The Quantum Conspiracy: What Popularizers of QM Don’t Want You to Know

The Quantum Conspiracy: What Popularizers of QM Don’t Want You to Know

August 25, 2019 100 By Stanley Isaacs


>> GLECKLER: Hi everyone. I’m Arthur Gleckler
and I’m happy to introduce Dr. Ron Garret here, who’s going to be speaking about quantum
mechanics today. He’s a former Googler from the very early days of the company, around
2000. He was the lead engineer on the first release of AdWords and the original author
of the Google translation console. He also wrote the first billing system that Google
used. Also, for many years, he worked at the NASA Jet Propulsion Lab in Pasadena, specializing
in AI and robotics. I’m hoping to convince him to come back and talk about his experiences,
debugging spacecraft 250 million miles from the earth. Here’s Ron.
>>GARRET: Thanks. So I’m told that my abstract caused a little bit of a kerfuffle so let
me start out with a couple of disclaimers upfront to kind of manage expectations. The
title of the talk was intended to be tongue-in-cheek. There is no actual conspiracy, at least, as
far as I know but there is a fairly big disconnect between what you read about quantum mechanics
in the popular press and what the actual underlying truth is, and that’s what this talk is about.
I am not a physicist. Do we have any actual physicists in the crowd? Oh, boy, okay. You
can make sure you keep me honest. I’m a software engineer. I came upon this about actually
20 years ago when I read an article in Scientific American and I thought, “This can’t possibly
be right.” And it took me 10 years to finally find a physicist at Caltech who could explain
to me why in fact it wasn’t right and at that point, everything just kind of clicked and
quantum mechanics made a lot more sense to me than it did before. And that’s what this
talk is about. It’s about–it’s about a different way to think about QM that hasn’t gotten very
much attention and dispels this idea that quantum mechanics is sort of intractably weird.
Somebody has said to me once that quantum mechanics obeys the law of conservation of
weirdness. And to a certain extent, that is true. There is a certain amount of–quantum
mechanics extracts a toll on your intuition and some of that will never go away. But I
don’t think that quantum mechanics needs to be fundamentally any more incomprehensible
than, say, relativity which most technical people seem to have no trouble wrapping their
brains around nowadays. So with that sort of expectation management out of the way,
I want to start out by inviting you to think about the question, “What does it mean to
‘measure’ something?” So, imagine that we’re sitting here doing some experiment. We have
some system–let me grab a pointer–that we want to measure some property of it so we
have some, you know, sensor here like a camera, and it gathers some data and we feed it to
a computer, and that data shall pop up from the screen, and we look at that with our eyes,
and we form some mental image in our head, and how do we know that this mental image
that we form in our head actually corresponds to underlying physical reality? Well, one
indication that we have of this is that we can do experiments more than once and observe
that we get consistent results. So, for example, what color is this?
>>Green.>>GARRET: Green, yes. So we can observe through
our common everyday experience that the results of measurements are consistent across space
and time. And, I mean, this is really a very reliable aspect of our universe, but it’s
actually a very deep mystery why this is so. And Einstein famously said that, “The most
incomprehensible thing about the universe is that it is comprehensible.” We can actually
do experiments and get results that are consistent across space and time and we don’t really
know why that, any inherent reason, why that should be the case. Now, there is one very
plausible sounding explanation of why this is the case, and that is that the results
of these measurements are actually an accurate reflection of some underlying metaphysical
reality. That reality, that there really is a universe out there and when we measure it,
we’re getting back actual information about that underlying physical reality. And that
is the reason why these measurements are consistent because reality sees to it that that’s the
case. Well, it turns out that we can demonstrate that that’s not true. I’m about to lead you
down a rabbit hole but my purpose in leading you down this rabbit hole is to do it in such
a way that you can find your way back out again. So I’m going to do it very carefully,
step by step, and tell you in advance where we’re going. I’m going to start out by reviewing
the usual QM story. What you will read if you go to a popular account of quantum mechanics
that you read, you know, pick up at Amazon or a bookstore or read about it in Wired or
whatever. I’ll then show you how that story can’t possibly be true, because if that story
were true, it would lead to a violation of relativity, in particular, it would lead to
faster-than-light communication. And it doesn’t do this in the usual way that most people
think that it leads to faster-than-light communication, it does it in a more subtle way that really
hasn’t gotten a lot of attention. So you physicists in the room, bear with me. Then, I’m going
to walk you through some of the actual underlying mathematics of quantum mechanics, in a way
that is accessible to anyone who knows–can do basic algebra and knows what algorithm
is. And finally, tell a new story based on our understanding of what the underlying mathematics
actually says about what’s really going on and hopefully we’ll achieve enlightenment
at the end of that. So, is there anybody here who has not heard of the two-slit experiment?
