[ Music ]
[ Applause ]
>> Thank you, very much.
And Gus, thanks for that
really nice introduction.
So, I am on sabbatical
and one of the privileges
of academia is a sabbatical.
And generally, the duties
and the teaching are reduced.
But there's one thing
I've missed in particular
and that actually is hosting
and organizing Saturday
morning physics.
Which I'm not doing this year,
it's being so ably
done, otherwise.
But thanks very much for coming.
It's now my privilege
to tell you about some
of the work we're doing.
But that is in the context
of this wonderful
mysterious particle, the muon,
which I'll tell you about today.
So, let's go back
to the beginning.
Does this need any
adjusting, you think or?
We're good with the sound?
Okay. Sorry.
All right.
So, I will, will
start at the beginning
with the discovery of the muon.
And then, I will
tell you in addition
to how they're made
sort of naturally,
how we make muons,
how they're used.
And then, some of the
fundamental properties
that the muon that I'm
working now on measuring
and why that's so interesting.
So, the muon was discovered
in 1937, basically.
But I'm going to go back before
that a little bit and tell you
about what physics was
up to in the 1930s.
Because efforts were in
full swing in the 1930s
to understand what was
going on in the nucleus.
To understand the forces that
were binding the nucleus.
In 1928, French physicist
Paul Dirac developed a new
combination of relativity
and quantum mechanics.
So, two basic modern new
ideas that drove physics
in the 20th century,
starting at the very beginning
of the 20th century,
were relativity
and quantum mechanics.
But they hadn't been combined.
The relativity theory did not
include quantum mechanics.
Quantum mechanics
was not relativistic.
But Dirac put them together.
We'll tell you more
about what that told us.
But one of the main things
is it predicted antimatter.
In 1931, Harold Urey at Columbia
discovered heavy hydrogen
which we call deuterium.
And heavy water is made up
of deuterium and oxygen, D2O.
D is deuterium and it turns out
that deuterium is a nucleus made
up of a neutron and proton.
This was actually before
the neutron was discovered.
But how could it be that there
was a chemically hydrogen
nucleus in an atom that
was twice as heavy?
And it was actually a year later
that Chadwick discovered
the neutron.
And so, there was yet another
piece of nuclear matter
that needed to be put into
an understanding of this.
And one of the really puzzling
things about the nucleus
since it was known that
the nucleus was very small,
much smaller than the
extent of the atom.
In fact, I teach in this
classroom and I use this example
for my students who,
in the old days,
they used to have
a pencil or a pen.
[ Laughter ]
They took notes and
things like that.
And if you look at the tip
of your pencil and you're
in the middle of the
room, that is the size
of the nucleus compared to the
size of the room is the atom.
That is the ratio.
About nearly a million
from this, that size.
So, even though we draw
pictures of atoms where it looks
like the nucleus isn't a lot
smaller so that we can see it
on one scale, it's not
particularly accurate.
But it was known that the
nucleus was quite small.
About 10 to the minus 15 meters,
or when we call that
a femtometer.
Fifteen zeros before the
1 after the decimal point.
And into a nucleus, say
carbon or even helium,
there's more than one proton.
Protons are positively charged.
The force between two
like positively charged
protons is repulsive
and extremely strong,
yet the nucleus is bound
and held together.
And this mystery was approached
by a Japanese physicist,
Hideki Yukawa.
And he was exploring this idea
that there were particles
exchanged.
So, this idea had been
around Heisenberg, actually,
helped understand that.
So, this is one of the
equations that I want
to introduce here today.
This is a way of
writing the Heisenberg
Uncertainty Principle.
This says that it's possible to
produce a little bit of energy,
Delta e. So, Delta means
the change in energy.
For a short period
of time, Delta t,
as long as that's
bounded by this quantity
which governs quantum mechanics,
the H, which is constant.
And in fact, divided by 2 Pi.
So, Yukawa's idea
was that a proton
in the nucleus somehow
moving along,
along time on the bottom
axis in this picture
in space on the vertical axis.
Emits a particle x. We don't
know what that particle was.
He didn't know exactly
what it was.
But it's absorbed by
another proton in the nucleus
that really, really
wants to absorb it.
So, in the sense, that second
proton is drawn towards the
first proton by a
force much stronger.
Think about the sort
of attractions
that you just can't resist.
Right. Much, much stronger
than the electrical repulsion.
And because the size of
the nucleus is known,
and yet another thing.
We can turn Delta t and Delta
e into these two things.
Delta e, the change in
energy, is MC squared
for this particle x.
And Delta t is the size
of the nucleus divided by
a velocity which he put
in the speed of light.
And if you do that, it turns
out to this predicted a particle
about 200 times the
mass of the electron.
Now, the proton is 1,000 times
the mass of the electron.
Two hundred times
the mass of electron,
more than the electron,
less than the muon.
So, he called it, they use
the Greek term for medium.
They called it a
meson at the time.
There was that term
bounced around quite a lot.
So, let's move to
the experiments.
This is Carl D. Anderson,
who was using a device
called a cloud chamber.
And he wrote a paper in 1932
entitled, this is the title
of the paper, ''The
Positive Electron''.
And what they were
exploring is particles
that were produced naturally.
They were called cosmic rays
because they appeared to come
from the cosmos from
outside the earth.
And I love the way papers
were written at the time.
On this certain date, we
observed using a device
that was built by R.A. Millikan,
another famous physicist
at the time.
And this is what we saw.
Okay. So, let me
explain this to you.
First of all, it's a photograph.
It's a photograph in a vapor
where when a charged particle,
in this case, a positive
electron, goes through
and it tears the electrons
away from the atoms.
And in so doing,
causes the vapor
to condense little
droplets around that path.
And it traces out the path.
And the path sustains
itself long enough
to take a photograph of it.
So, they take a lot of
photographs and quite a number
of people investigate
these photographs.
And they found this
really amazing thing
which is interpreted in the
following way; if the positron,
the positive electron comes
from the bottom of this thing.
