Good morning everyone!
I'll speak about time measurement.

To talk about measuring time,
I will ask an obvious question, which is:

what time is it?

It may seem like a trivial question,

but if we performed an experiment today,
and had everyone looking at their watch,

everyone would have a different
time from his or her neighbor.

Particularly, you would have
a different time from the one

on this rather strange clock.

This is a clock that gives you
the atomic time.

I wasn't able to bring an atomic clock
along with me today.

The atomic time is built
at the Paris Observatory.

It is broadcast by radio waves,
and here, we receive that information.

If you compare the time
- that's the date, November 27 -

to the time here,
you see there's a difference.

My presentation is not only going
to explain to you how to reset the clock.

I am going to explain to you
how to measure time with high precision.

You will see that the magnitudes
in the precision are astonishing.

To provide you with some original
and fascinating applications,

I'll start with a very simple thing.
To measure time, we use a ruler.

I use the analogy between a time ruler
and a spatial ruler.

To measure a distance, you take
a ruler that's been calibrated.

You'll count the number of graduations,
for example, in centimeters,

so if you count five graduations,

assuming that one graduation
equals one centimeter,

you will deduce
a length of five centimeters.

With time, it's going to be the same.
We are going to use a temporal ruler.

A temporal ruler can take
the form of an oscillator.

An oscillator is a physical device

that gives you
a periodic signal with timing

- whose parameter is reproduced
in a periodic way with time.

I brought one with me,
Professor Calculus's pendulum.

This is an oscillator.

As you see, we can count time
by counting the number of round trips.

If we say a round trip takes one second,
we can count one, two, the time passing.

Using this time ruler,

which elementary calibration
- called period -

we are able to measure time.

We can imagine
that if we want a better precision,

we will need more graduations.

It is equivalent
to what we have with a ruler.

If your ruler, instead of being
calibrated in centimetres,

is calibrated in millimeters,

and that you measure 51
- tiny millimeter calibrations -

you can assume that your length
is 5.1 centimeters.

It is exactly the same for measuring time.

If you take a faster oscillator
than the one I showed you,

therefore, having a shorter period,
meaning a frequency,

a greater number of pulses per second

you will achieve a much better
resolution in time measure.

This is what has led research

since the invention
of time measure with oscillators.

Typically, given the magnitudes,
you take a mechanical clock,

it doesn't need to be a Swiss clock,

just a mechanical one,
similar to my little oscillator pendulum,

it beats at a pulse per second,

so you don't have a huge precision,
when you want to measure a second.

If you take an oscillator
that you carry with you,

like your watch or your mobile phone.

It has a quartz oscillator
using piezoelectricity,

it has the shape of a vibrating diapason
at a millimeter scale.

It is going to beat
at 32,768 pulses per second.

You are going to cut one second,
into 32,768 small elementary periods.

Why such a weird number?

Because it is easy to divide
by two, 15 times,

to get to one pulse per second,
and get the tick-tock of your watch.

And if we go to the ultimate,
to the fastest oscillators known today,

called lasers - oscillators,
in the optics field -

you see that a laser is an oscillator
that gives you an electromagnetic wave

beating extremely fast until it cuts

your second to 500,000
billions little pulses.

You can see the elementary calibration
is extremely small

We will count 500,000 billion and say
that one second has passed,

we will count again 500,000 billion etc.

You see, in measuring time,

having a frequency as high as possible
is what gives you greater precision.

We can say we have
almost solved the problem.

Not at all! In fact, what confidence
can we have in this measure?

I go back to the example with two rulers.

You buy two rulers, in two different
places, different countries, and measure.

Make the experiment and you will see.

It might not be as blatant,
but you will see it works very well.

For the same length,
you won't have the same calibrations.

So which should we trust?

Which rule should we trust,
which one has the right measure?

With the oscillators,
whilst measuring time,

we face the same problem.

Your oscillator,
two different oscillators,

won't give you exactly

the same number of period
for measuring a given duration;

each little calibration is different.

Or, if you take an oscillator,

according to the place,
or the moment you use it,

it won't give you the same measurement.

For example, the pendulum I showed you,

whether you use it
at the equator or at the poles,

because the oscillation's period depends
on the gravitational force,

after one year, you will have
around two days' difference

between the measures... that's huge.

Maybe not in everyday life,
though two days is significant.

But for the applications
I am going to show you,

it is something very annoying.

How do we solve this problem?

This is where we build atomic clocks.

The atom is the solution to this problem,

since the atom is going
to be our reference.

What happens in an atomic clock?
It is relatively simple.

You still have an oscillator,
but we will compare its frequency

to one that is infinitely stable,
universal, and extremely well-known.

It is the frequency of resonance
to hop from one atomic level to the next.

Why is this atomic frequency
very well known?

Well, because quantum mechanics
tells us that the states of energy

that is, energy levels
between which atoms transit,

these states of energy have

extremely stable
and well determined values.

Thus, the frequency of resonance
to go from a level to another,

will too be extremely well fixed.

Here you have a photo of the atomic clock

which is at the Paris Observatory.

Today, using atoms
which are a bit specific,

since they are cold atoms.

We cool them by laser,
to extremely low temperatures,

and we trap them with the laser light,

using optical oscillators
beating extremely fast.

We manage to have a precision
in measuring time

which is very impressive,

since a clock amongst the best
in the world today,

will only go off one second
after 3 billion years.

In other words, we are capable of giving

the value of a small graduation,
or of the frequency of the clock,

with 17 digits after the decimal point.

As you see, it is an application,

that is very highly impressive,
a very high level of stability

and which further more
has many many applications.

The first application
is the speaking clock.

