Bon soir.
My name is Raymond Laflamme, I'm on the faculty
here at the Institute for Quantum computing,
and welcome all of you to the Enangled: The
Series, a presentation that explores the intersections
of quantum information science and technology
research and a range of contemporary topics.
Many of you that have come to the Institute
for Quantum computing have heard that the
goal of the institute is to harness the properties
of quantum mechanics, turn them into tools
or technologies that can be useful.
But there's more to quantum mechanics than
just devices and widgets.
There's a profound understanding of the world
around us.
And this is what we're gonna hear about tonight.
We're incredibly lucky to have a wonderful
speaker, somebody who appeared recently in
?? Scientific, in the ????. Talks, two years
ago on the hundredth anniversary of ??? Appeared...Institution in the UK
and many more, if I list of all
them then you'll still be here in an hour or two,
so we'll stop here and welcome Faye
Dowker, Professor of Theoretical Physics at Imperial College
Professor Dowker did her PhD with Stephen
Hawking, graduated in 1990, and did a postdoctoral fellowship
in Fermilab, University of California Santa Barbara,
Cal Tech, and then took a position of lecturer
at Queen Mary University of London and joined
Imperial College in 2003 and became a professor
of theoretical physics. So join me to welcome Professor Dowker.
Thank you Raymond for that introduction and
good evening everyone.
I'm going to be presenting an argument to
you tonight, I'm going to argue in favour
of this claim that I'm making up here that
in our quest to understand the quantum world,
we must analyze and question the role of "logic"
in physics.
Now since I'm going to be presenting an argument,
I'm tempted to say logical argument,
but it'll be up to you to decide whether it's logical
or not.
I am, it's important to me that you follow
the argument and that you're able at the end
to come to a conclusion about whether or not
you agree with my claim.
And so I invite questions during the talk,
so that will help you, help everyone, to make sure
that you understand the steps that I'm
taking in the argument, and so please,
if you would like me to clarify something, or
go into something, or repeat something,
then please do let me know.
I would like this to be more of an exchange,
an interaction, and more of a conversation
between us than just simply me standing here
and talking at you.
So, before I start my argument, I need to
confront directly a reason that some people,
and in particular some of my colleagues, might
be a little hesitant, wary, of
questioning the role of logic at all.
Because, to question logic might suggest that
we're going to be illogical, and to be illogical
is a bad thing.
No one wants to be illogical, and, you know,
Spock's looking a little nervous there,
a little concerned.
We don't want to be illogical, we want to
be able to communicate with each other,
we want to be able to to understand the world
and understand each other.
What I mean, what I'm going to mean, by logic,
is rules for deducing correct statements about
the physical world from other correct statements
about the physical world.
And when you put it that way, clearly that's
not something we want to abandon, because
that deducing correctly about the physical
world from other correct statements about the physical world,
that's an integral part, a major part of science, so we don't want to get rid of that.
What I am going to argue, though, is that
we have to abandon a particular set of such rules.
And these rules are often referred to as rules
of inference.
So I will describe for you a set of rules
of inference that I claim we must give up
if we want to talk about, if we want to get
a picture of, the quantum world.
Now, when I show you these rules and I tell
you what these rules are, you might have difficulty
grasping them, even recognizing what they
are, that they, recognizing that they are rules of inference
And the reason for that is that we have actually
internalized them to such an extent that we
don't recognize that we're making these assumptions.
And then I'm going to tell you that we must
abandon these assumptions.
So it's very hard to give something up if
you don't know that you, give up some assumptions
if you don't know that you're making them.
So, in the end, I will want, I'll be asking
you to decide for yourselves whether I've
made a convincing case that you should, that
we should be giving up on these rules, these
rules of inference.
And at the end of my talk I'm going to present
to you a parable, it's called "the parable
of the quantum pie eater," and your response,
the way you feel about that parable,
will perhaps help you to decide whether or not
you're comfortable with giving up on these
rules of inference.
That's later, for the end of my talk.
So let's get started.
I will start with two experiments, two quantum
experiments.
The first one is one of the most iconic experiments
in physics, the so-called double slit experiment.
Here's a cartoon of the double slit experiment.
And it takes the form of a source of electrons,
so that could be a wire that you heat by running
a large current through the wire so it gets
very hot, the electrons boil off the surface
of the wire, and you apply an electric field
which accelerates the electrons toward this
glass screen.
And if an electron hits the screen at a particular
point, it causes a flash of light called a scintillation
And let's suppose that our source of electrons
is so weak that it's emitting electrons one
by one, so one at a time an electron will
pass through this apparatus and hit the screen
causing the scintillation.
And we can track, we can make a record of
the positions on the screen where the scintillations
occur, so we can just place a dot on the screen
whenever there's a scintillation, and then
the pattern, the dots, build up over time
as more and more electrons go through the
apparatus one by one.
Between the source and the screen we place
a metal plate that the electrons cannot penetrate,
and in the plate we make two holes to form
two slits, double slit - double slit experiment
- so electrons must pass through the slits
in order to reach the screen, if they actually
hit the metal then they are absorbed and don't
get through.
