STOR vs GTOR

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STOR vs GTOR

• Special Theory looked at only inertial frames.
  General theory looks at accelerated frames of
  reference
• Einstein added this 10yrs after special theory to
  deal with gravity, mass, and acceleration and how
  it applies to spacetime.

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Gravity vs Acceleration
Imagine yourself in a spaceship on a launch pad
on EARTH holding 2 bricks above the floor.
If the bricks are dropped at the same time from
identical heights, both bricks accelerate towards
floor equally.
Now, imagine identical situation in space, FAR
from any effects of gravity, what is the result
of dropping bricks?
Repeat experiment, but now accelerate ship in the
direction of ceilinghow does result change from
previous scenario?
LAUNCH PAD
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Gravity vs Acceleration
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Equivalence Principle
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GRAVITY TIME
Consider a high speed rotating platform with
three clocks positioned as shown. Clocks 2 3
are rotating and clock 1 is at rest on ground.
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3
1
GROUND
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2
3
1
GROUND
What will clock 1 say about the movement of clock
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What will clock 1 say about the movement of clock
3?
What will clock 1 say about the TIME of clock 2?
What will clock 1 say about the TIME of clock 3?
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3
2
1
GROUND
What will clock 2 say about time of clock 1?
Therefore, what MUST clock 2 say about time of
clock 3?
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Gravitational Time Dilation
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This was first measured by Pound and Rebka at
Harvard in 1960 in the physics building which was
74 feet high. They compared times between the
basement and the top floor.
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GPS again
Recall that atomic clocks on GPS satellites are
affected by their high speed above the earth
(STOR).
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Twin Paradox revisited
We showed that Twin who took space journey
Space twin experienced acceleration,
therefore could not make claims as to earth twin
being younger since space twin was not in
inertial frame
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Gravity and Light
But what if ship accelerates towards ceiling?
Imagine 2 people freely floating in space far
from gravitational effects. One person is
outside the ship and the other is inside.
If light is shone through a window, it is seen by
observer inside the ship to be a straight line,
entering and striking the opposite side and the
same height it entered.
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How come we dont notice light falling/bending
like a cannonball shot from cannon?
Recall how far objects will fall in 1second here
on Earth. y ½ gt2y 4.9m
In one second, how far will light fall?
How far will it travel horizontally in 1 second?
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We are able to see star at times when sun is not
in front of it, so we know its true position.
When Sun is blocking star, we can see the
apparent position of star during an eclipse.
This apparent position is due to how our brains
perceive light, illusions. Need eclipse to see
apparent position.
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Einstein predicts the bending of star light!
Need solar eclipse to prove this.
May 29, 1919, British scientists confirm
Einsteins prediction during solar eclipse. He
becomes an instant celebrity.
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If light is bent due to gravity, then consider 2
rays of light on a wavefront as it passes by a
massive object. A and B are in phase (moving
together) comprise the front.
Large mass
The ray at A moves to C and B moves to D. If CD
is to remain in phase (they are if they are from
the same wave), then time must be affected in
order for them to stay in phase.
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Large mass
AC is a larger distance than BD, but same speed.
Therefore AC time must be different than BD time
according to outside RF. Bending of light proves
time dilation.
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Black Hole
If a large enough star exhausts its nuclear fuel
(where then gravity takes over), the star will
collapse into a single point of infinite density
(Singularity).
Now that the star has a new radius, you must
recalculate its new gravity (smaller radius, same
mass larger gravity). This applies inside
original radius, but not outside.
Since the speed of light is the greatest launch
speed, that then determines how close you can get
to black hole and still turn around. This
distance is called the Event Horizon. The
gravitational field is so strong that even light
isnt fast enough to escape.
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The warp in spacetime is so immense that not even
light can escape! If light cannot escape,
neither can anything else. Everything is dragged
back by the gravitational field A BLACK HOLE.
Black because we cant see it directly. Once
inside the event horizon, no information can get
out.
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Schwarzschild Radius
The distance from the center of a massive object
to the Event Horizon is defined as
Every mass has RS, but physical meaning only
applies if the radius is outside the mass itself.
For example, for the earth to become a black
hole based on the formula above, it would have to
collapse to less than 1.8cm in diameter to become
a black hole.
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Approaching a black hole
First, as astronaut approaches the black hole the
difference in the gravitational pull on head
compared to (tidal forces) would rip you apart.
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Earth RF would never see astronaut cross the
event horizon. WHY?
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Einstein redefines Gravity
Einstein rejects 250yrs of Newtonian gravity.
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Gravity Space

• Re-interpret gravity as geometry
• Space and space-time are not rigid arenas in
  which events take place. They are influenced by
  the matter and energy content of the universe.