All right, good. I will just blast through this very quickly. So, we have a–this is–you
have a laser that shines through two-slits, and you get an interference pattern that shows
that light is a wave and can interfere with itself like any other wave. And there are
two strange things about this. If you look at the results of this experiment with very
low intensity light, what you find is, and this isn’t showing up very well, but this
top image here shows just some dots scattered randomly. And then dots get denser and denser
and denser until down here at the bottom you have a dense enough pattern of dots that you
can start to see this interference pattern start to emerge. And this is an actual photograph
of laser light going through a single slit and going through two slits. And you can see
this interference pattern here, this is actual, an actual photograph of the same experiment,
this particular one happened to be done with electrons but the underlying physics is the
same. And the–the thing to notice here is that the total amount of light that you get
in this pattern when there are two slits is brighter than the overall amount of light
that you get with one slit which is what you would expect but that there are some places
here where you have these dark bands that were bright up here when you only had one
slit. And this is the interesting part that you want to kind of focus your attention on
because what this means is that there’s a spot here where light was shining and then
you open up an extra path for light to get to the screen and that spot goes dark. And
that is the manifestation of interference. But the strange thing about it is that this
is not a continuous phenomenon, it’s an accumulation of all these particles. Now, I can actually–I
used to think that this was a fairly subtle experiment that you need a specialized equipment
to conduct this experiment. It turns out it’s not true, you can actually do this experiment
yourself. These are some pencil leads that I’ve taped together with scotch tape and this
is an ordinary laser pointer. And if I pass these, and there’s just some very narrow gaps
between these leads, so you can actually see this happen if I pass the leads in front of
this pointer, you can see the light start to spread out. And if you’re close enough,
you can actually see the interference bands. I don’t think you can see it in the back.
But if you’re interested, after the talk, come up, I’ll give you a closer look at it.
You can actually see the interference pattern. The point here is that this is not a subtle
phenomenon and it’s not something that you need expensive equipment to reproduce. This
is an everyday experience for modern humans, at least. Okay, so this is not yet intractably
weird, because there are all kinds of explanations that we can postulate about how this might
be happening. So, for example, photons and electrons might be real particles that have
real locations and velocities like our intuitions about particles that might be pushed around
by some kind of underlying wave. And–oh, I forgot to mention–whoops–the location
where these particles accumulate is random, there’s no known way to predict other than
statistically where these particles are going to end up on the screen. So, the randomness
might just be due to some underlying real physical property that we just don’t know
how to measure. But it turns out we can eliminate this possibility as well. And the way we do
that is by asking–by trying to track the path of a particle and ask with–on its way
to the screen, on its way to producing this interference pattern, which of these two slits
did it go through? And we could do that. We can add detectors to the slits and we can
measure which of the two slits a particle went through. But it turns out that when we
do that the interference pattern goes away and the phenomenon that we were trying to
get a better grip on has changed. And it turns out that this is an inherent feature of quantum
mechanics, that any modification that we make to this experiment that allows us to determine,
even in principle, which of these slits this particle went through destroys the interference.
This is the famous wave particle duality, any modification that allows us to determine
even in principle–yeah?>>You ask people in the VC to mute their
mics so…>>GARRET: So, I’ve been asked to ask the
people on the VC to mute their mics, did I get that right? Okay. Okay, anyway, so the
conclusion from this observation is that something has to be–something has to be at both slits
in order to produce interference. And the reason we know that is because we don’t actually
need both of these detectors, one of them is enough, because if we have one detector
and it fails to register that we know the particle went through the other slit. Now,
that particle going through the other slit, it never interacted with anything, the particle
never interacted with anything, but because it allows us to know where the particle was
even though we didn’t actually measure it, that’s enough to destroy the interference
and so this particle that’s over here must somehow have known that we were looking over
here even though the particle itself wasn’t there. So, something must have been there
to be able to tell that we had a detector here, but we don’t know what that is. Now,
it turns out, this is again, this is a universal property of quantum mechanics. It holds for
any kind of particle–in practice, that means photons and electrons because that’s all there
is in this universe unless you start getting into nuclear physics. And any kind of measurement,
and any kind two-slit experiment, any experiment where you provide two different paths for
the particle to potentially go down and bring it back together without knowing which way
it actually went will produce interference and any modification that you make that lets
you figure you out where it went will destroy that interference. Now, this is still not
intractably weird because we can still tell a reasonable story about why this might happen.
So, maybe measurement does something to this system. These are after all very small particles
and very delicate systems and so maybe it’s just physically impossible to make a measurement
without disturbing the system in a way that is the cause of the destruction of this interference.
Maybe the wave function collapses and becomes a particle somehow, this is the famous Copenhagen
interpretation of quantum mechanics. But it turns out that we can rule out that possibility
as well. And the way we rule out that possibility is by asking, “How and when does this collapse,
this purported collapse, happen?” Collapse has a number of features that ought to make
us very suspicious of it just at priority without even doing any experiments. It’s a
discontinuous and nonreversible phenomenon that once you know that a particle has gone
through one slit or the other, you can’t go roll back time and undo that. And if you look
at the mathematics of quantum mechanics, which we’ll get to later, there’s nothing in the
math that’s discontinuous. And more than that, all the math is actually time reversible so
we can make a–hypothesize that this collapse happens, but this is fundamentally at odds
with the mathematics of what quantum mechanics–of how quantum mechanic says that our universe
works. So we can actually do better than that. We can actually do an experiment to show that
collapse, if it happens, is a much subtler phenomenon than it would’ve first appear and
this is the famous–this is the quantum mystery number two, the famous quantum eraser. Now,
I–this is a two-slit experiment that I have now reduced to something more abstract. So
we have some particle source, this can be photons or electrons. We have some abstract
way of splitting up particles so that it has two different paths to go down and some abstract
way of recombining that particle so that both of those paths end up in the same place so
