Kind: captions
Language: en
the following is a conversation with
kamran vaffa a theoretical physicist at
harvard
specializing in string theory he is the
winner
of the 2017 breakthrough prize in
fundamental physics
which is the most lucrative academic
prize in the world
quick mention of our sponsors headspace
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in the description to support this
podcast
as a side note let me say that string
theory is a theory of quantum gravity
that unifies quantum mechanics
and general relativity it says that
quarks electrons and
all other particles are made up of much
tinier strings of vibrating energy
they vibrate in 10 or more dimensions
depending on the flavor of the theory
different vibrating patterns result in
different particles
from its origins for a long time string
theory was seen
as too good not to be true but has
recently fallen out of favor in the
physics community
partly because over the past 40 years it
has not been able to make any novel
predictions
that could then be validated through
experiment
nevertheless to this day it remains one
of our best candidates
for a theory of everything or a theory
that unifies the laws of physics
let me mention that a similar story
happened with neural networks in the
field of artificial intelligence
where it fell out of favor after decades
of promise and research
but found success again in the past
decade
as part of the deep learning revolution
so i think it pays to keep an open mind
since we don't know which of the ideas
in physics may be brought back
decades later and be found to solve the
biggest mysteries
in theoretical physics string theory
still
has that promise this is the lex
friedman podcast and here is my
conversation
with kamran vaffa what is the difference
between
mathematics and physics well that's a
difficult question because in many ways
math and physics
are unified in many ways so to
distinguish them
is not an easy task i would say that
perhaps the goals
are of math and physics are different uh
math does not care to describe reality
physics does that's the major difference
but a lot of the
thoughts processes and so on which goes
to understanding the nature and reality
are the same things that mathematicians
do so in many ways they are similar
mathematicians care about deductive
reasoning and physicists or physics in
general we care less
about that we care more about
interconnection of ideas
about how ideas support each other or if
there's a puzzle con
discord between ideas that's more
interesting for us
and part of the reason is that we have
learned in physics that the ideas are
not sequential
and if we think that there's one idea
which is more important and we start
with there and go to the next idea and
next one and deduce things from that
like mathematicians do
we have learned that the like the third
or fourth thing we deduce from that
principle turns out later on to be the
actual principle
and from a different perspective
starting from there leads to new ideas
which the original one didn't lead to
and that's the beginning of a new
revolution in science
so this kind of thing we have seen again
and again in the history of science we
have learned
to not like deductive reasoning because
that gives us a
bad starting point to think that we
actually have the original thought
process
should be viewed as the primary thought
and all these are deductions
like the way mathematicians sometimes
does so in physics we are learning to be
skeptical of that way of thinking we
have to be a bit open to the possibility
that what we thought is a deduction
of a hypothesis actually the reason
that's true
is the opposite and so we reverse the
order and so this
this switching back and forth between
ideas makes us
more fluid about a deductive fashion of
course
it sometimes gives a wrong impression
like physicists don't care about rigor
they just
you know they just say random things you
know they are willing to to say things
that are not backed by you know
the logical reasoning that's not true at
all so
despite despite this fluidity in saying
which one is a primary
thought we are very careful about trying
to understand what we have really
understood
in terms of relationship between ideas
so that's
that's the that's an important
ingredient and in fact
solid math being behind physics is i
think
uh one of the attractive features of a
of a physical law so we look for
beautiful math underpinning can we dig
into that process
of starting from one place and then the
uh ending up at like the fourth step and
realizing
all along that the place you started at
was wrong so
is that happen when there's a
discrepancy between
what the math says and what the physical
world shows
is that how you then can go back and do
the
revolutionary idea for different
starting place altogether
perhaps i'll give an example to see see
how it goes and in fact the historical
example
is newton's work on classical mechanics
so so newton formulated the laws of
mechanics
uh you know the force f equals to m a
and
his other laws and they look very simple
elegant and so forth
later when we studied more examples
of of mechanics and other similar things
physicists came up with the idea that
the notion of potential is interesting
potential was an abstract idea which
kind of came you could
take its gradient and relate it to the
force so you don't really need
it apiary but it solved helps some
thoughts
and then later euler and lagrange
reformulated newtonian mechanics in a
totally different way
in the following fashion they said if
you take if you want to know where
particle at this point and at this time
how does it get to this point at the
later time
is the following you take all possible
paths connecting this particle from
going from
the initial point to the final point and
you compute
the action on what is an action action
is the integral over time
of the kinetic term of the particle
minus its potential
so you take this integral and each path
will give you some quantity and
the path it actually takes the physical
path
is the one which minimizes this integral
or this action
now this sounded like a backwards step
from newton's newton's
form that seems very simple f equals to
m a and you can write f is minus the
