String theory Brian Greene
in the year 1919 a virtually unknown
German mathematician named Theodor
Kaluza suggested a very bold and in some
ways very bizarre idea he proposed that
our universe might actually have more
than the three dimensions that we are
all aware of that is in addition to
left-right back-forth and up-down gluts
to propose that there might be
additional dimensions of space that for
some reason we don’t yet see now when
someone makes a bold and bizarre idea
sometimes that all it is both bizarre
but has nothing to do with the world
around us this particular idea however
although we don’t yet know whether it’s
right or wrong and at the end I’ll
discuss experiments which in the next
few years may tell us whether it’s right
or wrong this idea has had a major
impact on physics in the last century
and continues to inform a lot of
cutting-edge research so I’d like to
tell you something about the story of
these extra dimensions so where do we go
to begin need a bit of backstory go to
1907 this is a year when Einstein is
masking the glow of having discovered
the special theory of relativity and
decides to take on a new project to try
to understand fully the grand pervasive
force of gravity and in that moment
there were many people around who
thought that that project had already
been resolved Newton had given the world
the theory of gravity late 1600s that
works well describes the motion of
planets the motion of the moon and so
forth the motion of apocryphal apples
falling from trees hitting people in the
head all of that could be described
using Newton’s work but Einstein
realized that Newton had left something
out of the story because even Newton had
written that although he understood how
to calculate the effect of gravity he
had been unable to figure out how it
really works how is it that the Sun 93
million miles away somehow defect
the motion of the earth how does the Sun
reach out across empty inert space and
exert influence and that as a task to a
Jain Stein set himself to figure out how
gravity works and let me show you what
it is that he found so Einstein found
that the medium that transmits gravity
is space itself the idea goes like this
imagine space is a substrate of all
there is Einstein said space is nice and
flat if there’s no matter present but if
there is matter in the environment such
as the Sun it causes the fabric of space
to warp to curve and that communicates
the force of gravity even the earth
warps space around it now look at the
moon the moon is kept in orbit according
to these ideas because it rolls along a
valley in the curved environment that
the Sun and the moon and the earth can
all create by virtue of their presence
we go to a full frame view of this the
earth itself is kept in orbit because it
rolls along a valley in the environment
that’s curved because of the sun’s
presence that is this new idea about how
gravity actually works now this idea was
tested in 1919 through astronomical
observations it really works it
describes the data and this gained
Einstein prominence around the world and
that is what got Colusa thinking he like
Einstein was in search of what we call a
unified theory that’s one theory that
might be able to describe all of
nature’s forces from one set of ideas
one set of principles one master
equation if you will so Coolidge’s said
to himself
Einstein has been able to describe
gravity in terms of warps and curves in
space in fact space and time to be more
precise maybe I can play the same game
with the other known force which was at
that time known as the electromagnetic
force we know of others today but at
that time that was the only other one
people were thinking about you know the
force responsible for electricity and
magnetic attraction and so forth so
Colusa says maybe I can play the same
game and describe electromagnetic force
in terms of warps and curves
that raised a question warps and curves
in what Einstein had already used up
space and time warps and curves to
describe gravity didn’t seem to be
anything else to warp a curve so Colusa
said well maybe there are more
dimensions of space
he said if I want to describe one more
force maybe I need one more dimension so
he imagined that the world had four
dimensions of space not three and
imagine that electromagnetism was warps
and curves in that fourth dimension now
here’s the thing when he wrote down the
equations describing warps and curves in
the universe with four space dimensions
not three he found the old equations
that einstein had already derived in
three dimensions those were for gravity
but he found one more equation because
of the one more dimension and when he
looked at that equation it was none
other than the equation that scientists
had long known to describe the
electromagnetic force amazing it just
popped out he was so excited by this
realization that he ran around his house
screaming victory that he had found the
unified theory now clearly Colusa was a
man who took theory very seriously he in
fact there’s a story that when he wanted
to learn how to swim he read a book a
treatise on swimming then toven to the
ocean this is a man who would risk his
life on theory now but for those of us
who are a little bit more practically
minded to questions immediately arise
from his observation number one if there
are more dimensions of space where are
they we don’t seem to see them and
number two does this theory really work
in detail when you try to apply it to
the world around us now the first
question was answered in 1926 by a
fellow named Oskar Klein
he suggested that dimensions might come
in two varieties there might be big easy
to see dimensions but there might also
be tiny curled up dimensions curled up
so small even though they’re all around
us that we don’t see them let me show
you that one visually so imagine you’re
looking at something like a cable
supporting a traffic lights in Manhattan