that we get interference. And here notionally, we have one detector at one of these dark
fringes and another one at a bright fringe so that if we introduce some kind of an abstract
measurement on one of these branches then the interference pattern fusses out, that
we now have the path, the amount of light, in each detector. So now we don’t have fringes
anymore, we have the spread-out pattern that we saw and the single slit version of the
experiment. Like I said, there are lots of different ways that you can do this–actually,
let me go on to the next one. So it turns out that you can erase this, that there are
physical ways that if this measurement, certain kinds of proto measurements, that you can
do here, you can then go back and erase after the fact and restore the interference. And
here’s a concrete example of that. If we depolarize light and–I’m actually going to show you
this in just a second, so bear with me if you don’t understand what I’m about to say,
you use polarized light and you do the measurement by rotating that light 90 degrees and then
erase it by filtering it 45 degrees, that is an actual concrete example of a quantum
eraser. And I can’t show you the interference part of it but I can show you the erasure
part. So what I have here is some Polaroid film, this is the same stuff that you find
in polarized sunglasses. And, I first want to convince you, has anyone not played with
this stuff before? Okay, so again, real quick. If the–if the axis of the film are aligned
then you can see through it. Can everybody see through this? And if I rotate it at 90
degrees then you can’t see through it anymore and that effect is independent of the absolute
orientation of the film so the light that’s going through to your eyes starts at unpolarized
over here, it gets–passes through this film and becomes polarized, let’s say in this direction,
and I can demonstrate then that it has become polarized in that direction by filtering it
out using a filter at 90 degrees. And there’s also this cool adjunct to the experiment that
you can do by adding a filter at 45 degrees. If you put it in front or behind, nothing
happens which is pretty much what you–what you’d expect. But if you slide this in between,
then suddenly you can see through it again. Pretty cool, huh? And the reason for that
is because if you start out with polarized light and you filter it at 45 degrees then
some of it gets through and it’s now polarized in this direction. And now I can do the same
operation again, which is now the relative orientation of these two are 45 degrees so
some of it gets through again. But that’s not what I want to show you, that’s not the
cool part. Cool part is this stuff. This is what they didn’t show you, what they didn’t
show you in high school. This film is actually a polarization rotator. If I’d stick this
in here, I can actually take this light that’s polarizing this direction, I can rotate it
to 90 degrees that it’s polarizing the same direction as this film. And the thing to notice
here is that the apparent brightness here in the center is the same as it is up here.
There’s before, if we did the high school version of the experiment–whoops–you’ve
gotten quite a bit of loss.
So, I really can take–I can take light and I can polarize it and I can take that polarized
light and I can rotate it by 90 degrees and so I can create two different paths so I can
tell which way the light went through. I can tell whether the light is going through here
or whether the light is going through here. Actually, let me back up a step. My claim
is, without this filter, it’s a little hard. My claim is that the light that’s coming out
of here is different than the light that’s coming out of here, so I can tell which way
it went. And the way that I can demonstrate that to you is with this measurement apparatus
that lets me filter out this light and tell which way it went. So this is a measurement.
This should collapse the wave function according to the Copenhagen interpretation. But I can
undo this, and the way I undo it is by filtering at 45 degrees. And now, I have to ask you
for a little bit of suspension of disbelief because this is not high precision optical
equipment and my angles aren’t aligned just right. And if you look very closely, you will
actually be able to tell the difference between these two paths, but the difference is now
much less than it was before. See that? Oh, I’m sorry. I didn’t realize there are people
over there. Okay, I’ll just show you all this at close range afterwards. So there’s a measurement.
There’s an erasure of that measurement. The light is going this way so the–in time, the
erasure has to happen after the measurement. And if I actually had a laser to shine through
this, I can demonstrate to you that the interference would go away and would come back. So again,
these are not subtle effects and they’re not effects that you necessarily need high precision
equipment to reproduce, it’s an everyday experiment. This is $30 worth of polarizing film. So this
leaves us with the philosophical conundrum that is embodied by Schrodinger’s cat. If
there’s no collapse, then if we set up a radioactive source that triggers some kind of a mechanism
that will break a bottle of poison that will kill a cat that’s in a sealed box, can this–what
happens? Quantum mechanics says that this cat isn’t a quantum superposition of being
alive and dead which is intuitively absurd but as far as we can tell, that’s really what
happens. So if that’s not intractably weird enough for you, this is the third quantum
mystery entanglement which is usually described as sort of an ancillary phenomenon to all
these other mysteries. And, oh, yes. It’s sort of–oh, by the way, has everybody seen
this picture? Has anybody not seen this picture before? Okay. This is what the production
of quantum entangled photons really looks like. You take a–this is not–this is not
an actual photograph, this is a drawing. But this is an actual photograph of the output
of one of these gadgets. There’s an ultraviolet laser that shines through a crystal of some
material called beta barium borate, details don’t matter, and this crystal has this interesting
property that it will absorb photons of ultraviolet light and reemit them in–and that it’ll kick
an electron up to an excited state, and then that electron will drop back down to its ground
state and it will do it in two steps. And so it will kick up in one step, down in two,
and in the process of coming back down, it will emit two photons instead of one so what
comes out of this system is visible light. And the photons always come out in pairs and
they come out in matched sets because of fundamental conservation laws. We have law–conservation
of energy and momentum and so–and electron–a photon that, say, comes out over here is a
red, photon will be matched by one that comes out over here as a blue photon, and the same
thing over here. And in the middle, you get this band where you get photons that come
out at the same wavelength and it just matched in position so a photon over here will be
matched by one over here. And they’ll also be matched in polarization as it turns out.
So this is the way it’s depicted conceptually. You have these ultraviolet lasers. It’s called
a down convert–this crystal is called a down converter, and you send these photons off
to opposite sides of the universe and what–and then you measure some property out of them.
Let’s say, we split them according to polarization or position them in, it doesn’t matter, any
quantum state variables, as long as you can filter them that way and what you find is
that they’re perfectly anti-correlated because of the conservations laws. So if you get a
photon up here, on the right side of the experiment at the upper detector, that will always be
matched by a photon over here on the left side of the experiment at the down detector.
