Lucien Hardy on quantum gravity and (apparent) paradoxes

Lucien Hardy is a theoretical physicist working at the intersection of the two pillars of modern physics – general relativity and quantum mechanics – in the quest for a single unifying theory: quantum gravity. Hardy joins co-hosts Lauren and Colin for a conversation about the puzzles that have driven him throughout his career, including the past 20 as a Perimeter faculty member. Hardy recalls the radio program that first sparked his childhood curiosity about the universe, describes his operational approach to big quantum puzzles, and explains the paradox that bears his name (as well as a second, somewhat-tongue-in-cheek paradox devised by his wife). View the episode transcript here.

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Conversations at the Perimeter is co-hosted by Perimeter Teaching Faculty member Lauren Hayward and journalist-turned-science communicator Colin Hunter. In each episode, they chat with a guest scientist about their research, their motivations, the challenges they encounter, and the drive that keeps them searching for answers.

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Episode Transcript

(00:00):
(bright music)
♪ Hey ♪
(bright music)
- Welcome back to "Conversationsat the Perimeter."
Today, we're bringing you aconversation with Lucien Hardy.
Lucien is a theorist hereat the Perimeter Institute,
and he works in quantumfoundations and quantum gravity.

(00:22):
- And Lucien was actually oneof the very first researchers
to come to PerimeterInstitute about 20 years ago,
when the institute itself was really
just a theoretical ideafrom Mike Lazaridis,
the founder and thecreator of the Blackberry.
So I loved hearing Lucien tell stories
about some of the early days working
with the other original researchers here,
like Lee Smolin and Rob Myers,
who's now the director here at Perimeter.

(00:43):
- I also really liked thepart of the conversation
where he told us that hisperspectives on physics
and specifically the operational approach
that he uses to study quantum theory was
significantly influenced by the time
that he spent in an experimental lab.
He actually says that every theorist
should have to spend time in a lab.
(Colin laughs)- And Lucien is also,
I'm pretty sure, the only personthat I've ever interviewed

(01:05):
who has a paradox named after him.
Hardy's paradox is this thought experiment
that he devised in the early 1990s,
and he tells us aboutin this conversation.
He also told us that Hardy's paradox
paradoxically may notactually be a paradox.
So try to get ready towrap your mind around that,
and let's step inside the Perimeter.
(light music)

(01:27):
Lucien, thank you so muchfor joining us here today.
- It's my pleasure.
- You've been with Perimeter Institute,
I looked, for 20 years.
It's 2002, and we're coming up on-
- Yeah, yeah-- Your 20-year anniversary-
- Almost 20 years.
- Can you tell us what does somebody do
as a theoretical physicistat Perimeter for 20 years?
- Well, I mean, lots of things.
(Lauren laughs)(Colin laughs)
I guess one of thegreat things about being

(01:48):
in an environment likethis is it influences you,
and you change your research direction.
So when I came here, I had someinterest in quantum gravity,
but that's now increasingly the main thing
I'm interested in, 'causeof people around it
are thinking about this, too.
So there's never a shortageof people to talk to,
and ideas to think about,and so, yeah, I'm busy.

(02:08):
I have lots of things to work on.
- You mentioned that rightnow you're really focused
on quantum gravity.
Can you tell us what that is?
- So I'd like to say that the,
like there's a problemwith quantum gravity,
and this is that we have two
less fundamental physicaltheories, so general relativity,
Einstein's theory ofgravity on the one hand
developed in 1915, 1916,

(02:29):
and then we have quantumtheory on the other hand
developed by a whole bunch ofpeople, including Einstein,
so Heisenberg, Schrodinger, many others,
developed in the mid-1920s.
And those two theories are bothvery successful predictively
where they apply, butthey don't fit together.
They don't fit together mathematically.
They don't fit together conceptually.
Really, it seems there ought to be
a kind of unity in nature.

(02:49):
We should really only have one theory
that describes all of nature.
So if we have two differenttheories describing
different parts of nature,
that isn't a satisfactory situation.
So the problem of quantumgravity is to find a new theory,
and probably a deeper,more fundamental theory,
which approximates to general relativity
on the one hand in situations
where that theory has beenexperimentally confirmed,

(03:11):
and approximates to quantumtheory on the other hand
in situations where that theory
has been experimentally confirmed.
- When I was preparing somenotes for this conversation,
I wrote down only one sentencethat had a big box around it
in big block letters, and it said,
"The problem with quantum gravity,"
because it seems likethat's a very big problem.
Why is it so difficult toreconcile quantum mechanics

(03:33):
with general relativity?
- Yeah, I don't know.(group laughs)
I mean, if I knew theanswer to that question,
I would have done it already.
You know, it's 100 years or so now
since the problem has been around.
- I'm not placing all theblame on you personally
for not having done it-- I have not done it so far.
(Lauren and Colin laugh)Yeah, I don't know.
What I think is happening is that I think
we're just not asking the right questions.
We're not thinking in the right way.

(03:55):
You know, if you look at,
you know, historicallyat other situations,
like after Newton developedhis theory of gravity,
his theory, universal theory of gravity,
he wrote down this equation,
he didn't like it, because ofit had instantaneous action,
a distance, like I mentioned,
and no substance mediating that force.
And so, he did the natural thing.
He tried to invent a sort of mechanism

(04:16):
by which gravity could act like that,
so two masses that are far apartcould influence each other,
and not just him.
Other people also tried to think of,
they were called, you know,mechanical aether models,
so mechanical models thatyou could use to explain
how gravity worked.
These models were, you know, amazing.
They were quite detailed,
and you know, people spent alot of time doing calculations,
and sometimes successfully reproducing

(04:36):
Newton's equation of gravity.
You know, for example,Newton himself had this idea
that the force that causedplanets to be attracted
to one another was the same as the force
that causes aeroplanes to fly.
So in some sense, he anticipatedthe work of Bernoulli,
which came, you know,about 50 years later.
You have an aeroplane wing.
Then the speed at whichthe air particles go

(04:58):
underneath the wing is faster
than at which they go over the wing,
and if the speed is reduced,if the particles go faster,
then they don't hit the wing as often,
so there's a lower pressure.
And so, that puts a force on the wing,
and makes the plane go up.
And Newton had this idea,you know, already back then,
and he thought he couldcome up with some mechanism
which explained gravity.
Rene Descartes had thisidea about vortices,

