Joel, thank you. I work with good people.
You just heard from one of the best. Thank
you very much. Also, I want to thank...there are
two things going on here. One is what I'm
going to say tonight and the other is a book.
You're not going to hear much about the
book, except the fact that there's some
parallel between what's in the book and
what I'm going to present tonight. But, I
have to commend Emily Cook and Andrea
Velasquez for the propaganda, I'll call it,
to suggest that a talk about quantum
mechanics could be a good thing. We will
find out. I'm also electronically
connected to things that should make me
audible. If I'm not heard by
somebody in the room who'd actually like to hear me,
you could make a commotion. I'll try to
improve on that. Two things I would like
to do is one to do with the book another
to do with the kitty cat. And
having acknowledged the folks who have helped
with this evening, I also want to
acknowledge the people made the book
possible. Lynn, who is subjecting yourself
to this stuff again, had a very different
notion of what my retirement would look
like. The idea of an elderly chap in the
back room huddled over a laptop about 12
months wasn't in her picture of what
that was. But that's what it turned out
to be. And she still is there and
she's still here. Thank you. Three people
read most of what's in the book. Read it
very carefully.
Commented on it. Made it better. Read it
again. Made it better again. And they are Paul
Bourdon, formerly of our math department.
And Dan and Irina Mazilu, currently
of our physics and engineering
department. Without them the book
would be much worse; but, it is not their fault.
What I want to do is to explain two
things. What is discreet about discrete
quantum mechanics? Apply that title. And the
other: who or what is Schrödinger's cat? And I
think if I succeed at one of those, I'll go
home happy. And I do plan to go home
before the Virginia Tech game starts,
before the Cubs game starts, and maybe before most
of you leave.
This is going to require talking quite a bit about the
history of quantum mechanics and it has
to start with the person that really
initiated the idea, Max Plank. He
presented a paper in December of the year 1900.
And there was this end of the
century idea among physicists, and
it happened again at the end of the 20th
century, of you know don't worry we got
this.
There's so much we know about nature
through physics, what's left is
details.
There's nothing new to be discovered and
that's what the majority opinion was at
the end of the 19th century. Two reasons
for that belief. One is Isaac Newton, from
middle of the 17th century, who had
presented a theory of how particles behave,
how they interact, how they move. A very
predictable, very deterministic theory,
where if you know enough about now you
can predict the future with perfect
precision.
Well, the problem, of course, was knowing enough about now.
But, that was the idea of Newton then. Only
about 50 years earlier about 18..in th e 1850s,
JC Maxwell developed a
theory of electricity and magnetism--
how those two phenomena were in fact one
phenomena. Two aspects of one phenomena.
And help describe radiation, light,
infrared, ultraviolet, all manner of
electromagnetic radiation. With those two
things in hand, it was good reason to
believe, you know, "we we got this."
There's a problem now, and the problem had been
about 10 years old as of the year
1900, having to do with this..
what's called black body radiation. If
you stick a piece of metal in a fire and
it heats up it will begin to glow and
the harder it gets, the more light comes off, the
greater the glow. And also the color changes--
the mix of colors that come off of a
growing body. That's called blackbody
radiation. And combination of Maxwell and
Newton were not enough to explain
what was going on. It was a very confounding
ideas. And at this December 1900 meeting,
Max Plank proposed that the glow was not
continuous. It was not kind of a
fluid of the energy. That it was lumpy.
If you assume that what comes off of
that glowing piece of steel in your
fireplace, is not continuous radiation
but photons, new idea that he presented,
energetic particles you could explain
both the color and intensity of
radiation that comes off of a
glowing-hot body. First quantum
explanation Max Plank 1900 is a Nobel
Prize and almost everybody I talk
about today will be a
Nobel Prize winner in physics. He won
the Nobel Prize in 1918 for this work. So,
we go down the gallery to the next
portrait and it's Erwin Schrödinger.
