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Norton 360 classical mechanics is great
if you know the state of a system say
the position and velocity of a particle
then you can use an equation Newton's
second law to calculate what that
particle will do in the future in
quantum mechanics if you know the
quantum state of a particle that is its
wave function you can use the
Schrodinger equation to calculate what
that particle will do in the future
usually it spreads out over time as it
is doing here note to make this
animation we really solved the
Schrodinger equation so there's a
beautiful symmetry here if you know the
initial state you can use an equation to
evolve that state smoothly and
continuously into the future the problem
is in quantum mechanics we never
actually observe the wave function like
this instead when we measure it we find
the particle at a single point in space
so how are we to reconcile the
spread-out wavefunction evolving
smoothly under the Schrodinger equation
with this point like particle detection
now I think it's understandable that
when the founders of quantum theory
approached this problem they considered
the measurement more real than the
wavefunction after all the measurement
was something we had actually observed
and it matches our experience of a world
of matter particles it was harder to say
what the wavefunction was exactly
Schrodinger formulated his wave equation
because scientists notably debroglie
suspected that matter has wave-like
properties but it took a third physicist
Max Born to propose how we should
interpret the wave function at each
point in space the wave function has a
complex amplitude essentially just a
real number plus an imaginary number Max
Born suggested if you take that
amplitude and square it you get the
probability of finding the particle
there the fact that you have to square
the amplitude actually appears as a last
minute footnote in boran's paper but
that is how probability was introduced
into the core of our picture of reality
that's a pretty big philosophical leap I
mean no longer is the universe
deterministic
this made a lot of scientists especially
Einstein uncomfortable but the born rule
as it is now called remains at the heart
of quantum mechanics because it is
spectacularly successful at predicting
the outcomes of experiments so the way
quantum mechanics came to be understood
and the way I learned it is that there
are two sets of rules when you're not
looking the wave function simply evolves
according to the Schrodinger equation
but when you are looking when you make a
measurement the wavefunction collapses
suddenly and irreversibly and the
probability of measuring any particular
outcome is given by the amplitude of the
wave function associated with that
outcome squared now Schrodinger himself
hated this formulation which is actually
why he invented the famous Schrodinger's
cat thought experiment put a cat in a
box with a radioactive atom add a
radiation detector that triggers the
release of poisonous cyanide gas now
although it was only meant as a thought
experiment Schrodinger helpfully notes
this device must be secured against
direct interference by the cat anyway
the whole point of the experiment is to
magnify the state of the atom up to the
state of something macroscopic and
tangible he could have picked anything
it didn't have to be alive but
Schrodinger selected a cat if the atom
decays the detector detects radiation
releases the poison and the cat dies if
the atom doesn't decay the detector
doesn't detect radiation poison is not
released and the cat remains alive since
the state of the cat and detector
apparatus are directly tied to the state
of the atom we say they are entangled
where things get weird is that according
to quantum mechanics the state of the
atom does not have to be either decayed
or not decayed generally it's in a
superposition of both decayed and not
decayed at the same time assuming no
measurements have been made this
superposition state of the atom gets
entangled with the detector and then the
cat so after some time the wavefunction
of everything inside the box is in a
superposition of the atom has not
decayed poison not released cat a live
state and the atom has decayed poison
released cat dead
date so according to quantum mechanics
the cat really is both alive and dead at
the same time only when we open the box
and make a measurement does the
wavefunction collapse and the cat
actually becomes either dead or alive
these days Schrodinger's cat is often
used as a way to show how weird quantum
mechanics is but that wasn't
Schrodinger's point he wanted to show
that quantum mechanics as formulated was
wrong so taking up Schrodinger's
argument in this video I want to show
that there is a better way to think
about Schrodinger's cat
in fact a better way to think about
quantum mechanics entirely that I'd
argue is more logical and consistent to
get there we have to examine the three
essential components of Schrodinger's
cat superposition entanglement and
measurement to see if any of them is
flawed the superposition is the idea
that quantum objects can be in two
different states at the same time this
seems like a crazy idea and something
we'd never observe but we do indirectly
with the double slit experiment fire
individual electrons through two slits
at a screen and the pattern you see is
not just the sum of electrons going
separately through one slit and the
other slit it is an interference pattern
we are forced to conclude that a single
electron somehow goes through one slit
and the other slit simultaneously
this is superposition of course it's
easy to understand superposition with
waves they are spread out in space and
it's clear how the peak of a wave from
one slit cancels with the trough of the
wave from another slit to produce the
interference pattern and luckily we know
that when we're not looking electrons
are represented by a wave the wave
function the double slit experiment then
is concrete evidence that this wave
enables individual electrons to pass
through both slits at the same time so
superposition is on solid ground the
next concept is entanglement consider
two electrons fired toward each other
with equal and opposite velocities we