And I'm going to show you a
demonstration so you'll have
to concentrate on
the outer parts here.
And there's a magnetic field
which produces a magnetic force.
And let me just illustrate what
happens to a negative electron
when we do a positive force.
So, can you see this
device here?
Right. So, this device is
it's called an oscilloscope
but for our purposes,
it's a beam of electrons
coming towards you
from the back of this.
And the electrons have a charge.
I can move the beam around just
by changing the electric
force on it.
Okay. So, I'm just changing
a voltage on some parts
of this device changes
the electric force.
But I have here what I
want you to recognize.
It's a magnet.
And how do we know
it's a magnet?
Well, it's a magnet
because it sticks to things.
Right. And in this case,
it's sticking to the board.
But you can recognize
this as a magnet.
And what I'm going to do is
with the magnetic field
strongest near the end
of this magnet here, I'm going
to bring this magnet towards
and away from my electron beam.
Negatively charged
electron beam.
I can't change those
to positive electrons.
But I can change the magnet
from North Pole to South Pole
and notice that it goes up.
So, by looking at the direction
that the particle was deflected
by the magnetic force,
that is the direction,
the curve of that
path is the direction
that a positive charge
would move.
Moreover, that charge went
through a lead plate about 1/3
of a centimeter, 3 and
1/2 millimeters of lead.
And can you see, can you
tell that the curvature
above is a little bit more,
it's more curved than below?
That means that the particle
lost some energy in the lead.
And this is how they understood
the properties of this particle
because it's positively
charged and it does,
it loses energy just like
an electron would in lead.
So, it was surmised that it
had the mass of the electron
but the opposite charge.
And this was the first, this was
the discovery of the antimatter
that was predicted by Dirac
just a few years before.
Anderson won a Nobel
Prize for that work
in 1936 but he did not rest.
And working with Seth
Neddermeyer, another physicist
at CalTech, they continued.
This is also one of
those photographs.
But it's a different one.
And there was this track that
was really hard to understand.
You can sort of see this
is the same picture.
There's a, a plate
through the middle.
And they didn't know
what this was.
It was mysterious.
People were discussing
it for quite a long time.
And so, they did some more
really detailed measurements,
a little more detailed
to describe.
And then, a year later, after
the Nobel Prize was awarded,
wrote this note on the nature
of these cosmic ray particles.
And they put a 1-centimeter
plate of platinum
and measured how
much the curvature
of these particles changed.
Right. And that is a measure
of how much energy they lose.
So, on the left graph,
the vertical axis shows how
much energy the particles lose,
essentially, given
by the curvature
after going through the plate.
And the horizontal axis
shows the amount of energy
that they had initially, the
curvature before the plate.
And electrons, this solid
line on the graph on the left,
the diagonal line is
the theory for electrons
which was working
very, very well.
But you can see that some of
the points fall well below
that line on the graph.
And on the right side,
we have what scientists
like to call a histogram.
This basically says if I
break my graph on the right
up into little boxes,
how many of these events,
they're called, go
into each box?
And the electrons clustered
around the center the way
they should as expected.
But then, it started growing
and appearing on the right side,
this shaded area which
lost much less energy.
The term was more penetrating.
And that was the muon.
And because the amount of
energy loss depends on the mass,
the energy lost was too small.
That meant the mass was much
larger than the electron
but smaller than the proton.
And so, it's those events
in the red circle that are
in the shaded region here.
So, we suggest again writing as
we can't get a paper published
like this, these days.
We should like suggest
merely as a possibility
that the strongly ionizing
particles of the type
in figure 13 in the upper left,
they occurred predominantly
with positive charge but
sometimes with negative charge,
maybe related with
this penetrating group
in the red circle above.
So, just to summarize
what they found.
That particles heavier
than electrons
but lighter than
protons existed.
So, they were medium
mass or meson particles.
There were both positive and
negative versions of these.
They could tell by the
curving left and right.
And of course, the question
was asked was this the particle
predicted by Yukawa?
And Yukawa, this was in 1936,
World War II ensued, etcetera.
But Yukawa kept working
very, very hard on this
about what the nature of
those particles should be.
And the answer is no.
But he did win a Nobel
Prize in 1949 for particles,
the pion which was discovered
just a few years before
in the positive and
negative version of the pion
and the neutral or Pi-0
version of that in 1950.
And one of the things that's
different about these is
that they have very strong
interactions with matter.
Whereas, muons and
electrons, no.
So, this was not
actually, that discovery
in 1936 was not Yukawa's
particle.
It was what we call the meson.
And we now know that it is
not strongly interacting.
It's weakly interacting.
I'll explain more
what that means.
And also, that it's a particle
that has intrinsic
angular momentum or spin.
And it's a particle that
would obey the Pauli exclusion
principle of chemistry.
But physicists call
that a fermion.
Okay. So, basically, a particle
with 1/2 this quantity H.
In this case, H-bar
of angular momentum.
And Rabi was one of the
leading physicists of the time.
Everybody would say well,
what do you think, Rabi?
And Rabi said who ordered that?
Okay. It's just,
it's just a mystery.
But now we know because we've
learned so much from the muon.
So, the muons that Anderson
first observed, Anderson
and Neddermeyer, and
have been observed since,
are cosmic ray muons.
And so, this is how
they're produced.
They're produced by,
mostly but not exclusively,
high-energy protons
coming from the cosmos,
coming from outer space.
That's good enough
for us, right now.
They collide with
the upper atmosphere.
So, the atmosphere of the
earth, of course, expends,
extends out extensively until at
some point you can say there's
not much atmosphere, anymore.
But, but it's very,
very tenuous.
There aren't many
molecules or atoms
in the atmosphere beyond
about 15 kilometers.
And at 15 kilometers
or so, the thickness,
the density of the
atmosphere gets sufficient
that the protons are
likely to find a nucleus.
The atmosphere is mostly
made up of nitrogen.
