you the syllabus for this term--not the detailed one,

just the big game plan.

The game plan is: we will do electromagnetic

theory.

Electromagnetism is a new force that I will introduce to you and

go through all the details.

And I will do optics, and optics is part of

electromagnetism.

And then near the end we will do quantum mechanics.

Now, quantum mechanics is not like a new force.

It's a whole different ball game.

It's not about what forces are acting on this or that object

that make it move, or change its path.

The question there is: should we be even thinking

about trajectories?

Should we be even thinking about particles going on any

trajectory?

Forget about what the right trajectory is.

And you will find out that most of the cherished ideas get

destroyed.

But the good news is that you need quantum mechanics only to

study very tiny things like atoms or molecules.

Of course the big question is, you know, where do you draw the

line?

How small is small?

Some people even ask me, "Do you need quantum

mechanics to describe the human brain?"

And the answer is, "Yes, if it is small

enough."

So, I've gone to parties where after a few minutes of talking

to a person I'm thinking, "Okay, this person's brain

needs a fully quantum mechanical treatment."

But most of the time everything macroscopic you can describe the

way you do with Newtonian mechanics, electrodynamics.

You don't need quantum theory.

All right, so now we'll start with the brand new force of

electromagnetism.

But before doing the force, I've got to remind you people

of certain things I expect you all to understand about the

dynamics between force, and mass, and acceleration that

you must have learned last term.

I don't want to take any chances.

I'm going to start by reminding you how we use this famous

equation of Newton.

So you've seen this equation, probably,

in high school, but it's a lot more subtle than

you think, certainly a lot more subtle

than I thought when I first learned it.

So I will tell you what I figured out over these years on

different ways to look at F = ma.

In other words, if you have the equation what's

it good for?

The only thing anybody knows right away is a stands

for acceleration, and we all know how to measure

it.

By the way, anytime I write any symbol on the board you should

be able to tell me how you'd measure it,

otherwise you don't know what you're talking about as a

physicist.

Acceleration, I think I won't spend too much

time on how you measure it.

You should know what instruments you will need.

So I will remind you that if you have a meter stick,

or many meter sticks and clocks you can follow the body as it

moves.

You can find its position now, its position later,

take the difference, divide by the time,

you get velocity.

Then find the velocity now, find the velocity later,

take the difference, divide by time,

you've got acceleration.

So acceleration really requires three measurements,

two for each velocity, but we talk of acceleration

right now because you can make those three measurements

arbitrarily near each other, and in the limit in which the

time difference between them goes to zero you can talk about

the velocity right now and acceleration right now.

But in your car, the needle points at 60 that's

your velocity right now.

It's an instantaneous quantity.

And if you step on the gas you feel this push.

That's your acceleration right now.

That's a property of that instant.

So we know acceleration, but the question is can I use

the equation to find the mass of anything.

Now, very often when I pose the question the answer given is,

you know, go to a scale, a weighing machine,

and find the mass.

And as you know, that's not the correct answer

because the weight of an object is related to being near the

earth due to gravity, but the mass of an object is

defined anywhere.

So here's one way you can do it.

Now you might say, "Well, take a known force and find the

acceleration it produces," but we haven't talked about how

to measure the force either.

All you have is this equation.

The correct thing to do is to buy yourself a spring and go to

the Bureau of Standards and tell them to loan you a block of some

material, I forgot what it is.

That's called a kilogram.

That is a kilogram by definition.

There is no God-given way to define mass.

You pick a random entity and say that's a kilogram.

So that's not right and that's not wrong.

That's what a kilogram is.

So you bring that kilogram, you hook it up on the spring,

and you pull it by some amount, maybe to that position,

and you release it.

You notice the acceleration of the 1 kilogram,

and the mass of the thing is just one.

Then you detach that mass.

Then you ask--Then the person says, "What's the mass of

something else?"

I don't know what the something else is.

Let's say a potato.

And you take the potato or anything, elephant.

Here's a potato.

You pull that guy by the same distance, and you release that,

and you find its acceleration.

Since you pulled it by the same amount, the force is the same,

whatever it is.

We don't know what it is, but it's the same.