Schrödinger 25 years later looked back at
the
collection of work that was done in both
experiment and theory for quantum phenomena,
things that did no longer agreed with
what Newton would have or with what Maxwell
would have, but were unusual. And these
experiments and the theoretical
explanations of those particular
experiments formed a body of work that was
not particularly coherent. What Schrödinger
did was to produce a coherent theory
that explained all of these things. And his
theory was a wave theory. It was based on
the notion that quantum things at this
point it was thought maybe electrons, maybe
atoms, maybe nuclei, not real sure about
other things...we'll find out that cats work
too, behave like waves. In this picture
represents...so you can imagine several
things, but if you imagine that overhead
view, have some very regular ocean waves
coming in towards a seawall where there are two
narrow gaps. And what happens when the waves
hit those gaps
is that the other wave's energy passes through
each gap. But what it doesn't do is
send a little gap shaped little wave in a
straight line. What happens to the energy
that comes through here is it spreads
out. And that phenomena is called
diffraction. Waves diffract. Water waves
diffract.
Sound waves diffract. Electromagnetic
waves, visible light, diffracts. The other thing
you can see going on here is that the
wave energy that came through this gap and
this gap overlap in a certain region
and strange stuff is going on in that
region. Because with these two sources
the waves, of up-and-down ungulations,
there are regions where the up-ungulation of
one source coincides with the
down-ungulation of the other source,
essentially canceling each other out. So
all this up and down over here with an
up-and-down over here turns into nothing.
The dark areas in that region correspond to
that kind of destructive interference.
As far as waterways concerned, if you were
standing in the water here, you would
feel no wave action or very minimal
wave action. But to your left and right
are regions that are colored in that
overlap region where the waves are higher
than the single ways that came through either the
gaps. Constructive interference. Waves do
that.
Particles don't do that. You don't throw
to baseballs together and find no
baseballs. But deBroglie proposed
something different. This is Louis deBroglie
finishing his dissertation at the University of Paris,
1924, and proposed only pretend electrons
do this. Electrons. Baseballs. Hard
particles. Let's assume they diffract and
they interfere.
Not only with each other but interfere
with themselves. Crazy idea. The faculty at
the University of Paris was not crazy about
the idea. They were all trained classical
physicists. And they sent this
dissertation to Berlin, which is where
Einstein was at the time. And he read it
and he said, "It's a crazy idea; but, it's
consistent. So give the boy his degree.
Send him away."
OK. So they did. 1924 he was sent on his way. Three
years later electrons were
experimentally see to interfere and diffract.
Three years after, deBroglie had his
Nobel Prize. So Albert got it
right. So, yeah Emily's cat had to leave
this evening, so we're using a different
cat. Those who know about Erwin
Schrödinger, know about Schrödinger's cat.
Very few people who don't know about one
know anything about the other. But if you
you go and google the term
Schrödinger's cat, you have about a half
million hits. So it's a very popular
notion.
Seldom is this cat given a name.
I propose to call it Flüffy. So, we'll talk a
lot tonight about Schrödinger's cat, about
Flüffy. We'll see a lot of him; but, not
immediately.
So we move down the the gallery to
another chap, Werner Heisenberg. Schrödinger
is Austrian. Heisenberg,
German. He also looked back at this 25
years of work, from 1900 until about 1925, and
said, "I can create an encompassing theory
of all this work, too." And it was profoundly
different than what Schrödinger had to do.
It was not waves. It was not
continuous behavior of things. It was
discrete. Thus, the name on the book. It
turns out, always by coincidence, that the
various things I did in my research
career, which were quite unrelated to one
another,
all seemed to be physics that was best
explained using Heisenberg's idea rather
than Schrödinger's idea. And so, when I sat
down to get something off my chest,
it happened to be the things I knew
best and that's why i wrote about
this. But Heisenberg published his
theory in 1925. The end of 1925 Schrödinger,
I think, was January 1926. So these guys
were totally independent of one another
and both claiming to have encompassed a
quarter-century of quantum science.