One of the things that
happens that I don't have
on this slide is
that nitrogen 14
and protons undergo a nuclear
reaction to produce carbon 14.
That is the production mechanism
for carbon 14 that's
used in carbon dating.
But muons are produced because
when high-energy protons collide
with nuclei, they produce
these particles pions.
So, if we go from the very
top of the graph downward,
you can see sort of the
transition of these particles
as they undergo their processes.
So, p plus n, protons
plus the nucleus goes
to these Pi-like particles
which are strongly interacting
but they're unstable.
They decay pretty quickly,
within a, nanoseconds,
basically, in to muons.
And both positively and negative
muons because both positive
and negative pions are made.
And then, this other particle
to the right of my red circle
which is the neutrino that
we now know is associated
with a neutron.
Another exotic particle.
Not really the topic
of today's discussion.
But what I do want
you to know is
when there is a weak
type radioactive decay
of a particle, neutrinos
show up.
They're very hard to detect.
That's an entire science in
itself and a very active field.
And there's a lot to
learn from neutrinos.
But today, we're
talking about muons.
So, some of them
get to sea level.
And what we're going
to show you this.
This is probably one
of the most-used Saturday
morning physics demos, ever.
Who's seen this one before?
This is the cosmic
ray telescope.
That's not so many hands.
But I have, too.
All right.
Any rate. So, what we have
here, it's called a telescope
because its job is to make sure
that the radiation [inaudible].
Is to help us determine
that the radiation
that the two radiation
detectors at the top
and bottom are detecting
are, indeed,
due the things mostly
coming vertically downward.
Okay. The downward part
is a little bit difficult
with this apparatus.
But trust me.
All right.
And what you can see here
on the oscilloscope trace
in the middle is
the top detector.
And every now and then, it gets,
we call that an event
or a pulse.
There's some electronics
that makes it look that way.
And then, the bottom detector.
And the purple line at the
very bottom is telling us
when the two of them come
close together in time.
I'm going to go ahead
and do this, now.
I'm going to go which is show
you that if we look at just one
of them, which is
the top one only,
there's not many we
call them coincidences,
with the bottom one.
However, when we require
the coincidences, every now
and then, there is one.
So, these we identify mostly
with cosmic ray muons,
these coincidences.
And I just want you
to get an idea
that this is a rule of thumb.
All right.
So, your thumb is about
1 square centimeter.
And there is about, if you do
this, there is about 1 square,
1 muon per minute per
square centimeter.
Okay. So, there you go.
Now, we're not going to
wait for the next one.
You hold out your
hand, that's about 100.
And, and of course, they're
going through out bodies
and there are many,
many, many consequences.
So, the muons get to sea level.
And this is an interesting
thing in itself
that we'll come back
to in a moment.
So, let me summarize what
we know about the muon now.
Well, we know it's mass.
Okay. It is a medium mass.
It's about 207 times the
mass of the electron.
And I have some little symbols
to indicate, in this case,
that the muon's a
particle with mass.
It has a charge that's
equal, positive or negative,
to the elementary charge,
the charge of the electron.
The negative and positive
muons have a very tiny limit
on the difference
of their charge here
and the charge itself.
Okay. So, it's a
little uncomfortable
to always use these not
necessarily meaningful
scientific units,
10 to the minus 19.
So, I decided to introduce
something even more confusing
which is a Greek
term which is Atto.
So, atto is 10 to the minus 18.
So, it's 18 zeros before the
1 on the bottom line here.
And I just have here for
your reference a little chart
of all these prefixes
that we use.
So, I don't, physicists don't
generally do this but now
if you ask a physicist what
is the charge of the electron,
they'll say 1/6 of
an atto-coulomb.
So, that's the charge.
And as I said, the positive
and negative muons have
very nearly the same charge.
The spin or the intrinsic
angular momentum is 1/2
of a fundamental unit of
quantum angular momentum.
So, it's 1/2 of that unit.
The number doesn't
matter, so much.
And the magnetic
moment of the muon,
a topic of my own
research, is here.
So, there aren't a lot of
equations in my talk today
but there are a lot of digits.
And this is to indicate
that these measurements
are extremely precise.
In fact, we don't usually
carry around all the digits
but we talk about things
like parts per million,
parts per billion, and even,
we hope, parts per trillion.
And just to let you know,
we're in the parts per
billion realm, right now.
So, PPB is parts per billion.
And the magnetic moment
is known to a fraction
of a part per billion,
just under that.
The magnetic moment of an
intrinsic particle with spin,
so the arrow represents
the spin,
really just gives it a North
and a South Pole like the magnet
that I showed you before.
So, it has a magnetic moment.
Any particle with spin
can also have a separation
of its charge along
the spin axis.
That's called an
electric dipole moment.
Something I also work on
but not today's topic.
And it is an unstable particle.
It decays itself.
When it decays, it decays
into lighter particles.
The electron for the
negative muon, the positron
for the positive muon.
And because it's a
weak interaction,
there are associated neutrinos.
And there's a large time of
the muon, 2.2 microseconds.
And that's very measurable.
The other thing is it
has no physical, it's,
as far as we know, it's
point-like or fundamental.
And it's considered a heavier
version of the electron
that occupies a place in the
set of fundamental particles
of what's called
the standard model.
Standard model being the
physics mathematical description
of what are the fundamental
pieces.
They're all shown here.
The top ones in red
are the quarks.
The bottom ones in green
are what we call the leptons
which are the electron, the
mu, and a third generation,
the tau which was
probably provided
because we couldn't figure
out why we got the muon.
And there are associated
neutrinos.
And then, ways to understand
what the force is among all
of these are called
force carriers.
And then, one more piece
that was first observed
as a physical particle
about seven years ago,
which is what's called
the Higgs.
So, muons decay.
So, let's start with a
muon, a positive muon.
And this is what a
decay looks like.
All right.
So, it disappears.
And it, there's a positron
and two neutrinos that emerge.
So, we can write the
decays like this.
the positive muon going to
a positive, to the electron.