Ok, so the question is what is the pattern
of dots, the pattern of scintillations, that
builds up on the screen as the experiment
proceeds?
So after many many runs, many electrons, what's
the pattern look like?
Well, we can ask a simpler question, a simpler
experiment, which is the single slit experiment.
So we block one of the slits and the electrons
now have to pass through the single remaining
open slit in order to get to the screen, and
we do many runs of the experiment, let many
electrons through, what does the pattern look
like?
Well, the pattern looks like this.
So the dots are pretty uniformly spread over
the, it'll just get thicker and thicker as
more and more electrons build up, and they're pretty
uniformly spread over the screen.
That's what happens in the electron pattern
when you have one slit open.
You can do the, you can cover the other slit
so that it's the opposite, the other slit
which is open and the other slit is blocked,
and again the pattern, run the experiment
again and the pattern will look something
like this.
Ok, so now let's open both slits and let the
electrons run through, what does the pattern look like now?
The pattern looks like this.
So the scintillations form bands of places
on the screen where the scintillations occur,
and then empty bands where there are no scintillations,
and then a band where the scintillations bunch up,
and then no scintillations, scintillations
here, no scintillations - you get the strip-y
effect in bands.
And if you think about it, that is very very
odd, so there are positions on the screen,
for example this empty position here, that
electrons can get to with one slit open, so
they can go through that slit and get to that
position on the screen, but if you open the
other slit and give them another way to go,
they can't get there anymore, they don't they
don't go there anymore.
They avoid this position if they've got two
ways to go, but if there's only one way for
them to go then they can go there.
Keep that in mind.
Now let's look at our second experiment, that's
an experiment very closely related to this one,
which is an experiment that Martin Laforest
does during open days, and outreach events
here at IQC, this is something that's here
in this building.
It's a ... and interferometer, and this is
a birds eye view of it, so these are components
which are screwed onto a flat table top, we're
looking down on it.
And here is a cartoon of that experiment,
so again, its a birds eye view of the experiment,
looking down on top of the table.
And the components of the experiment are a
single photon source here, which sends a photon
in through this direction the arrow shows,
and that photon - so, again, this is a one
particle at a time experiment, this is one
photon at a time through this apparatus.
The photon hits this yellow thing, which represents
a half-silvered mirror, or beam splitter,
and the photon can either reflect off the
mirror and go down this green path or go through
the mirror and go along this red path.
If it goes on the green path - this blue thing
here is a mirror and this blue thing here
is a mirror, an ordinary mirror - it will
bounce off this mirror, go along here,
and then hit another half-silvered mirror or beam
splitter, at which point it can either, again,
go through or reflect.
If it goes through, it enters a detector,
which I call "detector one," and just for definiteness,
let's say we rigged up the detector so that when it detects
the photon it clicks.
So if the photon goes through here into detector
one, the detector one will make an audible click.
And if it reflects off this half-silvered
mirror then it goes down to "detector 2" here
and detector 2 will click.
And similarly, if the photon goes through
the half-silvered mirror and along the red
path, it bounces off this mirror up here,
ordinary mirror, down here, and again has
a choice of going down to detector 2 or reflecting
and going to detector 1.
So that's the experiment, we can do the same
trick that we did before with the double slit
experiment, which remember was to block one
of the slits, so get rid of one of the options
that the particle has.
So in this case, to get rid of one of the
options the particle has, we can block off
this green path, so we just put something
here to block the photon, to absorb the photon
as it goes along the green path.
And if we do that, then the experimental results
are that 50% of the time, so for roughly half
of the runs, the detectors don't fire at all.
And that suggests that at this point, at this
moment of choice, there's a probability of
half of the photons being reflected and going
down here and being blocked, and so it just
doesn't reach the detectors at all.
And probability of half of it going through
the half-silvered mirror or the red path
and then reaching one of the detectors.
In the runs where one of the detectors does
fire, if you just consider those runs, so
you ignore the runs where one of the detectors
doesn't fire, in other words one of the runs
where the photon is blocked, half the time,
roughly 50% of the time, detector one will
fire or click and half the time detector 2
will click.
And that strongly suggests that when the photon
makes it through along the red path,
when it has a choice here at the half-silvered
mirror, it has a probability of half going
through detector 2, probability of half being
reflected off to detector 1.
So the data from this simpler experiment where
we block off one of the paths is very suggestive
of the path of the photon having a choice,
50/50 are going through or being reflected here,
or going through or being reflected here.
Ok, so let's again give our photon the two
choices now.
So we'll unblock the other path.
What's the experimental data now?
Now, the photon can still go along the red
path, but now we've given it the green path
to go along too, what's the data?
You would expect that 50% of the time it would
fire detector 1,
50% of the time it would fire detector 2.
That's not what happens.
What happens is that detector 2 never triggers,
it never clicks.
100% of the time, every single run, the photon
will end up in detector 1.
It just never gets to detector 2.