gradient of the potential
so why would anybody start formatting
such a simple thing in terms of this
complicated
looking principle you have to study the
space of
all paths and all things and find the
minimum and then you get the same
equation so what's the point
so euler and lagrange's formulation of
newton which is a
which was kind of recasting in this
language
is just a consequence of newton's law f
equals m it gives you the same
fact that this path is a minimum action
now
what we learned later last century was
that
when we deal with quantum mechanics
newton's law is only
an average correct and
the particle going from one to the other
doesn't take
exactly one path it takes all the paths
yes with the with the amplitude which is
proportional to the exponential of the
action times an imaginary number
i and so this fact turned out to be the
reformulation of quantum mechanics we
should start there as the basis
of the new law which is quantum
mechanics and newton is only an
approximation on the average correct
when we say amplitude you mean
probability but yes the amplitude means
if you com sum up all these paths with
exponential i times the action
if you sum this up you get the number
complex number
you square the norm of this complex
number gives you a probability to go
from one to the other
is there ways in which mathematics can
lead us astray
when we use it as a tool to understand
the physical world
yes i would say that mathematics can
lead us astray as much as
all physical ideas can lead us so
sure if you get stuck in some something
then you can easily fool yourself that
just like
the thought process we have to free
ourselves of that sometimes math does
that rule like say oh this is such a
beautiful math i definitely want to use
it somewhere and so
you just get carried away and you just
get maybe carried too far away so that
is certainly true but i wouldn't say
it's more dangerous than all physical
ideas to me
new math ideas uh is as much potential
to lead us astray as all physical ideas
which could be
long-held principles of physics so i'm
just saying that we should keep an open
uh mind about the role the math plays
not to be antagonistic towards it
and not to over overwhelming it we
should just be open to possibilities
what about looking at a particular
characteristics of both physical ideas
and mathematical ideas which is beauty
you think beauty leads us astray meaning
um
and and you offline showed me a a really
nice puzzle that illustrates this
this idea a little bit now maybe you can
speak to that or another
example where uh beauty
makes it tempting for us to assume that
the the law and the theory
we found is actually one that perfectly
describes reality
i think that beauty does not lead us
astray
because i feel that beauty is a
requirement
for principles of physics so beauty is a
fundamental in the universe i think
beauty is fundamental
at least that's the way many of us view
it it's not emergent
it's not immersion i think i think hardy
is the mathematician who said that
there's no
permanent place for ugly mathematics and
so i think the same is true in physics
that if we find a principle which looks
ugly
we're not going to be that's not the end
stage so therefore beauty is going to
lead us somewhere now it doesn't mean
beauty is enough
it doesn't mean if you just have beauty
if i just look at something is beautiful
then i'm fine no that's not the case
beauty is certainly a criteria that
every
good physical theory should pass that's
at least the view we have
why do we have this view that's a good
question
it is a partly uh you could say based on
experi
experience of science over centuries
partly is
a philosophical view of what what what
reality is or should be
and uh in principle you know it could
have been ugly
and we might have had to deal with it
but we have gotten maybe
uh confident through examples after
examples in the history of science to
look for beauty
and our sense of beauty seems to
incorporate a lot of things that are
essential for us to solve some difficult
problems like symmetry we find symmetry
beautiful and the breaking of symmetry
beautiful
somehow symmetry is a is a fundamental
part of how we conceive of beauty
at all layers of reality which is
interesting like
uh in in both the visual space like when
we look at art
we look at each other as human beings
the way we look at creatures in the
biological space
the way we look at chemistry and then
into the physics world as
as the work you do it's kind of
interesting it makes you wonder like
which one is the chicken or the egg is
symmetry the the chicken and our
conception of beauty the egg
or the other way around or somehow
the fact that every the symmetry is is
part of reality
is it somehow creates the brain that
then is able to perceive it
or maybe that's this is just because we
maybe it's so obvious
it's almost trivial that symmetry of
course will be part of every kind of
universe that's possible
uh and then our any kind of organism
that's able to observe that universe is
going to appreciate
uh symmetry well these are good
questions we don't have a deeper
understanding of why we get attracted to
symmetry
why do laws of nature seem to have
symmetries
underlying them and the reasoning or the
examples of whether
if it wasn't symmetric we would have
understood it or not we could have said
that yeah if there were
you know things which didn't look that
great we could understand them for
example we know
that symmetries get broken and we have
appreciated nature
in the broken symmetry phase as well the
word we live in
has many things which do not look
symmetric but even those
have underlying symmetry when you look
at it more deeply so
we have gotten maybe spoiled perhaps by
by the appearance of symmetry all over
the place
and we look for it and i think this is
this is perhaps related to the sense of
aesthetics that scientists have
and we don't usually talk about it among
scientists
in fact it's kind of a philosophical
view of
why do we look for simplicity or beauty
or so forth
and uh i think in a sense scientists are
ma
a lot like philosophers sometimes i
think especially modern science seems to
shine away
sean's philosophers and philosophical
views and i think
