DAVE GOLDBERG: Thank you, first
of all, for having me.
I'm going to give a very
general talk today.
The talk is one of these things
where the table itself
is going to give away,
basically, the crux of it,
which is why symmetry matters.
Now I would not be the least bit
surprised if in a Google
audience, some small-- perhaps
some large-- fraction of you
were physics majors
in college.
Just out of curiosity--
one, two, three, et cetera.
I stopped counting after three,
perhaps out of ability.
But one of things that is not
obvious-- even, by the way, as
a physics major in college--
is the sort of shorthand that
physicists especially sort of
use to describe the universe.
They'll say some theory is
elegant or beautiful.
Or they'll talk about the
importance of symmetry.
And here's a very famous quote
by the Nobel laureate Phil
Anderson, which is, it's only
slightly overstating the case
that the study of physics is
the study of symmetry.
And yet typically, when you see
physics in high school,
when you see physics in college,
even if you take
advanced courses in graduate
school, it's very
equation-driven.
The idea of what it is that
underlies our assumptions
about the universe, how it is we
got to where we are, why it
is that physics is sort of held
up as this paragon of a
beautiful academic discipline,
why is it the universe itself
is so beautiful--
that you don't learn about as
much, until much, much later,
until you delve much,
much deeper.
Indeed, I will say that even
as a practicing physicist,
until I started working on
this book, I didn't fully
appreciate how much of what we
know is really undergirded by
sort of these beautifully
symmetric, simple, in many
cases, assumptions about how
the universe works and how
much can be drawn from that.
So I'm going to begin with a
sort of working definition of
what symmetry is.
This is given by the
mathematician Hermann Weyl,
which is basically, a thing is
symmetric if there's something
you can do so it stays the same
after you've done it.
A wheel, a circle,
for example--
I can turn a circle in any given
direction, and it is the
same as it was before.
Or just another very simple
example, a triangle.
Now a triangle isn't quite as
symmetric as a circle is,
because there's only a couple
of things you can do.
You can rotate a triangle, but
only by a specified amount.
Only by 120 degrees,
a third of a turn.
Or you can reflect.
I'm drawing it as a rotation
on the bottom there-- or
rather, my great Illustrator,
Herb Thornby, who did all of
these, is drawing it
is as a rotation.
But it's really a reflection.
We're just taking the
triangle and we're
looking at it in a mirror.
And you know, we can talk about
geometric objects till
the cows come home,
and say, yes, they
are, of course, beautiful.
There is something very nice,
pleasing about it.
For those of us who simply
enjoy puzzles, there's
something appealing
to the human mind.
And I've just picked a few very
natural examples here of
symmetric objects in nature,
symmetric objects in art.
The Taj Mahal, for example.
Architecture, flowers.
We've got an MC Escher print.
There's the galaxy M81
in the lower right.
And for those of you who don't
do these sorts of things, I
occasionally compete in the
National Crossword Puzzle
Tournament here in New York.
Crossword puzzles obey, in the
US at least, a asymmetry where
you can either rotate by 180
degrees or reflect them, and
that's the rule for how the
black squares need to show up.
If you've ever noticed, the
grids for crossword puzzles
look also symmetric.
And these things appeal
to our mind.
I mean, nature seems
to enjoy symmetry.
But symmetry itself seems to
appeal to our mind and our
sense of order.
It also shows up in scientific
discoveries.
So when Rosalind Franklin, for
example, took her images of
the double helix, the fact that
DNA had this structure
allowed Watson and Crick-- well,
to uncover that it was a
double helix.
But also to start understanding
what the
workings of DNA were.
I mean, the double helix of
DNA is, of course, one of
these great natural symmetric
objects, insofar as you can
take this thing and twist it,
and it will look the same as
it did before.
But it's worth noting--
and double helix
is particularly
interesting in this way--
that it spirals in a particular
direction.
It's got one symmetry--
that is to say, I can twist
it as much as I like.
But if I were to look at a
double helix in a mirror, you
could tell it was wrong.
You could tell it did
not come from living
being here on Earth.
It would have the wrong
orientation.
So one of the things that's
going to be very interesting
for us about sort of
understanding symmetries in
the universe is to recognize,
symmetries are very beautiful.
They're going to give
us guidance.
They're going to help us
understand how things work.
But there's a symmetry
breaking here, or an
asymmetry, that's going to, in
some sense, give us even more
information.
That's going to allow for, it'll
turn out, nothing less
than our existence.
So all will recognize these.
I bet no small number of you
will recognize these from a
game-playing context of a
name-brand role-playing game.
You also, by the way, notice
that there is one missing.
These are the Platonic solids.
They are also applying
to "D&D" dice.
The missing one, of course, is
the D10, which is not in fact
a Platonic solid.
It is known as an antidypyramid
and has the
beautiful name "Bimbo's
lozenge," and doesn't have
these properties.
But the Platonic solids all
have wonderfully symmetric
properties.
And many, many thinkers, in
trying to uncover sort of the
secrets of nature, assume
that the Platonic
solids and the sphere--
which is basically the Platonic
solid with an
infinite number of faces--
that the Platonic solids must
ultimately give some sort of
clue as to how the
universe works.
