June 2, 2022 • 50 mins
François David is a mathematical physicist and a passionate educator with an infectious zest for decoding the mysteries of the universe. As a scientist based at the Institut de Physique Théorique (IPhT), he uses mathematical techniques and tools to tackle open questions in areas ranging from quantum gravity to statistical mechanics. He is also a popular lecturer among graduate physics students in his native France and at Perimeter Institute, where he has led classes in the Perimeter Scholars International (PSI) graduate program for over a decade. In this conversation, David discusses what it means to study simple complex models, ghosts that appear in quantum field theory, and how teaching young students from all over the world has energized his own passion for science. View the episode transcript here.
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(00:00):
(bright music)
- Welcome back toConversations at the Perimeter.
I'm Colin and I'm here withLauren, and we are thrilled
to share our conversationwith Francois David.
Francois is a mathematical physicist,
which means he tackles reallyhard problems of physics,
(00:22):
like quantum gravity, usinga mathematical toolkit,
and I have to admit that's a toolkit
that I didn't have a lot ofexperience with growing up.
So I was a little apprehensivegoing into this conversation,
but thankfully, Francoisis a very gifted teacher.
- Francois was actually one of my teachers
when I first came toPerimeter as a grad student
in the Perimeter ScholarsInternational master's program,
(00:44):
and he's been coming toteach in this program
from France for many, many years
and he has an amazingreputation among the students.
I'm now actually an instructorin that program myself,
and so I've been able tointeract with Francois,
both as one of my teachersand now as a colleague.
- So what's it likefor you to put Francois
in the hot seat now, whereyou ask all the hard questions
(01:04):
and he has to answer them?
- Honestly, it was areally different experience
because, back when I was a student,
I was usually toonervous to put my hand up
in class and ask questions.
He even mentions during this conversation
that he remembers I alwayshad a lot of questions,
but I know that I wouldusually stay after class
to ask those around just asmaller group of students,
and so this was really different,
(01:25):
that I got to ask questionsand share the conversation
with so many others.- And for me,
that apprehension I had off the bat,
it melted away so quickly when I realized
just how much he loves physics
and how infectious his love is for it.
I'm excited for otherpeople to get that sense
of the joy of physicsand math from Francois,
so let's step inside the Perimeter.
(01:50):
- Thank you so much, Francois,
for joining us for a conversation today,
and it's great to have you here
at PI all the way from France.
Would you mind telling us a little bit
about what you do as amathematical physicist
and what it means to work in that field?
- Well, first, thank youvery much for this invitation
to this kind of interview.
That's my first experiencein this, almost my first.
(02:13):
Okay, about my experienceas a mathematical physicist,
but I must say that I don't really know
exactly what is mathematical physics,
because it depends a bit on the country,
on the culture, or the person.
So I am partly a theoretical physicist
and partly a mathematicalphysicist or both.
And mathematical physicsis a field of research.
(02:36):
There is no real border, but interface
between mathematics andtheoretical physics.
Mathematical physicistsare more involved in using
recent and sophisticatedmathematical techniques and ideas
because mathematics are way much
than just techniques of calculations.
They are concept, ideas.
(02:57):
So mathematical physicistsare more interested
in the structure of physical theory
and understanding how that works,
what one can tell out of the mathematics
that governs the physical theory,
and understand, often on simple models,
not always, but they take a simple model,
not often directly related tosome real physical systems.
(03:22):
It may be, but they're often idealized
in order to keep track
just of the importantphysical feature they want
to understand and workingout, as deeply as possible,
the math and the theoryand see what comes out.
Are those theoretical modelsconsistent, for instance?
(03:42):
That's very important.
Can we compute exactly andprove properties of this model,
or are we just able to use
what are called phenomenological model?
So one makes assumptions,
some approximation, and then one relies
on calculation and alsophysical intuition,
(04:05):
and often it works, butsometimes it doesn't work.
You really have to work hard
and do hard math and some deep,
and sometimes unexpected results come out.
So that's mathematical physics.
- Francois, you used theword consistent there
to describe the research.
Does consistent mean that an idea is true,
(04:25):
or that it's true enough for now,
and is inconsistency an enemy of science?
- In my mind, consistency isa mathematical consistency.
It's related to another concept,
very important for somephysicists, not all of them,
but it's a mathematicalbeauty of a theory.
So it's something which wasvery important for Paul Dirac,
(04:45):
one of the creator andinventor of quantum mechanics,
who considered that atheory had to be true
if it was beautiful.
This led him, for instance, todiscover the Dirac equation,
though often, beauty is associated
to mathematical consistencyin the mind of mathematician
(05:06):
and in the mind of manytheoretical physicists.
There is something which ismore than just mere beauty
because some very simpleobject can be very beautiful.
Consistency means that,often in theoretical physics,
one needs to start with some assumption.
There is space, there is time.
(05:26):
For instance, one important assumption is
there is no difference betweenthe future and the past,
which seems a bit,
of course, contradictorywith our daily experience,
but that's the deep principle
of, nowadays, theoretical physics.
So one makes assumption, let'ssay what physical problem
or physical system is described
(05:47):
by one makes some assumption.
One assume the rules, for instance,
the rules of classical mechanicsor the rules of the law,
other than the rules of thelaw of quantum mechanics,
the law of hydrodynamics,the law of classical physics,
Newton Law, et cetera, and one see,
whether building out of that,
one doesn't run up into somemathematical inconsistency.
(06:09):
Sometimes it's easy to see
that there should be some inconsistency
in some direction, so don'tlook in this direction.
Look in the problems whereinconsistency doesn't appear.
And sometimes the inconsistencyappears in a surprising way.
And of course, if you run intoa mathematical inconsistency,
(06:31):
it means that you are to think more.
Either one of our assumptions was wrong,
or it might be a paradox,
but not a real inconsistencyif you work out enough.
Science and knowledgeprogress by making errors.
If everything was clearlyunderstandable and consistent
(06:52):
from the very beginning,it wouldn't be interesting.
- And could I also say maybe
that, if in physics we oftentend to start with assumptions
and, as you said, sometimesthose assumptions might lead
to inconsistencies and sometimes not,
would a goal of mathematical physics be
to provide more structureto those assumptions
(07:12):
so that there may be, at somepoint, no longer assumptions?
- Yeah, this happens, too.
Sometimes you start, from assumptions,
you work or after someother researchers come out
from different field or different ideas,
or even some mathematicians come out also,
and when discovered that thoseassumption were were correct,
(07:36):
it was not coming from some naturalness
or intuition that thingsshould be that way.
It comes out that they had to be this way.
And that's a differencebetween often, one start
by, oh, things shouldwork this way or that way.
And then you may have different theory,
which start from different point of view.
(07:57):
After working often very hard
by a team of very differentpeople, one comes out of that
that, in fact, oh, thingshad to be that way,
this way, and not that way, or sometimes,
oh, things had to be this wayand your two approach were
seemingly contradictory, but consistent.
One time, this happens in the early days
(08:19):
of quantum mechanics, veryoften, where people were starting
from some kind of wild assumptions.
- I often hear mathematicians talk
about the sense of beauty in mathematics,
and that's a beauty that, personally,
I haven't been able to experience
because I grew up alittle bit afraid of math.
Can you describe the sense of beauty
(08:39):
that you see in mathematics?
- I'm not a mathematician,
so I won't speak as a mathematician,
although I know some mathematics.
I was educated in mathematicssince the French high school,
and the university system is more focused
on mathematics than in other countries.
Also, I married a mathematician
and two of my daughtersare mathematicians.
(09:01):
My impression is thatmathematicians see beauty
in simplicity of structure,but consistencies of structure,
objects can be mathematical,theories can be complicated,
but there is some underlying structure
which enables you to come out to theorems
by abstract reasoning, not just heavy
and technical calculation.
Although they are also very important,
(09:23):
they also both in theoretical physics,
science in general, or in mathematics,
you see simplicity aftera lot of hard work.
It's a bit like diggingan archeological dig.
You find some beautiful archaeology,
but you had to work, work,and once you find something,
you say, "Oh, but I shouldhave looked in this direction,"
(09:44):
come to the results very easily,
but of course, you just knowbecause you worked hard.
So that's my feeling
of what a mathematician feel about beauty.
So one of my daughter is a mathematician.
She's doing algebra, geometry,a number of theories,
and she said, "I prefer mathto physics because in math,
"we are dealing with objectswe have created ourselves
(10:08):
"and so we know it'sconsistent, while in physics,
"there is some external worldand we start from that."
We want to understand theuniverse, we want to understand
how a cell works
or how the solar system works
or why there are chemical reactions,
and that's something which is given to us
(10:30):
or which is there for us to understand.
That's probably one reasonwhy I prefer to be a physicist
than a pure mathematician.
So probably my brain prefersto be a mathematician.
That's why I'm a mathematical physicist,
but my curiosity or my intuition prefers
to have surprises comingfrom where we live.
(10:52):
Especially here, you have
a group of very good people working
with the foundations of physics
and the foundation ofsome philosopher, too.
They will be able to tellmore, but it's unclear
whether the mathematicsare part of the real world
or something completely outside.
That's a view of many mathematicians,
that mathematics exists by themself.
(11:13):
This is more considered,mathematics as a tool.
There is a debate that goesback to the great philosophers
about what are mathematics and physics,
since they are intertwined
since they were created or discovered.
- From what you say, I mean,
you're giving us a nice description
that mathematics involvessome beautiful structures
(11:35):
that we can create, andphysics is about describing
these really interestingphenomena in our world,
so maybe mathematical physics is working
from both of those ends
to give some structure to the universe,
and oh, maybe that's not correct, but-
- No, I think that's a good view,
but I'm not an historian of science,
(11:55):
but many of the mathematicalobject were created
from the real worlds
and then evolved on theirown, and some structure
of the real worlds have beendiscovered through mathematics.