at their peril i think i think in my
view science
owes a lot to philosophy and
in my view many scientists in fact
probably all good scientists are
perhaps amateur philosophers they may
not state that they are philosophers or
they they may not
like to be labeled philosophers but in
many ways what they do is like what
is philosophical takes of things
looking for simplicity or symmetry is an
example of that in my opinion
or seeing patterns you see for example
another example of the
symmetry is like how you come up with
new ideas in science you see for example
an
idea a is connected with an idea b
okay so you you study this connection
very deeply
and then you find the cousin of an idea
a let me call it a prime
and then you immediately look for b
prime if a
is like b and if there's an a prime then
you look for b prime why well
it completes the picture why well it's
philosophically appealing to have more
balance in terms of that
and then you look for b prime and behold
you find this other phenomena which is a
physical phenomenon which you call b
prime so this kind of thinking motivates
asking questions and looking for things
and it has guided scientists i think
through many centuries and i think it
continues to do so today
and i think if you look at the long arc
of history i suspect that the things
that will be remembered
is the philosophical flavor of the ideas
of physics and chemistry and computer
science and mathematics
like i think the actual details
will be shown to be incomplete or maybe
wrong
but the philosophical intuitions will
carry through much longer
there's a sense in which if it's true
that we haven't figured out
most of how things work currently
that uh it'll all be shown as wrong and
silly it'd
almost be a historical artifact but the
the human spirit whatever like the the
longing to understand
the the way we perceive the world the
way we conceive of it
of our place in the world those those
ideas will carry on
i completely agree in fact i believe
that uh almost
well i believe that none of the
principles or laws of physics we know
today are exactly correct
all of them are approximations to
something they are better than the
previous versions that we had but
none of them are exactly correct and
none of them are going to stand forever
so i agree that that's the process we
are heading we are improving
and yes indeed the thought process and
that philosophical take
is common so when we look at you know
older uh
scientists or maybe even all the way
back to greek philosophers and the
things that the way they thought and so
on
almost everything they said about you
know nature was incorrect
but the way they thought about it and
many things that they were thinking
is still valid today for example they
thought about symmetry breaking
they were trying to explain the
following they were this is a beautiful
example i think they had figured out
that the earth is round
and they said okay earth is around they
have you know they have seen the
length of the shadow of this meter stick
and they have seen that if you go from
the equator upwards north
they find that depending on how far away
you are the length of the shadow changes
and from that they have either they had
even measured the radius of the earth
to good accuracy that's brilliant by the
way the fact that they did that
very brilliant very brilliant so these
greek philosophers were very smart and
so
they had taken it to the next step they
asked okay so the earth is round
why doesn't it move they thought it
doesn't move they they were looking
around nothing seemed to move so
so they said okay we have to have a good
explanation it wasn't enough for them to
you know be there so they really want to
deeply understand that fact and they
come up with a symmetry argument
and the symmetry argument was oh if the
earth
is a spherical it must be at the center
of the universe for sure so they said
the earth is at the center of the
universe it makes sense
and they said you know if the earth is
going to move which direction does it
pick
any direction it picks it breaks that
spherical symmetry because you have to
pick a direction
and that's not good because it's not
symmetrical anymore so therefore
the earth decides to sit put because it
would break the symmetry so
so they had the incorrect science they
thought earth doesn't move and they but
they had this beautiful idea that
symmetry might explain it
but they were even smarter than that
aristotle didn't agree with this
argument
he said why do you think symmetry
prevents it from moving because the
preferred position
not so he gave an example he said
suppose
you are a person and you put we put you
at the center of a circle
and we spread food around you on a
circle around you
loaves of bread let's say and we say
okay
stay at the center of the circle forever
are you going to do that just because of
the symmetric point
no you're going to get hungry you're
going to move towards one of those
levels of bread
despite the fact that it breaks the
symmetry so from this way he tried to
argue
being at this symmetric point may not be
the preferred thing to do
and this idea of spontaneous mystery
breaking is something we just
used today to describe many physical
phenomena so spontaneous symmetry
breaking
is the feature that we now use but this
idea was there
thousands of years ago but applied
incorrectly to the physical world but
now we are using it so these ideas are
coming back in different forms
so i agree very much that the thought
process is more important and these
ideas are more interesting than the
actual applications that
people may find today did they use the
language of symmetry and the symmetry
breaking and spontaneous symmetry that's
really interesting yes
because like i could see a conception of
the universe that kind of tends towards
perfect symmetry and is stuck there like
they
not stuck there but achieves that
optimal and stays there
the idea that you would spontaneously
break out of symmetry
like have these perturbations like jump
out of symmetry
and back that's not that's a really
difficult idea to uh
to load into your head like where where
does that come from
and then and then the idea that you may
not be at the center of the universe