A negative muon to a negative
electron and its neutrinos.
And this measuring actually
the half-life, essentially,
of the muon at rest has
been so fundamental.
There it is again.
That it has told us fundamental
features of the standard model.
It's really provided a
lot of the scale here.
The muon is charged so it
interacts with electric
and magnetic fields
at a magnetic moment.
And it also interacts weakly.
And in terms of the standard
model, we associate the electric
and magnetic interactions
with the gamma
which we, is the photon.
We call that a photon.
And the weak decay with another
particle called the W. So,
I want to tell you one way
to measure the muon lifetime
because I did it last week.
And this is a tank, a
55-gallon drum of filled mostly
with mineral oil and a
chemical called a scintillator
that has the property of
producing flashes of light
when ionizing radiation
goes past it.
And also, at the top in, in
gray, are two devices that look
into the tank and they can
detect the flashes of light.
Now, the muons that get
to sea level are mostly
going pretty fast,
close to the speed of light.
But there's a whole
spectrum of them.
Some of them are slower.
And every now and then,
one of them is slow enough
that it enters the
tank and it stops.
And when it does that,
it produces a big flash
of light, photons.
And those, some of those
get to our detectors
at the top and are detected.
And we do that here.
So, back to our cosmic
ray telescope.
And again, focusing just on.
On the top one here.
I can change something.
You see that yellow thing
going up and down here?
All right.
That tells the oscilloscope
to only look at,
remember I called them events,
that come above this
on the oscilloscope.
So, what you'll notice here is
that there are many
fewer very large ones.
Right. So, I'm now only looking
at the very large ones, again,
back to the small ones.
There are a lot coming
really fast.
And the really, really large
ones come rather infrequently.
And I don't know.
We'll leave it here, Monica.
Every 20 seconds or so, one
of those is a muon stopping,
as you can see here
on the right and left.
And then, basically, the
muon after it's stopped,
at some point it's
going to decay.
So, we can measure that time
when that and start a clock.
All right.
And let the clock tick.
And when the muon
decays, and again,
we're going to have to be there.
Maybe that was a muon decay
because it also showed
up in the a second
one of these here.
So, when the muon decays, we
get another big flash of light.
And because this isn't really
necessarily the best way
to do it, I've basically
shown you what happens
if you draw a spectrum
in time of these events.
So, at the beginning of
this graph on the right,
on the left, excuse me.
On the left is the
first big pulse.
There's our threshold as
a dotted line across this.
And sometime later,
there's another big flash
which we associate
with the muon decay.
And we measure that time.
And then, another event
comes through and it turns
out the time's rather different.
Okay. It's never
exactly the same
because there's a distribution.
In fact, the probability that
we'll see this muon decay
at a certain time after it stops
is there's a lot of muon decays.
And most of them are
at very short times.
And some of them, fewer of
them are at longer times.
And if we draw a
histogram of that, remember,
you just put boxes on here and
say how many fall on each box,
there are more shorter
times on the left
and fewer at longer times.
Now, these are data that
I produced on my computer.
The real data I spent
four days taking.
And that's shown here.
There are about 17,000
events in four days.
And it makes very much the
theoretically predicted shape.
And we can actually extract the
muon lifetime from that shape.
So, this was done.
This device, by the way,
is just down the hall
from my office on
the fourth floor.
And it's mostly used for
the senior physics lab
in the Physics Department.
So, there's a subtle thing here.
It doesn't exactly
follow the theory.
And that is because there's both
positive and negative muons.
And negative muons have this
really fascinating feature
that they can be
captured and make atoms.
And so, they have a
different lifetime.
So, it's a analysis problem
to isolate the muon lifetime.
And there it is again,
with all its digits.
It's known to about
a part per million.
It's known that the positive
and negative muon decay was
almost the same lifetime.
Those are the decays.
And we draw these decays
with a picture like this.
The muon comes along.
The positive muon, for example,
it changes into this w particle,
one of the fundamental pieces of
the standard model, emitting a,
a neutrino which goes
off and up to the left.
And the w particle then decays
into a positron and
its neutrino.
That's kind of a picture of
what's shown as an equation
in essence on the,
on the left in green.
And this is the most
fundamental weak interaction
because the muon, the positron,
and the electron are
point-like particles.
They have no extent.
They're not like nuclei that
take up a space, physically.
So, this actually sets the scale
for the, the fundamental scale
for the weak interaction and
measures the mass or is related
to the mass which was separately
measured of this w particle.
So, I'm going to tell
you quickly that one
of the interesting
mysteries, something else
that we teach our
physics students as soon
as we get them into
modern physics.
Is that 2.2 microseconds is
too short a time for a muon
to go 15 kilometers
because the fastest
that a muon could go
is the speed of light.
Right. So, that's shown here.
And that means it
takes 50 microseconds
to get to the ground.
About 25 times the
muon's lifetime.
And if you do the math, it
turns out the probability
of that is 10 parts per
trillion, 10 to the minus 11.
Really, really tiny.
Very few muons would
make it to sea level.
Not even one per square
centimeter per second.
And the reason is
because Einstein told us,
well, before that.
That time is stretched in the
frame of a moving particle.
So, if we're watching
muons go past us,
it turns out that the average
muon's lifetime in our frame,
when the muons are moving at
nearly the speed of light,
is about 50 to 60 times
longer or 125 microseconds.
Plenty of time for
about 2/3 of the muons
to make it to sea level.
All right.
So, what can we do
with those muons?
Well, one of them that's pretty
interesting has application has
been to use cosmic ray muons
which are coming out of the sky
to at different angles,
by the way.
So, this shows that at
zero degrees straight down
and at 90 degrees, it's been
very well studied how many muons
are coming.
So, well-studied, that if
we put a muon detector next
to the Pyramids and the
muons come screaming
in from outers pace
at some angle.
And there is that white
thing is some sort
of space inside the Pyramid
that no one has discovered
because there are no
paths to it or any tunnels
through the Pyramid
or anything like that.