It will only go to detector 1.
And again, that's very odd.
Something that the photon could do when it
only has one way to go, which is reach detector 2,
it can no longer do when it has two ways
to go.
So it has the original way to go, it still
has the red path it can go on, but now you
give it another option, the green way, it
can no longer get to detector 2.
Now what is going on, what is going on in
the - yes?
"Is 1 and 2 arbitrary?
Is is sometimes that it'll ... 2 and ... goes
to 1?"
You can set the experiment up so that100%
of the time it goes to 1 and it just
never goes to 2, if you fiddle with the experimental
details, that you can put what's called a
phase shifter, other bits of equipment you
can put here, then you can fiddle it so that
it only will turn up in detector 2, but in
the simple set up that we've got here, it
will only ever go to detector 1, it won't
go to detector 2.
Yup, good question.
Any other questions?
Ok, what's going on?
What's going on in the double slit experiment
and what's going on in the interferometer experiment?
Of course that's exactly the right question,
because physics is all about trying to work
out what the bleep is going on.
And this is a quotation from a spoof Brian
Cox video on YouTube, some of you may know
Brian Cox is a British particle physicist
who is an excellent communicator of science,
he's made many tv series about cosmology and
astrophysics and other other sciences,
and this spoof is pretty funny.
Actually, this is something that probably
the real Brian Cox would also agree with,
but the sentiment anyway.
So physics is all about trying to work out
what is going on.
What is going on in our interferometer experiment?
So I'm going to concentrate on that experiment
and also the double slit.
So here's our interferometer experiment.
What are we interested in?
We're interested in the firing or not of detector
2.
Now the clicking of detector 2 is an example
of an event, it's something that takes place
at a specific place and time, and it's something
that could happen,
and it either does happen or it doesn't happen.
So let me say that again, an event is something
that can take place at a particular place
and time, it could happen, and when all is
said and done,
it either has happened or it hasn't happened.
So when you do the run of the experiment,
before hand you know that detector 2 could,
its something that could happen, it could
trigger, could click.
You do the run, and it either does happen
or it doesn't happen.
So an event either happens or it doesn't happen.
Let me give you another example of event,
so event is going to be a very important concept
for my argument.
So another example of an event, something
that could happen that takes place at a specific
place and time is it rains in Waterloo tomorrow
between 1:00pm and 2:00pm.
That's an event.
And tomorrow evening, we will know.
Either it did rain, either that event happened,
or it didn't happen.
So it's something that could happen and it
will happen or it won't happen.
Another event is, an example of an event is
the ... girls who are my latest favourite
thing, the ... girls will win the gold medal
in the women's curling at the Winter Olympics
in Pyeongchang, so that's another something
that could happen and it either will happen or it won't.
Now there's an approach, a framework for quantum
theory which is based on this concept of event,
and this framework is closely associated with
the particle physicist Richard Feynman.
And he set out this approach to quantum theory
applied to quantum electrodynamics,
which is the theory of photons, interacting photons
and electrons.
And he did that in a series of lectures that
he did, public lectures, that he gave in 1985,
and they're collected in a small volume called,
it's just called QED, Quantum Electrodynamics,
and it's an excellent book, I thoroughly recommend
it.
And he describes the physics in terms of events,
things that can happen in a particular position
in space and a particular time and will, either
does or doesn't happen.
And he also describes the physics in terms
of another concept which is that of history.
A history is a particular detailed way in
which an event can happen.
So for example, let's consider our event of
rain in Waterloo tomorrow.
A history, an example of a history, is there
will be exactly 200,000 raindrops that fall
in this specific pattern, and the temperature
will be 2 degrees Celsius, and the wind speed
will be 5km per hour.
That will be a precise, detailed description
of the weather pattern in Waterloo tomorrow
in which it's raining.
So it corresponds to the event, but it's a
much more detailed thing.
It tells you much more than just it's raining.
Another history that corresponds to the event
of it is raining in Waterloo tomorrow would
be there's 5,298 raindrops that fall in this
particular pattern and the temperature is
such and such, and the wind speed is such
and such.
Of course, there are many, many, many histories
that correspond to the event of
it's raining in Waterloo tomorrow.
What about our other event, which is 
the one of interest to us in our quantum experiment,
the detector 2, detector 2 clicks.
Well, for that particular event, there are
only two histories.
The two histories are - let me go back to
our picture - the two histories are that correspond
to detector 2 clicking are the photon goes
along the red path, goes through the half-silvered
mirror, ends up in detector 2 and detector
2 clicks.
The other history that corresponds to the
event of detector 2 clicking is the photon
goes along the green path, reflects off the half-silvered mirror, entered detector 2 and detector 2 clicks.
So that's a lot simpler, there are only 2
histories that correspond to the event detector 2 clicks.
So event and history, so in Feynman's lectures
on QED, he frames the whole understanding
of what's going on in terms of these two concepts.
Feynman explains how quantum theory teaches, tells us how to calculate probability that an event happens.
