[MUSIC PLAYING]
SPEAKER: Hello.
Thank you all for coming.
This is going to be a talk
by my friend, the journalist
and science writer, Anil.
Please silence your phones.
And on Google, we can have
some copies of the book for you
to take home, if you're
interested by what
he has to say.
Anil and I worked together
as software engineers
more than 20 years
ago in Berkeley.
And we've been in touch,
but not nearly enough.
And he has had such
a exciting career
that went to the
edge of physics,
one of his other books.
And yes, please welcome
Anil for his presenting
his latest book that's just out.
[APPLAUSE]
ANIL ANANTHASWAMY: So
thank you, [? Arno, ?]
for that introduction.
[? Arno ?] and I
go back a long way.
I was a software engineer
before I became a journalist.
And it's really a pleasure to
be speaking here at Google.
The last couple of
times I came to speak,
for my previous two books, which
I really enjoyed the talks.
And the first one was called
"The Edge of Physics,"
and the second one was called
"The Man Who Wasn't There."
And both of those books,
I was able to sort of tell
stories about people and
places that I visited.
This book is somewhat different.
The protagonist of this
book is a single experiment.
It's an experiment with
a 200-year-old history.
And this book is
really the story
of quantum mechanics
told through the lens
of one experiment and
its modern variations.
So it's a slightly different
kind of book, in the sense
that it's hard to tell
stories in the way
that I could have done with
the previous two books.
So what I thought
I'd do is, I'll
start by just reading a few
pages, just four or five
pages from the book, the
opening four or five pages,
just to give you an idea of how
a writer might want to think
about opening a book,
which is actually
quite nerdy at some
fundamental level.
Because it really just gets
into the details of this one
experiment.
But you still want to
write it in a way that's
appealing to almost anybody
who wants to pick it up.
And then I have a
set of slides that I
would like to go
through just to tell you
what this experiment is.
Most of you will be very
familiar with this experiment.
It's called the "double
slit experiment."
But it's amazing how much of
this particular experiment
pervades quantum mechanics.
So I want to run you
through a few slides,
just to talk a
little bit about what
it tells us about the big
conceptual issues in quantum
mechanics.
And then we can
have a short Q&A.
So if you don't mind, I'm going
to start reading from the book.
So this is the prologue, the
story of Nature taunting us.
The office is simply the most
uncluttered of any physicist's
office I've ever seen.
There's a chair
alongside a small table
with nothing on it--
no books, no papers, no
lamp, no computer, nothing.
A sofa graces the office.
Large windows
overlook a small lake,
and the trees around
which are bare,
except for a few stragglers
that are holding onto their fall
foliage, defying the approaching
winter in this part of Ontario,
Canada.
Lucien Hardy puts his
laptop on the table,
pointing out that he does
most of his work in cafes,
and figures that all
he needs in his office
is a cafe-like small table
to set down his laptop.
There is the
obligatory blackboard,
taking up most of one
wall of his office.
It doesn't take long for
Hardy to spring up and start
chalking it up with diagrams
and equations, something
that most of the
quantum physicists
I meet seem inclined to do.
We start talking about some
esoteric aspect of quantum
physics when he stops, and says,
"I started off the wrong way."
To reset our
discussion, he says,
"Imagine you have a factory,
and they make bombs."
He has my attention.
He writes two names on
the blackboard, Elitzur
and Vaidman.
He's talking about something
called the Elitzur-Vaidman Bomb
Puzzle.
Named after two
Israeli physicists,
the puzzle exemplifies the
counter-intuitive nature
of the quantum world in
ways that non-physicists
can appreciate.
It confounds physicists,
too, in no small measure.
The problem goes
something like this--
there's a factory that makes
bombs equipped with triggers.
The triggers are so sensitive
that a single particle--
any particle, even a
particle of light--
can set them off.
There's a big dilemma, however.
The factory's assembly
line is faulty.
It's churning out
both good bombs
with triggers and bad
bombs without triggers.
Hardy writes them
as "good" and "bad,"
and quips about the
quotation marks.
Obviously, you have a different
moral perspective on it,
he says.
The task is to identify
the good bombs.
This means having to check
whether the bombs have
triggers.
But examining each bomb
isn't the correct strategy,
because in order to do so, you
will need to shine light on it,
however faint, and that would
cause a good bomb to explode.
The only ones unexploded would
be the duds without triggers.
So how does one
solve the problem?
If it helps, we are
allowed one concession.
We can detonate
some bombs, as long
as we're left with some
good, un-detonated bombs.
From our everyday experience
of how the world works,
this is an impossible
problem to solve.
But the quantum world--
the world of very small things,
like molecules, and atoms,
and electrons, and
protons, and photons--
behaves in bizarre ways.
The physics that
governs the behavior
of this microscopic world
is called "quantum physics"
or "quantum mechanics."
And we can use quantum
physics to find good bombs
without setting them off.
Even with a simple set up,
it's possible to salvage
about half the good bombs.
It involves using
a modern variation
of a 200-year-old experiment.
Called the "double
slit experiment,"
it was first done
in the early 1800s
to challenge Isaac
Newton's ideas
about the nature of light.
The experiment took
center stage again
in the early 20th century, when
two of the founders of quantum
physics, Albert
Einstein and Niels Bohr,
grappled with its revelations
about the nature of reality.
In the 1960s, Richard
Feynman extolled its virtues,
saying that the double
slit experiment contained
all of the mysteries
of the quantum world.
A simpler and more
elegant experiment
would be hard to find, the
workings of which a high school
student can grasp, yet profound
enough in its implications
to bewilder brains like
Einstein's and Bohr's,
a confusion that
continues to this day.
This is the story of quantum
mechanics from the perspective
of one classic experiment
and its subtle, sophisticated
variations, including
one that, as we will see,
solves the Elitzur-Vaidman
Bomb Puzzle.