right that is a really tough idea right
so symmetry sometimes is an explanation
of being at the symmetric point is
sometimes a simple explanation of many
things like
if you have a bowl a
circular ball then the bottom of it is
the lowest point so if you put a you
know pebble or something it will slide
down and go there at the bottom and
stays there
at the symmetric point because the
preferred point the lowest energy point
but if that same symmetric circular ball
that you had had a
bump on the on the bottom the bottom
might not be at the center
it might be on a circle on the table
yeah in which case the pebble would not
end up at the center would be the lower
energy point
symmetrical but it breaks the symmetry
once it picks a point on that circle
so so we can't have symmetry reasoning
for where things end up
or symmetry breakings like this example
would suggest
we talked about beauty i find geometry
to be beautiful
uh you have uh a few examples
that are geometric in nature in your
book
how can geometry in ancient times or
today be used to understand
reality and maybe how do you think about
geometry as a distinct tool
in mathematics and physics yes geometry
is my favorite part of math as well and
greeks were enamored by geometry they
tried to describe
physical reality using geometry and
principles of geometry and symmetry
platonic solids the five solids they had
discovered had these beautiful solids
they thought it must be good for some
reality there must be explaining
something they attached you know
one to air one to fire and so forth they
try to give
physical reality to symmetric objects
these symmetric objects are symmetries
of rotation
and discrete symmetry groups we call
today of rotation group in three
dimensions
now we know now we kind of laugh at the
way they were trying to connect that
symmetry to you know the laws of the the
realities of
of physics but actually it turns out
in modern days we use symmetries in not
too far away
exactly in these kind of thoughts
processes in the following way
in the co in the context of string
theory which is this
the field i study we have these extra
dimensions
and these extra dimensions are compact
tiny spaces typically but they have
different shapes and sizes
we have learned that if you if these
extra shapes and sizes have symmetries
which are related to the same rotation
symmetries that the greek we're talking
about
if they enjoy those discrete symmetries
and if you
if you take that symmetry and quotient
the space by that in other words
identify points under these symmetries
you get properties of that space at the
singular points
which force emanates from them what
forces
forces like the ones we have seen in
nature today like electric forces
like strong forces like weak forces so
these same principles
that was were driving them to connect
geometry and symmetries
to nature is driving today's
physics now much more you know modern
ideas but nevertheless the symmetries
connecting
geometry to physics in fact often we
sometimes we have we ask the following
questions suppose i want to get this
particular
you know physical reality i want to have
this particles with these forces and so
on what do i do
it turns out that you can geometrically
design the space
to give you that you say oh i put the
sphere here i would do this i will
shrink them
so if you have two spheres touching each
other and shrinking through
to zero size that gives you strong
forces
if you have one of them it gives you the
weak forces if you have this you get
that and if you want to unify forces do
the other thing
so these geometrical translation of
physics is one of my favorite things
that we have discovered in modern
physics in the context of strength
theory
the sad thing is when you go into
multiple dimensions and
we'll talk about it is we start to lose
our
capacity to uh visually intuit
the world we're discussing and then we
go into the realm of mathematics and
we'll lose that
unfortunately our brains are such that
we're limited but
before we go into that mysterious
beautiful world
let's take a small step back and you
also in your book have this
kind of through the space of puzzles
through the space of ideas have a
brief history of physics
of physical ideas now we we talked about
newtonian mechanics
uh leading all through different
lagrangian hamiltonian mechanics
can you describe some of the key ideas
in the history of physics
maybe lingering on each from
electromagnetism to relativity to
quantum mechanics and to today as we'll
talk about with quantum gravity and
strength theory sure so um i mentioned
the classical mechanics and the euler
lagrangian formulation
one of the next important milestones for
physics were the discoveries of laws of
their christian magnetism
so maxwell put put the discoveries all
together in the context of what we call
the maxwell's equations
and he noticed that when he put these
discoveries that you know faradays and
others had made
about electric and magnetic phenomena
the in terms of mathematical equations
it didn't quite work
there was a mathematical inconsistency
now
uh you know one could have had two
attitudes won't say okay who cares about
math i'm doing nature you know electric
force magnetic force
math i don't care about but it bothered
him it was inconsistent the equations
you were writing the two equations he
had written down did not agree with each
other
and this bothered him but he figured out
you know if you add this jiggle this
equation by adding one little term there
it works
at least it's consistent what is the
motivation for that term
he said i don't know have we seen it in
experiments no
why did you add it well because of
mathematical consistency so he said
okay math forced him to
do this term he added this term which we
now today call the maxwell term
and once he added that term his
equations were nice you know
differential equations mathematically
consistent beautiful
but he also found the new physical
phenomena he found that because of that
term
he could now get electric and magnetic
waves
moving through space
at a speed that he could calculate so he
calculated the speed of the wave
and low and behold he found it's the
same as the speed of light
which puzzled him because he didn't