- And is that why we need
mathematical physics, so that we make sure
that those two ends aretalking to each other?
- The interface has been there.
It has been important,
(12:17):
depending on the historicalperiod in science
and also on the countries,but the interface has to be.
Otherwise, there won't be goodphysics without mathematics,
of course, because I think Galileo stated,
one of the first to state,
that mathematics is a language, physics.
Also, a lot of mathematiciansnow, not all of them,
but of course, it depends,get inspiration from physics,
(12:39):
and the ideas which,somehow, a bit clumsy ideas,
created by theoreticalphysicists, common mathematics,
challenge things, andthen come back to physics
as a neat tool and with newideas provided mathematicians.
There are many examplesthat one can think,
(13:00):
but a few in the last decades.
- So mathematics, you said,is a tool that we can use
to make progress in bigproblems in physics.
So what are some of thebig problems in physics
that you are trying to tackleusing mathematical techniques?
- I've been very much interested.
In fact, I realized all along, my career,
(13:21):
not only this question,but about random geometry,
let's say starting fromgeometrical objects,
and see what's the role of randomness,
and one of my interests in thatcomes from quantum gravity,
so quantum physics and gravitation.
Theory of gravitation hasbeen born with Kaplan, Newton,
all the great mind in the 19th century.
(13:44):
Then Einstein discovered
that, in order to makehabitation compatible
with the theory ofrelativity that he discovered
in order to understand the behavior
between light and matter, no habitation,
he discovered that, infact, spacetime orders
that you shouldn't consider space and time
(14:05):
as two separate notion or entities,
but they have to be takenas a part of spacetime.
Einstein discovered that,in order to formulate
the consistency of gravity,the spacetime itself
as a internal structure, it has a metric
and it can be a geometrical object.
In fact, it is a curved object.
All of spacetime, so both space is curved.
(14:26):
Usually, you often form this fact.
You said that you have flatspace, you put the body in it,
like the sun, and it curves the space.
And then therefore, it's like a ball,
and you can have a marbles way
to explain empirically why theplanets orbit around the sun.
The theory of generalrelativity of Einstein says
(14:48):
that, also, time is curved,and that's something
which is more difficult, too,
that it's space and time whichare curved, not only space.
Productivity tells us that, in fact,
time is associated to space,so times has to be considered
as a separate time atdifferent points in space.
(15:09):
When you start tocompare what's happening,
when you go to a differentplace, you let run time
and then you come back at the same place,
you discover that spacebehaved in a different way
that you could have expectedif time was something uniform,
like in Newton theory of time,
especially when there isa gravitational field.
If you have a black hole and you are far
(15:32):
from the black hole, or ifyou go close to the black hole
and come back or close tothe sun and then come back,
then time has very differentlyapproach a black hole.
You come back, then theclocks are desynchronized.
There was a very nice example of that
in a movie, this "Interstellar."
This is checked in laboratories,not going near black holes,
(15:56):
but just having two atomic clocks.
As you raise one of theatomic clocks by a few meters,
drop it back on the tablewhere it started from,
and you can see such effects,
tiny effects, but they are measurable
and I agree with the theory.
Now come quantum mechanics,great discovery of last century.
Einstein also played arole, but less central,
(16:17):
compared to relativity.
And in quantum mechanics,
some very special kind of randomness,
rather than randomness, one choose it.
The role of chance is very important.
There is some indeterminacy.
You are never sure of what the results
of a measurement willbe, but this randomness,
(16:38):
in some senses, uncertainty is governed
by mathematical role whichare very, very precise,
so it's not randomnessjust because we don't know
exactly what's going on.
When you are interested in,
for instance, the theoryof quantization of gravity,
one of the great problemsnowadays of present physics,
(16:58):
you have to treat spacetime
as a curved object, a curved spacetime,
but with some randomness coming
from the quantum nature of the universe.
And we know that, for consistency,
this idea of consistency,the beauty of the theory,
the geometry of spacetime,the curvature of spacetime,
(17:20):
has to be treated as a random object,
but an object with randomness agreeing
with the law of quantummechanics, if, indeed,
gravitation is consistentwith quantum mechanics,
and we don't really knowif they are consistent.
We hope that it'sconsistent, we are trying
to make a consistenttheory of quantum gravity,
but maybe we'll come upinto an inconsistency,
(17:44):
which means that we will have to build
a new theory of nature, which will be
post-quantum and post-gravitational.
- So quantum gravity,it's essentially the quest
to reconcile two theories,
quantum mechanics and general relativity,
and to come up with abridge between the two?
- We need to have aconsistent physical theory,
(18:07):
which leads us
to a complete understandingof quantum mechanics
and a complete understanding of gravity.
We have to build such a theory.
Some physicists thinkthat it's not necessary,
that we can still livewith those two theories,
but the vast majority thinks
that, for just this reasonof consistency and beauty,
in the sense of logical consistency,
(18:28):
there has to be such a theory.
It depends with whom you talk, though.
There are several direction of research,
and it's a very active subject,
in part, well represented
here in the Perimeter, of course,
and there are many different ideas.
Some are mathematically well-developed,
some are less and more rely on intuition
(18:50):
or some toy model.
The two main ones are string theory,
and the other one is based
on still treating thegeometry of spacetime,
how four-dimensionalspacetime as some basic data
and quantizing it according tothe law of quantum mechanics,
while string theory iswider and more speculative.
- A lot of your contributions are
(19:12):
specifically to two-dimensionalquantum gravity,
and we had a really good question sent in
from Tebra in Bangladesh-- Ah, okay, yes.
- So maybe we can listen to his question.
- Hi, Francois, this is Tebra.
I'm a theoretical physicistbased in Bangladesh.
Of course, you and I know each other,
so this is for otherpeople, other listeners.
(19:34):
Anyway, I have a question for you.
Recently, there have been some buzz
in the physics circle
about your work in two-dimensional gravity
and how that has helped breakthroughs
in recent years, so I was just wondering
if you could explain in general terms
(19:54):
what your contribution was
to the field of two-dimensional gravity
and how that contributedto recent breakthroughs
in two-dimensional gravity.
Thank you for listening andthank you for your answer.
- Thank you, Tebra.
I've been specifically interested
and worked and got someinteresting results in a subfield
(20:17):
of quantum gravity calledtwo-dimensional gravity.
It's both a toy model anda very interesting model
for some physical application.
It's a model which isvery much simplified,
a core model where you canstudy one aspect of the physics.
- But the idea would be that,by working with this toy,
we can still gain some insightsthat will still help us
to understand the more complicated system?
(20:39):
- Yes, and so an example of a toy model,
which is a very useful example
for studying quantum gravityis to consider that spacetime,
instead of having threedimension one time,
or as in string theory,
nine or 10 dimensions of spaceand one dimension of time,
or maybe nine dimension of spaceand two direction of times,
(21:02):
would consider a very simplifying model
of spacetime, where you have
one direction of space,so space is just a line,
and one direction of time,
so spacetime is just a sheet of paper.
So it's a very simple model,
and you lose many aspectsof habitation theory.
In particular, you lose
a very important aspect of your operation.
(21:25):
You lose the law of attraction,
Newton's Law, for some technical reason.
So you have no habitationanymore, but you have geometry
because a sheet of paper can be curved.
If it's a rubber sheet, it has curvature,
so you keep one of the basic point,
that spacetime is curved.
So you can quantize it
(21:45):
and you can study the quantum effects.
In particular, that's the simple case
where you can build a consistentquantum model of gravity,
and you can build atheory on simple axioms
and compute things and go tothe end of your calculation
and get insights about whatquantum gravity could be,
(22:05):
or some aspects of quantumgravity could be or could not be.
So working with a two-dimensional model
or either one-plus-one-dimensional model,
spacetime, rather thantwo four-dimensional,
three-plus-one-dimensionalspacetime is very important
and is very interesting.
And I've been working,I think, since the 80s,
by some period on those models.
(22:28):
My contribution in this idea,
I've been twofold.
I've been one of the firstto implement the idea
that, instead of takinga continual spacetime,
you can approximate itby a discrete object.
Typically, you can see thatyou can build a surface
out of taking triangles, flattriangles, but gluing them,
(22:49):
and if you glue them in a proper way,
you can build polyhedra.
So you can build curved surfaces
or curved spacetimeout of discrete objects
and realize the quantumnest of a quantum spacetime
by looking at the common matrix
of this construction you can make
by building what's called triangulation.
(23:11):
If you glue a triangle,
you build a triangulation of a surface
or you build a discretizedsurface or a discrete surface,
and treating this objectat quantum means look
at the status, see that's a surface.
That's a typical, average size,
average shape, averagecurvature, or such an object,
and it seems they'renaive and simple ideas,
(23:34):
but it was motivated by thefact that this procedures is
now to work already in quantumphysics without gravitation.
When this idea wasintroduced, it was in the 80s.
Theoretical physicists had introduced
what they called lattice gauge theory,
discretized theory of the stronginteraction, for instance,
but on a discrete spacetimeby extension and energy,
(23:58):
we put high in it.
Other theoreticians andsome mathematician, too,
started to look at canyou make this idea working
for very simple, one-plus-onetheory of quantum spacetime?
And it turns out that youcan work and make calculation
in these toy models usingmathematical theory,
which came out from somethingcompletely different,
which is called thetheory of random matrices,
(24:21):
which comes from thestudy of quantum systems,
which are very complicated dynamics.
So not toy models, but very,very complicated models,
and looking for whether they still exhibit
some universal feature, which are there
because the system arevery, very complicated
instead of being very, very simple.
(24:43):
- The idea of a toy model,
is it akin to building a toy car
with just a wooden rectangleand four round wheels,
making sure it rolls, and then eventually,
gradually adding more and more features
until you've got a sports car?
- If we didn't have thetoy model to think about,
it would have been very difficult
to find in the very complicated system.