Whether these variations
are carried out
as thought experiments
by luminous minds,
or painstakingly
performed in the basement
labs of physics
departments, it's
the story of nature
taunting us--
catch me if you can.
So I will read a couple more
pages from the opening chapter.
And this chapter actually begins
by talking about a lecture
that Richard Feynman
gave, which is
one of the most extraordinary
lectures you can see.
It was given in 1964.
And it became a very nice way
to actually open the chapter,
just to talk about
what he was saying.
So Chapter One--
"The Case of the
Experiment with Two Holes--
Richard Feynman Explains
the Central Mystery."
Richard Feynman was still a
year away from winning his Nobel
Prize, and two decades
away from publishing
an endearing autobiographical
book that introduced him
to non-physicists as a
straight-talking scientist
interested in everything
from cracking safes
to playing drums.
But in November 1964, to
students at Cornell University
in Ithaca, New York,
he was already a star,
and they received him as such.
Feynman came to deliver
a series of lectures.
Strains of "Far Above
Cayuga's Waters"
rang out from the
Cornell chimes.
The provost introduced Feynman
as an instructor and physicist
par excellence, but
also, of course,
as an accomplished
bongo drummer.
Feynman strode onto the stage
to the kind of applause reserved
for performing artists,
and opened his lecture
with this observation--
"It's odd, but in the
infrequent occasions
when I have been called
upon in a formal place
to play the bongo drums,
the introducers never
seem to find it necessary
to mention that I also
do theoretical physics."
By his sixth lecture,
Feynman dispensed
with any preamble, even a token
hello to the clapping students,
and jumped straight into
how our intuition, which
is suited to dealing
with everyday things
that we can see
and hear and touch,
fails when it comes to
understanding Nature
at very small scales.
And often, he said,
"Its experiments
that challenge our
intuitive view of the world.
Then we see unexpected
things," said Feynman.
"We see things that
are very far from what
we could have imagined.
And so our imagination is
stretched to the utmost,"
he said, "not, as
fiction, to imagine things
which aren't really there.
But our imagination is
stretched to the utmost
just to comprehend those
things which are there.
And it's this kind of situation
that I want to talk about,"
he said.
The lecture was about quantum
mechanics, the physics
of very small things.
In particular, it
was about the nature
of light and subatomic bits
of matter such as electrons.
In other words, it was about
the nature of reality--
do light and electrons
show wave-like behavior
like water does, or do
they act like particles
like grains of sand do?
Turns out that saying
yes or no would
be both correct and incorrect.
Any attempt to
visualize the behavior
of the microscopic
subatomic entities
makes a mockery
of our intuition.
"They behave in their
own inimitable way,"
said Feynman, "which
technically could be called
the quantum-mechanical way.
They behave in a
way that is nothing
like you've ever seen before.
Your experience
with things that you
have seen before is
inadequate, is incomplete.
The behavior of things on a very
tiny scale is simply different,
he said.
"They do not behave
just like particles.
They do not behave
just like waves.
But at least light
and electrons behave
in exactly the same
way," said Feynman,
"that is, they're both screwy."
Feynman cautioned the
audience that the lecture
was going to be
difficult, because it
would challenge their widely
held views about how Nature
works.
"But the difficulty
really is psychological,"
he said, "and exists in
the perpetual torment that
results from your
saying to yourself,
But how can it be like that?
Which really is a reflection
of an uncontrolled,
but I say utterly
vain desire, to see it
in terms of some analogy
with something familiar.
I will not describe it in terms
of an analogy with something
familiar, he said.
I'll simply describe it."
And so to make a
point over the course
of an hour of
spellbinding oratory,
Feynman focused on
the one experiment
which has been
designed to contain
all of the mystery
of quantum mechanics,
to put you up against the
paradoxes, and mysteries,
and peculiarities of Nature.
It was the double
slit experiment.
It's difficult to imagine
a simpler experiment,
or, as we'll discover over
the course of this book,
one more confounding.
We start with a source of light.
Place in front of
the source a sheet
of opaque material
with two narrow,
closely spaced
slits or openings.
This creates two paths for
the light to go through.
On the other side of this
opaque sheet is a screen.
What would you expect
to see on the screen?
So that's how the book begins.
And I think for the
rest of the talk,
I just want to run
through the experiment,
and point out some of the big
conceptual issues in quantum
mechanics that this one
simple experiment addresses.
So this is the experiment that
was first done 200 years ago.
There's a source of light.
It's shining at an opaque sheet
with two slits cut into it.
And you're asked a
question, what would
you expect to see
on the other side?
Your intuition pretty
much says, oh, I
should just see two strips
of light on the other side.
Actually, the answer
really depends
on what you think is
the nature of light.
And in the 17th century,
thanks to Isaac Newton,
our ideas about
the nature of light
were really due to his
corpuscular theory of light.
Newton said that light is made
of corpuscles or particles.
So if light is
made of particles,
and if you're streaming a
beam of particles at these two
slits, then you expect
a certain result
to come out of this experiment.
And in sort of
thinking about light,
let's just for a moment just
think about, say, particles
that we understand-- particles
of sand, for instance.
So this might be a
sandblaster just blasting sand
at these two slits.
So if, say, the right slit is
closed, what do you expect?
You expect to see the sand
go through the left slit,
and hit the screen right
behind the open slit.
The same thing if the
left slit is closed.
You expect to see the sand
go through the other slit.
And the closed left slit
is obstructing the sand.
So basically, you are seeing the
particles hit the screen right
behind the open slit.
And if you were to
now open both slits,
our intuition tells us that
this is what should happen.
You should basically
see two strips
of particles hitting
the screen on the back
of the opaque screen.
This is not what happened.
When the experiment was
first done in the early 1800s
by an English physicist
called Thomas Young,
he saw something
completely different.
He saw this.
