Kind: captions
Language: en
the following is a conversation with
Sean Carroll part 2 the second time
we've spoken on the podcast you can get
the link to the first time in the
description this time we focus on
quantum mechanics and the many-worlds
interpretation that he details elegantly
in his new book titled something deeply
hidden I own and enjoy both the ebook
and audiobook versions of it listening
to Sean read about entanglement
complementarity and the emergence of
space-time reminds me of bob ross
teaching the world how to paint and his
own television show
if you don't know who Bob Ross is you're
truly missing out look him up he'll make
you fall in love with painting Sean
Carroll is the Bob Ross of theoretical
physics he's the author of several
popular books a host of a great podcast
called mindscape and is a theoretical
physicist at Caltech and the Santa Fe
Institute specializing in quantum
mechanics arrow of time cosmology and
gravitation this is the artificial
intelligence podcast if you enjoy it
subscribe on YouTube give it five stars
of iTunes
supported on patreon or simply connect
with me on Twitter Alex Friedman spelled
Fri D ma N and now here's my
conversation with Sean Carroll
Isaac Newton developed what we now call
classical mechanics that you describe
very nicely in your new book because you
do with a lot of basic concepts in
physics so was classical mechanics I can
throw a rock and can predict the
trajectory of that rocks flight but if
we could put ourselves back into
Newton's time his theories work to
predict things but as I understand he
himself thought that they were their
interpretations of those predictions
were absurd perhaps he just said it for
religious reasons and so on but in
particular sort of a world of
interaction without contact so action at
a distance
it didn't make sense to them in a sort
of a human interpretation level does it
make sense to you that things can affect
other things at a distance it does but
you know that so that was one of
Newton's worries you're actually right
in a slightly different way about the
religious worries he he was smart enough
this is off the topic with still
fascinating Newton almost invented chaos
theory as soon as he invented classical
mechanics he realized that in the solar
system so he was able to explain how
planets move around the Sun but
typically you would describe the orbit
of the earth
ignoring the effects of Jupiter and
Saturn and so forth just doing the earth
and the Sun he he kind of knew even
though he couldn't do the math that if
you included the effects of Jupiter and
Saturn the other planets the solar
system would be unstable like the orbits
of the planets would get out of whack so
he thought that God would intervene
occasionally to sort of move the planets
back into orbit which is how you could
only way you could explain how they were
there presumably forever but the worries
about classical mechanics were a little
bit different they worried about gravity
in particularly wasn't it worried about
classical mechanics worried about
gravity how in the world does the earth
know that there's something called the
Sun 93 million miles away
that is exerting gravitational force on
it and he said he literally said you
know I leave that for future generations
to think about because I don't know what
the answer is and in fact the people
under emphasize this but future
generations figured it out Pierre Simone
Laplace in circa 1800 showed that you
could rewrite Newtonian
gravity as a field theory so instead of
just talking about the force due to
gravity you can talk about the
gravitational field or the gravitational
potential field and then there's no
action at a distance it's exactly the
same theory empirically it makes exactly
the same predictions but what's
happening is instead of the Sun just
reaching out across the void there is a
gravitational field in between the Sun
and the earth that obeys an equation
Laplace's equation cleverly enough and
that tells us exactly what the field
does so even in Newtonian gravity you
don't need action at a distance now what
many people say is that Einstein solved
this problem because he invented general
relativity and general relativity
there's certainly a field in between the
Earth and the Sun but also there's the
speed of light as a limit in Laplace's
theory which was exactly Newton's theory
just in a different mathematical
language there could still be
instantaneous action across the universe
whereas in general relativity if you
shake something here its gravitational
impulse radiates out at the speed of
light and we call that a gravitational
wave and we can detect those so but I I
really it rubs me the wrong way to think
that we should presume the answer should
look one way or the other like if it
turned out that there was action at a
distance in physics and that was the
best way to describe things that I would
do it that way it's actually a very deep
question because when we don't know what
the right laws of physics are when we're
guessing at them when we're
hypothesizing at what they might be
we are often guided by our intuitions
about what they should be I mean
Einstein famously was very guided by his
intuitions and he did not like the idea
of action at a distance we don't know
whether he was right or not it depends
on your interpretation of quantum
mechanics and it depends on even how you
talk about quantum mechanics within any
one interpretation if you see every
forces of field or any other
interpretation of action at a distance
he's just stepping back to sort of
caveman thinking like do you really can
you really sort of understand what it
means for a force to be a field as
everywhere so if you look at gravity
like what do you think about I think so
it's just something that you've been can
and by society to think that to map the
fact that science is extremely well
predictive of something to believing
that you actually understand it like you
can intuitively under the how as the
degree that human beings can understand
anything that you actually understand it
are you just trusting the beauty and the
power of the predictive power science
that depends on what you mean by this
idea of truly understandings right right
