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General Theory of Relativity
• 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
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
ceiling…how does result change
from previous scenario?
Gravity vs Acceleration
Equivalence Principle
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.
What will clock 1 say about the movement of clock 2
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?
What will clock 2 say about time of clock 1?
Therefore, what MUST clock 2 say about time of
clock 3?
Gravitational Time Dilation
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.
GPS again…
Recall that atomic clocks on GPS satellites are
affected by their high speed above the earth
Twin Paradox revisited
We showed that Twin who took space journey:
1)Was younger by using flashes of light
2)Space twin experienced acceleration, therefore
could not make claims as to earth twin being
younger since space twin was not in inertial
But what if ship
Imagine 2 people freely
floating in space far from towards
gravitational effects. One ceiling?
Gravity and Light
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.
How come we don’t notice light falling/bending
like a cannonball shot from cannon?
Recall how far objects
will fall in 1second
here on Earth.
|y|= ½ gt2…y = 4.9m
In one second, how far will light fall?
How far will it travel horizontally in 1 second?
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.
Einstein predicts the bending of star light!
Need solar eclipse to prove this.
May 29, 1919, British scientists
confirm Einstein’s prediction during
solar eclipse. He becomes an
instant celebrity.
Revisit gravitational time dilation: Consider
2 rays of light on a wavefront which are
bent as they pass near a massive object.
A and B are in phase (moving together).
Large mass
Black Hole
If a large enough star collapses due to its nuclear fuel
being spent and gravity taking over, there will be a
critical distance (Event Horizon) from the collapsed star
where the gravitational field is so strong that the path of
the light is bent so severely that it returns to the star
Approaching a black hole
First, as you approach the black hole
Earth RF would never see you cross the event
horizon. WHY?
Einstein redefines Gravity
Einstein rejects 250yrs of Newtonian gravity.
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.
1) Mass & energy
2) Curved space
Orbit of Mercury, 1st test of GR
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.
As it orbits the Sun, it follows an ellipse.
However, it is found that the point of
closest approach of Mercury to the sun
does not always occur at the same place,
rather it slowly moves around the sun.
This rotation of the orbit is called a
The precession of the orbit is not
peculiar to Mercury, all the planetary
orbits precess. In fact, Newton's theory
predicts these effects, as being produced
by the pull of the planets on one
However, this discrepancy cannot be accounted
for using Newton's laws. At one time, they
proposed there was an undiscovered planet called
Vulcan that was causing this.
In contrast, Einstein was able to predict, without
any adjustments whatsoever, that the orbit of
Mercury should precess by an extra 43 seconds of
arc per century. This is due to the fact that
spacetime is more affected that close to the sun
versus the other planets, it is a very tiny
Simply stated:
Why star light BENDS
• Light actually follows the curve
in space created by massive
objects like the Sun. More to
How light ‘bends’ or is attracted by ‘gravity’
• Photons are affected by gravitational fields not
because photons have mass,
• The photons are
Gravitational Lensing
When light travels curved paths around
massive objects, we call this
Gravitational Lensing.
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.
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.
warp of spacetime again 2:30
• The Einstein Gravitational Field Equation is shown
below. 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 (righthand 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
spacetime…so what looks like 1 equation is actually
16 eqns! (4x4)