[I’ve meant for some while to try an automatic transcription
software, and Graham Farmelo’s interview of Edward Witten (mentioned by Peter Woit) seemed a
good occasion. I used an app called “Trint” which seems to work okay. But both
the software and I have trouble with Farmelo’s British accent and with Witten’s
mumbling. I have marked the places that I didn’t understand with [xxx]. Please
leave me a comment in case you can figure out what’s being said. Also notify me
of any blunders that I might have missed. Thanks!]
GF [00:00:06] A
mind of the brilliance of Edward Witten’s comes along in mathematical physics
about once every 50 years if we’re lucky. Since the late 1970s he’s been
preeminent among the physicists who are trying to understand the underlying
order of the universe. Or, as you might say, trying to discover the most
fundamental equations of physics. More than that, by studying the mathematical
qualities of nature, Witten became remarkably influential in pure mathematics.
The only physicist ever to have won the coveted Fields Medal which has much the
same stature in mathematics as a Nobel Prize has in physics.
GF [00:00:46] My
name is Graham Farmelo, author of “The universe speaks in numbers.” Witten is a
central figure in my book and he’s been helpful to me. Though he’s a reluctant
interviewee so I was pleased when he agreed to talk with me last August about
some aspects of his career and the relationship between mathematics and
physics. He was in a relaxed mood sitting on a sofa in his office at the
Institute for Advanced Study in Princeton wearing his tennis clothes. As usual, he speaks quietly so you’ll have to listen hard.
GF [00:01:20] He
uses quite a few technical terms too. But if you’re not familiar with them I
suggest that you just let them wash over you. The key thing is to get a sense
of Witten’s thinking about the big picture. He is worth it.
GF [00:01:32] He
gives us several illuminating insights into how he became interested in state-of-the-art mathematics while remaining a physicist to his fingertips. I began by
asking him if he’d always been interested in mathematics and physics.
EW [00:01:47] When
I was a kid I was very interested in astronomy. It was the period of the space
race and everybody was interested in space. Then, when I was a little older, I was
exposed to calculus by my father. And for a while I was very interested in
math.
GF [00:02:02] You
said for a while, so did that lapse?
EW [00:02:04] Yes, it did lapse for a few years, and the reason it lapsed, I think, was that after
being exposed to calculus at the age of eleven it actually was quite a while
before I was shown anything that was really more advanced. So I wasn't really
aware that there was much more interesting more advanced math. Probably
not the only reason, but certainly one reason that my interest lapsed.
GF [00:02:22] Yeah.
Were you ever interested in any other subjects? I mean because you know you
came on to study history and things like that. Did that really interest you
comparably to math and physics?
EW [00:02:31] I
guess there was a period when I imagined doing journalism or history or
something but at about the age of 21 or 22 I realized that I wasn't going to
work out well in my case.
GF [00:02:42] After
studying modern languages he worked on George McGovern’s ill fated presidential
campaign and even studied economics for one semester before he finally turned
to physics.
GF [00:02:53] Apparently
he showed up at Princeton University wanting to do a Ph.D. in theoretical
physics and they wisely took him on after he made short work of some
preliminary exams. Boy did he learn quickly. One of the instructors tasked with
teaching him in the lab told me that within three weeks Witten’s questions on
the experiments went from basic to brilliant to Nobel level. As a postdoc at
Harvard, Witten became acquainted with several of the theorist pioneers of this
model including Steven Weinberg, Shelly Glashow, Howard Georgi, and Sydney
Coleman, who helped interest the young Witten in the mathematics of these new
theories.
EW [00:03:33] The
physicists I learned from most during those years were definitely Weinberg, Glashow, Georgi, and Coleman. And they were completely different. So Georgi and
Glashow were doing model building, basically weak interaction model building, elaborations on the Standard Model. I found it fascinating but it was a little
bit hard to find an entree there. If the
world had been a little bit different, I might have made my career doing things
like they were doing.
GF [00:04:01] Wow.
This was the first time I’d heard Witten say that he was at first expecting to
be like most other theorists and take his inspiration from the results of
experiments building so-called models of the real world. What, I wondered, led
him to change direction and become so mathematical.