think light had anything to do with
electricity and magnetism
but then he was courageous enough to say
well maybe light is nothing but these
electric and magnetic fields moving
around
and he didn't he wasn't alive to see the
verification of that prediction and
indeed was true so this mathematical
inconsistency which which we could say
you know this mathematical
beauty drove him to this physical
very important connection between light
and electric magnetic phenomena which
was later confirmed
so then physics progresses and it comes
to einstein
einstein looks at maxwell's equation
this is beautiful these are a nice
equation except
we get one speed light who measures this
light
speed and he asks the question are you
are you moving are you not moving if you
move the speed of light changes but
maxwell's equation has no hint of
different speeds of light it doesn't say
oh
only if you're not moving you get the
speed it's just you always get this
speed so
einstein was very puzzled and he he was
daring enough to say well you know maybe
everybody gets the same speed for light
yeah and that motivated his theory of
special relativity
and this is an interesting example
because the idea was motivated from
physics from
maxwell's equations from the fact that
people tried to
try to measure the properties of ether
which was supposed to be the medium in
which the light travels through
and the idea was that only in that in
that medium the speed the speed of
if you're at rest with respect to the
ether this speed the speed of light then
if you're moving the speed changes
and people did not discover it
michaelson and morley's experiments
showed there is no ether
so uh then einstein was courageous
enough to say you know light is
the same speed for everybody regardless
of whether you're moving or not
and the interesting thing is about
special theory of relativity is that
the under the math underpinning it is
very simple
it's linear algebra nothing terribly
deep
you can teach it at a high school level
if not earlier
okay is does that mean einstein's
especially relativity is boring
not at all so this is an example where
simple math
you know linear algebra leads to deep
physics
einstein's theory of special relativity
motivated by this inconsistency at
maxwell
equation would suggest for the speed of
light depending on who observes it
what's the most daring idea there that
that the the speed of light could be the
same everywhere that's the basic that's
the guts of it that's the core of
einstein's theory that statement
underlies the whole thing speed of light
is the same for everybody is hard to
swallow
and it doesn't sound right it sounds
completely wrong on the face of it
and it was it took einstein to make to
make this the daring statement
it would be it would be laughing in some
sense how could possibly how could
anybody make this
possibly ridiculous claim and it turned
out to be true how does that make you
feel because it
it still sounds ridiculous it sounds
ridiculous until you learn that
our intuition is at fault about the way
we conceive of space on time
the way we think about space on time is
wrong because we think about the nature
of time as absolute
and part of it is because we live in a
situation where we don't go with very
high speeds that our speeds are small
compared to the speed of light
and therefore the phenomena we we
observe does not distinguish the
relativity of time
the time also depends on who measures
that there's no absolute time
when you say it's noon today now it
depends on who's measuring it and it
not everybody would agree with that
statement and to see that
you will have to have fast observer
moving you know
speeds close to speed of light so so
this shows that our intuition is at
fault
and a lot of the discoveries in physics
precisely is getting rid of the wrong
old intuition
and it is funny because we get rid of it
but it always lingers in us in some form
like
even when i'm describing it i feel like
a little bit like isn't it you know
funny
as you're just feeling the same way it
is yes it is but we kind of
replace it by an intuition
and actually there's a very beautiful
example of this how physicist do this
try to replace their intuition and i
think this is one of my favorite
examples about how physicists
develop intuition it goes to the work of
galileo
so you know again uh let's go back to
greek philosophers or maybe aristotle in
this case
now again let's let's make a criticism
he thought that objects
the heavier objects fall faster than the
lighter objects makes sense
it kind of makes sense and you know
people say about feather and swan but
that's because of the air resistant but
you might think like if you have a heavy
stone and a light pebble the heavy one
will fall first if you don't
you know do any experiments that's the
first gut reaction i would say everybody
would say that's the natural thing
galileo did not believe this and he kind
of
did the experiment famously it said he
went on the top of piso tower and he
dropped you know these heavy and light
stones and they fell at the same time
when they he dropped it at the same time
from the same height okay good so he
said i'm done you know i've showed that
the
heavy and lighter objects fought the
same time i did the experiment
scientists at that time did not accept
it
why was that because at that time
science was not just
experimental the experiment was not
enough
they didn't think that they have to sort
their hands in doing experiments to get
to the reality they said why is it the
case
why so galileo had to come up with an
explanation of why heavier and lighter
objects fought the same ray
this is the way he convinced them using
symmetry
he said suppose you have three bricks
the same
shape the same size
same as everything and we hold these
three bricks at the same height
and drop them which one will fall to the
ground
first everybody said of course we know
that symmetry
tells you know they're all the same
shape same size same height
of course they fall at the same time
yeah we know that next next
it's trivial he says okay what if we
move these bricks around with the same
height does it change the time they hit
the ground
they said if it's the same height again
by the symmetry principle because the
