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.
How is it possible to move along with
something that doesn’t exist?
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).
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.
THUS, THE LIGHT WAVE WOULD CEASE TO EXIST!!!!
A young physicist named Albert Einstein says:
YOU CAN’T.
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.]
2) It’s not logical.
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 Simultaneity
The ordering of events in time is relative to the
observer’s frame of reference,
assuming two conditions are met:
1) the events do not occur at the same location in
space
2) the events are not related by cause-and-effect
1.0 x 108 m
3.0 x 108 m
B
(A)
1.0 x 108 m/s
A
3.0 x 108 m
(B)
Time Dilation
• Moving clocks run slow
• The amount of “slowing” depends upon the clock’s
speed:
t
to
1 v
2
c
2
to is the proper time – the time measured by the clock
that observes the event to be at rest.
t is the coordinate time – the time measured by the
clock that observes the event to be moving.
Time Dilation
t
to
1 v
2
c
2
Since the event is moving, this clock is the “moving” clock
to is the proper time – the time measured by the clock
that observes the event to be at rest.
t is the coordinate time – the time measured by the
clock
thatisobserves
the
event to be moving.
This clock
the “at rest”
clock
Time Dilation
The 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.
(t o )
Time Dilation
to
t
1 v
2
c
2
to is the proper time – the time measured by the clock
that observes the event to be at rest.
Since the event is moving, this clock is the “moving” clock
t is the coordinate time – the time measured by the
clock that observes the event to be moving.
This clock is the “at rest” clock
Time Dilation
Light Clock Demo
Time Dilation
Since ‘Time’ is just a quantity we measure with a clock…
TIME runs slower in moving reference
frames!
So, creatures who are moving age less than the
observers who see them moving.
Time Dilation
What about the
TWIN PARADOX ?
1.0 x 108 m
3.0 x 108 m
B
(A)
1.0 x 108 m/s
A
3.0 x 108 m
(B)
Length Contraction
• Moving objects are shortened along the line of
motion.
L  Lo 1  v
2
c
2
Lo is the proper length – the “length” of the object when
it is at rest.
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 Contraction
The constructed dimensions of the Starship
Enterprise are as follows:
length: 288.6 m
width: 127.1 m
height: 72.6 m
length
The starship travels by the earth at 0.75c.
What would you measure the dimensions of
the starship to be?
Length Contraction
Fixes the TWIN PARADOX.
In the ‘astronaut’ twin’s F-O-R, the space between
the ship and the destination is SHORTENED
considerably.
The ‘astronaut’ twin would measure a shorter
time for the trip than the ‘Earth’ twin does due to
this contracted space.
Therefore, the ‘traveling’ twin would be the younger
one when they meet.
Length Contraction
This leads us to the
BARN PARADOX.
The “Fighting Twins” Paradox
Brad 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” Paradox
BRAD 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.
m
mo
1 v
2
c
2
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.
Mass Increase
When 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?
In order to increase the speed of an object, what
must be done to it?
How much force must be applied to it?
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.
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,
E  mc
E  energy (Joules)
m  mass (kilograms)
2
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)
E  mc
2
E
1,200,000 J
11
m 2
 1.3 x 10 kg
8 m 2
c (3.0 x 10 s )
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 Relativity
Einstein’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 Relativity
Decides 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-ofreference.
No experiment will show the difference
between the two – the results are the same
in either reference frame.
General Theory of Relativity
Thought 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
An object with mass distorts (curves) spacetime.
Gravity is the distortion
caused by the mass.
Light follows that distortion, and we observe it to bend.
Gravitational Lensing
sun
telescope
(Double image of the star is observed, one on either side of the sun.)
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.
Black Hole
An extremely massive object will warp spacetime to the point
that there is no bottom to the distortion.
Any object that moves into the distortion will not be able to
escape – EVEN LIGHT!
Since no light can come out of it, it would appear as a
black hole in space.
Black Hole
The spherical boundary of a black hole – called the
event horizon – represents the “point of no return.”
Any object that moves past that boundary will be unable
to escape.
Notice the gravitational lensing that occurs around the
event horizon.
wormhole
a connecting tunnel between two black holes
[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 TIME
The 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.