[MUSIC PLAYING]
PRESENTER: Before I
introduce today's speaker,
I wanted to say a word or
two about two great friends
of the department, Neil
and Jane Pappalardo.
Five years ago or so, the
MIT physics department
realized that we
had an opportunity
to join a consortium
to build two telescopes
on a mountaintop in Chile.
And we really wanted
to do this and couldn't
see any way to do it.
Neil and Jane Pappalardo
decided to help us do that.
And this December, Neil and
Jane and 350 close friends
gather together on the top
of this mountain in Chile
to have a celebration for the
inauguration of the Magellan
telescopes, truly magnificent
instruments, state of the art
telescopes which really
put us in the vanguard
of optical astronomy.
Then two years
ago, Neil and Jane
decided to help us
create a distinguished
post-doctoral program following
the model of the Junior
Fellows at Harvard.
And we began this in
the physics department.
And now we have this
year, for the first time,
three Pappalardo Fellows.
And there'll be another three
joining us next September.
This is really a wonderful
thing because over time,
we hope it will grow
into a program that
spans the School of Science.
Some of the other
departments are already
beginning to follow our example.
So there are a couple of
other Science Fellows.
And this kind of
program is wonderful
because it gives the opportunity
for brilliant young people
to do something that they
want to do that they think
is interesting on their
own, or in collaboration
with other people at MIT.
So Neil and Jane have helped
us in getting our hands
on absolutely
frontier technology,
and also getting our hands on
absolutely fantastic people.
And those are the two things
you need to do great science,
and certainly in physics.
You need great technology
and great people.
And so I'd like to just take
a moment now to ask all of you
to join me in thanking Neil
and Jane for what they've
done for us.
[APPLAUSE]
Now, speaking of great people
who make great physics,
it's time to
introduce this year's
distinguished
Pappalardo lecturer.
And you already have
a nice little summary
in here, which tells you a
little bit about Frank Wilczek.
Frank was just a kid
when he and David Gross
discovered asymptotic freedom.
This is really a critical, a
key aspect of our understanding
of the strong force.
He's made great
contributions, of course,
to our understanding
of the standard model,
to cosmology, to
condensed matter physics.
So he is truly an unusually
broad and deep physicist.
Furthermore, he
and his wife Betsy
wrote a magnificent book on
modern physics for the layman.
And he writes these wonderful
articles in Physics Today which
really are very deep, and
yet, at the same time,
understandable.
Frank is interested
in everything
and he understands everything.
So it's appropriate that he
speak today about everything.
It's all yours.
[APPLAUSE]
WILCZEK: Thank you.
I like to think of Pythagoras
as the first modern physicist.
Certainly, he made one
of the first discoveries
of a physical law
in the modern sense,
and that is a quantitative--
no-- fact about observable
realities of nature.
It's a very beautiful
law, and in a way,
it's a law that, to this
day, is not fully understood.
It's the law that the notes
that we see as harmonious are
the notes where the
length of a string--
he was the first
string theorist, also--
[LAUGHTER]
If you have different lengths of
string of the same composition
and under the same
tension, then the strings
will sound harmonious to
our ears when plucked if
and only if their lengths are
in simple numerical ratios.
So if the ratio of
the length is 2 to 1,
we'll hear them as
being an octave.
If it's 2 to 3,
we'll hear a fifth.
4 to 3, a fourth, and so on.
Well, being a
modern physicist, he
was very impressed
with his work,
and generalized it
to the principal
that all things are number,
that a complete description
of the world should be based
on numerical relationships.
This is what I think of
as the Pythagorean vision,
or, in modern language, the idea
that, as John Wheeler put it,
you get its from bits.
From purely conceptual
information theoretic notions,
if you like, you get a
valid description of nature.
That idea was profoundly
influential and inspiring
to the followers of Pythagoras
in physics, and especially
in astrology.
And one of the people who
made great contributions, both
to physics and astrology,
was Johannes Kepler,
who perhaps represented
the apogee of Pythagorean
thinking up until his day.
We learn in physics textbooks
about Kepler's three laws
of planetary motion, the
first, second, and third laws.
But less well known is
that there was a zeroth law
that he proposed that was the
first law of planetary motion
that he described, which
is entirely fallacious,
but which inspired his career
and was very Pythagorean.
His idea was that the different
distances-- well, first of all,
that the planets moved around
the sun in circular orbits,
and secondly, that the
sizes of those orbits
was fixed by circumscribing
and inscribing
the different regular solids.
So if I remember
correctly, there's
an icosahedron around
the innermost sphere.
And the sphere that
carries Mercury
is inscribed around
that icosahedron.
Then there's an octahedron
then a dodecahedron.
Then you can see the
tetrahedron and the cube.
And all these spheres
rotated carrying the planets
around them.
And as they rotated,
emitted musical notes,
which Kepler even figured out.
[LAUGHTER]
Well, soon after, Kepler
went from the zeroth law
to the first law.
And according to the first
law of planetary motion, which
he abstracted from the
observational data of Tycho
Brahe, the planets actually
move around the sun in ellipses.
So this beautiful construction
was to his credit,
immediately abandoned by him.
And this kind of idea that
the structure of matter
in the universe was dictated by
purely conceptual constructions
like regular solids, went into
an eclipse that lasted, really,
for 250 years.
In Newtonian mechanics
and classical mechanics,
which replaced Kepler's
early speculations,
the orbits of the planets
are largely arbitrary.
If you take the sizes of the
different orbits of the planets
and a star came by
our solar system,
the orbits would all change
and life would go on.
In fact, now we've even observed
extra solar planetary systems.