I mean, the sphere, of course,
is the most obvious.
The sphere prompted Aristotle,
for example.
He assumed that because the
sphere is this perfectly
symmetric thing that it
must describe nature.
We owe, ultimately, to him and
his contemporaries the idea of
the celestial sphere, the idea
that the Earth is at the
center of the universe,
that the orbits
of the various planets--
and the sun, for that matter--
are embedded in spheres around
us, and that the stars
are at the most
distant sphere of all.
And that must somehow, because
of it's beautiful simplicity,
that that must somehow be a
representation of nature.
Now the spheres were wrong,
in a lot of ways--
not least of which, the Earth
is not at the center of the
solar system.
The sun is.
But there are other
reasons, as well.
I mean, even if you accept that
the sun is at the center
of the solar system, something
that I'm hoping you will
accept, we are still left with
the fact that even the orbits
of planets are not perfectly
circular, obviously not
perfectly spherical.
They're elliptical, and it turns
out there's going to be
a deeper explanation for that.
Even as we moved forward, even
when thinkers started to
recognize that the sun was at
the center, they still tried
to exploit a lot of these
wonderfully symmetric figures
in order to describe
the universe.
This is Kepler's awesomely-named
"Mysterium
Cosmographicum." And basically,
what he did is he
took the various Platonic
solids and the sphere--
so there were five Platonic
solids, the
sphere gives us six--
and there were six planets then
known, out to Saturn.
And he said, oh, you know, six
Platonic solids including the
sphere, six planets--
maybe they're related somehow.
And he kept embedding them
in this turducken of a
cosmological model to try to
figure out-- he said, if you
embed the one in the other, in
the other, in the other, they
represent, basically,
distances.
And those might represent the
relative distances of the
planets from the sun.
And there might be something
profound and
fundamental about that.
It turns out, obviously, that
any match you have to this is
entirely coincidental.
Coincidental plus the fact, you
know, if you mix and match
them in any given way, you have
6-factorial possible orderings.
You're going to get close with
one of them, presumably.
But that was sheer luck.
We owe, of course, to Kepler,
we owe our knowledge of the
fact that the planets move
in elliptical orbits.
Ellipses, at first glance, do
not seem terribly symmetric.
It will turn out--
and we ow this to Isaac Newton--
that sure, the orbits
themselves aren't elliptical,
but the force of gravity is.
The force of gravity acts the
same in all directions.
And that is a very, very
important symmetry of nature.
I should note, by the way,
that the only reason that
Kepler did not immediately hit
upon the idea of planets going
in elliptical orbits, despite
the data that he got from his
mentor, Tycho Brahe, was he just
assumed that-- he didn't
even try it.
Because he figured if the orbits
of the plants were
something as simple as an
ellipse, surely someone would
have come up with it already.
I think it's giving his
predecessors a little bit too
much credit, perhaps.
So it is interesting to note
that when we talk about
symmetries in the universe, what
we really mean is, what
are some ways that
you could adjust,
say, the entire universe--
turning the universe, for
example, or moving forward or
backwards in time, or moving
throughout space--
and the laws themselves
don't change?
So the laws of physics are the
same here as they are here.
And the only reason anything
appears to be different is
because of my relative motion,
say, compared to all of you.
Or if I were to go 1,000 miles
up in the air, things are
different because of my relative
position to the
Earth, but not because anything
fundamental about the
laws of physics have changed.
So the laws of physics basically
say that all of
these things-- time,
orientation,
positions in space--
none of those matter in
the physical law.
Now that actually is
incredibly helpful.
That's way more helpful than you
might think, simply saying
the laws of physics can't
be dependent on
any of those things.
It means, for example, that if
you were to describe a giant
equation that describes all of
the physics of the universe,
where you are in it can't ever
appear in that equation.
Or when it is can't ever appear
in that equation.
Or there can't be any equation
that ever describes things
with an absolute direction.
Won't ever appear.
That makes the equations
a lot simpler than
they would be otherwise.
Those things turn out not to
matter in our symmetries of
our universe.
Other things seem like
they might matter
or might not matter.
One of them is physical scale.
And this is a trope of sort of
science-fiction and children's
books and things like that.
You know, "Horton Hears a Who,"
or the end of "Men in
Black."
The idea that you can
take our universe--
you know, we're this
giant universe.
We have these things
called atoms.
And if you look at the old
models of atoms, atoms look a
little bit like a sun with
things orbiting around it.
And you can imagine thinking of
that and saying, oh, maybe
you could be a tiny little
creature living inside of
that, with a life very much like
a human being's, except
much, much, much smaller.
Maybe the universe, on various
scales, is almost identically
the same as it is on
the human scale.
And we're just not able to see
it, because our perception
isn't good enough.
And you know, this is the sort
of question you have very,
very late at night in
your dorm rooms.
I think I'd be prudent, as this
is going to go on the
web, to not go any further.
But you get the point.
This is something we
might think of as a
property of the universe.
The question is, does physical
scale matter?
Well, one of the great thinkers
on the subject was
Galileo, who decided to ask
the question in sort of an
absurd way, which is to think
about the existence of giants.
So there are biblical
descriptions
of the ages of giants.