He saw bands of light and dark
appearing on the other side
of the two slits.
So here, think of the screen
as a photographic plate.
So the dark bands are where
most of the light is hitting.
And so it's a negative.
So the dark bands are
where the light is hitting.
And you can see that
there are alternating
dark and light bands.
So there's light.
There's no light.
There's light, no light.
This can only be
explained if you think
of light behaving like a wave.
So the wave hits the two slits.
And then from each slit, two new
sets of waves start coming out.
They spread.
Eventually, they will
interfere with each other.
And the places where
these two sets of waves
interfere constructively,
meaning the crests of a one
wave line up with the
crests of the other,
you get constructive
interference.
And when the crest and
the trough line up,
you get destructive
interference.
So essentially, you get
this interference pattern.
This is absolutely
characteristic of waves.
You can see this anywhere
you see waves, for instance,
with water waves on a
lake or in the ocean.
Now, this idea that light
behaves like a wave kind of
held pretty much
through the 1800s.
And then along came
quantum mechanics.
Early 1900, Einstein was the
first to point out that light,
there are certain situations in
certain phenomena in Nature--
particularly the
photoelectric effect,
which is what he was
talking about at the time--
can only be explained
if you think of light
as being made of particles.
So quantum mechanics says
that all energy is quantized.
Light is a form of energy.
And so light is made of
individual, indivisible quanta.
And these quanta can be
called particles of light.
Now, this same experiment
becomes incredibly confounding.
So if you go back to this, now
imagine that your source here
is beaming, say,
a red laser light,
so light of one frequency.
And we now know from
quantum mechanics
that light is made of particles.
So this is beaming out
individual particles.
Now imagine also that
you can turn down
the intensity of this
laser light to the point
that only one particle of
light is coming out at a time--
just one at a time, maybe
one every five seconds,
one every 10 seconds--
doesn't matter.
But just one particle is
going through that apparatus
at any given time.
And now what do you expect?
Now your intuition
pretty much says
that it should behave
like particles of sand,
because you know
classically, you're
thinking it should go through
one slit or the other.
And it should end up on
the photographic plate
right behind the open slits.
And any guess as
to what happens?
This is quantum mechanics.
Obviously, that's
not going to happen.
You get exactly the same
result, except that this
is what starts building up.
If there is a photographic plate
on the other side of the slits,
and if you're sending
one particle at a time,
in the beginning, it seems
like the particles are randomly
going to at certain
locations on the plate.
But over time, as
the pattern develops,
you see that the same
interference pattern develops.
This is, again, indicative
of some interference
that is going on, except--
and this is something really
important to appreciate--
you are creating a
particle, and you're
detecting a single particle.
And nothing-- when
a single particle
is going through the
double slit apparatus,
it is not interacting
with any other particle.
There's just one particle in
the apparatus at any given time.
Yet an interference
pattern is emerging.
So what is
interfering with what?
So this becomes a really
important question to ask,
and ends up being
the central question
in trying to understand some
of the conceptual issues
with quantum mechanics.
So if you're now shooting
individual photons of, say,
red light of a given frequency
at this particular double slit,
then you get this
interference pattern
at the back, which is
exactly the same that you
saw when there was lots of light
going through the double slit.
So the question is, what
is it that is interfering?
So mathematically,
there is an explanation.
So mathematically, each photon
or each particle of light
is represented by what
physicists call the "wave
function."
It's a mathematical abstraction.
This wave function
is a function.
It's a function
which tells you what
its value is at some
point in space and time.
And this function evolves
according to something called
the "Schrodinger equation."
So there is an
equation that tells you
how this wave function
changes with time.
And mathematically, the
way you model this system
is you let this wave function
propagate towards the two
slits.
It hits the two slits.
It acts exactly like a wave.
It goes through both slits.
On the other side, you have
two sets of waves coming out,
and they interfere.
And you get an
interference pattern.
But you're getting an
interference pattern
of a mathematical abstraction.
What is this wave function?
What has this wave function got
to do with a single particle?
And that is really
the central issue
that this particular
experiment starts addressing.
So we can start asking what
is it that's interfering?
There is a wave function that's
going through the two slits,
and interfering, and
creating an interference
pattern on the other side.
But the wave function is a
mathematical abstraction.
For any system of more
than two particles,
this wave function
doesn't even exist
in normal,
three-dimensional space.
It exists in a
mathematical space
called "configuration space."
It can have a large
number of dimensions,
depending upon what your
number of particles are.
So what is actually going
through the two slits?
And it's very, very unclear
as to what is happening here.
The wave function goes
through the two slits,
a mathematical abstraction.
You can calculate
what the interference
pattern is on the other side.
And then, the
interference pattern
tells you basically the
value of the wave function
at various points in space.
And you can then ask, what
is the value representing?
It turns out it's not
really telling you
where the photon is, or where
the particle of light is.
The value of the wave
function at any point in space
is only giving you
the probability
of being able to find the
photon there if you look for it.
So it turns out that
the interference pattern
created by the wave functions--
there are many,
many regions where
there is a non-zero probability
for the photon to end up in.
So you have a single photon that
is going through the two slits.
It's being represented by a
wave function, which essentially
goes through the two slits,
interferes on the other side,
and on the other side, you
have these various regions
of constructive
interference, which
all have non-zero probability
for the photon to end up in.
For any given photon, when you
send it through the two slits,
there is no way to tell
exactly where it'll end up.
So it's nondeterministic.
You've created a single photon.
It somehow has gone
through the two slits.
On the other side, it's going to
end up in one of many locations
which have a
non-zero probability.
So this wave function
is essentially
a way to calculate what is
the probability of finding
a photon in some location
on the other side.
And it turns out that when
you do a measurement--
in this case the
photon interacting with
your photographic plate
is the measurement--
that measurement somehow
collapses that wave function,
which, until the
measurement happened,
gave you probabilities of the
photon as possibly being--
gave you probabilities
of finding the photon
in many different places.