And they don't necessarily look
at all like our solar system.
In classical mechanics, and even
in classical electrodynamics,
this Pythagorean, Keplerian idea
that the structure of matter
is uniquely dictated
by conceptual elements
just doesn't hold.
Technically it's
because the equations
of classical mechanics
and also the equations
of electrodynamics fix no
particular scale of size.
If you take those equations
and multiply all the distance
scale by a constant, you
get the same equations.
So you map solutions
into solutions.
There can be nothing
that fixes the size
of particular materials,
and certainly nothing
that would lead to chemistry,
to lead to atoms of different
or materials of different
types in different places
in the universe being put
together the same way.
And that's really
the way it stood
until the early part
of the 20th century,
when especially in the
work of Niels Bohr,
the Pythagorean and Keplerian
ideas made a big comeback.
Bohr's original atomic
model was, in fact,
based on an analogy
to the solar system.
It was based on 1
over r squared forces,
electrical not
gravitational, but satisfying
mechanical equations.
But he added the extra
element, very reminiscent
of Kepler, that
only certain sizes
of orbits, only certain sizes
orbits, actually occurred.
But this time it's right, or
at least a fair approximation.
I'm looking for a pointer.
Ah.
Okay.
So you had different
possible orbits and electrons
in the atom could only
orbit in one particular way.
Then there was some kind of
mysterious non-causal process
where they could hop from
one orbit to another.
And you're not supposed to ask
where they were in between.
By reasoning like this, which
Einstein called the highest
form of musicality in
the sphere of thought,
somehow referring back to
the music of the spheres
and the discrete
relationships, Bohr
got a successful description
of the spectral lines
and their frequency,
which I've written
down here as an equation.
The details of the equations
aren't so important for us.
But I want to emphasize how
closely the idea of capturing
reality in terms of purely
conceptual notions-- that is,
ultimately numerical notions--
is realized in this formula
for the spectral lines.
Almost everything in
it, everything in blue
here is a number.
4 is certainly a number.
Pi is a number.
c, the speed of light, well,
that's an honorary number.
Why do I say it's
an honorary number?
Well, in the theory of
special relativity, which
is a deep, foundational
theory of physics,
we have a symmetry
between space and time.
Transformations,
symmetry transformations,
that allow us to mix up space
and time, the so-called Lorentz
transformations.
But space and time are
measured in different units.
So we have to have some
conversion factor that
converts those physically
identical objects, objects
related by a symmetry,
into the same units.
And that's what this
conversion factor does.
So you should think of it
as being like the three that
converts yards into feet.
Similarly, h bar,
Planck's constant,
can be thought of as
an honorary number
because in the deep theory
of quantum mechanics,
there is a relationship
between energy and frequency.
The energy of
oscillations is related--
the energy associated
with an oscillation
is related to the frequency
at which it occurs in time.
But energy and time are
measured in different units.
We need a conversion factor.
And that's Planck's constant.
Okay.
These n's are different numbers.
They describe the
different orbits.
And then we have some
things that are not numbers,
whether honorary or actual.
But there aren't
very many of them.
There's alpha, the
so-called fine structure
constant, numerically
equal to about 1/136,
which describes the absolute
strength with which protons
and electrons
attract one another.
So this is just telling
you about the strength
of the electrical forces.
And then we have a
mass factor, mass
of the electron times
the mass of the proton,
divided by the sum of the two.
This is almost equal to just
the mass of the electron
because the mass
of the proton is
much bigger and almost
cancels between numerator
and denominator.
Okay, so that's hydrogen,
and this physical spectrum
of hydrogen reduced
to almost purely
conceptual numerical elements.
In fact, it is reduced in
a very good approximation,
if we take the
mass of the proton
to be very large
compared to the electron,
to just two non-numerical
elements, that
is the mass of the electron and
the fine structure constant.
That's hydrogen. And
hydrogen described
in Bohr's provisional
theory, or Bohr's theory,
which was just a way station
to modern quantum mechanics.
The successor theory to
Bohr's theory of atoms,
modern quantum
mechanics, is based
not on a picture of electrons
as particles circling in orbits,
but rather electrons as
waves which oscillate
up and down around the proton--
yes, oscillate up and
down around the proton,
which has captured them in
different states of excitation.
And this is a beautiful
shareware program by Dean
[? Dowager ?] which shows
the different energy
levels, the different
stationary states of hydrogen,
how the electron behaves
in the modern analog
of these different orbitals.
It's Mac only.
[LAUGHTER]
And it's a beautiful thing.
In fact, it also allows you
to play microcosmic God.
You can grab the atom
and spin it around.
You can-- well,
fortunately, what
I see on my screen is much
better than what you see.
You can spin it around.
You can make
different transitions.
So here let's
transit down there.
See, that's this line here.
And this is the real thing.
This is actually being
computed in real time.
This is what
electrons actually do.
This is what we're made out of.
This is our most accurate
description of atomic nature.
And it only depends--
all this only--
this is hydrogen.
If you also go to more
complicated atoms,
if you go to
molecules, all you need
is the mass of the
electron and alpha.
So those are the two
first ingredients
in our numerical
recipe for nature.
So by 1930 or so, modern
quantum mechanics was in place.
And attention switched to
describing those atomic nuclei,
the protons and the
more complicated
atomic nuclei in bigger atoms.
Well, first of all, I
showed you the wave atoms.
And I think you'll agree,
you get a lot of structure
and a lot of physics out
of just these two numbers.
But this was approximate.
We had to neglect or take the
mass of the proton to infinity.