(05:20):
very detailed models.
There were many, you know,interesting characters,
and that seems to be a lotof what people were doing
were trying to come upwith mechanical models
to explain gravity.
And then even later with electromagnetism,
when Maxwell, Maxwellhimself actually used
a mechanical model to explain,
to derive his equationsof electromagnetism,
people were just trying to explain things

(05:40):
in terms of the concepts they understood,
in terms of the conceptsthey were familiar with,
and everyone was familiarwith stuff, you know,
stuff pushing on stuff.
That was a, that's a familiar concept.
And so, and I thinkthat's where we are now.
We're bringing to bear on theproblem of quantum gravity
the ideas that we understand,
and it's probably just not sufficient.
We probably have to find away to think beyond that,

(06:02):
or to somehow get out of ourselves,
and look at the problem froma different point of view.
It turns out to be very difficult.
- I think it's really a unique challenge
in this field, right?
Because you really, fromwhat you're describing,
you really need to find a wayto think in a different way,
and not rely too much on something
that you already understand,
whereas in other fields of research,

(06:24):
we would be trying to build on things
that we already understand,or look at consequences
of things that we already understand,
and whereas you have toprobably keep reminding yourself
don't think too much about those things
that you already understand,try to think in a new way.
So how do you train yourself to be
in a kind of state of mind
where that new way ofthinking is possible?

(06:44):
- You could imagine developinga systematic approach
to that sort of thing.
You could perhaps follow
sort of lateral thinking techniques,
or some sort of meditative approach.
I don't do that especially.
I think I just, you know, sortof throw myself in every day
and try to think of new ideas.
I don't have a goodanswer to that question,
but I think it's a questionthat people should think about.
What are the methodological tools
you should bring to bear on physics?

(07:06):
I've even asked philosophers.
You know, philosophers spend a lot of time
looking at physics, andoften speak about the work
after it's been done.
But philosophers could positionthemselves in such a way
as to attempt to provideworking physicists
with methodological tools.
You know, how do you go about,
well, in this case, for example,

(07:26):
finding a deeper, more fundamental theory
when you have two lessfundamental theories?
That seems like a fantasticphilosophical question.
You know, even if you don'tactually construct the theory,
just what are themethodological approaches
to solving that kind of problem?
But philosophers haven'treally worked on that
as far as I'm aware.
So yeah, it's a fantastic question.
I don't know the answer to it,
but I think we should think about it.
- That's great, yeah.

(07:47):
As a follow-up to that, I'm just curious
if there was a satisfyingsolution of quantum gravity
that was proposed in the near future,
either by you, or someone else,
so that you needed to gothink about some research
in another field, would you want to look
at the consequences of thissolution of quantum gravity,
or would you wanna finda new area of physics
where you need to find anothermore fundamental theory?

(08:08):
Because that's kind ofthe way of thinking.
- Oh, right, so that'sa good question, too.
If you look at, contrastNewton and Einstein,
the two people I keep confusing,
Newton spent a lot of time,you know, doing calculations,
and being very carefulabout what, you know,
what is theory reallypredicted, theory of gravity,
and Einstein has beencriticized for not doing

(08:30):
enough of that in the caseof general relativity,
and there was kind of alull in general relativity,
and then some years later,people took up the cause again,
and did all these amazing calculations.
So I hope in that particular case,
I would be more following along
this sort of Newton type approach.
It's difficult to anticipate-
- Of course.- In advance.
- Yeah.
- The challenge that you're working on,

(08:51):
it seems like there's aparallel to 100 years ago,
and how are you tryingto build a model of,
or a version of quantumgravity that overcomes
some of these differences
between quantum mechanics, relativity?
- So you mentioned thatparallel with the problem
100 years ago that was solved by Einstein
when he combined Newton'stheory of gravity

(09:12):
with his theory of a special relativity,
which included Maxwell's equations.
It's a sort of an example.
So I take that parallel very seriously,
and if you look at what Einstein did,
how did Einstein go aboutsolving that problem?
How did he go about coming up
with the theory of general relativity?
Well, he had to gothrough a number of steps,
but his starting point was

(09:32):
what he called the happiestthought of his life,
which was when he came up withthe principle of equivalence,
and the principle ofequivalence is really just this.
If you imagine having a box,and it could be an elevator,
and you have, you know, a personinside it and some objects,
and that box could be falling,
or it could be floating out in space,
and imagine there's no windows.

(09:52):
So the person inside has no idea
of which of the two situations they're in.
So I suppose they'd be screaming.
But aside from that, in thecase where the box is falling,
everything would befalling at the same rate.
And so, it would feel likeit was floating around.
It would feel like theywere floating out in space.
And so, Einstein said thesetwo situations are equivalent,
and that was the starting point,

(10:13):
and then that idea gets turned
into some beautiful mathematics,
and he ends up incorporatinggeometric ideas
that he learned from Minkowski,
and also from his childhoodfriend Marcel Grossmann.
Grossmann was a mathematician,
who knew about the sort offield of differential geometry,
which went back to the mid-1800s.
So there was lots of steps.

(10:34):
It took him from 1907,
when he had this happiestthought of his life
about the elevator, until 1915,
when he finally wrote downthe correct field equations.
- And how did he know in 1907
when he had this thoughtthat it was definitely
an important ingredient in formulating GR?
You know, it still tookhim eight years to finish,

(10:56):
so I'm just curious.
- Yeah, it's a great question,
and I'm not enough ofa historian of science
to know exactly what histhinking was around that.
But you can see looking at the idea
that it has lots of promise.
Suddenly, previously wethought of gravity as a force.
So Newton's first law saysthat a body will continue,

(11:16):
you know, at a state of rest,
or in a constant speed in a straight line
until it in essence is actedupon by an external force,
and gravity was regardedas an external force.
So under gravity, a bodywouldn't go in a straight line.
It would go along acurve, and that was okay,
because gravity was regardedas an external force.
And suddenly, Einstein saw a way

(11:36):
to stop thinking ofgravity as a force at all,
and think of it as, you know,more to do with geometry.
So a particle would actually be going
sort of in a straight line
once you're in thisfalling frame of reference,
I mean, for a while.
The principle of equivalenceonly applies in small boxes
over small periods of time.
He must have seen that,
and realized he was onto something big.