(25:05):
So that's one aspect of thetoy model, but then I could say
that there are other kind of toy models,
which is exemplified by thisidea of random matrices.
Want to explain, but think
about the matrices arejust a table of numbers,
like an Excel spreadsheet,where you can add them.
You know that you can add thecells up in a spreadsheet,
(25:26):
but you can also multiply them.
More complicated, but themathematician and physicist know
very well what it means.
And so order comes out of complexity,
or to mention a word
of a famous physicist, E. W. Anderson,
the sum is more than the parts.
It appears, for deep mathematical reasons,
(25:49):
then if you take a verycomplicated object made
out of simple objects, insteadof it becoming just a mess,
it becomes something whichexhibit very simple feature.
Some universal behaviorcomes out of complexity,
and the property of thesum of the subject is
not just emerging from theproperties of the small parts.
(26:11):
It's come out from the rule.
This is also an idea which is important,
for instance, in quantum gravity.
Many suspect that, in fact,
the fact that we have asmooth, neat spacetime
with a bit of curvature, explain gravity.
It may come out fromsomething at quantum scales
(26:32):
and below at some post-quantum scales,
which is completelydifferent and maybe random,
both the idea of taking toy models
to understand the real systemsand taking complicated system
to understand what's goingon for large systems.
There are two trends in common,
not in completely not incompatible ideas,
which are very important inmodern and theoretical physics,
(26:55):
because then you can make toy models
of very complex system and study them.
That's the idea of those fundamentals,
but they are simple, complex models.
- And I wanna go back to a wordyou said a little while ago,
which is this word universal.
You said sometimes in these systems,
you can end up finding somethingthat's actually universal,
so can you tell us what that means?
(27:16):
- Universality means that,out of very different systems,
exhibits the same behavior,
although, in some sense,this behavior is universal.
This concept, which is now oneof the very important concept
in theoretical physics,
come out, not from high-energyphysics, not from gravity.
It comes out from condensed matter.
It led to the discovery orthe creation of a theory
(27:40):
which is called the theoryof homogenization group,
but forget about the group.
You have some different physical system,
completely different,which in fact, exhibit,
in some regime, exactly the same behavior.
If you study the behaviorof ice and water,
water can be a liquid, can besolid, and it can be a gas.
(28:02):
Usually, it's one or the other,
but there is a very special point
when you have water at avery specific temperature
and a very specific pressure.
You reach what is called a critical point,
where water is neither aliquid or a gas, it's both.
At this point, there are huge fluctuations
(28:23):
of pressure and density.
These behaviors occurs for water,
but it occurs also for other gases.
In fact, it's better studied
in other gases or other liquids.
Usually, you have this function.
You heat water, and atsome point, it boils.
It's very simple, suddenly,vapor starts to happen,
(28:44):
so it's called the first-order transition,
but if you increase thepressure, there is a point
where the transitionbecomes smaller and smaller.
At some point, it disappear.
It turns out that youhave system of magnet.
I don't know if, in high school,
you might have done theexperiment that you take a magnet.
So the magnet has some magnetic property.
And if you heat a magnet,
(29:06):
you put it under a Bunsen flame,
at some point, the magnetstops being a magnet.
It's just a dull piece of metal.
So there is a critical temperature
where a magnet stops beinga magnet, and it turns out
that the property ofthis magnet are the same
or very similar to the property of water.
(29:28):
That's very strange.
This has not beenunderstood for many years,
and in the beginning of the 70s
and the 60s and end of the 70s,
physicists working incondensed matter understood
why this occurs, but they understood,
thanks to one of the greathigh-energy physicists
(29:48):
of that time, Ken Wilson,who started being interested
in what's called critical phenomena.
He built out of high ideas,
which came from high-energy physics,
the concept ofrandomization transformation
and what's called now randomization group.
The idea is that, ifyou start from a system,
for instance, which isdescribed at microscopic scales
(30:10):
by a collection of atoms,
atoms can behave as small magnets,
very little magnets, in fact.
That's the origin of magnetism.
You have atoms, you haveelectrons turning around,
and the electrons have a magnetic moment.
In the addition, theycreate magnetic moments
because they go around thenuclei of the atom, et cetera.
Okay, anyway, so that'sthe origin of magnetism,
(30:31):
but if you start from the magnet described
just by its microscopicstructure at the atomic scale
and you start to look
at what are the properties of this magnet,
if you go at larger and larger scales,
so changing the scalesor making some averaging,
the magnetic property of a magnet,
instead of looking atwhatever magnet you see
(30:52):
at the property, at the scale of an atom,
you see a cube, 10-by-10-by-10 atoms,
and you see what are theproperties of this magnet.
- Like zooming out on a picture?
- No, it's exactly like zooming out,
but zooming out being defined
in a proper mathematical way.- (laughs) Right.
- And if you do that,
it was discovered by KenWilson and explained,
(31:14):
and the other physicistworking in that field,
that this posed view sometimesconverges in substance.
You zoom out, you zoom out, you zoom out,
and when you have zoomed,you find something
which is the same kind of object,wherever you were looking,
at a magnet or at a fluid,
(31:34):
where you could say,"Okay, this tiny region
"of space can be eithera liquid or a gas."
So if you want, you would takethe molecule of your water,
and either they are very closely packed
and they are connected by hydrogen bonds
or there, they can wanderaround so they form a liquid.
So it's exactly the same thing.
You take very different system,
sometimes complicated objects,
(31:55):
so the dynamics can be complicated,
can be simple in your toy model.
It can be complicated in your model.
You zoom out, you zoom out, you zoom out,
and if you go zoom out enough,
sometimes you find the same object.
So in this sense,
simplicity or beauty is emerging
by zooming out what's goingon in the complicated system.
(32:18):
So this is the idea of universality,
which is very important in physics.
When you normalize, you average
and see what has a property.
This creates some kind ofnorm, and renormalization means
that you normal the scalesand you change the scale.
You renormalize, and youchange against the scale.
(32:38):
You will renormalize,et cetera, et cetera.
So you have this idea of toy models
and this idea of normalization,
so that the simple phenomenon come
out of very complicated object,
and irrespective of the detail
of what's going on the small scales.
- And it seems, Francois,like some of these tools,
like renormalization groupor random matrix theory,
(32:59):
they've allowed you to studyquite different problems.
You've talked just now about some problems
in condensed matter.
You were telling us about quantum gravity.
Would you mind maybe telling us the story
of your career and maybethe different problems
that you've looked at along the way?
- Yes, in fact, Irealize that this concept
of universality andnormalization group has been
(33:22):
one of the guiding line of my research.
Those tools were createdwhen I was in high school,
so I learned them when I started.
I was a graduate student,
and I've been trying toimprove them and apply them.
So I started in high-energyphysics and theory,
and then I started being interested
in whether I could apply thoseidea to condensed matter.
(33:44):
And then when I was a post-doc
in Princeton, I came in contact
with a researcher workingin quantum gravity,
this idea of discretizing spacetime,
and so I applied it to quantum gravity.
So I started to study this ideato work in quantum gravity,
so I studied mission model,a bit of higher dimension,
but this doesn't work so well,and then I came in contact
(34:07):
with another field of theoretical physics,
which is biophysics, in fact,and one very specific subject,
which is the study of membranes
who have two-dimensionalthemes in three dimensions,
because when I was in touchwith young physicists,
visiting (indistinct),and one got a position
and they were working in that field.
(34:27):
And this idea of universalityis very important
because, by discussing, wediscovered that, in fact,
some models of quantumgravity in two dimension
and some models ofmembranes were very similar.
They had some difference,in particular as a whole
of bending in two-dimensional gravity.
Bending is not important.
Well, it's very importantin a physical membrane.
(34:49):
So I've been working in this concept,
studying the physics ofwhat's called fluid membranes
and then crystalline membranes.
This was a very exciting fieldand it's still important,
but then a few years later,there was some great progress
in the theory of quantumgravity and in string theory,
(35:09):
made by a group of theoreticians,especially Russian ones,
this Russian school with Migdal, Polyakov,
and we made progress in thetwo-dimensional quantum gravity,
so I came back to that field.
And I was there, more interested
in not discretizing spacetime,but taking continuum theory
of two-dimensional gravity,a theory which was,
(35:29):
well, created and invented
by Polyakov, which iscalled Liouville theory.
Liouville is a famous French mathematician
from the 20th century.
He was mostly a number theorist,
but some of his equation wereimportant in quantum gravity.
So our model was neutral gravity,
which is connected to string theory.
(35:50):
It was developed by this Russian school,
and that tends to be knownas the Liouville theory,
but there are other theoriesup to Newton's quantum gravity,
like Kiev's Titan Boommodel and some other one,
but one is the Liouville theory,
and so I've been working on that.
After that, I came back
to quantum metric theory
for several years andwas interested in that,
(36:12):
in particular for quantum cows,
because quantum metrictheory has application
to quantum cows, and then Icame back to quantum gravity.
- The first time we spoke,
you used the term journeyto describe your career,
and you said thattheoretical physics requires
all sorts of different minds,
(36:32):
so what kind of mind do you bring
to the journey of theoretical physics?
- I would say there aredifferent kind of minds
in theoretical physics.
I'm not completely sure which mind I am.
Some likes to wander around.
I'm still a bit stubborn, soI come back to old problems.
When I'm stuck, sometimesI look elsewhere,
but I always come back.
(36:53):
I have some problem in my mind
that I have them since 20 years.
I'm just waiting forthe good idea, if any,
or if someone had a good idea to solve it,
they are still there.
- Some of these problemsthat you've described
to us are incredibly challenging.
Some of them are so difficult
that they may not see a solution
in our lifetimes, possibly ever.
(37:13):
Francois, given the hugenessof these challenges,
what keeps you going?
- Well, I think that's curiosity.
As long as I've not understood something,
I like to think about it.
I feel disappointed.
I feel the failure of nothaving made progress in a field.
If someone else made theprogress, that's fine.
