MALE SPEAKER: Good morning.
Thanks for coming.
I'm here to introduce Amanda Gefter and her book,
"Trespassing on Einstein's Lawn."
And I came to this book through a confluence
of several factors.
My late father was a physicist and had the opportunity
to exchange a few letters with Einstein himself
and always had them locked away in the safe deposit box.
It was always a special family thing.
And separately, he and my mother used
to go to a particular Chinese restaurant in Philadelphia
all the time, and the young five-year-old son of the owners
would always hang around, being playful.
But he also liked math a lot, and my dad
started tutoring him in math.
The young man grew up, went to Wharton,
and is now at Khosla Partners, a venture
capitalist out in Silicon Valley.
So my dad helped spawn a Silicon Valley hotshot.
So when I heard of Amanda's book and that it involved Einstein,
physics, fathers, Chinese restaurants, and Philadelphia,
where I'm from, I realized this was a book I had to read.
So without further ado, Amanda Gefter.
[APPLAUSE]
AMANDA GEFTER: So first I just want
to thank Google so much for hosting me here today.
It's a real privilege to be here in this building
and to get to talk to all of you.
So when I was 15 years old my father
took me out to dinner at our favorite Chinese restaurant
and asked me how I would define nothing.
And this was an odd dinner table question but not
entirely out of character for my father, who
was this sort of Zen guru, former hippy
turned radiologist.
And so I said I would define nothing
as the absence of something or the absence of everything.
And really this is how everyone defines nothing, as a void.
But my father had a different idea.
He had been thinking about this for a while, he told me.
And the other day he had had an epiphany.
He was at the mechanics waiting for his car to be fixed
and it dawned on him that you could define nothing
as "an infinite, unbounded, homogeneous state."
So a state of utter sameness that
extends, without bound, forever.
And this wasn't a semantic trick.
An infinite, unbounded, homogeneous
state would literally be indistinguishable from a void.
It's nothing.
But my father thought it was an interesting definition
because it defined nothing not in terms
of what it isn't but in terms of what it is.
And so he explained all this to me
over a plate of cashew chicken.
And then he asked me, do you think
this could help explain how the universe began?
Now you have to bear in mind, I'm his teenage daughter.
I was not exactly the most well-behaved kid.
I would not be described as studious.
I was failing math class.
I was not even taking physics class.
I had opted for meteorology because that
was what my high school offered in place of physics
for the underachievers.
And here my father is asking me how the universe began.
And he just sort of shrugged like it was a normal thing
to do and said, I think we should figure it out.
And so that is how, at 15 years old,
I found myself on a mission to figure out
the origin of the universe.
So my father and I started teaching ourselves physics.
We stayed up late every night, we
started amassing a crazy collection of physics books,
reading everything we could get our hands on,
and talking about all these ideas
until my mother would yell at us to go to bed.
Because if you want to understand this something that
came from nothing when the universe was born,
you have to look at both sides of the coin.
So my father had already thought long and hard about the nothing
part, and now we needed to understand the something.
And that's what physics is.
Incidentally, before I started this secret project
with my dad, I had no idea what physics was.
I didn't take physics class because I thought that physics
was like a set of rules and numbers
for describing how levers and pulleys work.
And now I know that physics is about uncovering
the reality behind appearances.
It's about glimpsing this deep and hidden architecture
of existence itself.
It's about embracing the fact that the world is not
what it seems and that everything is stranger
and simpler than we can imagine, and yet comprehensible.
And I think if I had known that from the start,
I wouldn't have taken meteorology.
But eventually I graduated high school,
and I move to New York City for college.
And then when I finish college I did
what any physics-loving, amateur reality hunter would do,
and I took a job at a bridal magazine.
So I was working as an assistant at "Manhattan Bride."
And I was there in the office, which was really
just the one-bedroom apartment of a guy named Rick, when
I read an article in "The New York Times"
announcing this huge physics conference that was going
to be happening in Princeton, New Jersey
called Science and Ultimate Reality.
And all the world's leading physicists
were going to gather there to talk about their most
cutting-edge ideas.
So I'm reading this article and a light bulb
goes off over my head.
I wait until Rick leaves for lunch
and then I pick up the phone, I call the people
in charge of publicity for the conference,
and in the most professional voice
that I can muster I lie and say that I am a journalist
and that I'm calling from "Manhattan
Magazine," because that sounded better,
and that I wanted to come cover the event.