And if we imagine a giant as
merely looking like a normal
human being, except scaled up
by a factor of 10 or 20 or
however much--
this is the same premises in
"Gulliver's Travels"--
would you be able to do that
without re-engineering the
entire thing?
And Galileo says no.
If you were to simply scale up
a human to giant size, you'd
have all sorts of problems.
I mean, after all, if I make you
10 times bigger in every
direction, you become 1,000
times more massive, 1,000
times more weight to support,
for example.
But the strength of your
bones are based on the
cross-sectional area.
So if I make you 10 times larger
in every direction,
your bones only become
100 times stronger.
You're supporting more weight
per unit area, basically, the
larger you are.
And so he said, look, you'd
basically have to totally
redesign the bone of a giant
until eventually, the thing
was entirely bones, and the
bones were incredibly,
incredibly thick, and the thing
wouldn't be able to
function at all.
And of course, the
opposite is true.
I mean, insects don't require
the internal skeletal
structure that we have.
They're of an entirely different
design, simply
because again, this is not
a symmetry of nature.
Which is again, like,
"Spiderman" is not such a
great premise.
Take a spider, scale him
up to human size, and
he'll squash himself.
I can't skip this adorable
quote by Galileo.
He talks about an oak tree.
You know, "Nature could not
produce a horse as large as
twenty ordinary horses or a
giant ten times taller than an
ordinary man."
And then he concludes with this
adorable imagery, which
unfortunately does not carry
with it an illustration.
Galileo's work is filled with
illustrations, but this isn't
one of them.
"Thus, a small dog could
probably carry on his back two
or three dogs of his own size,
but I don't believe that a
horse could even carry one
horse of his own size." I
choose to believe that
this experiment was
never carried out.
So some things are symmetries,
some things aren't.
But what about-- we have a human
intuition about what
should be a symmetry
of nature.
Antimatter is a very,
very important one.
We see antimatter in
science-fiction all the time.
We're able to produce
antimatter in a lab.
And if you know absolutely one
thing, only one thing about
antimatter, it's this--
if you have an antimatter
friend, do
not shake their hand.
Why?
Boom.
You will be completely
annihilated and
converted into energy.
But antimatter really
very much the
same as ordinary matter.
There's an antimatter version
of every particle.
An electron, for example, has an
antimatter particle called
a positron.
Same mass, but opposite
electric charge.
And it is absolutely true that
when you take matter and
antimatter of the same particle
type and bring them
into contact, they will
annihilate completely.
It is also true, by the way,
that if you produce matter and
antimatter in a lab, that we
are able to produce them in
equal quantities.
This raises kind of an important
question, one that
is not immediately obvious
how to resolve it.
Given the similarity between
matter and antimatter, given a
very important fact, which is
that the laws of physics don't
seem to care whether you're
talking about matter or
antimatter-- it's just the sign
that changes, and given
the fact that we produce and
annihilate them in equal
quantities, why are we here
and made of matter?
The laws of physics, I should
say, are almost completely
identical if we take matter and
convert it to antimatter.
I've got a little silly example
here, where I've done
two things.
I've got a current-carrying
wire, electrons.
Electrons have a negative
charge, so they go the
opposite direction of
the flow of current.
We owe that convention,
incidentally to Benjamin Franklin.
And it creates a
magnetic field.
And likewise, if we look at the
same thing in a mirror and
also change all of the matter
to antimatter, we get the
exact same magnetic field.
There's something intimately
related to mirrors and to
antimatter.
And those two combinations of
things, called CP symmetry--
Charge for antimatter and P
for parity or reflection--
that seems to almost be
a asymmetry of nature.
Almost.
I mean, clearly, as I've said,
it can't be a perfect symmetry
of nature, because there is
something different between
matter and antimatter.
And by the way, it's
not just us.
It's not just that we are all
made of matter, and the Earth,
and sun, and the solar system,
and our galaxy--
every galaxy seems to be made
ordinary matter and not
antimatter.
And we can tell that, because if
a galaxy and an anti-galaxy
were to collide with one
another, we would see that
across space.
And if there were antimatter
galaxies, it would happen
occasionally.
And we do see galaxies
colliding, by the way, and
they just have the regular sort
of gastrophysics that
you'd expect.
There's only the simplest
difference between even the
reflected version of this CP
transformation between matter
and antimatter, and that is that
we can see little things.
For example, this is the
cobalt-60 decay.
So you take cobalt-60, and
atoms have this property
called spin, which is, in
principle, directly
measurable.
And it turns out that the
ordinary matter version has
electrons preferentially given
off in the direction that the
thing is spinning.
So you use this thing called
the right-hand rule, and
preferentially, electrons are
ejected more in the direction
of the spin than opposite the
direction of the spin.
We've got little hints like
this, that there are slight
violations of symmetry in
nature, but we don't know
where they come from.
And they only show up in what
is known as the weak force.
The laws of physics are broken
down into sort of four
fundamental forces--
gravity, electromagnetism,
and the strong and
weak nuclear force.
And every one of them, except
for the weak force, seems to
not give any concern whatsoever
about the
distinction between matter
and antimatter.
It's only the weak force that
shows even the slightest
preference.