Now, that the discrete nature what Heisenberg
had to do relates to two things. If you
remember, when I mentioned Plank, I said
this radiation coming off of a hot
object when it glows was a lumpy. The
photon notion of light being made up of
little particles. That's one of the
discrete pieces that Heisenberg
jumped on. The other was the so-called Bohr
model of the atom. This was 1913.
Niels Bohr was working in the
Cavendish lab in England and studying
the nucleus and came up with this notion
that explained the experimental results they were getting--
that the atomic nucleus was
really dense and actually much smaller
than this picture would represent very
dense core carry most of the mass of an
atom and electrons kind of buzzed around outside
in discrete orbits, not anywhere they
wanted to. It wasn't planetary in the
sense that we still believe that if the
earth were placed ten percent more
distant from the Sun it'd be happy there.
If it had the right speed, it could orbit.
There's no particular groove that the planets have
to sit in in the solar system. But,
according to Bohr's model, there were
grooves for electrons. They couldn't be
elsewhere. If you tried to move one, tried
to move this little guy that way, it
wouldn't move until you pushed hard
enough to have it jump to the next level.
So one of the immediate successors of
what
Heisenberg did was to explain this
phenomena in a mathematical way.
So now we go back to Heisenberg and
Heisenberg's dog. Heisenberg's dog, I was stunned.
I googled Heisenberg's dog and I got nearly as
many hits on that phrase as I did on Schrödinger's cat!
And it turns out that some fairly
contemporary work in quantum information
theory has adopted this puppy and use
that term enough to keep google busy.
But Axel you find on facebook, he
does not have a Wikipedia page. You can
draw your own conclusions. OK. So I will
say no more about Axel and probably
it's not worth mentioning it you know
parties or anything, but I don't think
Heisenberg lived alone. He did have a
friend.
OK. So we've got Heisenberg / Schrödinger both
presenting a series that seemed so
distant and some people were suspecting
they were doing the same thing in
different languages, different mathematical languages.
Some people assumed they were
not compatible. And up comes the only
mathematician I'll mention tonight and
that's John von Neumann. And von Neumann was
working about eight years later, 1933.
We'll see
an image of the cover of a book her wrote. But,
what von Neumann did was to show the absolute
equivalence between Schrödinger's theory and
Heisenberg's theory. That neither was more
encompassing than the other. One could be
derived from the other. The other from
the one. That's his contribution plus a
very profound formalism for approaching
quantum problems whether you want to deal
with the continuous wave-like nature as
Schrödinger would have it or the discrete lumpiness
as Plank would have it. So there's
von Neumann's book. And he wrote this book as
Euclid did in dealing with
geometry. Euclid put down a handful,
tiny number of discrete postulates.
If we assume the following things are
true, all of geometry follows from it.
That's what Euclid did.
What von Neumann did was to say this about
quantum mechanics. He wrote a postulate
about quantum states, what they were, how
they looked how to treat them
mathematically. Another about how they
change. They aren't static objects. It's hard to make
them static. They change and they change in
two ways. The third postulate had to do
with quantum measurement, and this is a
profound movement away from the
deterministic Newtonian world. The fact...I
mean if you think like Isaac Newton
thought, particles bang against each other.
They do things. They move. And if you're
gentle enough, you can watch him do it
without bothering them. That the observer
is not a part of what's being
observed. Quantum mechanics threw that out the
window. And so the observer is as
profound a part of an electron experiment
as the electron might be. So there was
one of these four postulates on quantum
measurement. And the last thing, and we'll
see all of these kind of in action when
we get back to Flüffy, of composite
states. If you've got a quantum system, an
electron here, perhaps another electron
here, and they begin to work in aggregate,
how do you deal with that? How do you
treat that mathematically? So, those are the
primary postulates that von Neumann put
in his book. Now I'm pleased to give you
something you can google and not get any
hits...
and that's what von Neumann's duck.
