Kind: captions
Language: en
the following is a conversation with
peter white a theoretical physicist at
columbia outspoken critical string
theory and the author of the popular
physics and mathematics blog called not
even wrong
this is the lex friedman podcast to
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in the description and now here's my
conversation with peter white
you're both a physicist and a
mathematician
so let me ask what is the difference
between physics and mathematics
well there's kind of a conventional
understanding of the subject that
they're
two you know quite different things so
that mathematics is about you know
making
rigorous statements about
these abstract you know abstract things
things of mathematics and and proving
them rigorously and physics is about you
know doing experiments and
testing various models and that but i
think the more interesting thing is that
the
there's a
yeah there's a wide variety of what
people do as mathematics what they do is
physics and there's a significant
overlap and that i think is actually the
much much very very interesting area and
if you go back kind of far enough to in
in in history and look at figures like
newton or something i mean there it at
that point you can't really tell you
know was newton a physicist or a
mathematician yeah mathematicians will
tell you as a mathematician the
physicist will tell you as a physicist
but he would say he's a philosopher yeah
yeah
that's that's interesting but uh yeah
anyway there there was kind of no such
distinction then it's more of a modern
thing and
but anyway i think these days there's a
very interesting space in between the
two so in the story of the 20th century
and the early 21st century what is the
overlap between mathematics and physics
would you say
well i think
it's actually become very very
complicated i think it's really
interesting to see a lot of what my
colleagues and
math department are doing they
most of what they're doing they're doing
all sorts of different things but um
most of them have some kind of overlap
with physics or other
so i mean i'm personally interested in
one spec one particular aspect of this
overlap which i think
has a lot to do with the most
fundamental ideas about physics and
about
mathematics but um
there's just
you you kind of see this this uh
really really everywhere at this point
which particular overlap are you looking
at group theory yeah so the um
at least
what the way it seems to me that if you
look at physics and look at the our most
successful um
laws of fundamental physics
they're
really you know they have a certain kind
of mathematical structure it's based
upon
certain kind of mathematical objects and
geometry connections and curvature the
spinners the rock equation
and uh that
these this very deep mathematics
provides kind of a unifying
set of meth of ways of thinking that
allow you to to make a unified theory of
physics but the interesting thing is
that if you go to mathematics and look
at what's been going on in mathematics
the last
1500 years and even especially recently
there's a
similarly some kind of unifying ideas
which bring together different areas of
mathematics and which have been
especially powerful in number theory
recently and
there's a book for instance by um
edward frankel about love and math and
oh yeah that book is great i recommend
it highly it's uh partially accessible
but there's a nice audio book
that i had listened to while
running an exceptionally long distance
like across the san francisco
bridge
and uh there's something magic about the
way he writes about it but some of the
group theory in there is a little bit
difficult
uh yeah it's a problem with any of these
things to kind of really say what's
going on is
and make it accessible is very hard
he in this book and elsewhere i think
you know takes the attitude that kinds
of mathematics he's interested in and
that he's talking about are provide kind
of a grand unified theory of mathematics
they um they bring together geometry and
number theory and
representation theory a lot of different
ideas
in a really
unexpected way
but i think to me the most fascinating
thing is if you look at
the kind of grand unified theory of
mathematics he's talking about and you
look at the physicists kind of ideas
about unification it's more or less the
same mathematical objects are appearing
in both
so it's this um i think there's a really
we're seeing a really strong indication
that you know the deepest
ideas that we're discovering about
physics and some of the deepest ideas
that mathematicians are learning about
are really are you know intimately
connected
is there something like if i was five
years old you were trying to explain
this to me is there ways to try to sneak
up to the to to what this unified world
of mathematics looks like you said
number theory he said geometry
words like topology
what does this universe begin to look
like are these what should we imagine in
our mind is it a
a three-dimensional surface
and we're trying to say something about
it
is it uh
triangles and squares and cubes like
what what are we supposed to imagine our
minds is this natural number what what's
a good thing to try to
for people that
don't know any of these tools except
maybe some basic calculus and geometry
from high school that they should keep
in their minds
as to the unified world of mathematics
that also
allows us to explore the unified world
of physics
the i mean what i
find kind of remarkable about this is
the way in which
these we've discovered these ideas but
they're they're actually quite alien to
our everyday understanding you know we
grow up in this three spatial
dimensional world and we have
intimate understanding of certain kinds
of geometry and certain kinds of things
but um these things that we've
discovered in both math and physics are
that they're not at all
close have any obvious connection to
kind of human everyday experience that
they're really quite different and i can
say some of my initial fascination with
this when i was
young and starting to learn about it was
actually
exactly this um
this kind of arcane nature of these
things it was a little bit like being
being told well there are these kind of
