Special RelativitySpecial Relativity

Chapters 15 and 16Chapters 15 and 16

EinsteinEinstein

First to connect a relationship between First to connect a relationship between space and timespace and time

Developed the special theory of relativity Developed the special theory of relativity and general theory of relativity in the and general theory of relativity in the early 1900searly 1900s Both of these are not related to your Both of these are not related to your

everyday experiences and therefore seem to everyday experiences and therefore seem to defy common sense (that’s why he’s such a defy common sense (that’s why he’s such a genius)genius)

Space-TimeSpace-Time According to Einstein, time and space According to Einstein, time and space

only exist within the universeonly exist within the universe Space-time is a whole made of space Space-time is a whole made of space

and time, if one increases the other and time, if one increases the other decreasesdecreases When standing still, you move only through When standing still, you move only through

timetime When you move at a fast speed, you move When you move at a fast speed, you move

some through time and some through spacesome through time and some through space When you travel at the speed of light (c), you When you travel at the speed of light (c), you

only move through space (there is no time only move through space (there is no time change!)change!)

Motion is RelativeMotion is Relative Depends on the point of view of the Depends on the point of view of the

observerobserver To a person in a car, the cup in the To a person in a car, the cup in the

cupholder isn’t movingcupholder isn’t moving To a person standing on the curb as To a person standing on the curb as

the car passes, the cup is moving at the car passes, the cup is moving at the same speed as the carthe same speed as the car

Except for light!!!Except for light!!! It always moves at 300,000 km/s, regardless It always moves at 300,000 km/s, regardless

of the observers motionof the observers motion

The First PostulateThe First Postulate

All the laws of nature are the same in all All the laws of nature are the same in all uniformly moving frames of reference.uniformly moving frames of reference. There is no absolute to measure all motion There is no absolute to measure all motion

to, it is always relative to the observerto, it is always relative to the observer There is no experiment that can show that There is no experiment that can show that

something is in a uniform state of motion (if something is in a uniform state of motion (if you had no windows in your car, you you had no windows in your car, you wouldn’t be able to tell if you were moving or wouldn’t be able to tell if you were moving or not)not)

The Second PostulateThe Second Postulate

The speed of light is constant, regardless The speed of light is constant, regardless of the speed of the observer or the of the speed of the observer or the sourcesource Even if you could travel at the speed of light, Even if you could travel at the speed of light,

light would still travel at 300 000 km/s light would still travel at 300 000 km/s compared to you!!!compared to you!!!

This is what unifies space and timeThis is what unifies space and time The speed of light is an absolute constant.The speed of light is an absolute constant.

Time DilationTime Dilation The “stretch” observed in the passage of time The “stretch” observed in the passage of time

as speed approaches c.as speed approaches c. The faster you go, the slower time seemsThe faster you go, the slower time seems At c, time appears to stand stillAt c, time appears to stand still Time depends on the motion of the observer and the Time depends on the motion of the observer and the

sourcesource To someone is a ship traveling near c, those on the To someone is a ship traveling near c, those on the

ground appear to move in slow motion ground appear to move in slow motion To someone on the ground, those on a ship To someone on the ground, those on a ship

traveling near c appear to move in slow motiontraveling near c appear to move in slow motion However, each views their own time as normalHowever, each views their own time as normal

The Twin TripThe Twin Trip For identical twins, if one were to stay on Earth For identical twins, if one were to stay on Earth

and the other were to take a high speed trip in and the other were to take a high speed trip in space, the one on Earth will be older than the space, the one on Earth will be older than the one on the round trip at high speedone on the round trip at high speed At 50% c, 1 year to traveler = 1.15 years hereAt 50% c, 1 year to traveler = 1.15 years here At 87% c, 1 year to traveler = 2 years hereAt 87% c, 1 year to traveler = 2 years here At 99.5% c, 1 year to traveler = 10 years hereAt 99.5% c, 1 year to traveler = 10 years here

The Twin Trip ExplainedThe Twin Trip Explained

From Doppler Effect, we know that a From Doppler Effect, we know that a moving source or observer creates a moving source or observer creates a difference in the frequency of a sound difference in the frequency of a sound wave (even though speed is constant)wave (even though speed is constant) The same is true for lightThe same is true for light So if a ship emits light every 6 mins, a So if a ship emits light every 6 mins, a

receiver on Earth may only see it every 12 receiver on Earth may only see it every 12 mins if the ship is moving awaymins if the ship is moving away