I did find a few hits on some subject
that a writer thought von Neumann had
ducked. So it's not like you'll have
nothing to read; but, it has nothing to
do with Dagmar at all. And again,
there'll be nothing more said of von Neumann's duck.
OK. The postulate, the von Neumann postulate
about quantum states.
He was creat[ing] a mathematical theory so he
had to have some kind of symbolism for
quantum states. And there are a lot of pieces
of this that we don't need to deal with
tonight, but one that I will deal with
is called a ket. It's the right half
of a bracket. That's why it's called the
ket. And it's a straight vertical line
and angle bracket on the right and then
inside that you put something to
describe what it is you're talking about.
So, the ket up on that top line is
kind of an arbitrary thing that if you can
define what you mean by X then you begin
to talk about something that's physical.
But you can also use that notation to
instead of a simple letter or number you
can put a picture. And this picture is
supposed to represent protons and
neutrons in a radioactive nucleus.
Now my little angle bracket looks kinda
lost in translation here, but this is a second
ket with the blue arrow representing the fact
that an alpha particle has come away
from this radioactive nucleus. So we've
got a nucleus that can have lots of
different properties. We're interested
only in two things. The fact that it can
decay and the fact that will decay. So
this is the nucleus in its undecayed
state described by a von Neumann ket. And
this is in its decayed state described by
a von Neumann ket. What's unusual is the
fact that unlike Newtonian science these
things, anything that can be considered a
quantum state, can be put into a
superposition so there exists something
that is a radioactive nucleus that is at
the same time undecayed and decayed.
So-called superposition state. So we'll talk about
those things. The strange thing about
it is that if you happen to come across
one of these and look at it, it turns
into one of these. And that's kind of the
quantum measurement conundrum...that when you
get these interesting quantum states you
can't look. A lot of fairy tales like that.
So, von Neumann talked about how these things
change. And there are two ways they
change. One is if you just leave them alone,
they change. Those things transform into
something else. So we started with a
quantum state, call it X, and let it evolve
unwatched. It can change into state Y, or
choose not to change into state Y. And
you write a superposition this way with
the A and the B representing numbers.
And those numbers tell you something
about what's the likelihood if you do
look, that when you look you see that.
Turns out to be related A squared. If
you look and see that, it relates to the
number of B squared. And those two
probabilities have to add to one.
You can see one of the other but not the
combination. Combination truly exists as
long as you don't look. The other way
things can change is when you look. And
here it is. Here's the superposition but
when you look...that little arrow...what happens
when you look, you get that probability A squared.
That probability B squared.
And it seems almost artificial to create
these things you can never see and claim
they exist and yet when you look they
turn into something that you're familiar
with. It's not artificial in that there's
an awful lot of results, quantitative results,
you can get with this assumption
that this exists. That are absolutely
contradictory if you assume this doesn't
exist it's only this and this. So quantum
mechanics works as weird as it is, it
seems to work. OK. Here's an example. We
got a box. We're going to use the box for cat later.
We use for a radioactive nucleus right now.
We put it in the box and we wait. And
with the box closed up and not watching,
of course, it evolves. One half-life later...
half-life. Radioactive nucleus most of
them are described by having a half-life.
What does that mean? It means that you have a couple of
"bazillion" of these guys undecayed and
wait one half-life, let's say it's a
half-life of 24 hours, wait 24 hours and
look about have a "bazillion" of them will
be undecayed. The other half will be
decayed. Half-life. For anyone of them it could decay
in a minute. Or it could wait
for two weeks.
You cannot predict
in any deterministic way when the thing's
going to decay. But you can make this
statistical prediction about what's going
to happen on average. And as far as the
one nucleus in the box, if you wait a
half-life and open the box and look, you
will see this or this undecayed or
decayed with a probability of fifty
percent. It's all statistical. It is
not deterministic.