That that will actually
change the distribution
of muons on the telescope.
You can see that the third line
down has a little more muons
because the void
didn't sort of take
as many muons from
the space away.
And that void is pretty well
demonstrated in these bumps
in the spectrum here which
are identified with that.
So, although there is no
currently no information
about why that's there,
we know it's there.
And it's a big mystery,
of course,
to put together the entire story
of the construction
of the Pyramids.
Another use of cosmic
ray muons is actually
in what's called
muon tomography.
Since they come from
all different angles,
you can essentially do what is
done in computed tomography CT,
an X-ray diagnostic technique
that makes two-dimensional
images of what's going on.
And here on the upper left is
a picture of muon detectors,
just like our telescope, above
and below some container,
for example, that wants to be
examined in a portal monitor.
And the, they can make images of
what's on the different slices
of those and find out
if there's, for example,
very dense things which may be
uranium used for nuclear fuel.
And on the bottom, actually,
was a mock setup at Los Alamos
of uranium inside a, a
55-gallon drum on the right,
looking down to see how the
uranium is stored in the drum.
So, there are many,
many applications
of cosmic ray muons.
There's also bad news
because experiments that want
to measure extremely rare
events encounter backgrounds.
The cosmic rays that are coming
through our telescope are coming
into experiments that
are trying to see events
that perhaps happen only
once a week or once a month.
And per centimeter squared,
there's one muon per minute.
And so, that's dealt with.
This is the Mu2e experiment that
Professor Myron Campbell talked
about in Saturday
morning physics last year.
And it's looking for
very rare events.
And what they do is they
surround it with muon detectors
so you can't see the
experiment anymore.
And those muon detectors
will determine just
as our telescope does.
That instead of a real event
that they've been looking
for by going through both the
top and bottom or the sides,
that it was not an event
from inside cosmic ray muons.
The other thing that's done is
that experiments are now
being moved underground
and into mines and, and
so on, into caverns.
The Mont Blanc Tunnel.
So, tunnels under mountains.
So, that there is what's called
an over gird with a lot of rock
above that shield
the experiments
from cosmic ray muons.
Muons are also made
by accelerators.
And at Fermilab, for
the experiment I'm going
to tell you about, which is
there is a beam of muons.
This is produced in
very much the same way
but much more intense.
Much more intense.
Millions of muons per second,
actually, can be produced
with very high-powered beams
of protons from the part
of the Fermilab accelerator
complex.
And this is actually a picture
that the accelerator people have
drawn that shows on the left
with the green ring,
there's a proton beam
that hits a, a target of nuclei.
That produces pions.
The pions are charged.
They can be manipulated by
magnetic fields and focused
and Pi pluses, for example,
selected instead of Pi minuses.
And they move into a ring that's
on the right side
of this picture.
As they move around the ring,
at some point they decay.
And at the end, after three
cycles around the ring,
only a positive muon
beam comes out.
That's important.
And the other thing is
that muons, remember,
have spin and magnetic moments.
And when the pions decay, the
magnetic moment in the spin
of the muon at the instant of
decay, is perfectly aligned
with the direction
that the pion is going.
We're going to make use of that.
There are muon sources
all over the world.
Most of them are built not for
fundamental physics, like I do,
but most of them are
built to study materials;
biology, proteins, etcetera.
So, there are many,
many applications
that I won't talk about today.
What I am going to
talk about for the rest
of my talk is the muon
magnetic moment anomaly.
So, the magnetic
moment of the muon is,
again, the muon is spinning.
We'll show you many examples of
this in the next few minutes.
But the muon is spinning
around an axis and associated
with that is simply a
magnetic two pole or dipole.
And we believe that
physics should be able
to predict exactly what
that is or almost exactly.
Because nothing's that perfect.
So, the muon has
a magnetic moment.
A magnetic moment is
essentially generally produced
by some manner in
which charge is moving.
In the, in the primitive magnet,
that, that I've been using
for demonstration, that is
actually the spinning electrons
in iron atoms, predominantly.
So, but just to illustrate that
very, in a very rudimentary way,
what we have here,
I hope you can see,
is basically a coil of wire.
And that is hooked up
to, this is the evidence.
Right. That we have a
red and a, and a black.
That means that in some sense
it's hooked up to electricity.
Right. But it's off, right now.
And the compass needles are,
are very sensitive to, I mean,
the main, their main
purpose is to tell us
about the earth's
magnetic field.
But they happen to be spinning
there most of the time,
looking at this magnet.
Which I'm going to move away.
And now, they're pointing,
they're trying to point North.
Right. So, I can influence
them with my magnet.
But of course, I can
also influence them
in a very well-understood way
by putting current
through the coil.
That is a extreme influence.
Right. Where it falls off.
Okay. By putting
current through the coil.
In fact, it was such
an influence
that that one was
just overwhelmed.
Okay.
And I'm going to reverse
it because it's too much
like the earth right now,
the way we've lined this up.
If I reverse it, I don't
know if you remember
that the red was
pointing that way.
And now, the white's
pointing that way
because I reversed the current.
All right.
So, that's a demonstration
that when you have charge going
around the loop, it
makes a magnetic field.
And that magnetic
field has a North
and a South Pole
associated with it.
So, we'll call it
a magnetic dipole.
And the math is, is
pretty straightforward.
I'm not going to ask you
to do the derivation
here with me today.
So, I'm just going to
tell you the answer.
That when something is going
around like this, okay,
something's in motion,
it has angular momentum.
And we use the symbol L. The
arrow, remember, was the spin.
And it has a North
and a South Pole.
So, you just do the
math and it turns
out that the magnetic
moment, I'm sorry about this,
but we ran out of Greek letters
by the time the muon
was discovered.
We were already using Mu.
But meson is starts with
the Greek letter Mu.
So, we use, use that for
two things here today.
One of them is the
magnetic moment and one
of them is the muon itself.
So, I'm going to
really confuse you
when write Mu's Mu, Mu sub Mu.