If the ship is moving towards the Earth, an If the ship is moving towards the Earth, an observer may see it every 3 minsobserver may see it every 3 mins

Explanation Cont’dExplanation Cont’d

So in 60 min on ship, 10 pulses are sent but on So in 60 min on ship, 10 pulses are sent but on Earth it takes 2 hours to get the 10 pulses (10 x Earth it takes 2 hours to get the 10 pulses (10 x 12 = 120 min)12 = 120 min)

On the way back, in 60 min on ship, 10 pulses On the way back, in 60 min on ship, 10 pulses are sent but on Earth it takes only 30 min to get are sent but on Earth it takes only 30 min to get these pulses (10 x 3 = 30 min)these pulses (10 x 3 = 30 min)

The totals: 60 + 60 = 120 min on shipThe totals: 60 + 60 = 120 min on ship 120 + 30 = 150 min on Earth120 + 30 = 150 min on Earth

The Earth twin is 30 minutes older!!!The Earth twin is 30 minutes older!!!

What about if we shift What about if we shift the light source to Earth?the light source to Earth?

The receding ship will receive 5 flashes The receding ship will receive 5 flashes in 60 min of time (60/12 = 5)in 60 min of time (60/12 = 5)

Upon return, the ship will receive 20 Upon return, the ship will receive 20 flashes in 60 min of time (60/3 = 20)flashes in 60 min of time (60/3 = 20)

But on Earth, it would take 150 min to But on Earth, it would take 150 min to emit 25 flashes (25 x 6 = 150)emit 25 flashes (25 x 6 = 150)

The Earth twin is still 30 minutes older!!!The Earth twin is still 30 minutes older!!!

Space and Time TravelSpace and Time Travel

Because time dilates, a space traveler Because time dilates, a space traveler could travel to far distant galaxiescould travel to far distant galaxies While hundreds of years might pass on While hundreds of years might pass on

Earth, the space traveler would only age a Earth, the space traveler would only age a few decades if traveling close to cfew decades if traveling close to c

The closer to c you get, the more time would The closer to c you get, the more time would pass on Earth with little time passing for the pass on Earth with little time passing for the travelertraveler

Length ContractionLength Contraction

As objects move, an outside observer As objects move, an outside observer sees the objects contract in the direction sees the objects contract in the direction of the motionof the motion The contraction is more pronounced the The contraction is more pronounced the

larger the time dilationlarger the time dilation As the speed approaches c, the length gets As the speed approaches c, the length gets

closer to 0 (length cannot get less than 0, so closer to 0 (length cannot get less than 0, so c is speed limit of universe)c is speed limit of universe)

Remember, like time, the object notices no Remember, like time, the object notices no difference in its own length, but sees the difference in its own length, but sees the observer as length contracted to the same observer as length contracted to the same degreedegree

C is the speed limit of the C is the speed limit of the universe!universe!

At c, length becomes 0 ( you can’t get At c, length becomes 0 ( you can’t get less than that)less than that)

As speed approaches c, the impulse As speed approaches c, the impulse required to create the change in required to create the change in momentum necessary approaches momentum necessary approaches infinity (which is impossible)infinity (which is impossible)

As speed approaches c, the energy of As speed approaches c, the energy of the object approaches infinity (which is the object approaches infinity (which is impossible)impossible)

MassMass

Since momentum can increase and Since momentum can increase and speed must stop at c, then mass must speed must stop at c, then mass must “feel” greater at speeds close to c to “feel” greater at speeds close to c to compensatecompensate

Mass is actually just a form of energy (E Mass is actually just a form of energy (E = mc= mc22)) Even small masses have large amounts of Even small masses have large amounts of

energy because c is so largeenergy because c is so large We use this in nuclear reactors and bombsWe use this in nuclear reactors and bombs

Correspondence PrincipleCorrespondence Principle

If Einstein is right, then the new If Einstein is right, then the new equations he created to support his ideas equations he created to support his ideas must correspond to Newton’s laws of must correspond to Newton’s laws of motion at low speeds:motion at low speeds: They all do!!!They all do!!!