Time.
Time does not exist.
I have 15 minutes to convince you of it.
Take two watches.
Hopefully better than these old-fashioned pocket watches of my grandfather.
A bit more precise, okay?
Make sure that they show the same time.
They show the same time, the same as here,
around 2:45.
Now, try raising one of them and lowering the other.
Keep them like that for a while:
one, two, three.
Then bring them back together
and see what they show.
If the watches are a little more precise than these,
they no longer show the same time.
The watch held higher reads faster,
and the watch held lower reads slower.
This is a fact.
Obviously, with watches like these, it's not very easy to see that.
They're not precise enough.
However, today there exist extremely precise watches.
That's one of them.
It's the Boulder atomic clock in Colorado,
one of those that are used to fix the official time in the United States.
We have similar ones in Italy, in Florence, lots.
There are also smaller versions, more commercial versions,
that are good enough to observe this effect with.
They are in small boxes.
If you take one and put it low down,
and put another high up,
when you bring them back together again, they no longer show the same time.
Time goes faster higher up,
and slower lower down.
It's a fact.
For instance,
imagine you have a twin brother,
you are the same age, you grew up together.
Imagine that your brother goes to live in the mountains,
and you go to live by the sea.
If much later you meet up again,
your brother will be older, and you will be younger than he.
It's not just watches that are influenced
by the strength of the gravitational field,
but all phenomena connected with time.
Aging, the speed of our thoughts, a flower coming into bloom.
Everything.
A swinging pendulum.
Time goes faster higher up, and slower lower down.
You see, when at the beginning of the 90s,
the first satellites for GPS were sent into orbit,
for the sat nav devices we have in our cars
to tell us where we are,
physicists told engineers,
"Be careful, up there, on the satellites, time goes faster."
To work, the device needs to receive messages from a satellite.
On satellites, there's a clock.
The clock goes faster than what we would expect down here,
so they'd need to take that into account.
The engineers said, "Oh, okay."
However, the entire project was, and is, a project of the American military.
GPS is operated by the US military.
So, heading up the project were American generals.
The American generals were army generals.
When told time goes slower, faster, etc., their response was:
"Time goes slower? Faster? I don't believe it."
So, the first satellites were sent up with a double system
that could work taking or not taking into account this effect.
The version that didn't take this effect into account didn't work.
The GPS would not work
if it didn't take into account the fact that up there time went faster.
So, even the American generals could not be other than convinced
that time went faster up there.
What does this mean?
It means time is not what we imagine it to be.
We cannot think of a unique time that flows the same everywhere.
Somehow, we need to think
that higher up, lower down, more to the right, more to the left,
for who moves more slowly, for who moves faster,
time goes at different speeds.
We need to change how we see the world,
from a single clock beating the time,
to many clocks, each with its own time.
The world is a choir of these clocks that go at different speeds.
Strange and difficult.
But if you think about it,
it's not the first time we've changed how we see the world, is it?
Is the Earth flat or round?
This room, is it stationary or is it moving?
Stationary.
No, we know it's moving, travelling very fast around the sun.
(Hesitation)
A swallow comes from another swallow,
its mother was a swallow, its grandmother, and so on,
swallow, swallow, swallow.
I was born from a human being, who was born from another human being,
from another human being.
So it's impossible I and a swallow share the same ancestors.
Not the case.
We and the swallows have the same, common ancestors.
So, what's this all about?
We tend to develop simple, natural ideas about the world
that are wrong.
Not because they are not adaptable to our lives.
They are adaptable to our lives, indeed that's the case;
they refer to, are good on, our scale.
They are no longer good when we look at life,
not on a scale of 10, 100 or 1,000 years, but on a scale of millions of years,
or when we think about what happens very far away,
with very fast, very small, or very big objects.
There's an example I really like and think useful in understanding time,
that about high and low, right?
Things fall from high to low.
That is high, and this is low.
It's one of the basic structures of the world as we see it.
We organize our world in terms of high and low, right?
So in the universe, there's high and low.
Okay? A universal direction, which is higher or lower.
This isn't entirely true.