you know I mean can I Lily understand
four months Last Theorem you know it's
easy to state it but do I really
appreciate what it means for incredibly
large numbers right yeah I think yes I
think I do understand it but like if you
want to just push people on well you put
your intuition doesn't go to the places
where Andrew Wiles needed to go to prove
Fermat's Last Theorem and I can say fine
by something I understand the theorem
and likewise I think that I do have a
pretty good intuitive understanding of
fields pervading space time whether it's
the gravitational field or the
electromagnetic field or whatever the
Higgs field of course one's intuition
gets worse and worse as you get trickier
in the quantum field theory and all
sorts of new phenomena that come up in
quantum field theory so our intuitions
aren't perfect but I think it's also
okay to say that our intuitions get
trained right like you know I have
different intuitions now that I had when
I was a baby that's okay that's not an
intuition is not necessarily intrinsic
to who we are we can we can train it a
little bit so that's where I'm gonna
bring in norm Chomsky for a second who
thinks that our cognitive abilities are
sort of evolved through time and so
they're they're biologically constrained
and so there's a clear limit as he puts
it to our cognitive abilities and it's a
very harsh limit but you actually kind
of said something interesting and nature
versus nurture thing here is we can
train our intuitions to sort of build up
the cognitive muscles to be able to
understand some of these tricky casas so
do you think there's limits to our
understanding that's deeply rooted
hard-coded into our biology that we
can't overcome
there could be limits to things like our
ability to visualize okay but when
someone like Ed Witten proves a theorem
about you know hundred dimensional
mathematical spaces he's not visualizing
it he's doing the math that doesn't stop
him from understanding the result I
think and I would love to understand
this better but my rough feeling which
is not very educated is that you know
there's some threshold that one crosses
in abstraction when one becomes kind of
like a Turing machine right one has the
ability to contain in one's brain
logical formal symbolic structures and
manipulate them and that's a leap that
we can make as human beings that that
dogs and cats haven't made and once you
get there I'm not sure there are any
limits to our ability to understand the
scientific world at all maybe there are
there's certainly a ability limits on
our ability to calculate things right
you know people are not very good at
taking cube roots of million digit
numbers in their head but that's not an
element of understanding it's certainly
not a little bit in principle so of
course there's a human you would say
that doesn't feel to be limits to our
understanding but sort of hey have you
thought that the universe is actually a
lot simpler than it appears to us and we
just will never be able to like it's
outside of our okay so us our cognitive
abilities combined with our mathematical
prowess and whatever kind of
experimental simulation devices we can
put together is there limits to that is
is it possible there's limits to that
well of course it's possible there is or
is there any good reason to think that
we're anywhere close to the limits is a
harder question look imagine asking this
question 500 years ago to the world's
greatest thinkers right like are we
approaching the limits of our ability to
understand the natural world and by
definition there are questions about the
natural world that are most interesting
to us that are the ones we
but yet understand right so there's
always we're always faced with these
puzzles we don't yet know and I don't
know what they would have said five
hundred years ago but they didn't even
know about classical mechanics much less
quantum mechanics so we know that they
were nowhere close to how well they
could do right they could do normally
better than they were doing at the time
I see no reason why the same thing isn't
true for us today so of all the worries
that keep me awake at night the human
minds inability to rationally comprehend
the world is low on the list well put so
one interesting philosophical point and
quantum mechanics bring up is the that
you talk about the distinction between
the world as it is and the world as we
observe it so staying at the human level
for a second how big is the gap between
what our perception system allows us to
see and the world as it is outside our
minds I sort of so if not at the quantum
mechanical level yeah as just are these
particular tools we have which is a few
senses and cognitive abilities to
process those senses well that last
phrase having the cognitive abilities to
process them carries a lot right I mean
there is our sort of intuitive
understanding of the world you don't
need to teach people about gravity for
them to know that apples fall from trees
right that's something that we figure
out pretty quickly object permanence
things like that the three
dimensionality of space even if we don't
have the mathematical language to say
that we kind of know that it's true on
the other hand no one opens their eyes
and sees atoms all right or molecules
for ourselves for that matter forget
about quantum mechanics so but we got
there we got to understanding that there
are atoms and cells using the
combination of our senses and our
cognitive capacities so adding the
ability of our cognitive capacities to
our senses is adding an enormous amount
and I don't think there's a hard and
fast boundary you know if you believe in
cells if you believe that we understand
those then there's no reason you believe
we can't believe in quantum mechanics
just as well what to you is the most
beautiful idea in physics
conservation of momentum can you
elaborate yeah if you were Aristotle
when Aristotle wrote his book on physics
he made the following very obvious point
we're on video here right so people can
see this so if I push the bottle let me
cover this bottle so we do not have a
mess but okay so I push the bottle it
moves and if I stop pushing itself
moving yes and this is this kind of
thing is repeated a large number of
times all over the place if you don't