Oh, of course, we would love you to come, they said.
Great, I said, put me down plus one.
Now in that moment, I had no idea
how that one little lie would forever
alter the course of my life.
But I called my dad and I said, pack your bags,
we're going to Princeton.
So my dad and I show up in Princeton
and we crash this physics conference,
posing as journalists.
We found our press badges at the press table.
Mine said "Manhattan Magazine," I had a blank for my plus one.
And we put them around our necks and just wandered
amongst our heroes like two idiot deer
caught in genius headlights.
We got to listen to these physicists lecture
about their most recent ideas about the nature of reality.
And then, as if that wasn't good enough,
we got to go into this magical little room
that they call the press room, where you sit down
and they deliver to you, one by one,
each physicist so you can ask them questions.
It was the most amazing experience of my entire life.
And when the conference let out, my father and I
just sort of wandered through the town of Princeton
in a daze, talking about everything we had just heard.
And eventually we found ourselves
on Mercer Street, which is the street where
Einstein had lived.
And we found his house at 112 Mercer.
It was undergoing some sort of construction,
so it was sort of cordoned by yellow tape like a murder
scene.
But we just stood there in awe, trespassing
on Einstein's lawn, two bogus press badges still hanging
around our necks.
And it struck me then that this little private hobby
that I shared with my dad was maybe
going to be something bigger.
And it also dawned on me that I was not
ready to give up this journalism front because it was just
too good to be true.
All you need is this press badge and suddenly you
can learn physics directly from the physicists.
I figured the "Manhattan Magazine" scam wouldn't
work for long because someone was
bound to look it up and see that it didn't exist.
But I figured I would use it one more time.
So when I got back to New York I called an editor
at "Scientific American."
Again I lied and said that I was a journalist at the "Manhattan
Magazine" and that I had been to this conference
and that I wanted to cover it, or write
an article about physics for their magazine.
And miraculously he agreed.
So my article comes out in "Scientific American."
And suddenly my fake journalism career
has just morphed into a real journalism career,
and I was able to use that to sort of worm my way
into more situations where I didn't belong.
So I'm sure you can see Stephen Hawking there,
front and center.
And then there, inexplicably, is me.
It was the perfect scam.
And at this particular conference
I ended up meeting an editor from "New Scientist" magazine.
We struck up a conversation, and I
mentioned that I wrote for "Scientific American."
I didn't mention it was only once
and it was the only article I'd ever done.
And he suggested maybe I should write for "New Scientist."
And so I started writing articles for "New Scientist."
And then when I turned 25 "New Scientist"
asked me to be an editor there, landing
me the ultimate permanent press badge.
So once I was an editor at a major science magazine,
I had access to everything that my father and I needed
to learn physics and start to figure out
the origin of the universe, which was the whole point.
And I was learning so much, trying
to come to grips with this something that supposedly arose
from nothing 14 billion years ago.
And if you try to learn all of fundamental physics
from scratch, not only is it a lot to learn
but it can seem like a lot of crazy, unrelated facts.
But early on I had an epiphany that
made it infinitely easier to connect the dots
and to see the big picture.
And so I think if you want to know
one thing about fundamental physics,
this is the one thing to know.
Something is only real if it's invariant.
And I'll explain what that means.
Something is only real if it remains
unchanged in every reference frame.
If it changes or disappears from some perspective,
then it's not ultimately real.
And actually, even though this is a very deep idea,
it's something that we all sort of know intuitively.
Like if you were sitting in your lobby
and out of the corner of your eye you saw an elephant walk
by, even for Google that would be pretty unusual.
And you might find yourself wondering,
is that elephant real or am I having some kind of break down.
And instinctively you know there are
two strategies that you can use to find out.
So the first would be to get up, walk over to the elephant,
and just walk in a circle around it, eyeing it from every angle,
suspiciously.
Because you know that if at some angle it just vanishes,
then it was something more like a mirage
and less like a mammal.
And the other strategy you can use
is to just turn to the Googler next to you
and say, do you see that elephant too.
And if she says, no, or just stares at you
blankly, then you know that you should probably
go see a neurologist.
And why do you know that?
Because you know that something is only real
if it remains invariant in every reference frame.