know they will scatter off each other
but we don't know exactly how their
trajectories are given by spread out
wave functions that only give us
probabilities
but as soon as we measure the momentum
of one of the electrons we immediately
know the momentum of the other one it
must be equal and opposite otherwise
conservation of momentum would be
violated now this may seem obvious but
consider that before the measurement the
momentum of each electron was in a
superposition of states measuring one
instantaneously collapsed the
wavefunction of the other and this would
be true even if those electrons were
light-years apart these electrons are
entangled what's really going on here is
that after interacting the electrons do
not have separate wave functions at all
they are described by a single wave
function and this is what it means to be
entangled this explains why measuring
one immediately affects the state of the
other one because the single wave
function has collapsed in fact if we
were being rigorous we'd have to say
that there is only one wave function the
wave function of the entire universe
which includes absolutely everything but
in the case of isolated unentangled
quantum particles we can reasonably talk
about their individual wave functions
and then once they interact with
something else entanglement is the
result so what we've seen is
superposition is really the same thing
as describing systems with waves an
entanglement means that after particles
interact they are described by a single
wave function these are fundamental
parts of quantum theory describing
systems with wave functions that evolve
according to the Schrodinger equation
which leaves only measurement remember
the measurement postulate was added as a
second set of rules to connect the
mathematics of quantum mechanics to what
we actually observe but doesn't it seem
weird that there should be one rule for
how systems evolve when we're not
looking and a different rule for when we
are when you boil it down measurement is
just the interaction of one quantum
system electrons and photons with
another quantum system and we know
exactly how to deal with that we simply
evolve their wave functions according to
the Schrodinger equation so what if we
throw out all the rules associated with
measurement well then in the
Schrodinger's cat thought experiment
the radioactive atom in a superposition
of decayed and not decayed gets
entangled with the detector and in turn
the cat now remember we are also made of
electrons and atoms which obey the laws
of quantum mechanics so we are quantum
mechanical - so when we open the box
there is no measurement no wavefunction
collapse we simply get entangled with
the state of everything inside the box
so we see the cat alive and we see the
cat dead now how is that possible I'm
guessing you've never seen both an alive
and dead cat before but the solution is
it's because the you that saw the cat
alive and the you that saw it dead
actually inhabit separate worlds by that
I mean they exist in their own complete
realities and those realities will never
interact but where did these separate
worlds come from well something I
haven't mentioned yet are all the
particles of the environment the air
molecules photons everything that we are
not keeping track of if a quantum object
in a superposition gets entangled with
the environment it is said to undergo
environmental decoherence this branches
the wave function of the universe
essentially
splitting the universe into two slightly
different copies so a more realistic
account of Schrodinger's cat goes like
this the radioactive atom evolves from
100% not decayed into a quantum
superposition of decayed and not decayed
the detector becomes entangled with this
superposition state of the atom but the
detector is being bombarded by all these
air molecules and photons in the box
which would bounce off differently if it
is detected radiation than if it hasn't
so almost immediately the detector
becomes entangled with the state of the
environment it D coheres branching the
wavefunction in to at that moment you
are split into two identical copies one
entangled with each outcome of the
experiment you continue to be identical
until you open the box but in this case
the cat actually is alive or dead you
were just finding out by opening the box
what we are unaware of is that the other
outcome also happened just to someone
who is not you anymore I mean both
observers
came from you but they are no longer you
and they're no longer identical to each
other this interpretation of quantum
mechanics is called many worlds and it
was formulated by Hugh Everett and if
it's true the branching of the
wavefunction is happening all the time
so frequently in fact that the rate may
well be infinite creating infinite
subtly different worlds all the time may
sound implausible to put it mildly but
consider that all those worlds are
naturally part of the mathematics of
quantum mechanics many worlds just takes
them seriously to get rid of them
requires something like the collapse of
the wavefunction and the point is our
experience of reality would be the same
in the many-worlds picture as it is if
the wavefunction collapses but the
formalism is so much cleaner and more
elegant all we have are wave functions
that evolved under the Schrodinger
equation the implication is that the
founders of quantum theory may have got
it exactly backwards the wavefunction is
the complete picture of reality and our
measurement is just a tiny fraction of
it the part we become entangled with
when we interact with a quantum object
in a superposition the universe also
goes back to being deterministic every
outcome happens a hundred percent of the
time it only doesn't look that way to us
because we only experience our tiny
sliver of the multiverse now I imagine
that a lot of you have questions and
possibly objections to this so I went to
the expert okay so I wanted to make this
video about many worlds but I was
concerned I was gonna screw it up so
I've come here to meet Caltech professor
Sean Carroll who has literally written
the book on many worlds look something
deeply hidden available wherever books
available
let's ask probably the common sort of