keep pushing things they stop moving
this is a indisputably true fact about
our everyday environment okay and for
Aristotle this blew up into a whole
picture of the world in which things had
natures and teleology x' and they had
places they wanted to be and when you
were pushing them you were moving them
away from where they wanted to be and
they would return and stuff like that
and it took a thousand years or fifteen
hundred years for people to say actually
if it weren't for things like
dissipation and air resistance and
friction and so forth the natural thing
is for things to move forever in a
straight line there's a constant
velocity right conservation of momentum
and that is the reason why I think
that's the most beautiful idea in
physics is because it shifts us from a
view of nature's and teleology to a view
of patterns in the world so when you
were Aristotle you needed to talk a
vocabulary of why is this happening
what's the purpose of it what's the
cause etc because you know it's nature
does or does not want to do that whereas
once you believe in conservation of
momentum things just happen they they
just follow the pattern you give me you
have Laplace's deamon ultimately right
you give me the state of the world today
I can predict what's gonna do in the
future I can predict where it was in the
past it's impersonal
and it's also instantaneous it's not
directed toward any future goals it's
just doing what it does given the
current state of the universe that I
think even more than either classical
mechanics or quantum mechanics and that
is the profound deep insight that gets
modern science off the ground
you don't need nature's and purposes and
goals you just need some patterns
so it's the first moment in our
understanding of the way the universe
works where you branch from the
intuitive physical space to kind of the
space of ideas and also the other point
you said which is conveniently most of
the interesting ideas are acting in the
moment you don't need to know the
history of time or the future then of
course this took a long time to get
there right I mean the conservation
momentum itself took hundreds of years
it's weird just like someone would say
something interesting and then the next
interesting thing would be said like 150
or 200 years later right they weren't
even talking to each other there was
reading each other's books and probably
the first person to directly say that in
outer space in the vacuum projectile
would move at a constant velocity was
Avicenna even Sina and the Persian
Golden Age circa 1000 and he didn't like
the idea he used that just like
furniture used Schrodinger's cat to
studies freely you don't believe that
right even Sina was saying surely you
don't believe there really is a vacuum
because if there was a really vacuum
things could keep moving forever right
but still he got right the idea that
there was this conservation of something
impetus or mile he would call it and
that's 500 years 600 600 years before
classical mechanics and Isaac Newton so
you know Galileo played a big role in
this but he didn't exactly get it right
and so it just takes a long time for
this to sink in because it is so against
our everyday experience do you think it
was a big leap a brave or a difficult
leap of sort of math and science to be
able to say that momentum was conserved
I do you know I think it's a example of
human reason in action you know even
Aristotle knew that his theory had
issues because you could fire an arrow
and it would go a long way before it
stopped so if his theory was things just
automatically stopped what's going on
and he had this elaborate story I don't
know if you've heard the story but the
arrow would push the air in front of it
away and the molecules of air would run
around to the back of the arrow and push
it again and anyone reading this is
going like really that's that's what you
thought but it was that kind of thought
experiment that
we got people to say like actually know
if it weren't for the air molecules at
all there I would just go on by itself
and it's always this give-and-take
between thought and experience back and
forth right theory and experiment we
would say today another big question
that I think comes up certainly with
quantum mechanics is what's the
difference between math and physics to
you to me you know very very roughly
math is about the logical structure of
all possible worlds and physics is about
our actual world and it just feels like
our actual world is a gray area when you
start talking about interpretations of
quantum mechanics or no I'm certainly
using the word world in the broadest
sense all of reality so I think the
reality is specific I don't think that
there's every possible thing going on in
reality I think there are rules whether
it's the Schrodinger equation or
whatever so i think i think that there's
a sensible notion of the set of all
possible worlds and we live in one of
them the world that we're talking about
might be a multiverse might be many
worlds of quantum mechanics might be
much bigger than the world of our
everyday experience but it's still one
physically contiguous world in some
sense but so if you look at the overlap
of math and physics it feels like when
physics tries to reach for understanding
of our world it uses the tools of math
to sort of reach beyond the limit of our
current understanding what do you make
of that process of sort of using math to
so you start maybe with intuition or you
might start with the math and then build
up an intuition or but this kind of
reaching into the darkness into the
mystery of the world would math well I
think I would put it a little bit
differently I think we have theories
theories of the physical world which we
then extrapolate and ask you know what
do we conclude if we take these
seriously well beyond where we've
actually tested them it is separately
true that math is really really useful
when we construct physical theories and
you know famously Eugene Wigner asked
about the unreasonable success of method
Mattox and physics I think that's a
little bit wrong because anything that
could happen any other theory of physics
that wasn't the real world with some
other world you could always describe it