(11:56):
I can see that would have been the case.
- Mmm-hmm.
- In terms of your researchinto quantum gravity,
what is the sort of parallel challenge,
or the parallel path you'retrying to take to make progress?
- So Einstein, as I said, started
with this equivalence principle.
And so, the idea is that perhaps there is
a quantum equivalence principlethat can play a similar role

(12:19):
in constructing a theoryof quantum gravity
that the equivalence principle played
in constructing the theoryof general relativity.
So I should try to explain
the quantum equivalence principle,
but to do that, I kindof need to back up a bit.
You're asking the questionof how do I combine
general relativity and quantum theory,
where you should lookat these two theories,
and ask, you know, whatkind of theories are they?

(12:40):
They each have conservativeand radical features.
So general relativity is conservative
in that it's deterministic.
It's a classical theory.
- By conservative, do youjust mean that it's similar
to other theories that came before it?
- Similar to, yes, theoriesin the past, yeah, yeah, yeah.
I think that's what I mean.
Yeah, it's not surprising in some sense,
and perhaps it's not surprisingbecause of that similarity.

(13:01):
- Mmm-hmm.- So it's conservative
in that sense, that it's deterministic.
But it's radical in thatthe causal structure is
dynamically influenced bythe distribution of matter.
So the causal structure is thepattern of before and after,
things, how things are, things,
events are before other events.
It's this pattern of events
that are before and after each other,
and that pattern is influenced

(13:22):
by the curvature of space-time.
So if you, if matter affectsthe curvature of space-time,
then matter affects the causal structure.
And so, that's radically different
from Newtonian physics, for example,
where time was regardedas this absolute structure
in the background.
Time just evolved,unaffected by anything else.
So dynamical causal structureis this radical element

(13:44):
from general relativity.
And now, if you look at quantum theory,
well, it also has radicaland conservative elements.
The conservative element is
that the causal structure is fixed.
Just like Newtonian causalstructure, it's fixed.
It's in the background.
It doesn't change.
And the radical elementis it has this property,

(14:05):
I would call it indefiniteness.
So a particle, if it cango along one of two paths,
it actually goes along both paths at once.
It doesn't go along a definite path.
So it's indefinite as towhich path it goes along.
But I call that indefiniteness.
So if you take those tworadical properties together,
and if you believe a theory ofquantum gravity has to follow
the radical path in both cases,

(14:25):
then you expect a theoryof quantum gravity
to have indefinite causal structure.
Causal structure will notjust be something that varies,
that changes, but also there will be
two different causal structures
at the same time, in some sense.
Same time is the wrong word,
but two different causalstructures will both,
would both be, would both hold.
So that's, I think, thesort of the central property
we're likely to have intheory of quantum gravity.

(14:47):
And that's a really strange idea,
the idea that if you have two events,
you know, usually you'd think,
"Well, one event isbefore the other event."
You know, event A is before event B.
But here, you could have it being true
that event A is before event B,
and also event A is after event B.
Both of those things would betrue, not just one of them.
Yeah, so you'd have indefiniteness
as to the causal structure.

(15:07):
That is not something that we're used to,
or it is not, that we'renot used to thinking
about the world in those terms.
So the question is how doyou make sense of that?
How do you do physics still
when you have something like that?
And so, the idea is tolook at what Einstein did
with the equivalence principle,
and what he did was he said,well, you may have behavior,

(15:28):
which is, let's see, like non-inertial,
so it looks like thingsare moving in curved lines.
It looks like things arebehaving in a weird way.
But you can always transforminto a frame of reference
where you just have objectsmoving in straight lines,
where Newton's laws apply,where things are just moving
in straight lines, and that'scalled inertial behavior.
So, and the way you do thatis just by looking at it

(15:48):
in a frame of reference that's falling.
At least for short while locally
things will be moving in a straight line.
So a different way ofunderstanding what Einstein did
with the equivalence principle is to say
the equivalence principlesays that there always exists
a frame of reference with which,
with respect to whichthe behavior is inertial
in a small vicinity around any point.

(16:09):
The question is can wetake that principle forward
to the problem of quantum gravity?
And the idea is to draw ananalogy between inertial behavior
and definite causalstructure on the one hand,
and non-inertial behavior andindefinite causal structure,
'cause in general relativity,
non-inertial behavior isthe sort of the weird thing
that you're trying to tame by going

(16:30):
to a falling frame of reference.
In quantum gravity,indefinite causal structure is
the weird thing thatyou're trying to tame.
So that's the sort of background,
and now, what would the principle say?
Well, the principle would say can you find
a sort of frame of reference,
where you get rid ofindefinite causal structure,
at least locally in a small region?
Well, that's not quite enough.
What you need to do is find

(16:51):
what's called a quantumframe of reference,
and this is a subject thatwas developed many years ago
by Yakir Aharonov, and other people,
quantum frames of reference.
And it turns out you can do this.
So what you can do is you could find
a quantum frame of reference,
a quantum coordinate system to measure
that frame of reference,
where locally in thevicinity of a small point,

(17:11):
you get rid of indefinitecausal structure.
The causal structure becomes definite.
- So you know that A causes B?
- Yeah, you know that A causes B.
Now, what you do when you impose that,
you try to make it work in a small region,
and then everywhere else itgoes haywire, but that's okay,
'cause you can hope to use the tricks
that Einstein used in general relativity.
In his case, he knew he could

(17:32):
locally make everything inertial,
and if he did that, you know,far, far away from there,
it would kind of go haywire.- Mmm-hmm.
- Crazy, non-inertialbehavior, but that's okay,
because he could write down some equations
at that point that worked.
And so, the hope is to beable to do the same trick
in quantum gravity.
- Is it especially difficult
because you're dealingwith these more radical,
what's the other word?

(17:52):
- Non-conservative?- Non-conservative element?
Is there more uncertainty,or just probabilities,
as opposed to certainties?
- A different approachwould be to say, "Well, now,
"I'm gonna take the moreconservative path in each case.
"I'm gonna look for a theorywhich is deterministic
"and has fixed causal structure."
It just seems unlikely tome that that would work.
I mean, it's not completely impossible.
It may be you could find some theory

(18:13):
that was in some sense more classical,
more like older theories,where that worked,
and there are even ideas
that I think fit into that category.
It seems to me to be the wrong idea.
One should embrace the radical elements,
and see what, how to go forward.
- And is that what's really unique
about your approach to quantum gravity?
Is that what sets your approachapart from other approaches?