An unfortunate artifact of the English language that words “left” and “lower” both start with
a letter L so I’m going to switch back and forth between them. This is what the–what
Einstein famously called, “Spooky action at a distance.” If you take this phenomenon,
this isn’t controversial, this is an experimental–an undeniable experimental result, this really
does happen, combine that with a fact if there is no collapse with the wave function and
the inescapable conclusion seems to be that as it was put in Wired as recently as last
June, that when an aspect of one photon’s quantum state is measured, the other photon
changes in response even when the two photons are separated by large distances. And this
would seem to be impossible because it would seem to violate relativity because it’s an
instantaneous effect and we know that we can’t communicate information faster than light,
because if we could do that then we could communicate information back within time and
that would cause all kinds of problems with causality and just be a horrible mess. So
these instantaneous effects are supposed to be impossible but there is one thing that
comes to save us and that is this quantum randomness. We don’t actually have any control
over whether the photon on one side ends up at the upper detector or the lower detector
and so we can’t actually send information up here to there, we know that if we see the
photon up on the upper detector over here, then our counterpart across the universe must
have seen it at the lower detector over there but we haven’t transmitted any information
from A to B. And you can actually prove this mathematically that it’s impossible to transmit
information using this phenomenon. But it turns out that the proof of the impossibility
has a loophole. So that is the end of step one. I’m now going to on the step two and
show why the story that I’ve just told you can’t possibly be true. So let’s summarize
and take stock. A split/combine experiment produces interference. Any which-way measurement
destroys that interference, there’s some which-way that the proto measurements that we can go
back and erase after the fact and restore the interference and measurements on entangled
particles are perfectly anti-correlated. So the quantum conspiracy is that all of these
things cannot possibly be true and here’s why. So this is a thought experiment. This
experiment has not actually been done that, again, with tongue slightly in cheek, I’ve
done the Einstein-Podolsky-Rosen-Garret paradox, and it’s two-slit experiments that are fed
by quantum entangled photons produced by one of these down converter setups in the middle,
and I want you to consider the question of if we measure on the left, do we destroy the
interference on the right? So, if the answer is yes, then we have faster-than-light communication
because this interference is a macroscopic effect. It’s really easy to see if you have
interference or not. You just look at it with your eyes. You don’t need any kind of delicate
detectors or anything so you just measure over here and take measurement away, measure,
take the measurement away, and over there on the other side of the universe, this interference
pattern will come and go and you can send Morse code instantaneously. That’s obviously
impossible, so the answer must be no. But if the answer is no, then we know the position
of one particle but we have interference regardless and that contradicts the fundamental principle
of quantum mechanics, which is that we can’t know the position of the particle and still
have it interfere. Now, this is not yet an iron-clad argument. There is one other possibility
that I have not mentioned here. Can anybody think of what it is? Any of the physicists
in the crowd? Oh, good. So, this one last possibility, and that is that if there was
no interference to begin with. It might be that entanglement sort of counts as one of
these subtle proto-measurements that destroys the interference so we didn’t have any interference
to begin with. But it turns out that doesn’t get us out of this faster-than-light conundrum
because, fine, if that’s the case, then we can still produce faster-than-light communications
by putting in a quantum eraser and destroy the entanglement. Entanglement is a very–is
a very delicate property. Physicists work very hard to produce it and maintain it. It’s
very easy to destroy. So, just destroy the entanglement and produce interference where
there was none before and, again, we have a faster-than-light signal-ly mechanism. Now,
that is a very compelling argument that the story that I have told you, the usual quantum
story is wrong. That argument is, in fact, correct. The story that I have told up until
now is, in fact, wrong, and that’s why.>>You said this experiment hasn’t been done,
why not?>>GARRET: Because all physicists know what
the outcome will be. And I’m about–I’m about to tell you what the outcome will be. And
by the time I finish telling you, you will be convinced enough that the outcome is what
I tell you that it will be that you won’t need–feel the need to do the experiment either.
I promise you–hmm?>>GLECKLER: Why don’t you repeat the question.
>>GARRET: Oh, I’m sorry. The question was, why hasn’t this experiment been done. Yeah?
>>So the entanglement is about polarization, in which way it goes through a splitter, is
that about exactly the same polarization, we know they’re the same?
>>GARRET: That’s right. So, I assuming here, like I said, there are lots of different ways
that you can do the split-combine experiments. You can use some thing called a Mach-Zehnder
interferometer. You can use something called a Stern-Gerlach device. You can, you know,
lots of different ways. When I talk about polarization, the way that the splitting is
done is with the device called the polarizing beam splitter, which is exactly like one of
these, except instead of just absorbing half the photons and letting half the–half of
them go through, it reflects them. So it look like a mirror, a half-silvered mirror, and
what comes out this direction is photons that are polarized one direction and what gets
reflected at the other direction are photons that are polarized in the opposite direction.
Okay, so we are now in the depths of the rabbit hole and now, it’s time to find our way back
out. We’re going to do some math. Don’t panic, it will not be as bad as you think. This is
the mathematics of quantum mechanics right here. This is the famous Schrodinger wave
equation. It’s–this is the free variable here is this thing called psi. Psi is the
quantum wave function and it obeys the dynamics of this partial differential equation, which
those of you who are proficient in partial differential equations, will recognize as
a wave equation like any other equation that describes waves, and that’s why these particles
seem to propagate like wave because this is the map that describes how they propagate.
The point here is that these, the dynamics of this thing, are continuous and time-reversible.
All wave equations have continuous time-reversible dynamics. And the second part of quantum mechanics
is that you take this quantum wave function, which is a function of position and time and
is a complex number, you take the norm, the magnitude of that complex number and square
it, and that gives you the probability of measuring a particle at this position X at
a time T. That’s really all you need to know about the mathematics of quantum mechanics.