mathematically it's just it might be a
mess the surprising thing is not that
math works but that the math is so
simple and easy that you can write it
down on a t-shirt right I mean that's
what is amazing that's an enormous
compression of information that seems to
be valid in the real world so that's an
interesting fact about our world which
maybe we could hope to explain or just
take as a brute fact I don't know but
once you have that you know it there's
this the indelible relationship between
math and physics but but philosophically
I do want to separate them well we what
we extrapolate we don't extrapolate math
because there's a whole bunch of wrong
math you know that doesn't apply to our
world right we extrapolate the physical
theory that we best think explains our
world again an unanswerable question why
do you think our world is so easily
compressible into beautiful equations
yeah I mean like I just hinted at I
don't know if there's an answer to that
question there could be what would an
answer look like well an answer could
look like if you showed that there was
something about our world that maximized
something you know the the mean of the
simplicity and the powerfulness of the
laws of physics or you know with maybe
we're just generic maybe in the set of
all possible worlds this is what the
world would look like right like I were
I don't really know I tend to think not
I tend to think that there is something
specific and rock-bottom about the facts
of our world that don't have further
explanation like the fact of the world
exists at all and furthermore the
specific laws of physics that we have I
think in some sense we're just gonna at
some level we're gonna say and that's
how it is and you know we can't explain
anything more we I don't know how if
we're anywhere close to that right now
but that seems plausible to me and
speaking of rock bottom one of the
things so your book kind of reminded me
a reveal to me is that what's
fundamental and what's emergent it just
feels like I don't even know anymore
what's fundamental in
in physics if there's anything it feels
like everything especially with quantum
mechanics is revealing to us is that
most interesting things that I would as
a he as a limited human would think are
fundamental or it can actually be
explained as emergent from the the more
deeper laws I mean we don't know of
course is you had to get that on the
table like we don't know what is
fundamental we do know we do have reason
to say that certain things are more
fundamental than others right atoms and
molecules are more fundamental than
cells and organs quantum fields are more
fundamental than atoms and molecules we
don't know if that ever bottoms out I I
do think that there's sensible ways to
think about this the if you if you
describe something like this table as a
table it has a height and a width and
it's made of a certain material and has
a certain solidity and weight and so
forth that's the very useful description
as far as it goes there's a whole nother
description at this table in terms of a
whole collection of atoms strung
together in certain ways the language of
the atoms is more comprehensive than the
language of the table you could break
apart to the table smash it to pieces
still talk about it as atoms but you
could no longer talk about it as a table
right so I think of this
comprehensiveness the domain of validity
of a theory gets broader and broader as
the theory gets more and more
fundamental so what do you think Newton
would say maybe write in a book review
if you read your latest book on quantum
mechanics something deeply hidden would
take a long time for him to think that
any of this was making any sense you
catch him up pretty quick in the
beginning yeah give him a shout out
that's right I mean he used the man I'm
happy to say that Newton was the
greatest scientists who ever lived I
mean he met in calculus in his spare
time which would have made it the
greatest mathematician just all by
himself right I'll buy that one thing
but of course you know it's funny
because Newton was in some sense still a
pre-modern thinker rocky Kolb who is a
cosmologists at at the University of
Chicago said that you know Galileo even
though he can be
for Newton was a more modern thinker
than than Newton was like if he got
Galileo and brought him to the present
day
you take him six months to catch up and
then he be in your office telling you
while your most recent paper was wrong
whereas Newton just thought in this kind
of more mystical way you know he wrote a
lot more about the Bible and alchemy
didn't he ever did about physics and but
he was also more brilliant than anybody
else and and way more mathematically
astute than Galileo so I really don't
know you know he might have he might
just yeah say like give me the textbooks
leave me alone for a few months and then
be caught up but he but he or he might
have had mental blocks against against
seeing the world in this way I really
don't know or perhaps find an
interesting mystical interpretation of
quantum mechanics very possible yeah is
there any other scientists or
philosophers through history that you
would like to know their opinion of your
book that's against a good question um I
mean Einstein is the obvious one right
y'all and he was not that long ago but
speculate at the end of my book about
what his opinion would be I am curious
as to you know what about older
philosophers like Hume or Conte right
like what would they have thought or
Aristotle you know what would they
thought about modern physics because
they do in philosophy your predilections
end up paint playing a much bigger role
in your ultimate conclusions cuz you're
not as tied down by what the data is in
physics you know physics is lucky
because we can't stray too far off the
reservation as long as we're trying to
explain the world that we actually see
in our telescopes and microscopes but
it's it's just not fair to play that
game because the people were thinking
about didn't know a whole bunch of
things that we know right like we lived
through a lot that they didn't live
through so by the time we got them
caught up they'd be different people so
let me ask a bunch of basic questions I