(18:35):
- Definitely it's true that my approach is
to put this indefinite causal structure
front and central, I think.
This is the central conceptual problem,
and then we work out from that.
Other approaches, in asfar as I understand them,
are not doing that.
But you know, everyone hastheir own take on this.
So I think what's important
when it comes to solving problems
like the problem of quantum gravity is

(18:55):
that there are many different approaches.
So pluralism is essential in physics,
as it is in other walks of life.
And so, I'm hoping to bring, you know,
a different kind of approach.
I mean, there are otherpeople now thinking
about indefinite causalstructure and quantum gravity,
so I'm hoping there's startingto be a bit of a community.

(19:18):
- Basically a 100-year-old problem
more so in terms ofmarrying these theories.
Is that challenging for a researcher
to be working on a problemthat has passed through
other researchers' careerswithout being solved?
- Yeah-- Do you foresee
a day when you say, you,or a colleague says,
"Oh, yes, that's quantumgravity, we've done it"?

(19:39):
- I mean, I think we can do it.
I mean, there are,
I don't know the particular approach
that I'm taking is the right one,
and you know, it may wellnot be the right one.
There could be some youngphysicist at the moment
who has the right idea, orsomebody who's, you know,
yet to even enter the field of physics.
- Mmm-hmm.- Typically,
big breakthroughs are madeby young people in physics.

(20:03):
And so, that's really where the hope lies.
- And what would it mean if it were,
maybe you haven't even thought about that,
but if there, these bigquestions had a solution,
if the new theory, theunifying theory, was found,
what would that mean for physics?
Would physics be, doneand we can all go home?

(20:23):
- Yeah.
(Lucien laughs)(Colin laughs)
I mean, again, it really depends
on what the answer is, doesn't it?
I don't know.
You know, people were thinking
about electricity and magnetism,
and people started to become aware
that there were these electric,
started sending electricity through wires,
and well, they had, youknow, magnets forever.

(20:43):
And I don't know if people before,
before the subject wasreally completed by Maxwell,
I don't know if people reallyunderstood what it would mean,
what it would mean to haveMaxwell's equations written out.
Maxwell's equations have had
a tremendous impact on humanity.
So much of our technologyrelies on understanding
electricity and magnetism,and conceptually, you know,

(21:04):
I'm not sure if peopleanticipated that this would lead
to problems with relative motion.
Problems come up when you get an answer,
when you start to get a theory,
and you can't reallyanticipate that in advance.
Who knows?
When someone comes up witha theory of quantum gravity,
I think we'll be surprised by it.
It'll be interesting,
and I think it will lead to questions
that we can't possiblyanticipate at at this stage.

(21:26):
- I know that one thingthat's important in your work,
if I understand correctly, isthat you have a set of axioms
that you use as kind ofthe center of your work,
and can you talk about whyyou use that kind of approach?
- Yeah, so this is what happened.
I mean, I should talk about my career.
I started off in quantum foundations.
I did my PhD in, from 1989 to 1992,

(21:49):
a time that the field ofquantum foundations was
very concerned withinterpretations of quantum theory,
you know, how do you makesense of quantum theory?
And there was all thesedifferent interpretations,
like the many worlds interpretation,
where every time there is aquantum choice to be made,
both things actually happen.
The world splits into two copies
with one thing happeningin each copy of the world.

(22:11):
And by the world, I meanthe universe, everything,
and there's the de Broglie-Bohm model,
where the quantum wave function guides
actual particles that exist,
and those particles are guidedalong a path by this wave,
and many other interpretations.
And so, that was whatpeople were thinking about,
and that's what I was thinking about.
I became a bit unsatisfiedwith that way of thinking,
because it didn't really seemto lead to any new ideas.

(22:34):
It didn't seem to lead to the possibility
of real progress in fundamental physics.
It was a lot like the aether theories,
the mechanical aether theories.
You know, people took Newton'stheory, or Maxwell's theories
and tried to make senseof those equations,
and those ideas turnedout not to be useful,
and my feeling increasingly was
that this wasn't a usefulway of making progress
in quantum foundations.

(22:57):
And then I came under theinfluence of Chris Fuchs,
and he was asking this question.
He was saying, "Well, canyou derive quantum theory?
"Can you derive quantum theoryfrom some more basic ideas?"
He wasn't the first personto ask that question,
but it was the first timeI'd encountered the question.
In his case in particular, he was working
in this sort of new fieldof quantum information,
and he was saying, "Well, can you give

(23:18):
"an information theoretic reason
"for the axioms of quantum theory,
"for the structure ofquantum theory as it was?"
And so, I set about working on that.
This was in 2000, 2001.
And you know, eventually, I found a way
to approach that problem.
So the idea was to be very operational.
What I mean by operationalis to just talk about
what it is you do, the settingsof knob settings, and so on,

(23:39):
and what it is you see,
like detectors clicking, lights flashing.
So he-- Sorry to interrupt, though,
but as a theorist, you areproposing the theories,
but you're not the oneactually turning the knobs,
and watching the lights blink on and off?
- Well, I mean, I,
I mean, as an aside, I actually,
I worked for two years in laboratories.
So I worked for one year in the laboratory
of Anton Zeilinger inInnsbruck as it was then.

(24:02):
I mean, I was a theorist,
but I was allowed tolook at the experiments.
- You're allowed to touch the lasers?
- No, that was-- Okay.
- A step too far.- Yeah.
- I was allowed to be in thesame room as the experiments,
and again with the samerestrictions I worked in Rome
in the research groupof Francesco De Martini.
- Mmm-hmm.- So actually,
he was more willingfor me to get involved,
but by that point, I was too cautious.

(24:23):
And that was reallyinteresting to actually see
people doing experiments, you know,
'cause it's a remarkable skill.
People, experimentalistshave to solve problems
that theorists can't even imagine.
So for example, Rome, it's very hot,
and the temperature goes up and down,
and the air conditioning was broken.
So you'd have these beamsplitters mounted on a metal base,

(24:43):
but the metal would contract and expand,
and that would mess the experiment up.
They had to find a wayto solve that problem.
They had to buy this metal called Invar
that has a very low expansion coefficient,
and then the experiment was stable.
I find that fascinating, you know?
The real stuff of experimentsis really interesting,
and how do you get theinformation from here to here,
the electronics attaching to it?
So I think every theoristshould be forced to work

(25:06):
in another laboratory for a while.
- You think that informedyour operational-
- Absolutely, yeah-- Approach?
- So I think, so that wasprobably in the back of my mind,
and so, that's what pushed me towards
this operational approach.
So the operational approach is really
just taking it seriously.
Experimentalists have to do experiments.
They have to go into the world,
and put things in differentplaces, and set, you know,
set knobs to differentpositions, and read off the data.