And that slightest preference
seems to be, in very, very
subtle ways-- it doesn't even
mean that more matter is
created than antimatter.
It's just in what we can do in
a lab, we see very, very tiny
differences that say, somewhere
in the equation--
and we can identify
those terms--
but somewhere in the equations
is a tiny difference.
The universe knows about the
difference between the two.
But how did it choose that?
We don't know.
Here's just one other sort of
illustration of the same thing.
This is just a matter
of a particle
known as the neutrino.
A neutrino is a relic, generally
speaking, of weak
nuclear interactions.
And one of the things that's
very interesting about a
neutrino is that if it is
created in a reaction, it
always flies out in such a way
that it's spinning as given by
your left hand.
Anti-neutrinos are always
spinning in a way that would
be given by your right hand,
with your thumb giving its
direction of motion.
And as I was implying, they
look basically the same.
If you take all anti-neutrinos
and turn them into neutrinos,
and vice versa, and take
everything and look at it in a
mirror, which makes the spins
go the opposite way.
Except that cobalt-60 thing.
It turns out that we can even
make that difference between
matter and antimatter go away.
There's an interesting
discussion, and I've
excerpted it here.
But the crux of it is, in his
Nobel Laureate speech, Richard
Feynman, one of the great
physicists of the 20th
century, was relating a
conversation that he'd had
with his advisor, John
Archibald Wheeler.
And Wheeler had this idea.
And he had a lot more that went
into it, but the idea
was, he said, you know, the
physics of positrons looks
almost exactly the same as the
physics of electrons, if you
assume that positrons
are electrons going
backwards in time.
And it's true.
And so we ask the question.
We've got this combination.
We've got three symmetries that
I've mentioned so far.
Three symmetries, three very
good approximations to almost
perfect symmetries in nature.
Take matter, turn it into
antimatter, look at it in a
mirror, and reverse
it in time.
CPT, it's called.
And every single reaction in
nature that we've ever
discovered--
ever--
will work totally the
same if you do those
three reversals, basically.
Incredible.
Surprising.
And also very, very weird,
when you think about it.
Because when you think about
what that third one is, that
third one, time reversal--
time reversal seems like it is
hardwired into our laws of
physics, right?
Time reversal should
not be an even
approximate symmetry of nature.
I mean after all, you don't know
how this talk is going to
end, but you do know
hot it started.
You remember the past.
You do not remember
the future.
There's a thing called
cause and effect.
I could go on and on.
I mean, we almost don't have the
words to explain how weird
it is that there is such a thing
as the arrow of time.
And yet there is an
arrow of time.
But that said, if you look at
microscopic interactions--
and after all, what are
macroscopic interactions, but
a collection of microscopic
interactions?
A big collection.
You look at these things, and
you can reverse them in time.
This is my time mirror that
I had my illustrator draw.
You take a movie of, say, two
electrons scattering off of
one another and look at that
scatter in a mirror.
That process looks
equally valid.
I take a ball, I throw it though
the air-- well, I throw
it a little bit more
professionally.
I throw a ball through the
air, it makes an arc.
I take a movie of it, watch
that arc in reverse.
It also looks like a valid
trajectory that
a ball could make.
The laws of physics seem
perfectly comfortable being
run forward or reversed.
But obviously there is
a complication--
one that shows up in a fairly
complicated way.
And that is with the
idea of entropy.
So entropy's one of these words
that's thrown around.
It's generally considered
to be--
we talk about it as something
like disorder, for example.
But entropy, we think about
entropy with gas molecules,
for example, and entropy, to a
physicist, is really just a
measure of possibilities.
So what we've got here is
a little cartoon of gas
molecules in a box.
And we've got the same number
of molecules in both
illustrations, 10,
jumping around.
In the left box, we've got
almost all of the gas
molecules in the right
partition.
Now there's very, very
few ways to do that.
If I were to number all my
atoms, for example, there's
only 10 different atoms that
can be the sole atom in the
left partition.
This is what's called low
entropy, or very high order.
In other words, it's like
putting away your room.
I mean, there's a lot of
empty space once you've
cleaned up your room.
On the other hand, in the right
box, we've got this
thing called high entropy And
high entropy is basically,
everything is much more
uniformly distributed.
I cannot stress this strongly
enough, because this is a very
popular misconception, even when
people have encountered
thermodynamics in high
school and college.
But going from low entropy to
high entropy, something that
is so well-established that it
is known as the second law of
thermodynamics, is not
really a law at all.
It's merely a very, very
good suggestion.
More or less even distributions
like this right
image are just far more likely,
because there's far
more ways to distribute your
air molecules than
the ones on the left.
It is absolutely possible--
possible, within the
realm of physics--
that spontaneously, all of the
air molecules on that side of
the room migrate for some short
period of time over to
that side of the room.
And all of you asphyxiate, and
all of you, I guess, get
crushed from air pressure?
We could probably survive.
We could probably survive
two atmospheres.
I think you guys are
gonna be fine.
I'm sorry to you.
But it's incredibly unlikely
that that would happen.
But possible.
That said, this is our biggest
clue as to how the arrow of
time works.
The idea that things go from low
entropy/high order to high
entropy/high disorder.