height translation horizontal
translation the symmetry
no it doesn't matter they all fall the
same rate good doesn't matter how close
i bring them together no it doesn't
okay suppose i make the two bricks touch
and then let them go do they fall out
the same raid
yes they do but they said well the two
bricks that touch
are twice more mass than this other
brick and you just agreed that they
fought the same rate
they say yeah yeah we just agreed that's
right that's strange yes
so he deconfused them by the symmetry
design so this way
of repackaging some intuition a
different intuition
when the intuitions clash then you then
you decide on the you replace the
intuition
that's brilliant i i in some of these
dif
more difficult physical ideas
physics ideas in the 20th century in the
21st century it starts becoming more and
more difficult
than replace the intuition you know what
does the world look like for an object
traveling close to the speed of light
you start to think about like the edges
of supermassive black holes
and you start to think like what what's
that look like
or uh i've been re into gravitational
waves recently
it's like when the fabric of space-time
is being morphed
by gravity like what's that actually
feel like
if i'm writing a gravitational wave
what's that feel like
i mean i think some of those are more
sort of hippie
not useful uh intuitions to have
but if you're an actual physicist or
whatever the particular discipline is i
wonder if it's possible to meditate
to sort of uh escape through thinking
prolonged thinking and meditation on a
war
on a world like live in a visualized
world that's not like our own
in order to understand a phenomenon
deeply so like replace the intuition
like through rigorous meditation on the
idea
in order to conceive of it i mean if we
talk about multiple dimensions
i wonder if there's a way to escape with
the three-dimensional world
in our mind in order to then start to
reason about it
it's uh the more i talk to topologists
the more they seem to not operate at all
at all in the visual space
they really trust the mathematics like
which is really annoying to me because
topology
and differential geometry feels like it
has a lot of potential for beautiful
pictures
yes i think they do actually i would not
be able to
uh do my my research if i don't have an
intuitive feel about geometry
and i i will get to it as you mentioned
late uh before that
how for example in strength there you
deal with these extra dimensions and
i'll be very happy
to describe how we do it because with
that intuition we will not get anywhere
and i
i don't think you can just rely on
formalism i don't
i don't think any physicist just relies
on formalism that's not physics that's
not understanding
so we have to intuit it and that's
crucial and this there are steps of
doing it and we learned it might not be
trivial
but we learned how to do it similar to
this galileo picture i just told you
you have to build these gradually but
about to connect the bricks
literally yeah so yeah so then uh so
going back to your question about this
the path of the history of the science
so i was
saying about the existing magnesium and
the special relativity where simple idea
led to special relativity but then he
went further
thinking about acceleration in the
context of relativity and he came up
with general relativity
where he talked about you know the
fabric of space time being curved and so
forth and
matter affecting the the curvature of
the space on time so
so this gradually became a
connection between geometry and physics
namely he replaced newton's
you know gravitational force with
a very geometrical beautiful picture
it's much more elegant than newton's but
much more complicated mathematically
so so when we say it's simpler we mean
in some form it's simpler but not in
pragmatic terms of equation solving the
equations are
much harder to solve in einstein's
theory and in fact so much
so much harder that einstein himself
couldn't solve many of his many of the
cases he thought for example you
couldn't solve the equation for a
spherical symmetric matter uh like like
if you had this symmetric sun
he didn't think you can actually write
this solve his equation for that and
a year after he he said that it was
solved by by short child so it was
it was that hard that he didn't think
it's going to be that easy so yeah the
formalism is hard
but the contrast between the special
relativity and general relativity is
very interesting because one of them has
almost trivial math
and the other one has super complicated
math
both are physically amazingly important
and so so we have learned that you know
the physics
may or may not require complicated math
we should not shy from using complicated
math like einstein did
nobody einstein wouldn't say i'm not
going to touch this math because it's
too much you know
tensors or you know curvature and i
don't like four-dimensional space-time
because i can't see four-dimension
he wasn't doing that he was willing to
abstract from that because
physics drove him in that direction but
his motivation was physics physics
pushed him
just like newton pushed to develop
calculus because physics pushed him that
he didn't have the tools so he had to
develop the tools
to answer his physics questions so his
motivation was physics again
so to me those are examples which showed
that math and physics have this
symbiotic reality relationship which
which kind of reinforce each other here
i'm using i'm giving you examples
of both of them namely newton's work led
to development of mathematics
calculus and in the case of einstein he
didn't develop
the premium geometry just use them so so
it goes both ways
and in the context of modern physics we
see that again and again it goes both
ways
let me ask a ridiculous question you
know you talk about your favorite soccer
player at a bar
i'll ask the same question about
einstein's ideas which is
uh which one do you think is the biggest
leap of genius
is it the uh e equals mc squared
is the brownian motion is it special
relativity is the general relativity
which which of of the famous set of
papers he's written in
1905 and in general his work was the
biggest leap of genius
in my opinion special relativity the