And similarly, we'd have
to put in from experiment
the masses of other nuclei if
we wanted to really account
for matter in full accuracy.
So it's only an approximate
recipe for nature,
even for ordinary matter.
And the attention of physicists
starting in 1930 or so
switched or began to
focus on doing justice
to those atomic nuclei inside.
The first great breakthrough
in understanding
that was the
discovery by Chadwick
in 1932 of the neutron
and the swift emergence
of the modern picture
that nuclei are basically
weakly bound assemblages
of protons and neutrons.
But then it emerged--
and in this development,
crucial experiments
were done by Friedman,
Kendall, and Taylor
in an MIT collaboration--
that protons had
internal structure,
that they're not simple
objects, but are assembled out
of some kind of
simpler structure.
And then, in a
complicated history,
which fortunately has an outcome
that's much simpler to describe
than the history, we arrived
at the modern understanding
of what holds protons
and neutrons-- what
protons and neutrons
are made out of,
what holds them
together, and what
holds more complicated
atomic nuclei together.
This theory is called quantum
chromodynamics, or QCD.
In quantum
chromodynamics or QCD,
we describe the stuff
that makes protons
in terms of two different
flavors of quarks,
the U and the D
quarks, each of which
comes in three so-called colors.
They're actually
red, white, and blue.
But the white was not
suitable for the transparency.
So you should imagine that
these are white quarks.
And a bunch of gluons.
Now, these are just symbols.
And clearly, I'm
just joking when
I say that they're colored.
What this color really means
is not, of course, the color
you would see it of physical
light of these quarks.
Color is actually
a generalization
of electromagnetic charge.
It's more to be
thought of as a charge.
QCD is a generalization,
a vast generalization,
of quantum electrodynamics,
of the theory
of electrical and
magnetic forces.
Whereas electrical
and magnetic forces
are based on electric
charge, these
are based on the three
kinds of charges,
all different, red,
white, and blue.
And the gluons are the analog of
the photons of electromagnetism
that allow--
that respond to these charges.
The big difference between QCD
and QED, the big difference
that comes from having
three colors instead of one,
is that gluons--
which can change one
kind of color quark
into another by carrying
off, say, the green--
excuse me, white-- color
and carrying in a red color,
thus changing the green one,
the white one, to the red one--
themselves have
unbalanced color charge.
See, something that does that
has not zero charge, as it
would be if you had just
one electric charge or you
changed an electric charge
into an electric charge
of the same value.
The photon has zero charge
that it carries off.
Charge is conserved.
Here, if you change
one color into another,
the gluons have
unbalanced charge.
It has one unit
of green charge--
white charge-- and minus
one unit of red charge.
So the gluons themselves carry
the color charge which licenses
you to draw the
Mercedes-Benz diagram,
where gluons which
respond to color--
that's what they care about--
interact with each other.
Many of you have
probably seen Star Wars
and remember the
laser swordfights.
Well, laser swordfights
would actually
be very tedious affairs
because if you use photons,
they'd just wave
through each other.
Any of you who've
worked in a laser lab
probably haven't
noticed lasers clinking
against-- laser light
clinking against each other
when they happened to cross.
Of course, it's a movie about a
different galaxy in the future.
I conjecture that they're
using color lasers with gluons.
Then something
dramatic would happen.
I'm not sure exactly what, but
there would be quite a bang.
Anyway, this changes
the equations,
it makes them much
more difficult to solve
and leads to many, many
fascinating phenomena
that I won't be able
to do justice to,
of course, in this reflector.
I'm not even doing justice
to them in my QCD course
this semester.
But among the rest, it can be
thought of as mediating forces
similar to
electromagnetic forces
that cause quarks to attract
one another, similarly
to the way that electrons
and protons attract and bind
each other into atoms.
Systems of quarks can
attract and bind each other
into other kinds of particles.
Well, that's a very imaginative
picture, you may say.
How do we know
that it's correct?
And how do we make
it quantitative?
Well, the key is symmetry.
Well, the key is
analogy and symmetry.
As I've told you, there
are deep analogies
between how gluons
interact with color charges
and how photons interact
with electromagnetic charges.
And in fact, we just steal the
equations from electrodynamics
and use basically the same
equations in this context,
with the modification that
we have this Mercedes-Benz
process.
So we know exactly what the
form of the interactions is.
And it's postulated to be
perfect symmetry among all
the different colors.
So there's no arbitrariness in
how strongly one kind of quark
interacts with another.
Every single allowed
process occurs
with a definitely
determined strength.
And we have absolutely
unambiguous predictions
of the theory, if we can just
manage to do the calculations.
And after something like 10
to the 18th floating point
operations, you can calculate
with only fundamental
microscopic input the masses
of protons and neutrons--
those are called
nucleons on this plot--
and a whole lot of
other particles made out
of just the up and
down quarks, the gluons
that appear in the
strong interaction,
and there's also
another quark that
doesn't occur in
ordinary matter,
but I left it in here to have a
bigger diagram with more things
to compare--
the strange quark.
So these black horizontal
lines-- so we're
plotting here just different
kinds of particles, and here
their masses.
The experimentally
observed masses
are these horizontal lines.
And the calculated masses with--
and this is the
profound point I want
to emphasize-- no input except
purely conceptual input,
the nature of the theory
and its symmetries,
and two mass parameters
for the up and down quarks,
and if we want to do
strange quarks, one
more mass parameter.
This is all output.
So you compute the
masses of the particles
here with 10% accuracy in terms
of very, very few parameters.
By the way, there are
later calculations
that are beginning to
nibble away at that 10%.
And there's every reason to
think that the agreement will
be precise.