Magnetic moment of the muon.
But nevertheless, it's the
current times the area.
And I went a little
too far, too fast.
So, let me back up here.
And it's just a charge
of the particle.
We know that.
The mass of the particle.
We know that, very well.
Divided by 2 times the angular
momentum of the particle.
And since we know the angular
momentum of the muon is the spin
of the muon, you
can plug that in
and it turns out
it doesn't work.
It's off by a factor of 2,
so we put this extra
factor G in front.
And experiments show
the G was about 2.
Now, Dirac, whose theory
predicted antimatter
by combining quantum mechanics
and relativity, also predicted
that G would be exactly
2, not 1 which it is
for an orbiting particle.
So, that was a, that
was a triumph.
Dirac did also win
a Nobel Prize.
But then, precise measurements
in complicated atoms.
Sodium atoms and gallium atoms
at Columbia in the 1940s showed
that G wasn't even exactly 2
so that Dirac wasn't
perfectly right.
Now, I'm going to try to
explain why G is not 2.
But before I do, I want
to tell you about how
that magnetic moment
could be measured not
in complicated atoms
like sodium and gallium,
but for a free particle.
And then, before
we get to the muon,
I'm going to start
with the electron.
Because this work was done here.
Dick Crane is shown here.
And this is a picture of him.
And he was a physics
professor for 42 years here.
He would actually have to retire
because it was mandatory
at the time in 1977.
But he didn't slow down.
He moved on to be
one of the founders
of Ann Arbor's Hands-On Museum.
Please, check it
out if you haven't.
And he won the National Medal
of Science for his measurement
of the magnetic moment
of the free electron.
So, that was a much simpler than
putting an electron in an atom
which could have been the reason
that G appeared not to be 2.
So, here's a sculpture that
is actually right outside.
You can check this out.
By Jens Zorn.
Jens is here.
He's over, Emeritus
Professor in our department.
A tremendous artist
and historian
of physics in the department.
And has been making
physics sculptures.
And this one commemorates
the experiment of Crane.
Now, to explain how
the experiment works,
I'm actually going to use a
sketch from Jens' notebook here.
And what you can see here is
there's a magnetic field that's
vertical in this picture that's
applied from the outside.
And the blue spiral is
the, is the helical track
that an electron would
take in going through this.
Now, we have a picture
here, a demonstration here
of an electron beam
in a magnetic field.
Do I have to turn anything on?
Okay. Bottom, the bottom one.
Okay. Oh, yeah.
Okay. Good.
So, what I want you to notice is
from the direction
we're looking,
which we'd be looking
straight down in
that previous, in that picture.
The electron has
a circular orbit.
I also want you to
notice with this knob
that Monica just reminded me of,
that we can make the magnetic
field stronger and weaker
and change the orbit
of the electrons.
Now, all the electrons in that
beam that you see are moving
with the same velocity.
And so, by making
the circle smaller.
Oop. The time it takes to go
around a shorter
distance is shorter.
Right. So, I can
correlate the time
which we actually use
the inverse of time,
which is the frequency.
With the strength of
the magnetic field
and other properties
of the electron.
This is actually how the ratio
of the charge to the mass
of the electron was discovered.
So, that orbit is called
the cyclotron motion.
And, and it has a
frequency which is the charge
over the mass times the
strength of the magnetic field.
B is the magnetic field.
There's also the magnetic
moment is processing.
And now, we have to demonstrate
this concept of spin procession.
So, spin procession occurs
when a spinning object
experiences a torque.
Now, I'm going to start
with this spinning
object, a bicycle wheel.
Direction of rotation.
Okay. Great.
Okay. With a bicycle wheel here.
And before I actually make
this bicycle wheel spin,
I'm going to apply a, a,
show you that there's
a torque on the wheel.
All right.
And the torque is
simply due to gravity.
It's suspended here and
gravity pulls it down.
That's a torque.
It's changing that.
Right. But now, I'm
going to make it spin.
So, there's an axis of rotation.
I hope that's enough.
And when you have a
spinning axis of rotation,
the axis moves around.
Careful. The axis rotates.
There. And that rotation of that
axis is what we call procession.
So, that's the spin procession.
And since a muon is spinning,
and we can apply a torque
with a magnetic field
which Monica's going
to help me demonstrate here
because she's very skilled
at this and I'm not.
So, what you see here is a
little magnet mounted into.
Is this the wrong one?
A little magnet that's
mounted into a ball.
By suspending the ball
with a cushion of air,
we can reduce the
friction significantly
so that once it spins,
there it is.
Once it spins, the axis
around which it's spinning,
you can kind of see.
And what Monica's going to do
is change the magnetic field
produced by these coils.
When the magnetic
field is large,
it's spinning around faster.
This is the axis going around.
And when the magnetic
field is small,
the procession is very small.
Okay. Great.
Where did I leave my?
Aha, good.
So, that is called the
spin procession frequency.
And it's also proportional
to the magnetic field.
So, if we divide that G, the
factor that we're interested in,
times E, the charge over the
mass times the magnetic field.
You divide those out, I don't
know how fast you can do
that in your head.
But if turns out that the
magnetic field disappears.
And in fact, we only get G
over 2 when you do the math.
So, by measuring
those two frequencies,
we can measure this quantity.
And this is the number of digits
with which it has been
measured for the electron.
This is the most precise
quantity every measured
for a fundamental
particle of any sort.
This is the magnetic moment.
It is a fraction of
a part per trillion.
That's pretty amazing.
Now, to do the muon, we do
it a little bit differently.
All right.
Instead of taking the
ratio, we subtract the two.
That's all.
And what that does is it
subtracts the cyclotron motion
from the spin motion.
And that's done in
a magnetic field.
But the magnets are rather
large and the top you can see,
the device that was used for
this experiment in the 1950s
through 1970s at
CERN in Switzerland.
And the scale of the
magnet is a little unclear.
But it's, it's bigger
than a person,
like much bigger than a person.