in Central Park that’s it’s kind of
irrelevant but the cable looks
one-dimensional from a distant viewpoint
but you and I all know that it does have
some thickness it’s very hard to see it
though from far away but if we zoom in
and take their perspective to say a
little ant walking around little ants
are so small that they can access all
the dimensions the long dimension but
also this clockwise counterclockwise
direction and I hope you appreciate this
it took so long to get these ants to do
this but this illustrates the fact that
dimensions can be of two sorts big and
small and the idea is that maybe the big
dimensions around us are the ones that
we can easily see but there might be
additional dimensions curled up sort of
like the circular part of that cable so
small that they have so far remained
invisible let me show you what that
would look like so if we take a look say
at space itself I can only show of
course two dimensions on a screen some
of you guys will fix that one day but
anything that’s not flat in the screen
is a new dimension goes smaller smaller
smaller and way down in the microscopic
depths of space itself this is the idea
you could have additional curled up
dimensions here is a little shape of a
circle so small that we don’t see them
but if you were a little
ultra-microscopic ant walking around you
can walk in the big dimensions that we
all know about that’s like the grid part
but you could also access the tiny
curled up dimension that’s so small that
we can’t see with the naked eye or even
with any of our most refined equipment
but deeply tucked into the fabric of
space itself the idea is there could be
more dimensions as we see there now
that’s an explanation about how the
universe could have more dimensions than
the ones that we see but what about the
second question that I asked does the
theory actually work when you try to
apply it to the real world well it turns
out that Einstein includes and many
others worked on trying to refine this
framework and apply it to the physics of
the universe as was understood at the
time and in detail it didn’t work in
detail for instance they couldn’t get
the mass of the electron to work out
correctly in this theory so many people
worked on it but by the 40s certainly by
the 50s
this strange but very compelling idea of
how to unify the laws of physics had
gone away until something wonderful
happened in our age in our era a new
approach to unify the laws of physics is
being pursued by physicists such as
myself many others around the world it’s
called super string theory as you were
indicating and the wonderful thing is
that super string theory has nothing to
do at first sight with this idea of
extra dimensions but when we study super
string theory we find that it resurrects
the idea in a sparkling new form so let
me just tell you how that goes super
string theory what is it
well it’s a theory that tries to answer
the question what are the basic
fundamental indivisible uncuttable
constituents making up everything in the
world around us the idea is like this so
imagine we look at a familiar object
just a candle and a holder and imagine
that we want to figure out what it is
made of so we go on a journey deep
inside the object and examine the
constituents so deep inside we all know
you go sufficiently far down you have
atoms we also all know that atoms are
not the end of the story
they have little electrons that swarm
around a central nucleus with neutrons
and protons even the neutrons and
protons have smaller particles inside of
them known as quarks that is where
conventional ideas stop here is the new
idea of string theory deep inside any of
these particles there is something else
there’s something else is this dancing
filament of energy it looks like a
vibrating string that’s where the idea
of string theory comes from and just
like the vibrating strings that you just
saw on a cello can vibrate in different
patterns these can also vibrate in
different patterns they don’t produce
different musical notes rather they
produce the different particles making
up the world around us so these ideas
are correct this is what the
ultra-microscopic landscape of the
universe looks like it’s built up of a
huge number of these little tiny
filaments of vibrating energy vibrating
in different frequencies the different
frequencies produce the different
particles the different particles are
responsible for all the richness
in the world around us and there you see
unification because matter particles
electrons and quarks radiation particles
photons
gravitons are all built up from one
entity so matter and the forces of
nature all are put together under the
rubric of vibrating strings and that’s
what we mean by a unified theory and
here is the catch when you study the
mathematics of string there you find
that it doesn’t work in a universe that
just has three dimensions of space
it doesn’t work in a universe with four
dimensions of space nor 5 nor 6
finally you can study the equations and
show that it works only in a universe
that has ten dimensions of space and one
dimension of time leads us right back to
this idea of Kaluza and Klein that our
world when appropriately described has
more dimensions than the ones that we
see now you might think about that and
say well ok you know if you have extra
dimensions and they’re really tightly
curled up yeah perhaps perhaps we won’t
see them if they’re small enough but you
know if there’s a little tiny
civilization of green people walking
around down there you make them small
enough and we won’t see them either that
is true one of the other predictions of
string theory no that’s not one of the
other predictions of string theory but
it raises the question are we just
trying to hide away these extra
dimensions or do they tell us something
about the world and the remaining time
I’d like to tell you two features of
them first is many of us believe that
