Chapter 27Wave/Particle Exp.

Chapter 26Relativity Intro.

Hint: Be able to do the homework (both theproblems to turn in AND the recommended ones)you’ll do fine on the exam!

Monday, May 10, 1999 10:30am - 11:20amChs. 20, 26, and 27

You may bring one 3”X5” index card (hand-writtenon both sides), a pencil or pen, and a scientificcalculator with you. Same format!

Hint: Review notes from my review lectures! Tryto do some of the old homework recommendedhomework, and exam problems.

Monday, May 10, 1999 11:30am - 12:30pm

everything we’ve covered

You may bring one 8.5”X11” sheet (hand-writtenon both sides), a pencil or pen, and a scientificcalculator with you.

Monday, December 15, 1997 11:30am - 12:30pm

everything we’ve covered

Format: 5 problems, pick 4.

1 problem on each of the following topics:

Electrostatics Circuits Magnetism

Optics Modern

x ph

4

Which says that it is impossible to knowboth the position and momentum of aparticle with infinite accuracy.

In fact, if you know the position of aparticle precisely, you have no clue asto its momentum!

And if you know its mass and velocity precisely, you have no clue as to where it is!

There is an alternate form of theuncertainty principle, one relatingtime and energy. It says:

E th

4

Where t is the time required to makea measurement and E is the uncertaintyin a particle’s energy.

Consider the following system:

electronThe reflected photonallows us to determinethe location of the electron.

In the collision, momentum is transferred betweenthe photon and the electron, however!

If particles really have wave properties,I should be able to observe interferenceeffects.

So, let’s redo Young’s Experiment usingelectrons instead of light and see whathappens….

electrongun

photographicplate

elec

tron

s

When you developthe plate, what do you see???

Gun fires exactlyone electron at atime

Zeroth ordermaximum

1st 1st2nd 2nd

001 1

dark fringes

The familiar 2-slit interference pattern!!!

REMEMBER, only one electron passesthrough the slits at a time! So the electronis interfering with itself!!

You’re saying to yourself,“That electron has got to passthrough one slit or the other!”

Okay, let’s change the experiment to find out!

electrongun

photographicplate

elec

tron

s

Gun fires exactlyone electron at atime

Detector will tell us whenthe electron passes throughthe bottom slit.

Now we know which path each electron takeson its journey to the photographic plate.So what do we see when we develop the plate?

Bright spots behind the slits! No interference!

By observing this system, we’ve changedthe system and the results indicated onthe photographic plate!

We leave behindthe world ofquantum physics…for now!

Thanks for visiting

Quantum World.

Hope you enjoyed

your stay!

Albert Einstein

Essentially in parallel with the entirelyseparate development of quantum mechanics,Einstein developed relativity:

Developed in 1905 handles the comparisonof measurements made in different inertialreference frames.

An inertial reference frame is a frame notthat is not being accelerated.

A frame that is not being accelerated must be at rest or moving with a constant velocity.

Developed in 1915 handles non-inertialreference frames (i.e. accelerating referenceframes) and gravity.

Problems in general relativity require theuse of sophisticated mathematical techniques.

We won’t attempt to cover generalrelativity here.

We already have a notion of relativity.Newtonian mechanics told us that the laws of mechanics worked equally well standing still on the surface of the Earth as riding a train (provided, of course, that the train was moving with a constant velocity).

Such a train provides an example of aninertial reference frame!

GM R/R

Physics

Rules

u

Here, a woman juggles on amoving train car.

Our friend, “The Shadow,” standsstill and watches the train (and thejuggler) go by.

When asked to describe the motion ofthe juggling balls, these two people willhave very different things to say!

To the woman jugglingon the train, she is unableto detect the motion of thetrain, so long as the traindoes not accelerate.

The juggling balls will follow a simple,parabolic path to the right from her lefthand to her right hand across a distance, d.

d

In fact, if you sat in a soundproof boxcar,with no windows, you could not tell thedifference between the train moving ata constant speed of 100 m.p.h. or the trainstanding still!

It’s only the fact that the train goes up anddown hills, speeding up and slowing down,hitting bumps, that allows you to know thedifference between motion and rest!

What will our friend, theshadow say?

Things seem quite differentto him...

GM R/R

Physics

Rules

uGM R/R

Physics

Rules

u

The Shadow sees the red ball releasedfrom the juggler’s left hand at point A.

A B

A short time later, the ball is caught bythe juggler’s right hand at point B.

The shadow would say that the ball movedto the right in a parabolic path from A to B.

Notice that we have a seeming contradiction!

“The balls move from myleft to my right.”

“The balls move from myleft to my right.”

How did classicalmechanics handle this?

GM R/R

Physics

Rules

u

SThe “lab” frame. It’s theone “at rest.”

S’

u

the movingframe

Moves with a velocityv relative to frame S.

Well, the position of the ball in the frameS’ is given by:

x’ = x - ut

And the x-direction velocity of the ball inthe frame S’ is given by:

v’ = v - u

where v is the apparent velocity in the lab frame.

With this simple transformation (named for its inventor), we can reconcile the apparently contradictory observations of our two observers.

There is no preferred inertial referenceframe in which to describe the laws ofmechanics. These laws are invariant.

The stationary observer measures the velocity of the juggling ball to be 19 m/s to the right and the Velocity of the train to be 20 m/s to the right. What is the velocity of the ball relative to the train?

v’ = v - uGM R/R

Physics

Rules

20 m/s19 m/s

v’ = 19 - 20

v’ = -1 m/sOn the boxcar,the ball movestoward the back!

Two cars, each driving 50 mph, travel in opposite directions on a 2-lane road.You ride in one car. How fast does the other car appear to be approaching?

50 mph

50 mph

You’re inthis car

S’

50 mph

v’ = v - u

v’ = -50 - 50

v’ = -100 mph

This classical theory of relativity workswell for juggling balls and railroad cars,but what happens when we try to applyit to electromagnetic waves (i.e., light)?

The solution to Maxwell’s equations,which describe light waves, doesn’t obeythese classical principles! The solutionto his equations always travels at thespeed of light in free space!

What would happen if light did obeythe classical theory?

You’re in a spaceship travelling away from the Sun at 0.9c. How fast does light from the Sun fly past you?

Well, according to classical theory

v’ = v - u

v’ = c - 0.9c = 0.1c

An electron is accelerated across an electrical potential of 100 million volts. What is the final speed of the electron?

PE = qV = (1.6 X 10-19 C)(108 V)

Initially, the electron’s energy is all potentialenergy...

= 1.6 X 10-11 J

electron

When the electron reaches the opposite plate,all the energy will be kinetic

electron

KE = 1/2 mv2 = 1.6 X 10-11 J

m = 9.1 X 10-31kg

v = 5.9 X 109 m/s = 19.7c !!!!