YouTube questions the good arguments
against this yes how many how many
worlds are there now the first one is
energy energization
how is energy conserved is completely
clear in the math the energy of the
whole wavefunction is a hundred percent
super-duper conserved but there's a
difference between the energy of the
whole way
function and the energy that people in
each branch perceive so what you should
think of is not duplicating the whole
universe but taking a certain amount of
universe and sort of subdividing it
slicing it into two pieces the pieces
look identical from the inside except
that one has spin up the one has spin
down or something like that but they're
really contributing less than the
original to the total energy of
everything let's ask the question about
how many words there are how frequently
are they branching right we have no idea
there's a short answer to this and I
think it's embarrassing that we don't
have any idea it's certainly often it's
certainly a lot right the universe
branches whenever a quantum system in
superposition becomes entangled with its
environment so you have atomic nuclei in
your body that are radioactive they
decay 5000 times a second there's a
radioactive decay in your body every one
of those either decays or doesn't do you
think of it as a superposition once it
decays it sort of interacts with what's
around it becomes entangled and the
universe branches its wave function
right so branching is happening many
many times a second just because a
radioactive decays in your body now is
it happening infinitely often we don't
know because we don't know whether the
total number of possible branches is
infinitely big or finite its joy mungus
by any stretch there's plenty of room
for all these branches to exist and it
might very well be finite but that the
details hinge on things we don't
understand about quantum gravity and
cosmology and the theory of everything
and all that stuff so it's a big number
but we don't know how big let's deal
with the misconception that many-worlds
means everything that could possibly
happen happens yeah that's not true many
worlds means the wavefunction obeys the
Schrodinger equation that's what it
means the Schrodinger equation predicts
many things could potentially happen but
not everything so for example an
electron will never convert into a
proton it would violate conservation of
mass conservation of charge all of these
things things of the Schrodinger
equation gives zero probability to ever
happening what about you becoming
president yes that could happen there
there is a world in which you're
president there is a world well to be
SuperDuper clear
not be me who is president Raney a
version of me right right but there is
the branching happens your those are two
separate people now but there is a
version of you who is currently
president yes that's right and who was
tweeting it's a very low amplitude world
it's a very small probability but it's
there yes I mean I think this is the way
in which it feels more complicated than
or it feels more ridiculous then
Copenhagen because Copenhagen's like
there's just one world this is it that's
what you experience and but look the
universe the good old universe
forget about quantum mechanics okay just
like the cows mantra universe where we
see all the galaxies and everything we
don't see the whole universe we see a
finite amount of it because light moves
at the speed of lights is a place beyond
which we can't see the universe could be
infinitely big we don't know
it's certainly very plausible universe
is infinitely big it's plausible that
everywhere in the universe looks more or
less like what we see with galaxies and
stars in the whole bit if that's true
there's an infinite number of copies of
people exactly like you some of them are
presidents some of them are winning NBA
championships some of them are
supermodels whatever this just because
there's a lot of different shuffling
around of the atoms okay has nothing to
do with quantum mechanics or weirdness
does that bother you does that like rub
you the wrong way
kind of I think but but but I agree it's
less weird than the quantum idea and I
think in both cases it's it's because
you know human beings there's some
cognitive bias I don't know what it's
called but there's a cognitive bias that
says the only probabilities for anything
or 0% 50% 100% and when I tell you
something can happen but the probability
is really really really really really
really really really low you feel like
but it could happen
let me focus on that come on that
possibility that it happens I'm like no
don't do that it's just not sufficiently
probable that it's worth worrying about
in any way when the world branches here
does it branch instantly far away
the answer is it's up to you this is the
annoying part of the answer I can write
down a description in which the
branching happens instantly throughout
all of space I use that description to
make predictions about what people will
see all those predictions come out
percent completely true I can write an
alternative description in which the
branching sort of spreads out of the
speed of light and I make a different
set of predictions but guess what
they're exactly the same predictions
there's no difference between what those
two pictures actually predict and what
this is reflecting is God doesn't know
about branches
there's the wave function of the
universe that's all it really exists
okay
breaking the wave function the universe
into different pieces that you and I
call branches or Worlds is very
convenient for us human beings but
that's all it is it's not built into the
fabric of reality itself it's just like
it's exactly like for the air in this
room rather than listing the position
and velocity of every single air
molecule I just tell you the temperature
and the pressure and things like that
right that's a convenient description
for us human beings it's not the full
description of the reality and branches
are exactly the same way so if you get
annoyed that there's two different ways
of describing the branching you have to
remember that the whole idea of
branching is just a human convenience
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