Special Relativity

•Einstein (1905): Three Nobel-Prize worthy publications

•On unrelated subjects:

Brownian motion

Photo-electric effect (Nobel prize)

“On the electrodynamics of moving bodies”... ⇐

Special Relativity•Requires only three assumptions:

★ The laws of physics are the same in every uniformly moving laboratory

★ (if I hit my head, an observer moving relative to me will also see me hitting my head)

★ Space is “homogeneous” and “isotropic”★ (a yardstick at rest is exactly a yard long,

regardless of where it is used and which way it is pointing)

★ The speed of light is constant and the same in every frame of reference

• (Maxwell’s equations are the same in every lab)

Radical changes...

•This implies that space and time are no longer independent.

•Space and time are interwoven into a fabric, called “spacetime”.

•Maxwell’s laws still hold, but Newton’s must be altered.

Frames•A “frame” is really just an imaginary

laboratory attached to some object or observer.

•A frame can be moving with some fixed velocity

• Such a frame is called an “inertial frame”

• Natural laws are formulated in inertial frames

Frames•A “frame” is really just an imaginary

laboratory attached to some object or observer.

•A frame can be accelerated

• Rotating frames are accelerated

• An accelerated frame is bad for formulating the laws of physics

Frames•Each object has a “frame” that is

attached to it

• In this frame it is not moving and not rotating

• That frame is called the “rest frame” of that object (because it is at rest in that frame).

Spacetime...

•Consider a flash of light

•Its rays will move outward on a sphere

Spacetime...

•Now add another observer, moving at some velocity (say, half the speed of light)

•Light flash is emitted when observers pass

Spacetime...

•Now consider the other observer...

•Light flash is emitted when observers pass

Spacetime...

•In our rest frame, the light arrives at the two outer clocks and the observer arrives at the inner clock at the same time

Spacetime...•In “moving” frame, the light has

already passed the right clock and not yet arrived at the left clock when the inner clock reaches him

Bye-bye simultaneity

•Things that happen simultaneous for one observer are not longer simultaneous for other observers in special relativity

Bye-bye simultaneity

•Things that happen simultaneous for one observer are not longer simultaneous for other observers in special relativity

Spacetime• That means: separation in space between two

things can turn into a separation in time and space

⇒ Space and time are now coupled to each other

⇒ 3 space dimensions + 1 time = 4 dimensions

Measuring a length

•Use a ruler (of course)

•Easiest when the car is at rest (of course)

L

Measuring a length

•When the car is moving, measure both ends at the same time (of course)

15cm

Measuring a length• From the point of view of the car:

Right measurement before left measurement!

⇒ The ruler appears shorter than the car!

⇒ Moving objects are length contracted!

???

Length contraction•By symmetry: moving car must also appear

shorter

•Example:

Car is 25cm long when it is at rest

If it is moving along with velocity v=4/5c, how long do we measure the car to be?

★ Newton: 25 cm

★ Einstein: 15 cm

• In other words: walking is slimming, but driving is even more slimming!

The best diet...

•The moving car is contracted

The best diet...

•To the car, the observer is contracted

Time “dilation”•Now the car shines a light upward

This takes a This takes a certain certain

amount of amount of timetime

Time “dilation”•Now look at this when the car is moving

•The light has to travel a longer distance

•That means on our clock it takes longer

How long it How long it takes when takes when the car is the car is movingmoving

How long it How long it takes when takes when the car is at the car is at

restrest

Time “dilation”•Moving clocks go slower!

•A clock moving at 80% of c moves 40% slower than a clock at rest

Time “dilation”•Of course, from the point of view

of the moving clock, it is our clock that is moving (backwards), so our clock is moving slower

Example:• “Muons” created high in

earth’s atmosphere from energetic particles from outer space

Muons decay in 2μs

Light travels 6 kilometers in 2μs

But muans actually travel 30 kilometers down to us

• Their clocks go 5x slower!

2μs

Velocity addition•Consider a train with some velocity

v and car with velocity v ontop

The looks is shortened

Time is dilated

Car is moving at less than v+v

Doppler shift•The siren of a police car

driving by sounds like it is getting lower when the car passes.

•This is the Doppler effect:

The police car is catching up to the emitted sound waves

Same thing happens with light

Additional effect: Time dilation (slower clock)

“Beaming”•Consider a photon emitted by a

standing car

“Beaming”•What happens when the car is

moving? Light moves forward (also called aberration).

Doppler boosting•Putting the Doppler shift and beaming

together:

Light bulb at rest