What's high here is low in Sydney.
What's more, if we leave the Earth, there's not really high and low.
Astronauts, we saw the pictures, they move in any direction.
The notion of high and low doesn't exist out there in the universe;
it's a notion appropriate only here to us.
It's convenient and useful to organize phenomena around us,
but it becomes useless and meaningless the moment we leave our planet
and go to the moon, as our astronauts did.
In all these cases, we find our simple way of looking at the world is wrong,
and things are a little more complicated.
The nice thing is that in all these cases, including time -
I'm coming back to time -
Nowadays, it's easy to think that the Earth is round,
and that outside of it there's no high or low.
We've seen the pictures taken by the astronauts of Apollo 11
on their way to the moon.
The Earth is round.
But we knew that before.
Some of us already knew that the Earth was round, right?
Aristotle knew, Anaximander knew that the Earth was round and flew.
The Earth is moving.
Now we've seen it from beyond it,
but Galileo and Copernicus deduced it without needing to see it.
Darwin didn't see species change; he deduced it.
How did they deduce these things?
Simply by starting with what we know about the world,
observing, and putting together known facts,
and noticing that the known facts can be better understood
if we change our conception of the structure of,
our way of looking at, the world.
In this way, all these people came to understand something new,
something crucial.
The fact that time goes slower lower down and faster higher up,
that we nowadays observe:
we just need to buy those very precise clocks,
and anyone can see it's the case.
It was understood before it was observed,
by Einstein,
almost 100 years ago, 97 years ago, in 1915,
who was simply trying to clarify the ideas of the physics of the world of his day.
On one hand, Einstein had Newton's theory, the great theories of mechanics;
on the other, he had electromagnetism.
Endeavouring to combine these two things
in order to have a coherent picture of the world,
he realized that time doesn't go at the same rate for everyone,
that there are many different times, that time goes at different rates.
This was 100 years ago.
The same thing is happening today.
Because, today, we are again in the same situation.
Today, we have the great inheritance of Einstein's very beautiful theories,
which, for a century, we have discovered work perfectly.
We have confirmed them,
we've seen there are black holes, etc.
Alongside it, throughout the 20th century, quantum mechanics was advancing.
This morning we heard Marco telling us about the world of particle physics,
all in terms of quantum mechanics, an outstanding theory of motion,
but which doesn't work well with Einstein's theories,
with general relativity.
So science tried once again with endeavors
to use what we know to try to gain greater insight.
In 1963, two brilliant America scientists,
Joe Wheeler, the man in the black and while photo,
and Bryce DeWitt, the man in the color photo,
simply took Einstein's general relativity equation,
Einstein's theories,
and quantum mechanics,
and put them together and wrote an equation
that Wheeler called "DeWitt's Equation," and Dewitt "Wheeler's Equation,"
and everyone else, a bit fed up, "Wheeler-DeWitt's Equation."
It's that one there, but I won't go into details.
An equation that to start with was very confusing.
It was studied a lot, and today we continue to study it.
Today, the theory has been developed,
and we can write it more precisely,
and we can better understand its significance.
That's what I work at.
This equation has a characteristic that was stunning at the time,
and left everyone open-mouthed.
This equation was created putting together all that we know about the world
from one end to the other.
It has the characteristic as follows.
All equations, if you remember something of school physics,
all the important fundamental equations of physics
from Galileo to Newton, Maxwell, Einstein, and so on,
they say how things change with time -
back to time again -
and so they all have "t," time, in them, whether it's velocity or acceleration,
changes in time, there's always time in the equations.
This equation here doesn't have time in it,
the variable "time" has been left out, it's vanished, it's not there.
It's as if trying to write all we know about the world,
time is no longer there.
What does this mean?
That is what I'll try to explain in the remaining four minutes.
If you listen to me carefully,
I hope I'll be able to make clear to you
what it means to write an equation to describe the world without time.
Let's go back to simpler physics.
The first thing that those who enroll in physics study
is how a pendulum moves, for example, or something else that moves.
We need to describe how its position changes with time.
So we need to measure the position and the time with a clock, right?