OK.
So just because something's not ultimately real
it doesn't mean it has to be a hallucination, right?
Take a rainbow.
Is a rainbow real?
Not really, right?
It's not subjective.
It's not a hallucination.
But it's also not a physical object hanging in the sky.
You can't go touch it.
Because it's a product of your reference frame.
You see a rainbow when you're standing
in just the right spot and the sun's streaming
in from behind you, and the light's
being refracted by the moisture in the air.
And if you ask the guy next to you,
do you see that rainbow too, he'll probably say, yes.
But if you run the test of walking around it in a circle,
you will eventually see it disappear.
Because it's not invariant.
It's not ultimately real.
It's not a fundamental ingredient of ultimate reality.
And so if you want to find the fundamental ingredients
of ultimate reality, the something that
arose from nothing, you have to find what's invariant.
So if there's one thing that you remember about physics,
let it be that.
It was Einstein who first recognized
this link between invariance and reality.
And I would actually argue that this
was Einstein's single greatest contribution to physics, which
I realize is a very bold statement.
He did a lot of things-- special relativity, general relativity.
That's not even what he won the Nobel Prize for.
He won it for the photoelectric effect.
Which is just so badass, if you think about it.
Because the thing he won the Nobel Prize
for barely cracks the list of the best things he ever did.
But the best thing he ever did was
to illuminate this link between invariance and reality.
Because it set the future trajectory of modern physics
in motion.
And it changed physics from being
a set of rules and numbers that describe
how levers and pulleys work to being a way
to glimpse the reality behind appearances.
And there's a good reason that no one before Einstein
thought of this link between invariance and reality.
And it's that before Einstein, everyone
shared the same reference frame.
So in a Newtonian universe the speed of light
is instantaneous, which means everyone sees the same thing.
So everything's invariant.
And in Einstein's universe this is no longer true.
So Einstein realized that in order for every observer
to see the same laws of physics, every observer
has to measure the speed of light to be the same.
And so it doesn't matter if you're
running a million miles an hour or you're standing still.
As you measure a beam of light, that beam of light's
going to be moving at 186,000 miles per second.
And what's important about that number is that it's finite.
Light does not travel instantaneously.
It takes time.
Light from the sun takes eight minutes to reach us.
Light from distant galaxies takes millions or even
billions of years.
And so looking out into the universe
is a way of looking back in time.
But the point is you can't see everything.
The universe you can see is bounded by the fact
that light has only had 14 billion years to reach you.
And so beyond that the universe for you is dark.
Now the boundary that marks the very edge of what you can see
is called your horizon.
And it's uniquely yours.
You are sitting at the center of a sphere that encompasses
your one-of-a-kind universe.
And the person next to you is sitting
at the central of a different sphere.
Now they mostly overlap, but not entirely.
And so Einstein realized that in a universe
with a finite speed of light, every observer
occupies a unique reference frame.
So you can no longer just describe the universe
without first specifying from who's
frame you're describing it.
Because things might look very different from one
frame to another.
And if things look very different from one frame
to another, this introduces a fundamentally new problem.
How do you know which things are real?
And Einstein figured out the solution.
Something is real if it's invariant in every reference
frame.
So it was this way of thinking that led Einstein
to his famous discovery.
By analyzing how things look from different frames,
he was able to see that space and time, which
everyone had always assumed were the same for every observer,
are in fact not the same for every observer.
They look different from one reference frame to another.
So what I see as space, you might experience as time.
And vice versa.
And so space and time are not invariant.
They are relative to your reference frame.
That's what relativity is.
But he found that there is something
that remains invariant.
And that is this combination of space and time.
This unified four-dimensional spacetime.
So we might disagree on measurements of space
or of time, but everyone will always
agree on measurements of this combined spacetime.
OK.
So space and time are not real, spacetime is real.
And everyone always focuses on the first part
because it's really mind-blowing,
that space and time aren't real.
But Einstein actually cared more about the second part.
Because he knew that the key to finding ultimate reality
is to find the invariant.
And actually later in life he said
that he regretted calling it the theory of relativity
and wished that instead he had called
it the theory of invariance.
So once we knew all this, my father and I
now had a concrete plan.
The question, what is ultimately real,
what is the something that arose from nothing,
it was no longer this vague philosophical question.