(25:29):
So I set up a framework like that,
and then furthermore,add in probabilities,
because quantum theory isall about probabilities.
You know, in the end, quantum theory,
in some sense, quantum theoryis a more natural descendant
of classical probability theory
than it is of Newton's theory.
Quantum theory is a probabilistic theory.
- Mmm-hmm.
- And so, I set up this way to write down

(25:51):
sort of just probabilistic theories
that pertain to operational situations.
So you have an operational situation.
You have probabilities.
You can write down amathematical framework
that applies to that situation.
- Mmm-hmm.
- And then once you havethat mathematical framework,
you can say, well, you know,
maybe I can find someprinciples, or postulates,
or I call them axioms, that constrain you.
And you know, so say, you know,

(26:11):
initially you have all possibleprobabilistic theories,
but now you want to specialize
to particular probabilistic theories.
And so, the axioms I wrote down,
I wrote down enough axioms
that would get you to quantum theory,
and that was work I did in 2001.
So that was a very interesting exercise,
and I felt like that kind ofwork helped to make progress.
I felt like I was understandingquantum theory in a new way

(26:32):
that I hadn't previously understood it.
- You said you think all theorists should
have to spend some time in the lab.
Is that, is it a differentpart of the brain
that activates to work ina experimental setting?
- Absolutely, yeah.
I mean, like I said, I've never actually
sort of actually got myhands dirty, so to speak,
and moved these things around,
but really a laboratory looks nothing like
a bunch of equations,like these equations here.

(26:53):
It's a completely differentworld from a laboratory,
and you don't really understandphysics until you understand
that it is about the experimental world.
It's about experiments in the end.
- And would it be the same framework
that you hope might give quantum gravity,
but with a different set of axioms?
- Yes, so what happens isI did that work in 2001,
just before I came to Perimeter Institute,

(27:14):
and then I came here,
and people were thinkingabout quantum gravity.
You know, there was string theorists,
Rob Myers and Lee Smolinworking on loop quantum gravity.
And so, quantum gravitywas very much in the air
at Perimeter Instituteback then, as it is today.
And I started thinking,"Well, perhaps we can take
"this kind of generalprobabilistic technique
"that I developed, and apply it
"to the problem with quantum gravity."

(27:35):
Otherwise, what is it good for?
You know, it's a lot of fun to,
it's called reconstruct quantum theory.
So you start off withsome general framework,
you write down some axioms,and you get quantum theory.
But we already knewwhat quantum theory was,
so it wasn't really pushing us forward.
It was just providing a newway of understanding things.
What would be a real testwould be if we could start off
with some general framework,apply some axioms,
and get quantum gravity,a new physical theory.

(27:56):
That would be a great test.
So I started thinking about that.
One of the problems was thatthe operational framework
I developed wasn't really hospitable
to a theory of quantum gravity.
I realized you'd have this property
of indefinite causalstructure I mentioned earlier.
The order of events would be indefinite,
and well, the operationalframework had boxes
with wires connecting them,
and those wires werethe direction of time.

(28:17):
So a wire, a particle would leave one box
and go into another box,
and that would behappening forward in time.
So it wasn't the right framework
to treat the problem of quantum gravity.
So I set about building a framework
that would be hospitable toquantum gravity, I hoped,
and this was a frame, aprobabilistic framework
that was capable of admittingindefinite causal structure.

(28:38):
I took a very generaloperational approach.
I tried to really sit back and ask,
you know, what is an experiment?
You know, what do we do in an experiment?
How can we translate thatinto a mathematical framework?
You know, so in an experiment,
what you do basically is you make choices.
Like I said, you know,you set knob settings,
and you collect data.
And so, I imagined amathematical framework

(29:00):
that was capable of analyzing
that sort of situation probabilistically,
but very generally, without assuming
any definite causal structure.
So that was work I did in 2005,
and I called it the causaloid framework,
'cause the central mathematicalobject in that framework
was something I called the causaloid,
and that's really driven allmy research since then is

(29:20):
the attempt to formulate quantum gravity
in this kind of more generalmathematical framework.
You know, if you think about it,
Einstein, when he wasdeveloping general relativity,
needed a mathematicalframework to do that in,
and he was lucky thatRiemann 65 years earlier,
or thereabouts, had developedRiemannian geometry.
This is a framework of curved spaces,
and Einstein was able to take
that mathematical framework directly,

(29:42):
and use it for general relativity.
And so, the questionwas, well, maybe we need
some similar sort ofmathematical framework,
but for the problem of quantum gravity.
So that was the idea.
But that, you know, that was 2005,
and I'm still working on it.
So it's not clear to me
that that's exactly the right framework,
but at least it was an idea,
and it's something thatcame out of my earlier work
on axioms for quantumtheory that you asked about.

(30:03):
- Mmm-hmm.- I jotted down
some of the places that you've been.
You've mentioned Ireland.
You went to Tirol, Durham, and Rome,
and Oxford, and then you came here.
You mentioned to us how youwere convinced to come here.
Can you just share thatbriefly with (laughs)-
- Yeah, I was in Oxford.
I was happy in Oxford.
I mean, I had a position thatwould've lasted for 10 years,

(30:24):
and I was about halfway through that.
I was very happy there, and I did seem,
I just saw my life as continuing there.
But then at a certain point,
a sort of curious charactervisited called Howard Burton,
and you know, I chattedwith him for a little while.
He said he was working on this project
to set up a new institute,and then he went away,
and I kind of forgot about it.
About a year later Iwas getting, you know,

(30:45):
communications from him, emails,
and he was trying to call me.
- And this is just when PerimeterInstitute is starting at-
- Yeah, so this was even before
Perimeter Institute really existed,
and he, I mean, I guessformally it existed perhaps
at that point, and he was, you know,
he was starting to try andrecruit people, you know?
So at that point, I don't know
that he'd recruited anyone at that point.
But then when he started tocommunicate with me later,

(31:06):
the place actually existed.
There were people here.
Lee Smolin was here,
and Rob Myers were herealready, and other people.
And he was calling,
and of course, I never answer the phone,
and he was sending emails,and I never answer emails,
and I was very busy at thetime with just life generally.
And so, I ignored allthose communications.
I mean, I meant torespond, but I never did.