There are some things to note about this. There is this distinction between the underlying
amplitudes, which are complex numbers, and the probabilities, which are of where we find
these particles, which is the only thing that we can measure which are real numbers. And
the reason that particles can interfere is because complex numbers with magnitudes greater
than zero can add to zero. You can have a complex number that points off in this direction,
another complex number that point off in that direction. They always have magnitudes greater
than zero but they can add and destructively interfere. The dynamics are continuous, time-symmetric,
fully deterministic and hence, reversible, and so there’s no place where you–there’s
no place you can find anything that resembles collapse in this math. And no randomness either,
by the way. Going from amplitudes to probabilities by taking this wave function and squaring
it has no physical justification or whatsoever. It’s purely a hack. But it’s a hack that works
really, really well. So here’s what the actual math looks like for the two-slit experiment.
This is, and if you go to actual papers on quantum physics you won’t find this in the
popular press, this is what you will find in physics journals. This is–or physics texts–this
is the state, the amplitude of the photon being at the upper detector. This is the amplitude
of photon being at the lower detector and we have to divide by the square root of two
in order to make the total probability come out to be one. So to figure out the probability,
we take this number, which is a complex number, and take the modules and square it. And when
we do that, it’s almost exactly the same as just squaring A plus B in 8th grade algebra
class, you get A squared plus B squared plus AB plus BA. You have to take these complex
conjugates because they’re complex numbers, and the square root of negative one pops in
there to do some weird things, those kind of details don’t matter. The point is this
is a complex number, psi U is a complex number. Its magnitude is a real number and when you
square it it’s a positive real number. So here we have a positive real number, here
we have another positive real number, the sum of those two has to be a positive real
number. But over here we have two different complex numbers and two different complex
numbers that were multiplied together so this sum can be negative. So this is–this is where
the interference comes from. This is the mathematical manifestation of interference in quantum mechanics.
That’s what it looks like in terms of Greek symbols. So, what happens when we add detectors?
Well, when we add detectors, the amplitude starts to look like this. We have the amplitude
for the photon to be at the upper detector times the amplitude for the detector to be
in the state where it shows that the particle is at the upper detector and the same thing
at the lower detector. So this is just the mathematical description of that. And when
you–when you–when you take the amplitude to that and square it, here’s what you get,
same thing as before, psi U squared plus psi L squared. And this, which looks an awful
lot like an interference term, right, which is weird because I just got though telling
you that if we have a detector that we know–tells us which way the particle went, that destroys
the interference. Well, there’s this subtle difference here between what we have now-what
we have before, and that’s this weird notation here, which is called the rock–bracket notation.
You don’t need to concern yourself with it. Just take my word for it when I tell you that
this quantity here is the amplitude for the detector to spontaneously switch between indicating
that the particle is at the upper slit and the lower slit. In other words, it’s a measure
of the reliability of the detector. That just comes out when you do the math. And if the
detector is working properly, that value–oops–this–this value is the amplitude for it to spontaneously
switch between UNL and spontaneously switch between L and U, those are both zero so this
term goes away. That’s the math of how measurement destroys probability. And the interesting
thing about this is that measurement is a continuum. It’s not a dichotomy. The math
tells us that we can measure just a little bit or we can measure mostly but not quite.
And we have vary–it’s a varying levels of interference that we get depending on whether
the measurement that we’re making is reliable or not. That’s what the math says. So what
about entanglement? Well, this is, if you go to a physics paper that talks about entangled
particles, this is what you will see as the mathematical description of a pair of entangled
particles. What this means is that you have an amplitude for the particle on the left
to be in the up state and the particle on the right to be in the down state superimposed
with an amplitude for the particle on the left to be in the down state and the particle
on the right to be in the up state; again, divided by the square root of two. Now, this
looks a lot like the–or the unmeasured two-slit description. But there’s some notational sleight
of hand going on here because this is shorthand for this and it’s an unfamiliar notation.
This vertical bar, followed by the bracket, this is a term. So you got–this is a quantum
wave function here. This is another quantum wave function here. This is the wave function
for the upper particle. This is a wave function for the lower particle. Another way to write
that is–you don’t have to use arrows, that’s just a notational convenience, so I could
call this the left upper particle and the right downward particle, and the left downward
particle on the right upper particle. And this is just another way of writing this Psi,
this quantum wave function. So this and this are the same thing in different notations.
And this should now look familiar. This is exactly the same as–oops–as this, the two-slit
experiment with the detector, module of a few labels. And so, that is now the answer
to the first part of the EPRG Paradox. In fact, entanglement does count as a proto-measurement
that destroys interference. But it’s actually much deeper that that. According to the math,
entanglement and measurement or the exact same phenomenon, the math is exactly the same,
and that is why entanglement destroys interference because entanglement is measurement. And I
have a lot more to say about that later in the talk. So okay, so there’s no interference
but now what about this last–the idea of creating the interference using a quantum
eraser. So let’s take another look at our–I’m running little short on time so I’m just going
to blast through this. This is what the state equation looks like for the quantum eraser
after the so-called measurement but before erasure. So you have an upper photon that’s
horizontally polarized because we’ve–let’s assume we start with a vertically polarized
light going in here and we measure by rotating 90 degrees. So we have now the upper photon
rotated from vertical to horizontal and the lower photon still vertical and this you will
now–you should recognize as a measured and therefore non-interfering state. And it turns
out that if you filter now at 45 degrees this is the state function, the quantum wave function,
that you end up with. You now have a photon that’s either in the upper or lower slit and
that’s either horizontally or vertically polarized, and this kind of makes sense because if you
think of these as vectors and you have a horizontal polarization plus a vertical polarization,
that’s a 45-degree polarization, which is exactly what you would expect to see if we’re
filtering it 45 degrees, right? But remember the square root of two term here that I told
you was there in order to make the total probability to come out to be one? Now, that’s a two root
though, and if you run the math on this you find out that the total probability is not
one, it’s one-half. So either we’ve made a mistake or half our photons have gone missing.