And on the bottom is a magnet
that was used at Brookhaven
over about a five or
six-year cycle built
for another half-decade
before that.
And that is 50 feet across.
Okay. So, there's the stairs
that gives you some
idea of what that is.
And it's that magnet
on the bottom
that I'll be telling you
quite a bit about today.
And the way the experiment
is done, as I said,
is to take the difference
of the spin frequency
and the cyclotron frequency.
That can be measured by taking
advantage of the muon decays.
And it just gives us we call
this a wiggle plot for reasons
that are unclear to me.
But maybe you can figure it out.
And basically, this
is wrapped around so
at the very top, the
data are in blue.
And the experimental
mathematics that's done
to extract this frequency
by saying oh,
this is what we think it
looks like is in green.
And you can see how
well they match up.
Can also see the very first,
this goes from zero
to 100 microseconds.
These muons are moving at nearly
the speed of light like most
of the cosmic ray muons.
So, their lifetime is extended
to about 60 microseconds.
And they so, this is the first,
the top of row is the
first 100 microseconds.
Then, you go down one.
The second 100 microseconds,
the third, fourth, fifth,
sixth 100 microsecond.
So, this entire thing
is 1, 2, 3, 4, 5, 6,
700 microseconds of data.
And by the end, the
muons are going away.
That's why the line gets fuzzy
at the very bottom right.
Okay. It's because so many
of the muons are decayed.
But we can use all of those.
And at the top, well at the
bottom on the right is shown,
if G is exactly 2, then
the cyclotron frequency
with which they go
around the magnet
and the spin procession
frequency are the same.
And they stay together.
There are no wiggles.
G is not 2.
And so, we get the wiggles.
So, we just extract our
data from those wiggles.
But since we're taking
the difference.
Oops. Okay.
So, there's the answer.
It's G over 2 is known to
about half a part per million.
That should be PPM not PPD.
I'm sorry.
That's a typo.
All right.
So, let me explain why
G is not exactly 2.
And I'm going to
invoke Feynman, here.
And he wrote this book on
quantum electrodynamics that was
from popular lectures.
I've been working
through that book.
And so, I'm going to
tell you a little bit
about what I learned
from Feynman.
But I'm going to start by saying
he reminded me, just yesterday,
that if you can't explain
something in simple terms,
you don't understand it.
So, that's, that's a high bar.
Let's see how I do.
So, what Feynman
told us to do is look
at a space-time picture
like this.
Okay. So, space on
the horizontal axis.
And motion in space could
include rotation and a path
from point A to point
B on this graph.
And there's the rotating
processing spin.
But Feynman said no.
The way to look at this actually
along this path is like this.
Okay. It's taking a path.
There's many paths.
But here's one.
The most fundamental one from A
to B is that the particle starts
at A, starts moving
through space and time.
But then, it encounters
the magnetic field
which he indicated
by the squiggly line
which is called an
external photon.
So, electric and
magnetic interaction
of the photon is
represented this way.
And Feynman gave us a set
of rules to calculate this.
But for this path,
G is exactly 2.
That's one possible path.
There are other possible paths.
In quantum mechanics, these
paths may be called amplitudes
for those people who
have heard that term.
So, another possible path
includes what was called an
internal photon.
Remember Yukawa's particle was
exchanged between two protons.
Well, this is between
two parts of the path
that a particle is exchanged.
It's electromagnetic.
Magnetic. So, it's called an
internal, internal photon.
I keep saying infernal photon.
But that's when I try to
do the calculation myself.
So, we have to add
that new path which is
in quantum mechanics is
called adding an amplitude.
And Julian Schwinger showed
that this was adds a
factor of 1 over 137 Pi.
Really, interesting number.
Does anybody recognize 137?
Okay. This is really
important in physics.
This is the charge of the
electron squared divided
by (h) Planck's constant and c.
And Feynman very quickly
told us how this comes about.
Each time a photon
interacts, you get a factor
of e. So, there's two.
That's e squared.
Okay. So, I'm just going
to motivate this by noting
that every time we
invoke quantum mechanics,
there must be Planck's
constant (h).
And every time it involves
relativity, there's a c. So,
that's if I, hopefully, I
do understand it, I think.
All right.
Anyway, that predicts
this for g.
But there are many,
many other paths.
There's an infinite
number of paths.
Schwinger, who calculated this,
was so enamored with
alpha over Pi.
But when we multiply by
2, we have to divide by 2.
So, alpha over 2 Pi.
But he put it on
his, his gravestone
which was also a
monument for his wife.
So, there are more.
Another path could be that
that internal photon breaks
into two pieces,
electron and positron.
They get reabsorbed.
It could be a muon.
The, the contribution here goes
like the mass of the particle
if it's an electron or
muon, divided by Mu.
So, it's much larger for Mu
because the muon is
207 times more massive.
You could put pions in there
that I told you about today.
There can be weak interactions.
You can really have a great
time drawing these diagrams.
There can be also ones involving
the neutrino which was the w.
In fact, there are professionals
who can calculate this
and they, they do this.
Right. Every time there's
an extra connection,
there's an extra factor of
e. And these become weaker
and weaker and weaker.
By the way, this really
does take professionals.
Don't try it at home.
And so, there are almost 13,000
of these that have been put
into the code to calculate very
precisely what the magnetic
moment is.
I don't know what to
do with this picture.
So, I thought I'd just point
out a few really cool looking
ones with my own diagrams.
This is my square.
This is my triangle.
And I think this is my
hexagon surrounding some kind
of Sesame Street character.
So, the point is that this
is a really intricate thing
that people have
done professionally.
So, the standard model can
very precisely predict these
g factors.
And there they are.
It's good enough to do that.
They've been measured
experimentally.
And this is just
pointing out that
that one diagram makes the
muon and electron different.
Experimentally, those are the
numbers and they're different.
Okay. How can I show you
they're different, quickly?
Well, I can subtract them.
I can put them on graphs
if I've done on the right.