some semi-mystical experience that you
can acquire by a long study and whatever
except
that that it was actually true there's
actually evidence that this actually
works
so you know i'm a little bit wary of
trying to give people
and that kind of thing because i think
it's mostly misleading but one thing to
say is that you know that geometry is a
large
part of it and um
maybe one interesting thing to say very
that's about more recent some of the
most recent ideas is that it um when we
think about the geometry of our space
and time it's kind of three spatial and
one
time dimension it's a um
physics is in some sense about
something as kind of four dimensional in
a way and that a really interesting
thing about um some of the recent
developments and number theory have been
to realize that the um
these ideas that we were looking at you
know naturally fit into a context where
your theory is for is kind of four
dimensional
so
so so so i mean geometry is a big part
of this and we know a lot and feel a lot
about you know two one two three
dimensional geometry so wait a minute so
we can at least rely
on the four dimensions of space and time
and say that we can get pretty far by
working that in those four dimensions i
thought you were going to scare me that
we're going to have to go to many many
many many more dimensions than that
my point of view which is which goes
against a lot of these ideas about
unification is that no this is really
everything we do we know about really is
about four dimensions that um
and and that you can actually understand
a lot of these structures that we've
been seeing in fundamental physics and
in
in number theory just in terms of
four dimensions that it's kind of
it's in some sense i would claim
has been a really um
has been kind of a mistake that
physicists have made and
for decades and decades to try to
to try to go to higher dimensions to try
to formulate a theory in higher
dimensions and then then you're stuck
with
the problem how do you get rid of all
these extra dimensions that you've
created and
because we only ever see anything
important
that kind of thing leads us astray you
think so so creating all these extra
dimensions just to get to give yourself
extra degrees of freedom
yeah it's not i mean isn't that the
process of mathematics is to create
all these trajectories for yourself but
eventually you have to end up at the uh
like a final place but it's okay to
it's okay to sort of um
create abstract objects on your path to
uh proving something
yeah so yeah certainly but and from from
mathematicians point of view
i mean
the kinds of mathematicians also are
very different than physicists and that
we like to develop very general theories
we like to if we have an idea we want to
um see what's the greatest generality in
which you can talk about it so from the
point of view of most of the ways
geometry is formulated um
by mathematicians it really doesn't
matter it works in any dimension we can
do
one two three four any any number
there's no particular
for most of geometry there's no
particular special thing but for
but um
and anyway but but what physicists have
have been trying to do over the years is
try to understand
these fundamental theories in a
geometrical way and it's very tempting
to kind of just
start bringing in
extra dimensions
and using them to explain the structure
but
um
typically this this attempt kind of
founders because you just don't know
you end up not being able to explain why
we only see four and anyway
it is nice in the space of physics that
uh like if you look at from o's last
theorem
it's much easier to prove that there's
no solution for n equals three
than it is for the general case
and and so i guess that's the nice
benefit of being a physicist is you
don't have to worry about the general
case because we live in a universe with
n equals
four in this case
yeah the physiophysicists are very
interested in
saying something about specific examples
and
i find that interesting even when i'm
trying to do things in mathematics and
i'm trying even teaching courses and
mathematics students i find that
i'm teaching them in a different way
than um most mathematicians because i'm
very often very focused on examples on
what's
what's kind of the crucial example that
shows how this um
this powerful new mathematical technique
how it works and why you would want to
to do it
and i'm less interested in kind of
you know proving a precise theorem about
exactly when it's going to work and when
it's not going to work do you think
about really simple examples like uh
both for teaching and when you
try to solve a difficult problem are you
do construct like the simplest possible
examples that captures the fundamentals
of the problem and try to solve it yeah
yeah exactly that's often
a really fruitful way to if you've got
some idea to you just kind of try to
boil it down to what's the simplest
situation in which this kind of thing is
going to happen and then try to really
understand that and understand that and
that that is almost always a really good
way to get insight into do you work with
uh paper and pen or like for example for
me
coming from the programming side if you
if i look at a model if i look at some
kind of mathematical object
i like to mess around with it sort of
numerically i just visualize different
parts of it visualize however i can so
most of the work is like with neural
networks for example as you try to play
with the simplest possible example and
just to build up intuition by
um you know
any kind of object has a bunch of
variables in it
you start to mess around with them in
different ways and visualize in
different ways to start to build
intuition
or do you go to einstein route and just
imagine
like
everything inside your mind and sort of
build like thought experiments and then
work purely on paper and pen
well the problem with this kind of
stuff
i'm interested in is it you you rarely
can kind of
it's really something that is really
kind of
or even the simplest example
you know it can is you can kind of see
what's going on by it looking at
something happening in three dimensions
there's there's generally this the
structures involved are um
either they're more abstract or if you
try to kind of embed them in some kind