But the moment you
do a measurement,
when the photon interacts, when
the wave function interacts
with the photographic plate,
the wave function collapses.
The photon is
found in one place,
and not in any of the other
places that it could have been.
So this act of measurement kind
of collapsing the wave function
is a huge issue in
quantum mechanics,
because quantum
mechanics basically
says that it's the
measurement that
is causing the collapse
of the wave function.
But it doesn't actually
define what a measurement is.
Standard quantum mechanics
just divides up the world
into quantum systems
that are being measured
and apparatuses that
are doing the measuring.
But there's no distinction,
mathematically speaking,
as to what constitutes
a quantum system,
and what constitutes a
measuring classical apparatus.
There's also another
mystery that this experiment
highlights.
Now, if you try to
figure out which
slit the photon
is going through,
your intuition is telling you,
come on-- it's a single photon.
It has to go through
one slit or the other.
And say you set up a system
where you can tell you
which slit the photon
is going through,
without destroying the photon.
Then the interference
pattern disappears.
So if you try to
look to see which
slit the photon went through,
the interference pattern
disappears.
If you don't look, there's
an interference pattern.
So all of these
things start leading
to questions about
what is really
happening at that very,
very basic level of reality.
It's very clear intuitively
that the photon can't possibly
be going through
both slits at once.
I mean, you've created
a single photon.
You've detected a single photon.
All your classical
intuition is telling you it
surely is not going
through both slits at once.
But something is going
through both slits
at once, because you are
getting an interference pattern.
So this is the
wave function going
through both slits at once?
But then what is
the wave function?
The function is a
mathematical abstraction.
We have no idea what that is.
It exists in some abstract
configuration space,
and interferes.
But that's just mathematics.
We don't know if that is real.
So if that's not
real, then again,
the question comes
back-- then what
is going through both slits?
So this circular
argument keeps going.
This idea of the wave function
being real or not real,
whether it is actually
representing something
that is happening in reality,
in the sense that it represents
something actual
about reality, it's
part of the ontology
of the world,
or does it just
represent our knowledge
about what's happening?
So is the wave function ontic,
ontological or is it epistemic?
These questions are yet
undecided in quantum mechanics.
We really don't know the
status of the wave function
as to what that really is.
So you can see there just
this one simple experiment.
The moment you try to
understand what's happening,
it completely explodes
this whole business
of what actually is
the nature of reality.
I just want to run you through
one very simple version,
the modern version of this
double slit experiment.
It's called the
Mach-Zehnder interferometer.
And this will lead us to
trying to answer the question
about how do you
detect that bomb which
had light triggers versus
a bomb that had duds.
So this is the
beginning of what's
called a Mach-Zehnder
interferometer.
A photon or light
hits this thing
called a beamsplitter A
beamsplitter is simply
a half-silvered mirror.
Any window pane actually works.
You can see, if you look at a
window pane, some of the light
is getting transmitted and some
of it is getting reflected.
So if you imagine a
laboratory-grade beamsplitter,
it's reflecting
exactly half the light,
and transmitting
exactly half the light.
Half the energy of
the light that's
incident on this beamsplitter
it goes one way, half of it
goes the other way.
And that kind of
works when you're
thinking about a lot of light.
If you just take a
flashlight, and shine it
at the beam splitter,
and half is reflected,
half is transmitted.
That makes sense.
But now, remember,
it's quantum mechanics,
where you're allowed to
talk about single particles
of light.
So now what happens if a
single particle of light
is incident on
this beamsplitter?
Now, we know from quantum
mechanics that the single
particle of light cannot
be divided any further.
It is the quantum of energy.
It is the smallest
quantum of energy.
So turns out, quantum
mechanics says,
that the photon
in this case will
be reflected with
50% probability,
and transmitted
with 50% probability
when it hits a beamsplitter.
So basically, it's either going
to be reflected or transmitted.
And for any given photon, you
can't tell what it will do.
But if you send thousands
and thousands, on average,
half will go one way, half
will go the other way.
So we can now put detectors
at the end of these paths.
And these detectors are
going to click half the time
for the photon being reflected,
half the time for the photons
being transmitted.
So we can now sort of
make this configuration
a little bit bigger.
All that this figure
has done is it
has turned the paths of the
two beams at right angles.
It's still the same.
A photon goes into the
first beamsplitter,
and then ends up
either in detector D1,
or ends up in detector D2.
So if you were to send 10,000
photons into this beamsplitter
one by one by one,
on average, 5,000
are going to be reflected.
5,000 are going
to be transmitted.
And half the time,
D1 will click.
Half the time, D2 will click.
You can do this in the lab.
This will happen all the time.
Here's what happens
when you complete
the Mach-Zehnder interferometer.
Something very, very
intriguing happens.
If you put another
beamsplitter exactly
in the place where the two
beams cross, now if D1 clicks,
if you look at the
previous figure,
if D1 clicks here, if
the detector D1 clicks,
it's very clear that the
photon took the reflected path.
If D2 clicks, it's very
clear that the photon
took the transmitted path.
But in the full
interferometer, now the photon
is reflected or transmitted
by the first beamsplitter.
And it's also reflected
and transmitted
by the second beamsplitter.
So if now D1 clicks, can
you tell which path it took?
Any thoughts?
So there's no way to tell.
I mean, if D1 clicks,
the photon could
have been reflected first
and transmitted next,
or it could have been
transmitted first and reflected
next.
And now, if you send, say, 5,000
photons into this one by one,
what do you expect if
you do the numbers?
Previously, remember, we said
half will-- if we send 5,000
into it, 2,500 will go to D1,
2,500 will go to D2 on average.
We can't tell what any single
photon will do, but on average.
Now what about this now?
Where else would they go?
[INAUDIBLE] classic.
