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Language: en
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
a 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 of 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 wavefunction 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 wavefunction 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 up 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 world
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 sub subsystem of it
so how many worlds are there you don't
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
just a very very big number in one of
their talk 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 a you know
overlap a duplicate world that you
returned 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 overtime 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 at 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 fast from 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
time of 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
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 some
time once you branch 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
which means 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
reasonable worry about where all the
energy for that came from so a
pre-existing universe splitting into two
skinnier universes is a better way of
thinking about it and mathematically
it's just like you know if you draw an x
and y axis and you draw a vector of
length one at 45 degree angle you you
know that you can write that vector of
length 1 as the sum of two vectors
pointing along x and y of length 1 over
the square root of 2 okay so I write one
arrow as the sum of two arrows but
there's a conservation of air Onis right
like if now two arrows the length is the
same I just been describing it in a
different way and that's exactly what
happens when the universe branches the
the wave function of the universe is a
big old vector so to somebody who brings
up a question of saying doesn't this
violate the conservation of energy can
you give
further elaboration right so let's just
be SuperDuper perfectly clear yeah
there's zero question about whether or
not many-worlds violates conservation
energy yes it does not great and I say
this definitively because there are
other questions that I think there's
answers to but they're legitimate
questions right about you know where
does probability come from and things
like that this conservation of energy
question we know the answer to it and
the answer to it is that energy is
conserved all of the effort goes into
how best to translate what the equation
unambiguously says into thing plain
English right so this idea that there's
a universe that has that that the
universe comes equipped with a thickness
and it sort of divides up into thinner
pieces but the total amount of universe
is is conserved over time is a
reasonably good way of putting English
words to the underlying mathematics so
one of my favorite things about many
worlds is I mean I love that there's
something controversial in science and
for some reason it makes people actually
not like upset but just get excited why
do you think it is a controversial idea
so there's there's a lot of it's
actually one of the cleanest ways to
think about quantum mechanics yeah so
why do you think there's a discomfort a
little bit among certain people
well I draw the distinction of my book
between two different kinds of
simplicity in a physical theory there's
simplicity in the theory itself right
how we describe what's going on
according to the theory by its own
rights but then you know a theory is
just some sort of abstract mathematical
formalism you have to map it onto the
world somehow right and sometimes like
for Newtonian physics it's pretty
obvious like okay here is a bottle and
it has a center of mass and things like
that sometimes it's a little bit harder
with general relativity curvature of
space-time is a little bit harder to
grasp quantum mechanics is very hard to
map what you're the language you're
talking into wave functions and things
like that onto reality
and many worlds is the version of
quantum mechanics where it is hardest to
map on the underlying formalism to
reality so that's where the lack of
simplicity
comes in not in the theory but in how we
use the theory to map onto reality and
in fact all of the work in sort of
elaborating many-worlds quantum
mechanics is in the this effort to map
it on to the world that we see so it's
perfectly legitimate to be bugged by
that right to say like well no that's
just too far away
from my experience I I am therefore
intrinsically skeptical of it of course
you should give up on a skepticism if
there are no alternatives and this
theory always keeps working then
eventually you should overcome your
skepticism but right now there are
alternatives that are that you know
people work to make alternatives that
are by their nature closer to what we
observe directly can you describe the
alternatives identically touched on it
so that the Copenhagen interpretation
and the many-worlds
maybe there's a difference between the
effort of already in many worlds and
many worlds as it is now like has the
idea sort of developed and so on and
just in general what is the space of
promising contenders we have democratic
debates now there's a bunch of candidate
well candidates on stage what are the
quantum-mechanical candidates on stage
for the debate so if you had a debate
between quantum-mechanical contenders
there'd be no problem getting 12 people
up there on stage but there would still
be only three frontrunners and right now
the frontrunners would be Evert hidden
variable theories are another one so the
hidden variable theories say that the
wavefunction is real but there's