Maybe you have to do 10
to the 20th floating point
operations instead of 10
to the 18th to get there.
Underlying this,
these calculations,
is a vast generalization
of those beautiful pictures
of the different
states of atoms being
waves oscillating in space.
All these different particles
consist of quarks, either three
quarks or a quark
and an anti-quark,
oscillating, making
wave patterns like that.
So they're oscillating in
the same way as electrons,
but also oscillating in an extra
three dimensional color space.
The different colors
getting mixed up.
It really taxes the imagination
to try to think of all this.
But if you liked those
pictures of hydrogen,
and if you have a
lot of imagination,
you would love what
protons look like.
And in a very precise sense,
the different kinds of particles
are made up of--
the different kinds of
particles we observe in nature
are made out of quarks
and gluons oscillating
in different ways with the
different waves beating
against each other
in stable patterns.
The different
stable patterns are
what makes the different
particles we observe.
They are, in a
very precise sense,
like the tones that
the vacuum can sound,
that space can sound.
Space can produce
these particles
and they interact with each
other in certain stable ways.
That's exactly how we get tones
from a musical instrument.
And it's even similar
equations, with waves
oscillating in space.
So we get a lot
from very little.
In fact, the more you look
at this, the more impressive
it is because the
mass of the gluon
is taken to be 0,
not for convenience,
but because the
symmetry of the theory
requires that the mass of
the gluon be rigorously 0.
And you notice that the mass
of the up and the down quarks
in these units isn't making
a negligible contribution
to the mass of most
of these particles,
certainly to the proton.
The mass of the proton is
about 1 in these units, 1 GEV.
The mass of the
things that are in it
is contributing almost
nothing to that.
The mass of the proton doesn't
come from its being made out
of heavy objects.
It comes from the fact that
these objects are being bound
together by attractive forces.
They're are trying to pull
away because they're waves
and they want quantum
mechanically to just dissipate
away.
But there are forces
pulling them back.
And so there's energy in the
oscillations, the pull and tug
between the forces and the
quantum mechanical uncertainty.
And when you have energy,
according to a slight
modification of Einstein's
familiar equation--
not e equals mc squared, but m
equals e divided by e squared--
you can turn pure
energy into mass.
And that's, in fact,
the source of most
of the mass in the universe.
So really, to do a really
good job on ordinary matter,
you need you mu,
md, and apparently
some analog of the
fine structure constant
that tells you how strongly
the gluons couple, just
how numerically
powerful the force is.
But actually, two
of these masses
are almost insignificant,
quantitatively.
One sign of that is that
I didn't show arrows here.
Experimentally,
they're not really
known to within better
than a factor of two,
even though they're the most
fundamental constituents
of matter that have mass.
But it's even better than that.
So so far we've gotten
a description of nature,
of ordinary matter in
terms of five parameters.
We had the mass of the electron,
the fine structure constant,
and then we have two that
don't matter very much,
the masses of the up and down
quarks, and apparently the fine
structure constant, the
analog of the fine structure
constant that tells us exactly
how strong the interaction
between quarks and gluons is.
But now we come to another
crucial, beautiful aspect
of QCD, which is that the
strength of the interaction
depends on the distance
at which you measure it.
This is due to the fact that in
the quantum mechanical theory,
you have virtual particles
which come to be and pass away.
And what we see as empty space
is actually a dynamical medium
that can screen
charges and affect
how charges at great
distances see each other.
They don't see each
other directly,
but they see each
other as modified
by the intervening medium.
So the strength
of the interaction
depends on the distance.
It's easier, for
technical reasons,
to measure how the
probability of radiation
varies as you change energy.
But theoretically,
that's the same--
or the inverse, rather--
of how the force
changes with the distance.
And here experimentally you
see a tremendous variety
of experiments indicating that
as you go to higher energies,
the probability of
radiating gluons
goes down, indicating
that the force is getting
weaker at large
energies or equivalently
at small distances.
Or put another way,
the force grows
as the distance
increases, which is
an explanation of why
quarks can't get very far
away from each other.
In any case, from our sort
of philosophical point
of perspective of seeing exactly
how much it takes to describe
the world, the
important phenomenon
is that we can eliminate
one of the numbers.
And we've gotten down to five.
Every step down is
a significant step.
So we've simplified the
description of the world by 20%
because we don't have to
specify a fine structure
constant for the
strong interaction.
We don't have to specify
how strong it is.
It can be any strength you want.
The strength varies
with the distance.
So I can trade the
strength of the coupling
for a measure of distance.
So the strength of
the coupling is not
an independent parameter in some
sense-- well, in this sense.
It's simply telling you how
to measure the scale of energy
or distance because any
value of the coupling
is actually realized that
some energy or distance.
So we've gotten mass
without mass, which tells us
that out of the three apparent
non-conceptual elements of QCD,
two of them are
pretty insignificant.
And then a third one is
absolutely insignificant.
It can be defined away.
So we've gotten a great deal
the whole structure of protons
and neutrons and
the masses of nuclei
practically from pure
concepts from nothing at all.
But to be accurate, now
our numerical recipe
contains four elements,
the mass of the electron,
the fine structure
constant, and the masses
of the up and down quarks.
And this gives us a superbly
accurate description
of ordinary matter.
It tells us why the thing we
call hydrogen exists and looks
like hydrogen and has
all its properties,
why water is what
it is in principle.
Of course, none of
this we can compute.
Because of experiments
like the ones
I alluded to, the fundamental
interactions that we
can compute, we have great
confidence that the underlying
theory is sound.
Well, that and this.
