[MUSIC PLAYING]
Now, Phyllis set me
up rather nicely,
as I would have expected.
Yeah, this does
seem a little bit
like I'm reneging on a
position I adopted when I wrote
this book called Farewell
to Reality, which is highly
critical of string
theory, and in particular,
an extension or addendum to
string theory, which has become
obsessed with the notion that
we might live in a multiverse,
and dismissed it as physicists,
theoretical physicists
in particular, going
off on one, speculating
when they had no real
grounds for this speculation,
and certainly, no empirical
evidence to back up
anything they were saying.
And it seems like I'm going
against that position,
because I'm about to talk
to you now this evening
about another theory,
which by the way,
has no empirical
evidence to support it,
which is entirely contrived
from the imaginations
of theoretical physicists.
And you might say, well, Jim,
that's just a little bit wrong.
Now, my excuse is that one of
the modes of belief adopted
by many theoretical physicists
working in the string community
is that there is no alternative.
Well, we keep plugging away,
Jim, with string theory,
because there is no alternative.
If you want to do something
that transcends what's
known as the standard
model of particle physics
or the standard big
bang model of cosmology,
then we need string theory.
And I've taken umbrage at that.
I happen to have got to know
two of the key theorists
behind what I'm about to
tell you this evening.
I don't know them very
well, and I trust them.
And certainly, the claims that
they have made for this theory
that I'm going to talk
to you about tonight
does not, for me,
cross the boundary
between misleading, falsifying,
miss-selling claims.
Now, I have nevertheless felt
obliged to change slightly
the title for this
evening's talk.
And again, I hope you
won't be too disappointed.
The talk was advertised as why
space is quantum in nature.
And given that
I've just said this
is a theory for which there
is no empirical support,
I thought I better
change that to why space
might be quantum in nature.
And this is very much not
a theory of everything.
A theory of everything
would somehow
be one set of
mathematical equations
that somehow over here gives
us all the particles we know
that exist, over here would give
us the universe that we know
that exists, all in
one consistent set
of theoretical structures.
That theory still
eludes us today.
We have theories of big
bang cosmology based
on Einstein's general
theory of relativity, which
we'll talk about.
And we have quantum
field theories,
which we use to build something
called the standard model
of particle physics.
And so far, the two have
never really come together.
And here is one of the reasons.
Einstein's general theory of
relativity is about gravity,
or at least it provides
an explanation for what
we experience as gravity.
And it explains this in
terms of interactions
between mass and mass
energy and spacetime itself.
In the general
theory of relativity,
spacetime is dynamic.
There's an equation that says
space equals, time equals,
whereas most theories of
physics say this equals,
and space and time are
variables in that equation.
So this is very, very different
as far as theories of physics
is concerned.
And it is said to be
background independent.
So we don't presume the
pre-existence of space and time
when we use the general
theory of relativity.
And you'll have
an understanding,
I hope, in about 15
or 20 minutes or so
as to why that might be.
It applies to big
stuff and the universe
as a whole, planets,
stars, black holes.
All of these things that
we've come to terms with
and make life quite exciting
from a scientific perspective
are all described in terms
of Einstein's general theory
of relativity.
It's not a quantum theory.
And so the other piece of
the-- the other ingredient that
somehow needs to be folded in--
we're thinking of a
recipe in the kitchen,
we need to fold in
this ingredient-- is
quantum mechanics.
Problem is that quantum
mechanics describes
the composition and behaviour
of matter in terms of its
elementary constituents.
It means that these are
equations in which stuff equals
something in which
space and time,
but they're in the background.
They are assumed to be a...
Spacetime is passive.
It's assumed to be a
continuous form against which
physical events
happen, stuff happens.
And it applies to
tiny bits and pieces,
like electrons,
quarks, molecules, even
biological molecules.
But nevertheless,
small things that you
wouldn't find under
a microscope even.
And so the idea of
bringing together
the general theory
of galaxy, which
describes big stuff
in the universe,
and quantum mechanics,
which applies to very, very
small stuff, you can
already get the sense
as to why this might be tricky.
By the time you're down at the
level of tiny bits and pieces,
gravity is irrelevant down here.
Gravity is a very weak force.
It has no impact on electrons,
or quarks, or protons,
or neutrons.
By the time you're up at
the level of a black hole
or a planet or a star, do you
really need to think about
the behaviour of
individual electrons?
Probably no.
So the situation is that these
two great theories for which
there's lots of evidence to
support that they reflect
or represent the
real state of affairs
that we find in the physical
world can't be bought together.
Now what I'm going to
describe is a journey
that a few theorists have
taken over the course of about
the last 30 years
or so attempting
to bring them together.
Now this is a theory
for which, as I've said,
there's no empirical
evidence to support it.
And I think by the end,
you'll understand why that is.
At least, I hope you will.
And I also want to
be clear that it's
one of many different
approaches that can be taken.
And I want to give you a flavour
for why I think it's actually
a very instructive way to go.
So I'm going to start
with a question.
Now, you'll get used
to this from me.
These questions are
always rhetorical.
So you can put your hand
up and volunteer and answer
if you wish.
I'm not expecting you to.
So I'm going to ask,
where are you in space?
That seems like
an easy question.
Phil's already
jumping up and down
ready to put his arm in the air.
Well, what would
you do if you're
in a school science class?
You know what you'd do.
You'd start with a
coordinate system.
An x-coordinate, a
y-coordinate, a z-coordinate,
because we're in
three-dimensional space.
You'll know from
your physics class
that Newtonian mechanics,
Newton's theories of motion,
rely on the notion that
space and time are absolutes.
Again, things like force equals,
mass equals, energy equals,
and space and time are
variables in the equation.
And here we are in this
wonderful lecture theatre.
So that's where
you are in space.
Well, except that we know this
lecture theatre is in The Royal
Institution.