EW [00:04:19] Let
me provide a little background for listeners. Up to and including the time I
was a graduate student, for 20, 25 years, there had been constant waves of new
discoveries in elementary particle physics: strange particles, muons, hadronic
resonances, parity violations, CP violation, scaling and deep inelastic
scattering, the Charm particle, and I’m forgetting a whole bunch. But that’s enough to give you the idea. So that was over a period of over 20 years. So even
after a lot of the big discoveries that was one every three years. Now, if
experimental surprises and discoveries had continued like that, which at the time
I think is what would have happened because it had been going on for a quarter century, then I would have
expected to be involved in model building, or grappling with it, like
colleagues such as Georgi and Glashow all were doing. Most notably, however, it
turned out that this period of constant surprise and turmoil was ending just
while I was a graduate and therefore later on I had no successful directions.
GF [00:05:20] Do
you remember being disappointed by that in any sense?
EW [00:05:23] Of
course I was, you never stop being disappointed.
GF [00:05:27] Oh
dear, oh it’s a hard life.
GF [00:05:31] You
were disappointed by the drawing up so to speak of the.
EW [00:05:33] There
have been important experimental discoveries since then. But the pace has not
been quite the same. Although they’ve been very important they’ve been a little
bit more abstract in what they teach us and definitely they’ve offered fewer
opportunities for model building than was the case in the 60s and 70s. I’d like
to just tell you a word or two about my interaction with the other physicists. There was Steve Weinberg and what I remember best from Weinberg. He was one of the
pioneers of a subject called current algebra which was an important part of
understanding the nuclear force. But he obviously thought most other physicists
didn't understand it properly and I was one of those. So whenever current
algebra was mentioned at a seminar or a discussion meeting he would always give
a short little speech explaining his understanding of it. In my case after
hearing those speeches the eight to 10 times [laughter] what Steve was telling
us.
EW [00:06:28] Then
there was Sidney Coleman. First of all Sidney was the only one who was
interested in strong coupling behavior of quantum field theories which is what
I’d become interested in as a graduate student with encouragement from my
advisor David Gross. So, he was really the only one I could interact with about
that. Others regarded strong coupling as a black box. So, maybe for your
listeners, I should explain that if you’re a student in physics they teach you
what to do when quantum effects are small, but no one tells you what to do when
quantum effects are big, there’s no general answer. It’s a smorgasbord of
different methods that work for different problems and a lot of problems that
are intractable. So, I'd become interested in that as a student but I was mostly
beating my head against a brick wall because it is usually intractable, and
Sydney was the only one of the professors at Harvard interested in such
matters. So, apart from interacting with him about that, also he exposed me to a
number of mathematical topics I wouldn’t have known about otherwise but that
eventually were important in my work which most physicists didn’t know about.
And certainly I didn’t know about.
GF [00:07:27] Yeah, can I ask were you consciously interested in advanced pure math at that time?
EW [00:07:32] Definitely
not
GF [00:07:32] You
were not?
EW [00:07:32] No,
most definitely not. I got dragged into math gradually because you see the
standard model had been discovered so the problems in physics were not exactly
the same as they had been before. But there were new problems that were opened
up by the standard model. For one thing there is new math that came into
understanding the standard model. Just when I was finishing graduate school
more or less Polyakov and others introduced the Yang-Mills instanton which has
proved to be important in understanding physics. It’s also had a lot of
mathematical applications.
GF [00:08:02] You can think of instantons as fleeting events that occur in space and time on
the subatomic scale. These events are predicted by the theories of the
subatomic world known as gauge theories. A key moment in this story is Witten’s
first meeting with the great mathematician Michael Atiyah at the Massachusetts
Institute of Technology. They will become the leaders of the trend towards a
more mathematical approach to our understanding of the world.
EW [00:08:32] So
Polyakov and others had discovered the Yang-Mills instanton and it was
important in physics and proved to have many other applications. And then
Atiyah was one of the mathematicians who discovered amazing mathematical
methods that could be used to solve the instanton equations. So he was
lecturing about that when he visited in Cambridge. I think in the spring of
1977, but I could be off by a few months, and I was extremely interested. And so we
talked about it a lot. I probably made more of an effort to understand the math
involved than most of the other physicists did. Anyway this interaction surely
led to my learning all kinds of math I’d never heard of before, complex manifolds, sheaf cohomology groups.