So an event could happened after the fact
it either has happened or it hasn't happened,
but before it happens you'd like to know how
likely it is.
And Feynman tells us how to calculate the
probability of any event.
And the rule is the following: you take your
event, and you find all the histories that
correspond to it, all the detailed ways in
which that event can happen.
Quantum theory assigns to each of those histories
a number called the amplitude of that history,
there are specific rules that quantum mechanics
gives us to find what this
number is for each of the histories.
You take those numbers for all the histories
that correspond to that
event and you add them all up, and then you
square it, and that's the probability.
Now you might say, well that's a really bizarre
thing, who ordered that?
And you would be not alone in thinking that,
pretty much everyone who hears these rules
for the first - these rules of calculating
probability - for the first time think that's
not the way I would design a theory if I was
starting from scratching just, you know, sketching
out how I would, how I would make the rules
of physics work.
That's not what I would think of the first
thing.
And the second thing you would think of is,
well, why?
Why, why is this rule the right rule?
And again, you wouldn't be alone in thinking,
in asking that question why.
What we do know is that this works.
It works in giving us the correct probabilities
of events which are outcomes of experiments
that - quantum experiments - that we'd do
in the lab.
So for example, here's our interferometer
experiment again, we know that detector 2
never clicks, and this rule will corroborate
that.
Before we do the experiment Richard's calculation
will calculate that the probability of this
event with detector 2 clicking is zero.
And that's because when you follow the rules
you find that the amplitude of the - there
are two histories that correspond to our event
of detector 2 clicking, they're going along
the red path or going along the green path,
and when you follow the rules you find that
the amplitude of going along the red path
is equal and opposite to the amplitude of
going along the green path.
So they cancel each other.
So the sum of these two amplitudes is actually
zero, and zero squared is zero,
so the probability of the event is zero.
And that agrees with the experimental results,
detector 2 never clicks.
Now this framework of events and histories
is often called the Sum-Over-Histories for
obvious reason, because here you're summing
over the histories that correspond to the
event to give you the probability.
And with it, with this framework, with these
concepts of history and event, we have everything
that we need in order to explore the role
of logic in quantum physics.
And to do this, to set out these rules of
inference, I'm going to use a very useful
representation of events and histories which
may be familiar to some of you, but I'll explain it.
So this representation is in terms of something
called Venn diagrams, if you haven't heard
of those I'm going to explain what Venn diagrams
are.
This is a representation of events and histories
that correspond to the physical system of
weather in Waterloo tomorrow between 1:00pm
and 2:00pm.
Each of these red stars represents a history,
now of only...(counting)...so there are way more than
eleven histories, the detailed weather patters
for the weather in Waterloo tomorrow,
but I've just chosen eleven representative ones.
So just bear in mind that are also things
that I haven't shown.
So here they are, each one corresponds to
a detailed weather patter, detailed description
of the weather in Waterloo tomorrow.
And this circle represents the event "rain"
and what that means is that these five histories
which fit inside that circle, in all of them
it's raining.
So each of these has a certain number of raindrops,
and more than that, the histories which lie
outside the circle don't have rain in them,
so these histories correspond to weather patterns
in which it's not raining.
So every history in which it's raining is
in this circle, and every history in which
it's not raining outside the circle.
Here's another event, which is wind, it's
windy.
And all the histories in which it's windy
are inside that circle, and all the histories
in which it's not windy are outside, so this
one, this one, this one...They're outside the circle.
It's not windy.
So this is a Venn diagram, it represents events,
which are these regions within the diagram,
these circles, and histories, which are these
stars which lie inside or outside these regions.
Are there any questions about that?
That will be familiar to some people who've
seen this concept of Venn diagrams.
Ok, and what about our other physical system?
The interferometer experiment?
Well, here we many fewer histories.
There is the event which is detector 1 clicks,
and there are two histories that correspond
to that, that is going on the green path and
then going through horizontally here into
detector 1, and there's a history which is
going along the red path and bouncing off
the half-silvered mirror and going into detector
1.
And then there is the event which is detector
2 clicks, and again that corresponds to two histories.
So the Venn diagram for this case is much
simpler.
There's four histories, this region over here corresponds to detector 1 clicks, that's the event, detector 1 clicks.
There are only two histories in it.
This is going along the red path and detector
1 clicking, this is going along the green
path and detector 1 clicking.
This event, this region, corresponds to detector
2 clicks, and here is going along the red
path and detector 2 clicks, this is going
along the green path.
That's much simpler, much less going on.
Now, this Venn diagram depiction of these
events allows us to easily build, construct
new events from the ones we already have.
So, for example, the event "it's raining and
windy" is perfectly comprehensible, and that
corresponds to the region which is the intersection
of this circle with that circle, so it's this
lozenge shape thing, like that.
So this is rain and wind, and the histories
in that region, in each of those it's raining
and it's windy, because this star here, this
history is in the event rain, so it's raining
in that history, and it's also in the event
wind, so it's windy in that history, so it's
rainy and windy for that history.
And in none of the other histories is it both
raining and windy.