But this is quantum mechanics.
This is a loaded
question already.
AUDIENCE: [INAUDIBLE].
ANIL ANANTHASWAMY: Who said all
of the particles will go D1?
Yes.
So this is the weird part--
all of them will go to D1.
And this very,
very simple device
illustrates just how funky
quantum mechanics is.
What's happening here-- if you
try to model mathematically
what's happening here, the
wave function of the photon--
remember, some
mathematical abstraction,
which we don't know
whether it's real or not--
enters the first beamsplitter.
Now, part of it is
going to be transmitted.
Part of it is going
to be reflected.
And it's going to continue
on those two paths.
And then at the second
beamsplitter, each component--
the reflected component
is again going
to be reflected and transmitted.
The transmitted
component is going
to be, again, reflected
and transmitted.
So if you now look
D1, D1 is going
to be the combination in
terms of the wave function.
We're not thinking of
the photon right now.
We have to explain.
So if you did this
experimentally,
if you just did this in
the lab, all of the photons
are going to go to D1.
None will go to D2.
As long as the path between
the two beamsplitters
is exactly the same, all
of them will go to D1.
None will go to D2.
And that's a really
counter-intuitive result
that you need to explain,
the mathematics explains it.
So basically now,
you have to think
in terms of the wave function.
The wave function has split into
two at the first beamsplitter,
and then split into two again.
Each component splits
into two again.
And then on the way to D1, there
are two components of the wave
function that are recombining.
And on the way to D2, the two
components are recombining.
But it turns out that when
you're going towards D1,
the two components of
the wave function--
one which has been reflected
and then transmitted,
and the other which has
been transmitted and then
reflected--
remember, we're
talking waves, even
though in mathematical space.
These waves are in
phase, because they
have endured the same amount
of reflection and transmission,
so they're actually in phase.
So these two waves
mathematically are in phase,
and they constructively
interfere.
Whereas the waves that
are going towards D2
has endured two reflections
and two transmissions.
So one component is lagging the
other in phase by 180 degrees.
The crests of one wave are
lining up with the troughs.
That's destructive interference.
So in that mathematical
configuration space,
the wave functions
have interfered,
so that all of the
stuff is going to D1,
and none is going to D2.
But remember, this is happening
in abstract mathematical space.
But this is
representing the photon.
So the photon always goes to D1.
None will go to D2.
And you can mess
with these numbers
by changing the length of
the paths between the two
beamsplitters.
But for now, if you
think of them as equal,
then D1 represents
constructive interference,
D2 represents
destructive interference.
No photon will go to D2.
This does not make
classical logical sense,
but that's how the
quantum world works.
And you can only
explain this if you're
thinking in terms of
the wave function,
and what's happening
to the wave function.
But the questions remain--
what is the status of the wave
function?
Is it real?
So if you, for instance, now put
a block in one of these arms,
what do you think will happen?
Now, let's say we
send 5,000 photons
into the first
beamsplitter, but there's
a block in one of the arms.
What do you think might happen?
AUDIENCE: [INAUDIBLE]
ANIL ANANTHASWAMY: Sorry?
AUDIENCE: [INAUDIBLE]
ANIL ANANTHASWAMY: Half, but
what happens to the numbers?
So you send 5,000 into the--
so it turns out that
the block will cut down
the number of photons by half.
But now, the wave function
that is-- so it's cutting down
the wave function component
that's going along one path,
so nothing is going to
progress along that path.
The wave function that
goes along the other path
is now hitting the
second beamsplitter.
But now, there's
no interference,
because there's nothing
coming from the other side.
So now it's just
acting like before--
half of it goes one way, half
of it goes the other way.
So if you send 5,000, you're
right-- half will go to D1,
half will go to D2,
but half of 5,000.
So 2,500 are blocked.
The other 2,500 will hit
the second beamsplitter
and then go half one way,
and half the other way.
This is now showing you that
there's no interference.
Putting that block is
analogous to trying to see
which way the photon is going.
In the double slit, if you
blocked one of the slits,
this is analogous to that.
You're basically saying, I'm
blocking one of the slits.
I know now that the photon has
to go through the other slit.
Well, it does go
through the other slit,
and there's no interference.
In this case, it becomes
a very clear demonstration
of the lack of interference
when you block one slit.
You open both slits, suddenly
all the photons would go to D1.
None of them would go to D2.
So this is showing
you interference,
or rather, this is
showing you the photons'
particle-like behavior.
It's acting like a particle.
There's no interference.
But the moment you remove that
block, the moment you don't try
to see which path
the photon is taking,
the system seems to
behave like a wave,
and you get interference.
So now I want to sort of talk
about how this simple thing can
help you solve the
Elitzur-Vaidman bomb puzzle.
So let me just tell you
about the bomb puzzle again.
What was the question?
The question is, there's a
factory that's making bombs.
And these bombs have triggers
that extremely sensitive,
so sensitive that even a single
particle of light falling on it
will detonate the bomb.
The problem is that the
factory is also producing
duds, bombs without triggers.
So your task is to
figure out which
bombs have sensitive,
functioning triggers and which
are the duds.
Now, in our classical
way of thinking
about this problem, if you
are to look at the bomb
to see if it has a
trigger, it'll explode.
Because looking involves
shining light or something.
You'll have to use some
energy to look at it.
And so even a single photon
will detonate the bomb.
So there's no way classically,
in our classical way
of thinking, no way
to solve this problem.
But you can solve this problem.
You can find out--
you can distinguish the
duds from the live bombs
using this Mach-Zehnder
interferometer.
You're allowed to
detonate some bombs.
So can you now--
so what happened?
Now say I have placed this bomb.
Let's assume that
all of this is being
done in a dark room with
robots, and you're not
worried about blowing up the
bombs because of handling them.
So let's assume that we
can place the bomb right
next to one path, and this
one doesn't have a trigger.