GF [00:09:16] This
was news to you at that time.
EW [00:09:18] Definitely.
So I might tell you at an even more basic level the Atiyah-Singer index theorem
had been news to me a few months earlier when I heard about it from Sidney
Coleman.
GF [00:09:28] The
index theorem first proved by Michael Atiyah and his friend Isidore Singer
connects two branches of mathematics that had seemed unconnected. Calculus,
that’s the mathematics of changing quantities, and topology about the
properties of objects that don’t change when they’re stretched, twisted, or
deformed in some way, topology is now central to our understanding of
fundamental physics.
EW [00:09:51] Like
other physics graduate students of the period, I had no inkling of any 20th
century math, really. So, I’d never heard of the names Atiyah and Singer or of
the concept of the index or if the index theorem until Albert Schwarz showed
that it was relevant to understanding instantons. And even then that paper
didn’t make an immediate splash. If Coleman hadn’t pointed it out, I’m not sure
how long it would have been before I knew about it. And then there was
progress in understanding instanton equations by Atiyah among others. The first
actually was Richard Ward, Penrose’s doctoral student. So, I got interested in that but I was
interested in a sense in a narrow way which is what good would it be in
physics. And I learned the math or some of the math that the teacher was using.
But I was a little skeptical about the applicability for physics and I wasn’t
really wrong because the original program of Polyakov didn’t quite work out. The
details of the Instanton equations that were beautifully elucidated by the
mathematicians were not in practice that helpful for things you can actually do
as a physicist. So, to sort of summarize what happened in the long run, Atiyah’s
work and that of his colleagues made me learn a lot of math I’d never heard of
before which turned out to be very important later but not per se for the
original reasons.
GF [00:11:10] When
did you start to become convinced that math was really going to be interesting?
EW [00:11:14] Well that gradually happend in the
1980s I guess. So, for example one early episode which was in 1981 or two I was
trying to understand the properties of what's called the vacuum the quantum
ground state in supersymmetric field theories and it really had some behavior
that was hard to explain using standard physics ideas and since I couldn't
understand it I kept looking at simpler and simpler models and they all had the
same puzzle. So finally I got to what seemed like the simplest possible model
which you could ask the question and it still had a puzzling behavior. But at a
certain point, I think when I was in a swimming pool in Aspen Colorado, I
remembered Raoul Bott and actually Atiyah also had given some lectures to physicists a couple of years earlier in Cargesse, and they had tried to explain something
called Morse theory to us. I’m sure there are like me many other physicists
that have never heard of Morse theory or are familiar with any of the questions it
addresses or.
GF [00:12:11] Would you like to say what Morse theory is roughly speaking?
EW [00:12:14] Well
if you’ve got a rubber ball floating in space it’s got a lowest point, where
the elevation is lowest, it’s got a highest point where the elevation is
highest. So it’s got a maximum and a minimum. If you have a more complicated
surface like for example a rubber inner tube, it’ll have saddle points of height
function as well as a maximum and minimum. And Morse theory relates the maxima
and minima and the saddle points of a function such as height function to the
topology of a surface or topological manifold on which the function is defined.
GF [00:12:48] You
see that paper by Maxwell on that what he spoke about see in 1870.
EW [00:12:52] I’ve
not read that.
GF [00:12:53] Oh
I’ll show it to you later. It’s “
On Hills and Dales,” gave it in Liverpool, very
thinly attended talk, erm, anyway.
EW [00:13:01] So
was he in fact describing the two dimensional version of Morse theory.
GF [00:13:04] I can’t
go into detail but the historians of Morse theory, they often refer to that. At a public meeting
incidentally in Liverpool.
EW [00:13:13] Actually
now you mentioned it, I heard the title of the Hills and Dales talk by Maxwell that had something
to do with the beginnings of topology. And topology was just barely beginning in roughly that period.
GF [00:13:23] But
this was useful in physics. Your Aspen swimming pool revelation...
EW [00:13:28] Well,
it shed a little bit of light on the vacuum state in super symmetric quantum
theories. So anyway I developed that further so you know at first that seemed
exceptional but eventually there were too many of these exceptions to
completely ignore.