So it's only in this intersection region that
the histories correspond to rain and wind.
So this event, rain and wind, is this intersection
of the event rain and the event wind.
What about if you're interested only in whether
it's raining or windy?
You've got a bad cold, you don't want to do
out if it's raining or it's windy.
So, in that case, the event corresponds to
this region, which is called the union of
the event rain and the event wind.
So in each of these histories it's either
raining or it's windy, and for any of these
histories you're just not going to go out.
So this is a new event, rain or wind, and
it corresponds to these instances.
So if, for example, in these histories out
here, it's neither raining nor windy,
but in these histories it's either raining or
it's windy.
And finally, another event that you can construct
from the events that we already have is not rain.
And not rain is the region of this diagram
outside the circle for the event rain, because
in all of these histories it's not raining.
So these histories all correspond to the event
not rain.
So this Venn diagram picture gives us a nice representation of events and events that you can construct
from events that you've already had.
So here's a list of some of the events.
There's rain that will either happen or not
happen, wind either happens or it doesn't happen,
rain or wind either happens or it
doesn't happen, rain and wind that happens
or it doesn't happen, not rain either happens
or it doesn't happen, below freezing that
either happens or it doesn't happen, it's
below freezing and it's windy that either
happens or doesn't happen, you get the picture.
Every single possible event that you can think of for the weather in Waterloo tomorrow will be in this list.
Yes?
"I missed something earlier, so if the way
the.. illustration based on histories, so
so there must be a .. because in the experimental
set up you have ... so how can we now compare
a random history with ..."
So there's nothing
periodic about the weather, well apart from seasonal variation.
At the moment I'm just talking in general
about the concept of events I'm not specifically
referring to the quantum experiment, I'll
discuss the quantum experiments also, but
for the moment let's just concentrate on this
set up on the weather.
Ok so here I've got a little title statement:
in the world, every event either happens or doesn't.
Oh yes?
"......?"
Oh you can have that as well, so this
is inclusive all, "..." so that's another event.
So it's somewhere down here in the list.
Other questions?
Ok so, we can make statements about the world
of the following type: the event rain happens,
the event wind doesn't happen, the event rain
or wind does happen, the event not rain doesn't
happen, so there are all sorts of statements
that you can make about the world of that type.
And now I'm finally ready to give you an example
of a rule of inference.
Remember, a rule of inference is a way in deducing correct statements about the world from other correct
statements about the world.
So a rule of inference is something with the
form "if...(statement)...then...(other statement)."
So here's the rule, I'm going to show it to you, and if you feel the inclination to laugh, please do so.
IF "rain or wind" happens, THEN "rain" happens
or "wind" happens.
No one's laughing but I find that amusing.
Why is it funny?
It's funny because it's very hard to see those
statements "rain or wind" happens and "rain"
happens or "wind" happens as different.
It just sounds like you've said the same thing
in two different ways but really they have
the same meaning, that's the way it definitely
feels when you first hear that.
Here's a more general statement where X is
just sum of X, it's one of those events in
the list, alright, it could be it's below
freezing and it's windy, and Y could be a
statement like it's not snowing.
So IF "X or Y" happens, THEN "X happens" or
"Y happens."
This is just a special case of this one, so
that's an example of a rule of inference.
Now why is this not a tautology, why does
this actually have content, meaningful content?
How do we see that we're not just saying exactly
the same thing in two different ways?
How do we see that this is really, it actually
means something, it's actually a rule
that has content, it's not just circular.
And interestingly, it's in thinking about
the quantum experiment that we can see that
this is not a tautology, that it actually
has content.
So let's think about our quantum experiment
again.
So our experiment is the surprising thing
that when you send a photon through, it never
ends up at detector 2, it always ends up at
detector 1, detector 1 clicks, detector 2 never clicks.
So you know, its often said that this experiment,
these experimental results must be interpreted
as telling us that the photon does not go
on one or the other of these two paths.
You may have heard that commonly said in a
quantum experiment.
And let me remind you that a phrase that you
have probably heard, which is that Schrodinger's
cat is not dead or alive, but is in some kind
of superposition of the two, or is both dead
and alive, or it is dead in one world and
alive in another world, so it's both dead and alive.
So those sorts of statements you commonly
hear, so it's often said, let me repeat this,
it's often said that this experiment tells
us that the photon does not go on the green
path or the red path, it doesn't go on a single
path.
So what does that mean?
Well let's think about our histories and our
events for this quantum interferometer.
For one run on our interferometer, this region
here, remember, is the event detector 1, and
we can divide it in two events, one is detector
1 clicks and the photon goes on the red path,
the other is detector 1 clicks and the photon
goes on the green path.
And the event detector 1 clicks is the union
of the two.
So detector 1 clicks is the event it goes
on the red path and detector 1 clicks or it
goes on the green path and detector 1 clicks.
Let me say that again.
The event detector 1 clicks is the event detector
1 clicks and the photon goes on the green
path OR detector 1 clicks and the photon goes
on the red path.