We look at the position and what the clock reads,
make a chart,
and write an equation that describes how the position changes with time.
But, here, we are not observing time;
here, we are looking at the hand's position, right?
The hand is moving,
and this is moving.
We're just describing how this position shifts
when the hand's position shifts.
And if you think about it, it's what we always do.
We always describe something as a function of something else.
Clocks are just things among others that move,
but that have the characteristic of all moving together ...
more or less all together.
What does this mean?
It means that we can do without time
and just talk in terms of how the pendulum moves
as a function of the position of the hand.
Instead of saying, "I woke up at 8 this morning,"
I could say that I woke up when the sun was in a given position,
that I started talking the moment the lights went off,
and so on and so forth,
with no reference to time at all.
Let's take "high" and "low," for example.
I could say this is high, and this is low,
or I could avoid mentioning "high" or "low."
I could say this is towards that bright light there,
and this is towards the red circle underneath me.
If I'm on Earth, I complicate life.
But if I'm an astronaut in a capsule and say to my friend,
"Hey, Anderson, could you pass me that clock up there?"
he'll reply, "Where's up there?"
But if I say "the one towards the red mat" instead,
he'll be, "Oh, the one towards the red mat."
So the notion of high or low is meaningless when we leave the Earth.
Well, the notion of time becomes meaningless, disappears,
as soon as I leave normal space
and enter one where I have to use quantum gravity, this equation here.
And where is this space?
Where things are extremely big or extremely small:
there where we're still without clear ideas on the world.
If we observe the extremely small,
observe on an extremely small scale,
space, space itself fluctuates, spikes,
it's like a stormy sea,
but what it is, is space-time in the extremely small,
as if time jumps.
These two clocks, each weaving its own path at a different speed,
in the smallest of places, they go forward and backward, they move, etc.
On this extremely small scale,
our notion of time is no longer good, no longer useful, no longer works well.
So we have to re-describe the world in terms of those variables,
one by one, without reference to time,
as if we had a lot of clocks that had lost their hands,
and we could only see how one moves in respect to the other.
Imagine, to give you an idea,
how we think about the world as a combination of things that move,
that change, that dance, all together,
in time to a conductor of an orchestra
who gives the beat: 1, 2, 1, 2 ... all together ... 1, 2.
This picture no longer works for the small.
In the extremely small, there's no unique beat for all,
and the world is as if it were a dance of every microelement with its neighbor,
but not all together.
What's the moral of this whole story?
Time is a useful concept,
it organizes our daily experiences,
but it is not a fundamental concept.
Just as "high" and "low" are very useful concepts,
but don't work anymore when we leave our everyday surroundings.
This is true of a lot of things.
It's this that I love about science.
What science teaches us is that our image of the world,
our perception of the world,
is very often wrong, limited,
working only in our usual surroundings.
The human race is like someone born in a small town
where everyone behaves in the same way,
until they leave and say, "Oh, but there's more.
We can eat different things, say different things,
speak different languages, have different ideas."
Humanity leaves behind the smallness of its thoughts
and discovers that everything's different:
species transform from one to another,
"high" and "low" are not real,
time is not what it seems.
The world is bigger, more beautiful, more diverse, and more thought-provoking
than what it seems at first sight,
this thing, a little banal, with "high" and "low,"
with people that move, and rocks that fall.
It's much richer.
And to understand that, we have little need of ancient knowledge.
Ancient knowledge, all ancient knowledge,
what our forefathers taught us,
really only applies here.
If we look a little further, it's no longer valid.
As was said in the first video today, the universe is endless.
We were born in a tiny, little corner of it,
have ideas that apply only to this tiny, little corner,
when we then start to look a little further afield.
I think what we discover at each step -
and I'm concluding -
is far more extensive, more beautiful, more complex,
than any of the ideas our forefathers told us about,
or our moms and dads taught us.
And this beauty that overwhelms us,
this mystery that always lies before us
to which we gain access, step by step, little by little,
but which forever remains boundless,
draws us, fascinates us, and we want to get to see it.
This, for me, is science.
Thank you.
(Applause)