Well, in fact, half our photons have gone missing which is also shouldn’t be too surprising
because we filtered–we put this 45-degree–we put this filter in place. This filter is filtering
out half the photons that go through it. If it–if they come in at 45 degrees then half
of them come out polarized this way and the other half get blocked. So it turns out that
the other half, the half that didn’t get through, have a different wave function that has a
negative sign over here, which again, makes intuitive sense because the filter lets these–the
filter is at 45 degrees so it lets this axis through and this axis, which is the H minus
V axis it blocks. And these photons interfere with themselves and these photons also interfere
with themselves. So the photons that passed through the filter display interference fringes
and the photons that don’t pass also display interference but it turns out that they’re
anti-fringes. They’re exactly like the bright spots in the interference fringes for the
photons that got filtered out, exactly lined up with the dark spots of the fringes for
the photons that were let through. And they sum together to produce what we perceived
when we look at it as non-interference. So this quantum eraser doesn’t actually erase
anything and it doesn’t produce interference, it just filters out interference that was
actually already there all along. And it turns out that we can actually do this in the EPR
experiment too. And the way that we–but in order to do it, we have to transmit classical
information from one side of the other in order to do the filtering. The way it works
is you make a record of all the photons that you collected over here and keep it in order
so you’ve got this record of first photon was at the upper detector, the second photon
was at the down detector, and so on and so forth, and over here you keep track of which
photons ended up where on your screen, and then you take this record and you transmit
it over here by some classical slower-than-light channel. And you look at all the up photons
and sure enough there’s an interference pattern, and you look at all the down photons and sure
enough there’s an interference pattern. But the only way to see that is to take classical
information and move it from here to here. And that is the last nail in the coffin. I
was very disappointed when I learned this 10 years ago because I was really counting
on winning a Nobel Prize and taking over the world but, oh, well, this is the next best
thing. So the take-home message up to this point is measurement and entanglement are
the same phenomenon, and what you will find in many, many accounts and even some professional
accounts, is that they’re completely different. That measurement is this common everyday thing
that we can sort of intuitively grasp and entanglement is the quintessential quantum
mystery and in fact they are really the exact same thing. Now, having come to that realization
we can now tell a different story about quantum mechanics that to my software engineer’s mind
is much more intuitively pleasing than any of the other competing alternatives. So Copenhagen
is the most popular but as we’ve seen it, it’s scientifically untenable. There just
is no collapse. Their–the next most popular interpretation is the so-called “many worlds”
interpretation where it says that anytime that a particle can go multiple ways, the
entire universe splits and the math actually supports that, but I personally find that
that takes a heavier toll on my intuition than I’m really willing to concede. There’s
another thing that nobody’s ever heard of called the “transactional” interpretation
by fellow named Cramer at the University of Washington. Actually, if you’re really interested
in this stuff, I encourage you to take a look at because it is kind of interesting. It postulates
that the backwards in time solution for Maxwell’s equation are physically real and if you make
that assumption then you can explain a lot of stuff, but I don’t have time to get into
that. What I want to talk about here is the quantum information theory which I have dubbed
the “zero-worlds” interpretation of quantum mechanics. It’s an extension of classical
information theory with complex numbers and if you run through that math you get some
very interesting results. So here is a lightning introduction to classical information theory.
It’s the study of this quantity called the Shannon entropy of a system A, which can be
in any one of a number of classical states, and it’s defined as the sum of the probability
that the system is in sum state A times the log of that probability and then you take
a negative sign. And intuitively, it’s a measure of the amount of randomness that’s in the
system A. So just to simplify things for the purpose of this talk, if the system has an
equal probability of being in one of N states, then the entropy is just the log of N. So
when N is one and the system is definitely in one state then the entropy is zero. And
if it can be in one of two states with equal probability and we take this log base two,
we measure information content in bits, then it has one bit of randomness in it. You can
define all kinds of other derived quantities like the joint entropy of multiple systems
and the conditional entropy, and this quantity here which is called the information entropy
which is a measure of how much information a system A contains about a system B, and
the interesting thing to note about it is it’s the sum of some of these other quantities
that had been defined up here. And the information entropy ranges between zero and one, where
zero means that this system has no–system A has no information about system B, they’re
completely uncorrelated, and one means that they’re perfectly correlated. So for example,
because they’re sums we can describe these quantities as Venn diagrams. So this circle
here on the left is system A and this circle on the right is the system B, and the total
entropy is contained inside these circles, the total entropy for each system, and the
information entropy is here in the intersection, and that leaves the conditional entropy out
here because the information entropy is the system’s individual entropy minus the conditional
entropy, just simple addition. This is the important part. If we flip two coins so that
they’re completely independent of each other, this is what the numbers end up looking like.
The conditional entropy, the coin A has one bit of randomness and coin B has one bit of
randomness so the total entropy in the system is two bits of randomness. The system as a
whole of these two coins can be in one of four states, the log of four is two, and there’s
no information that one coin contains about the other. By way of contrast, if we have
a coin with a sensor, just looking at that coin telling us whether it’s landed heads
or tails then–and the sensor is working properly, then we have one bit of information entropy
because the sensor gives us perfect information about the coin and vice versa by the way.