idea that speed of light is the same
for everybody is the beginning of
everything he did at the beginning is
this the beginning it's just once you
embrace
that weirdness the all the weirdness i
would say that's
that's it even though he says the most
beautiful moment for him yes he says
that is when he realized that if you
fall in an elevator you don't know if
you're falling or whether you're
in the whether you're in the falling
elevator or whether you're next to the
earth gravitational field
that that to him was his aha moment
which inertial mass and gravitational
mass being identical
geometrically and so forth as part of
the theory not because of
uh you know some some funny coincidence
uh that's for him but i feel from
outside at least it feels like
the speed of light being the same is the
is the really
aha moment the general relativity to you
is not
like the conception of space time in a
sense the conception of space time
already was
part of the speciality when you talk
about length contraction
so general relativity takes that to the
next step but beginning of it was
already
space link contracts time dilays so once
you talk about those then yeah you can
dilate more or less different places
than it's curvature
so you don't have a choice so it's kind
of started just with that same simple
thought
speed of light is the same for all where
does uh
quantum mechanics come into view exactly
so this is the next step so einstein's
you know
uh develops general activity and is
beginning to develop the foundation of
quantum mechanics at the same time the
photoelectric effects on others
and um so so quantum mechanics overtakes
in fact einstein in many ways because he
doesn't like the
probabilistic interpretation of quantum
mechanics and the formulas that's
emerging
but physicists march on and try to for
example
combine einstein's theory of relativity
with quantum mechanics so dirac takes
special relativity
tries to see how is it compatible with
quantum mechanics
can we pause and briefly say what is
quantum mechanics oh yes sure so quantum
mechanics
so i i discussed briefly when i talked
about the connection between newtonian
mechanics
and the euler lagrangian formulation of
of the newtonian mechanics and
interpretation of this
audio dot grunge formalism in terms of
the paths that the particle take
so when we say a particle goes from here
to here
we usually think it classically it
follows a specific trajectory
but actually in quantum mechanics it
falls
follows every trajectory with different
probabilities
and so there's this fuzziness now
most probable it's the path that you
actually see
and the deviation from that is very very
unlikely and probabilistically very
minuscule
so in everyday experiments we don't see
anything deviated from what we expect
but quantum mechanics tells us that the
things are more fuzzy things are
are not as precise as the line you draw
things are a bit like cloud so if you go
to microscopic
uh scales like atomic scales and lower
these phenomena become more pronounced
you can see it much better the electron
is is not at the point but
the clouds spread out around the nucleus
and so this fuzziness this probabilistic
aspect
of reality is what quantum mechanics
describes can i briefly pause on that on
that idea
do you think this is quantum mechanics
is just a really damn good approximation
a tool for predicting reality or does it
actually describe reality
do you think reality is fuzzy at that
level well i think that
reality is fuzzy at that level but i
don't think quantum mechanics is
necessarily the end of the story
right so um so quantum mechanics is
certainly an improvement over classical
physics that much we know by experiments
and so forth
whether i'm happy with quantum mechanics
whether i view quantum mechanics
for example the the thought the
measurement uh
description of quantum mechanics am i
happy with it am i thinking that's the
end stage or not
i don't i don't think we're at the end
of that story and many physicists
may or may not view this way some do
some don't
but i think that it's the best we have
right now that's for sure
it's the best approximation for reality
we know today and so far we don't know
what it is the next thing that
improves it or replaces it and so on so
but as i mentioned before i don't
believe
any of the laws of physics we know today
are friends
that's exactly correct it doesn't bother
me yes i'm not like dogmatic say i have
figured out this is the law of nature
i know everything no no that's that's
the the beauty about science is that we
are not dogmatic
and we are we are willing to in fact we
are encouraged to
be skeptical of what we ourselves do so
you were talking about dirac
yes i was talking about direct right so
direct was trying to now combine this
schrodinger's equations which which was
described in the context of you know
trying to
talk about how these probabilistic waves
of electrons move
for the atom which was good for for
speeds which were not too close to the
speed of light
to what happens when you get to the near
the speed of light
so then you need relativity so then
dirac tried to combine einstein's
relativity with quantum mechanics
so he tried to combine them and he wrote
this beautiful equation
the dirac equation which roughly
speaking take the square root of of the
einstein's equation in order to connect
it to schrodinger's time evolution
operator which is
first order in time derivative to get
rid of the
the naive thing that einstein's equation
would have given which is second order
so you have to take a square root
now square root usually has a plus or
minus sign when you take it
and when he did this he originally
didn't notice this
didn't pay attention to this plus or
minus sign but later physics pointed out
to direct says look there's also this
minus sign and if you use this minus
sign you get negative energy
in fact it was very very annoying that
you know somebody else tells you this
obvious mistake you make paulie
famous physicist told direct this is
nonsense you're going to get negative
energy with your equation with negative
energy without any bottom you can go all
the way down to negative
infinite energy so it doesn't make any
sense direct thought about it and then