OK. Back to Flüffy and back to the
story of Schrödinger's cat. And it comes
from probably not a direct discussion
but a controversy that Einstein carried
on for
probably the next 25 years. Einstein got
one Nobel Prize in physics. In my
estimation, he did work that was worthy
of at least three. Particularly with the
gravitational wave discovery of last
fall. That would be his third in my book.
But, the only one that he was awarded
the Nobel Prize for was a quantum
explanation. He spent the rest of his
career trying to discredit quantum mechanics. He
did not believe it. He did not believe
that God played dice. He did not believe
probabilistic results where the best
prediction we could get. It should be a
theory that tells you what's going to
happen, not what's maybe going to happen.
He didn't like it. And Albert...one of the
ideas that Einstein presented
was, "OK, I'll admit that you've got math
that will tell you about radioactive
nuclei and how they decay; but, it cannot
have anything to do with macroscopic
objects. It has to be just something that
coincidentally works for little tiny
things." Well, Schrödinger's reply to that
challenge was a box. And this represents
the inside of the box. He said, "OK. Let's
take our radioactive nucleus and put in
the box, the little chamber here, with a
mechanism whereby if the nucleus
decays
the alpha particle is emitted will be
detected, by this little yellow detector, that
a mechanism in it. The mechanism holds up a
hammer about a vile of cyanide
liquid or something pretty awful. And if
the nucleus decays and is detected by
this mechanism, the hammer falls and the
vial is smashed and the cat changes from
this cat that cat." So, that's the
Schrödinger's cat story. And he said
basically to Einstein, "The cat is a
quantum entity in this story."
Before you open the box, you don't know
whether you will see a decayed nucleus
and undecayed nucleus and quantum
mechanics says it's the superposition
thing. But you also don't know whether you're going to
see a live cat or a dead cat. It's this
quantum superposition thing. And the cat
is as profoundly alive and dead before
you open the door to the box as the
nucleus is decayed and undecayed. So this is why
Schrödinger came up with this up this story. So,
here's kind of the quantum mathematics
of it. We put the cat in box inside the
box, we've got the nucleus that's evolving
unwatched into or part undecayed and part
decayed state and Flüffy who is
evolving into part live kitty-cat, part dead
kitty-cat.
Should we look? Well, depends on how you feel
about nuclei and cats. There's another notion
that came out of this story of Schrödinger
having to do with entanglement. Now this
is one of von Neumann's postulates about
how do you deal with composite states. Two
things that are quantum-like but how
do you do with them all at once? And
for von Neumann that was pretty easy. Whatever
this symbol represents mathematically, you
simply take that symbol and multiply it by
that symbol. That becomes your complex,
coherent state of the two things at once.
And if we're trying to describe the
Schrödinger's cat experiment using this
symbol, we're saying what happens after one
half-life of the nucleus is that we get
this state undecayed nucleus happy cat
and this state decayed nucleus dead cat
with equal probability. So, whatever A is is
the same in both cases after one
half-life.
Composite states behave this way.
Entanglement is something that only got
taken seriously probably 25, 35 years
after Schrödinger's work, and von Neumann's
work, and Heisenberg work...and that is to
have two things that don't have a life
of their own. That the life of the cat is
profoundly connected to, entangled with,
the nucleus. And you cannot have
in this box a live cat and a decayed
nucleus. It ain't going to happen. So, let's
talk about entanglement in ways that put
fewer cats at risk. And in particular
let's think about electrons or atoms. And
these, this blue ket and this orange ket,
represent two things. Let's say two
electrons. And the arrow represents a spin
direction. Electrons, most atoms, most
nuclei have a behavior that's very
similar to that of a spinning top. And it
can spin clockwise. It can spin
counterclockwise and they're usually
symbolized by an up arrow for one of
those two ideas and a down arrow for another.
