Alright. So i like this one, if you had to pick one
differential equation as the one that advance the study of physics the
most, which one would you pick?
Hamilton's equation for Classical Mechanics, Maxwell's
for Electrodynamics, Schrodinger equation for Quantum
Mechanics, Einstein Field Equations, or something else?
>> That's like asking me to choose between my children. I mean,
they're not my children but that is like, they're all remarkable structures.
Which one has changed the, the physics the most? Go back
[LAUGH]
give them to me again.
>> Hamilton.
>> Okay, so Hamilton's equations are the basic equations of classical
mechanics. They tell you how classical
mechanical systems. They have a predictive
equations for how particles move, or how anything changes with time. Obviously
they have had a enormous impact on Physics. And the impact
covers every area of physics, every area. They're
there in quantum mechanics, they're there in classical
mechanics, they're there in quantum field theory, they're
every where. Okay, what was the next one?
>> Next one is Maxwell's equations
>> Alright, Maxwell's equations are a little
more special. They're a little more special,
they have to do with a specific
class of phenomenon. Electricity and magnetism, electromagna-, electromagnetic
fields. So they're a little bit narrower,
but on the other hand, they did something
remarkable. They taught us what light is. Up
until Maxwell's equations, nobody knew what light was.
So how do you compare something like Maxwell's
equations with. that other fellow, Hamilton's equations. Which
one is more important? It's a matter of
taste. Do you think explaining light was more
important or less important than having a framework for, in
a sense, all of physics? It's a matter of taste.
>> I like those t shirts that have the Maxwell's equation.
>> Have the Maxwell's equation.
>> Let there be light.
>> What was the third one?
>> next was Schrodinger's equation.
>> Okay so Schrodinger's equation there, Schrodinger's equation
has different meanings to sometimes the physicists It
can mean a very general kind of equation
which tells you how the quantum state of a
system changes with time. Or it can mean the
very specific equation that Schrodinger wrote down. The very
specific equation that Schrödinger wrote down had to with
again a special class of phenomena, motion of a
particle, quantum mechanical motion of a particle. But there's
a, there's a generalization of it. There's a generalization
of it that has to do with how any quantum system behaves. In the sense it's
as broad and as important as Maxwell's sorry,
Hamilton's equations. It's, it is the quantum mechanics.
What Hamilton's equations were to classical mechanics. So
extremely important. But I think in the end
you're going to have a hard time getting me to say I favor one over the other.
>> What about what about the
field equations?
>> The Einstein field equations. Yes,
They of course are the sort of
quintessential deep, deep, equations about what space and
time are. They're like Maxwell's equations in
that they govern a special class of phenomena,
gravity, in this case. But, they're more
than that. They're telling us something extremely deep
about the nature of space and time, that it's curved, that it it that the
geometry of space and time is not what Euclid thought it was. And how that
geometry responds to matter. So again its you, you certainly
picked what I would say are the four most important deepest favorite
equations of a theoretical physicist for sure
I, I am going to refuse to pick between them. There are four of
them. I have four children, and never would I pick between my four children.
[LAUGH]
>> When we get a theory that describes the encompasses all
of this, is it going to be described with a differential equation?
>> Oh boy. Is it going to, is the final theory going to be
described by a differential equation? Okay. So
there're a lot of people And I'm not
going to place right now. There are a lot of people who think the
world is really discreet. Space and time
might be discreet. Comes in little elementary steps.
If that's the case, then at that
level, at that, the smallest possible distances in the world. It might
mean that the mathematics of it is discrete mathematics, the mathematics of
little steps, indivisual, indivisible steps, and
not smooth continuous evolution. If that's the case,
no, it won't be described by differential equations, but we don't know.
If, if I knew the answer to that, I would publish it.
>> As in this classic model, the model phenomena, discretely. >>Yes.
>> You have even with the underlaying assumptions that it's continued.
>> Exactly
>> For the computer programs I'll have to
[INAUDIBLE]
>> Exactly, so see that, that in many cases it really is not possible
to tell Whether a certain equation is
describing something which is truly continuous or whether
it's describing some discrete phenomena where the little steps occur fast enough
and one after another, too fast to be able to see. Okay, so we don't know what
the final theory of nature will be