Now, I want to put in a plug
for physics not being over.
There's been a lot of-- there
is a tendency to talk loosely
about the theory of everything.
And it should be understood
that that's a term of art that
has a very specific meaning.
In that sense, I think we do
have a theory of everything
about ordinary matter.
We have a very precise
theory with algorithms
only a very, very small number
of parameters, which I showed
you, which I think is
going to be our working
description of matter
for a very long time,
and probably forever.
Does that mean we have
a theory of everything
for ordinary matter?
No, of course not, because
what it really means
is that we have nothing more
to tell chemists or biologists
or something, that everything
we're ever going to tell them,
we've already told them.
And there's a
tremendous challenge
and a tremendous opportunity to
take the fundamentally simple
laws and build up a description
of nature that really
does justice to the
complexity and the richness
of real matter.
Now we know what the rules are,
we can try to be designers.
Some of us heard
a brilliant talk
at lunchtime today by
Professor Joe [? Annopolis, ?]
who's crafting ways based on
the fundamental laws of physics
to move light around.
And that's an
example of exploiting
our knowledge, our hard won
knowledge, and an example
of how having the fundamental
laws, in many ways,
is not the end but the beginning
of challenging problems
in physics.
Okay, so much for
ordinary matter.
We have a quite economical
description of ordinary matter
that I think Pythagoras would
have been very pleased with.
Now let's get a
little more ambitious
and try to do
astrophysics, as well.
To do astrophysics, I claim we
need just two more parameters.
One class of processes that's
very important in astrophysics
are the processes that
cause stars to burn.
And those are the
weak processes.
At a fundamental level,
they're described
in terms of the
possibility of down quarks
turning into up quarks plus
electrons plus anti neutrinos.
Or actually, this is the
process of beta decay.
It's closely related.
You just bend around
the lines and you
get the processes
that are responsible
for stellar burning.
So this, although it just
looks like a silly picture,
to a physicist who knows about
relativistic quantum field
theory, which has
very, very rigid rules,
is actually associated with
a complete and unambiguous
description of the
weak interactions.
And all we need to add
to our numerical recipe
is one parameter which tells us
about how big this process is,
how rapidly it occurs over
a one overall new constant.
And that's called the
Fermi constant, G sub f.
And then for astrophysics,
the other thing
that's very important that
we haven't mentioned so far
is gravity.
Gravity, you might think,
is, since it's so obvious,
must be a very powerful
force, and we've
been silly to be
neglecting it so far.
However, at a fundamental
level, gravity
is actually
extravagantly feeble.
It only wins in
astrophysics by default.
If you, for instance, compare
the strength of the attraction
between a proton
and electron due
to their electrical
interaction, which
goes like 1 over r squared, to
their gravitational attraction,
which also goes like
1 over r-squared,
you'll find that the
electric attraction is
about 40 orders of
magnitude larger,
one followed by 40 zeros.
An extraordinarily large number.
Physicists like
to put it in terms
of something called the
hierarchy problem to make
it quantitative.
If we want a
quantitative measure
of how strong gravity
is fundamentally, well,
we have to ask,
compared to what?
And since most of the mass
of matter is made in protons,
we have to construct a
dimensionless quantity,
a pure number, out of
the honorary numbers,
Newton's constant and
the mass of the proton.
And that can be done in
one and only one way.
And it gives a number, 10
to the minus 38, that tells
us that gravity in any natural
sense, in a fundamental sense,
is an extravagantly
feeble force.
It can dominate in astrophysics
because the other, more
powerful forces,
being more powerful,
rearrange matter in such a way
as to cancel each other out
to reach equilibrium
and neutrality.
But gravity keeps adding
up, and eventually,
on large enough scale, wins out.
Now previously I said
that Planck's constant, h
bar, and the speed
of light, c, should
be thought of as
honorary numbers
because in profound
theories of nature,
they occur as
conversion factors.
Now I'd like to argue that
Newton's constant that
governs the strength of gravity
is also an honorary number.
That's because it's associated
with the profound theory
of general relativity
as a conversion factor.
In general relativity,
there is a relationship
between the curvature
of space time
and the energy
density of matter.
But those have different units.
The curvature of space-time has
different units from the energy
of density--
density of matter.
We need a conversion
factor to relate them.
And that conversion factor turns
out to be Newton's constant.
So if we think that Gn
is an honorary number,
the question posed by this
extravagantly weakness
of gravity gets viewed in
a totally different way.
G Newton is not small.
It just is what it is.
It's a conversion--
it's a primary number.
It's a conversion factor.
h bar and c, all of them
are honorary numbers.
They just are what they are.
There's no way of them
being either large or small.
So the real question is, why
is the proton mass so light?
Why is the proton so light?
Well, why is the
proton so light?
Well, earlier in the
lecture, I told you
how the proton gets its mass.
So we can address the question,
why is the proton so light?
And the answer is that you
must walk before you run.
Well, that, I think,
probably sounds
very cryptic to most of you.
So let me explain it better.
As I discussed, the
strength of the interaction
with which quarks attract each
other depends on the distance.
And the dependence
is something that we
can predict theoretically,
and has also
been measured in a
variety of experiments,
up to energies of 100 GEV.
We can extrapolate all the
way to the fundamental energy,
which, if we believe
that Newton's constant is
a honorary number,
we can identify as 10
to the 19th proton masses,
or 10 to the 19th GEV,
way out here somewhere.
And the thing that governs
the mass of the proton
is that at these
distances out here,
at the fundamental
distances, the forces
are too weak for quarks to
keep them locked to each other.
It has to build up.