That's OK, we just make
our coordinate system
a bit bigger so it wraps
around the entire building.
But then you say,
wait, hang on, Jim.
The Royal Institution's
in London.
OK, we'll make our coordinate
system a bit bigger.
We'll wrap the entire
of London in it.
I had a word with Sadiq Khan.
I'm sure he won't mind.
OK?
But London is in the UK,
which is part of Europe.
OK, but that continent of Europe
is on the surface of the Earth.
We just make our
coordinate system
just that little bit bigger,
put it around the entire planet.
We don't really need a grant
for this, so that's OK.
We don't need funding.
But hang on, the Earth is just
the third planet from the Sun.
So we'll put the
coordinate framework
around the entire solar system.
You know where this
is going by now.
Solar system's in the Milky Way.
The Sun is simply one star
in probably 200 billion stars
in the Milky Way galaxy.
Although you can't
see it, there's
a little point on this
picture here that says Earth.
OK, we've drawn a
coordinate system now
around the entire
Milky Way galaxy.
But the Milky Way
is actually part
of a cluster of galaxies
known as the local group.
OK, we'll draw the
box around that.
Well, we might as well admit
now where we're going with this,
and say, OK, let's put
the whole universe.
You are here.
Now you see what we've done.
By assuming absolute
space and time,
we've ended up with a
coordinate system that goes
around the entire universe.
I think of it as a
kind of god's eye view,
almost as if you could
step out of the universe
and look down on all creation.
But we also need to
think about time.
Now I can't read
cosmic metronome
without thinking of some
1970s progressive rock band.
Have you heard the new album
from cosmic metronome, Jim?
It's really good.
But yeah, we need something
to orderly keep orderly time.
Otherwise, again, there's
no absolute measure
that we can make it work.
And I think you'll agree that
this is now starting to look
a little bit philosophical.
Newton, who was quite
comfortable with the notion
of absolute space and time
because his equations of motion
worked quite happily with that
assumption, was under fire.
His arch rival, Leibniz,
German philosopher,
criticised him for
this, accused him
of introducing occult forces.
That was, by the
way, a fancy way
of arguing in the
time of Newton.
If you wanted to dismiss some
mathematical philosopher's
notion, you'd just
accuse that person
of introducing occult forces
into their model of physics.
Einstein rejected-- 200 years
later, rejected this notion.
There were other reasons,
other experiments
had been done that suggested
the notion of absolute space
and time really wasn't
a very desirable notion.
Newton believed that
everything there is
should be in the universe.
And that meant that
this idea of having
a coordinate framework that
sits outside the universe
couldn't be right.
He introduced two principles
in a paper published in 1905.
The first is that
the laws of physics
should be the same for everyone.
That's a wonderful slice of
democracy for you right there.
The laws of physics should
be the same for everyone.
In other words, it doesn't
matter where you are or how
fast you're travelling,
if you're travelling with
a uniform speed, the laws of
physics that you measure should
be the same as the laws of
physics that someone who
remained sitting in
this room can measure.
Who's familiar with
The Lord of the Rings?
Book or film, I don't mind.
There's a great passage.
You weren't thinking of special
relativity when you read it,
I'm sure, or when you
saw it on the screen.
But it's when Pippin
rides on Shadowfax
in front of Gandalf in haste
from Edoras to Minas Tirith.
And there's a
passage that reads,
"as he fell slowly into sleep,
Pippin had a strange feeling.
He and Gandalf were
still as stone,
seated upon the statue
of a running horse,
while the world rolled
away beneath his feet
with a great noise of wind."
And the point about
the laws of physics
being the same for everyone
is that if you are moving
or if you're still, you can't
use the laws of physics,
you can't use physical
measurements to tell you which
is moving and which is still.
Speed is relative.
Now, you see that if
you're riding a horse,
that's an experience
that you can judge.
The horse needs hay,
it needs feeding
at the end of its long
journey, and there's evidence
that it was the horse that
was moving all the time.
But abstract it down
to inanimate particles,
objects moving through space and
time, and you can begin to see,
well, when this electron
goes from here to here,
is it really going
from here to here,
or is the thing observing
it moving from here to here,
and the electron is stationary?
This is what you have to start
torturing your mind with when
you start to want to make
space and time relative,
not absolute.
The other thing that
Einstein adopted,
the other principle was
that the speed of light
is finite and constant.
There were good reasons to
believe that this was the case.
Something called a
Michelson-Morley experiment up
on a mountain at the
end of the 19th century
had demonstrated
fairly unequivocally
that the speed of light
is a constant independent
of the speed of the
source of that light.
Now, if the speed of light
is finite and constant,
imagine you witness a
remarkable occurrence.
You're out in some remote
field in a thunderstorm,
and you witness two
bolts of lightning strike
simultaneously.
[THUNDER CRASHING]
This is you.
You have no hesitation.
Those bolts strike the
ground at the same time.
The light travelling, giving you
that information, travels very,
very quickly.
You don't, in fact, even sense a
delay between the bolt striking
and you seeing the bolt strike.
I, on the other hand--
[THUNDER CRASHING]
--from left to right at
a very, very fast speed,
a substantial fraction
of the speed of light.
Don't ask me how I'm doing that.
I see something quite different.
In this situation
with the twin bolts
striking the ground, because
I'm moving from left to right,
I see the right-hand
bolt strike first.
Because the light--
and remember,
I'm travelling now at a
substantial proportion
of the speed of light--
the light takes a
finite time to reach me,
and it gets to me sooner
because I've moved to the right.
Then the left-hand bolt, that
takes actually a bit longer,
because it has a bit
more ground to cover.
No big deal.
You see the lightning bolt
strike simultaneously.
I don't.
I see the right-hand
bolt strike first,
and then the left-hand bolt.
Who's right?