The coin gives us perfect information about the sensor, there’s no directionality here,
and the total entropy in the system is one bit so it’s only going to be in one of two
states, heads and sensor says heads, or tails and sensor says tails. If we extend, do the
same math again except using complex numbers instead of real numbers then you end up with
something called the Von Neumann entropy which is called S and this hairy-looking equation
over here, which I don’t have time to go into, but the intuition is kind of the same as it
was before when we talked about how interference was produced. Because we’re now dealing with
complex numbers rather than real numbers, the information entropy is no longer restricted
to the range zero and one. And, in fact, entropies are no longer restricted to be positive real
numbers, they can be negative. And this turns out to be, if you do the math, the entropy
diagram for a pair of entangled particles. You get a negative bit of entropy over here.
And the information entropy, the amount of information that one particle quantum information
now, that one particle contains about the other is two bits. So you can think about
two entangled particles, the math is telling us that these particles are now, somehow,
better than perfectly correlated. They have become super correlated and the total entropy
of this system, the sum of all these numbers, is zero. There’s no randomness. That’s not
yet the cool part. What happens when we take a measurement? Well, when we take measurement,
we have a particle that becomes entangled with a macroscopic system of particles. So
what happens if we have three mutually entangled particles? You end up with a Venn diagram
that looks like this and if we assume a two-state system then the actual numbers come out looking
like this. You’ve got one bit of information entropy between A and C, one bit between A
and B, and you’ve got this negative, this weird negative entropies over here and it’s
all kind of mind-boggling. But let’s imagine that this particle down here is the one that
we’re measuring and this is our–these two particles here are our measurement apparatus.
And let’s look just at the measurement apparatus and ignore the fact that we’re actually measuring
a particle here. So we’re going to take this particle C, we’re just going to throw it out
for a minute. It turns out that ignoring C is exactly what is represented by this trace
operator here that ends up showing up in the math. Look what happens. This one bit of information
entropy–we lose this boundary so this one, the negative one, cancel out and become a
zero, same thing over here, and what we have is if we ignore this is exactly the same system
from an information theoretical point of view as a coin with a sensor, we have two classical
particles that are perfectly correlated with each other in a classical sense. I should
remind you of the experiment that we did at the beginning of the talk where everybody
agreed that that’s something was green. And we can get that from quantum mechanics, we
get these two systems that are in classical correlation. But we did that not by actual–not
by having an objective physical reality that we reflect but actually by ignoring the thing
that we’re measuring, or that we think we’re measuring. As it turns out that this extends
to any macroscopic ecosystem. If you add an arbitrary number of particles the entropy
diagram ends up looking exactly the same. So, this is now the mathematical description
of a quantum measurement. You have the system that you’re measuring. It’s particle Q. It
interacts and gets entangled with A particle, which is in the parlance of the theory called
an ancilla which is why they label it A, and that ancilla then gets entangled with a macroscopic
measurement apparatus in system of 10 to the 23 particles, and the entropy diagram ends
up looking exactly the same where this entire system has the same quantum information, theoretical
information content, as the third particle in a three-particle entangled system. So,
that is now a description of what measurement looks like purely in terms of quantum mechanics.
And the interesting thing about that is it describes all of the microscopic phenomenon
that we see that we naively observe about classical measurements but it’s purely in
terms of quantum mechanics, which means that it’s reversible. So, their–so, somehow, we
ought to be able to undo an actual physical classical measurement but in practice we can’t
seem to. And the reason for that is because in order to do that–in theory, it’s possible,
but in practice we would have to undo all of the entanglements in this macroscopic system.
So, for me, to now go back in–back in time, you know, we aren’t really going back in time,
but for me to erase all of your memories of having seen this green thing on the screen
and agreed that it was green at the beginning of the screen, I would have to undo this enormous
web of entanglement that has since proliferated at the speed of light. I have to bring all
those particles back together and recombine them. And in principle, that’s possible and
in practice, obviously, it’s not, which is why classical measurement seems to be irreversible
despite the fact that the physics of the universe say that everything is reversible. So, this
has some philosophical implications. I call it the zero universe interpretation of quantum
mechanics. If you really–if you buy this as a description of what the physics of the
universe is really like, then it tells you unambiguously that it is not the case; that
the reason that measurements are consistent across space and time is because there’s a
real underlying metaphysical reality out there. It tells you in fact, the exact opposite,
that what we really are is, as David Mermin puts it, “correlations without correlata.”
We are not made of atoms we are actually made of bits. We are our thoughts and these thoughts
actually reside, if you will forgive stretching a metaphor to the breaking point, we are a
simulation running on a quantum computer. I’m going to skip that. So, the take-home
message is, going back to this Einstein quote that, “The most incomprehensible thing about
the universe is that it’s comprehensible.” Here’s an explanation in terms of physical
theory of why the universe is comprehensible. Quantum mechanics actually predicts a comprehensible
universe but at the cost of forcing you to believe that what you perceive as physical
reality is not actually real it’s actually an illusion. And the motto here is that “spooky
action at a distance” is no more and no less mysterious than the “spooky action across
time” that lets us perceive the universe as consistent from one moment to the next. They’re
both produced by the exact, same physical phenomenon, namely entanglement. And I’ll
leave you with this quote from an ancient Japanese Zen master and open the floor for
questions. Uh-oh, the physicists are walking out. Yeah?
