Welcome to our Special Relativity Minicourse

Brought to you by

Quarknet

Physics Department of the

University of Houston

Physics and Astronomy Department of

Rice University

Einstein’s Legacy

Last year we celebrated the 100th anniversary of Einstein’s miraculous year, when he wrote down the special theory of relativity, explained the photoelectric effect, and found a way to calculate Avagadro’s number.

I’m only going to talk about the first one…

Relativity

The story of relativity starts not with Einstein or even with Newton, but with Galileo.

Reference frames

One observer sees the ball go straight up and down.

The other observer sees the ball go in a parabola.

Who’s right??

Galileo thought about how the same event would look to different observers.

Both right!

They’re both right of course, and Galileo wrote down the rule for going from one reference frame to another.

S S’

V

S’ moves with velocity V along the x-axis of S.

x’

x

Galilean transformation

Observations in different frames are related by the Galilen transformations:

x’ = x-Vt V=relative velocity of the frames

y’=y

t’=t

Knowing what happens on the cart allows you to know what the observer on the ground saw, and vice-versa.

No absolute motion

Newton articulated the idea that there is no such thing as “absolute motion ” or reference frame.

All “inertial” frames are equivalent, and the laws of physics are the same in all frames.

Inertial=moving with constant velocity, ie not accelerated.

No absolute motion

If you are in a railroad car with no windows or doors, moving at constant velocity, there is NO EXPERIMENT that you can do to tell that you are moving.

You’re NOT moving, as far as you can tell.

V

A ball on a string hangs straight, as long as V is constant

Accelerated motion

In contrast you CAN tell if you are being accelerated.

If the car is accelerating, the ball hangs at an angle.

But special relativity deals only with inertial frames.

a

Maxwell’s equations

The 1800’s saw the discovery of the wave nature of light (Young, 1802) and the discovery of the laws of electromagnetism, culminating in Maxwell’s Equations in 1868.

Maxwell’s Equations

Maxwell’s amazing discovery was that

C2 = 1/µ00

Constants that arose from Coulomb’s law and Ampere’s law were related to the speed of light!

Light propagation

If light is a wave, it needs a medium, just like sound waves need a medium. The speed of propagation is defined with respect to the medium.

(This was the thinking in 1900).

Michaelson-Morley experiment

Michaelson spent years attempting to measure the motion of the earth through the aether.

Michaelson-Morley experiment

A very sensitive interferometer rotated on a bed of mercury. The interference fringes should shift if the earth is moving through the aether.

Interference of two waves

When the waves arrive in phase, there is a bright spot

When they arrive out of phase, there is a dark spot

Interference pattern

The result is a pattern of light and dark regions sensitive to the path length difference of the two beams of light.

Michaelson-Morley experiment

In his final experiment, done in 1887, Michaelson, along with Morley, had an apparatus with a sensitivity of .005 fringes. The expected effect was a shift of the interference pattern of 0.4 fringes. They measured NO shift of the interference fringes.

“The result of the hypothesis of a stationary ether is thus shown to be incorrect.”--Michaelson

“Experiment is the sole judge of scientific truth.” Feynman

Enter Einstein

The laws of physics are the same in all reference frames…and therefore…

The speed of light is the same in all reference frames, independent of the motion of the source or observer.

Velocity addition classically

If you throw a baseball out of a moving train with velocity vo, an observer on the ground sees it moving with velocity V + vo

V

vo = velocity of ball with respect to the train

The ball is moving toward

me at V+vo

The ball is moving away from me at v0

Velocity addition for light?

If you shine a flashlight out the front of a moving train, what does an observer on the ground measure for the velocity of the wavefront of light?

V

Beam of light

The light is moving toward me at c

The light is moving away from me at c

Consequences of a simple assumption

Newton is on the train, in the center of the car

Einstein is on the embankment, also at the center of the car

The train is at rest. They both agree, lightening strikes the two ends of the car at the same time!

Consequences of a simple assumption

Newton is on the train, in the center of the car

Einstein is on the embankment, and when the middle of the car passes him, lightening strikes both ends of the train

V

Now suppose the train is moving with velocity V

Simultaneity

Einstein says:

The light from the two ends of the train reached me at the same time. The center of the train was passing me when the lighting hit, so these events were simultaneous!

But since both flashes of light are moving toward Newton at c, and Newton is moving to the right at V, the light from the front of the train will reach him first, and the light from the back of the train will reach him later. To Newton these events will not be simultaneous!

Simultaneity

Newton says: The front and back of the train are the same distance from me. I see the flash of light from the front of the train first, and the flash from the back later. These events are not simultaneous!

Einstein is moving to the left at V, and because the light from the front of the train has a longer distance to go to reach him, Einstein will see the two flashes reach him at the same time. In his frame, these events will be simultaneous!

Consequences

Once you accept the statement

the speed of light is the same in all reference frames independent of the motion of the source or observer,

you must accept the consequence that

events simultaneous in one frame are not simultaneous in another frame.

Newton insisted there is no such thing as absolute motion, now Einstein shows us there is no such thing as absolute time.

Consequences

There are lots of other mind-boggeling consequences of Einstein’s theory, all of which are c onfirmed…

Time dilation and the twin paradox

The equivalence of mass and energy

Einstein’s Legacy

To me, Einstein’s greatest gift was his ability to embrace ideas that overthrew all conventional notions of just about everything.

The passage of time is different in

different reference

frames.

Einstein’s Legacy

What would you have done if your reasoning led you to the concept of non-absolute time?

The light clock

Each time the light pulse hits the bottom mirror is

one tick of the clock.

The moving light clock

If the clock moves to the right, we observe a longer flight path for the light !