It was a rigorous physics question.
What is invariant?
And so we were out to breakfast at a pancake house,
and we wrote a list of possible ingredients of ultimate reality
on a napkin.
So things like spacetime, dimensionality, particles,
strings, et cetera.
This image, by the way, is a recreation.
The original napkin was eventually lost
or possibly sneezed in.
But we made this list, and then I used my journalism career
to investigate each one.
And I want to tell you about two of the items on the napkin.
So the first one is particles.
Particles seem pretty fundamental.
If you ask, what is all the stuff in the universe made of,
particles is the obvious answer.
That's what I thought, until I encountered
the work of Stephen Hawking.
So I have to confess something.
When I was first learning all of this stuff,
I had this suspicion that Stephen Hawking was overrated.
I just wasn't convinced that his contribution to physics
could be proportionate to his fame.
Because there's just something about a guy that
speaks in a computer voice that sort of automatically
sounds like a genius.
He automatically sounds like he knows
something no one else could possibly know.
But as I studied his work, I learned
that he had done this remarkable calculation in the 1970s.
Actually he was annoyed at another physicist,
and so he was doing this calculation in order
to show that this other guy was wrong.
And the calculation proved three things.
First, that revenge is an excellent fuel for genius.
Second, that I was an idiot.
Because if anything, Hawking is underrated.
His physics is brilliant.
And the only thing that's disproportionate
is the fact that everyone knows who Stephen Hawking is,
but if you ask them, what did he actually
do that was so important, hardly anyone knows.
But now you guys will know, because I'll
tell you the third thing.
His calculation proved that particles are not
ultimately real.
And here's why.
So thanks to quantum mechanics, empty space
is not really empty.
The uncertainty principle tells us there's
a trade-off between time and energy, which
means that on incredibly short time scales--
a fraction of a fraction of a fraction
of a second-- large amounts of energy
can bubble up out of empty space.
And this energy takes the form of pairs
of particles and antiparticles that emerged from empty space
and then meet and annihilate and in the blink of an eye,
disappear.
And this is happening all the time
all around us, these particles and antiparticles
emerging, meeting, annihilating, and disappearing.
But it happens so quickly that we just
refer to them as virtual particles.
But when Hawking was doing this calculation
he realized that something different
happens when you have a horizon.
And so, as you already know, a horizon
marks an edge beyond which light can't reach an observer.
So we talked about the horizon that
surrounds your unique universe.
And there's an analogous kind of horizon--
it's actually a mathematically equivalent kind of horizon--
that surrounds a black hole.
So in this case the horizon marks the edge
beyond which light can't escape gravity's clutches in order
to reach an observer on the outside.
So if you're standing outside the black hole,
the horizon marks the edge of what you can see.
So Hawking realized that if these pairs
of particles-- virtual particles and antiparticles--
are bubbling up out of empty space in the vicinity
of a horizon, something sort of amazing can happen.
The horizon can separate the pairs.
So that where one particle is just outside the horizon,
its antiparticle partner can be just inside the black hole.
And now they can no longer annihilate.
And so instead of disappearing they just stick around.
These virtual particles are not so virtual anymore.
They're actually totally normal particles.
They're exactly the same as the particles
that make up anything in this room.
You could collect a bunch of them and build a chair.
But there would be something really weird about that chair.
Because it would owe its existence to the horizon,
but the horizon's not a real thing.
The horizon is not like a brick wall that's floating in space.
The horizon's like a rainbow.
It's a product of a reference frame.
Namely, the reference frame of an observer who
is lucky enough to remain outside the black hole.
And textbooks tend to call the observer outside the black hole
Bob.
I like to call him Safe.
There's another kind of observer who is not so lucky.
An observer who's in inertial motion-- free-fall--
can't escape gravity's clutches and falls straight
through the horizon and into the black hole.
And I like to call him Screwed.
So from Safe's point of view, these once-virtual particles
that can no longer annihilate with their partners
are streaming out from the horizon,
as if the black hole is radiating.
That's why we call it Hawking radiation.
But for Screwed, there is no horizon.
He just falls straight through, and there's
no edge of what he can see.
So for Screwed, these virtual particles
just continue to annihilate and disappear like always.
And so where Safe sees this stream of hot particles,
Screwed just sees ordinary empty space.