GF [00:13:42] Am I
right in saying, not to put into your mouth, but it was the advent of String Theory post Michael
Greene and John Schwartz where these things started going front and center, is that
fair?
EW [00:13:50] After...
Following the first super string revolution as people call it which came to
fruition in 1984 with the work of Greene and Schwarz on the anomalies after that
the sort of math that Atiyah and others had used for the instaton equation was
suddenly actually useful. Because to understand string theory, complex
manifolds and index theory sheaf cohomology groups, all those funny things were
actually useful in doing basic things like constructing models of the elementary particles in string theory. I should give a slightly better explanation. In
physics there are the forces that we see for the elementary particles that
means basically everything except gravity. Then there's gravity which is so
weak that we only see it for macroscopic masses like the earth or the sun. Now
we describe gravity by Einstein's theory and then we describe the rest of it by
quantum field theory. It's difficult to combine the two together. Before 1984
you couldn't even make a halfway reasonable models for elementary particles
that included all the forces together with gravity. The advance that Greene and
Schwarz made with anomaly cancellation in 1984 made that possible. But to make
such models you needed to use a lot of the math that physicists had not used
previously but which was introduced by Atiyah and others when they solved the
instanton equations and you had to use complex manifolds, sheaf cohomology
groups and things that were totally alien to the education of a physics
graduate student back in the days when I'd been a student. So those things were
useful even at a basic level in making a model of the elementary particles with
gravity. And if you wanted to understand it more deeply you ended up using
still more maths. After string theory was developed enough that you could use
it in an interesting way to make models of particle physics it was clear that a
lot of previously unfamiliar math was important. I speak loosely when I say
previously unfamiliar because obviously it was familiar to some people. First
of all the to the mathematicians. Secondly in some areas like Penrose had used
some of it in his Twister theory. But broadly speaking unfamiliar to most physicists.
GF [00:15:46] So
we actually went very well in physics very very important for mathematicians in
mathematics a very important physicist they're working harmoniously alongside
each other. You go back to Leibnitz who used to talk about the pre
established harmony between math and physics. That was one of Einstein's
favorite phrases. Is there something you regard as a fact of life or is it
something you would regard as possibly can be explained one day will never be
explained. Do you have any comment at all on that relationship.
EW [00:16:09] Well, the intimate tie between math and physics seems to be a fact of life. I can't
imagine what it would mean to explain it. The world only seems to be based on
theories that involve interesting math and a lot of interesting math is at
least partly inspired by the role that it plays in physics. Not all of course.
GF [00:16:25] But
does it inspire you when you see a piece of math that's very relevant to
physics and vice versa when you're helping mathematicians. Does that motivate
you in some way to think you're on the right track.
EW [00:16:35] Well
when something turns out to be beautiful that does encourage you believe that
it's on the right track.
GF [00:16:39] Classic
Dirac. But he took it as he put it to almost a religion. But I sense you
are a little bit more skeptical, if
that's the right word or hard nosed about it I don't know.
EW [00:16:51] Having
discovered the Dirac equation, Dirac was entitled to commit its use to extremes, to put it that
way.
GF [00:16:58] Witten
has long been a leading pioneer of the string framework which seeks to give a
unified account of all the fundamental forces based on quantum mechanics and
special relativity. It describes the basic entities of nature in terms of tiny
pieces of string.
GF [00:17:14] Go
back to string theory. Do you see that as one among several candidates or the
preeminent candidate or what? I mean what do you see the status of that
framework in the landscape of mathematical physics.
EW [00:17:24] Id
say that string slash M theory is the only really interesting direction we have
for going beyond the established framework of physics by which I mean quantum
field theory at the quantum level and classical general relativity at the
macroscopic scale. So where where we've made progress that's been in the string
slash M theory framework where a lot of interesting things have been
discovered. I'd say that there's a lot of interesting things we don't
understand at all.
EW [00:17:48] But
you’ve never been tempted down the other route. The other options are not.
EW [00:17:52] I’m
not even sure what you would mean by other routes.
GF [00:17:54] Loop
quantum gravity?
EW [00:17:56] Those
are just words. There aren’t any other routes.
GF [00:17:58] Okay,
all right, fair enough.