I said, "Okay, I was not smart enough.
(37:34):
"I didn't have the idea."
There is change in research.
Sometimes you just have agood idea at a good time
and sometimes you had it too early,
and you couldn't make out something of it.
- So Francois, we alsogot a question for you
that was sent in from one of the students
that you're currently teaching
(37:56):
within your quantum field theory course
within the Perimeter ScholarsInternational program.
Let's play the question from Anna Kanur.
- You teach a course onquantum field theory,
and one of the topics is ghosts.
Without writing down any integrals,
how would you explainwhat these ghosts are?
(38:16):
- Well, the denominationghost has been given
by the physicists whocreated this concept.
It was a Russian, Faddeev and Popov,
but I'm not completely sure anyway.
Physics likes to find nice nameswhen they have new objects.
Sometimes the names are well-suited.
Sometimes they are silly, but okay.
So ghosts, in fact, arearticles in a quantum theory
(38:39):
with probability to be there is negative.
If you think about probability,
it's a very important tool of mathematics.
And the probability of an event,
if you have some uncertaintyon something happening,
for example, if you play coins
and it has a probability 1/2
to be heads and 1/2 to be tails.
Okay, if the probabilityof some events is one,
(38:59):
it means that it's certain, you are sure.
If it's zero, it meansthat it never happens.
So the probability are numbers which are
in between zero and one, or 0% and 100%.
You cannot have a probability of two.
The sum of the probabilityof all realization
of an event has to be one,'cause something happens.
(39:20):
Whatever it is, you'resure it's going to happen.
If you have a head andtails, 1/2 plus 1/2 is one.
In quantum theory, whetherit's change and uncertainty,
you can calculate probabilitiesof something to be measured,
and so some of the probabilitiesof all possible outcomes
of the experiments ormeasurements has to be one.
In the inconsistent quantum theory,
(39:41):
the sum of probability isone, it's called unitality,
but it turns out that,in some quantum theory,
you get probability twoand probability minus one,
but it's not a physical theory
because you have aprobability, for instance,
to get a particle created,which is minus one.
When you have a theorywhich such particles,
(40:02):
they are called ghosts.
Sometimes when you make a theory
and you get probability which are negative
or greater than one, that's anexample of an inconsistency.
- I was gonna say, itsounds like something
that must bother mathematicians.
- It bothers mathematiciansand it bothers physicists, too,
(Lauren laughs)of course,
because there are many theory
(40:23):
of quantum gravity which have ghosts.
The first theories of stronginteraction are the ghosts.
Most of the ghost'sparticles, when you see them,
it means there's a theory,you can put it aside
and start with a better theory.
In the lecture that I gave, it's a theory
where you try to quantize thetheory of strong interactions.
(40:44):
In this theory, well, you runinto technical difficulties,
and one way to deal with this difficulty
and to solve the problem is tointroduce a fiducial particle
in the theory, whichprecisely has this property
of having negativeprobability to be observed
or larger than oneprobability to be observed.
(41:06):
The fact that you haveto consider those parts
of those kind of ghostly particle
when you make calculationcomes out from the math.
So they have to be there,
but when you work out more on the theory,
you see that you can never observe them.
They are virtual particles that are there
in the quantum vacuum of the theory,
or when you make calculation,you have two particles.
(41:29):
You sew them on together in accelerator,
you have a quantum theory
that this type of what'sgoing on when they interact,
and you have a lot ofvirtual quantum process.
And then there is an outcome,
some other particles,two, three, four, many,
because you can createparticles, come out.
When you do the calculation, you see
that you never see any ofthose ghostly particles.
(41:51):
So those ghostly particlesare there in your calculation.
So in some sense, ifyou are mathematician,
you see if it's in the calculation,
it's something that exists,but you can never observe it.
So in some sense, it's afeature of the calculation.
In some sense, they are likeimaginary numbers in algebra.
I never thought about this analogy,
(42:12):
but I think it's a good analogy.
Imaginary numbers are numbersa bit like real numbers,
but the most importantimaginary number is called i
for imaginary, and i is a number
so that its square is minus one.
So in some sense, you cansay it's not a real number,
but now when you are in high school,
(42:32):
you learn about imaginary numbers
because they are everywhere
when you do calculationin math and in physics.
And in fact, imaginarynumbers were invented by,
I think, Italian mathematicianin the 15th century
to solve a quadraticequation, algebraic equation
that mathematician weresolving since the Greek
and the Egyptians andmaybe the Babylonians.
(42:53):
Okay, and in order to find the solution
of equation involving real numbers,
they discovered that it was notquadratic equation, in fact,
but it was question of degree theory.
Anyway, so algebraic equation,
they discover that it was very convenient
to introduce this numberwhere the square is minus one
and consider it as a real number.
(43:15):
Just make calculationand consider it at par
with a number we're used to at that time.
And so now you discusswith a mathematician
or with a physicist, oreven with the engineering.
Those are useful when youstudy electric currents.
Well, they said, "Okay,well, i is a number,
"as one or minus one."
(43:37):
They treat it as just an ordinary number,
although if you measure something,
if you measure lengths,
you measure an electric current,
you are never going to find object
where the length is minusi one meter or one inch.
So ghost particles are similar,
particles that you never observe,
(43:59):
so in some sense, they do not exist,
but if you introduce them and treat them
in your calculations,they'll obey the same rule.
For instance, i is maybeconsidered as a ghostly number,
The first ghostly number ever-- (laughs) Okay.
- To be considered.
One shouldn't be toomuch afraid about ghosts.
(44:21):
- (laughs) Good, and Francois,
you've been teaching here at Perimeter
for more than 10 years, teaching students
about ghosts and quantum field theory,
and actually, I wanted to share
that you taught me many yearsago when I was a student
in this program.- Yes, I still remember you.
(Francois laughs)- (laughs) You remember.
- Which means that you ask question.
- I ask, oh, good, well, I'mstill asking questions now.
(44:41):
(laughs) I wanted to tellyou I still remember,
there was one day afterone of your lectures
where a group of myclassmates and I were talking,
and one student came over and he said,
"That lecture by Francoistoday was just perfect."
He said, "There's no waythat anyone could have been
"in the room and not understand
"everything that he wrote down,"
and I never heard him say that again
(45:02):
about any other lectures,(laughs) so yours was
definitely one of the best.- Okay, great, thank you.
- And we have one morequestion about your teaching,
in fact, from another student
from a few years ago that you taught.
- Hey Francois, this isFarthi from PSI, 2019 Class.
I was wondering, actually,
(45:23):
when did you realizethat you loved teaching?
Would you mind tellingmore about your journey
into becoming a teacher?
- Good question, in fact,I realized I love teaching
when I started teaching.
I don't know if it's achance or an unfortunate fact
to get researcherposition in France at CNRS
(45:44):
when I was a young scientist.
From start, I didn'thave any teaching duty.
It's good to teach, but I had all my time
for doing my research, and I know
that most young scientists nowadays
in France and everywhere,they have to teach.
As long as they have to teacha reasonable amount of time,
(46:04):
that's okay, but often, it's too much.
So I had this great chanceand I think this helped me.
So I was not especiallylooking for doing teaching,
but I was offered first in France,
whether I was alreadyolder, to give some lecture
at a level of master or graduate school.
(46:24):
I realized that I liked it.
So I had the chance, in fact,
to teach first in France inEcole Normale with a group,
it was for about more than 15 years,
some course in applicationof quantum theory
to structural mechanics.
This has been a very good experience
because the students were
some of the best student in France.
(46:45):
Then I was offered this change.
One of the greatestexperience in my career
to teach at PSI, which was really great.
Well, first I discovered
a new research institute,Perimeter Institute,
(47:06):
which was still in the phase one building.
I discovered entire differentworlds of students coming
from many, many different countries
with different backgrounds.
This was different fromteaching in France,
where I had very, very good students,
but somehow, more from thesame mouth, very good mouth,
(47:27):
but the mouth of French physicseducational system in Paris.
So this was complimentary.
It was an international problem,
where, in France, wemostly had French students.
Well, now this haschanged in the last year.
It's really European, but here,
it was the first time I had student
from Africa, South Africa, Far East,
(47:50):
and this mixture and seeing
how the students wereinteracting together,
how the Perimeter was accommodating them,
taking care of them, also having
a decent proportion
of women compared to men.
Great things about this program.
This was a discovery for me.
(48:12):
- Francois, I'd actuallylike to read something
that you wrote a couple of years ago.
It's from a book that PerimeterInstitute put together
to celebrate the 10th anniversary
of the Perimeter ScholarsInternational program,
the PSI program, whichyou've been involved with
since practically the beginning.
You wrote, "Every year was memorable,
"with a special remembrancefor the adventures
(48:34):
"and heroic first yearsin the old post office."
The old post office, by the way,
was Perimeter's first building,
just a few blocks from where we are now.
You wrote, "The old post office building,
"with its sofas and the billiard table
"and the big coffee machine,
"an evening spent preparingthe next day's tutorials.
"Long life to the PSI program
(48:55):
"and to all the studentswho have benefited from it."
Now I just thought thatwas a beautiful sentiment
in the book, and now thereare a lot of students
after 10 years who havebenefited from that PSI program.
What keeps you coming backyear after year to teach,
and what do you get out of it nowadays?
- Well, I come becauseI'm very happy to come.
(49:15):
I think it's a chance for me.
I hope the students still enjoy it,
but I consider it as both a privilege
and this bring me happiness teaching
in front, enjoying the students.
Very interesting group,all the interacting
with the other lecturer and teacher.
Well, last year and thisyear had been much disrupted
(49:38):
by pandemics, and also, seeing this,
that's an opportunity forme to visit the Perimeter
as a scientific research institute,
which is a great, new, vibrant place
for doing theoretical physics.
- Great, well, we're reallyglad to have you here
and part of the teaching hereand the research community.