of space and where you could um
manipulate them in some kind of
geometrical way it's going to be a much
higher dimensional space so even simple
examples
the embedding them into
three-dimensional space you're losing a
lot yeah or but to capture what your
what you're trying to understand about
them you have to go to four or more
dimensions so it starts to get to be
hard to
i mean you can
train yourself to try it as much as to
kind of
think about things in your mind and you
know i often use pad and paper and often
if i'm
in my office often use the blackboard
um and you are kind of drawing things
but they're really kind of more abstract
representations of how
things are supposed to fit together and
they're not really
unfortunately not just kind of really
living in three dimensions where you can
are we supposed to be sad or excited by
the fact that our human minds can't
fully comprehend the kind of mathematics
you're talking about i i mean
what do we make of that i mean to me
that makes me quite sad it makes me it
makes it seem like there's a giant
mystery out there that we'll never truly
get to experience
directly it is kind of sad you know how
difficult this is i mean or i would put
it a different way that um
you know most questions that people have
about this kind of thing
you know you couldn't you can give them
a really a true answer and really
understand it but
the problem is is one more of um of time
it's like
yes you know i could explain to you how
this works but you have to be willing to
sit down with me and you know work at
this repeatedly for
you know for hours and days and weeks
and you you mean it's just going to take
that long for your mind to really wrap
itself around what's going on and um
and that so that does make things an
inaccessible which is uh
which is sad but it again i mean it's
just kind of part of life that we all
have a limited amount of time and we
have to decide what we're going to
what we're going to spend our time doing
speaking of a limited amount of time we
only have a few hours maybe a few days
together here on this podcast
let me ask you the question
of um
amongst many of the ideas that you work
on
in mathematics and physics what to use
the most beautiful idea or one of the
most beautiful ideas maybe a surprising
idea and once again unfortunately the
way life works we only have a limited
time together try to convey such an idea
okay well actually let me just tell you
something which i i'm tempted to kind of
start trying to explain what i think is
this most powerful idea that brings
together math and physics ideas about
groups and representations and how it
fits quantum mechanics and but in some
sense i wrote a whole textbook about
that and
i don't think we really have time to get
very far into it so well can i actually
on a small tangent you did write a paper
towards the grant unified theory
mathematics and physics
um maybe you could step there first what
is the key idea in that paper well i
think we've kind of gone over that i
think that the key idea is what we were
talking about earlier that um
that just kind of a claim that if you
look and see what's that have been
successful ideas in unification in
physics and over the last
um 50 years or so and what
has been happening in mathematics and
the kind of thing that
frankl's book is about that these are
very much the same kind of mathematics
and so it's kind of an argument that
there really
is
you shouldn't be looking to unify just
math or just
fundamental physics but taking
inspiration for looking for new ideas in
fundamental physics that they are going
to be in the same direction of
getting deeper into mathematics and
looking for more inspiration mathematics
from
these successful ideas about fundamental
physics
could you put words to sort of the
disciplines we're trying to unify so you
said number theory are we literally
talking about all the major fields of
mathematics so it's like the number
theory geometry
uh so the differential geometry topology
like yeah
so the i mean one one name for this
that this is acquired in in mathematics
is the so-called language program
and uh so this started out in
mathematics it's that
you know robert langland's kind of
realized that a lot of what people were
doing and um
that was starting to be really
successful in number theory in the
60s and so that this actually
was
anyway that this could be could be
thought of in terms of um
these ideas about symmetry in groups and
representations
and and
in a way that was also close to some
ideas about about geometry and um then
it more later on in the 80s and 90s
there was something called um
geometric language that people realize
that you could take what people have
been doing in number theory in language
and and and get re just forget about the
number theory and ask what is this
telling you about geometry and you get a
whole some new insights into certain
kinds of geometry that way
so it's anyway that that's kind of the
name for this area is langlins and
geometric language
and just recently in the last few months
there's been um
there's kind of a really major paper
that uh appeared by uh peter schultz and
laurel farg where they
you know made you know some serious
advance and trying to understand
a very much
kind of a local problem of what happens
in number theory near a certain prime
number and they
turn this into a problem of exactly the
the kind the geometric
language people had been doing these
kind of pure a pure geometry problem and
they
found
by generalizing the mathematics they
could actually reformulate it in that
way and it worked perfectly well
one of the things that makes me sad
is you know i'm um pretty knowledgeable
person and then
uh what is it at least i'm in the
neighborhood of like theoretical
computer science right
and it's still way out of my reach and
so many people talk about like language
for example is one of the most brilliant
people in mathematics and just really
admires work
and i can't
it's like almost i can't hear the music
that he composed and it makes me sad
yeah well i mean i i think that
unfortunately it's not just
you as i think even most mathematicians
have no really don't actually understand
this about them in the the group of
people who really understand
