Okay. We have our second question very high.
So Paris, I'm wondering if you know about Sasha's recent work, about fine structure coefficient and what do you think about it?
If you know, fine structure, constant and so, so much so recently, Sartre has made a mark of it here.
Yeah, yeah. Some classes that he saw had all that out.
I prefer not to comment to that because I've never seen it. I have.
Yes, I've had I've heard this because I wasn't sure that he wasn't making this.
There's a claim that he didn't necessarily believe, but he says he's an old man.
He's allowed to do things like this. So quite right, too.
He has a lot of these amazing things in his history.
And so he's allowed to play around with things which might be a bit controversial.
I do not know. I've not seen it, so I can't comment on that. Okay, let's go over here.
One do do you have any female questioners? Would be nice.
Says no. Even one. There we go. Okay.
Can we go there? And then I'll come over that scientist. Yeah. Okay, good. Thank you.
The question was what would a model look like?
Infinite time where you see, if it's my cosmology, cosmology model, expansion of time, it's just this boundary.
I mean, this is where you have to do the mathematics, you see. I've got this model with this.
It's you squash infinity down, and then you stretch the big bang of the next iron out and it joins together.
Now, does that make sense? You rather have equations which govern this transition from one to the other.
So if you ask me that question, what's it like? Well, I got some equations which tell you what it looks like, but I am not going to write the data.
I don't have a nice place to write them down.
But you can use the point of view really is there's a way of looking at what happens in between, which means different things are important.
It's hard to say, but. I used to worry about this, you see.
Suppose you had a time capsule and you had people that said this is so strong that people
could keep in it and it would would survive right out to infinity or something like that.
But then in the model I have, the trouble with that is that the matter in it would gradually lose its mass and it would
stop and whatever images of it would evaporate away and it wouldn't hold itself together.
So somehow everything in the limit becomes without mass.
And so it doesn't know what it feels like to be. But still, I don't know.
How do I know? Okay, let's go over here.
So we could go. Well, your nearest microphone. That's okay.
First to you and then will come to you after. Hi. Oh, you.
I've asked lots of people this question and no one since your to give me an answer.
So doing. Do we know the answer is, is gravity a force or an effect?
No one seems to know the answer. No one's been able to answer that question to me. And I'm I am not a scientist.
Well, I can tell you what your current view on that is partly depends on which community you're in.
It's a very ironic thing. You see, according to Einstein's general theory of relativity, gravity is not a force.
It's the irony is, you see, how did the notion of force come by while Newton had his notions of force and all that stuff,
his second ball and whatever it was and all these things and the notion of force was real and the main candidate was gravity.
And you see, look, it works so beautifully. You get these orbits and you get everything.
Beautiful theory. And then Newton also thought, well, there must be other forces with different laws, maybe not inverse square learners.
And he looked at this in his principle, his study of different kinds of ways, of different kinds of attracted.
And now we have other kinds of forces in physics, strong force, the weak force and the electromagnetic force, the charged electric force.
And all these things are what we now call forces.
But when you go back to gravity and you say, well, you just fall freely and you and it goes on.
So it's not a force in the technical sense, all these other things.
There is a difference which I can't go into. There's a technical difference, which means that gravity is something a bit different.
And in order for it, the principle of equivalence, this is things falling together that the gravity they gather,
their thing of a big mass of little mass falling together is something which holds only for gravity.
If you had an electric charge or to electric charges,
and that you had gravity as air and electric charge at one end of the other, they would fall completely differently.
It's only for gravity in which you have this principle equivalent, so it's not a force in this refined way of looking.
However, you can treat it as a force, and often people do.
So the answer is a bit slippery out. So in a way that's a yeah.
You treat it as a force, you do your Newtonian mechanics,
which is works extremely well and you often don't think it's in the general relativity way and you treat it as a force just like every other force.
Quantum mechanics you probably put a term in the Hamiltonian is do with any other force and you get away with it.
So you get away with it being a force, but it's not really.
How about that? I think that's a bit. I think I think there's actually a gentleman in front of you last time.
So if I gave you that. And then. And then you. Hi, Roger. I've got two questions.
If I know you. We're running short on time, so you gotta think your best one and the two.
All right. You mentioned that you didn't like the term dark energy for cosmological constant.
If you had a a free hand to put a new name out there, a popular name, what would it be?
The trouble with cosmological constant got all the syllables to it. Dark energy.
Dark energy. Well, that's. It's for cosmological constant.
Yes, that's a bit longer. Lambda, how about that, lambda lambda.
That's only two syllables. Call it lambda. It's this capital inside.
Einstein had a little lambda, but the Capital One is what they use now.
How about lambda? It's lambda. Yeah, I think that's.
That's another bad name. Um, dark energy.
Just maybe it was this other question. Let me just answer. You see, there are two dark things.
This dark energy and this dark matter. Now, I don't like either of those terms because they're not dark.
That's transparent. You can see through them there is dust and that's dark.
And you can see pictures of the galaxies with a dark st right across the middle.
That's dark. But dark matter and dark energy.
No, they're not dark and transparent, but dark is a nice short word. So that's why it's.
See, I suppose. Is that how is this pick words for things.
Just the shortness of its the shortness with how it is. So if you had to say cosmological constant all the time, it's a bit of a mouthful, but lambda.
Yeah. Okay. From here on and from here on in. Okay.
I think we have one question here and then I'm going to ask one more. So who really will go?
We're going to first and then, you know, the rest of you have to fight.
And can you tell us a little about what motivated you to come up with the very elegant ideas behind Twister Theory?
And are you still working in that area? Oh, gosh.
I have the second question. That was two questions. Can I ask this?