It is within the realm of
physics that if I break a set
of cue balls, a racked set of
cue balls, that they're going
to scatter around.
If I hit a ball in just the
right way, that they might
reassemble into a triangle.
I would not try to
make that shot.
It would be almost vanishingly
difficult to do so.
But it is within the
realm of physics.
It's just there's not that many
ways that a set of balls
can be arrayed in a triangle.
It's extremely difficult.
It's extremely unlikely.
So the increase in entropy is
a probabilistic statement of
the universe.
It's just there's so many
particles out there that those
probabilities become
almost certainties.
There are even games
that people play--
yeah, I like that.
This is one of my favorites.
There are even games that people
play to try to see
whether the second law of
thermodynamics can be toyed
with, not just in a
probabilistic sense, but if we
might be able to do this.
This is something known as
Maxwell's demon, the idea that
we might be able to make a low
entropy and a high entropy--
make a low-entropy system merely
by having a robot or
some other brain open a box
and let particles through
depending on the nature
of those particles.
So in this case, we might
imagine Maxwell's demon takes
the high-energy particles and
tries to sort them to the left
side of the partition
and the low-energy
particles into the right.
This would be a zero-energy way
of basically creating a
refrigerator.
Put all the hot air on one side,
put all the cold air on
the other, and that
indeed would be
a decrease in entropy.
It turns out especially
philosophers of science have
thought about this.
And one of the problems with a
scenario like Maxwell's demon
is that in making these
determinations, it isn't a
zero increase in entropy.
You'd basically have to have the
demon itself record, say,
the speed of the particle in
its brain, and then when it
made the next measurement, it'd
have to sort of erase
that measurement and
put it again.
And that erasure is going to
increase the net entropy of
the universe.
So time itself seems
to have an arrow.
And if you notice that I haven't
actually resolved why
it is that we have this arrow
of time, you'd be right.
We do not presently know, we do
not really know, why it is
that there is the arrow of time
and that it's one way and
not the other.
We do not know whether entropy
increases with time, or
whether entropy is what makes
the arrow of time.
You know, one of the great
observations that we've made
about the universe is--
tempted to see-- ah, yes,
it is a pointer.
This is the microwave background
of the universe.
It represents hot points--
those are the reds--
and cold points in
the universe.
Hot and cold in this case being
about one part in 100,000.
And the very early universe,
the universe was very, very
ordered, very, very
low entropy.
This is very, very smooth.
And so the question is, did the
universe start with low
entropy, or are we only in a
universe where the arrow of
time is defined because we
define the past as being
low-entropy?
We do not know.
There are, however,
other symmetries
that we can look at.
And in particular, we see that
the universe is largely the
same in all directions.
That is a symmetry not just of
the laws of physics itself,
but of the universe,
apparently.
We can see that not just in
the distribution of the
microwave background, but
also over here with the
distributions of galaxies.
The question is, what
does this mean?
What do all of these symmetries
that we've talked
about, what ultimately
do they mean?
Many of you could rightly look
at them and be like, yeah,
that's an interesting
curiosity.
Yeah, sure, that's great.
But why?
Why do they ultimately
matter, apart from
saying, isn't this beautiful?
This is, after all-- we're
talking with physics.
This is not an art museum.
We can't look at it to be
beautiful just for the sake of
being beautiful.
So one of the great
breakthroughs with regards to
understanding why symmetry is
so important came up with a
mathematician by the name of
Emmy Noether Mathematicians
tend to revere her,
by the way.
But many physicists either
haven't heard of her or
remember very vaguely hearing
about Noether's theorem in one
class when they were, say,
a sophomore or junior in
college, and then they promptly
forgot about her.
She is, to my mind, one of the
most important mathematicians
that we haven't really
heard of.
And I was in the same boat.
I mean, I'd seen Noether's
theorem and promptly forgotten
about it, when I saw
it in college.
And yet she is the foundation,
in many respects, of things
like supersymmetry and these
grand unified theories, all of
our understanding of why we have
a fundamentally unified
theory-- a standard model,
for that matter--
of particle physics.
And you know, she's an
interesting case study for
many reasons.
I'm going to give you a couple
slides, because I want to
point this out.
She has this parallel, in
many ways, to Einstein.
Einstein very famously toiled in
obscurity in a Swiss patent
office until his great
breakthroughs, his miracle
year of 1905.
Noether had similar, but the
motivations of the problems
were different, around
the same time.
She was born in Erlangen.
Her father was a mathematics
professor.
And in 1898, 1900, when she was
going to school or would
have gone to school, they
basically said, no, we can't
admit women.
That would overthrow
all academic order.
So she audited all
her classes.
She was-- you know, one of these
cyber-schools that we'd
now have, I guess.
And she basically went in just
to take her final exams in
Nuremberg--
which she, of course, aced.
She pursued her Ph.D.
Eventually, of course, this
restriction on women
was lifted.
She got her Ph.D. at Erlangen.
And she wasn't able
to get a position.
She stayed at home, basically,
writing important mathematics
papers, occasionally
substitute-teaching for her
father, and that was it--
until Einstein came up with
his theory of general
relativity.
So 1915, he came up his theory
of general relativity.
Everyone recognized the
importance of it almost
immediately.