all these ideas and so for instance this
paper of
schultz and farg that i was talking
about the number of people who really
actually understand how that works is
anyway one
very very small and so it's uh so i i
think even
you find if you talk to mathematicians
and physicists even they will often feel
that you know there's this really
interesting sounding stuff going on and
which i should be able to understand
it's kind of in my own field i have a
phd in but it still seems it's pretty
clearly far beyond me right now
well if we can step into the back to the
question of beauty uh
is there an idea that maybe is a little
bit smaller
that you find beautiful in the space of
mathematics or physics
there's an idea that you know i kind of
went got a physics phd and spent a lot
of time learning about mathematics and i
guess
it was embarrassing and i hadn't really
actually understood this very simple
idea
um until and kind of learned it when i
actually started teaching math classes
which
is maybe that there there may be
there's a simple way to explain kind of
the fundamental way in which algebra and
geometry are connected so you normally
think of geometry is about these spaces
and these points and
and you think of algebra is this very
abstract thing about with these
abstract objects that satisfy certain
kinds of relations you can multiply them
and add them and
do stuff but it's it's completely
abstract and there's nothing geometric
about it but the um
the kind of really
fundamental idea is that unifies algebra
and geometry is to is to realize is to
think when whenever anybody gives you
what you call an algebra some abstract
thing of things that you can multiply
and add
that you should ask yourself
is that algebra the space of functions
on some geometry
so one of the most surprising examples
of this for instance is a
i mean a standard kind of
thing that seems to have nothing to do
with geometry is the um
is the
the integers so then they're you can you
can multiply them and add them it's
it's an algebra but the um
it has seems to have nothing to do with
geometry but what you can it turns out
but if you ask yourself this question
and ask you know is are integers can you
think if somebody gives you an integer
can you think of it as a function on
some space
on some geometry and it turns out that
yes you can and the space is the space
of prime numbers
and so what you do is you just if
somebody gives you an integer
you can make a function on the prime
numbers by just
you know at each prime number taking
that
that integer modulo that prime so if uh
if you say i don't know if you get given
you know 10 and you ask what is its
value at 2 well it's
it's 5 times 2 so mod 2 it's zero so it
has zero one what what is what is this
value at three
well it's nine plus one so it's it's one
mod three
so it's about it's zero at two it's one
at three and you can kind of keep going
and so
this is really kind of a
truly fundamental idea it's at the basis
of what's called algebraic geometry and
it just links these two parts of
mathematics that look completely
different and it's just an incredibly
powerful idea and so much of mathematics
emerges from this kind of
simple relation so uh you're talking
about mapping from one discrete space to
another to another so
um
for a second i thought perhaps
uh mapping like a continuous space of
discrete space like functions over a
continuous space
because yeah well you can i mean you can
take if somebody gives you a space
you can ask you can say well let's let's
and this is also this is part of the
same idea the part of the same idea is
that if you try and do geometry and
somebody tells you here's a space
that what you should do is you said wait
say wait wait a minute maybe i should be
trying to solve this using algebra and
so if i do that the way to start is you
give me the space
i start to think about the functions of
the space okay so for to each point in
the space i associate
a number i can take different kinds of
functions and different kinds of values
but but basically functions on a space
so
what this
insight is telling you is that if you're
a geometer often the way to to to work
is to trans change your problem into
algebra by changing your space stop
thinking about your space and the points
in it and think about the functions on
it got it and if you're if you're an
algebraic and you and you've got these
abstract algebraic gadgets that you're
multiplying and adding say wait a minute
are those gadgets
can i think of them in some way as a
function on a space what would that
space be and what kind of functions
would they be and that going back and
forth really brings these two
completely different looking areas of
mathematics together do you have uh
particular examples where it allowed to
prove some difficult things by jumping
from one to the other is that something
that's a part of modern mathematics
where such jumps are made oh yes this is
kind of all the time
a lot much much of modern number theory
is kind of based on this idea but
and and when you start doing this you
start to realize that you need you know
what simple
things simple things on one side
algebras start to require you to think
about
the other side about geometry in a new
way you have to kind of get a more
sophisticated idea about geometry or if
you
start thinking about the functions on a
space
you may have you may need a more
sophisticated kind of algebra but um but
in some sense i mean much or most of
modern number theory is
based upon this move to geometry and um
there's also a lot of geometry and
topology is also based upon
yeah changing if you want to understand
the topology of something you look at
the functions you do dram comology and
you get the topology
anyway
well let me let me ask you then the
ridiculous question you said that this
idea is beautiful
uh can you formalize the definition of
the word beautiful
and why is this beautiful like first why
is this beautiful and second
um what is beautiful
well
and i think there are many different
things you can find beautiful for
different reasons i mean i think in this
context
the notion of beauty i think really is
just kind of
an idea is beautiful if it's
packages a huge amount of kind of