(31:27):
And then Mike Mosca was visiting Oxford,
and Mike Mosca had done his PhD in Oxford,
so I knew I knew him very well.
And then he had come overhere to, he's Canadian,
he'd come to Waterloo,and was very involved
in setting up Perimeter Institute.
So Mike Mosca was visitingOxford, and he came,
and Howard sent a planeticket with Mike Mosca

(31:49):
for me to travel to Canada.
- A plane ticket with your name on it-
- With my name on it, yeah, yeah.
- That's bold-- And so,
so I guess I just agreed, I guess,
at some point after he did, but I didn't-
- And here we are, 20 minutes later.
It wasn't a return ticket.
(Lucien laughs)(Lauren laughs)
- Actually, it was a return.
(Colin laughs)(Lauren laughs)
I remember being, you know, impressed,
because, you know, I was,

(32:09):
I remember being impressedwhen I got to the airport
and there was a limousine waiting
to bring us to the institute.
I'd never been inlimousine like that before.
So you know, he broughtme here, and I met him,
and I met Lee, and Rob,
and I met Mike Lazaridis.
I met Mike Lazaridis and David Johnston,
and who subsequently becamethe Governor General of Canada.

(32:29):
At that point, he was thehead of the university.
I met them in Ethel's Diner,
(Lauren laughs)
which was the location just on University-
- Still there.- Still, actually, no,
it burned down,
(Colin laughs)(Lauren laughs)
and then they built a new one.- Yeah.
- So the particular onethat we met in burned down.
- That one was on University-- Yeah, yeah-
- That one, oh, I didn't know that.

(32:50):
- Yeah it did.- Okay.
- So we met there, and I chatted,
and you know, I realized that this was
a really serious endeavor,
and there was a lot of backing behind it.
And so, I kind of, I caught the bug,
and I agreed to come to Canada-
- Did you agree on the spot?
- So the way Howard did it backthen was he would, you know,

(33:10):
he would bring people over,
and then he would have themvisit lots of different people,
and then he would takethem to a restaurant.
It was just me and Howard,
and he wrote a number ona piece of, on a napkin,
which was the salaryI was supposed to get,
and he pushed it towards me.- Oh, no-
- Like a movie!- Yeah!
(group laughs)
- Well, I think Mike haddone the same thing on Howard
when he recruited Howard.
So,(Lauren laughs)
and I didn't understand exactly

(33:30):
what a Canadian dollar was worth,
but it was, it seemed good,
and so, I agreed at that point to come.
- Going back even further, was this,
were you a born physicist,you were meant for this,
and this was the path all along,
or did you, did it take some time to find?
Can you tell us a bit about
when you first got interested in science?
- I mean, of course, whenI was five years old,

(33:50):
I wasn't reading physics textbooks.
There were no physics textbooks around.
More likely to be astrology textbooks
than the physics textbooksin my background.
But I think I was alwaysinterested in, you know,
making things, hammeringtogether pieces of wood.
At a certain point, we moved to a house,
and across the back from the house,
there was an electrical repair shop.
This shop had, you know,televisions, broken televisions.

(34:14):
You know, the guy, whenhe couldn't fix something,
he threw it out the back.
So there were broken televisions,and broken record players,
and broken radios, all sorts of things,
and I was allowed to justgo and take that stuff,
and look at it.
So you know, I would take the stuff apart.
There were, in those days,things had vacuum tubes,
rather than integrated circuits,
which made a very satisfying noise
when you threw them down.

(34:34):
(Colin and Lauren laugh)Bang.
And so, I would take thosethings, and I would, you know,
like combine two brokenrecord players to make
one functioning record player.
I can't claim that I really understood
exactly what was happening,
but I think it got me interested.
And so, that was probablyone of the earliest times
I started to think, "Well,this is something I could do,"
and my mom said, "Well, you know,
"this is a job you could have.
"You could fix electrical objects,"

(34:55):
and that seemed to be exciting to me.
- So then how did becoming atheoretical physicist happen?
- Well, and then at a certain point,
they started teaching physics at school,
and I was very interested in that,
and I studied it really, really hard.
And so, I think, I guessat that point it becomes
a fairly, fairly standard sort of path.
And the school I went towasn't terribly academic,
but the teachers were very good,

(35:16):
and the physics teacherwas great, Mr. Barnforth,
and he got me interested in physics.
So I, of course, I passed all those exams,
and got to university.
But even before I got to university,
there was a radio program on BBC Radio 3
that was made by PaulDavies, who's a physicist,
but also a very goodpopularizer of physics,
and it was called "The Ghost in the Atom."

(35:37):
My dad recorded it on a tape cassette.
Had the radio playing, andhe put the tape recorder
next to it, recorded it,
and he gave that tape cassette to me.
So I had this tapecassette in my possession
for a number of years,and I would listen to it
over and over again, andthere were lots of physicists,
some of which I got to know later,
but he had people likeJohn Bell, David Deutsch,
Alain Aspect, many othervery interesting physicists

(35:59):
who were thinking about thefoundations of quantum theory,
and they were speaking in a way
I'd never heard anyonespeak about physics before.
This is a very weird subject, you know?
How did you interpret quantum theory?
What does the wave function mean?
All these-- Mmm-hmm.
- All these questionswere completely new to me,
and I think that was when Igot hooked on quantum theory-
- And then-- Quantum foundations.
- "The Ghost in theAtom," the radio series,

(36:19):
it was collected as abook as well, I believe-
- That's right, yeah, youcan still buy that, I think.
- And then there was a bookcalled "Elegance and Enigma"-
- Yup.
- "The Quantum Interviews,"which in the introduction
it says this book is in some ways
sort of a spiritual successorto "The Ghost in the Atom,"
and you are throughout this book.
How did you go from being inspired
by "The Ghost in the Atom"to essentially contributing

(36:41):
to its sequel-- To its successor, yeah.
So I hadn't thought of it like that.
Well, it was a great ideathat Max Schlosshauer had
to put that book together,and he sort of interviewed,
or he didn't interview us,you know, in an audio way.
He got us to write little pieces,
and answer to a bunch of questions he had.
I guess he was asking questionsto the kind of successors
of the figures that appearedin "The Ghost in the Atom."