Now you start sending in
photons through this apparatus,
through this interferometer.
What do you expect?
So 10,000 photons are going in.
What do you expect?
Where would the photons go?
There's no difference
between the previous--
there's no difference
between this and this,
because the bomb is just sitting
there, and it has no trigger.
There's no obstruction.
So this should just behave
like a regular Mach-Zehnder
interferometer.
All of the photons
should end up at D1.
None should go to D2.
So you really can't tell
anything at this point.
So let's say you're trying to
do this in a statistical sense.
You say, I'm going to
send a million photons
into this, which you can do in
labs these days very quickly.
All of them will go to D1.
None will go to D2.
That's a very, very
good indication
that you have a dud next
to your interferometer.
Now if you have
a live bomb, live
meaning a trigger
that will actually--
it's placed so that it will
obstruct the photon path.
Now what happens?
Now you start sending
in one photon at a time.
This trigger now is like the
block that we put earlier.
Remember we had this set-up,
where if we put a block,
that block is going to
obstruct half the photons.
So this trigger now
is like that block.
Half the time, the photons
are going to hit this block,
and half the time, the
bomb is going to detonate.
So it'll blow up, blow the bomb.
The bomb will blow up.
So will the Mach-Zehnder
interferometer.
You'll have to rebuild it.
Assume we can do all that.
This is a thought experiment,
so you can do all this.
So half the time, the
whole set-up will blow up.
The other half of the time
is the interesting part.
The other half of the
time, the wave function
is going through the other side.
It's going to the other side.
It hits the second beamsplitter.
And then what happens?
AUDIENCE: [INAUDIBLE]
ANIL ANANTHASWAMY: Yes.
So in this case, half the
photons will end up at D2.
So if you send 5,000 photons
in, 2,500 of them, on average,
will blow up the whole thing.
The other 2,500 will get split
up in the second beamsplitter,
and half of them will go to D2
and half of them will go to D1.
If they go to D1, it's
kind of inconclusive,
because D1 was happening
previously, also.
But if any photon
ends up at D2, that's
a sign that there's a live
bomb in the other path.
But here's the
interesting thing--
you haven't interacted
with the live bomb,
because if you had interacted
with the live bomb,
it would have blown up.
No, but if it goes to D2,
you know there's a live bomb.
You can just pick that
up, and say, OK, this
is what we're going to ship now.
AUDIENCE: [INAUDIBLE] half the
bombs and a quarter of them
are [INAUDIBLE].
ANIL ANANTHASWAMY: Yeah, you
can work out the probability.
So this is the bare minimum.
And you can fine-tune
this experiment
to improve that probability.
But the idea here is something
very, very profound--
that quantum
mechanics has allowed
you to detect the
presence of something
without interacting with it.
These are called
interaction-free measurements.
It does not happen
in classical physics.
You cannot measure something
without interacting with it.
Here, we have physically
interact-- well,
physically is a different term.
Something has interacted
with the bomb.
The photon hasn't, because
otherwise, the bomb
would have exploded,
but something
interacted with the bomb.
And we got information
about the bomb
without actually blowing it up.
So this is an
interaction-free measurement.
This makes the case for the
reality of the wave function.
It's probably the wave function
that is sensing the bomb.
This argument can go
round and round and round.
Yeah.
AUDIENCE: So that makes me think
of the Heisenberg Uncertainty
Principle.
And I can't remember
from [INAUDIBLE]
is that related to Newtonian
physics or [INAUDIBLE]??
ANIL ANANTHASWAMY: Heisenberg's
Uncertainty Principle
is very much-- we will
come back to questions.
So why don't we
just wait for the--
I'll just finish up, and
then we'll come back.
In fact, I'll just talk
about that principle.
So this is an
example of how this--
this is a very special case
of the double slit experiment.
This is the experiment
that is done
in labs on optical benches.
It's very, very easy to
configure, and work with.
And much of when
physicists say that they're
doing a double slit
experiment these days,
they are more often
than not building
a Mach-Zehnder interferometer
and working with it.
And there are variations
of this in many forms.
And it's amazing how this
one simple experiment
allows you to understand some
of the very, very basic issues
in quantum mechanics,
like superposition.
So superposition is this idea
that we just talked about--
that the photon can end up
being in two paths at once.
It doesn't make any sense.
So there's a mathematical
way of representing it.
The way of talking
about it is to say
that the photon is in a
superposition of taking
both paths.
It's not the same
as saying the photon
is actually taking both paths.
It's just a way of
saying that the quantum
states are such that it behaves
as if it is taking both paths.
So it's the wave function
that's taking both paths.
But we don't know what the
ontological status of the wave
function is.
So it's not the same
as saying the photon
is taking both paths.
The uncertainty principle--
these experiments allow you
to talk about the
uncertainty principle,
which is the simple idea that
there are certain parameters
in quantum mechanics, in
particular the position
and momentum of a particle,
you cannot measure both sort
of accurately.
If you measure one
very accurately,
you mess up the other one.
So the more precisely
you measure the position
of a particle, the more
uncertain the momentum,
and vice versa.
So that's the
uncertainty principle.
There's complementarity
or wave-particle duality--
complementarity being
the idea that Nature
has two faces, the wave
nature and particle nature.
And you can only observe
one or the other.
And what you observe
depends on the apparatus
that you've built.
So we saw that there were
different configurations
of that interferometer
that you can build,
which will either show you the
particle nature or the wave
nature.
But you can't see
both at the same time.
Determinism versus
non-determinism-- classical
physics is deterministic.
So if you throw a ball, and
you know all the forces that
are acting on it,
you can predict
exactly where it will go and
the trajectory of the ball.
Whereas here, when
you're talking
of a photon going
through the double slit,
you can only talk in
terms of probabilities.
You can only assign
probabilities
to where it'll end up.