power and information into
something very simple so in some sense
you i mean
you can almost kind of try and measure
it in the sense of you know what's the
what are the implications of this idea
what
non-trivial things does it tell you
versus
you know how how how how simply can you
can you express the idea and so so level
of compression yeah uh what is it
correlates with uh beauty yeah that's
that's one and one aspect of it and so
you can start to tell that an idea is
becoming uglier and uglier
as you start kind of having to
you know it doesn't quite do what you
want so you throw in
something else to the idea and you keep
doing that until
you get what you want but that's how you
know you're doing something uglier and
uglier when you have to kind of keep
adding in
more
more into what was originally a fairly
simple idea and making it more and more
complicated to get what you want
okay so let's put some uh philosophical
words on the table and try to make some
sense of them one word is beauty another
one is simplicity as you mentioned
another one is truth
so
do you have a sense if i give you two
theories one is
simpler one is more complicated
do you have a sense which one is more
likely to be true
to uh
capture
deeply
the fabric of reality
the simple one or the more complicated
one yeah i think all of our evidence
what we see in the history of the
subject is the the simpler one though
often it's a surprise it's simpler in a
surprising way but um
yeah that that we just don't we just
anyway when the kind of best theories
have been coming coming up with are
ultimately when properly understood
relatively simple and uh much much
simpler than you would expect them to be
do you have a good explanation why that
is is it just because humans want it to
be that way are we just like ultra
biased then we we we just kind of
convinced ourselves
that simple is better because we find
simplicity beautiful or is there
something about at the our actual
universe
that uh at the core is simple
my own belief is that there is something
about a universe that that's simple and
i was trying to say that you know there
is some some kind of fundamental thing
about math physics
and physics and all this picture which
is um
which which is in some sense simple
it's true that you know it
it's of course true that you know our
minds have certain have
are very limited and can certainly do
certain things and not others so it
it's it's in principle possible that
there's some
great insight there are a lot of
insights into the way the world works
which is aren't accessible to us because
that's not the way our minds work we
don't and that what we're seeing this
kind of simplicity is just because
that's
all we ever have any hope of seeing but
so there's a brilliant
physicist by the name of sabine
hasenfelder who both agrees and
disagrees with you i suppose agrees
that uh
the final answer will be simple yeah
but uh simplicity and beauty leads us
astray in the lo in the local pockets of
scientific progress
uh do you uh do you agree with her
disagreement do you disagree with her
agreement
i agree with the agreement uh well i i i
i i i
yes i thought it was really fascinating
reading your book and and and anyway it
was finding disagreeing with with a lot
but then at the end when she says yes
when we find
there when we actually figure this out
it will it will be simple and yeah and
okay so
we agree in the end
does beauty lead us astray which is the
the core thesis of her work
in that book i actually i guess i do
disagree with her on on that so much i
don't think and especially and i
actually fairly strongly disagree with
her about sometimes sometimes the way
she'll refer to math and
so the problem is
you know
physicists and people in general just
refer to as math and and they're often
um
they're they're often meaning not what i
would call math which is the interesting
ideas of math but just
cause some complicated calculation and
and so um
i i guess
my feeling about it is more that it's
very
the problem with talking about
simplicity and using simplicity as a
guide
is that it's very um
it's very easy to fool yourself and you
know it's very easy to decide
to you know to fall in love with an idea
you have an idea you think oh this is
this is great and you fall in love with
it and it's like any kind of love affair
it's very easy to believe that you know
you're the object of your affections is
much more beautiful than they others
might think and they're that they really
are and that's
very very easy to do so um if you say
i'm just gonna pursue ideas about
beauty and
this and mathematics and this it's
extremely easy to to just fool yourself
i think um and i think that's a lot of
what
the story is she was thinking of about
where people have gone astray that i
think it's i would argue that as more
people it's not that there was some
simple powerful wonderful idea which
they'd found and it turned out not to be
um
not to be useful but it was more that
they kind of fooled themselves that this
was actually a better idea than it
really was and it was
simpler more beautiful than it really
was is a lot of the story um i see so
it's not that the simplicity would be
lisa's astrays that's just people or
people and they
uh fall in love with with whatever idea
they have and then they they weave
narratives around that idea or they
present in such a way that uh emphasizes
uh the simplicity and the beauty
yeah that's part of it but i mean the
thing about physics that you have
is that you you know what what really
can tell
if you can do an experiment and check
and see if nature is really doing what
your your idea expects that you you do
in principle have a way of really of
testing it and and it's certainly true
that if you um
you know if you thought you had a simple
idea and that doesn't work and you got
into an experiment and what actually
does work is somewhere maybe some more
complicated version of it that can
certainly happen and
that that that can be true
i think her emphasis is more that i
don't really disagree with is that
um
people should be concentrating on
when they're trying to develop better
theories on
morons on self-consistency not so much
on beauty but you know not is this idea
beautiful but you know is there