But the coupling due to
quantum mechanical fluctuations
that we talked about, the
screening effect, only
changes very, very slowly at
first, until a cloud of charge
builds up and gets
bigger and bigger.
So it's walking.
It's actually sort
of limping along
like a wounded snail
for a long time,
until it slowly builds up.
And then finally, at, of course,
not coincidentally, a length
corresponding to the
mass of the proton,
it becomes strong enough to
bind the quarks together.
That's why protons are so
light in natural units.
It comes about because the
coupling was a little bit
small at the fundamental scale.
And given that it's
a little bit small,
it takes a long, long
time for the small quantum
mechanical effects to
build up and make it big
and eventually bind protons--
bind quarks into protons.
Now, as I said, so
now we've introduced--
we have a description
of matter which
is a very accurate description,
including both ordinary matter
and astrophysics, based on six
quantities-- the fine structure
constant, the mass of
the electron, the masses
of the up and down quarks, the
Newton constant, and the Fermi
constant.
They're the things that
appear in red on your program.
But I've just been trying
to actually improve.
I said each time you make
an improvement on that,
you're making a major
contribution to physics.
So I've just been trying to
implement the idea, if you
like, or discuss the idea that
Planck's constant, too, should
be regarded as an
honorary number.
And we scored a significant
success for that point of view
by explaining how the
proton could be so absurdly
light measured in
those natural units,
or putting it another way,
why gravity is so feeble.
Now, if that explanation--
if we're going to succeed
in actually promoting
the Newton constant
to an honorary number
and reduce our
numerical recipe, it
has to work not only
for QCD, but also
for the other
interactions in the world.
Or let me put it another way.
We would like to see that same
scale, that Newton constant,
emerge in some
other way in physics
that's independent of
the theory of gravity.
Well, remarkably enough,
there is another way
in which the Newton
constant emerges
from quite different
considerations
in our fundamental
theories of physics.
As I told you, the couplings
change with distance very,
very slowly.
Here, to make the
plot look simple
and be able to fit it
on one little sheet,
we've switched to
a logarithmic scale
and plotted inverse couplings
instead of couplings.
And I have here the fine
structure constant for QCD,
the fine structure constant
for electrodynamics,
and an analogous thing that
occurs in the weak interactions
that I haven't described,
but is something that is
important in particle physics.
And you can ask if all these
different interactions that we
see at low energies might
be different manifestations
of a unified theory that
is simple in its operations
at short distances, but
gets obscured from us
by these same quantum
mechanical fluctuations
and screening effects that
make the couplings change
with distance.
So operationally, we have
to take these guys from
experiment-- that's
where we measure them--
and then theoretically
calculate what
the effect of the screening
is to see if they could have
derived from a unified theory.
And remarkably enough,
the measured values
are consistent
with their emerging
from a unified theory
where they all become equal
and all become different
facets of one interaction.
And that occurs at
an energy that's
very similar to the energy
we extract, the Planck scale
we extract, from Newton's
constant, this 10
to the 19th GEV.
So if we ask, could there be
a unified theory of matter,
we get the resounding
answer that yes,
not only could there be, but
there's a strong indication
that the very different
looking interactions
we see at low energies are
all facets of one unified
theory at high energies.
And if we do
further experiments,
further discoveries-- including
the existence of neutrino mass,
which, in its details, supports
the idea of such unified
theories--
the unified theories
also predict
that protons should decay.
That one hasn't
been observed yet.
So we get two exclamation
points and a question
mark to our question, is there
a unified theory of matter
that congeals at something
close to this Planck scale.
But then the final step must
be to bring back in gravity.
Well, gravity is also sensitive
to the energy at which you
measure, and not just
because of subtle quantum
mechanical effects, but
because gravity just
cares about energy.
The gravitational force is
proportional to mass or energy,
according to e
equals mc squared.
So the higher the energy,
the stronger gravity
appears relative to
the other interactions.
And so the inverse
coupling of gravity
on this logarithmic scale
happens to look like that.
And you can see
that gravity also
seems to be joining
the other interactions.
We can't do this
calculation very accurately,
but to the accuracy
that it deserves,
it's consistent with the idea
that all these interactions
unite together.
So the basic idea
that Newton's constant
can be regarded as
an honorary number,
and should be the
fundamental mass that
appears in the fundamental
unified theory,
holds up very well from two
very different perspectives.
It's the scale at which
there's independent indication
of a fundamental
theory of emerging
of the non-gravitational forces.
And it's also the
scale at which gravity
meets those and potentially
a fully unified theory that
includes not just
a theory of matter,
but also the theory of
space and time, which
is what gravity is in Einstein's
general relativity theory.
So to the question, do
these considerations
of the numerical
recipe for nature point
us toward a unified theory
of space-time matter,
this one does.
But really, that's the only
quantitative indication
so far along those lines.
And there are big
puzzles in trying
to construct a unified
theory with gravity
and the other interactions.
There's the puzzle of why empty
space doesn't weigh anything.
And there's just
the puzzle that we
don't have any very concrete
theory along these lines.
There are the germs
of ideas coming
from string theory that
perhaps will congeal
into a well-defined theory.
But at present, it's kind of
a vague assemblage of ideas.
So let me summarize.
To construct ordinary matter,
to construct a description
of ordinary matter that's
extremely precise and very well
verified, we were able to get
by with a couple of honorary
numbers, h bar and c, and
four non-numerical quantities,
exactly four--
the mass of the electron,
the fine structure constant,
and the masses of the
ups and down quarks.
And among those, the masses of
the up quarks and down quarks
didn't matter very
much quantitatively.