The laws of physics are
the same for everyone.
If you accept that
first principle,
and you accept that the speed
of light is finite and constant,
then you have no
choice but to say
there can be no such thing
as absolute simultaneity.
I might witness
two events that are
simultaneous in one frame of
reference, as it's called,
but there might be
another frame of reference
which is moving relative
to the other where
things aren't simultaneous.
And if I cannot get a sense
of there being absolute
simultaneity, it
means basically,
there is no such thing
as absolute time.
Now we all know that this--
out of this, this
little set of mind games
that Einstein played with
himself as he was actually
working as a patent clerk
in the patent office in Bern
in Switzerland resulted in
Einstein's special theory
of relativity published
in 1905, as I've said.
And one of the consequences is
that we know that time dilates.
Based on the speed with which
a frame of reference adopts,
space contracts.
And of course, we do know
about energy and mass
being equivalent.
These are all the results
of special relativity.
And here's one consequence of
Einstein's famous relation.
[BOMB EXPLODING]
But he wasn't quite done.
Special relativity
is called special.
When it was published, it
was the theory of relativity.
But it was realised that
work wasn't quite complete,
like a portrait that
hasn't quite been finished.
It's special
because acceleration
in special relativity
is "problematic".
I've put it in inverted commas.
It doesn't mean that you
can't do acceleration
in special relativity.
It's just that
acceleration doesn't
have the same status it had in
Newton's theories of motion.
The other thing it can't
account for is gravity.
Now, gravity was
still a mystery.
What keeps the Moon locked in
Earth's gravitational embrace?
When I do this, what pulls
the book to the ground?
Something mysterious
reaching up from the ground,
reaching up from the core of
the Earth, pulling it down?
This was the occult forces
that Leibniz referred to,
criticising Newton's
universal law of gravitation.
I will come and pick that up.
And then in November,
1907, two years
after publishing his
breakthrough paper,
Einstein had his
happiest thought, still
working in the patent--
by the way, he'd
had a promotion.
So that was OK.
He had his happiest thought.
He was sitting in a chair
in his patent office,
and suddenly, a
thought struck me.
If a man falls freely, he
would not feel his weight.
I was taken aback.
This simple thought experiment
made a deep impression on me.
Now, OK, Einstein was a genius.
I could have sat for
hours in my office
thinking that a man falls freely
not feeling his own weight,
and I'm afraid I would have
never have made the connection.
[MAN SCREAMING]
You want to see that again?
[MAN SCREAMING]
And what Einstein was led
to is something called
the equivalence principle.
Basically, gravity
and acceleration
are the same thing.
Gravitational mass, the mass
of the Moon and the Earth
and the way that in Newton's
universal law of gravitation
they're drawn together
by the force of gravity
is the same as acceleration.
So if we sit onboard a spaceship
accelerating at high velocity
through the atmosphere
or into outer space,
and we have the
unfortunate experience
of being left stranded
at the mercy of Earth's
gravitational pull,
then, in fact,
there's nothing to choose
between these circumstances.
There's an equivalence
between what
we experience as gravity,
what that book experienced,
and acceleration.
And if you have a mind
like Einstein's, you'll
work out that that is
actually because spacetime
itself can be curved.
Now at this stage,
our brains start
to melt. We start to get
boggled, because how can that
possibly be?
Well, bear in mind,
you can't see space.
I can't see space.
You can't see it.
We know we're in it,
but we can't see it.
We can't see time.
I can measure it.
I've got a watch.
But I can't see it.
How do I know what shape it is?
By definition.
And so when a book falls from
a height and hits the floor,
it's not the force of gravity
reaching up and pulling it down
towards the core of the Earth.
It can't hang on against
the local curvature
of spacetime in this room.
Don't look for it,
you won't find it.
But it's a way that Einstein
reconciled the fact that occult
forces can't possibly be right.
This is science we're
talking about, not magic.
And therefore, one
explanation for what
happens with gravitating
objects, objects
exposed to the
"force" of gravity--
I'm going to keep using scare
quotes when I say force--
is that they're sliding,
sliding down curved spacetime.
And if we got a planet
the size of the Earth,
it distorts spacetime around it.
This is the typical picture.
But it's a little
bit misleading,
because you can't
see space and time.
All you can do is
make measurements.
And there are measurements that
have been exquisite satellite
measurements of things that
are known as frame dragging.
And it's literally
the satellite,
gyroscopes on the satellite
being dragged by space
and time itself as
the Earth turns.
It drags spacetime
around with it.
Beautiful.
But don't overimagine it.
Now, John Wheeler summed
this up very, very neatly.
An American physicist
in the 1950s,
he wrote a book about
gravitation that says,
spacetime tells
matter how to move,
whilst matter tells
spacetime how to curve.
And the two are--
it's like a symbiosis, OK?
I got a heavy mass.
It curves spacetime.
And that spacetime tells me
how that mass, that matter
is going to move.
And what we get, we
get something called
gravitational time dilation.
It's different from
the time dilation
from special relativity.
That was because
we were going fast.
Now we're just
going up, fighting
against the gravitational
field, which
is the same thing as spacetime.
We get something called
gravitational redshift.
We get black holes.
We like those.
And we get gravitational waves.
All right, all good stuff.
All coming from what
was the general-- what
is the general
theory of relativity,
which Einstein finally figured
out how to write down in 1915.
A question you might
have is, fantastic.
What good is it?
It's those kind of-- those are
the kinds of times we live in.
And I just wondered,
did anyone here
use GPS on their phone,
maybe Google Maps
to find The Royal
Institution this evening?
Anybody?
Show of hands.
A few.
A few.
Fact is quite interesting,
the pioneers of GPS--
four American
engineers-- were actually
awarded the Queen Elizabeth
Engineering Prize today.