something about the theory which is not
quite consistent
and that and use that as a guide
that there's something wrong there which
needs fixing and and so i think that
part of her argument i think i was
we're on the same page about
uh what's what is consistency in
inconsistencies
what what exactly um
do you have examples in mind
well it can be just simple inconsistency
between theory and an experiment that if
you so we have this
great fundamental theory but there are
some things we see out there which don't
seem to fit in it like like dark energy
and dark matter for instance
but if there's something which you can't
test experimentally i think
you know she would argue and i would
agree that for instance if you're trying
to think about
gravity and how are you going to have a
quantum theory of gravity you should
kind of
be you know and test any of your ideas
with kind of
kind of a thought experiment you know is
does this actually give a consistent
picture what's going to happen of what
happens in this particular situation or
not
so this is a good example you've written
about this um
you know since quantum gravitational
effects are
really small
super small arguably unobservably small
should we have hope to arrive at a
theory of quantum gravity somehow
what are the different ways we can get
there you've mentioned that you're not
as interested in that effort because
basically
yes you cannot
have uh ways to scientifically validate
it given the tools of today yeah i've
actually you know i've over the years
certainly spent a lot of time learning
about
gravity and about attempts to quantize
it but it
it hasn't been that much
in the past the focus of what i've been
thinking about but
i mean my feeling was always you know as
i think speed would agree that the uh
you know one way you can pursue this if
you if you can't do experiments is
just this kind of search for consistency
you know it can be remarkably hard to
come up with a completely consistent
model of model of this in a way that
brings together quantum mechanics and
general relativity
and that's i think kind of been
the traditional way that people who have
pursued quantum gravity have often
pursued you know
we have the best route to finding a
consistent
theory of quantum gravity and string
theorists will tell you this
other other people will tell you it it's
it's kind of what people argue about but
but the problem with all of that is that
you end up
um
the danger is that you end up with that
that everybody could be successful
everybody everybody's
program for how to find a theory of kind
of gravity you know ends up with
something that is consistent
and so
in some sense you could argue this is
what happened to the strength there is
they um
they solved their problem of finding a
consistent theory of quantum gravity and
they ended but they found 10 of the 500
solutions so
you you know
if you believe that everything that they
would like to be true is true well
okay you've got a theory but it's
it ends up being kind of useless because
it's just one of
an infant essentially infinite number of
things which you have no way to
experimentally distinguish and so this
is a
just a depressing situation
um but but i but i do think that there
is a um
so again i think pursuing ideas about
what
more about beauty and how can you
integrate and unify
these issues about gravity with other
things we know about physics and can you
find a theory which were they were these
fit together in a in a way that makes
sense and and hopefully predict
something that's much more promising
well it makes sense and hopefully i mean
we'll sneak up
onto this question a bunch of times
because you kind of said
uh a few slightly contradictory things
which is like it's nice to have a theory
that's consistent
but then
if the theory is consistent it doesn't
necessarily mean anything
so like it's it's not enough it's not
enough it's not enough and that's the
problem so it's like it keeps coming
back to
okay there should be some experimental
validation
so okay
let's talk a little bit about string
theory you've been uh
a bit of an outspoken critic of strength
theory
maybe one question first to ask is what
is string theory
and uh
beyond that why is it
wrong
or rather the title of your blog says
not even wrong okay
well one interesting thing about the
current state of strength theory is that
i think it i'd argue it's actually very
very difficult to at this point to say
what string theory means if people say
they're string theorists what they
mean and what they're doing is uh
it's kind of hard it's hard to pin down
the meaning of the term but the but the
initial meaning i think goes back to um
there was kind of a series of
developments starting in 1984 in which
people felt that they had found a
unified theory of
our so-called standard model of of all
the standard
well-known kind of particle interactions
and gravity and it all fit together in a
quantum theory and that you could do
this
in a very specific way by
instead of thinking about
having a quantum theory of particles
moving around in space time think about
uh quantum theory of kind of
one-dimensional loops moving around in
space-time so-called strings and so
instead of one degree of freedom
these have an infinite number of degrees
of freedom it's a much more complicated
theory but you can imagine
okay we're going to quantize this theory
of loops moving around in space-time
and what they found is that they
is that you could make you could do this
and you could fairly relatively
straightforwardly make sense of
of such a quantum theory but only if
space and time together were
10-dimensional
and so then you had this problem again
the problem i referred to at the
beginning of okay now once you make that
move you've got to get rid of six
dimensions
and so the hope was that
you could get rid of the six dimensions
by making them very small and that
consistency of the theory would require
these that these six dimensions um
satisfy a very specific condition called
being a claudio manifold and that we
knew very very few examples of this
so what got a lot of people very excited
back in
84 85 was the hope that
you could just take this some 10
dimensional string theory and
find one of a limited number of possible