(50:00):
Thank you so much for sharing your time
with us today.- Thanks.
(bright music)
- Thanks so much for listening.
Perimeter Institute is a not-for-profit,
charitable organization thatshares cutting-edge ideas
with the world, thanksto the ongoing support
of the governments of Ontario and Canada
and thanks to donors like you.
(50:22):
Thanks for being part of the equation.
(bright music)
- Welcome back toConversations at the Perimeter.
I'm Colin and I'm here withLauren, and we are thrilled
to share our conversationwith Francois David.
Francois is a mathematical physicist,
which means he tackles reallyhard problems of physics,
(00:22):
like quantum gravity, usinga mathematical toolkit,
and I have to admit that's a toolkit
that I didn't have a lot ofexperience with growing up.
So I was a little apprehensivegoing into this conversation,
but thankfully, Francoisis a very gifted teacher.
- Francois was actually one of my teachers
when I first came toPerimeter as a grad student
in the Perimeter ScholarsInternational master's program,
(00:44):
and he's been coming toteach in this program
from France for many, many years
and he has an amazingreputation among the students.
I'm now actually an instructorin that program myself,
and so I've been able tointeract with Francois,
both as one of my teachersand now as a colleague.
- So what's it likefor you to put Francois
in the hot seat now, whereyou ask all the hard questions
(01:04):
and he has to answer them?
- Honestly, it was areally different experience
because, back when I was a student,
I was usually toonervous to put my hand up
in class and ask questions.
He even mentions during this conversation
that he remembers I alwayshad a lot of questions,
but I know that I wouldusually stay after class
to ask those around just asmaller group of students,
and so this was really different,
(01:25):
that I got to ask questionsand share the conversation
with so many others.- And for me,
that apprehension I had off the bat,
it melted away so quickly when I realized
just how much he loves physics
and how infectious his love is for it.
I'm excited for otherpeople to get that sense
of the joy of physicsand math from Francois,
so let's step inside the Perimeter.
(01:50):
- Thank you so much, Francois,
for joining us for a conversation today,
and it's great to have you here
at PI all the way from France.
Would you mind telling us a little bit
about what you do as amathematical physicist
and what it means to work in that field?
- Well, first, thank youvery much for this invitation
to this kind of interview.
That's my first experiencein this, almost my first.
(02:13):
Okay, about my experienceas a mathematical physicist,
but I must say that I don't really know
exactly what is mathematical physics,
because it depends a bit on the country,
on the culture, or the person.
So I am partly a theoretical physicist
and partly a mathematicalphysicist or both.
And mathematical physicsis a field of research.
(02:36):
There is no real border, but interface
between mathematics andtheoretical physics.
Mathematical physicistsare more involved in using
recent and sophisticatedmathematical techniques and ideas
because mathematics are way much
than just techniques of calculations.
They are concept, ideas.
(02:57):
So mathematical physicistsare more interested
in the structure of physical theory
and understanding how that works,
what one can tell out of the mathematics
that governs the physical theory,
and understand, often on simple models,
not always, but they take a simple model,
not often directly related tosome real physical systems.
(03:22):
It may be, but they're often idealized
in order to keep track
just of the importantphysical feature they want
to understand and workingout, as deeply as possible,
the math and the theoryand see what comes out.
Are those theoretical modelsconsistent, for instance?
(03:42):
That's very important.
Can we compute exactly andprove properties of this model,
or are we just able to use
what are called phenomenological model?
So one makes assumptions,
some approximation, and then one relies
on calculation and alsophysical intuition,
(04:05):
and often it works, butsometimes it doesn't work.
You really have to work hard
and do hard math and some deep,
and sometimes unexpected results come out.
So that's mathematical physics.
- Francois, you used theword consistent there
to describe the research.
Does consistent mean that an idea is true,
(04:25):
or that it's true enough for now,
and is inconsistency an enemy of science?
- In my mind, consistency isa mathematical consistency.
It's related to another concept,
very important for somephysicists, not all of them,
but it's a mathematicalbeauty of a theory.
So it's something which wasvery important for Paul Dirac,
(04:45):
one of the creator andinventor of quantum mechanics,
who considered that atheory had to be true
if it was beautiful.
This led him, for instance, todiscover the Dirac equation,
though often, beauty is associated
to mathematical consistencyin the mind of mathematician
(05:06):
and in the mind of manytheoretical physicists.
There is something which ismore than just mere beauty
because some very simpleobject can be very beautiful.
Consistency means that,often in theoretical physics,
one needs to start with some assumption.
There is space, there is time.
(05:26):
For instance, one important assumption is
there is no difference betweenthe future and the past,
which seems a bit,
of course, contradictorywith our daily experience,
but that's the deep principle
of, nowadays, theoretical physics.
So one makes assumption, let'ssay what physical problem
or physical system is described
(05:47):
by one makes some assumption.
One assume the rules, for instance,
the rules of classical mechanicsor the rules of the law,
other than the rules of thelaw of quantum mechanics,
the law of hydrodynamics,the law of classical physics,
Newton Law, et cetera, and one see,
whether building out of that,
one doesn't run up into somemathematical inconsistency.
(06:09):
Sometimes it's easy to see
that there should be some inconsistency
in some direction, so don'tlook in this direction.
Look in the problems whereinconsistency doesn't appear.
And sometimes the inconsistencyappears in a surprising way.
And of course, if you run intoa mathematical inconsistency,
(06:31):
it means that you are to think more.
Either one of our assumptions was wrong,
or it might be a paradox,
but not a real inconsistencyif you work out enough.
Science and knowledgeprogress by making errors.
If everything was clearlyunderstandable and consistent
(06:52):
from the very beginning,it wouldn't be interesting.
- And could I also say maybe
that, if in physics we oftentend to start with assumptions
and, as you said, sometimesthose assumptions might lead
to inconsistencies and sometimes not,
would a goal of mathematical physics be
to provide more structureto those assumptions
(07:12):
so that there may be, at somepoint, no longer assumptions?
- Yeah, this happens, too.
Sometimes you start, from assumptions,
you work or after someother researchers come out
from different field or different ideas,
or even some mathematicians come out also,
and when discovered that thoseassumption were were correct,
(07:36):
it was not coming from some naturalness
or intuition that thingsshould be that way.
It comes out that they had to be this way.
And that's a differencebetween often, one start
by, oh, things shouldwork this way or that way.
And then you may have different theory,
which start from different point of view.
(07:57):
After working often very hard
by a team of very differentpeople, one comes out of that
that, in fact, oh, thingshad to be that way,
this way, and not that way, or sometimes,
oh, things had to be this wayand your two approach were
seemingly contradictory, but consistent.
One time, this happens in the early days
(08:19):
of quantum mechanics, veryoften, where people were starting
from some kind of wild assumptions.
- I often hear mathematicians talk
about the sense of beauty in mathematics,
and that's a beauty that, personally,
I haven't been able to experience
because I grew up alittle bit afraid of math.
Can you describe the sense of beauty
(08:39):
that you see in mathematics?
- I'm not a mathematician,
so I won't speak as a mathematician,
although I know some mathematics.
I was educated in mathematicssince the French high school,
and the university system is more focused
on mathematics than in other countries.
Also, I married a mathematician
and two of my daughtersare mathematicians.
(09:01):
My impression is thatmathematicians see beauty
in simplicity of structure,but consistencies of structure,
objects can be mathematical,theories can be complicated,
but there is some underlying structure
which enables you to come out to theorems
by abstract reasoning, not just heavy
and technical calculation.
Although they are also very important,
(09:23):
they also both in theoretical physics,
science in general, or in mathematics,
you see simplicity aftera lot of hard work.
It's a bit like diggingan archeological dig.
You find some beautiful archaeology,
but you had to work, work,and once you find something,
you say, "Oh, but I shouldhave looked in this direction,"
(09:44):
come to the results very easily,
but of course, you just knowbecause you worked hard.
So that's my feeling
of what a mathematician feel about beauty.
So one of my daughter is a mathematician.
She's doing algebra, geometry,a number of theories,
and she said, "I prefer mathto physics because in math,
"we are dealing with objectswe have created ourselves
(10:08):
"and so we know it'sconsistent, while in physics,
"there is some external worldand we start from that."
We want to understand theuniverse, we want to understand
how a cell works
or how the solar system works
or why there are chemical reactions,
and that's something which is given to us
(10:30):
or which is there for us to understand.
That's probably one reasonwhy I prefer to be a physicist
than a pure mathematician.
So probably my brain prefersto be a mathematician.
That's why I'm a mathematical physicist,
but my curiosity or my intuition prefers
to have surprises comingfrom where we live.
(10:52):
Especially here, you have
a group of very good people working
with the foundations of physics
and the foundation ofsome philosopher, too.
They will be able to tellmore, but it's unclear
whether the mathematicsare part of the real world
or something completely outside.
That's a view of many mathematicians,
that mathematics exists by themself.
(11:13):
This is more considered,mathematics as a tool.
There is a debate that goesback to the great philosophers
about what are mathematics and physics,
since they are intertwined
since they were created or discovered.
- From what you say, I mean,
you're giving us a nice description
that mathematics involvessome beautiful structures
(11:35):
that we can create, andphysics is about describing
these really interestingphenomena in our world,
so maybe mathematical physics is working
from both of those ends
to give some structure to the universe,
and oh, maybe that's not correct, but-
- No, I think that's a good view,
but I'm not an historian of science,
(11:55):
but many of the mathematicalobject were created
from the real worlds
and then evolved on theirown, and some structure
of the real worlds have beendiscovered through mathematics.
- And is that why we need
mathematical physics, so that we make sure
that those two ends aretalking to each other?
- The interface has been there.
It has been important,
(12:17):
depending on the historicalperiod in science
and also on the countries,but the interface has to be.
Otherwise, there won't be goodphysics without mathematics,
of course, because I think Galileo stated,
one of the first to state,
that mathematics is a language, physics.