So, here we have two unentangled,
let's say, electrons. Both spin up. But if you
put these things in your microwave or
some quickly varying magnetic field, you can
transform that pair of electrons into a
superposition state of up up and down down.
So you've got two electrons that
probably...that have exactly the same
probability of being found both spin up
and both spend down and absolutely zero
probability being found one up and one
down.
And that's called entanglement. Neither of these states,
just like Flüffy and the nucleus, has a
life of its own. They are profoundly entangled.
And that brings me to the...
probably the most modern use of this notion
of entanglement and the most promising
use of this having to do with quantum information
theory and the notion of qubits--Q for quantum
and bit for the notion of computer
science of bit.
Bit stands for binary digit. And you all
know that we can send any amount of
information using 1s and 0s.
Using things that he can have one of two
states, classical bits. And sometimes
these are magnetic memory. Sometimes
they are other items that you can send
information in 1s and 0s.
If those things are electrons, for
instance, or atoms and we're looking at
their spins, they become qubits because
they have a possibility of becoming
entangled with one another. And they have the
probability of showing superposition. So
that a qubit can be spin up or spin down
or any linear combination which means
that infinite possibility. So the little
bit of information you can store on a
bit, a yes-or-no kind of answer, is
paltry compared to what you can store in a
qubit, which has, if you can control that
qubit enough and control its
superposition enough, you can send an
infinite amount of information. You can
encode war and piece on a single qubit.
The problem with that is that if you have one
piece on a qubit and look at the qubit,
bang, it's gone.
Bummer. People have worked hard to try to
figure out how to get around that "don't
look" thing. And I'll talk in detail about
one of these and then just mentioned the
other. But quantum dense coding, which
I'll explain in a bit. Quantum teleportation, the
beam me up Scotty thing. Has been their
experiments that have done that with
with infinitely variable quantum
superpositions. Quantum cryptography.
Remember if you look, it changes you can
send encrypted messages and if somebody
eavesdrops, they've looked at it and the
arrives altered. And you know it has been
looked at. So you can send it again. So
the notion of quantum crytography is much
better.
There's actually quantum entanglement
clocks. And there's a lot of time spent
now and quantum computing. Let's talk
about dense coding. And let me, allow
me, to read a bit, a little story, about
Della and Jim. Della and Jim are young,
poor, and in love. Alas, Jim must soon
depart for a faraway land.
The trip is hard and dangerous. The return
trip ever more so. Jim tells Della that whether
he even attempts to return will depend
on the answer two questions--answers
which you must send him by year's end.
Question one: Did the Cubs win the World
Series?
Question two: Did the Democrats win the
presidential election?
On his last visit to Della before his
departure, Jim arrives distraught and
disheveled. He has just come from the shops
where he pawned his most precious and only
valuable possession, a gold watch. With
the proceeds, he has purchased two qubits for
Della to use to send him the answers to his
questions. But he had so little money
left
he could only buy a prepaid card
enabling her to send one. Not knowing the
answer to both questions he cannot
return.
"Whoa," says Jim, "is me." Della, ponders. She
could manipulate one qubit to be an
up-or-down send it to Jim and he could
determine its orientation. If they've
agreed that up means yes and down no, she
could inform him of the Cubs ultimate
fate. But if she can send only one qubit,
how can she convey both answers? Seeking
a resolution Della, takes the qubits
rushes out the door towards the shops,
her beautiful long hair, pay attention, long hair
flowing behind her. Entering a wigmaker shop,
she emerges almost at once. Fleeced as
well as shorn,
clutching a modest fist full of coins. Standing
dejectedly by the curb grasping the two
qubits and the meager compensation, she's
approached by a strange man with an even
stranger cat. "May I be of assistance?"
he offers. "If only," sobs Della and tells
the man of her predicament.