So you see what's happening here.
The particles are not invariant.
And that's what Hawking discovered that's so important.
Particles are not ultimately real.
They're a product of your reference frame.
Not only in the vicinity of a black hole
but everywhere, because every one of us
is surrounded by a horizon.
So my father and I crossed particles off the list
on the napkin.
Now Hawking's discovery has driven,
and continues to drive, theoretical physics forward
for the last four decades.
Because it's rife with paradoxes.
And there is nothing that a physicist
loves more than a paradox.
And I'll give you an example.
So let's take our elephant from the lobby
and throw him into a black hole.
All right, there he goes.
So Safe is watching this from afar.
And so we can ask, in Safe's reference
frame, what does this look like.
And fair warning, It's not pretty.
So from Safe's point of view, the elephant
is going to fall towards the black hole
and then encounter this stream of hot Hawking radiation.
And he's going to be burned to a crisp
before he ever crosses the horizon.
And his ashes will just emanate back into the universe.
OK.
So that gruesome and terrible.
But we can also look at Screwed's point of view.
Because Screwed is just falling straight
through alongside the elephant.
And for Screwed there is no horizon.
So there are no hot particles to harm any animals.
And so for Screwed, the elephant is just
in ordinary empty space.
And he can live out the rest of life
until he eventually reaches the center of the black hole.
So there's a problem.
The laws of physics require that both of these stories be true.
If either one of them were not true,
you'd violate a law of physics.
And so the elephant has to be both dead in a pile of ashes
outside the black hole and alive and well inside the black hole.
That alone is just weird.
But the problem comes in because there's
another law of physics that's equally as
fundamental as the others that says you can't have
two copies of the same elephant.
So both stories have to be true, and both stories can't be true.
That's the paradox.
And it was a physicist named Lenny Susskind
who solved this paradox.
He said, as long as you stick to one observer's reference frame,
as long as you talk about the Safe sees or what Screwed sees,
all the laws of physics remain intact.
It's only when you try to talk about their points of view
simultaneously that you see these two
illegal copies of the elephant.
So it's this picture that's the problem.
Einstein had said, if you describe the universe,
you have to first specify your reference frame.
And the fact is this is an unphysical reference frame.
It's impossible.
There's no one who can see inside and outside a horizon
simultaneously.
That's the idea of a horizon.
And so as long as we just stick to physical reference
frames, what an observer could actually see,
we never see two copies of the elephant.
And all the laws of physics remain intact.
So the problem is solved.
But there's still something very unsettling about that.
Because we would like to think that there's
some actual answer to the question,
where is the elephant?
Is the elephant dead outside the black hole
or alive inside the black hole.
We like to think that there's some real answer.
And what this is telling us is that there's not.
So Susskind realized that the location
of the elephant in spacetime is not invariant.
So spacetime-- this unified, four-dimensional spacetime
that was left invariant by Einstein's theory
of invariance-- turns out not to be invariant after all.
And so my dad and I had to cross spacetime off the list.
So we continued our search for these ever-elusive invariants,
these fundamental ingredients of ultimate reality.
I was running around the world having
fascinating conversations with these brilliant physicists
and usually making a total fool of myself in the process.
And often my dad was there with me.
And when he couldn't be, I would report back to him
and detail all of my crazy adventures and everything
I had learned.
But looking back on this 17-year journey, here's
what I realize now.
If it weren't for my father I would've
never done any of this.
Even if I had somehow become interested in physics
on my own, I would've never crashed
a conference posing as a journalist.
I would have never turned one little lie
into an entire career.
Because without my dad there at my side
or on the other end of the phone,
it wouldn't have been fun and it wouldn't have meant anything.
And that's the thing about invariance.
It doesn't just make objects real, it makes our lives real.
And I really think that's why we need other people.
We need them because they bear witness to our lives.
And in doing so, they anchor us to the world.
They anchor us to a reality that can be seen from every angle
when you walk around it.
I needed my dad because that second reference frame
gave my life a sense of invariance
and created between us a shared reality.
So that every time I learned something deep and wondrous
about the universe, I could turn to my dad and say,
do you see that too.
And he could smile back at me and say, yes.
But just as we were creating this shared reality
we were also chipping away at it piece by piece
as we crossed item after item off the napkin,
slowly undermining the very notion of a shared reality.