If we want to do
astrophysics as well,
we needed to add just
two more numbers--
the Fermi constant describing
the weak interactions
and the Newton's
constant describing
the strength of gravity.
And then finally,
I gave you a series
of arguments sort of at
the frontiers of physics
indicating that the idea that
we can treat Newton's constant
also as an honorary number is
becoming very, very plausible.
We get at that number
from considering
unified theories of
the other interactions
and how they emerge.
We get a convincing
explanation of why
gravity is so feeble based on
interpreting it as actually
the lightness of protons--
which in turn was
interpreted as the coupling
having to walk before it runs--
and then finally from the
just straight calculation
of whether gravity unifies
with the other interactions.
So the Pythagorean
vision that the world
can be described in
terms of pure numbers
is very, very close
to being realized
in a very concrete
and beautiful way
that I hope I've given
you some inkling of.
Thank you.
[APPLAUSE]
PRESENTER: I'm sure Frank
will answer questions.
WILCZEK: Yes.
AUDIENCE: Thanks.
Since you talked about
[INAUDIBLE] very troublesome
[INAUDIBLE] We have no
theoretical explanation
or description.
And that area of
physics [INAUDIBLE]
to what you called very
briefly [INAUDIBLE]??
WILCZEK: Well, yes.
I tried to dissociate
myself very carefully
from the philosophy,
if you want to call it
that, that in physics, you're
done once you write down
the equations.
It's an important
part of physics
to write down the equations.
But to really be
able to solve them
in meaningful circumstances,
to be able to do them justice,
to relate them to the
world, is a tremendous art,
and every bit as
important and challenging
as finding the equations.
Yes.
AUDIENCE: Electron has
a charge and the quarks
have charges of
one third and 2/3
and they exactly match, how
does that come out of your
[INAUDIBLE]?
WILCZEK: Oh, well that
does actually come out of--
so the question
was, if you actually
look in detail at some of
the properties of our quarks
and electrons, they're
a little funny.
For instance, the electric
charge of the up quark
has to be 2/3 the
electric charge of--
or minus 2/3 the electric
charge of the electron.
And the electric charge
of the down quark
is one third the electric
charge of the electron.
Where did these funny numbers
like 2/3 and one third
come from?
Well, first of all,
since they're numbers,
they're not anti-Pythagorean.
But secondly, and
more seriously,
they are among the most--
I haven't been able
to do it justice.
And I won't be able to do it
justice in this brief lecture.
But they emerge in a
very compelling way
from these unified theories.
Let's see, how can I say
this in a simple way?
You see-- yeah.
The physical photon,
as we observe it,
is some mixture of the gluons
in the fundamental theory.
And so are the gluons of
the strong interaction.
They are mixtures.
And which particular
mixtures emerge as the photon
and emerge as the
color gluons is
determined by the details
of how this symmetry breaks,
of how the big symmetry of
the original underlying theory
breaks.
So to address questions
like the relative charges
of different objects,
we need to be specific
about what this theory was, and
about how the original, highly
symmetrical theory
broke down into the less
symmetrical theories we
actually see at low energies.
I can be a little bit
more specific about this
and give you some
idea of how it works.
But to really do it would
require some equations.
I emphasized that the
theory of electrodynamics
was based on very similar
concepts to the theory of QCD.
They were both based on
different kinds of charges,
also called colors, and
their transformations
and interactions with
photons or gluons.
The form of this
unified theory--
oh, and I should say, the
theory of the weak interaction
is based on a similar idea
involving two other colors.
So all these theories
are different kinds of--
theories of different
kinds of charges
interacting with
different kinds of gluons.
The unified theory is simply
including all possible
transformations among all
the colors-- strong, weak,
and electromagnetic--
and seeing if they can be
incorporated on equal footing.
And the calculation here
shows that that idea succeeds.
Then you have to discuss,
well, why isn't the world--
why in the real world don't
we see all these interactions
on an equal footing?
What happened?
And that's the subject--
the phenomenon is called
spontaneous symmetry breaking.
And it will sound poetic,
but it's literally the case
that what's involved
here is the concept
that the whole world is a
multi-layered, multicolored
superconductor.
Ordinary superconductors
are governed by the concept
that you have so-called
Cooper pairs of electrons,
pairing up and filling a metal
and giving a photon a mass
and effecting the
properties of photons,
effectively giving photons a
mass inside superconductors.
In these theories, what we
need is not pairs of electrons,
as in superconductors, but
pairs of similar things
carrying other kinds
of color charges,
filling what we think
of as empty space.
But of course, it's not empty.
It's a multi-layered,
multicolored superconductor
because it has these pairs.
It's filled chock-a-block
with pairs of particles
with different colors.
And it's the presence
of that medium that
distinguishes the different
colors between strong
electromagnetic and weak.
Say these pairs have more--
are more aligned
in the direction
of the weak interaction
than the strong interaction,
and that distinguishes
the two directions
and breaks the symmetry.
Well, I'm trying
to say something
that's easier done than said.
But the-- well,
maybe I'm giving you
some sense that it's the
details of how this symmetry is
broken that determines the
charges at the end of the day.
And if you take sort of the
simplest possibilities for how
this symmetry is broken,
that's what gives you
the structures we
observe at low energies,
including things
like the charge 2/3
and one third on the quarks
that otherwise seem so funny.
Yeah.
AUDIENCE: It seems that
you're being [INAUDIBLE]
the question I had
since the early slide
when you were showing the pairs.
There are paired
reds, paired blues,
but no green pair on that slide.
Is that
[INTERPOSING VOICES]
WILCZEK: Gluons?