Therefore we know the acceleration of 1 kilogram times

1 kilogram is equal to the unknown mass times the

acceleration of the unknown mass.

That's how by measuring this you can find what the mass is.

In principle you can find the mass of everything.

So imagine masses of all objects have been determined by

this process.

Then you can also use F = ma to find out what forces

are acting on bodies in different situations,

because if you don't know what force is acting on a body you

cannot predict anything.

So you can go back to the spring and say,

"I want to know what force the spring exerts when it's

pulled by various amounts.

Well, you pull it by some amount x.

You attach it to a non-mass and you find the acceleration,

and that's the force.

And if you plot it, you'll find F as a

function of x will be roughly a straight line and it

will take the form F = -kx,

and that k is called a force constant.

So this is an example of your finding out the left hand side

of Newton's law.

You've got to understand the distinction between F =

-kx and F = ma.

What's the difference?

This says if you know the force I can tell you the acceleration,

but it's your job to go find out every time what forces might

be acting on a body.

If it's connected to a spring, and you pull the spring and it

exerts a force, someone's got to make this

measurement to find out what the force will be.

All right, so that's one kind of force.

Another force that you can find is if you're near the surface of

the earth, if you drop something,

it seems to accelerate towards the ground,

and everything accelerates by the same amount g.

Well, according to Newton's laws if anything is going to

accelerate, it's because there's a force on it.

The force on any mass m must be mg,

because if I divide by m I've got to get g.

So the force on masses near the earth is mg.

That's another force.

Something interesting about that force is that unlike the

spring force where the spring is touching the mass,

you can see it's pulling it, or when I push this chair you

can see I'm doing it, the pull of gravity is a bit

strange, because there is no real

contact between the earth and the object that's falling.

It was a great abstraction to believe that things can reach

out and pull things which are not touching them,

and gravity was the first formally described force where

that was true.

And another excursion in the same theme is if this object

gets very far, say like the moon over there,

then the force is not given by mg,

but the force is given by this law of gravitation.

For every r near the surface of the earth,

if you put r equal to the surface of the earth you

will get a constant force that is just mg,

but if you move far from the center of the earth you've got

to take that into account, and that's what Newton did and

realized the force goes like 1 over r^(2).

So every time things accelerate you've got to find the reason,

and that reason is the force.

Many times many forces can be acting on a body,

and if you put all the forces that are acting on a body and

that explains the acceleration, you're done,

but sometimes it won't.

That's when you have a new force.

And the final application of F = ma is this one.

If you knew the force, for example,

on a planet, and here's a planet going

around the sun and it is here.

This is the sun, and you know the force acting

on it given by Newton's Law of Gravity you can find the

acceleration that will help you find out where it will be one

second later, and you repeat the calculation,

you will get the trajectory.

So F = ma is good for three things,

that's what I want you to understand: to define mass,

to calculate forces acting on bodies by seeing how they

accelerate, and finally to find the

acceleration of bodies given the forces.

This is the cycle of Newtonian dynamics.

And what I'm going to do now is to add one more new force,

because I'm going to find out that there is another force not

listed here.

I'm going to demonstrate to you that new force,

okay?

Here's my demonstration.

The only demonstration you will see in my class,

because everything else I've tried generally failed,

but this one always works.

So, I have here a piece of paper, okay?

Then I take this trusty comb and I comb the part of my head

that's suited for this experiment,

then I bring it next to this, and you see I'm able to lift

that.

Now, that's not the force of gravity because gravity doesn't

care if you comb your hair or not, okay?

And also when I shake it, it falls down.

So you're thinking, "Okay, maybe there is a new force but

it doesn't look awfully strong because it's not able to even

overcome gravity, because it eventually yielded

to gravity and fell down," but it's actually a mistake to

think so.

In fact this new force that I'm talking about is 10 to the power

of 40 stronger than gravitational force.

I will tell you by what metric I came up with that number,

but it's an enormously strong force.

You've got to understand why I say it is such a strong force

when, when I shook it the thing fell down.

So the reason is that if you look at this experiment,

here's the comb and here's the paper,

the comb is trying to pull the paper,