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Simply stated for a planet orbiting a star
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How light bends or is attracted by gravity
Photons are affected by gravitational fields not
because photons have mass, but because
gravitational fields change the shape of
space-time.
Light has zero rest mass, and anything with zero
rest mass always has to go at the speed of light
along light-like trajectories in spacetime. To be
anthropomorphic (human-like) about it, a photon
doesn't experience the passage of time. To it, it
is everywhere at once.
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EXPERIMENTAL TESTS OF GENERAL RELATIVITY

• GRAVITATIONAL LENSING
• PRECESSION OF MERCURY
• GRAVITATIONAL REDSHIFT
• GRAVITATIONAL WAVES

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Gravitational Lensing
This was the 1st test to prove Einstein correct
with the eclipse of the sun.
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This can lead to multiple images and even rings
if the geometry of the situation is just right.
Example A planet with a mass lower than that of
Neptune has been detected as its gravity bent the
light from a remote star. This lensing technique
adds to our arsenal for spotting small planets
outside the Solar System.
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The famous "Einstein Cross" is a case where a
single object is seen four times.
In this image, a single object appears as four
objects. A very distant quasar is thought to be
positioned behind a massive galaxy. The
gravitational effect of the galaxy has created
multiple images through gravitational lensing on
the light from the quasar.
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2 Precession of Orbit of Mercury
A long-standing problem in the study of the Solar
System was that the orbit of Mercury did not
behave as required by Newton's equations.
The orbits of the planets are slight ellipses as
we already know. The elliptical orbits themselves
move.
This motion is called precession. This is caused
by the pull of other planets and predicted by
Newton's laws. The predicted precession of the
planets all agreed with observation.
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At one time, the scientific community had
proposed there was an undiscovered planet called
Vulcan that was causing this peculiar effect.
EINSTEIN to the rescue!!
Einstein used his GR equations to prove that the
orbit of Mercury should precess by an extra 43
seconds of arc per century.
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3 Gravitational Redshift
According to General Relativity, the wavelength
of light passing through a gravitational field
will be shifted towards redder regions of the
spectrum.
Einstein's says that as a photon fights its way
out of a gravitational field or well, it loses
energy. It has to since PE is increasing yet
speed MUST stay c.
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As previously mentioned, in 1960, this was
demonstrated that a beam of very high energy
gamma rays was ever so slightly redshifted as it
climbed out of Earth's gravity and up an elevator
shaft in the Jefferson Tower physics building at
Harvard University. The redshift predicted by
Einstein's Field Equations for the 74 ft. tall
tower was but two parts in a thousand trillion.
The gravitational redshift detected came within
ten percent of the computed value. Also, a team
at Princeton University measured the redshift of
sunlight. Though small, given the Sun's mass and
density, the redshift matched Einstein's
prediction.
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4 Gravitational Waves
Recall the cosmic catastrophe we already viewed
where if the sun were to disappear, the earth
could no be released until the gravity wave
reached us. Einstein predicted that gravity
waves must exist.
The first binary pulsar (rotating neutron star),
i.e., a pulsar orbiting another star, was
discovered by Joseph Taylor and Russell Hulse in
1974. The discovery earned Hulse and Taylor the
Nobel Prize in Physics because the object is so
exotic and so well suited to testing modern
theories of gravitation such as Einstein's
General Theory of Relativity.
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In this system discovered in 1974, it was
observed that the two stars' orbits are shrinking
at a rate of 1 cm/day. This shrinkage is caused
by the loss of orbital energy due to
gravitational radiation, which is a travelling
ripple in spacetime that is predicted by
Einstein's General Relativity Theory but never
previously verified. Observations show that the
pulsar orbit is shrinking at exactly the rate
that general relativity predicts it should, if
gravity waves exist and are carrying away the
expected amount of energy.
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• This is the Einstein Gravitational Field
  Equation. This equation states that the spacetime
  curvature of anyplace in the universe (left-hand
  side of the equation) must be equal to the
  distribution of matter and energy in that part of
  the universe (right-hand side of the equation).
  It is this equation that was 50 years ahead of
  its time when Einstein proposed it.

Each subscript refers to each dimension of
spacetimeso what looks like 1 equation is
actually 16 eqns! (4x4)