ways of
of getting rid of six dimensions by
making them small and then you would end
up with a an effective four-dimensional
theory which looked like the real world
this was the hope so then
there's been a very long story about
what happened to that hope over the
years i mean
i i would argue and like part of the
point of the book and its title was that
um
you know that this this ultimately was
it was a failure that you ended up that
this idea just didn't um
there ended up being just too many ways
of doing this and you didn't know how to
do this consistently
that it was kind of
not even wrong in the sense that you
couldn't even you never could pin it
down well enough to actually get a real
falsifiable prediction out of it that
would tell you it was wrong but it was
um
it was kind of in the in the realm of
ideas which initially looked good but
the more you look at them
they just um
they don't work out the way the way you
want and they don't actually end up
carrying the power or the that you
originally had this vision of
and yes the the book title is not even
wrong your blog your excellent blog
title is not even wrong
okay but there is nevertheless been a
lot of excitement about string theory
through the decades as you mentioned uh
what are the different flavors of ideas
that came
uh
like they branched out you mentioned 10
dimensions you mentioned
loops with infinite degrees of freedom
what what other interesting ideas to you
that kind of emerge from this world
well yeah i mean the problem in talking
about the whole subject and well partly
one reason i wrote the book
is that you know it it gets very very
complicated i mean there's a huge amount
you know you a lot of people got very
interested in this a lot of people
worked on it and and in some sense i
think what happened is exactly because
the idea didn't really work
that this caused people to
you know instead of focusing on this one
idea and digging in and working on that
they just kind of
kept trying new things and so
people i think ended up wandering around
in a very very rich space of ideas about
mathematics and physics and discovering
you know all sorts of really interesting
things it's just the problem is there
tended to be an inverse relationship
between how interesting and beautiful
and fruitful this new
idea that they were trying to pursue was
and how much it looked like the real
world
so there's a lot of beautiful
mathematics came out of it
i think one of the most spectacular is
what the
physicists call two-dimensional
conformal field theory and so these are
basically
[Music]
quantum field theories and kind of think
of it as one space and one time
dimension which
you know have just this huge amount of
symmetry and a huge amount of structure
which
and just some totally fantastic
mathematics behind it and um and again
and and some of that mathematics
is exactly also what appears in the
language program so a lot of the um
first interaction between math and
physics around the language program has
been around these two-dimensional
conformal field theories
is there um something you could say
about what the major problems are with
strength theory
so
like um
besides
that there's no experimental validation
you've written that a big hole
in string theory has been its
perturbative definition yeah
perhaps that's one can you explain what
that means well maybe to begin with i
mean i think i mean the simplest thing
to say is
you know the the initial idea really was
that
okay we're we have this
instead of what's great is we have this
thing that only works
that's very structured and has to
work in a certain way for it to make
sense
and um
but but then you ended up you ended up
in ten space time dimensions and so to
get back to physics you had to get rid
of five of the dimension six of
dimensions
and
the bottom line i would say in some
sense it's very simple that what people
just discovered is just
there there's kind of no particularly
nice way of doing this there's an
infinite number of ways of doing it and
you can get whatever you want depending
on how you do it so the you you end up
the whole program of starting at ten
dimensions and getting to four
just kind of collapses out of a lack of
any way to kind of get to where you want
because you can get anything
the hope around that problem has always
been that
the standard formulation that we have of
string theory which is
you can go in by the name perturbative
but it's kind of um
there's a standard way we know of given
a classical theory of constructing
a quantum theory and
and working with it which is
that's the so-called perturbation theory
that um that we know how to do
and that
that by itself just just doesn't doesn't
give you any hint as to what to do about
the six dimensions
so actual perturbed string theory by
itself really only works in 10
dimensions
so
you have to start making some kinds of
assumptions about how i'm going to
go beyond
this formulation that we really
understand of string theory and get rid
of these six six dimensions so kind of
the simplest one was the um
the claudio
postulate
but um
when that didn't really work out people
have tried more and more different
things and and the hope has always been
that
the solution
this problem would be that you would
find a a deeper and better understanding
of what string theory is that would
actually go beyond this perturbative
expansion and which would um which would
generalize this and and that once you
had that it would um
it would solve this problem of
it would pick out what to do with the
six dimensions how difficult is this
problem so
if i could restate the problem it seems
like there's a very consistent
physical world operating in four
dimensions
and uh how do you map a consistent
physical world in 10 dimensions to a
consistent physical world in four
dimensions right and how how difficult
is this problem is is that something you
can even answer
um
just
in terms of physics intuition in terms
of mathematics mapping from
ten dimensions to four dimensions well
basically i mean you have to get rid of
the of six of the dimensions so there's
i mean there's kind of two ways of doing
it one is what we call compactification
you say that
there really are 10 dimensions but for