And Noether was invited by David
Hilbert and Klein to go
to Gottingen to explain it.
They said, basically,
I'm sorry, the
university won't pay you.
I mean, Hilbert was this
incredible advocate for her,
but he was very unsuccessful
for a very, very long time.
But she went.
She went, and almost immediately
created this
wonderful work which is known
as Noether's theorem, which
I'm going to relate to
you in just a moment.
But again, it's worth relating
a little bit more her story.
Hilbert--
there's a quote here.
You know, "I don't see the sex
of a candidate as an argument
against her admission as
a Privatdozent." That's
basically an associate
professor.
"After all, we're a university,
not a bathhouse."
She developed her theorem, and
it wasn't for another seven,
eight years that she was able
to get any sort of paycheck,
incredibly tiny amount-- by the
way, not just because she
was a woman, but also because
she was a pacifist and a Jew
and a socialist, as
I understand it.
1933, Nazis come to power and
she goes to Bryn Mawr College,
and sadly, about 18 months
later, passed away due to
complications from
cancer surgery.
And here's this wonderful
comment by Einstein.
"The most competent living
mathematicians, Noether was
the most significant creative
mathematical genius thus far
produced since the education of
women began." And I mean,
that's understanding it.
I mean, not just amongst women,
but among men, as well.
She was an incredible
mathematician.
So what is it she told us?
What is it she said?
I mean, Noether's theorem, in
words, sounds very, very--
it sounds pithy.
It almost sounds content-free.
But it says that every one of
these symmetries that we've
been talking about produces
a conserved quantity.
And conserved quantities, I will
say, to physics is the
bread and butter of
the universe.
We hear about things like
conservation of energy.
Conservation of energy is
incredibly useful because it
says, look, if you start off
with an energy budget, if you
start off with the sun, and the
sun does something, the
energy of the sun needs
to go somewhere.
Either it heats the Earth, or
it's converted into mass, or
whatever it may be--
the universe will contain a
constant amount of energy, or
electric charge, or
what have you.
And what Noether said is
all these symmetries--
symmetries give rise to
conserved quantities.
So for example, what she showed
was the fact that the
laws of physics are the same
everywhere in the universe
immediately gives rise to the
conservation of momentum.
This is a big deal.
Conservation of momentum,
of course, was known.
It's Newton's first
law of motion.
Objects in motion stay in
motion, blah, blah, blah.
But that was the
starting point.
What Noether's theorem
essentially did was she pushed
us back a step.
She said, no, there's
something even more
fundamental than that.
Newton's first law itself is
built on the idea of a
symmetry, on the fact that
the laws of physics
are constant in space.
The fact that the laws of
physics are the same in all
directions, that there's no
terms that tell you about a
fixed direction of the universe,
say that there's a
conservation of angular
momentum.
The fact that the laws of
physics are constant in time
immediately gives rise to this
conservation of energy.
And there's more.
Now I'm sure some of you may
have pure mathematics
backgrounds.
I don't expect you to parse
this, either way.
I'm only putting this up here
just to mention how important
this ends up being
in our modern
understanding of physics.
Our modern understanding of
physics is all of those
fundamental forces that we talk
about are fundamentally
built on symmetries.
And these symmetries basically
describe how the quantum
mechanical waves of a system can
be changed without any of
the underlying quantities
changing and without the
energies of interaction
changing.
And it turns out you can
describe, for example, U1.
I'll just give this
simple example.
That's the phase of a wave.
If you can adjust the phase
of a wave without changing
anything, that's a symmetry.
And what Noether--
well, what her successors
ultimately showed is that
immediately gives rise to all
of Maxwell's equations.
Absolutely incredible.
And show that there
are conserved
quantities like charges.
And subsequently predicted the
particle that's associated
with that, which
is the photon.
In other words, Noether's
theorem is the first of an
incredibly important
step in showing--
make this very simple assumption
about the laws
work, and you get the nature
of the interaction, all the
equations, and the particle
that relates it.
Same is true for the weak force,
which produce the W and
Z particles, and for the strong
force, which created
the gluons.
All built on symmetries.
Even if there those symmetries
themselves don't look elegant,
putting a little plot of all the
particles in the standard
model does start to
look symmetric.
I mean, this does look much more
orderly, where what we've
got here, ranked from bottom to
top, are the charges of the
various particles.
And besides ordinary electrical
charge, there are
various weak charges that
are associated, as well.
And we can plot these things,
and yes, indeed, this forms a
very beautiful pattern.
So one of the things that
modern-day particle physicists
do is they come up with models
based on symmetries.
And when you hear about things
like at the Large Hadron
Collider, or Brookhaven, or
elsewhere, discovering a new
particle that they thought to
exist, it was because there
was a hole in this diagram of
what we actually discovered
versus what had been
predicted.
Even things that seem like they
are symmetry breaking--
and they are symmetry breaking,
things like the
discrete discovery about the
Higgs boson, for example--
are built on the idea
of a fundamental
symmetry of the universe.
The idea of the Higgs boson
is that there is
an additional field.
An additional field that-- you
know, you can look at that
little pattern--
was initially symmetric, but
at some early time when the
universe became colder, much
like ice freezing into a
crystal or anything else, that
initial symmetry breaking got
frozen into the universe.