In which you can see is that
the experimental number,
for example, for the
electron in the upper left,
is not quite overlapping
the theory numbers.
And for the muon, it's
also shown on the right
where the vertical dotted line
is the standard model theory.
There's about a 15% probability
that this would be random error
for the electron and about
5% probability for the muon.
And this is considered
to be perhaps indications
that the standard model
is not quite right.
So, there could be more
of the standard model
like a new particle
that is being exchanged.
The new particle would add,
this is a different picture
of that set of standard
model particles.
They're all there.
Trust me. The electron, the
Mu, the tau, all the quarks.
And the force carriers and
the Higgs, in this case.
And there's a theory called
supersymmetry that suggests
that there's a whole
new set of these.
One corresponding to each of
them that we haven't observed
yet in any experiment.
But that could be x the unknown.
That the muon is not point-like.
That there are a new
photon-like particles.
Or that the experiment is wrong.
So, I want to finish
up by telling you
that we're repeating the
experiment at Fermilab.
We did this by moving the magnet
from Brookhaven to Fermilab.
There's the magnet
arriving at Fermilab
at the iconic Wilson Tower
that the founding director
of Fermilab was Robert Wilson
and he also was an
architect and designed that.
His sculptures are awesome.
We make a muon beam which
I told you about before.
We improve everything and
do the experiment again.
So, that's what we've been
doing for the past seven years.
And the thing that's most
important is measuring b.
But I just want to show you
I have a little slideshow
of moving the magnet.
Because this is one of the most
celebrated activities in physics
in probably the last few years.
At least, when the
magnet was moved.
So, there's the magnet
getting packed
up at Brookhaven
onto the Spider.
Those silvery things
are the magnet coils.
Then, it was covered
and lifted onto a truck.
It was trucked only at night
because it was a wide load.
On highways to the
Mississippi to be floated
up the Mississippi
to Chicago area.
And then, all the canals around
Chicago went past Saint Louis.
And here it is near Fermilab.
And this is just an indication
at how celebrated this was.
People would come out at
night to see it move past.
And there it is arriving
at Fermilab
with hundreds of
people around it.
And that magnet was installed.
There it is.
In a new building that was
built for us at, at Fermilab.
Okay. That didn't work.
There's a collaboration
of about 200 people
from three continents
that we can't.
I can't show the names.
But I can give you a sense
that there are quite a number
of countries involved with that.
The last thing I want to tell
you about is that the one
of the crucial things is to
know how strong the magnetic
field is.
And that's what my group does.
And there it is.
The quantity we want to measure
is A. The magnetic field is B.
So, that's the one that
we want to measure.
And there are many, many ways
to, to measure a magnetic field.
The I'm going to skip this.
But I'm going to tell you that.
Actually, I'm going to skip.
I'm sorry.
But your, all of
your cellphones.
I was going to show
you my cellphone.
But I won't take
the time to do that.
But I want to assure you that
those of you who have cellphones
and have used it for
navigation have probably noticed
that it tells you what
direction the phone is facing
or what direction North is.
And that must be because there's
some kind of detector inside
that knows, you know, earth.
And it's not a compass
inside the cellphone.
It's a magnetic field
detector called a Hall probe.
And so, you can buy those.
But most very sensitive
magnetic field detectors,
certainly as sensitive
as we need,
subpart per million part
per billion, you can't buy
in the hardware store.
And it works very simply from
a quantum mechanical sense.
There's spin up and spin
down represent magnetic
field pole North up or down.
And so, in a magnetic field,
they have different energies.
So, at that magnetic field,
there are these energies.
And we can measure that energy.
Actually, we measure
a frequency.
And all we have to know to do
that is the magnetic
moment of the particle.
You just do the math again
after measuring the frequency.
And the very best quantum
magnetometer has been developed
now in my lab which
uses helium 3.
It's in a little glass cell.
It glows because we
make a discharge in that
to help us prepare
the helium 3 atoms.
And then, we put
that in a device
that in its prototype
stage looked like this,
involving a laser coming in
the white line from the right.
The laser is the black thing
on the left and a little bit
of a magnetic field
in our development.
And with my graduate student
Mithat Faruk [assumed spelling],
and some others, we went
to use this MRI magnet.
By the way, you're
probably used to looking
at MRI magnets like that.
But what's on the
inside is that.
And because they're all being
upgraded, we have access
for free, all we have to
do is pay to move them,
to that magnet which we've used.
And the device has
changed the way it looks.
The blue on the left and on the
right are fiber optic cables
that bring the light
in from the laser.
And we mounted it on the device
where we basically
recalibrated it.
The frequency was
measured from figuring
out how fast the wiggles
were in signals like that.
And it can give you an idea of
between 84 and 86 on that is
about 30 parts per billion.
So, we're measuring this
with all the corrections
to 20 parts per billion
which is entirely sufficient.
So, to summarize, the muon which
was discovered in cosmic rays
and is produced in cosmic rays
and cosmic ray muons
are both used and, and,
and a pain for some experiments.
Confirms Einstein's
time dilation prediction
because we get them
at sea level.
It's a tool for archaeology
and Homeland Security.
The muon lifetime
sets the strength
of the weak interaction.
The magnetic moment anomalies
are intriguing challenges
to the standard model.
It may be where we're going
to find new physics
beyond the standard model.
And this adventure of g minus
2 from moving the magnet
to making the world's best
magnetometers has been
extremely exciting.
So, that's the new
standard of magnetometry.
So, I want to thank the
Chupp Lab, that most,
many of them are shown here.
I want to thank my
collaborators including the ones
who helped very much with
the helium 3 development.
The funding from the
National Science Foundation,
the Office of Science and
the Department of Energy.
And the Gordon and
Betty Moore Foundation
which is partially supporting
my sabbatical this year.
Ramone Torrez, who helped me
measure the muon's lifetime.
And of course, the Demo Lab
staff, Monica, James, and Nick.
You're wonderful.
And thank you, everybody.
[ Applause ]
[ Music ]