There is no clear trajectory
that you can map out
that the photon takes.
And basically, this whole
system is non-deterministic.
And you can talk
about determinism
versus non-determinism in the
context of the double slit
experiment.
The biggest problem, really, is
this thing called the collapse
of the wave function.
Remember, the wave function
goes through both slits,
interferes, and
on the other side,
you get this wavy thing that
tells you mathematically
what are the chances of
finding the photon here
versus here versus here?
And if you did the
measurement, it'll
end up in one of those places.
Until you did a measurement,
the probabilities
existed in this wave
function, but the moment you
do the measurement, the
wave function collapses,
and peaks at one point.
The probabilities
go to 0 everywhere.
And it becomes 1 at the
point where it's measured
or where it's found.
And there is nothing
in quantum mechanics
that tells you what
this collapse really is.
It's just a postulate.
It's a postulate.
It's an axiom in
quantum mechanics
that says when you
do a measurement,
the wave function collapses.
We don't know what the
wave function really
is in terms of its reality.
We don't know what the actual
process of collapse is.
And this thing is called
"the measurement problem."
The idea that measurement
causes collapse,
without being able to define
what a measurement really
is, is the cause of many,
many conceptual problems
within quantum mechanics.
And a lot of the alternatives
to standard quantum mechanics
that you hear about
are alternatives
that are trying to solve
the measurement problem.
There's realism versus
non-realism-- realism being
this idea that there's
an objective reality that
exists independent
of observation,
that you don't need to
be observing in order
to know that there is
a reality out there.
Quantum mechanics, at
least the standard way
of thinking about quantum
mechanics, questions that.
The photon, in
this case, doesn't
have a reality until
you observe it,
because there is nothing
in the mathematics that
captures the trajectory
of the photon
from the source to the detector.
That is, you cannot
calculate the trajectory.
It could end up-- it could have
five different trajectories,
or any number of trajectories.
There's no way to tell.
The only reality
ascribed to the photon
is at the point of creation
and the point of observation.
So in one way of thinking about
standard quantum mechanics,
it actually denies
reality until observation.
So it is an observer-dependent
theoretical framework.
I mean, there are lots
of issues with this.
People debate this
endlessly, over and over
again as to is that
what it's really saying?
But one way of interpreting
standard quantum mechanics
is to say that it
is anti-realist.
Then the questions
about the wave function,
which I just told you
about-- is it really
something that exists?
Or is it representative of
something that actually exists?
Or is it just our knowledge,
half-baked knowledge
about what's happening?
Is it epistemic or is it ontic?
I haven't even touched
upon the other big issue
in quantum mechanics.
But the double slit
experiment allows
you to talk about
that, also, which
has to do with entanglement
or non-locality--
the idea that if there are
two quantum systems that
have somehow interacted
at some point,
once they have interacted,
they are now represented
by the same wave function.
And this wave function
starts spreading,
which means that maybe the
particles are going apart.
And if you do a measurement
on one particle,
you can instantly influence the
state of the other particle,
even if these things
are kilometers apart.
And that cuts against
the idea of locality,
which is the bedrock
of relativity,
which is the idea that what you
do in one region of space-time
cannot influence something else
in another region of space-time
any faster than
the speed of light.
Quantum mechanics apparently
suggests that there
is instantaneous influence.
Action in one region can
instantly influence the state
of some other system, and
faster than the speed of light.
So again, there are debates
about whether that's really
what it's saying.
But there is enough proof that
the underlying quantum reality
is indeed non-local.
And the double slit
and its variations--
I just showed you one, the
Mach-Zehnder interferometer--
there are many, many
experiments that have been done
that play on this principle.
There's the Wheeler's
Delayed-Choice Experiment.
I don't think we have
time to go through.
I'll just name them, and when
you see them, you'll realize--
when you see them in
literature elsewhere-- you'll
realize that these are all
variations of the double slit--
the Quantum Eraser Experiment,
Delayed-Choice Quantum Eraser,
Interaction-Free Measurements
we just talked about.
There are experiments
that have actually
tried to measure
particle trajectories.
I actually told you
just now that you
can't talk about trajectories
in standard quantum mechanics.
But there are other
interpretations, other quantum
formalisms, that allow you
to talk of trajectories,
and there are ways in
which you can measure them.
And they are very controversial,
but nonetheless, you
can do double slit
experiments where
you can map these trajectories.
You can probe the divide between
the quantum and the classical.
Is the world quantum
all the way through?
Or is there some divide where
the quantum world gives way
to the classical world?
We don't know the
answer to that yet.
And there are a whole
range of other things
you can do that probe
sort of conceptual issues
in quantum mechanics, all using
the double slit experiment.
And my entire book is
basically an exploration
of how this double slit
experiment has been
used for all these purposes.
And I talk about five
interpretations--
the Copenhagen interpretation,
which is the standard quantum
mechanics interpreted by
the people who started out
in Copenhagen, Niels
Bohr, Werner Heisenberg,
and a whole bunch
of other people--
Wolfgang Pauli--
all these people
who are involved in an
interpretation which
is now called the
"Copenhagen interpretation."
There's the De Broglie-Bohm
interpretation,
which is a very different view
of the quantum world, which
basically says the quantum world
is both a wave and a particle.
I don't think we have time
to go into the details.
There are collapse theories.
So I talked about how the
collapse happens because
of measurement, and
it puts observers
at the center of everything.
But there are theories
which remove the observer.
They basically cause collapse
stochastically, and then lead
to the same predictions.
And then there are people who
take the wave function really
seriously.
They basically say that the
wave function splits, and never
collapses.
And each splitting wave
function is giving rise
to a different world.
So essentially,
every time a photon
goes through a beamsplitter
and goes left and goes right,
you have created
two universes-- one
universe in which
the photon went left,
one universe in which it
went right, and so on.