think it would be interesting useful for
people are not familiar but even for
people who are extremely well familiar
let's start with what is quantum
mechanics quantum mechanics is the
paradigm of physics that came into being
in the early part of the 20th century
that replaced
classical mechanics and it replaced
classical mechanics in a weird way that
we're still coming to terms with so in
classical mechanics you have an object
it as a location has a velocity and if
you know the location and velocity of
everything in the world you can say what
everything's gonna do quantum mechanics
has an aspect of it that is kind of on
the same lines there's something called
a quantum state or the wave function and
there's an equation governing what the
quantum state does so it's very much
like classical mechanics the wave
function is different it's sort of a
wave it's a vector in a huge dimensional
vector space rather than a position in a
velocity but okay that's a detail and
the equation is the Schrodinger equation
not Newton's laws but okay again a
detail where quantum mechanics really
becomes weird and different is that
there's a whole nother set of rules in
our textbook formulation of quantum
mechanics in addition to saying that
there's a quantum state and it evolves
in time and all these new rules have to
do with what happens when you look at
the system when you observe it when you
measure it in classical mechanics there
were no rules about observing you just
look at it and you see what's going on
that that was that right in quantum
mechanics the way we teach it there's
something profoundly fundamental about
the act of measurement or observation
and the system dramatically changes its
state even though it has a wave function
like the electron in an atom is not
orbiting in a circle as sort of spread
out in a cloud when you look at it you
don't see that cloud when you look at it
it looks like a particle with a location
so it dramatically changes its state
right away and the effects of that
change can be instantly seen and what
the electron does next so that's the
again we need to be careful because we
don't agree on what quantum mechanics
says that's what I need to say like in
the textbook view etc right but in the
textbook view quantum mechanics unlike
any other theory of physics places uh
gives a fundamental role to the act of
measurement so maybe even more basic
what is an atom and what is an electron
sure this all came together you know in
a few years around the turn of the last
century right around the year 1900
Adams predated then of course the word
Adam goes back to the ancient Greeks but
it was the chemists in the 1800's that
really first got experimental evidence
for atoms they realized you know that
there were two different types of tin
oxide and in these two different types
of tin oxide there was exactly twice as
much oxygen in one type as the other and
like why is that why is it all why is it
never 1.5 times as much right and so
Dalton said well it's because there are
10 atoms and oxygen atoms and one form
of tin oxide is one atom of tin and one
atom of oxygen and the other is one atom
obtained and two atoms of oxygen and on
the basis of this is you know
speculation a theory right a hypothesis
but then on the basis of that you make
other predictions and the chemists
became quickly convinced that atoms were
real the physicists took a lot longer to
catch on but eventually they did and I
mean Boltzmann who believed in atoms was
God he had a really tough time his whole
life because he worked in Germany where
atoms were not popular they were popular
in England but not in Germany and there
in general the idea of atoms is it's the
most the smallest building block of the
universe for for them that's the kind of
how the Greek idea but the chemists in
the 1800's jumped the gun a little bit
so these days in atom is the smallest
building block of a chemical element
right hydrogen tin oxygen carbon
whatever but we know that atoms can be
broken up further than that and that's
what physicists discovered in the early
1900's Rutherford especially and and his
colleagues so the atom that we think
about now the cartoon is that picture
you you always seen of a little nucleus
and then electrons orbiting it like a
little solar system and we now know the
nucleus is made of protons and neutrons
so the weight of the atom the mass is
almost all in its nucleus protons and
neutrons or something like 1,800 times
as heavy as electrons are electrons are
much lighter but they're because they're
lighter they give all the life to the
atoms so when atoms get together combine
chemically when electricity flows
through a system it's all the electrons
that are doing all the work
and we're quantum mechanic steps in as
you mentioned with position or velocity
with classical mechanics and quantum
mechanics is modeling the behavior of
the electron I mean you can model the
behavior of anything but the electron
because that's where the fun is
the electron was it was the biggest
challenge right from the start yeah so
what's a wavefunction you said it's an
interesting detail yeah but in any
interpretation what is the wave function
in quantum mechanics well you know we
had this idea from Rutherford that atoms
look like little solar systems but
people very quickly realize that can't
possibly be right because if an electron
is orbiting in a circle it will give off
light all the light that we have in this
room comes from electrons zooming up and
down and wiggling and that's what
electromagnetic waves are and you can
calculate how long would it take for the
electron just to spiral into the nucleus
and the answer is 10 to the minus 11
seconds okay a hundred billions of a
second so that's not right
meanwhile people had realized that light
which we understood from the 1800s was a
wave had properties that were similar to
that of particles right this is Einstein
and plunk and stuff like that so if
something that we agree was a wave had
particle-like properties then maybe
something we think is a particle the
electron has wave-like properties right
and so a bunch of people eventually came
to the conclusion don't think about the
electron as a little point particle
orbiting in like a solar system think of