(37:02):
It's a long story, 'cause I,(Lauren laughs)
I did a degree in physics.
You know, if you wantto become a physicist,
probably the best way to dothat is do a degree in physics,
and then I did a PhDin quantum foundations.
I mean, even that in itselfwas a difficult thing to do
because there were very few people doing
quantum foundations at the time.
It was regarded rather unfavorably.

(37:23):
It was not thought of asbeing a sort of subject
you would do if you were serious.
But I was too interestedin it to care about that.
So I found somebody who waswilling to supervise a PhD,
which was my supervisor, Euan Squires.
I did a PhD in it, and just kept going.
You know, once you startdoing research in physics,
you just keep going, andit's endlessly fascinating.

(37:45):
Quantum theory is endlessly fascinating.
It's constantly surprising.
You think you've understood everything
there is to understandabout quantum theory.
You work on it for 20 years, 30 years,
and then it surprises you yet again.
So it's easy to keep going.
It's a really, really interesting subject.
- Well, we have more questions,
and they're not even from us.
We collected some questions from students.

(38:05):
So Lauren, do you want to-
- Sure, yeah, we have some great questions
from some graduate students here.
So I think we're ready for the first one.
- Matt Duschenes, a PhDstudent at Perimeter.
I'm wondering do you feelaxiomatic approaches allow
for easier collaborationand mutual understanding,
as everyone is coming fromthe same starting point?
- Let me think about that.

(38:28):
I think that's right.
What these axiomatic approaches do is
they force you to clarifyvery basic concepts,
so that you can talk to people,
and you end up having toclarify these concepts
outside the naturalhabitat of quantum physics.
So an example would be, you know,

(38:48):
in quantum theory you have Hilbert spaces.
You don't need to knowwhat a Hilbert space is,
but it's an object thathas a dimension, N.
So N is an integer.
It can be one, two,three, four, et cetera,
and that's just a number thatappears in quantum theory.
But if you want to understand
what that concept really means,
then you should think aboutit in operational terms.
And what it really meansin operational terms is

(39:09):
what are the number of preparations
that you can prepare for your system
that can be perfectly distinguished?
So by thinking in operational terms,
you're forced to clarify concepts
that might have just been elements
of an obscure mathematical framework,
and I think that's truenot just for that example,
but there's many concepts like that.
They help people make progressin physics, I think, yes.

(39:32):
- The next question isfrom another student
here at Perimeter Institute.
It was sent in anonymously,so I'm gonna read it.
The question is,
"You've famously axiomatizedquantum mechanics.
"Do you think that a part oftrouble with quantum mechanics
"is similar to the one we have
"in the foundations of mathematics,
"where we know that thereare a lot of true statements
"that are not provable from the axioms?

(39:53):
"Similarly, in quantum mechanics,
"even though we have a set of axioms,
"there will always bestatements in quantum mechanics
"that are true, but we can't derive them,
"or understand them startingfrom first principles
"of quantum mechanics, such as axioms."
- So people have thoughtabout this kind of question.
I'm not among them.
There's this very interesting work
the question alludes to onthe logic of mathematics,

(40:16):
and whether that work hassome corresponding element
in physics, and people havedefinitely thought about that.
I think it's a difficult question,
and it makes my mind go blank every time
I try to think about it.
I don't know how to beginto answer that question,
but perhaps somebody whodoesn't have my blind spots can.
I really have no good things to say about,

(40:37):
no good answers to provide towhat is a very good question.
- It maybe requires a new wayof thinking like you said-
- Yeah, I, maybe I'm too old now to think
(Lauren laughs)like that, yeah-
- Great, we have one more question,
and it's from someonethat you know quite well.
- I'm Nitica Sakharwade,
a PhD student of Lucien'sat Perimeter Institute.
I'm graduating soon.

(40:58):
I had a question for Lucien about,
like a broad question about thefield of quantum foundations
as it has evolved thelast couple of decades.
So I was just wondering,I was, since I have been,
I had been writing my thesis recently,
I was also going through your thesis,
and I was just wonderingwhat it was like, right,

(41:22):
talking about nonlocality ofa single photon at that time,
when quantum foundations wasn't recognized
as a field in itself quite,
and how you think it has evolved?
In the decades since, like theredefinitely has been a boom,
and I was wondering,
so with the rise of quantum information,

(41:45):
and then now more recentlyquantum computing,
quantum hardware, quantum software,
all of these things that are coming up,
I was wondering whatquantum foundations has
to offer to them, and what are the things
that quantum computing can bring?
What questions it can bringback to quantum foundations?

(42:07):
- Good questions, Nitica.
So yeah, definitely,
it was a very differentsituation back then.
You know, you didn't gointo quantum foundations
if you wanted a job, you know?
It was sort of, you know,
a temporary state of affairs
before you had to findemployment elsewhere,
at least that was the idea,
and nobody was taking it seriously.
It started to be taken more seriously,
I think, with experiments,

(42:28):
so experiments in quantumoptics in particular.
So already, even before I started,
Alain Aspect did this sortof test of Bell's theorem,
and even earlierexperiments have been done
by John Clauser and Freedman.
But in the 1990s, these experiments became
more and more serious.
Leonard Mandel in Rochester,not so far away from here,
did all these beautifulquantum optical experiments.

(42:50):
You know, when people do experiments,
the rest of the physics world starts
to take you more seriously,
and these experimentalistswere hungry for ideas,
things that they could test.
So that was a very goodcollaboration between
the field of quantum foundationsand experimentalists.
And then as quantuminformation came along,
and also quantum computing,
in the early days, thefields of quantum information

(43:11):
and quantum computing were really,
it was really just a joining of the fields
of quantum foundationsand computer science.
So if you went to conferences
in the subject of quantum information,
then half the participants would be
from a background in quantumfoundations, people I knew,
and half would be peoplefrom computer science,

(43:31):
and it was just these twosubjects talking to each other,
trying to get a common language, you know,
like for example, Ben Schumacher,
who was the quantum foundations person,
came up with the term qubit, you know,
qubit sort of borrowing on the term bit,
which is basic in computer science,
bits at one, or zero.
Well, qubit is thequantum version of that.