Oh, yes.
Well, yeah, totally unorganized.
[LAUGHTER]
So you might think,
if we have gluons
that change any possible
color into any other color,
including the same
one, that there
would be nine possibilities,
three times three.
And there are, of course.
But one of those
colored gluons, well,
the joke I might like to make
is that these are gauge bosons.
But one of them
is a gauge bogon.
It's bogus.
There's one that's
different from all the rest.
And it's composed of
an equal combination
of the red, anti-red,
blue, anti-blue,
and white, anti-white,
or green, anti-green.
In quantum mechanics,
you are allowed
to take linear combinations of
these different possibilities.
And the gluon which treats
all those colors symmetrically
obviously has
different properties
than any of these
other guys which
don't treat the different
colors symmetrically.
If you know a
little group theory,
if you take a
product of a triplet
and an anti-triplet
representation of color, which
is what we have here, they
form an octet, eight gluons,
which is perfectly
symmetrical, and a singlet,
which has different properties.
So in the theory of
the strong interaction,
that singlet
doesn't participate.
It's different from the rest.
And so to enforce
the proper symmetry
of the strong interaction
and agree with nature,
it's consistent and
necessary to throw it out.
So actually, it's a slight lie--
well, it's a big lie--
to just leave out the
green, anti-green.
What I should have written here
was red, anti-red minus blue,
anti-blue and something
like blue, anti-blue minus
green, anti-green.
Then it would have
been mathematically
correct but probably
even more confusing.
Yes.
AUDIENCE: Your graph of
the various [INAUDIBLE]
versus energy, it looks
on the low energy side
as if you're changing the
fine structure constant
by a few percent every decade.
WILCZEK: This is-- wait, wait.
This one.
This one?
AUDIENCE: No, you had the quark,
the three different coupling
constants.
WILCZEK: Yes.
AUDIENCE: The straight and
the gravity was [INAUDIBLE]..
WILCZEK: Right.
AUDIENCE: So if I
just extrapolate
that down a few more
orders of magnitude,
then I raise the
question, why do I
see nine decimal
places, the same fine
structure constant in hydrogen
and in singly ionized helium?
WILCZEK: You don't.
I mean, when you do accurate
calculations of the force
between, say, electrons--
between an electron and
a positron or whatever,
I guess you find that the force
does change logarithmically.
This is the Uehling effect
or vacuum polarization which
appears in atomic physics.
So--
AUDIENCE: I'm aware of that,
but it's a whole lot flatter
and straight per decade so
something must be happening
is my question.
WILCZEK: Yeah.
Well, these calculations
are done basically
neglecting the
masses of particles
relative to the energy.
And that's valid for all
the particles we know
about sort of from here on out.
But it would be totally invalid.
AUDIENCE: So they flatten out?
WILCZEK: Yeah, they flatten out.
Well, they flatten out
in these two cases.
In this case, well,
it's not exactly known.
It becomes a strong
coupling problem.
And it's not really
well-defined.
But anyway, yeah, you can't
just extrapolate these curves.
That's quite right.
Yes.
AUDIENCE: If we use this
slide and the convergence
of these curves to
sort of try to dub
a couple of your constants
into honorary numbers--
WILCZEK: Just [INAUDIBLE].
AUDIENCE: Okay.
But don't you get if you--
WILCZEK: So the
question is, can--
well, go ahead.
Ask your question.
[LAUGHTER]
I'll ask the question
you should be asking.
AUDIENCE: I guess what I mean
is I have a feeling that you've
somehow got one more honorary
than you're really entitled to.
I mean, for instance,
alpha s, you
turned that into an honorary
number by saying, well, really,
lambda QCD just sets
the length scale.
It's sort of the
natural unit of length.
But then the Planck
length you're
trying to tell me is the
natural unit of length.
I mean, can't you only use one--
WILCZEK: Yes, I did do somewhat
of a sleight of hand here.
If I make the Planck
length the scale of length
and run through my explanation
of why gravity is feeble
or why protons are so
light, that explanation
required knowing what
the value of alpha s
was at the Planck length.
So if I do it that
way, I reintroduce
a numerical parameter.
So you're quite right, yes.
Yeah.
AUDIENCE: I'm actually speaking
with the voice of Pythagoras.
If you can show me
your Pythagoras thing,
we have noticed that you have an
error in your numerical table.
WILCZEK: Oh, is that?
AUDIENCE: You could leave it
as an exercise for the audience
to figure out what the error is.
WILCZEK: Okay.
AUDIENCE: The error is that the
ratio of e to c is actually,
I worked it out here, 81 to 64.
Any violinist understands that.
WILCZEK: Oh, well.
[LAUGHTER]
[INTERPOSING VOICES]
AUDIENCE: It is a terrible
scale because everything
sounds dissonant.
[INAUDIBLE]
WILCZEK: I believe it's the
scale that Pythagoras used.
AUDIENCE: No, it's not.
It's not.
No.
The ratio of e to c is 81 to 64.
WILCZEK: You mean a to the gap?
Well, I don't know.
Okay.
AUDIENCE: It's a music thing.
WILCZEK: I don't
know this history.
But--
AUDIENCE: If you can find
a hint related to it,
[INAUDIBLE] where you'll
find that the magic ratio
God made when he made the
world, the ratio was 256 to 243.
[INAUDIBLE]
WILCZEK: All right.
Well, for those of you
who didn't catch this,
let me just remark
that 81 divided by 64
is very close to five.
[LAUGHTER]
PRESENTER: On that note, I think
we should thank Frank again
for--
[APPLAUSE]