What I can tell you is if the
tiny atomic clocks onboard
the 24 satellites
that girdle the Earth
and create the GPS
system, if those clocks
weren't corrected using
special and general relativity,
we would run up
clock errors which
would give rise to distance
errors of a rate of about
11 kilometres per day.
Now I can guarantee you that if
you were relying on GPS to find
your way here
tonight and you were
working within an
11 kilometre radius
circle, good luck with that.
But that's per day.
After a week, it's useless.
You can't use it at all.
So if you want to know
why it's important,
next time you pull
out your phone,
use GPS, when you sail about,
use GPS, just remember,
without relativity,
you'd be lost.
Now that's relativity.
I hope you've got the sense
for what relativity is about.
Relativity is not
a quantum theory.
It assumes that spacetime,
although it curves,
is continuous.
It can be stretched like the
surface of a trampoline, which
is the analogy that
we often use when
we see the Earth as a
big heavy ball sitting
on a trampoline creating a dent,
and that's gravity, basically.
But Einstein was
also at the root
of another incredible
innovation.
You want to know why physicists
get so excited about Einstein?
It's because he did all
these incredible things.
He really did.
His latter years weren't
quite so productive, but boy,
he'd earned his badge of
honour already by 1915, 1930s.
Now Einstein and
de Broglie together
conspired to change
completely our understanding
of the little bits and pieces.
In 1905, he published a paper
separate from relativity
saying "monochromatic
light," basically--
monochromatic means the
same colour, so blue light,
if you want, green light--
"behaves as though the radiation
were a discontinuous medium
consisting of energy quanta."
Light waves can be particles.
We know what these particles
are called today, don't we?
Photons.
Next time you see
a photon torpedo
fired in an episode
of Star Trek,
blame Einstein for explaining
that light waves can
be particles.
Prince Louis, 5th Duke de
Broglie, then a few years later
in the early 1920s had an idea.
If light can be
waves and particles,
then can particles be waves?
And he suggested that the
idea could be generalised
by applying it to all
material particles,
and notably, to electrons.
Electrons can be waves.
Now that notion of
wave particle duality--
debates still rage about whether
it's a real thing or not--
but it's the root
of everything that
came afterwards that we know
today as quantum mechanics.
And quantum mechanics,
those waves now extended--
three-dimensional
extended objects,
if you want to think
about them like that,
are now thought of
as quantum fields,
a field just being a
fancy term for something
that stretches out.
And they underpinned this
thing called the standard model
of particle physics.
And here's the physicist's
equivalent of the chemist's
periodic table.
It's a list, a list of
ingredients, if you like,
about which all material
substance is composed.
You want to know how
to build a proton,
you take two up quarks,
you, on the left there,
and a down quark,
put them together,
bind them together with
force-carrying particles
called gluons, that's the little
g, and you've got a proton.
You want to build a neutron,
take two down quarks and an up
quark, bind them
together with gluons,
and you've got
yourself a neutron.
You want to build an atom,
you take your protons
and your neutrons and
you wrap electrons
in orbit around the nucleus.
Now you've got atoms.
You want molecules, get the
electrons outermost in atoms
to hang, to hook
together, and you've
got a chemical bond between
atoms, and so on, and so on.
Next thing you know, you've got
DNA, and you've got biology.
Now there are other
things in this list.
I don't to go into
too many details,
because I don't need everything.
I want though to leave
you with one thought.
You know that
experience that you
had as kids when you took
two small bar magnets--
you know what I'm about to say--
and you got the north
poles-- or the south poles,
it doesn't matter-- and you
tried to push them together.
You know what you experienced.
Some mysterious resistance.
There's nothing there to see,
and yet, the magnetic fields
resisted.
Flip them the other
way, and they attracted
and they snapped together.
Well, how does a
force like that work?
That's the
electromagnetic force.
And it's carried by photons.
So photons that are ubiquitous,
photons in this room,
they're responsible for
carrying electromagnetism
from one particle to the next.
And in this idea, let's
say we have two electrons,
and then we're going to
run them into each other.
So let's see what
happens when we do that.
They come in and they collide.
They exchange
virtual photon, which
doesn't sound like a
lightsaber in real life,
and they go off in
different directions.
So that's the way
we understand how
forces work in the standard
model of particle physics.
This is a force of repulsion.
Excuse me.
Two like charges
repel each other.
But what happens is
that force of repulsion
is felt through the
exchange of a photon.
And that exchange
pushes them apart.
OK, you've now more or less
got all the ingredients.
I know I promised you a lecture
on loop quantum gravity,
and I've said nothing at all
about quantum gravity yet.
And you're looking at your
watch saying, hang on,
Jim, get on with it.
OK.
But before I finish, let's just
have a quick look at what we
understand about the
universe, because that
will come in handy as well.
So you might be familiar
with a picture like this.
We begin-- [EXPLOSION]
--big bang.
There's a period, a very
snappy period of something
called cosmic inflation.
Very controversial, but
again, broadly accepted
for the time being
as something that
must have actually happened.
That kind of blows up the
universe from something
that's the size of a quantum
dot to something probably,
I don't know, the size of
a grapefruit or something,
the entire universe.
After 380,000 years,
we've got particles
that are formed, including
protons and electrons.
And for the first time
after 380,000 years,
these particles combine.
It's called recombination,
but forget the re.
They're combining
for the first time
in the history of the universe.
It should be called combination.
And when that happens, a whole
load of light that was bouncing
back and forth, these
electrically charged
particles-- remember,
virtual photons--
is released.
And we know these photons
today, this light today
as the cosmic microwave
background radiation.
At the temperature
of the universe then,
about 3,000 degrees,
some of this light
would have been visible light.
So the universe lit up.
Literally, let there be light.
But as the universe
expanded further and cooled,
that light faded.
That means the energy of
the photons was reduced.