something in addition to the
wavefunction the wavefunction is not
everything is part of reality but it's
not everything what else is there
we're not for but in the simplest
version of the theory there are
literally particles so many world says
that quantum systems are sometimes are
wave-like in some ways and particle-like
in another because they really really
are waves but under certain
observational circumstances they look
like particles whereas hidden variable
says there they look like waves and
particles because there are both waves
and particles involved in the dynamics
and that's easy to do if your particles
are just nonrelativistic Newtonian
particles moving
they get pushed around by the wave
function roughly it becomes much harder
when you take quantum field theory or
quantum gravity into account the other
big contender are spontaneous collapse
theories so in the conventional textbook
interpretation we say when you look at a
quantum system its wavefunction
collapses and you see it in one location
a spontaneous collapse theory says that
every particle has a chance per second
of having its wavefunction spontaneously
collapse the chance is very small for a
typical particle it will take hundreds
of millions of years before it happens
even once
but in a table or some macroscopic
object there are way more than a hundred
million particles and they're all
entangled with each other so when one of
them clacks it collapses it brings
everything else along with it there's a
slight variation of this that's a
spontaneous collapse theory there are
also induced collapse theories like
Roger Penrose thinks that when the
gravitational difference between two
parts of the wave function becomes too
large the wavefunction collapses
automatically so those are basically in
my mind the three big alternatives many
worlds which is just there's a
wavefunction and always a basis reading
your equation hidden variables there's a
wave function that always the base of
Schrodinger equation but there are also
new variables or collapse theories which
the wave function sometimes obeys the
Schrodinger equation and sometimes it
collapses so you can see that the
alternatives are more complicated in
their formalism than many worlds is but
they are closer to our experience so
just this moment of collapse do you
think of it as so is a wave function
fundamentally sort of a probabilistic
description of the world and its
collapse sort of reducing that part of
the world into something deterministic
or again you can now describe the
position and the velocity in this simple
classical model well there is a hard
thing about collapse there is a fourth
category is a 4th contender there's a
mayor Pete of quantum mechanical
interpretations which are called
epistemic interpretations and what they
say is all the wavefunction is is a wave
making predictions for experimental
outcomes it's not mapping onto an
element of reality in any
realsense and in fact two different
people might have two different wave
functions for the same physical system
because they know different things about
it right the wave function is really
just a prediction mechanism and then the
problem with those epistemic
interpretations is if you say okay but
it's predicting about what like what is
the thing that is being predicted and I
say no no that's not what we're here for
we're just here to tell you what the
observational outcomes you're gonna be
but the other the other interpretation
is kind of think that the wave function
is real yes that's right
so that's an antic interpretation of the
wave function ontology being the study
of what is real what exists as opposed
to an epistemic interpretation of the
wave function epistemology being the
study what we know now actually just
love to see that debate on stage there
was a version of it on stage at the
world science festival a few years ago
that you can look up online I need you
yep it's on you do okay awesome I'll
link it watch it anyone i won there was
no vote those there's Brian Greene was
the moderator and David Albert stood up
for spontaneous collapse and Shelley
Goldstein was there for hidden variables
and Ruettiger shock was there for
epistemic approaches why do you I think
you mentioned it but just why do you
find many worlds so compelling well
there's two reasons actually one is like
I said it is the simplest right it's
like the most bare-bones austere pure
version of quantum mechanics and I am
someone who is very willing to put a lot
of work into mapping the formalism onto
reality I'm less willing to complicate
the formalism itself but the other big
reason is that there's something called
modern physics with quantum fields and
quantum gravity and holography and
space-time doing things like that and
when you take any of the other versions
of quantum theory they bring along
classical baggage all of the other
versions of quantum mechanics prejudice
or privilege some version of classical
reality like locations in space okay and
I think that that's a barrier to doing
better at understanding the theory of
everything and understand
quantum gravity and the emergence of
space-time whenever if you change your
theory from you know here's a harmonic
oscillator oh there's a spin here's an
electromagnetic field in hidden variable
theories or dynamical collapse theories
you have to start from scratch you have
to say like well what are the hidden
variables for this theory or how does he
collapse or whatever whereas many worlds
is plug-and-play you tell me the theory
and I can give you as many worlds
version so when we have a situation like
we have with gravity and space-time
where the classical description seems to
break down in a dramatic way then I
think you can start from the most
quantum theory that you have which is
really many worlds
you