it as a wave that is spread out they
cleverly gave this the name the wave
function which is the dopiest name in
the world for one of the most profound
things in the universe the there's
literally you know a number at every
point in space which is the value of the
electrons wave function at that point
and there's only there's only one wave
function that yeah they eventually
figured that out that took longer but
when you have two electrons you do not
have a wave function for electron one in
a wave function for electron two you
have one combined wave function for both
of them and indeed as you say there's
only one wave function for the entire
universe at once and that's where this
beautiful dance
can you say what is entanglement it
seems one of the most fundamental ideas
of quantum again well let's temporarily
buy into the textbook interpretation of
quantum mechanics and what that says is
that this wave function so it's very
small
outside the atom very big in the atom
basically the wave function you take it
and you square it you squared the number
that gives you the probability of
observing the system at that location so
if you say that for two electrons
there's only one wave function and that
wave function gives you the probability
of observing both electrons at once
doing something okay so maybe the
electron can be here or here here here
and the other electron can also be there
but we have a wave function setup where
we don't know where either electron is
going to be seen but we know they'll
both be seen in the same place okay so
we don't know exactly what we're gonna
see for either electron but there's
entanglement between the two of them
there's a sort of conditional statement
if we see one in one location then we
know the other one's going to be doing a
certain thing so that's a feature of
quantum mechanics that is nowhere to be
found in classical mechanics in
classical mechanics there's no way I can
say well I don't know where either one
of these particles is but if I know if I
find out where this one is then I know
where the other one is that just never
happens they're truly separate and in
general it feels like if you think of a
wave function like as a dance floor it
seems like entanglement is strongest
between things that are dancing together
closest so there's a there's a closeness
that's important well that's not that
that's another step we have to be
careful here should cause in principle
if you if you're talking my the
entanglement of two electrons for
example
they can be totally entangled or totally
unentangled no matter where they are in
the universe there's no relationship
between the amount of entanglement and
the distance between two electrons but
we now know that you know the reality of
our best way of understanding the world
is through quantum fields not through
particles so even the electron not just
gravity and electromagnetism but even
the electron and the quarks and so forth
are really vibrations in quantum fields
so even empty space is full of vibrating
quantum fields and those quantum fields
in empty space are entangled with each
other in exactly the way you just said
if they're nearby if you have like two
vibrating quantum fields that are nearby
them it'll be highly entangled if
they're far away they will not be
entangled so what do quantum fields in a
vacuum look like empty space just so
like empty space it's as empty as it can
be but there's still a field it's just
yeah it uh what is nothing just like
right here or this location in space
there's a gravitational field which I
can detach by dropping something yeah I
don't see it but there it is so we got a
little bit of idea of entanglement now
what is Hilbert space and Euclidean
space yeah you know I think that people
are very welcoming over their lives not
knowing what Hilbert space is but if you
if you what I dig in a little bit more
into quantum mechanics it becomes
necessary you know the English language
was invented long before quantum
mechanics or various forms of higher
mathematics were invented so we use the
word space to mean different things of
course most of us think of space as this
three dimensional world in which we live
right I mean some of us just think of it
as outer space okay but space around us
it gives us the three-dimensional
location of things and objects but
mathematicians
use any generic abstract collection of
elements as a space okay a space of
possibilities you know momentum space
etc so Hilbert space is the space of all
possible quantum wave functions either
for the universe or for some specific
system
and it could be an infinite dimensional
space or it could be just really really
large dimensional but finite we don't
know because we don't know the final
theory of everything but this abstract
hilbert space is really really really
big and has no immediate connection to
the three-dimensional space in which we
live what what do dimensions in hilbert
space mean you know it's just a way of
mathematically representing how much
information is contained in the state of
the system how many numbers do you have
to give me to specify what the thing is
doing so in classical mechanics I give
you the location of something by giving
you three numbers right up down left
likes XYZ coordinates but then I might
want to give you its entire state
physical state which means both its
position and also its velocity the
velocity also has three components so
it's state lives in something called
phase space which is six dimensional
three dimensions of position three
dimensions of velocity and then if it
also has an orientation in space that's
another three dimensions and so forth so
as you describe more and more
information about the system you have an
abstract mathematical space that has
more and more numbers that you need to
give and each one of those numbers
corresponds to a dimension in that space
so in terms of that amount of
information
what is entropy this mystical word
that's overused in math and physics but
has a very specific meaning in this
context sadly it has more than one very
specific meeting this is this is reason
why it is hard and roomy means different
things even to different physicists but
one way of thinking about it is a
measure of how much we don't know about