And we have a period
called the dark ages.
Over time, maybe about
100 million years
after the Big Bang, we
begin to get the first stars
and galaxies.
So matter was beginning
to be condensed.
We get the first stars form.
As more and more gas
condenses into stars,
we start to get galaxies form.
We have to wait about
nine billion years
for our solar system to be
formed, along with Earth,
of course.
And right at the death,
we have Homo sapiens.
And judging from what we're
doing with the planet,
I guess there's a sense
in which we might merely
be a blip in the
history of the universe.
Now that spans 13.8 billion
years from start to finish,
from start to present day.
And that's the universe.
Now all of that knowledge,
all of that structure
is based on a combination of
general relativity and particle
physics, the standard
model of particle physics
in terms of our
understanding of how
the universe began and evolved.
It's not based on bringing
the two theories together.
We use quantum mechanics
over here, quantum field
theory over here, and we use
general relativity over here.
But we don't bring them together
to create a picture like this.
Quantum gravity, you knew
I'd get to it in the end.
Now, physicist Lee Smolin--
nice guy-- he published
a book about 2000,
so about 19 years ago, Three
Roads to Quantum Gravity.
So there are three
different ways
we can try and bring general
relativity and quantum
mechanics together under
one roof, as it were.
You can start with
these two structures.
And you can try starting
with quantum field theory
and trying to find a way to make
space and time emerge in it,
make it background independent.
Richard Feynman actually
had a go at that,
but then got hopelessly bogged
down and it didn't work.
But he wasn't disheartened.
That was about the 1960s.
You can say, well, forget
general relativity and quantum
mechanics.
I'm going to start over.
And a few brave souls have
actually taken that road.
I'll talk about one
of them later on.
Or you can do where I'm
going to talk about,
which is start with
general relativity,
and find a way to, as it
were, quantize this, introduce
a quantum element to it.
OK.
So the first thing
you need to do
is to start by reformulating
general relativity so
that it looks like a
quantum field theory.
Now, if you're not familiar
with the mathematics,
you might say, oh,
Jim, that's easy.
I could do that over breakfast.
Let me tell you, it's not easy.
Here's the problem.
When a particle moves
about on a flat surface,
we don't have to worry
about which way it points.
Now, why should I be
worried about which
why anything points?
Well, physics is full of
things called vectors.
An electron has a spin and
it points in a magnetic field
up or down.
So vectors are important.
And the way things point is
fundamental to the way physics
works.
So if I have a particle
pointing upwards,
let's say, and I move it about
on a flat surface, that's OK.
I can happily do that.
The way I move it about won't
affect the way it's pointing.
But in general relativity,
spacetime can be curved.
Well, here's the ultimate
curvature, a sphere.
Let's see what
happens to a vector
as we move it around a sphere.
Now I'm going to use a wickedly
ingenious invention here called
a south-pointing chariot.
The Chinese invented
these in the 3rd century.
This is before the
magnetic compass.
And if you wanted to have any
idea of where you were going,
you needed something.
So they came up with this
south-pointing chariot,
which has a carving on
the top that points,
and this ingenious gear
mechanism underneath that
means it keeps pointing
in that direction,
even though the cart may turn.
Isn't that clever?
So let's take our
south-pointing chariot
and wheel it all the
way to the equator,
starting from the North Pole.
We get it to the equator,
and then we turn to the east.
But remember, the south-pointing
chariot keeps pointing south.
OK, so we'll go a quarter of
the way around the equator,
and then we'll make
our way back home.
And you can see that by the time
we get back to the North Pole,
the chariot is now
pointing at right angles
to where it was pointing
when it set off.
Moving, although we haven't
done anything specifically
to the way it points,
moving it around the surface
of the sphere has changed the
orientation of the vector.
Now any theory based on
general relativity which
allows for spacetime
curvature has
to accept it's known as the
parallel transport of a vector.
Fortunately, in the early
1980s, two Indian theorists,
Amitabha Sen and Abhay
Ashtekar, came up
with a connection theory which
allowed general relativity
to be reformulated.
And when it was reformulated,
it looked exactly
like a quantum field theory.
Now again, I don't want
to take credit away
from Sen and Ashtekar who
worked on this, but Einstein,
and in fact, Austrian
physicist Erwin Schrodinger
were there before,
but they struggled
with the mathematics of these
connection type theories.
In fact, at one point, Einstein
wrote to Schrodinger and said,
it looks like a gift from
the devil's grandmother,
suggesting he wasn't
too enamoured of where
the maths was taking him.
But if it looks just like
a quantum field theory,
your next question is, well, a
quantum field theory of what,
exactly?
We're going to create a quantum
field theory of gravity.
We need objects for it to
be a theory of, don't we?
Well, the inspiration for
what this might be a theory of
came from something called
lattice quantum chromodynamics.
Now, quantum chromodynamics
is the field theory
for what's known as
the colour force,
and the colour force is what
binds quarks together inside
protons and neutrons.
What I didn't tell
you when I put up
the little equivalent
of the periodic table
was that quarks are
not only up and down,
charm and strange, top
and bottom, although I do
wish we'd stuck with
the original names
for those last two quarks,
which was truth and beauty.
In addition to flavour,
up, down, charmed, strange,
and so on, quarks
also possess colour.
Now physicists were running
out of ideas at this time,
so they just call them
red, green, and blue.
They're not literally
red, green, or blue, OK?
But they have quantum
properties that we characterise
as red, a red quark, a red
up quark, a green down quark,
and a blue up quark
together make a proton.
And what you can see
in these little threads
here with the arrows is the
gluons that bind them together.
And the way that
this force works
is in fact like
they're held in a net.
If I try to pull and
separate the quarks,
I'm actually going to
hit some resistance.
They're really held together
very, very strongly.