And then there's
something called
"quantum Bayesianism,"
which is actually
quite a complicated
one to discuss easily.
But anyway, these are
the interpretations
I deal with in the book.
So I think I'll stop
here, and take questions.
I hope that was informative.
Thank you.
[APPLAUSE]
AUDIENCE: Much of what
you spoke about, I
think, the kind of
questions that were raised,
but probably I don't even--
probably, say, back
in the '50s or '60s.
What has happened since then?
ANIL ANANTHASWAMY:
Good question.
So since the mid '30s,
late 1920s and early 1930s,
was when the standard
formulation of quantum
mechanics got formulated.
So people like mainly due
to von Neumann, Paul Dirac,
and others.
So the standard quantum
mechanics that exists
is basically due to
them, that by mid '30s
was pretty much cast in stone.
And then-- but these conceptual
issues, like you say,
have been around.
I mean, they were around
even before 1950s.
Einstein was arguing
against these things
throughout his career
in quantum mechanics.
Remember, he's one of the
founders of quantum mechanics,
even though people don't--
people ascribe to him--
his greatest achievements
are usually thought of as
the theories of relativity.
He is one of the founders
of quantum mechanics.
And he had serious issues
with these sort of questions
that were raised just now.
They haven't been solved.
So the issues remain.
The amazing thing about
standard quantum mechanics
is, it is extremely successful.
These probabilistic predictions,
this mathematical framework
that is used to make
probabilistic prediction
is the most successful physical
theory we have in everything.
All of the stuff
that is happening
right now with
electronics is happening
because that theory works.
But nonetheless, it raises
fundamental questions
about the nature of reality.
We don't know.
And so 1950 was the beginning
of David Bohm's ideas.
1951 was when he came up
with his Bohmian mechanics.
But that has a precursor.
It goes back to de
Broglie in 1927.
So the theory now is
called the De Broglie
bomb, where you have
a particle which
is being guided by a wave.
And the wave is real
in Bohmian mechanics,
except that again, it
doesn't move in 3D space.
It moves in this mathematical
configuration space.
But in Bohmian mechanics,
it is described reality.
It is part of the
ontology of the universe.
And somewhere in the 1980s,
collapse theories came about--
so this idea that
the wave function
can collapse spontaneously,
stochastically,
without observers,
without measurement.
And then there's Penrose,
Roger Penrose's ideas,
which I didn't touch upon.
It's not really
mainstream, but he
has some very interesting
ideas about why gravity needs
to be brought into the mix.
So when you have two
masses in superposition
of being here and
here, his argument
is that these two masses will
curve space-time differently.
And then the two
curvatures of space-time
will also be in
superposition of being
in two different curvatures.
And that's unstable.
And he figures out a reason--
he admits himself that it's
kind of rough calculations,
but this instability of the two
configurations of space-time
will lead to a
spontaneous collapse.
And of course, small particles
will take forever to collapse,
whereas something
larger, like a cat,
will collapse immediately
to either one or the other.
Then there's
quantum Bayesianism,
which is very recent--
last 10, 15 years.
So it's happening.
The point is that these
issues are not resolved.
Because all of these
formulations or interpretations
make exactly the
same predictions.
They have to make the
same predictions in order
to tally with experiments.
So right now, experimentally,
you cannot distinguish between
these formulations.
So Bohmian mechanics and
standard quantum mechanics
make exactly the
same predictions.
But they have a
very different view
of what the
underlying reality is.
Anyone else?
AUDIENCE: I guess
following up on that,
are any of these
interpretations testable?
Or are they always just
going to be pure guesses?
ANIL ANANTHASWAMY: At this
point, they're not guesses.
They are mathematical.
They're trying to-- so Bohmian
mechanics, for instance,
the underlying
reality is considered
to be particles that are
being guided by waves.
These waves are considered
real, except the waves
more in configuration space.
And the mathematics
is formulated
to make exactly the same
predictions as standard quantum
mechanics, because otherwise
it wouldn't be a valid theory.
So right now, there's
no way to distinguish
between standard
quantum mechanics
and Bohmian mechanics.
Standard quantum mechanics,
the other advantage
is that it has actually
been pushed along.
It has been combined
with special relativity
to become quantum field
theory, and so on.
It's proving much harder to do
that with Bohmian mechanics.
So there are other
issues that happen
with these different
interpretations that
can lead to people believing in
them or not believing in them.
But right now, I don't want
to call it a matter of faith.
I mean, it is solid mathematics
in all of these things.
But they are not
empirically distinguishable.
Except for collapse theories.
Collapse theories do
make a prediction.
They predict where the
quantum classical divide lies.
So the collapse
theories basically
point out that if the mass
of the system that you're
looking at gets beyond
a certain point,
it will spontaneously collapse
within a certain time frame.
And so now, you can imagine
doing the double slit
experiment with larger
and larger entities.
So starting with
electrons, you can then
go to atoms, molecules, to see
if you get the interference
pattern.
And the moment the interference
pattern disappears,
it means that the quantum
object that you're sending
through the double slit
has collapsed in such a way
that it's only going
through one or the other,
and it's not
interfering anymore.
So those experiments
are being done.
They have actually managed
to send C-60 molecules--
60 carbon atoms--
through this double slit.
It interferes.
The largest molecule
that has been
sent, so far,
through a double slit
has, I think, 800 atoms or
10,000 atomic mass units.
These are massive molecules.
And they will go to the
double slit and interfere.
They behave as if they're
going through both.
So the quantum classical
boundary has not yet been seen.
But collapse theories
do make predictions
that are not quite within
reach of experiments,
but maybe in another
five, 10 years.
AUDIENCE: Thank you.
ARNO: We should take further
questions after giving people
a chance to leave.
There are copies of
the book available,
if you would like to pick
one up on the way out.
ANIL ANANTHASWAMY:
Thank you very much.
Thank you.
[APPLAUSE]