Because once you know this one thing about physics,
that what's real is what's invariant,
the entire trajectory of physics snaps into focus.
The whole history of physics, from Einstein
to exactly what's going on right now,
has been a steady and relentless progression of invariant
after invariant giving way to observer dependence
and illusion.
And so the list of fundamental ingredients of reality
is getting shorter and shorter and shorter.
And so we can ask, where does this trajectory end.
Does it end with one fundamental ingredient, one invariant, one
thing that everything else is made of?
Well, that used to be the hope.
A lot of people thought that.
That was sort of the idea of string theory.
That all these different things, all this variety
we see in the world, is actually all just
made up of this one ingredient, these little vibrating strings.
But the most exciting and interesting and challenging
thing that's happened in string theory in recent years
is that it's turned out that strings are not invariant.
And so physicists are starting to think that maybe there's
not one fundamental ingredient.
So where does the trajectory end?
Does it end at nothing?
Because here's the interesting thing about nothing.
If you think about it not in terms
of what it isn't but in terms of what it is,
an infinite, unbounded homogeneous state
is by definition invariant in every possible reference frame.
So my dad had started with this sort of existential question
of, how do you get something from nothing?
And now everything we were learning
was presenting us with the very real possibility
that that something might not be made of anything.
That the something might be nothing.
And on the one hand, that's really good news.
Because that actually offers a possible solution
to this ancient existential riddle.
But on the other hand, it's kind of a bummer when you've just
spent 17 years trying to create a shared
reality with your father, only to learn
that there may be no such thing.
Physics taught me that I have my reference frame
and my dad has his reference frame.
And they mostly overlap, but not entirely.
Which I think is just another way
to say that over the past 17 years,
physics has taught me what it means to grow up.
But still I am comforted to know that there is a reference
frame in which we are together, side by side, my dad and me.
And that's the reference frame that
sits between the covers of my book.
So thank you very much.
[APPLAUSE]
I can take questions, if anyone has.
AUDIENCE: What's a good suggestion
for getting our daughters involved in math and science?
You have a chance to speak with a lot of people
who have made this be their profession.
And from their experience and yours,
what do you think is a good first step?
AMANDA GEFTER: So I think it depends on personality a lot.
So for me, I was sort of this rebellious kid.
And I think if physics had been presented
to me in any normal way, like as something you
have to study in school, I just don't
think it would have ever captured my imagination.
I think it was the fact that my dad presented it
as this secret thing that we were going to do,
and it was this mission and we were
going to figure out the origin of the universe.
And it felt like by doing physics
I was rebelling in some way.
Actually, I've thought about this a lot.
I think physics is a very inherently rebellious subject.
Because it requires you to question everything
we think we know about reality.
And if you look at the greatest physicists of all time
they tend to be very rebellious characters.
So I think it's a shame because a lot of times the people who
are encouraged to go into science and math
tend to be the very studious people who go by the book.
And you need that, but that's not always
going to be the most creative thinkers.
And I think sometimes we weed out creative thinkers who
could have really contributed to physics
by not appealing to that type of kid.
But I realize not everyone's going
to go on a secret mission for 17 years
to figure out the nature of the universe.
So I really think the physics that's
taught in school-- you don't get to the really good stuff
until you've already committed.
You do Newtonian physics in high school,
and then it's not until-- if you did physics in college,
you'll start to get into relativity and quantum
mechanics.
And that's where it gets really cool.
But I think you could actually present those topics to kids
without needing a crazy amount of math that they don't have.
And so I think if there was a way
to present the cooler parts of physics, the really
exciting, mind-blowing stuff earlier on-- so that they would
see that, OK, I have to get through all this other stuff,
but it's going to be really good-- I feel like people
would be more into it that way.
AUDIENCE: Hi.
So I'm actually about 50% through your book right now.
And I have this problem when reading
these sort of theoretical physics books.
Which is that I usually follow through special relativity
and general relativity, but once I
get to sections about supersymmetry and string theory
and things like that, I just stop understanding.
And you actually talk a little bit about this in your book,
that part of the problem here is that these descriptions aren't
actually accurate.
Because really they're just describing
these mathematical equations.
So is it impossible to understand this stuff
without understanding the math involved?
Or is this something that you encountered
when you were learning this?