These force lines are loose when
the quarks are close together,
but if I try to pull them
apart, they kind of snap
and prevent me from
getting the quarks out.
Now the problem is the equations
of quantum chromodynamics
are really quite
complex, and they're
impossible to
solve analytically.
You won't find a
book where you've
got an answer at the end that
says, quark energy is, QED.
You need to solve these
equations on a computer.
And one of the techniques
used to solve these equations
on a computer is called
lattice quantum chromodynamics.
It's a technique.
Now, again, I couldn't
run calculations
of lattice QCD on my laptop.
I need a supercomputer and
a lot of supercomputer time.
In other words, I need a grant.
And you construct a lattice.
This is space, and
for that matter, time.
Entirely artificial.
I assume that I can
organise my quarks
and my gluons on this lattice.
I put the quarks at
the intersection points
of the lattice, and
I allow the gluons
to run between them in
all the different ways
that gluons can interact.
And the way that
lattice QCD works
is that I have a certain
distance between the lattice
points and I do a calculation.
I then shrink a little
bit that distance and I
do another calculation.
And I shrink it a bit more
and I do another calculation,
and so on and so on.
And then I extrapolate all the
way to zero lattice separation.
That is, a zero lattice link.
And that allows me
to get to something
that looks like a
continuum of space and time
without the need to actually
do a calculation at zero.
But look at this picture.
Of course, we've got the quarks.
We've got gluons running
around the lattice, the links
between the lattice points.
But over on the
left there, we've
actually got quarks
running around in a circle
without any--
we've got gluons-- sorry--
running around in a circle
without any quarks.
One of the reasons
that's possible
is that unlike a
photon, a photon
is not electrically charged.
So when I bring the two
electrons together that you saw
in an earlier slide, and a
virtual photon passes between
them and they move off
in a different direction,
that photon is not charged, but
the gluons have colour charge,
as it said.
So they not only
interact with quarks,
they interact with
themselves, which
is why quantum chromodynamics
is a bit of a beast.
Everything interacts
with everything else.
It's a real mess.
But it means that gluons
can run round in circles.
So here's a thought.
The physicist Kenneth
Wilson had the idea.
He was interested in trying to
create an analytical structure
for quantum chromodynamics.
And he wondered if it
might be possible to create
a situation whereby we
do without the quarks
and the lattice, and
all we've got left
then is the loops, the loops
of force running around
in a circle.
And this was the inspiration
for loop quantum gravity.
Except the loops are not gluons.
They're now loops of
gravitational "force",
in inverted commas.
OK.
So loop quantum gravity kicked
off in about the mid-80s.
And initially, it was all
about the loops and the way
that these intersect.
Then it became, well,
maybe they knot.
And so the physicists,
the theorists
involved reached for
the theory of knots.
I'm not going to say
that's a knotty problem.
So you've got some
characteristic knots here.
That's a trefoil knot
on the top left there.
Underneath, you've
got a trefoil knot,
but it's just going
round and round
so you can get a
perspective on it.
Next to it is something
called a Whitehead link.
Two loops, but twisted
together and knotted together
so they can't be separated.
And the final one there is
called the Borromean rings.
Fans of the Marvel cinematic
universe in the audience?
Knots feature very heavily
in Norse mythology.
So next time you look at an
older version of an Avengers
movie or a Thor movie, look
for the knot on Thor's hammer.
You'll find, in fact
they've used a trefoil know.
Something you can do
in an idle moment.
OK, then-- OK, maybe
what's important
is the way that we weave
these loops together.
Now this is a weave
created by taking
a whole bunch of key rings
and linking them together.
In fact, the Italian
theorist Carlo Rovelli
joked that he used all the
available key rings in Verona
to build this.
And then in the
final step, these
were replaced by something
called Penrose spin networks.
Now Roger Penrose was
Stephen Hawking's PhD advisor
at Cambridge.
He's a smart guy.
But he also likes--
he's that kind of theorist
that likes to plough
very much his own furrow.
And he invented this
structure primarily
as a way of satisfying what he
thought space ought to be like,
which is quantum in
nature, by coming up
with a network that
would do just that.
He didn't have any
physical significance
attached to these networks.
And so what happened is that
the theorist developing loop
quantum gravity found
the networks that Penrose
had invented some years
before entirely at a whim.
And that kind of thing
happens in science.
It's a happy set
of circumstances.
So I want to be clear, we
will look at these pictures
and imagine these loops
existing in space.
That's the way I've drawn them.
How else can I draw them?
But in fact, in loop quantum
gravity, these are space.
Space is these.
They don't exist in
space, they make space.
I know.
It's difficult to
get your head round.
And the two principal
architects--
there were other
theorists involved
that certainly
helped along the way.
The two principal
architects was--
you already know Lee
Smolin, American theorist
who now works in Perimeter
Institute in Canada.
And you, I'm sure, have heard of
Carlo Rovelli, Italian theorist
who's worked quite closely
with Lee Smolin over the years.
And this was all work that
the two forged together
in the mid-90s,
towards the mid-90s.
Now as I've said,
loop quantum gravity
implies that space itself
is quantum in nature.
What does that mean?
Well, here's a spin network.
It's got nodes and
it's got links.
And what Smolin and
Rovelli discovered
was that the maths
came out to tell them--
and I'm going to give you
some maths in a minute.
Be ready.
They realised that what was
actually happening was that
the nodes, the points in this
diagram is where you find
quanta of volume,
the volume of space.
No, I don't know either.
[LAUGHTER]
And along the links, you'll find
the quanta of area of space.
The inevitable
consequence of quantizing
Einstein's general
theory of relativity,
you make space
quantum in nature.
OK, so these are the
quantum states of space.
Now I'm waiting for a
cry from the audience.
But Jim, but what about time?
Oh, well, you see, in this
road to quantum gravity,
you lose time.