"This is your lucky day," he says, relieving
Della of her qubits and, of course, her money. The
qubits he puts into a small crate. The cat
follows and the crate doors closed. Soon he
opens the crate. The cat emerges. He
reaches in to remove two tiny cheap
lockets. "This is what you need," he assures Della, handing her the lockets.
Thanks
to my cat, Flüffy, the qubits have been
entangled and one is within each locket.
Quickly moving to open a locket, Della's
is hand is restrained. "You must never look!"
she's told.
"But I must be sure you're at least
giving me back my qubits." "Do not doubt, you can
trust me. I'm a physicist."
That wasn't supposed to be a laugh line.
this is what he told her to do. Two
lockets, a qubit in each, locked away so
neither can look at them. And it's an
entangled pair that I will describe by that
symbol. And when Jim departs he takes his
with him. She keeps hers. The notion
of entanglement does not diminish with
distance. So, he can go to darkest Peru
if he chooses and the two qubits are
still as entangled as they were when
they were side-by-side. Della, by December,
knowing the answer to both of the
questions that Jim needs to know, works on
her qubit alone. She has a microwave
oven.
Puts it in there. They are entangled
qubits; so, as she changes hers, his changes.
This is what Einstein referred to a spooky
action at a distance. He didn't like it.
But, experiment has shown that this happens. There's an angle pair. As she alters, his
is altered. And because there are two qubits,
there are
four distinct states. If you think of the...
even if you look at them...if you think
of the classical notion of two bits: up
up, up down, down up, and down down. Four
distinct states and she can change the
entangled pair that the to have in their
lockets into any one of these four
state. Then, she uses a prepaid card sent
to a single qubit to Jim, even as both
he can measure the pair and he can find
one of four answers. Yes yes, yes no, no
yes, no no. He knows what he needs to know
to decide whether it's worth coming come.
OK. That's quantum dense coding. That's the simplest
example where you can send a
single bit and convey two bits of
information. And you just as easily
magnified into sending many more than
two times the amount of information as
you could classically send by conveying
qubits instead of bits. So, back to the
notion of quantum information theory
in these things. That's this quantum dense
coding. Quantum teleportation, very briefly, is
a notion of sending a quantum entity, a
qubit, in a superposition state so
it has this infinite variety. You can
transport that totally with total
fidelity over a distance as long as the
sender and the receiver share an
entangled pair of qubits. The
sender entangles the unknown with, let's say,
her qubit, and then
at the other end Jim can measure...and...
his particle and yet the single state
that he had is transformed into this
unknown state. So, you can do
teleportation with electrons, presumably
with cats, presumably with starship
captains. I've talked a little bit about
cryptography and about how you can know
if somebody's cheating and looking at
what you're sending because it
changes the answer. Quantum time
keeping is interesting. Right now the
time standard is a clock, atomic clock,
that loses about one second, or has a
variability one second, in 300 million
years in a million years. 300 million years ago beetles
were showing up on the planet...the first
beetles. and if these... not the other
ones. And if these, you know first two
beetles that emerged, had watches of
that sort, their watches would still
agree right now to within a second.
There is however a...an entanglement clock
that, were it built, would keep time--lose one
second in15 billion years. Interesting
number of years. That's the age of the
universe. That's how long ago the Big
Bang happened. And it's probably not
worth getting any better than that.
Then, quantum computing. There is a lot of
work done in quantum computing. And one
of those profound pieces of things that
has been proven in principle...this effect
that using quantum computing, you can
factor large integers.
Why is that important? Most of the bank
encryption that are keeping our accounts
safe worldwide is based on the fact that
factoring large integers is something
that would take hundreds, if not
thousands, of years for a regular digital
computer to do. A quantum computer could
do it in a matter of seconds. So it would
totally disrupt that kind of encryption,
if we had that. So that's enough of me. I
do want to ensure, assure Emily, and anyone
else in the audience who is worried about these
cats, that they all came home the very
same day. Thank you.
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