It's just another way of saying the event
detector 1 clicks.
Ok so, remember that rule of inference, that
IF X or Y happens, THEN X happens or Y happens.
What does that mean if instead of X or Y we
have detector 1 clicks and red path
or detector 1 clicks or green path.
Well, that rule of inference becomes in our
case "IF 'detector 1 clicks' happens, THEN
'photon goes on green path and detector 1
clicks' happens OR 'photon goes on the red
path and detector 1 clicks' happens."
But this is exactly what is commonly denied
in explanations of interpretations
of this quantum interferometer experiment.
Yes?
"Is the reason why the statement's not a tautology
because there is a case that X and Y
depend upon each other?
So can we say that it's a tautology if X and
Y and not dependent on each other?"
No that's not the relevant thing, so in this
case X and Y are distinct alternatives, so
there's no overlap there, they're distinct, you know, one or the other, there's no interception between them
Yes?
"I'm wondering if this is a problem of
English grammar?
So 'X or Y' is not the same thing as 'detector
1 clicks', because in the phrase 'X or Y'
you're given an event with two choices, but in 'detector 1 clicks,' you're given an event with one choice."
Ok so, it was just a lack of space that I
didn't write, so 'detector 1 clicks' is the
event which is detector 1 clicks and red path
OR detector 1 clicks and green path,
I just shortened it, so I should have written here
'detector 1 clicks and green path OR detector
1 clicks and red path,' so I just shortened
it.
Are there other questions?
"You wouldn't have so much trouble if you clarified whether it was inclusive or exclusible...if that's an exclusible..."
This is inclusible, although in this
case it doesn't matter because there's no intersection.
"But it has to be that, and that cannot be that, so if it's inclusive, then both can"
If it's inclusive both
can happen, that's true.
"If you go back to the previous one and look at it, either inclusive or exclusive, you'll see that they're different."
So I'm using 'or' here to be inclusible, but
in this particular case it doesn't matter
because there's no intersection, so inclusible
and exclusible are the same in this case.
But in general I'm using 'or' as inclusible.
Let's talk about it after.
So this rule of inference is not a tautology
because we can conceive of, people have suggested
and we can conceptualize, there not being
a fact of the matter about which path
the photon has travelled.
That's something that is conceptually possible
for us.
So this is not a tautology.
It can happen that X or, it can be the case
I'm not going to use the word happen, it can
be the case that X or Y happens, but it's
not so that X happens or Y happens.
So then this rule of inference fails.
So in that case it fails, it's not a tautology,
if it can fail it's not a tautology, tautology
just means what you're saying is circular,
you're saying the same thing.
So you're not saying the same thing, because
it can fail.
Yes?
"...(question)"
I'll tell you about the quantum pie
you've turned later on.
"..."
It's about pie, so it won't be quantum,
the quantum is a joke, you'll see.
...
alright here's another collection of rules
of inference.
So here's the one we've already looked at:
IF 'X or Y' happens, THEN 'X' happens or 'Y' happens.
And here's another one: IF 'X and Y' happens,
THEN 'X' happens and 'Y' happens.
Another one: IF ' X' happens, THEN 'not X'
doesn't happen.
And all sorts of others of this ilk.
And together, these seeming tautologies form
a set of rules of inference called classical logic.
And as I said before, they seem like tautologies,
you just have to try extraordinarily hard
to see that these are actually different statements.
And why is that?
Why do we not notice when we're making these
assumptions, why are we able, it seems, most
of the time just to ignore?
See, you've got all these inverted commas
here to say that this is an event and this
is a separate event and that's a separate
event.
Just ignore the inverted commas, X or Y, you
don't have even have to say, this
this just is the same statement as that, why is that, why
is it very difficult?
A question?
"We just consider them accidents, right? Even in math when we learn logic, we define
all these three as accidents, and then we build our math on it."
Correct, so if it's an accident it can't be
a tautology, so you still have to see them as different.
"But if we assume accidents are truth then
we can build on top of it..."
So why do we not know so many, why do they still seem tautology-like?
Here's my explanation: we learn a classical
world view for many different reasons -
we're taught it in school, we deal with microscopic
objects that behave in a classical way.
And in this classical world view, the world
is one history.
That's what the classical world view is, that's
classicality, if you like.
The world is one history.
What does that mean, for example, for our
weather in Waterloo example?
So here are our histories.
The world is one history, so what actually
corresponds to the world, to the weather in
Waterloo tomorrow between 1:00 and 2:00 is
one of these histories, one of them, precisely one.
And if that's the case, then all those rules
of inference follow from that.
Let's do an example.
Yeah?
"So when you say the world is one history,
could you also say that every history is an
event, meaning that every history either happens
or doesn't?"
Yeah, so it's a sort of minimal kind of event,
so you can consider an event which just corresponds
to a single history, that's true.
Ok so, let's say that, let's consider the
rule of inference, which is 'IF 'rain and
wind' happens THEN 'rain' happens and ' wind'
happens'.
So what does that mean?