And I don't mean that in a
sense you wake up one morning
and you say, what
happened to the last year?
Although I'm sure
that does happen.
I mean time disappears
from the equations.
It's known as the
problem of frozen time.
So these quantum states of
space, they're quantum states,
and so there's a sense
in which they fluctuate,
that they get the jitters.
Something called Heisenberg's
uncertainty principle
means they don't stay still.
They move about.
We need to find a way to put
time back into this picture.
And what Smolin and
Rovelli and others did
was to imagine that fluctuations
in the quantum states of space
create the appearance of time.
What happens is that as we
change the number of nodes,
never mind the number of
links, the clock ticks.
And that represents an
advancement in time.
So we see something
like this going on.
As these quantum states
of space bubble and froth,
we get the illusion
of time emerging.
I'm going to come back to this.
All right, now, again,
I want to remind you
that there's an important
question of scale here.
What I don't want you
to do is to say, look,
I went to The Royal
Institution this evening,
and I had a great talk from Jim.
He told us all about the
quantum states of space,
and I'm going to look for them.
I'm going to look for them.
You won't find them for
a very simple reason.
Now ignore the maths.
That's area.
This little guy here is
called the Planck length.
And it appears squared
in this equation.
And j into j plus
1 square root of
is just the quantum number of
space, area of space, actually.
It's the Planck length
that I'm interested in.
The Planck length, it's
called that because, in fact,
it was Max Planck back in
the early 20th century who
realised, in fact, that with the
discovery of his own constant,
which is h bar here,
is h divided by 2 pi,
Planck's constant
divided by 2 pi.
g is Newton's
gravitational constant,
and c is the speed of light.
He realised that by combining
these fundamental physical
constants he could come up
with some fundamental units
of length, time, energy, mass.
Now you can see the Planck
length appears squared
in this equation for area.
Don't worry about the equation.
It's incredibly small.
A Planck length is 1.6 times
10 to the minus 33 centimetres.
So that's naught,
0.33 naughts, 16.
No, no, don't even try
and think about it.
The loops or
networks are presumed
to exist on this scale.
You won't find them.
Don't look for them.
The Planck length
is to a height--
I did some jiggling
around with scales.
The Planck length is
to a hydrogen atom
what a large amoeba is
to the Milky galaxy.
You won't find them.
A single proton
contains about 10
to the power 65
quanta of volume.
To all intents and purposes,
a proton doesn't care.
An amoeba doesn't care.
The Milky Way galaxy
certainly doesn't
care that space is
quantized at this level.
So you might then
have a perfectly
realistic and legitimate
question, so, Jim, honestly,
why?
Why?
Well, let's take the
theory at face value
and see what it tells us.
Particle physicists
love particles, OK?
That's what makes them tick.
That's why they like to build
ever larger colliders so they
can see more particles.
And it's long been thought that
the force-carrying particle
for gravity is this
thing called a graviton.
Just like the photon carries
the electromagnetic force when
two electrons come
together, when two masses,
when two objects
come together, they
transfer gravitons
between them, and that
carries the force of gravity.
That's what particle
physicists tend to think.
But loop quantum gravity says
that gravitons are actually
so-called pseudo particles.
They're not force particles.
And to get some sense
for what that means,
I know that you saw in the media
a few years ago these fantastic
reports of gravitational waves.
Remember that?
Yep.
And you couldn't barely believe
what the scientists were
telling you, because
they said these
are gravitational waves produced
by two black holes merging.
My god, really?
But yes, so here are
two black holes spinning
around each other and merging.
And as they do so, remember,
we can detect frame
dragging around the Earth.
So when you're talking
about massive objects
like black holes, they
really do mess about
with the fabric of space
time, creating waves, ripples.
Now, Einstein, de Broglie,
remember what they said.
If we can have
waves, then there are
associated particles in that.
And those associated
particles would be gravitons.
So loop quantum gravity
has quite a nice way
of treating gravitons as in
effect, pseudo particles,
not force particles.
Particles like electrons
can be modelled
as open loops which
puncture the spin network
and move around on it.
So this isn't just
some kind of abstract.
That theory sits over
there, and meanwhile, we
get on with the good stuff.
It is possible to start
to bring particles
from the standard
model and put them
onto this model of spacetime
from loop quantum gravity,
and that's a great step forward.
The theory can be
used to calculate
the entropy of a black hole.
Don't worry about
what entropy is.
Anybody read Hawking's
A Brief History of Time?
Did you get through it
all the way to the end?
You might remember a
chapter, it was titled
Black Holes Ain't so Black.
It bugged him, but
he realised, in fact,
that black holes
have an entropy,
and things with an entropy
have a temperature, Which.
Means they glow.
Very upsetting, because
how can a black hole glow?
Well, it's very subtle.
It's called Hawking radiation.
And it's so weak that
you can barely detect it
above the cosmic
background radiation that
pervades the whole universe.
But nevertheless,
he was reconciled--
this little equation
on the right-hand side
here is called a
Bekenstein-Hawking formula
for the entropy of a black
hole, and it's really simple.
Entropy is equal to
area, the surface area
of the black hole divided by 4.
And here's this Planck
length squared again.
OK, so loop quantum gravity,
remember, we have networks,
spin networks.
Because this pervades the
entire universe, remember,
this is space and time.
Where the lines puncture
the surface of a black hole,
they endow the surface
with some area.
Remember, the links are where
we find the quanta of area.
Now you calculate the
entropy not by working out
how many links puncture the
surface of a black hole,
but how many different
ways they can puncture
the surface of a black hole.
And that gives you a
handle on the entropy.
And what you get is the
Bekenstein-Hawking formula.
Yay.
The theory eliminates
singularities.
Now I haven't
mentioned these yet,
but the thing about
general relativity
is it's a continuous theory.
It assumes a continuum
of space and time.