(43:51):
And then once you startthinking in that way,
all sorts of questions come up
that weren't there previously,
and you know, I worked in thefield of quantum information
a little bit myself for a while.
I have papers on quantumcryptography, for example.
So this is a very excitingnew way of thinking,
and people in quantum foundations were
in a really great positionto contribute to that,
to the development, and just even the idea

(44:12):
of what that field was.
And more than that, what was happening
in quantum informationand quantum computing was
that you were finding a wayto use quantum weirdness.
So previously, quantum weirdness was
sort of an embarrassment.
It was something thatpeople hoped would go away,
you know, trying to find aninterpretation to get rid of it.
Suddenly, now quantumweirdness was a resource.

(44:33):
It was something that you could use.
This is a point that CharlieBennett makes frequently
that rather than people inquantum foundations being,
well, an embarrassment tophysics, suddenly, we were useful.
We could contribute.
That was a great-- 'Cause you knew
all about the weird stuff?
- We knew all about the weird stuff.
Yeah, that's right, yeah.(Lauren laughs)
(Lucien laughs)Just for that reason.
So, and it was a wonderful period,
and when it really wasn't.

(44:53):
It was just an idea thatcame from, you know,
marrying these two fields together,
and it was a very, veryfruitful way of thinking,
and so much was possible, you know?
But in those days, you didn'thave to think very hard
to write a paper that wasrelatively significant
in the field.
The field of quantuminformation has since become
much more technical, and people will build
their whole career in thefield of quantum information,

(45:16):
you know, without having worked separately
in quantum foundations, or in quantum,
or in computer science.
- So the conferences nowadays are
all quantum computing expertsinstead of computer scientists
and quantum foundations?
- I mean, that's the impression I have.
I mean, not all, but they-- Right.
- That's definitely-- Primarily-
- The predominant makeupof those conferences,
I think, which is, you know, is great,

(45:37):
because there's a lot ofvery technical questions,
but I think it's importantstill to keep looking
to people in those twomore basic subjects,
because there's new ideas.
One question I think is really important,
and I still think this is something
that we need to understand is what is it
that gives quantum computers their power?
Why are quantum computers more powerful

(45:58):
than classical computers?
And this is a question I remember
when the field of quantum computing
first started to be worked on
that people in quantum foundationswere very interested in.
I went to conferences withpeople in quantum foundations,
and philosophers who were veryinterested in this question.
What is it that makes aquantum computer so powerful?

(46:18):
And there's many possible answers.
You might say, well, it'sbecause of quantum parallelism.
You have, you know,different, in quantum theory,
you can have different thingshappening at the same time,
this indefiniteness I mentioned.
- Mmm-hmm.- David Deutsch believed
that it was, that quantumcomputing was proof
of the many worlds interpretation,
'cause in the many worlds interpretation,
you have all these different realities

(46:38):
being true simultaneously.
And other people thought,well, maybe, you know,
maybe it's quantum nonlocality.
Maybe the fact that you have entanglement,
and entanglement enables akind of nonlocal influence
between different distant systems,
and maybe that's whatpowers quantum computing,
and people have workingon this to some extent.
You know, recent workshowing that actually

(46:59):
the advantage of quantum computers,
it does relate back to Bell's theorem,
does relate back to this-
- Foundational?
- Yeah, that relate backto these foundational ideas
of John Bell proving nonlocality.
Another thing thatpeople have shown is that
it relates to something calledquantum noncontextuality.
I'm not gonna explain what that is,
but it's a very, a basicidea in quantum foundations,
and there seems to be a connection to,

(47:22):
it seems that you can prove
that quantum computingis related to that, too.
So Joe Emerson at the atUniversity of Waterloo nearby
has worked on that, and there was a paper
on the archive today talking about that.
So people are thinking about that,
but I think there's still a lot more scope
for that kind of interactionbetween quantum foundations
and quantum information.

(47:42):
- We're running out of time,
but I have to ask, 'cause I'veinterviewed a lot of people,
but I've never interviewed anybody
with a paradox named after them.
What is Hardy's paradox,
and what's it like to have a paradox?
- My wife asked me thisquestion, you know,
"How can you have a paradox?"
And I said, "Well, you can't.
"There isn't really anysuch thing as a paradox.
"So you can't really have a paradox
"in physics, or mathematics.
"It's always the caseof you're not thinking

(48:03):
"about the situation right.
"So it looks like a paradox,but it's not really a paradox."
And she said, "Okay, so I'm gonna call,
"invent Hardy's paradox,
"which is that there's nosuch thing as a paradox."
And in that case, theHardy is her, you know?
So she called that Hardy's first paradox.
- Right-- Zivy Hardy's paradox.
And so, then my paradoxbecame Hardy's second paradox,
and my paradox, which hasto do with quantum theory-

(48:24):
- I had a feeling it would.(group laughs)
- Yeah, it has to do with quantum theory.
So it goes back to workI did during my PhD,
and it's really a situation
where you have quantum entanglement,
and you have two systems,
and you can makemeasurements on each of them.
I don't want to explain all the details,
but one way of thinking of it,
it's not the way Ioriginally thought of it,
but other various peopledid, is that you can see it

(48:47):
as a breakdown of logical transitivity.
So if you have A impliesB, that's a true statement,
and then if B implies C, and C implies D,
so if all those things are true,
then you would expectfrom normal logic to have
that A implies D,
and there's a situationwhere that's not the case.
So you can have A impliesB, B implies C, C implies D,

(49:09):
but A does not imply D.
- Sounds like a paradox.
- So it seems like a paradox.
Now, it's only an apparent paradox
because what's happening is as you go
from each of thosestatements one to the next
you're changing other things,
not the things that thestatement is concerned with,
but other stuff is being changed,
and so, we can't actuallymake those logical inferences.
It's only an apparent paradox.
I mean, I didn't call it a paradox myself,

(49:29):
but I was quite happy to have a paradox.
- Second paradox.(Lauren laughs)
Yeah, your wife gets the first paradox-
- Yeah, the first paradox, yes, yeah.
- Well, I think we're out of time,
but thank you so much for joining us.
I'm sure we could ask athousand more questions,
but we won't.
Maybe another time?- Yeah, well, thank you.
It's been a pleasure.
(upbeat music)

(49:50):
- Thanks so much for listening.
Be sure to subscribe,
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(50:12):
and thanks for being part of the equation.
(upbeat music)