the state of a system right so if I have
a bottle of water molecules and I know
that okay there's a certain number of
water molecules I could weigh it right
and figure out I know the volume of it
and I know the temperature and pressure
and things like that
I certainly don't know the exact
position and velocity of every water
molecule right so there's a certain
amount of information I know certain
amount that I don't know that is that is
part of the complete state of the system
and that's what the entropy
characterizes how much unknown
information there is the difference
between what I do know about the system
and its full exact microscopic state so
when we try to describe
a quantum mechanical system is infinite
or finite but very large yeah we don't
know that depends on the system you know
it's easy to mathematically write down a
system that would have a potentially
infinite entropy an infinite dimensional
hilbert space so let's let's go back a
little bit we said that the hilbert
space was the space in which quantum
wave functions lived for different
systems that will be different sizes
they could be infinite or finite so
that's the number of numbers the number
of pieces information you could
potentially give me about the system so
the bigger hilbert spaces the bigger the
entropy of that system could be
depending on what I know about it if I
don't know anything about it then you
know as a huge entropy right but only up
to the size of its hilbert space so we
don't know in in the real physical world
whether or not you know this region of
space that contains that water bottle
has potentially an infinite entropy or
just a finite entropy we have we have
different arguments on different sides
so if it's infinite how do you think
about infinity is this something you can
your cognitive abilities are able to
process or is it just a mathematical
tool it's somewhere in between right I
mean we can say things about it we can
use mathematical tools to manipulate
infinity very very accurately we can
define what we mean you know for any
number n there's a number bigger than it
so there's no biggest number right so
there's something called the total
number of all numbers that's infinite
but it is hard to wrap your brain around
that and I think that gives people pause
because we talk about infinity as if
it's a number but it has plenty of
properties that real numbers don't have
you know if you multiply infinity by 2
you get infinity again right that's a
little bit different than what we're
used to okay but are you comfortable
with the idea that in thinking of what
the real world actually is that infinity
could be part of that world
are you comfortable that a world in some
dimension and somehow comfortable with
lots of things I mean you know I don't
want my level of comfort to affect what
I think about the world you know I'm
pretty open-minded about what the world
could be at the fundamental level
yeah but infinity is a is a tricky one
it's not almost a question of comfort
it's a question of is it an overreach of
our intuition sort of it could be a
convenient almost like when you add a
constant to an equation just because
it'll help it just feels like it's
useful to at least be able to imagine a
concept not directly but in some kind of
way that this feels like it's a
description of the real world think of
it this way there's only three numbers
that are simple there's zero there's one
and there's infinity a number like 318
it's just bizarre like that that you
need a lot of bits to give me what that
number is yeah but zero and one infinity
like once you have 300 things you might
as well have infinity things right
otherwise yet to say how when to stop
making the thing that's right so there's
a sense in which infinity is a very
natural number of things to exist that I
was never comfortable with it because
it's just such a kick but it was a too
good to be true mmm
because in math it just helps make
things work out when things get very
it's when things get very large close to
infinity things seem to work out nicely
it's kind of like because of my deepest
passion it's probably psychology and I'm
uncomfortable how in the average the the
beauty of the very very the how much we
vary is lost in that same kind of sense
infinity seems like convenient way to
erase the details but the thing about
infinity is you it seems to pop up
whether we like it or not right right
like you're trying to be a computer
scientist you ask yourself well how long
will it take this program to run and you
realize well for some of them the answer
is infinitely long it's not because you
tried to get there
you wrote a five line computer program
it doesn't halt so coming back to the
textbook definition of quantum mechanics
this idea that we I don't think we
talked about can you this one of the
most interesting philosophical points we
talked at the human level but at the
at the physics level that it that at
least the textbook definition of quantum
mechanics separates what is observed and
what is real one how does that make you
feel and and two what does it then mean
to observe something and why is it
different that what is real yeah you
know I my personal feelings such as it
is is that things like measurement and
observers and stuff like that are not
going to play a fundamental role in the
ultimate laws of physics but my feeling
that way is because so far that's where
all the evidence has been pointing I
could be wrong and there's certainly a
sense in which it would be infinitely
cool if somehow observation or mental
cogitation did play a fundamental role
in the in the nature of reality but I
don't think so I can I don't see any
evidence for it so I'm not spending a
lot of time worrying about that
possibility so what do you do about the
fact that in the textbook interpretation
of quantum mechanics this idea of
measurement or looking at things seems
to play an important role well you you
come up with better interpretations of
quantum mechanics and there are several
alternatives my favorite is the
many-worlds interpretation which says
two things number one you the observer
are just a quantum system like anything
else there's nothing special about you
don't get so proud of yourself you know
