I am floating in a river and observe a twenty-ton barge moving down the river at 1.0 ft/s. In 2.0 seconds I have brought the barge to rest without touching it or communicating with the people onboard.

HOW DID I DO IT?

All motion is relative.

Light is a combination of a changing ELECTRIC FIELD creating a changing MAGNETIC FIELD.

If you began moving in the same direction as the light wave, the electric field would not change as quickly (causing the magnetic field wave to diminish).

THUS, THE LIGHT WAVE WOULD CEASE TO EXIST!!!!

So, if you would move along at the same speed as the light wave, the electric field would not change at all…and the magnetic field would disappear.

How is it possible to move along with something that doesn’t exist?

A young physicist named Albert Einstein says:

YOU CAN’T.

2) It’s not logical.

1) If you could make a light wave disappear by moving with it, that would prove that you were moving. [ This would violate Galileo’s idea of relative motion.]

Special Theory of Relativity(1905)

Two main postulates:

1) All physical laws are valid in any inertial frame of reference.

No experiment can determine if you are at rest or moving at a constant velocity.

Special Theory of Relativity(1905)

Two main postulates:

2) The speed of light is the same to all observers, regardless of their reference frames.

Whether you see the light source at rest or moving, the speed of the light moving away from that source is the same. (c = 3.0 x 108 m/s)

3 spaceships in space; middle ship is commander’s ship

Order is given – via a radio (light) signal - by the captain for the front and back ships to fire a single photon torpedo simultaneously to signal a peaceful approach to planet.

What would a person on the planet – who sees the ships moving – observe?

The two torpedo blasts are ORDERED IN TIME! (One occurs after the other.)

The Relativity of SimultaneityThe ordering of events in time is relative to the observer’s frame of reference,

assuming two conditions are met:

2) the events are not related by cause-and-effect

1) the events do not occur at the same location in space

A

B(B)(A)

1.0 x 108 m/s

1.0 x 108 m 3.0 x 108 m

3.0 x 108 m

Time Dilation• Moving clocks run slow

to is the proper time – the time measured by the clock that observes the event to be at rest.

• The amount of “slowing” depends upon the clock’s speed:

22

1c

v

tt o

t is the coordinate time – the time measured by the clock that observes the event to be moving.

Time Dilation

to is the proper time – the time measured by the clock that observes the event to be at rest.

22

1c

v

tt o

t is the coordinate time – the time measured by the clock that observes the event to be moving.

Since the event is moving, this clock is the “moving” clock

This clock is the “at rest” clock

Time DilationThe Starship Enterprise is traveling at 0.50c toward the Andromeda galaxy, and the cook is preparing a turkey. The oven clock records a time of 2.0 hours. What time interval does a Federation scientist’s wristwatch on Earth record for this event?

Which clock observes the event (the cooking turkey) to be at rest?

This clock records the PROPER TIME for the event. )( ot

Time Dilation

to is the proper time – the time measured by the clock that observes the event to be at rest.

22

1c

v

tt o

t is the coordinate time – the time measured by the clock that observes the event to be moving.

Since the event is moving, this clock is the “moving” clock

This clock is the “at rest” clock

Time Dilation

Light Clock Demo

Time Dilation

TIME runs slower in moving reference frames!

Since ‘Time’ is just a quantity we measure with a clock…

So, creatures who are moving age less than the observers who see them moving.

Time Dilation

What about the TWIN PARADOX ?

A

B(B)(A)

1.0 x 108 m/s

1.0 x 108 m 3.0 x 108 m

3.0 x 108 m

Length Contraction• Moving objects are shortened along the line of

motion.

Lo is the proper length – the “length” of the object when it is at rest.

22

1c

vLL o

L is the coordinate length – the length measured when the object is moving.

Only the dimension parallel to the motion is shortened; the others remain unchanged.

Length ContractionThe constructed dimensions of the Starship Enterprise are as follows:

length: 288.6 mwidth: 127.1 mheight: 72.6 m

The starship travels by the earth at 0.75c. What would you measure the dimensions of the starship to be?

length

Length ContractionFixes the TWIN PARADOX.

In the ‘astronaut’ twin’s F-O-R, the space between the ship and the destination is SHORTENED considerably.

Therefore, the ‘traveling’ twin would be the younger one when they meet.

The ‘astronaut’ twin would measure a shorter time for the trip than the ‘Earth’ twin does due to this contracted space.

Length Contraction

This leads us to the BARN PARADOX.

The “Fighting Twins” ParadoxBrad and Adam - identical twins - REALLY mad at each other - want to fight each other

You send them away on trains going in opposite directions at near light speed.

The trains are going to pass close to each other, traveling in opposite directions.

The “Fighting Twins” ParadoxBRAD thinks:

I’m going to punch Adam, and I know he’s going to think the same thing. So our equal-mass fists are going to hit together.

But since he is moving at a really large speed and time on his train is running slow, his fist will move much slower than mine.

My fist will have more momentum than his. When they collide, my fist will shove his fist back into his mouth!

The “Fighting Twins” Paradox

ADAM thinks THE EXACT SAME THING AS BRAD, since he sees Brad moving while he is at rest.