he remembered paulie's exclusion
principle before just before him paulie
had said you know
there's this principle called the
exclusion principle that you know two or
two electrons cannot be on the same
orbit
and so direct said okay you know what
all these negative energy states
are filled orbits occupied
so according to you uh
mr paulie there's no place to go so
therefore they only have to go positive
sounded like a big cheat and then paulie
said oh you know what
we can change orbits from one orbit to
another what if i take one of these
negative energy orbits and put it up
there
then it seems to be a new particle which
has opposite
properties to the electron has positive
energy but it has positive charge
what is that like
the iraq was a bit worried he said maybe
that's proton because proton has plus
charge he wasn't sure but then he said
oh maybe it's proton
but then they said no no no it has the
same mass as the electron cannot be
proton because proton is heavier
the iraq was stuck he says well then
maybe another part we haven't seen
by that time dirac himself was getting a
little bit
worried about his own equation and his
own crazy interpretation
yes until a few years later anderson in
photographic cosmic uh
in the photographic place that he had
gotten from this cosmic rays
he discovered a particle which goes in
the opposite direction that the electron
goes when there's a magnetic field
and with the same mass exactly like what
the iraq had predicted
and this was what we call now positron
and in fact
beginning with the work of dirac we know
that every particle has an anti-particle
and so this idea that there's an
anti-particle came from the simple math
you know there's a plus and a minus
from the directs quote-unquote mistake
so again trying to combine ideas
sometimes the math is smarter than the
person who uses it to
apply it and you try to resist it and
then you you kind of confront it by
criticism which is the way it should be
so physicist comes and said no no that's
wrong and you correct it and so on so
that
is the development of the idea there's
particle there's antiparticle and so on
so this is the beginning of
development of quantum mechanics and the
connection with relativity but the thing
was more challenging because
we had to also describe how electric and
magnetic fields
work with quantum mechanics this was
much more complicated because it's not
just one point
electric and magnetic fields were
everywhere so you had to talk about
fluctuating and a fuzziness of
electrical field and magnetic fields
everywhere
and the math for that was was was very
difficult to deal with
and this led to a subject called quantum
field theory fields
like electric and magnetic field to be
quantum had to be described
also in a wavy way feinman in particular
was one of the pioneers along with
schwinger's and others
to try to come up with the formalism to
deal with fields
like electric and magnetic fields
interacting with electrons
in a consistent quantum fashion and they
just developed this beautiful theory
quantum electrodynamics from that and
later on that same formalism quantum
field theory led to the
discovery of other forces and other
particles all consistent with the idea
of quantum
mechanics so that was how physics
progressed
and so basically we learned that all
particles and all the forces
are are in some sense related to
particle exchanges
and so for example electromagnetic
forces are
are mediated by a particle we call
photon and
uh and so forth and the same for other
forces that they discovered strong
forces and the weak forces so
so we got the sense of what quantum
field theory is is that a big leap
of uh of an idea that uh
particles are fluctuations in the field
like the idea that everything is a field
is the old einstein
light is a wave both a particle and a
wave kind of idea is that is that a huge
leap in our understanding of conceiving
the universe's fields
i would say so i would say that on
viewing the particles
this duality that bore mentioned between
particles and waves that waves can
behave sometimes like particles
sometimes like waves
is one of the biggest leaps of
imagination
that quantum mechanics made physics do
so i agree that that is
quite remarkable is duality fundamental
to
to the universe or is it just because we
don't understand it fully like we'll
eventually collapse into a clean
explanation that doesn't require duality
like
th that that a phenomenon could be two
things at once and both
to be true so that seems weird so in
fact i
i i was going to get to that when we get
to string theory but maybe i can comment
on that now
duality turns out to be running the show
today is the whole thing
that we are doing in strength duality is
the name of the game
so it's the most beautiful subject i
want to talk about let's let's talk
about it in the context
let's talk about the other strengths so
we uh do want to take a next step into
because we mentioned general relativity
we mentioned quantum mechanics
is there something to be said about
quantum gravity yes that's exactly the
right point to talk about
so namely we have talked about quantum
fields and i talked about electric
forces
photon being the particle carrying those
forces so for gravity
quantizing gravitational field which is
this curvature of space time according
to einstein
you get another particle called graviton
so what about gravitons should be there
no problem so then you start computing
it
what do i mean by computing it well you
compute scattering of one graviton off
another graviton maybe with graviton
with an electron and so on see what you
get
feynman had already mastered the this
quantum electrodynamics you said no
problem let me do it
even though these are such weak forces
the gravity is very weak so therefore to
see them
these quantum effects of gravitational
waves is was impossible
it's even impossible today so feynman
just did it for fun
he usually you know had this mindset
that i want to do something which i will
see an experiment but this one let's
just see what it does
and he was surprised because the same
techniques he was using for doing
the same calculations quantum
electrodynamics when applied to gravity
failed the formula seemed to make