whatever reason six of them are really
are so so small we can't see them
so you basically start out with ten
dimensions and what we call you know
make make six of them
not go out to infinity but just kind of
a finite extent and then make that size
go down
so small it's unobservable but that's
like that's a math trick
so
can you also help me build an intuition
about
how rich
and interesting the world in those six
dimensions is
because so compactification seems to
imply
well that's very interesting well no but
the problem is that what you learn if
you start doing math mathematics looking
at geometry and topology and in more and
more dimensions is that
i mean
asking the question like what are all
possible six dimensional spaces it's
just a it's kind of an unanswerable
question it's just uh i mean it's even
kind of technically undecidable in some
way they're just they're just too too
they're too many things you can do with
all these
if you start trying to make if you start
trying to make one-dimensional spaces
it's like well you got a line you can
make a circle you can make graphs you
can kind of see what you can do but as
you go to higher and higher dimensions
there's just so many ways you can
put things together of and get something
of that dimensionality and
so it it
unless you have some very very strong
principle which is going to pick out
some very specific
ones of these six dimensional spaces
and
they're just too many of them and you
can get anything you want but um so if
you have 10 dimensions
the kind of things that happen
say that's actually the way
that's actually the fabric of our
realities 10 dimensions there's a
limited set of behaviors of objects i
don't even know what the right
terminology to use that can
occur when within those dimensions like
in reality yeah
and so like
what i'm getting at is like is there
some consistent constraints
so if you have some constraints that map
to reality
then you can start saying like
dimension number seven is kind of boring
all the excitement happens in the
spatial dimensions one two three yeah
and time is also kind of boring
yeah and like
some are more exciting than others or we
can use our metric of beauty
some dimensions are more beautiful than
others once you have an actual
understanding of what actually happens
in those dimensions in our physical
world as opposed to sort of all the
possible things that could happen in
some sense i mean just the basic factors
you need to get rid of them we don't see
them so you need to somehow explain them
what you have to the main thing you're
trying to do is to explain why we're not
seeing them
and so you can you have to come up with
some theory of these extra dimensions
and how they're going to behave and
string theory gives you some ideas about
how to do that but
but
the bottom line is where you're trying
to go with this whole theory you're
creating is
to just make all of its effects
essentially unobservable so it's a it's
not a really
it
it's an inherently kind of dubious and
worrisome thing that you're trying to do
there why are you just
adding in all the stuff and then trying
to explain why we don't see it i mean
it's just good this may be a dumb
question but it's is this an obvious
thing to state
that
those six dimensions are unobservable or
anything beyond four dimensions is
unobservable or
do you leave a little door open to
saying
the current tools of physics
and obviously our brains aren't unable
to observe them
yeah but we may need to come up with
methodologies for observing so as
opposed to collapsing your mathematical
theory into four dimensions
leaving the door open a little bit too
maybe we need to come up with tools that
actually allow us to directly measure
those dimensions
yes i mean but you mean you can
certainly ask you know assume
that that we've got
model look look at models with more
dimensions and ask you know what would
the observable effects how would we
know this and you go out and do
experiments so for instance
you have a
like
gravitationally you have an inverse
square law of forces okay if you had
more dimensions that inverse square law
would change something else
so you can go and start
measuring the inverse square law and say
okay an inverse square law is working
but maybe if i get get and it turns out
to be actually kind of very very hard
measuring gravitational effects and even
kind of
you know somewhat macroscopic distances
because they're so small so you can you
can start looking at the inverse square
law and say start trying to measure it
at shorter and shorter distances and see
if there were extra dimensions at those
distance scales you would start to see
the inverse square law fail and um so
people look for that and again you don't
see it but
you can i mean there's all sorts of
experiments of this kind you can you can
imagine which test
for effects of extra dimensions at
different at
different distance scales but
you know none of them
i mean they they all just don't work
nothing yet i think yeah but you could
say ah but it it's if it's just it's
just much much smaller you can say that
which by the way makes ligo and
the detection of gravitational waves
quite an incredible project
ed whitten
is often brought up as one of the most
brilliant mathematicians and physicists
ever
what do you make of him and his work on
string theory
well i think you know he's a truly
remarkable figure i've
you know had the pleasure of meeting him
first when he was a postdoc and um i
mean he's a
just completely
amazing um mathematician and physicist
and uh you know he's
quite a bit smarter than just about
about any of the rest of us and also
more hard working and it's a it's a kind
of frightening combination to see how
much he's
been able to do
and um but i would actually argue that
you know his his greatest work the
things that he's done that have been of
just this mind-blowing significance of
giving us i mean he's completely
revolutionized some areas of mathematics
he's totally revolutionized the way we
understand the relations between
mathematics and physics
and most of those
his greatest work is is stuff that
doesn't have has little or nothing to do
with string theory i mean for instance
he um
you know he so he was actually one of
fi