It is an application
which generally speaks to the public.

Where does the speaking clock come from?

It was created at
the Paris Observatory in 1933,

At that time, it was the role
of astronomers to give the time.

It was not atomic physics yet.

The line of the Paris Observatory
always took care of it,

Because everybody
called Ernest Esclangon,

who was the Director of the Observatory,
to get the time.

Ernest Esclangon had the idea
of developing this speaking clock.

There has been several generations
of speaking clock.

Today, the speaking clock presented
here gives you the time

with 50 milliseconds of uncertainty.

As metrology is an experimental science,
we will call the speaking clock.

I have the authorization to keep it
connected, it is my privilege!

It is always a risk, in experiments:
it might not work.

Clock: It is 5 pm, 7 minutes 10 seconds.

ND: We are going to wait just a little,

But you can see the red lights there.

Speaking clock: It is 17 hours,
7 minutes, and 20 seconds.

ND: There, it works! Thank you!

(Applause)

This application might be harmless,
but it is important especially

at the time of changes
between summer time and winter time.

If we want to give the time
in a more precise way,

we can also use Internet,
telecommunication satellites, or GPS, etc.

This is the first application.

The second application,
which is very fashionable,

and is also very important

is the use the atomic clocks
to test Einstein's law of relativity

that tells you, for the last 100 years,
that time is not absolute.

That is, if you take identical clocks,

and you put them
in different frames of reference,

which move relative to one another,

or which have different
environmental parameters,

you will find and measure differences

between the times
and frequencies of the clocks.

This non-absolute character of time
is already tested on the ground.

We are going to test it
extremely precisely in space,

by installing in a few years,
an ultra-precise clock

aboard the International Space Station.

And by comparing the time
and frequency of this clock in space

with the time and frequency
of clocks situated all around the Earth,

it will become possible
to validate Einstein's theory.

Knowing that all modern theories

predict a violation of Einstein's theory.

So there is a real
scientific benefit in doing that.

We are going to test various aspects
of general relativity.

For instance, we will test
a rather interesting property, which says:

fundamental constants are constant.

This is not trivial!

In physics, a whole set of constants
is supposed to be constant.

In fact, all modern theories predict
these constants vary in time and in space.

We will be able to test this precisely.

We will also test an original effect
of general relativity,

time passes at a different rhythm
according to the altitude.

For instance, you, who are
sitting in the first row,

you do not age at the same speed
as those sitting in the last row,

since you are sitting
at different altitudes.

But to reassure you,
on the length of my presentation

the difference of aging
is around one picosecond.

10 to the power of -12 seconds,
a billionth of a billionth of a second.

So, there is no need to run up and down,
remain in your seats!

We will also test
the speed of light is constant.

This is an extremely strong postulate
of special relativity:

the speed of light is independent
from the frame of reference

against which the measure is taken.

This is an extremely important property,

which is used to measure distances
from time measurements.

If you want to measure a distance
you use a signal which will propagate,

and by knowing the time of propagation,
knowing the speed of propagation,

which is the case with the speed of light,
you can infer the distance.

One could say there is no need

for an ultra-stable clock to do that.
But yes, there is a need for it.

Light goes fast, at 300,000 km per second.

If you make a nanosecond error,
a billionth of a second,

you are wrong by 30 centimeters.

Typically, this kind of application,
measuring distances from measures of time,

is used to measure Earth-Moon distance.

By sending impulses to the Moon,

which are reflected by retro-reflectors
installed by the Apollo missions

to measure the Earth-Moon distance
better than to the centimeter.

When we have a distance to measure,
we know where to position.

How do we do this?

With the GPS, for instance,

if you have a cluster of satellites
with synchronized atomic clocks,

by measuring the travel time of each wave,

from each satellite to your receptor,

you measure your distance
from each satellite,

and by triangulation,
you measure your position.

You need four satellites,
because in the time-space

there are four coordinates: x, y, z and t,

since time is also needed
to position one self in time-space.

You can see that the GPS's applications

are not only to position
oneself in one's car

an area where we need
a resolution of a few meters.

There are also applications in geophysics.

We will be able to analyze
the movement of tectonic plates

with resolutions down
to a few centimeters per year,

which is an excellent resolution.

It is interesting,

since from time measurements,
we know the functioning of the Earth,

we infer fluctuations
of the rotation of the Earth.

It is interesting because historically,
it was the exact opposite.

It was the Earth's rotation
which gave the hour.

At present it is the opposite.

The measurement of time gives us
the fluctuations of the Earth's rotation.

Another thing you might have heard,
on the radio or on television,

are the famous intercalary seconds.

As the Earth does not go
perfectly round, as we all know,

and the atomic time is infinitely stable,

meaning that both time scales linked
to Earth's rotation and to atomic clocks

are going to diverge from one another.

To prevent them diverging too much,

we voluntarily add,
at the international level,

a extra second, called
the intercalary second.

This means that generally every two years,

either on June 30, or December 31,
- December 31 is less bothersome -

one minute is actually made of 61 seconds.

This leap must be made
everywhere, all over the Earth.

So as a conclusion,

I would like to show you

time measurement has left
the field of astronomy

to land in the domains of atomic physics,
and of quantum mechanics.

Since the invention of clocks,
around the mid-20th century,

we have gained
a factor of 10 every 10 years.

It is really impressive progress.

Each time we improved the precision,
we said to ourselves:

there is no need for all these
figures after the decimal point.

It is not true.

Each time, an application appeared,
10 years later, 20 years later,

which used that precision.

I think that I'll conclude and say

that those who measure time
are ahead of their time

is totally appropriate in this case.

Thank you very much.

(Applause)