The second one is yes, I am still working on it on that one, but it has been stuck for about 40 years and a certain problem.
But I think now you see there is me being big headed again.
I think we have the answer to the problem that's sticking as it was think called the Google problem,
which I think I know the way to do it, but it's pretty difficult to do so.
I need some spare time or a good graduate student or about six graduate students actually to work on that.
Elegance. Yes. Elegance was important. And it. But it's a complicated story.
I can't really go into this. It wasn't just one thing.
You see, there were if I could locate this page somewhere in one of my notebooks, I could remember what it is.
But I remember having a big page full of all sorts of connections between things, which seemed to me needed some unifying idea.
And that was what underlay twisted theory.
But that came about from. Okay.
The thing which. Really was the trigger was something very elegant in mathematics, which I knew which was Clifford Parallels.
People know about spheres. They're not so familiar, perhaps with spheres in four dimensions.
Known for dimensions, you have the analogue sphere. It's a three dimensional space, goes up and closes up on itself.
But there's a practice you can get a feeling for this thing. But Clifford described these things, which people refer to as Clifford Parallels.
So you have two things which are parallel. Well, they're parallel.
They never meet, you say, but you're going to have kinds of geometries,
like the Beltrami pictured of hyperbolic geometry where the parallels don't meet.
They get from further apart. You can have a geometry where they come and they do meet.
So if you have a an ordinary spherical surface and you try to make two lines, straight lines, what do they have to be?
Great circles. They gradually come and meet now in the sphere in three, a three sphere in four dimensions.
You can trust them a little bit so they don't meet. They just restrained each other.
And you can make them all circles.
And you fill the whole space with these circles and they twist around in this very, very beautiful way, which is known as Clifford PAGELS.
And I known about these things for a long time and they're very, very elegant mathematical structure.
So when I realised that this thing in physics which to do with, I can't go into it,
but there was these solutions of the maximus equations which also do the same thing,
and I realised that that was what I was looking for, to work, to see why they were.
That was what I was looking for. I'd have to go into something too complicated to explain here, but it was a revelation.
But I thought, gosh, and only because these are solutions of Maxwell's equations,
which overall Robinson, a colleague of mine, had been studying and he knew these things.
They were. Yeah, that's it. If I had to go back to back home and and work it out.
And it was it was. But then it took God back decades, decades to realise that did various things that he was supposed to do with great difficulty.
I'm still thinking on it now. Yes. Okay.
I realise I've gone horribly over time. So the last one has to be a really quick question.
Got a quick question? Okay, let's go.
Let's go for you there. Say if you could shout out the. Do you think it's going to be constrained further or.
Let me just repeat the question.
Questions they put the fact that it was the half life of a proton has been constrained to something like 10 to 30 years.
And then the last bit was, do you think that constrains?
Okay. Let me address that question. The thing I need for this scheme, is it out to the 30 years you might say, okay,
that's nothing compared with 10 to 100 years, which is what you need for the back house.
But the thing is, where the protons go, well, they go if that's what happens to them,
they decay into into positrons and something that the electric charge has to be preserved.
So even if they decay into less massive particles, which very possibly they do, it depends on your particle physics theory.
I'm quite prepared to believe they do decay in general years. I don't know.
I don't have a view on that. But they would decay because of and charge conservation into a charged particle.
So the problem I have is not so much with protons, but with these charged smallest mass particles.
We have the electron and the positron.
Now, what about neutrinos where they don't have charge? So I don't care too much about them.
They could they could be masses where they actually couldn't for a technical point.
But but it's really the the the positrons which are the problem.
Now, I'm not saying they decay because they've got nowhere to go.
What I am saying is that the very notion of mass fades out and that fade out comes about in this scheme.
It's not fully worked out, but it comes about in this scheme because of Lambda.
Now you see in particle physics people,
one of the first things they do in particle physics is to classify particles according to what's called the Poincaré group,
and this has what's called to Casimir.
Often I'm using technical jargon here, but it has these two very important things called Casimir operations, which commute.
Well, that's another technical term with all the other operators of the group, which means they have to be absolutely conserved.
What are they? Their mass and spin.
Now, mass, that means is a fundamental thing, which must if you have a stable particle, it must change.
But when you put lambda in, it changes the game.
It introduces something, a tiny little effect, which means what are the Casimir properties where they're not mass and spin?
I suppose spin probably is not so, but it's not mass. You find it's corrected.
There's something now. I don't know whether to make this into a good theory or not.
Nobody's done it as far as I know. But there's good reason to believe that when you put Lambda in,
you're going to have a change and that mass is not completely, absolutely constant and over timescales,
like when lambda starts to kick in, as they say that something like the current age of our universe from Big Bang to now,
which is what, about 4000 million years, that kind of time?
When is about the sort of scale when these kind of particles are going to start to?
Lose a bit of their mass. And then finally they would decay gradually and asymptotically become zero.
So that's that's the picture. Just to check when you say lambda there you do you talking about dark energy.
Yes. That's how are calling it that, you see, because it's neither dark nor and it's not necessarily good.
But you see some people use absolutely no. No. For a general public.
Yes. That Ducat is Stockholm. Okay. Unfortunately, I think we have to leave it there.
So a few of you, I think,
have got VIP wristbands and are invited to a drinks reception over in the mass gallery where so much it will be the rest of you.
I'm afraid you're stuck with me. If you come downstairs is the gallery can come and say hi.
But I think all that remains.
Oh, no, I need to say actually first we need to exit first if you give us a few seconds to leave before you eventually follow us.
But all that remains really is to say an enormous thank you, Roger, for joining us.
I think we could have gone on all night, actually. Fascinating. Thank you very much, indeed.
Thank you for that.