Also, a lot of mathematiciansnow, not all of them,
but of course, it depends,get inspiration from physics,
(12:39):
and the ideas which,somehow, a bit clumsy ideas,
created by theoreticalphysicists, common mathematics,
challenge things, andthen come back to physics
as a neat tool and with newideas provided mathematicians.
There are many examplesthat one can think,
(13:00):
but a few in the last decades.
- So mathematics, you said,is a tool that we can use
to make progress in bigproblems in physics.
So what are some of thebig problems in physics
that you are trying to tackleusing mathematical techniques?
- I've been very much interested.
In fact, I realized all along, my career,
(13:21):
not only this question,but about random geometry,
let's say starting fromgeometrical objects,
and see what's the role of randomness,
and one of my interests in thatcomes from quantum gravity,
so quantum physics and gravitation.
Theory of gravitation hasbeen born with Kaplan, Newton,
all the great mind in the 19th century.
(13:44):
Then Einstein discovered
that, in order to makehabitation compatible
with the theory ofrelativity that he discovered
in order to understand the behavior
between light and matter, no habitation,
he discovered that, infact, spacetime orders
that you shouldn't consider space and time
(14:05):
as two separate notion or entities,
but they have to be takenas a part of spacetime.
Einstein discovered that,in order to formulate
the consistency of gravity,the spacetime itself
as a internal structure, it has a metric
and it can be a geometrical object.
In fact, it is a curved object.
All of spacetime, so both space is curved.
(14:26):
Usually, you often form this fact.
You said that you have flatspace, you put the body in it,
like the sun, and it curves the space.
And then therefore, it's like a ball,
and you can have a marbles way
to explain empirically why theplanets orbit around the sun.
The theory of generalrelativity of Einstein says
(14:48):
that, also, time is curved,and that's something
which is more difficult, too,
that it's space and time whichare curved, not only space.
Productivity tells us that, in fact,
time is associated to space,so times has to be considered
as a separate time atdifferent points in space.
(15:09):
When you start tocompare what's happening,
when you go to a differentplace, you let run time
and then you come back at the same place,
you discover that spacebehaved in a different way
that you could have expectedif time was something uniform,
like in Newton theory of time,
especially when there isa gravitational field.
If you have a black hole and you are far
(15:32):
from the black hole, or ifyou go close to the black hole
and come back or close tothe sun and then come back,
then time has very differentlyapproach a black hole.
You come back, then theclocks are desynchronized.
There was a very nice example of that
in a movie, this "Interstellar."
This is checked in laboratories,not going near black holes,
(15:56):
but just having two atomic clocks.
As you raise one of theatomic clocks by a few meters,
drop it back on the tablewhere it started from,
and you can see such effects,
tiny effects, but they are measurable
and I agree with the theory.
Now come quantum mechanics,great discovery of last century.
Einstein also played arole, but less central,
(16:17):
compared to relativity.
And in quantum mechanics,
some very special kind of randomness,
rather than randomness, one choose it.
The role of chance is very important.
There is some indeterminacy.
You are never sure of what the results
of a measurement willbe, but this randomness,
(16:38):
in some senses, uncertainty is governed
by mathematical role whichare very, very precise,
so it's not randomnessjust because we don't know
exactly what's going on.
When you are interested in,
for instance, the theoryof quantization of gravity,
one of the great problemsnowadays of present physics,
(16:58):
you have to treat spacetime
as a curved object, a curved spacetime,
but with some randomness coming
from the quantum nature of the universe.
And we know that, for consistency,
this idea of consistency,the beauty of the theory,
the geometry of spacetime,the curvature of spacetime,
(17:20):
has to be treated as a random object,
but an object with randomness agreeing
with the law of quantummechanics, if, indeed,
gravitation is consistentwith quantum mechanics,
and we don't really knowif they are consistent.
We hope that it'sconsistent, we are trying
to make a consistenttheory of quantum gravity,
but maybe we'll come upinto an inconsistency,
(17:44):
which means that we will have to build
a new theory of nature, which will be
post-quantum and post-gravitational.
- So quantum gravity,it's essentially the quest
to reconcile two theories,
quantum mechanics and general relativity,
and to come up with abridge between the two?
- We need to have aconsistent physical theory,
(18:07):
which leads us
to a complete understandingof quantum mechanics
and a complete understanding of gravity.
We have to build such a theory.
Some physicists thinkthat it's not necessary,
that we can still livewith those two theories,
but the vast majority thinks
that, for just this reasonof consistency and beauty,
in the sense of logical consistency,
(18:28):
there has to be such a theory.
It depends with whom you talk, though.
There are several direction of research,
and it's a very active subject,
in part, well represented
here in the Perimeter, of course,
and there are many different ideas.
Some are mathematically well-developed,
some are less and more rely on intuition
(18:50):
or some toy model.
The two main ones are string theory,
and the other one is based
on still treating thegeometry of spacetime,
how four-dimensionalspacetime as some basic data
and quantizing it according tothe law of quantum mechanics,
while string theory iswider and more speculative.
- A lot of your contributions are
(19:12):
specifically to two-dimensionalquantum gravity,
and we had a really good question sent in
from Tebra in Bangladesh-- Ah, okay, yes.
- So maybe we can listen to his question.
- Hi, Francois, this is Tebra.
I'm a theoretical physicistbased in Bangladesh.
Of course, you and I know each other,
so this is for otherpeople, other listeners.
(19:34):
Anyway, I have a question for you.
Recently, there have been some buzz
in the physics circle
about your work in two-dimensional gravity
and how that has helped breakthroughs
in recent years, so I was just wondering
if you could explain in general terms
(19:54):
what your contribution was
to the field of two-dimensional gravity
and how that contributedto recent breakthroughs
in two-dimensional gravity.
Thank you for listening andthank you for your answer.
- Thank you, Tebra.
I've been specifically interested
and worked and got someinteresting results in a subfield
(20:17):
of quantum gravity calledtwo-dimensional gravity.
It's both a toy model anda very interesting model
for some physical application.
It's a model which isvery much simplified,
a core model where you canstudy one aspect of the physics.
- But the idea would be that,by working with this toy,
we can still gain some insightsthat will still help us
to understand the more complicated system?
(20:39):
- Yes, and so an example of a toy model,
which is a very useful example
for studying quantum gravityis to consider that spacetime,
instead of having threedimension one time,
or as in string theory,
nine or 10 dimensions of spaceand one dimension of time,
or maybe nine dimension of spaceand two direction of times,
(21:02):
would consider a very simplifying model
of spacetime, where you have
one direction of space,so space is just a line,
and one direction of time,
so spacetime is just a sheet of paper.
So it's a very simple model,
and you lose many aspectsof habitation theory.
In particular, you lose
a very important aspect of your operation.
(21:25):
You lose the law of attraction,
Newton's Law, for some technical reason.
So you have no habitationanymore, but you have geometry
because a sheet of paper can be curved.
If it's a rubber sheet, it has curvature,
so you keep one of the basic point,
that spacetime is curved.
So you can quantize it
(21:45):
and you can study the quantum effects.
In particular, that's the simple case
where you can build a consistentquantum model of gravity,
and you can build atheory on simple axioms
and compute things and go tothe end of your calculation
and get insights about whatquantum gravity could be,
(22:05):
or some aspects of quantumgravity could be or could not be.
So working with a two-dimensional model
or either one-plus-one-dimensional model,
spacetime, rather thantwo four-dimensional,
three-plus-one-dimensionalspacetime is very important
and is very interesting.
And I've been working,I think, since the 80s,
by some period on those models.
(22:28):
My contribution in this idea,
I've been twofold.
I've been one of the firstto implement the idea
that, instead of takinga continual spacetime,
you can approximate itby a discrete object.
Typically, you can see thatyou can build a surface
out of taking triangles, flattriangles, but gluing them,
(22:49):
and if you glue them in a proper way,
you can build polyhedra.
So you can build curved surfaces
or curved spacetimeout of discrete objects
and realize the quantumnest of a quantum spacetime
by looking at the common matrix
of this construction you can make
by building what's called triangulation.
(23:11):
If you glue a triangle,
you build a triangulation of a surface
or you build a discretizedsurface or a discrete surface,
and treating this objectat quantum means look
at the status, see that's a surface.
That's a typical, average size,
average shape, averagecurvature, or such an object,
and it seems they'renaive and simple ideas,
(23:34):
but it was motivated by thefact that this procedures is
now to work already in quantumphysics without gravitation.
When this idea wasintroduced, it was in the 80s.
Theoretical physicists had introduced
what they called lattice gauge theory,
discretized theory of the stronginteraction, for instance,
but on a discrete spacetimeby extension and energy,
(23:58):
we put high in it.
Other theoreticians andsome mathematician, too,
started to look at canyou make this idea working
for very simple, one-plus-onetheory of quantum spacetime?
And it turns out that youcan work and make calculation
in these toy models usingmathematical theory,
which came out from somethingcompletely different,
which is called thetheory of random matrices,
(24:21):
which comes from thestudy of quantum systems,
which are very complicated dynamics.
So not toy models, but very,very complicated models,
and looking for whether they still exhibit
some universal feature, which are there
because the system arevery, very complicated
instead of being very, very simple.
(24:43):
- The idea of a toy model,
is it akin to building a toy car
with just a wooden rectangleand four round wheels,
making sure it rolls, and then eventually,
gradually adding more and more features
until you've got a sports car?
- If we didn't have thetoy model to think about,
it would have been very difficult
to find in the very complicated system.
(25:05):
So that's one aspect of thetoy model, but then I could say
that there are other kind of toy models,
which is exemplified by thisidea of random matrices.
Want to explain, but think
about the matrices arejust a table of numbers,
like an Excel spreadsheet,where you can add them.
You know that you can add thecells up in a spreadsheet,
(25:26):
but you can also multiply them.
More complicated, but themathematician and physicist know
very well what it means.