you're just a bunch of atoms you have a
wavefunction you obey the Schrodinger
equation like everything else and number
two when you think you're measuring
something or observing something what's
really happening is you're becoming
entangled with that thing so when you
think there's a wavefunction for the
electron it's all spread out but you
look at it and you only see it in one
location what's really happening is that
there's still the wave functions the
electron in all those locations but now
it's entangled with the wave function of
you in the following way there's part of
the wave function that says the electron
was here and you think you saw it there
the electron was there and you think you
saw it there the electron was over there
and you think you saw it there etc so
and all of those different parts of the
wave function once they come into being
no
longer talk to each other they no longer
interact or influence each other it says
if they are separate worlds so this was
the invention of Hugh Everett the third
who was a graduate student at Princeton
in the 1950s and he said basically look
you don't need all these extra rules
about looking at things just listen to
what the Schrodinger equation is telling
you it's telling you that you have a
wavefunction that you become entangled
and that the different versions of you
no longer talk to each other so just
accept it it's just he did therapy more
than anything else you know he said like
it's okay you know you don't need all
these extra rules all you need to do is
believe the Schrodinger equation the
cost is there's a whole bunch of extra
worlds out there so how the worlds being
created whether there's an observer or
not the worlds are created anytime a
quantum system that's in a superposition
becomes entangled with the outside world
what's the outside world it depends
let's back out yeah
whatever it really says what his theory
is is there's a wave function of the
universe
and a base the Schrodinger equation all
the time that's it that's the full
theory right there okay the question all
of the work is how in the world do you
map that theory on to reality on to what
we observe right so part of it is
carving up the wavefunction into these
separate worlds saying look look it
describes a whole bunch of things that
don't interact with each other let's
call them separate worlds another part
is distinguishing between systems and
their environments and the environment
is basically all the degrees of freedom
all the things going on in the world
that you don't keep track of so again in
the bottle of water I might keep track
of the total amount of water and the
volume I don't keep track of the
individual positions and velocities I
don't keep track of all the photons or
the air molecules in this room so that's
the outside world the outside world is
all the parts of the universe that
you're not keeping track of when you're
asking about the behavior of some
subsystem of it so how many worlds are
there you want to know that one either
there could be an infinite number there
could be only a finite number but it's a
big number one way or the other it's a
very very big number
one of you talked somebody asked well if
it's a if it's finite
so actually I'm not sure exactly the
logic you used to derive this but is
there you know going to be the you know
overlap a duplicate world that you
return to so you've mentioned and I'd
love if you can elaborate on sort of
idea that it's possible that there's
some kind of equilibrium that these
splitting worlds arrive at and then
maybe over time maybe somehow connected
to entropy you get a large number of
worlds they're very similar to each
other yeah so this question of whether
or not Hilbert space is finite or
infinite dimensional is actually
secretly connected to gravity and
cosmology this is a the part that we're
still struggling to understand right now
but we discovered back in 1998 that our
universe is accelerating and what that
means if it continues which we think it
probably will but we're not sure but if
it does that means there's a horizon
around us there there's because the
universe not only expanding but
expanding faster and faster things can
get so far away from us that from our
perspective it looks like they're moving
away faster than the speed of light
you'll never see them again
so there's literally a horizon around us
and that horizon approaches some fixed
distance away from us and you can then
argue that within that horizon there's
only a finite number of things that can
possibly happen the finite dimensional
hilbert space in fact we even have a
guess for what the dimensionality is
it's 10 to the power of 10 to the power
of 122 that's a very large number yes
just to compare the age of the universe
is something like 10 to the 14 seconds
10 to the 17 or 18 seconds maybe the
number of particles in the universe is
10 to the 88th but the number of
dimensions of Hilbert space is 10 to the
10 to the 120 - so that's just crazy
thing if that story is right that in our
observable horizon there's only a finite
dimensional hilbert space then this idea
of branching of the wavefunction the
universe into multiple distinct separate
branches has to reach a limit at
once you read branched that many times
you've run out of room in hilbert space
and roughly speaking that corresponds to
the universe just expanding and emptying
out and cooling off and and entering a
phase where it's just empty space
literally forever what's the difference
between splitting and copying do you
think like in terms of a lot of this is
an interpretation that's that helps us
sort of model the world so perhaps
shouldn't be thought of as like you know
philosophically or metaphysically but in
even at the physics level do you see a
difference between two generating new
copies of the world or splitting I think
it's better to think of in quantum
mechanics in many worlds the universe
splits rather than new copies because
people otherwise worry about things like
energy conservation and no one who
understands quantum mechanics worries
about energy conservation because the
equation is perfectly clear but if all
you know is that someone told you the
universe duplicates then you have a
reasonabl