these extra dimensions hold the answer
to what perhaps is the deepest question
in theoretical physics theoretical
science and that question is this when
we look around the world as scientists
have done for the last hundred years
there appear to be about 20 numbers that
really describe our universe these are
numbers like the mass of the particles
like electrons and quarks the strength
of gravity the strength of the
electromagnetic force a list of about 20
numbers that have been measured with
incredible precision but nobody has an
explanation for why the numbers have the
particular values that they do now
the string theory often answer not yet
but we believe the answer for why those
numbers have devised they do may rely on
the form of the extra dimensions and the
wonderful thing is if those numbers had
any other values than the known ones the
universe as we know it wouldn’t exist
this is a deep question why those
numbers so finely tuned to allow stars
to shine and planets to form when we
recognize that if you fiddle with those
numbers if I had 20 dials up here and
I’ll let you come up and fiddle with
those numbers almost any fiddling makes
the universe disappear so can we explain
those twenty numbers and string theory
suggests that those twenty numbers have
to do with the extra dimensions let me
show you how so when we talk about the
extra dimensions in string theory it’s
not one extra dimension as in the older
ideas of Kaluza and Klein this is what
string theory says about the extra
dimensions they have a very rich
intertwined geometry this is an example
of something known as a claw be a shape
name isn’t all that important but as you
can see the extra dimensions fold in on
themselves and intertwine in a very
interesting shape interesting structure
and the idea is that if this is what the
extra dimensions look like then the
microscopic landscape of our universe
all around us would look like this on
the tiniest of scales when you swing
your hand you’d be moving around these
extra dimensions over and over again but
they’re so small that we wouldn’t know
it so what is the physical implication
though relevant to those twenty numbers
consider this if you look at the
instrument of French horn notice that
the vibrations of the airstreams are
affected by the shape of the instrument
now in string theory all the numbers are
reflections of the way strings can
vibrate so just as those air streams are
affected by the twists and turns in the
instrument strings themselves will be
affected by the vibrational patterns and
the geometry within which they are
moving so let me bring some strings into
the story and if you watch these little
fellas vibrating around they’ll be here
in a second right there notice that the
way they vibrate is affected by the
geometry of the extra dimensions so if
we knew exactly what the extra
dimensions look like we don’t yet but if
we
we should be able to calculate the
allowed notes the allowed vibrational
patterns and if we could calculate the
allowed vibrational patterns we should
be able to calculate those 20 numbers
and if the answer that we get from our
calculations agrees with the values of
those numbers that have been determined
through detailed and precise
experimentation this in many ways would
be the first fundamental explanation for
why the structure of the universe is the
way it is now the second issue that I
want to finish up with is how might we
test for these extra dimensions more
directly is this just an interesting
mathematical structure that might be
able to explain some previously
unexplained features of the world or can
we actually test for these extra
dimensions and we think this is I think
very exciting that in the next five
years or so we may be able to test for
the existence of these extra dimensions
here’s how it goes in CERN Geneva
Switzerland a machine is being built
called a Large Hadron Collider it’s a
machine that will send particles around
a tunnel opposite directions near the
speed of light every so often those
particles will be aimed at each other so
there’s a head-on collision the hope is
that if the collision has enough energy
it may act some of the debris from the
collision from our dimensions forcing it
to enter into the other dimensions how
would we know it well we’ll measure the
amount of energy after the collision
compare it to the amount of energy
before and if there’s less energy after
the collision than before this will be
evidence that the energy has drifted
away and if it drifts away in the right
pattern that we can calculate this will
be evidence that the extra dimensions
are there let me show you that idea
visually so imagine we have a certain
kind of particles called a graviton
that’s the kind of debris we expect to
be ejected out if the extra dimensions
are real but here’s how the experiment
will go
you take these particles you slam them
together you slam them together and if
we are right some of the energy of that
collision will go into debris that flies
off
into these extra dimensions so this is
the kind of experiment that we will be
looking at in the next five seven to ten
years or so and if this experiment bears
fruit if we see that kind of particle
ejected by noticing that there’s less
energy in our dimensions then when we
began this will show that the extra
dimensions are real and to me this is a
really remarkable story and a remarkable
opportunity going back to Newton with
absolute space didn’t provide anything
but an arena a stage in which the events
of the universe take place
Einstein comes along and says well space
and time can warp and curve that’s what
gravity is and now string theory comes
along and says yes gravity quantum
mechanics electromagnetism all together
in one package but only if the universe
has more dimensions than the ones that
we see and this is an experiment that
may test for them in our lifetime
amazing possibility thank you very much