>>So you have the three particles when you remove from the shell what the main two look
like and they were building to the point in the sensor. Why not leave the–what happens
when you leave a third particle away? And if you’re taking that as another thought experiments
and say, “Well, this is equivalent too.”>>GARRET: Yeah. Well, this is–so these are
all just math, right?>>Right.
>>GARRET: So, these are all mathematical manipulations, the results of which we interpret
in order to tell stories about what our world is like. And if you leave it in, then what
you have is a description of the unadulterated underlying physical reality, which is quantum.
And the reason that’s hard to wrap your brain around is because your brain is classical,
everything that you are is classical. You’re made of classical bits that ones–or you’re
a Turing machine, you’re not a quantum computer, but you’re made out of a quantum computer.
And that’s why there’s this fundamental disconnect that will always take a toll in our intuitions
that will never go away because they’re really fundamentally different. The difference between
real numbers and complex numbers, the underlying reality is complex, but the thing that is
processing the information that lets you think about these things is real. It’s made of real
numbers. That’s really the underlying–the pithiest way I know of summarizing this so
it just depends on what point of view you want to take.
>>I’d like to make a short pitch for the multiple universes and hear your response.
The multiple universes, one way to look at it is the natural equation, it allows for–because
it’s linear, you can have things occurring that live in the same equation and sometimes,
say, with the dead and a live cat, you can see that you can actually sort of separate
them, each goes its own way, they don’t interact much, so a very good approximation is to consider
them one at a time. However, when real quantum effects go then you cannot do it this way.
So, there are–there are some things that you can separate and some not. So, now, you’re
saying that you have an interpretation of a one universe so…
>>GARRET: No, not one. Zero.>>Zero, all right.
>>GARRET: Very important distinction. One universe, one classical universe really is
untenable.>>Well…
>>GARRET: You can–you can–that’s Copenhagen.>>Yeah.
>>GARRET: You can–you can–yes, the–so the question was, what do I think about multiple
universes? Multiple universes are just as tenable, according the math, as zero universes.
The only thing that’s not tenable is one classical universe, that’s–that’s the only thing that
the math tells you unambiguously does not exist. And it’s a matter of taste. You know,
I personally–one of the things that the–that the math tells you if you think about it in
terms of multiple universes, is that once you get beyond a certain level of separation
these universes are forever inaccessible to us, even, you know, to any reasonable degree
of approximation. And then there’s this philosophical question of is the thing actually real and
the analogy that–the best analogy that I’ve heard is imagine a photon that leaves the
back of the sun and goes away from us and so it’s forever outside our light cone, is
that photon real? And my reply to that is there’s a difference between the photon that
leaves the back of the sun and travels away from us because there’s always the possibility
that somewhere out there’s a mirror that’s going to reflect that photon back to us and
we won’t know that until that mirror actually reflects it and it comes back and we can see.
But in the case of multiple universes, we know unambiguously the math tells us so that
once another universe splits off, it’s never coming back. There’s no way to bring it back.
>>After a concurrent time, it will.>>GARRET: Excuse me?
>>After a concurrent time, it will.>>GARRET: Okay, in any amount of time that
we have any practical reason to care about. So, yes, if you’re thinking cosmologically,
multiple universes is a–is a tenable interpretation. If you’re thinking in terms–if–if you want
a story that you can help you to understand how the universe works in terms of your everyday
life and what your fundamental nature is, I personally find that I gravitate more towards
the information theoretic point of view and believing that–that I’m–I–the universe
that I exist in is a very good high-quality simulation. But that’s a matter of taste.
>>So do multiple universes conserve mass energy?
>>GARRET: That I don’t know. I have to defer that to the physicists. That’s a very good
question. I don’t–I actually don’t know the answer to that.
>>Could you amplify a bit more for what does a zero universe mean?
>>GARRET: This–oh, by the way, the question back here was do multiple universes conserve
mass energy. It’s a very–a very good question because–and I don’t know the answer. I should–I
should ask–I need to ask a physicist who…>>I’ve asked this question of “many worlds”
proponent and the answer I got is, yes, that you’re not actually doubling the amount of
mass, you’re dividing the amount of mass into two effectively but…
>>GARRET: Oh, okay. So somebody in the audience is saying that when universes split, the total
amount of mass in the universe gets evenly divided between the two universes and I’m
guessing that math works out in such a way that if you reduce the amount of mass in a
classical universe uniformly by one half, that everything ends up working out the same
as it did before. But I’m going to have to think about that.
>>So this is just even one universe does not conserve mass energy with anything. Universes
as whole…>>GARRET: Okay.
>>And yet, in one–in the universe we’re in, we don’t seem to see this mass dwindling
away.>>But it’s, you know, because we’re doing
the same…>>GARRET: Yeah. So in that, we are now beyond
the limits of my knowledge of this stuff. Yeah?
>>For those of us who are intrigued and teased, where can we learn more?
>>GARRET: So, I have paper about this. It’s on the web. I highly recommend David Mermin’s
book, Boojums: All the Way Through, where he doesn’t actually talk about this but he
talks about the Bell inequality in a very accessible way, which is also–I didn’t have
time to talk about that but it’s very worthwhile knowing about. Or send–send me an email.
I can actually put you in touch with the guys whose research this talk is based on. They’re
down at Caltech, I think. Yeah?>>So is this an entirely local theory that
all interactions are interacting locally propagating at the speed of light, or is it?
>>GARRET: Well, so this get–so, the question was is this a local, purely local theory.
It’s quantum mechanics. And whether quantum mechanics is purely local is the subject of
debate. And it depends–it depends on what you mean by purely local. Classically, it’s
not, and quantum mechanically, it is. You know, I–this sheds no extra light on that
question. Okay, I guess, that’s it.