And so order comes out of complexity,
or to mention a word
of a famous physicist, E. W. Anderson,
the sum is more than the parts.
It appears, for deep mathematical reasons,
(25:49):
then if you take a verycomplicated object made
out of simple objects, insteadof it becoming just a mess,
it becomes something whichexhibit very simple feature.
Some universal behaviorcomes out of complexity,
and the property of thesum of the subject is
not just emerging from theproperties of the small parts.
(26:11):
It's come out from the rule.
This is also an idea which is important,
for instance, in quantum gravity.
Many suspect that, in fact,
the fact that we have asmooth, neat spacetime
with a bit of curvature, explain gravity.
It may come out fromsomething at quantum scales
(26:32):
and below at some post-quantum scales,
which is completelydifferent and maybe random,
both the idea of taking toy models
to understand the real systemsand taking complicated system
to understand what's goingon for large systems.
There are two trends in common,
not in completely not incompatible ideas,
which are very important inmodern and theoretical physics,
(26:55):
because then you can make toy models
of very complex system and study them.
That's the idea of those fundamentals,
but they are simple, complex models.
- And I wanna go back to a wordyou said a little while ago,
which is this word universal.
You said sometimes in these systems,
you can end up finding somethingthat's actually universal,
so can you tell us what that means?
(27:16):
- Universality means that,out of very different systems,
exhibits the same behavior,
although, in some sense,this behavior is universal.
This concept, which is now oneof the very important concept
in theoretical physics,
come out, not from high-energyphysics, not from gravity.
It comes out from condensed matter.
It led to the discovery orthe creation of a theory
(27:40):
which is called the theoryof homogenization group,
but forget about the group.
You have some different physical system,
completely different,which in fact, exhibit,
in some regime, exactly the same behavior.
If you study the behaviorof ice and water,
water can be a liquid, can besolid, and it can be a gas.
(28:02):
Usually, it's one or the other,
but there is a very special point
when you have water at avery specific temperature
and a very specific pressure.
You reach what is called a critical point,
where water is neither aliquid or a gas, it's both.
At this point, there are huge fluctuations
(28:23):
of pressure and density.
These behaviors occurs for water,
but it occurs also for other gases.
In fact, it's better studied
in other gases or other liquids.
Usually, you have this function.
You heat water, and atsome point, it boils.
It's very simple, suddenly,vapor starts to happen,
(28:44):
so it's called the first-order transition,
but if you increase thepressure, there is a point
where the transitionbecomes smaller and smaller.
At some point, it disappear.
It turns out that youhave system of magnet.
I don't know if, in high school,
you might have done theexperiment that you take a magnet.
So the magnet has some magnetic property.
And if you heat a magnet,
(29:06):
you put it under a Bunsen flame,
at some point, the magnetstops being a magnet.
It's just a dull piece of metal.
So there is a critical temperature
where a magnet stops beinga magnet, and it turns out
that the property ofthis magnet are the same
or very similar to the property of water.
(29:28):
That's very strange.
This has not beenunderstood for many years,
and in the beginning of the 70s
and the 60s and end of the 70s,
physicists working incondensed matter understood
why this occurs, but they understood,
thanks to one of the greathigh-energy physicists
(29:48):
of that time, Ken Wilson,who started being interested
in what's called critical phenomena.
He built out of high ideas,
which came from high-energy physics,
the concept ofrandomization transformation
and what's called now randomization group.
The idea is that, ifyou start from a system,
for instance, which isdescribed at microscopic scales
(30:10):
by a collection of atoms,
atoms can behave as small magnets,
very little magnets, in fact.
That's the origin of magnetism.
You have atoms, you haveelectrons turning around,
and the electrons have a magnetic moment.
In the addition, theycreate magnetic moments
because they go around thenuclei of the atom, et cetera.
Okay, anyway, so that'sthe origin of magnetism,
(30:31):
but if you start from the magnet described
just by its microscopicstructure at the atomic scale
and you start to look
at what are the properties of this magnet,
if you go at larger and larger scales,
so changing the scalesor making some averaging,
the magnetic property of a magnet,
instead of looking atwhatever magnet you see
(30:52):
at the property, at the scale of an atom,
you see a cube, 10-by-10-by-10 atoms,
and you see what are theproperties of this magnet.
- Like zooming out on a picture?
- No, it's exactly like zooming out,
but zooming out being defined
in a proper mathematical way.- (laughs) Right.
- And if you do that,
it was discovered by KenWilson and explained,
(31:14):
and the other physicistworking in that field,
that this posed view sometimesconverges in substance.
You zoom out, you zoom out, you zoom out,
and when you have zoomed,you find something
which is the same kind of object,wherever you were looking,
at a magnet or at a fluid,
(31:34):
where you could say,"Okay, this tiny region
"of space can be eithera liquid or a gas."
So if you want, you would takethe molecule of your water,
and either they are very closely packed
and they are connected by hydrogen bonds
or there, they can wanderaround so they form a liquid.
So it's exactly the same thing.
You take very different system,
sometimes complicated objects,
(31:55):
so the dynamics can be complicated,
can be simple in your toy model.
It can be complicated in your model.
You zoom out, you zoom out, you zoom out,
and if you go zoom out enough,
sometimes you find the same object.
So in this sense,
simplicity or beauty is emerging
by zooming out what's goingon in the complicated system.
(32:18):
So this is the idea of universality,
which is very important in physics.
When you normalize, you average
and see what has a property.
This creates some kind ofnorm, and renormalization means
that you normal the scalesand you change the scale.
You renormalize, and youchange against the scale.
(32:38):
You will renormalize,et cetera, et cetera.
So you have this idea of toy models
and this idea of normalization,
so that the simple phenomenon come
out of very complicated object,
and irrespective of the detail
of what's going on the small scales.
- And it seems, Francois,like some of these tools,
like renormalization groupor random matrix theory,
(32:59):
they've allowed you to studyquite different problems.
You've talked just now about some problems
in condensed matter.
You were telling us about quantum gravity.
Would you mind maybe telling us the story
of your career and maybethe different problems
that you've looked at along the way?
- Yes, in fact, Irealize that this concept
of universality andnormalization group has been
(33:22):
one of the guiding line of my research.
Those tools were createdwhen I was in high school,
so I learned them when I started.
I was a graduate student,
and I've been trying toimprove them and apply them.
So I started in high-energyphysics and theory,
and then I started being interested
in whether I could apply thoseidea to condensed matter.
(33:44):
And then when I was a post-doc
in Princeton, I came in contact
with a researcher workingin quantum gravity,
this idea of discretizing spacetime,
and so I applied it to quantum gravity.
So I started to study this ideato work in quantum gravity,
so I studied mission model,a bit of higher dimension,
but this doesn't work so well,and then I came in contact
(34:07):
with another field of theoretical physics,
which is biophysics, in fact,and one very specific subject,
which is the study of membranes
who have two-dimensionalthemes in three dimensions,
because when I was in touchwith young physicists,
visiting (indistinct),and one got a position
and they were working in that field.
(34:27):
And this idea of universalityis very important
because, by discussing, wediscovered that, in fact,
some models of quantumgravity in two dimension
and some models ofmembranes were very similar.
They had some difference,in particular as a whole
of bending in two-dimensional gravity.
Bending is not important.
Well, it's very importantin a physical membrane.
(34:49):
So I've been working in this concept,
studying the physics ofwhat's called fluid membranes
and then crystalline membranes.
This was a very exciting fieldand it's still important,
but then a few years later,there was some great progress
in the theory of quantumgravity and in string theory,
(35:09):
made by a group of theoreticians,especially Russian ones,
this Russian school with Migdal, Polyakov,
and we made progress in thetwo-dimensional quantum gravity,
so I came back to that field.
And I was there, more interested
in not discretizing spacetime,but taking continuum theory
of two-dimensional gravity,a theory which was,
(35:29):
well, created and invented
by Polyakov, which iscalled Liouville theory.
Liouville is a famous French mathematician
from the 20th century.
He was mostly a number theorist,
but some of his equation wereimportant in quantum gravity.
So our model was neutral gravity,
which is connected to string theory.
(35:50):
It was developed by this Russian school,
and that tends to be knownas the Liouville theory,
but there are other theoriesup to Newton's quantum gravity,
like Kiev's Titan Boommodel and some other one,
but one is the Liouville theory,
and so I've been working on that.
After that, I came back
to quantum metric theory
for several years andwas interested in that,
(36:12):
in particular for quantum cows,
because quantum metrictheory has application
to quantum cows, and then Icame back to quantum gravity.
- The first time we spoke,
you used the term journeyto describe your career,
and you said thattheoretical physics requires
all sorts of different minds,
(36:32):
so what kind of mind do you bring
to the journey of theoretical physics?
- I would say there aredifferent kind of minds
in theoretical physics.
I'm not completely sure which mind I am.
Some likes to wander around.
I'm still a bit stubborn, soI come back to old problems.
When I'm stuck, sometimesI look elsewhere,
but I always come back.
(36:53):
I have some problem in my mind
that I have them since 20 years.
I'm just waiting forthe good idea, if any,
or if someone had a good idea to solve it,
they are still there.
- Some of these problemsthat you've described
to us are incredibly challenging.
Some of them are so difficult
that they may not see a solution
in our lifetimes, possibly ever.
(37:13):
Francois, given the hugenessof these challenges,
what keeps you going?
- Well, I think that's curiosity.
As long as I've not understood something,
I like to think about it.
I feel disappointed.
I feel the failure of nothaving made progress in a field.
If someone else made theprogress, that's fine.
I said, "Okay, I was not smart enough.
(37:34):
"I didn't have the idea."
There is change in research.
Sometimes you just have agood idea at a good time
and sometimes you had it too early,
and you couldn't make out something of it.
- So Francois, we alsogot a question for you
that was sent in from one of the students
that you're currently teaching
(37:56):
within your quantum field theory course
within the Perimeter ScholarsInternational program.
