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 1873.

Maxwell’s Equations

Maxwell’s amazing discovery was that

c2 = µ00

Constants that arose in

electrostatics and

magnetostatics gave 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.

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

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