The Higgs--
yet another one of these
fundamental discoveries of how
we understand the universe
to work--
also built upon this symmetry
foundation.
So if there are such beautiful
symmetries in the universe--
and there are--
the question is, why isn't
everything perfectly symmetric?
I mean, I've pointed to
individual cases--
matter and antimatter don't
perfectly annihilate because
there seems to be a
slight symmetry
breaking, blah, blah, blah.
But we can ask the question,
where did all
of that come from?
And the answer seems to be
that for all of these
symmetries in the universe,
there's also sort of a
corresponding effect that
makes the universe
interesting, that they can give
rise to things like us,
that are complicated.
That are, if you don't mind me
calling you this, breaks,
mars, in the beautiful
simplicity and
symmetry of the universe.
And that is the randomness
that comes
from quantum mechanics.
So quantum mechanics has random
effects going into it.
And I've got a little
illustration here.
You can imagine starting
a series of tops,
just perfectly arrayed.
You may recognize these
from a popular movie.
And you know that if you start
spinning a top, eventually, a
real top will eventually
topple.
Or not, depending on how much
you choose to read into that.
[LAUGHTER]
DAVE GOLDBERG: But which one
starts to topple first, and
which direction it
topples in--
you can imagine these things,
and you can see a few of them
starting to topple,
just in this case.
You start with something
perfectly symmetric.
You add a random component, and
all of a sudden, you get
some beautiful, beautiful
structure.
And in short, that is the
story of our universe.
Thanks very much.
[APPLAUSE]
DAVE GOLDBERG: Questions?
This is the point when we
have questions, right?
AUDIENCE: You were talking about
how all of the particles
have anti versions
of themselves.
What about the photon?
Is there an anti-photon?
DAVE GOLDBERG: So
you're right.
I did do a little bit of
shorthand, because I didn't
want to do too many caveats.
You're absolutely correct.
There are a few-- very few,
fewer than you'd think--
particles that are their
own anti-particles.
A photon is its own
anti-particle, as
is the Higgs boson.
But most other particles are not
their own anti-particles.
So for example, if I take an
electron and a positron,
particle and anti-particle
collide,
it creates two photons.
And there is no distinguishing
between which one's the
particle version and which
one's the anti-particle.
But you're quite right.
AUDIENCE: What's your personal
opinion of supersymmetry,
given that LHC hasn't
found it yet?
DAVE GOLDBERG: So that's
a really good question.
So supersymmetry involves--
just to give a background to
those who are unfamiliar.
Supersymmetry involves the
relationship between the two
different fundamental
types of particles.
There are particles called
fermions that are electrons
that are the quarks that make up
our protons and neutrons--
basically, the particles
of matter.
And there are particles called
bosons, which are essentially
the force-carriers.
Those include photons and
gluons and the Higgs.
And the idea is, why should we
have two such different groups
of particles in different
quantities?
And not just why should
we, but there's
other technical reasons.
You end up with, for example,
certain particles based on
interactions should be hugely
more massive than they are,
because the fermions sort
of subtract mass
and bosons add mass.
And unless they cancel or
partially cancel, what ends up
happening is you end up
with a huge deficit,
one way or the other.
So there's a lot of sort
of fundamental reasons.
And the idea that the people
come up with is that for every
fermion, there must be a
corresponding boson, and every
boson, there must be a
corresponding fermion.
And many of these particles
are undiscovered.
Many of these particles are
likely to be unstable.
One hope, by the way, is that
there is such a thing called
the lightest supersymmetric
particle, one that probably
doesn't interact
very strongly--
which we've sort of have
a placeholder called a
neutralino--
that might be this missing
dark-matter particle that
we've been looking for.
But we haven't detected
any of these partners.
And experiments like Large
Hadron Collider are capable of
measuring some of these,
in principle.
And hasn't-- that's the upshot
of your question.
So now you're caught
up with the actual
nature of the question.
So the problem is--
I mean, supersymmetry is such a
beautifully elegant theory.
And here's the problem
with it.
I mean, it solves a lot of
problems in particle physics.
It is almost impossible to
disprove, because the number
of parameters that you
can keep adjusting--
there's what's called minimal
supersymmetric model, which
with reasonable parameters that
most physicists would
agree are reasonable, has been
essentially ruled out.
But you can keep adding bells
and whistles, and you could
put in unreasonable that don't
disprove the model.
My personal feeling is
it's grasping at
straws, at this point.
I don't know what the
better solution is.
There might be a more
complicated version of
supersymmetry that could turn
out to be correct, but it's
not looking good.
In fact, that's a position I
take in the book, as well.
I sort of say, look, here's
why we introduced it.
Here's why there are problems.
It hasn't been observed.
And every time every time that
the threshold for observation
gets higher and higher, things
look worse and worse.
So honestly, my gut is saying,
at this point, no.
But I don't know.
I honestly don't.
And I really don't know what
a better answer is.
Yes?
AUDIENCE: Hi.
So I have a question about
the arrow of time.
So I've heard general arguments
about how, like,
things are differentially
symmetric in time.
So you could go backwards
in time, and it
still looks like physics.