If rain or wind happens, that means that the
world is one history, that means that the
world must be either that history or that
history.
If rain and wind happens it must be in the
event 'rain and wind,' which is this one,
this lozenge shaped intersection.
So it's this one or that one.
But then, those two histories are in the event
'rain', and so the event 'rain' happens.
And the two histories are in the event 'wind',
and so whichever one of these happens, they're
both in 'wind', so the event 'wind' happens.
So because the world is one history, IF 'rain and wind' happens, THEN 'rain' happens and 'wind' happens.
Let's consider one of the other ones which
is "IF 'rain' happens THEN 'not rain' doesn't happen."
So if rain happens, and the world is one history,
then the world will correspond to one of these
histories in the 'rain' event.
But that means that it's not one of these
histories which correspond to 'not rain,'
so 'not rain' doesn't happen.
And you can go through all the rules of inference,
classical rules of inference that are included
in this list of classical logic, and they
all hold, they all follow from the assumption
that the world is one history.
So if the world is one history, then these
classical logical rules of inference follow,
and it turns out that the converse of that
saying is also true.
If you can reason classically, IF the classical
logical rules of inference hold,
THEN the world must be one history.
So I'm not going to show you that, but you
can prove that.
So the two things are equivalent to each other.
IF we can reason classically using these rules,
which we kind of internalize and don't even
notice that we're making, THEN the world is
a single history.
IF the world is a single history, THEN we
can reason logically using the classical rules of logic.
The classical world view that the world is
a single history is equivalent to classical logic.
So classical physics, in classical physics
the world is a single history.
And the question is: are we forced to give
up this view?
Does quantum mechanics force us to give up
that view?
We've already heard, I've already claimed
that the interferometer experiment, for example,
leads people to say things like the particle
doesn't follow a single history, it doesn't
follow the green path or the read path.
But what would go wrong if I said I don't
care what you say I'm just going to say that
it follows the red path or the green path,
what happens, does my head explode?
Are we forced to give up this view?
The answer is yes, we actually are forced
to give it up, we have no choice in the matter,
we're forced to give up the view.
If we keep to this sum of histories framework
of events and histories, and if we accept
that events of zero probability do not happen.
And this little picture here is a sketch of
events - I haven't drawn on the histories,
those little dots, there're actually eight
dots in each of these regions - so this is
a sketch of the events and histories in a
Venn diagram for a particular quantum experiment
which is a ... state for three spin-half particles
which are sent through a series of ... apparatuses
which send the particles into different beams
depending on whether they're spin-up or spin-down
in the X and Y directions.
So something like that.
And there are four events which have zero
probability in this set up, and I've depicted
them as three of them are these three circles,
so they have zero probability.
If you use the Feynman rule, which is take
all the amplitudes of the histories of those
events, add them up and square it and get
zero.
Zero probability for this event, zero probability
for this event, zero probability for this
event, and zero probability for a fourth event,
which is the union of the region outside these
three circles together with this shape, this
shape, and that shape.
That's also zero probability.
And if you think about those four regions, you see that every single history is in one of those regions.
Those regions, all together, their union is
the whole set of histories.
Every history is in one of those events that
have zero probability.
And so no single one of those histories can
happen, the world cannot correspond to one
of those histories because which history would
it be?
Say it was history here, well if that history
is the world, this event would happen,
and that has zero probability so it can't happen.
If the history were here, well it's in two
events of zero probability, so it can't happen.
If it was here, it's in the fourth event of
zero probability, which can't happen.
So no single history can happen.We cannot,
in this experiment, maintain the view
that the world is one history. We cannot.
Alright, so the world is not one history in
quantum theory.
Well what is it then?
And the answer is we don't know, yet.
We are seeking the answer to this question, and we're guided by some principles, some ideas, some rules.
One of the rules is that every event either
happens or doesn't happen.
The second rule is that this is a one-world
theory.
So there is one world in which every event
happens or doesn't happen, and I mention that
just because, of course, in questions of the
foundation of quantum theory, what's really
going on in quantum theory, how do we understand
quantum theory, includes one interpretations
is the so-called 'many-worlds' interpretations.
This is not a many-worlds interpretation,
it's a one-world theory, there's just one
world, in which every event happens or doesn't
happen.
Yes, question?
"The previous slide with the zero probabilities,
presumably calculated by these rules,
what's the possibility that there's an error in those,
and that something that calculates to zero
should in fact have a positive probability?"
Good, so I'm assuming that the standard laws
of quantum theory are correct, and that the
Feynman rules in the experiment that I described
are actually equivalent to the usual rules
of quantum mechanics.
So if quantum mechanics is right, then the
Feynman sum of the histories rules are right,
so I'm absolutely assuming this.
I mean, there are alternatives to quantum
theory in which the probabilities of events
are actually different from those in quantum
theory, but I'm not considering that, I'm
just assuming that quantum theory as we know
it is correct, and the probabilities that
you calculate using the Feynman sum of histories
are just the same as the ones you would calculate
in ordinary quantum theory.