And theories like that, they
can give rise to infinities,
things can become
infinitesimally
small or infinitely large.
It's just in the
nature of the maths.
It's the nature of the beast.
Penrose and Hawking,
in fact, together,
produced various
theorems in the 1970s
to say that there was no
way you could avoid these.
If you look at the centre of
a black hole or at the origin
point of the big bang,
origin of the universe,
you'd expect to
find a singularity,
things that have gone infinite.
Now there's actually no such
thing as infinity in nature,
so something has gone wrong.
Loop quantum gravity says
that spacetime is granular.
It's got bits.
I can have an ultimate unit
of space, volume, or area.
I can't squeeze
that any further.
It's a bit that it's like an
electron, a single electron
or a single photon.
I can't get smaller than that.
I can't divide that any smaller.
And it means there can be no
such thing as singularities.
There has to be--
if the universe collapses down
or begins in a very tight,
highly dense object, it
cannot be a singularity,
because quantum nature of
space won't allow that.
In actual fact, what
Abhay Ashtekar discovered
was an intriguing possibility.
We talk about the big bang
origin of the universe,
and we've got lots
of evidence that
suggests that that's indeed--
although that evidence
comes from moments
after the big bang, by the
way, not the big bang itself.
That remains mysterious.
That's when space and time
were supposed to have begun.
But loop quantum cosmology,
the universe equivalent
based on loop
quantum gravity says
that there could be
no singularities,
and maybe, therefore, the
universe begin not with a bang,
but a bounce.
In other words, there
may have been a universe
before that condensed,
contracted, compressed,
and once it ran up against
the ultimate indivisible
quantum of space, it bounced.
Make of that what you will.
However, loop quantum
cosmology does predict
some interesting things.
I don't think this will be
by any means definitive.
And if you want to
know why I think that,
I can maybe tell you later.
This, by the way, at the bottom
is a picture, probably not
a familiar picture, of the
cosmic background radiation.
But what we've got
plotted here is the square
of the temperature
variation with something
called angular scale.
So imagine the
universe as a sphere,
and we're looking at different
angles along that sphere.
Now these peaks that you
can see, three of them,
one tall one, and then two
of equal size, equal height,
they're actually quite
characteristic of the equations
of hydrodynamics.
And because the cosmic
background radiation
was formed 380,000 years
after the big bang,
it's left an imprint
of what was going
on in the universe at that time.
And what these are are sound
waves bouncing back and forth
in the early universe,
acoustic waves.
I like to think the universe
was singing, or maybe screaming.
[SCREAMING]
I leave you to decide.
But notice in this
picture, a difference.
The standard model
of big bang cosmology
based on general relativity
predicts a slightly different
curve at high angular scale.
Loop quantum cosmology
predicts the lower curve.
And as you can see, the
error bars on the data,
most recent data from
the Planck satellite,
don't allow us to be able to
make a choice at this stage.
But when, with future
satellite missions,
we have the equivalent
of DNA fingerprinting
at this high angular
scale, who knows?
My feeling is it
won't be definitive,
because it will probably
be easy to come up
with a theory that will
reproduce whatever experiments
says, but hey.
Finally, I have maybe
painted a picture
that Smolin and Rovelli,
they're not only
great scientific collaborators,
they're also good friends.
But don't take that to mean
they agree on everything.
In fact, I picked up
a beautiful phrase,
I think from Lee Smolin's
wife, I think, Dina.
If you both agreed about
everything, then one of you
would be redundant.
Which I think is
a beautiful way--
maybe it's the way to
understand a marriage.
I've said this approach
to quantum gravity
means we lose time.
It disappears from
the equations.
Carlo Rovelli-- again, you
might be familiar already
with his book, The
Order of Time--
has no problem with that.
Einstein had no problem
with that, by the way.
"One after another, the
characteristic features of time
have proved to be
approximations,
mistakes determined
by our perspective,
just like the
flatness of the Earth
or the revolving of the Sun.
The growth of our knowledge has
led to the slow disintegration
of our notion of time."
Ah, but Smolin doesn't agree.
He published a book a little
while ago called Time Reborn.
"I no longer believe
that time is unreal.
In fact, I have swung
to the opposite view.
Not only is time real, but
nothing we know or experience
gets closer to the
heart of nature
than the reality of time.
I believe that to make
sense of the universe,
we must embrace the reality
of time in a new way."
That comes with a
fairly hefty trade-off,
by the way, because
if time is real,
then space is an illusion.
So just so you know.
I'll leave you with
a couple of quotes.
You've probably got the idea
that I'm a big fan of Einstein.
Still, one of my favourite
Einstein quotes is this one.
"Reality is an illusion,
albeit a very persistent one."
But maybe just a
little better than that
is the great science
fiction writer--
American science fiction
writer Philip K Dick
who once said, "reality is that
which when you stop believing
in it, doesn't go away."
Now, if you wouldn't
mind exiting
through the gift shop, where
I believe copies of this book
are available.
I do want to take
this last moment
to say a big, big thanks
to both Lee and Carlo,
who were reading
over my shoulder
while I wrote the
manuscript for this book.
We finished off
with a Skype call
where we chatted
together, looked back
over the history
of collaboration,
and looked a little bit
forward to the future.
And Lee quoted a guy
called George Braque, who
worked with Pablo Picasso
and pioneered cubism.
And Braque said it was
like being roped together
on a mountain, and Lee
thinks that's a good aphorism
for his own collaboration
with Carlo Rovelli,
like being roped
together on a mountain.
I also have to thank these good
folks, busy, busy scientists
who gave of their valuable
time to read the manuscript
and made sure I hadn't
committed too many howlers,
the folks at Oxford
University Press who
helped make the book a reality.
And you can find me on my web
page or follow me on Twitter.
Thank you very much.
[APPLAUSE]
