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How Fast Are You Moving Right Now?

0 m/s relative toyour chair 400 m/s relative toearth center (rotation)

30,000 m/s relative tothe sun (orbit)

220,000 m/s relative tothe galaxy center (orbit)

Relative to What??

This is the gist of special relativity

its the exploration of the physics of relative motion

only relative velocities matter: no absolute frame

very relevant comparative velocity is c= 300,000,000m/s

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A world without ether

For most of the 19th century, physicists thought thatspace was permeated by luminiferous ether

this was thought to be necessary for light to propagate

Michelson and Morley performed an experiment to

measure earths velocity through this substance first result in 1887

Michelson was first American to win Nobel Prize in physics

Found that light waves dontbunch up in direction of

earth motion shocked the physics world: no ether!!

speed of light is not measured relative to fixed medium

unlike sound waves, water waves, etc.

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Einsteins Two Postulates of Special

Relativity

The Speed of Light is Constant for anyobserver, regardless of the motion of theobserver or the motion of the light source.

The laws of physics are always the same inall inertial ( non-accelerating) frames ofreference.

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Simultaneity is relative, not absoluteObserver riding in spaceship at

constant velocity sees a flash of

light situated in the center of the

ships chamber hit both ends at

the same time

But to a stationary observer (or any

observer in relativemotion), the

condition that light travels each way

at the same speed in their own frame

means that the events will not besimultaneous. In the case pictured,

the stationary observer sees the flash

hit the back of the ship before the

front

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One persons space is anothers time

If simultaneity is broken, no one can agree on auniversal timethat suits all

the relativestate of motion is important

Because the speed of light is constant (and finite) forall observers, space and time are unavoidablymixed weve seen an aspect of this in that looking into the distance

is the same as looking back in time

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Why dont we see relativity every day?

Were soooo slow(relative to c), that lengthcontraction and time dilation dont amount to

much

30 m/s freeway speed has v/c= 10-7

= 1.000000000000005

30,000 m/s earth around sun has v/c= 10-4

= 1.000000005

but precise measurements see this clearly

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Velocity Addition

Also falling out of the requirement that the speed oflight is constant for all observers is a new rule for

adding velocities

Galilean addition had that someone traveling at v1

throwing a ball forward at v2would make the ball goat v1+v2

In relativity,

reduces to Galilean addition for small velocities

can never get more than cif v1and v2are both c

if either v1OR v2is c, then vrel= c: light always goes at c

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Velocity Addition Example

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A spaceship moving at .5c, fires a projectile at .6c in thedirection its moving. What is the speed of the projectile

measured by an observer at rest with respect to the ship?

V1= .5c V2= .6c

Vrel= (.5c + .6c) / ( 1 + (.5c)(.6c)/c2 ) = 1.1c / ( 1 + .3)

= (1.1)c/(1.3) = .85c NOT 1.1 c !

No correct calculation will ever give you any speed greater

than c.

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Velocity Addition Example

A spaceship moving at .5c, fires a laser in thedirection its moving. What is the speed of the

laser light measured by an observer at rest

with respect to the ship?

V1= .5c V2= c

Vrel= (.5c + c) / ( 1 + (.5c)(c)/c2 ) = .6c / .6

= c ( it had to be c - the speed of light is

invariant. )

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Classic Paradoxes

The twin paradox: one twin (age 30) sets off in rocket at high speed, returns to

earth after long trip

if v= 0.6c, 30 years will pass on earth while only 24 will passin high speed rocket

twin returns at age 54 to find sibling at 60 years old why not the other way around?

The moving twin is NOT in an inertial systemthere is noparadox.

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What would I experience at light speed?

It is impossibleto get a massive thing totravel truly at the speed of light energy required is mc2, where as vc

so requires infinite energy to get all the way to c

But if you are a massless photon to the outside, your clock is stopped

so you arrive at your destination in the sameinstantyou leave your source (by yourclock)

across the universe in a perceived instant

makes sense, if to you the outside worlds clockhas stopped: you see no ticks happen beforeyou hit

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Experimental Confirmation

We see time dilation in particle lifetimes

in accelerators, particles live longer at high speed

their clocks are running slowly as seen by us

seen daily in particle accelerators worldwide

cosmic rays make muons in the upper atmosphere

these muons only live for about 2 microseconds

if not experiencing time dilation, they would decay before

reaching the ground, but they doreach the ground in

abundance

We see length contraction of the lunar orbit

squished a bit in the direction of the earths travel around thesun

E= mc2extensively confirmed

nuclear power/bombs

suns energy conversion mechanism