Yes?
"How exactly did you differentiate from the
microscopic world to the macroscopic world?
Because I'm assuming it's very different."
Yes, good question, in fact there's no line,
it's a subjective choice what's macroscopic
and what's microscopic, indeed.
So you're reading ahead here, so let me come
up on to that.
Another of the things we're using to guide
us is that 'events with zero probability don't happen.
And we also like classical logic to be recovered
for macroscopic events, we want to be able
to reason classically about things like tables
and chairs and the wind and the rain.
It would be difficult if we had to include
that if it's raining and windy then it's not
true that it's raining and it's windy, ordinary
life would come grinding to a halt if we weren't
able to make such deductions.
So we want classical logic to be recovered
from macroscopic events, but we're more flexible
about microscopic events, you know, the passive
electrons and passive photons if they're doing
funny things which we can't reason classically,
logically about, maybe we're happy with that.
But you're absolutely right that the boundary
between these two things is subjective,
so maybe there's more non-classicality in things
that someone might think of as being macroscopic
than you would expect.
We don't know yet.
We also like classical dynamics to be recovered
for macro events, that's something that we
would have to be able to derive from whatever
understanding we gain about the quantum world.
Yes?
"What does one-world theory mean?"
It's hard for me to express what I mean by
that because I can't understand what a theory
that wasn't a one world theory would look
like, that's the thing.
"Can you tell us what it's not?
Is it just, from buzzwords, is it not parallel
universes?"
Right, exactly. It's just not that, it's just one world, right. And the one world is this world.
"And that's separate from the one history?"
Right, yeah, it's one world but it's not one
history, that's right.
And the question is what is it?
Yes?
"So these two problems of recovering classical
logic for macroscopic events and the other
problem of classical dynamics recovered for
macro events are these the same problems or
are they two different problems?"
They're two different problems.
"They look like two different problems, but
if motivation for introducing a change to
classical logic, for ... is to in fact understand
what's really going on, then it seems like
it should be connected, right, they should
be...are they completely independent?"
Oh, no I doubt they're completely independent,
but a priori they're not the same problem,
if you solve this problem you won't necessarily
solve this problem, and the other way.
So I beg your indulgence, I've run over time
a little bit, I beg your indulgence to go
on a little bit further, I've only got two
more things to say.
I promised you the parable of the quantum
pie eater.
So remember that a particle like a photon
or an electron going through one of our quantum
experiments, it can do something if one option
is open to it, but once you introduce another
option it changes it's mind, it can no longer
do that thing.
So here's the parable of the quantum pie eater.
So the quantum pie eater goes to the pie show
and says: 'what pies do you have today?'
The pie shop owner says: 'apple and blueberry.'
The quantum pie eater says: 'ok I'll take
the apple pie.'
Then the pie shop owner says: 'actually, I
forgot, there's cherry pie.'
And the quantum pie eater says: 'oh, in that
case I'll have blueberry.'
Electrons and photons reason like this, so
the joke is that the fact that there's cherry
pie available shouldn't have anything to do
with whether the quantum pie eater chooses
the apple pie or the blueberry pie.
It's irrelevant that there's also cherry.
Now, when you tell random people, I suggest
you try it tomorrow in the street, tell them
this and say, do you find that odd?
Most people don't find it odd, it's an interesting
experiment to do, most people say, yeah, I
think like that all the time.
Maybe, it turns out, that we are more flexible
in our thinking than we might think, that
we don't apply classical logical rules of
inference in our everyday interactions, maybe
we're more quantum, more non-classical than
we might think.
Yes?
"..."
So I want to end with a perspective
that I learned from Rafael Sorkin, a physicist
who's here tonight and works at Perimeter
Institute, which is the following: great advances
in science are often characterized by the
fact that they bring into the purview of science
something which was previously considered
to be fixed and immutable and a background,
they're not actually part of the dynamic laws
of nature.
So there are many examples, one is the theory
of evolution by natural selection.
Before that understanding, the species of
living things on Earth and their distribution
was considered to be fixed and unchanging,
but afterwards we realized that that's just
not the case, that the species evolve, they
die out, they change enormously over time,
they have their own laws of evolution.
So something that had been considered to be
fixed, unchanging, was discovered, realized
to be itself dynamical.
Another example is general relativity.
Before general relativity, the geometry of
space and time was considered to be fixed,
a fixed background, an arena, a fixed, rigid,
background arena in which physics takes place.
But general relativity revealed that the geometry
of space and time is not fixed, it's dynamical,
it has it's own laws of motion, it bends and
warps and ripples, and it's an active participant
in our physical world.
So geometry became part of physics.
So if the lines of inquiry that my colleagues
and I are following, trying to use the idea
of non-classical logic in understanding the
quantum world, if those are right, if that
line of inquiry is correct, then quantum theory
will join those other great advances in physics
in revealing something that we thought of as fixed and rigid to be part of science and have dynamics of its own.
And that's something will be logic itself.
So I'll end with that, thank you very much
for listening.