YOU see them both moving at equal speeds. You should see their fists move at the same speed, having equal momentum, and the fists should stop right where they collide!

So, what happens when the fists hit? That’s the paradox.

Mass Increase• The mass of a moving object is greater than its

mass when at rest.

mo is the proper mass – the mass of the object when it is at rest.

m is the coordinate mass – the mass measured when the object is moving.

22

1c

v

mm o

Mass IncreaseWhen construction of the Starship Enterprise was complete, its mass was measured to be 173,000,000 kg.

As it travels by the earth at 0.86c, what would you measure its mass to be?

Mass Increase sets a speed limit in the universe.

What happens to the mass of an object as its speed approaches the speed of light?

Nothing that has mo > 0 can ever move at (or faster than) the speed of light, because its mass approaches infinity as its speed approaches c.

In order to increase the speed of an object, what must be done to it?

How much force must be applied to it?

Where does this added mass come from?It comes from the kinetic energy the object has due to its motion. Energy and mass are really the same thing!

Generally speaking,

2mcE

E energy (Joules)

m mass (kilograms)c speed of light (3 x 108 m/s)

When you consume a Snickers bar, you gain 250,000 calories (1,200,000 J) of energy. By how much has your mass increased due to this influx of chemical energy? (not including mass of Snickers bar itself)

2mcE

2cEm 2

sm 8 )10 0.3(

J 000,200,1x

kg 10 3.1 11 x

General Theory of Relativity

I. Background

• Newton’s theory of gravity describes it as an attractive interaction (force) between two masses.

Acts over long distances instantaneously.

In other words, if the sun would disappear, the effect on the motion of the earth would be immediately felt.

General Theory of RelativityEinstein’s Special Theory of Relativity states that the instantaneous effect is an impossibility, since NOTHING can travel faster than light.

It takes light 8 minutes to get to earth from the sun. If gravity changes were detected everywhere instantly, we would know it disappeared before we saw it disappear.

The information would have traveled faster than the speed of light!

General Theory of RelativityDecides that a new theory of gravity is needed.

Realizes that the effects of acceleration are the same as the effects of a gravitational field.

Observers in an accelerated reference frame experience forces that feel the same as gravitational forces.

Ex: Dropping a ball in an upwardly-accelerating spaceship.

Ex: Riding a spinning amusement park ride.

Ex: Simulating gravity in a rotating spaceship.

General Theory of Relativity

Establishes the Principle of Equivalence:

A gravitational field environment is equivalent to an accelerated frame-of-reference.

No experiment will show the difference between the two – the results are the same in either reference frame.

General Theory of RelativityThought experiment:

A laser is attached to the wall of a spaceship; it will shine a beam straight across to the other side.

General Theory of Relativity

If the ship accelerates upward at a sufficient rate, the beam will hit the other wall lower, due to the ship’s upward motion (and beam’s straight-line path).

‘at rest’ observer

General Theory of Relativity

An astronaut riding in the ship would see the light bend downward, hitting the opposite wall at a spot lower than the position of the laser.

General Theory of Relativity

Because of the Equivalence Principle, the astronaut would not know she is accelerating. She may – correctly – believe she is at rest in a gravitational field.

General Theory of Relativity

She would conclude – correctly – that the light was bent by the gravitational field!

This contradicts Newton’s theory, which said gravity only affects objects with mass. Since light has no mass, gravity should have no effect.

General Theory of Relativity

Einstein decides that gravity can’t be a force…

…Gravity is a geometry.

Gravity is a distortion of spacetime.

4-dimensional “fabric” of the universe(x, y, z, t interwoven together)

Gravity’s Effect on Light

• Light moves through spacetime, following the shape of it.

Where there are no objects, spacetime is undistorted and light travels in a straight line.

Gravity’s Effect on Light

Light follows that distortion, and we observe it to bend.

An object with mass distorts (curves) spacetime.

Gravity is the distortion caused by the mass.

Gravitational Lensing

Extremely massive objects bend light considerably, causing the images of background stars to be shifted or distorted.

Acts the same as an optical convex lens.

(Double image of the star is observed, one on either side of the sun.)

sun telescope

Black Hole

An extremely massive object will warp spacetime to the point that there is no bottom to the distortion.

Since no light can come out of it, it would appear as a black hole in space.

Any object that moves into the distortion will not be able to escape – EVEN LIGHT!

The spherical boundary of a black hole – called the event horizon – represents the “point of no return.”

Black Hole

Any object that moves past that boundary will be unable to escape.

Notice the gravitational lensing that occurs around the event horizon.

a connecting tunnel between two black holes

wormhole

[No experimental evidence of this phenomenon at this time.]

Gravity Waves

Fluctuations (changing disturbances) of spacetime, caused by an accelerating mass.

These disturbances travel through spacetime at the speed of light.

Video

Gravity’s Effect on TIMEThe further one moves into a gravitational field, the slower clocks run; therefore, the slower an object moves through time.

This person is further into the earth’s gravitational distortion; his time runs slower than the orange man’s time.

This is an “absolute” effect. Both people would agree with the time differences.