Let's play the question from Anna Kanur.
- You teach a course onquantum field theory,
and one of the topics is ghosts.
Without writing down any integrals,
how would you explainwhat these ghosts are?
(38:16):
- Well, the denominationghost has been given
by the physicists whocreated this concept.
It was a Russian, Faddeev and Popov,
but I'm not completely sure anyway.
Physics likes to find nice nameswhen they have new objects.
Sometimes the names are well-suited.
Sometimes they are silly, but okay.
So ghosts, in fact, arearticles in a quantum theory
(38:39):
with probability to be there is negative.
If you think about probability,
it's a very important tool of mathematics.
And the probability of an event,
if you have some uncertaintyon something happening,
for example, if you play coins
and it has a probability 1/2
to be heads and 1/2 to be tails.
Okay, if the probabilityof some events is one,
(38:59):
it means that it's certain, you are sure.
If it's zero, it meansthat it never happens.
So the probability are numbers which are
in between zero and one, or 0% and 100%.
You cannot have a probability of two.
The sum of the probabilityof all realization
of an event has to be one,'cause something happens.
(39:20):
Whatever it is, you'resure it's going to happen.
If you have a head andtails, 1/2 plus 1/2 is one.
In quantum theory, whetherit's change and uncertainty,
you can calculate probabilitiesof something to be measured,
and so some of the probabilitiesof all possible outcomes
of the experiments ormeasurements has to be one.
In the inconsistent quantum theory,
(39:41):
the sum of probability isone, it's called unitality,
but it turns out that,in some quantum theory,
you get probability twoand probability minus one,
but it's not a physical theory
because you have aprobability, for instance,
to get a particle created,which is minus one.
When you have a theorywhich such particles,
(40:02):
they are called ghosts.
Sometimes when you make a theory
and you get probability which are negative
or greater than one, that's anexample of an inconsistency.
- I was gonna say, itsounds like something
that must bother mathematicians.
- It bothers mathematiciansand it bothers physicists, too,
(Lauren laughs)of course,
because there are many theory
(40:23):
of quantum gravity which have ghosts.
The first theories of stronginteraction are the ghosts.
Most of the ghost'sparticles, when you see them,
it means there's a theory,you can put it aside
and start with a better theory.
In the lecture that I gave, it's a theory
where you try to quantize thetheory of strong interactions.
(40:44):
In this theory, well, you runinto technical difficulties,
and one way to deal with this difficulty
and to solve the problem is tointroduce a fiducial particle
in the theory, whichprecisely has this property
of having negativeprobability to be observed
or larger than oneprobability to be observed.
(41:06):
The fact that you haveto consider those parts
of those kind of ghostly particle
when you make calculationcomes out from the math.
So they have to be there,
but when you work out more on the theory,
you see that you can never observe them.
They are virtual particles that are there
in the quantum vacuum of the theory,
or when you make calculation,you have two particles.
(41:29):
You sew them on together in accelerator,
you have a quantum theory
that this type of what'sgoing on when they interact,
and you have a lot ofvirtual quantum process.
And then there is an outcome,
some other particles,two, three, four, many,
because you can createparticles, come out.
When you do the calculation, you see
that you never see any ofthose ghostly particles.
(41:51):
So those ghostly particlesare there in your calculation.
So in some sense, ifyou are mathematician,
you see if it's in the calculation,
it's something that exists,but you can never observe it.
So in some sense, it's afeature of the calculation.
In some sense, they are likeimaginary numbers in algebra.
I never thought about this analogy,
(42:12):
but I think it's a good analogy.
Imaginary numbers are numbersa bit like real numbers,
but the most importantimaginary number is called i
for imaginary, and i is a number
so that its square is minus one.
So in some sense, you cansay it's not a real number,
but now when you are in high school,
(42:32):
you learn about imaginary numbers
because they are everywhere
when you do calculationin math and in physics.
And in fact, imaginarynumbers were invented by,
I think, Italian mathematicianin the 15th century
to solve a quadraticequation, algebraic equation
that mathematician weresolving since the Greek
and the Egyptians andmaybe the Babylonians.
(42:53):
Okay, and in order to find the solution
of equation involving real numbers,
they discovered that it was notquadratic equation, in fact,
but it was question of degree theory.
Anyway, so algebraic equation,
they discover that it was very convenient
to introduce this numberwhere the square is minus one
and consider it as a real number.
(43:15):
Just make calculationand consider it at par
with a number we're used to at that time.
And so now you discusswith a mathematician
or with a physicist, oreven with the engineering.
Those are useful when youstudy electric currents.
Well, they said, "Okay,well, i is a number,
"as one or minus one."
(43:37):
They treat it as just an ordinary number,
although if you measure something,
if you measure lengths,
you measure an electric current,
you are never going to find object
where the length is minusi one meter or one inch.
So ghost particles are similar,
particles that you never observe,
(43:59):
so in some sense, they do not exist,
but if you introduce them and treat them
in your calculations,they'll obey the same rule.
For instance, i is maybeconsidered as a ghostly number,
The first ghostly number ever-- (laughs) Okay.
- To be considered.
One shouldn't be toomuch afraid about ghosts.
(44:21):
- (laughs) Good, and Francois,
you've been teaching here at Perimeter
for more than 10 years, teaching students
about ghosts and quantum field theory,
and actually, I wanted to share
that you taught me many yearsago when I was a student
in this program.- Yes, I still remember you.
(Francois laughs)- (laughs) You remember.
- Which means that you ask question.
- I ask, oh, good, well, I'mstill asking questions now.
(44:41):
(laughs) I wanted to tellyou I still remember,
there was one day afterone of your lectures
where a group of myclassmates and I were talking,
and one student came over and he said,
"That lecture by Francoistoday was just perfect."
He said, "There's no waythat anyone could have been
"in the room and not understand
"everything that he wrote down,"
and I never heard him say that again
(45:02):
about any other lectures,(laughs) so yours was
definitely one of the best.- Okay, great, thank you.
- And we have one morequestion about your teaching,
in fact, from another student
from a few years ago that you taught.
- Hey Francois, this isFarthi from PSI, 2019 Class.
I was wondering, actually,
(45:23):
when did you realizethat you loved teaching?
Would you mind tellingmore about your journey
into becoming a teacher?
- Good question, in fact,I realized I love teaching
when I started teaching.
I don't know if it's achance or an unfortunate fact
to get researcherposition in France at CNRS
(45:44):
when I was a young scientist.
From start, I didn'thave any teaching duty.
It's good to teach, but I had all my time
for doing my research, and I know
that most young scientists nowadays
in France and everywhere,they have to teach.
As long as they have to teacha reasonable amount of time,
(46:04):
that's okay, but often, it's too much.
So I had this great chanceand I think this helped me.
So I was not especiallylooking for doing teaching,
but I was offered first in France,
whether I was alreadyolder, to give some lecture
at a level of master or graduate school.
(46:24):
I realized that I liked it.
So I had the chance, in fact,
to teach first in France inEcole Normale with a group,
it was for about more than 15 years,
some course in applicationof quantum theory
to structural mechanics.
This has been a very good experience
because the students were
some of the best student in France.
(46:45):
Then I was offered this change.
One of the greatestexperience in my career
to teach at PSI, which was really great.
Well, first I discovered
a new research institute,Perimeter Institute,
(47:06):
which was still in the phase one building.
I discovered entire differentworlds of students coming
from many, many different countries
with different backgrounds.
This was different fromteaching in France,
where I had very, very good students,
but somehow, more from thesame mouth, very good mouth,
(47:27):
but the mouth of French physicseducational system in Paris.
So this was complimentary.
It was an international problem,
where, in France, wemostly had French students.
Well, now this haschanged in the last year.
It's really European, but here,
it was the first time I had student
from Africa, South Africa, Far East,
(47:50):
and this mixture and seeing
how the students wereinteracting together,
how the Perimeter was accommodating them,
taking care of them, also having
a decent proportion
of women compared to men.
Great things about this program.
This was a discovery for me.
(48:12):
- Francois, I'd actuallylike to read something
that you wrote a couple of years ago.
It's from a book that PerimeterInstitute put together
to celebrate the 10th anniversary
of the Perimeter ScholarsInternational program,
the PSI program, whichyou've been involved with
since practically the beginning.
You wrote, "Every year was memorable,
"with a special remembrancefor the adventures
(48:34):
"and heroic first yearsin the old post office."
The old post office, by the way,
was Perimeter's first building,
just a few blocks from where we are now.
You wrote, "The old post office building,
"with its sofas and the billiard table
"and the big coffee machine,
"an evening spent preparingthe next day's tutorials.
"Long life to the PSI program
(48:55):
"and to all the studentswho have benefited from it."
Now I just thought thatwas a beautiful sentiment
in the book, and now thereare a lot of students
after 10 years who havebenefited from that PSI program.
What keeps you coming backyear after year to teach,
and what do you get out of it nowadays?
- Well, I come becauseI'm very happy to come.
(49:15):
I think it's a chance for me.
I hope the students still enjoy it,
but I consider it as both a privilege
and this bring me happiness teaching
in front, enjoying the students.
Very interesting group,all the interacting
with the other lecturer and teacher.
Well, last year and thisyear had been much disrupted
(49:38):
by pandemics, and also, seeing this,
that's an opportunity forme to visit the Perimeter
as a scientific research institute,
which is a great, new, vibrant place
for doing theoretical physics.
- Great, well, we're reallyglad to have you here
and part of the teaching hereand the research community.
(50:00):
Thank you so much for sharing your time
with us today.- Thanks.
(bright music)
- Thanks so much for listening.
Perimeter Institute is a not-for-profit,
charitable organization thatshares cutting-edge ideas
with the world, thanksto the ongoing support
of the governments of Ontario and Canada
and thanks to donors like you.
(50:22):
Thanks for being part of the equation.
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