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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

hey this portion of the video is

Parallel Worlds Probably Exist. Here’s Why

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