GF [00:18:01] So there we have it. The preternaturally
cautious Witten says that if we want to discover a unified theory of all the
fundamental forces, string theory is the only interesting way forward that’s
arisen.
GF [00:18:17] Where
we are now strikes me as being quite an unusual time in particle physics
because so many of us were looking forward to the Large Hadron Collider, huge
energy available ,and finding the Higgs boson and maybe supersymmetry. And
yet it seems that we have gotten the Higgs particle just as we were hoping and
expecting. But nothing else that’s really stimulating. What are your views on where
we are now?
EW [00:18:39] My
generation grew up with a belief very very strong belief which by the way was
drummed into us by Steven Weinberg and by others. That when physics reached the
energy scale at which you can understand the weak interactions. You would not
only discover the mechanism of electroweak symmetry breaking but you’d learn what
fixes its energy scale as been relatively low compared to the scale of gravity.
That’s what ultimately makes gravity so weak in ordinary terms. So, it came as a
big surprise that we reached the energy scale to study the W and the Z and even
the Higgs particle without finding a bigger mechanism behind it. That’s an
extremely shocking development in the context of the thinking that I grew up
with.
EW [00:19:22] There
is another shock which also occurred during that 40 year period which possibly
should be comparative. This is the discovery that the acceleration of the
expansion of the universe. For decades physicists assumed that because of the
gravitational attraction of matter the expansion of the universe with be
slowing down and tried to measure it. It turned out that the expansion is
actually speeding up. We don't know this for sure it seems quite likely that
the results from the effects of Einstein's cosmological constant which is
incredibly small but non-zero. The two things the very very small but non-zero
cosmological constant and the scale of weak interactions the scale of
elementary particle masses which in human terms can seem like a lot of
energies. But it's very small compared to other energies in physics. The two
puzzles are analogous and they're both extremely bothersome. These two puzzles
although primarily the one about gravity which was discovered first are perhaps
the main motivation for discussions of a cosmic landscape of vacua. Which is an
idea that used to make me extremely uncomfortable and unhappy. I guess because
of the challenge it poses to trying to understand the universe and the possibly
unfortunate implications for our distant descendants tens of billions of years
from now. I guess I ultimately made my peace with it recognizing that the
universe hadn't been created for our convenience.
GF [00:20:43] So you come to terms with it.
EW [00:20:45] I've
come to terms with the landscape idea and the sense of not being upset about
it. As I was for many years.
GF [00:20:49] Really
upset?
EW [00:20:50] I
still would prefer to have a different explanation but it doesn't upset me
personally to the extent it used to.
GF [00:20:56] So
just to conclude what would you say the principal challenge is all down to
people looking at fundamental physics.
EW [00:21:01] I
think it's quite possible that new observations either in astronomy or
accelerators will turn up new and more down to earth challenges. But with what
we have now and also with my own personal inclinations it's hard to avoid
answering new terms of cosmic challenges. I actually believe that string slash
M theory is on the right track toward a more deeper explanation. But at a very
fundamental level it's not well understood. And I'm not even confident that we
have a good concept of what sort of thing is missing or where to find it. The
reason I'm not is that in hindsight it's clear that a view we might have given
in the 1980s was what was missing was too narrow. Instead of discovering what
we thought was missing instead we broadened the picture in the 90s in
unexpected directions. And having lived through that I feel it might happen
again.
EW [00:21:49] To
give you a slightly less cosmic answer if you ask me where I think is the most
likely direction for another major theoretical upheaval like happened in the
80s and then again in the 90s. I've come to believe that the whole it from qbit
stuff, the relation between geometry and entanglement, is the most interesting
direction.
GF [00:22:12] It
from bit that was a phrase coined by the late American theoretician John
Wheeler who guessed that the stuff of nature the "it" might
ultimately be built from the bits of information. Perhaps the theory of
information is showing us the best way forward in fundamental physics. Witten
is usually wary of making strong pronouncements about the future of his
subjects. So I was struck by his interest in this line of inquiry, now
extremely popular.