But a lot of arguments I hear
about the arrow of time being
biased in the way we perceive
it isn't this
differential argument.
It's this argument about
ensembles and entropy and
stuff like that.
So to me, those two thoughts in
my head are not reconciled
in any constructive way.
So could you elaborate
on the relationship
between those two?
DAVE GOLDBERG: Right.
So yeah, I tried to take entire
of Chapter Two of my
book and brush it into about 30
seconds of exposition here.
So it's a fair question.
So the issue is we've got
two different senses--
at least two different
philosophers would probably
give several more of
the arrow of time.
One, you could call
it, almost, a
psychological arrow, right?
The remembering the past
and not the future.
You've got an entropy arrow,
which is the increase in
entropy goes toward
the future.
We've also got an
arrow of time--
at least in the equations, where
we're implying them-- in
the weak force.
Because we say the arrow goes
this way, and that's the one
that defines how matter
works, and so on.
And so part of the problem--
and this is something I try
to approach in the book by
getting humans out of the
equation entirely.
Like we don't know
how brains work.
But thinking about how a robot
or a disk drive or something
like that would work.
And you're a robot.
You're awoken.
You look at your disk.
And you do not know--
I mean, this is not about
the arrow of time.
This is just sort of about
the relationship between
information and entropy
and memories.
You look at your disk, and
you see that all of your
bits are set to 0.
And you say, OK, this
is a clean slate.
I am--
I have no memories.
On the other hand, I wake you
up as a robot, and there is
this pattern of zeros
and ones.
A complicated pattern,
not 0101.
Some complicated thing that
you can't figure out,
necessarily, what it means.
You don't know anything else.
The question is, are those
legitimate memories, or is
that noise?
And this is something we have
no great reconciliation to.
Because our universe did start
with low entropy, and yet
there's no physical principle
that says why that should be.
And so the assumption is either
there's a physical
principle we don't know, or
there are two states of the
universe, one at low entropy and
one at high entropy, and
there is another physical
principle that basically says
the arrow of time is, by
definition, moving from the
low to the high.
Now I'll tell you what my
problem with that is, the sort
of entropy making time.
It is almost impossible to ever
describe a single state
of the universe.
I mean, because the universe is
not causally connected at
any point to one another.
So saying "The universe is
increasing in entropy" is an
almost meaningless statement,
because there's no process by
which something over the
entire universe can be
integrated and calculated.
So the fact that the whole
universe, or some part of the
multiverse, which is now not
causally connected to one
another, where some property
defined over that entire
region then defines the arrow
of time, I don't see any
mechanism for how
that could work.
So it is absolutely an open
question, as to why the one
should be related
to the other.
The fact that time exists as a
dimension that behaves very,
very different from space--
like one could almost an
anthropic argument about that.
So time does behave differently
from space.
Regardless of which direction
the arrow of time is, the fact
that there is dimension means
that we can do things like
learn from the past, and make
inferences, and so on.
Which we would not be able to do
in quite the same way if we
lived in, say, four dimensions
in space with a universe with
no time at all.
And it may be that
there are part--
if you believe in
the multiverse--
there are parts of the
multiverse with different
dimensionality, and we are
simply here because this is
the most complicated one that
is anthropically favorable,
such that we would be able to
exist at all, or anything
would be able to exist at all.
So I fully recognize I've given
you a non-answer, but
I've hopefully sort of at least
laid out the space of
the problem.
Yes?
AUDIENCE: So this is a question
about Noether's
theorem and the weak force.
So in Noether's theorem, the
things that are in variance,
like space and time, give us
various conservation laws,
like momentum and energy.
So in a sort of
not-to-mathematical, elaborate
way, what's the non-conserved
thing?
What's the variant?
What is the dissipative piece of
some equation that gives us
the lack of conservation,
of CPT in weak force?
DAVE GOLDBERG: So this is the
answer is, it's not a matter
of saying that it's not
a conservation.
It's more a matter of saying
that there's a very specific
thing that is being conserved,
and it's the handedness.
So it's not just a matter of
creating, in the weak force,
creating particles
of all type.
It's that when you create a
particle, you're creating a
left-handed neutrino.
Specifically a left-handed
neutrino, and specifically a
right-handed anti-neutrino.
And what that means--
the reason that it's
left-handed versus
right-handed means that
essentially, you're creating
half as many types
of particles.
We think, oh, what does it
matter whether the thing is
spinning this way or
spinning that way?
But from a physics perspective,
those are two
different particles.
And so what it means is that
we are essentially--
we are essentially getting half
as many particles out of
the equations, half as many
particles getting dumped out
of these equations, as we might
otherwise have if the
thing was both left-handed
and right-handed.
So we're only getting one.
So from a practical perspective,
when we think
about all the statistics of
the universe, we count in
order to figure out things like
pressure and so on, how
many different particles
could exist.
Electrons, which can be
either spin direction,
we count for two.
Neutrinos, for each species,
we only count for one, for
exactly that reason.
Because there's essentially half
as many effective species
as there might otherwise be.
Are there other questions?
No.
Thank you.
Oh.
[APPLAUSE]
DAVE GOLDBERG: Thanks
so much for coming.