At some point did you just say, wow, I didn't take physics
but now I have to learn differential equations just
to even understand this at all?
AMANDA GEFTER: That's a really good question.
And I sort of struggled with this.
Because there definitely were times where I was like,
oh my god.
I'm reading through these papers and I'm
like, if I knew this math, this would be a lot easier.
And I think it's true, what you were referring to,
this idea that physics is expressed in mathematics.
And then if you try to translate that into English,
there's not a one-to-one correlation
between English and math.
And so something is inevitably lost in the translation.
And science writers tend to rely a lot on metaphors.
And so now you're almost at another level
where you're losing a little bit of something else.
It might make it easier to sort of understand,
but on the other hand you're losing more of the nuance.
And so you might say you can't really understand it
unless you understand the math.
But on the other hand-- the joke that the meaning
of life, the universe, and everything
is 42, the reason that's funny-- why
is 42 not a satisfying answer?
Because you want an answer in English.
A number wouldn't be the answer, because we
want to know what it means.
And so the math doesn't tell you what anything means.
And so even though you lose something in the translation,
you gain a sense of meaning.
And a lot of physics is really based
on principles and having these foundational principles
and then deriving the math from that.
And that's how Einstein worked.
And so you can understand all the principles
without understanding the particular solutions
of equations.
And so I think you actually can have a complete big picture
understanding, even if you can't sit down
and actually do a particular problem.
AUDIENCE: So my understanding of string theory-- by the way,
I really enjoyed your talk-- my understanding of string theory
is a little bit outdated.
Why are strings not invariant?
AMANDA GEFTER: Yeah, great question.
So there was a period of time where everyone
was hoping that that was the case.
And then physicists realized they
had five different versions of string theory
that were all completely consistent.
And so this was sort of an embarrassment of riches.
You don't want five theories of everything,
you want one theory of everything.
And so this was sort of a crisis.
And Ed Witten came along, and he realized
that actually these five string theories,
even though they look very different,
are all mathematically equivalent.
There are transformations that you
can make to go from one to another.
And that's really unexpected.
Because you have a theory with strings vibrating
in 10 dimensions, and then you have
a theory of these membranes in 11 dimensions,
and then you have particles.
And you have radically different spacetime geometries
and what would look to us like drastically different
physical worlds.
And they're actually all descriptions of the same thing.
And so people refer to that as the second superstring
revolution.
And that was considered this amazing step.
Because, oh, we don't really have five theories,
we have one theory.
And now we'll call it M-theory.
And that's great.
But what M-theory is telling you is
that things like dimensionality and strings are not invariant.
Because what look like strings in one point of view,
one of these theories, look like particles in another.
And they look like membranes in another.
And what looks like 10 dimensions in one
is 11 dimensions in another.
And it's not like one's right and one's wrong.
It's just that there are two different ways
of looking at the exact same thing.
And so now M-theory basically undermined the idea
that you can have an invariant fundamental ingredient.
AUDIENCE: I was snooping at your bookshelf,
so I know you've run into a couple of these.
And I'm not going to remember the guys' names,
but there are a couple people who look at the evolving
contradictions and-- if you wind up
proving that nothing is real-- If all of our particles that
make up us in this room right now originated as Hawking
radiation, so there's some frame of reference from which
absolutely nothing is real, that you sort of
need to find another kind of answer to things.
I think of that as sort of like Godel's notion of completeness
and being able to prove the system is complete.
So you've got the guy who thinks that the entire universe is
a cellular automata.
And then there's also the thought experiment thing
that suggests that maybe the entire universe is
a simulation in somebody else's universe.
And I just wondered what you thought
about those kind of notions.
AMANDA GEFTER: Yeah, so they're all really interesting.
I think the same problems sort of plague all of those ideas.
And the simulation question is really interesting.
And it's actually directly related
to Godel's incompleteness theorem.
Because the main conceptual difficulty
in talking about the universe as a whole,
especially when you have to apply quantum mechanics
to the universe as a whole, is the fact
that unlike anything else that we know of,
the universe only has an inside.
It doesn't have an outside.
It's like a one-sided coin.
And so you can't have an observer outside the universe.
The universe is this set that contains itself.
You get into these weird paradoxes.
And there's no way for an observer
to describe the universe without it being self-referential
in some sense, because the observer's
part of the universe.