EW [00:22:39] I
feel that if in my active career there will be another real upheaval that's
where it's most likely to be coming [xxx]
EW [00:22:47] I
had a sense both in the early 80s and in the early 90s. I had a sense a couple
of years in advance of the big upheavals where they were most likely to come
from it and those two times did turn out to be right. Then for a long long time
I had no idea where another upheaval might come from. By the last few years
I've become convinced that it's most likely to be the it from qbit stuff of
which I have not been a pioneer now. But I was not one of the first to reach
the conclusion or a suspicion that I'm telling you right now. But anyway it's
the view I've come to.
GF [00:23:20] There's
a famous book about night thoughts of a quantum physics. are there night
thoughts of a string theorists is where you have a wonderful theory that's developing you know unable to test it. Does that ever bother you.
EW [00:23:31] Of
course it bothers us but we have to live with our existential condition. But
let's backtrack 34 years. So in the early 80s there were a lot of hints that
something important was happening in string theory but once Greene and Schwartz
discovered the anomaly cancellation and it became possible to make models of
elementary particle physics unified with gravity. From then I thought the
direction was clear. But some senior physicists rejected it completely on the
grounds that it would supposedly be untestable. Or even have cracked it would
be too hard to understand. My view at the time was that when we reached the
energies of the W, Z and the Higgs particle we'd get all kinds of fantastic new
clues.
EW [00:24:11] So.
I found it very very surprising that any colleagues would be so convinced that
you wouldn't be able to get important clues that would shed light on the
validity of a fundamental new theory that might in fact be valid. Now if you
analyze that 34 years later I'm tempted to say we were both a little bit wrong.
So the scale of clues that I thought would materialize from accelerators has
not come. In fact the most important clue possibly is that we've confirmed the
standard model without getting what we fully expected would come with him. And
as I told you earlier that might be a clue concerning the landscape. I think
the flaw in the thinking of the critics though is that while it's a shame that
the period of incredible turmoil and constant experiment and discovery that
existed until roughly when I started graduate school hasn't continued. I think
that the progress which has been made in physics since 1984 is much greater
than it would have been if the naysayers had been heeded and string theory
hadn't been done in that period.
GF [00:25:11] And it's had this bonus of benefiting mathematics as well.
EW [00:25:14] Mathematics
and by now even in other areas of physics because for example new ideas about
black hole of thermodynamics have influenced areas of condensed metaphysics* even in the study of quantum phase transitions, quantum chaos and really other
areas.
GF [00:25:31] Well
let's hope we all live to see some revolutionary triumph that was completely
unexpected that's the best one of all. Edward thank you very much indeed.
EW [00:25:38] Sure
thing.
GF [00:25:43] I’m
always struck by the precision with which Edward expresses himself and by his
avoidance of fuzzy philosophical talk. He's plainly fascinated by the closeness
of the relationship between fundamental physics and pure mathematics. He isn't
prepared to go further to say that their relationship is a fact of life. Yet no
one has done more to demonstrate that not only is mathematics unreasonably
effective in physics physics is unreasonably effective in mathematics.
GF [00:26:15] This
Witten said makes sense only if our modern theories are on the right track. One
last point. Amazingly Witten is sometimes underestimated by physicists who
characterize him as a mathematician, someone who has only a passing interest in
physics. This is quite wrong. When I talk with a great theoretician Steven
Weinberg he told me of his awe at Witten's physical intuition and elsewhere
said that Witten's got more mathematical muscles in his head than I like to
think about. You can find out more about Witten and his work in my book
"The universe speaks in numbers.
--
* Condensed matter physics. I am sure he says condensed matter physics. But really I think condensed metaphysics fits better.
The French translation of my book “Lost in Math” has now appeared under the title “Lost in Maths: Comment la beauté égare la physique”.
I declined the invitation to the Nobel Laureate meeting in Lindau because I was informed they would only cover my travel expenses if I agree in advance to write about their meeting for a 3rd party. (If you get pitches about the meeting, please ask the author for a COI.)
[I’ve meant for some while to try an automatic transcription
software, and Graham Farmelo’s interview of Edward Witten (mentioned by Peter Woit) seemed a
good occasion. I used an app called “Trint” which seems to work okay. But both
the software and I have trouble with Farmelo’s British accent and with Witten’s
mumbling. I have marked the places that I didn’t understand with [xxx]. Please
leave me a comment in case you can figure out what’s being said. Also notify me
of any blunders that I might have missed. Thanks!]