And so with the simulation question,
you're saying, what if this whole universe is actually
a simulation embedded on a computer in some higher
reality.
Well, for one thing, I don't know
that it would matter that much.
There would still be some fundamental laws of physics
that I really believe you would be able to figure out.
But in order to assess the reality of reality,
you have to step outside of it.
So to know that you were a simulation,
you'd have to be outside the simulation.
And then how do you know that that's not a simulation.
You'd have to be outside of that.
And so it's again this question of,
what is your reference frame.
Because by definition you can't be outside reality.
And so there is no reference frame
from which you can determine the reality of reality.
I don't know if that totally answers your question,
but I think all of these issues that you're raising
are very related.
And Stephen Wolfram's theory that you were referring to
is really interesting.
I don't really know it well enough
to comment that intelligibly, but it's
going to be subject to the same issues
that we're talking about here.
Because it's another way of doing things,
but it still has to replicate all of physics as we know it.
And so it's going to run into these same questions.
Anyone else?
AUDIENCE: One more question, but I want to see if it make sense.
Because this stuff's amazing but also makes my head spin.
You said there is a trajectory and what
is invariant's become smaller and smaller,
and it may be nothing.
But what is the endgame?
Obviously there's an endgame for people
that study this and are amazed by it and everything else.
But for someone who doesn't have this understanding--
and if there is an endgame where it does become figured out,
what effect could it have on people outside of just
in theory?
AMANDA GEFTER: Probably none.
[LAUGHTER]
I don't think it's going to have technological applications.
You never know, right?
You never know.
You can never see these things coming.
I think this is really just about answering
deep existential questions that humans have been asking
for as long as there have been humans.
The question of what is real, what am I, how am I here,
what am I seeing?
I think it's just things that we deeply want to know.
And it's funny because on the one hand
it seems incredibly abstract, especially if you're
talking about 14 billion years ago
and the origin of the universe.
Or the cosmos, which is so huge.
And quantum mechanics, which the scale is so tiny.
And you can't place yourself in these things.
But I always have these moments where--
because I start thinking about this stuff and I kind of start
taking it for granted a little bit.
And then all of a sudden I'll have this moment
where I'm like, oh my god, I'm talking about,
literally, this isn't real.
I'm talking about the stuff right here and me
and all of us.
And so it's not that abstract.
It's just you can't really live your life thinking about it
every minute like that, or else you're going to have a problem.
I think any time you have a better understanding of the way
that nature works it's going to have some effect.
It's going to be useful in some way.
But when you get to this level, will it be practical?
Probably not.
AUDIENCE: Sorry for being a stick in the mud,
but if strings aren't invariant, are there
any invariants in M-theory?
There are not that anyone knows of.
And it's really interesting because when
I've talked to string theorists--
string theorists will say things like,
we don't really know what the theory is.
We have all these equations, we have the theory,
but we don't know what it's a theory of.
And what they mean by that is quantum field
theory is the theory of quantum fields,
string theory was the theory of strings.
M-theory, they don't know.
They have this theory and they don't
know what it's describing.
There's no basic ontology there.
And they're well aware of that.
They see it as either something will emerge
and there will be something that it's
describing that we just don't realize yet.
I happen to think it's actually more useful if there's not
an ontology there.
Because now you can answer this question
of how you get something from nothing.
It's really fascinating.
M-theory-- if you read physics books, everything you read
will say, nobody knows what the M stands for.
Maybe it stands for mystery or mother or magic.
There was a Nobel Prize winner who said,
it's the upside down W for Witten.
And people had all these theories.
You read Stephen Hawking's book and it's
like, no one knows what the M stands for.
And I'm like, how can no one know?
Ed Witten coined it, and he's still alive.
Why doesn't someone just ask him?
So I went and I asked him.
And he was like, it stands for membrane.
I originally said, oh, it could be mother or mystery
or whatever, but I was kidding.
And nobody really got the joke.
But so the M stands for membrane.
But membranes are not invariant in that theory.
And so there's a deeper point to the no one
knows what M stands for, which is even though literally it
stands for membrane, I think part
of what that means is they don't know what it's a theory of.
Which has never really happened.
It's a weird way of doing physics.
But fascinating.
All right, thank you guys so much for coming.
[APPLAUSE]