Download Special Theory of Relativity

General Theory of Relativity
(Part 2)
STOR vs GTOR
• Recall 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.
I. 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?
LAUNCH PAD
Gravity vs Acceleration
II. Equivalence Principle
III. 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.
IV. Does Light Bend due to gravity?
Imagine 2 people freely
floating in space far from
gravitational effects. One
person is outside the ship
and the other is inside.
ENGINE
If spaceship accelerates past person on outside
of ship, what is observed according to outside
and inside RF?
How come we don’t notice light falling/bending
like a cannonball shot from cannon?
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.
We are able to see
stars at times when
sun is not in front of it,
so we know where it
REALLY is.
When Sun is blocking
star, we can see the
apparent position of
star during an eclipse.
This is due to how our
brains perceive light &
illusions. Need eclipse
to see apparent position.
Einstein predicted the angle between the true and
apparent position during an eclipse as seen from
Earth. His prediction was exactly correct.
Bending of star light
• Light actually follows the curve
in space created by massive
objects like the Sun.
How light ‘bends’ or is attracted by ‘gravity’
• Photons are affected by gravitational fields not
because photons have mass, but
V. 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.
2
3
1
GROUND
3
2
1
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?
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?
2
3
1
Clock 1 states that 3 is slow due to ?
Clock 2 says that 3 is slow due to ?
Gravitational Time Dilation
The effect is so small that it would add
just 90 billionths of a second to a 79
It's taken a century but scientists have year life span. The extraordinary
finally prove that Albert Einstein was
experiment - published today in the
right - time really does past more quickly respected journal Science if you stand on a step ladder. In a bizarre demonstrates one of the strangest
experiment using the most accurate
consequences of Einstein's theories of
atomic clocks ever invented,
relativity. In 1907 his General Theory of
researchers showed that clocks run Relativity showed that clocks run more
faster if they are raised by just 12
quickly at higher altitudes because
inches. However, anyone hoping that a they experience a weaker gravitational
lifetime living in a basement is the secret force than clocks on the surface of the
to longevity will be disappointed.
Earth.
GPS again…
• Recall that the clocks on GPS satellites are
affected by their high speed above the earth…
•GPS satellites are 20,000km above the earth
VI. 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
itself. The distance is less than the original star radius.
Entering a black hole
• First, as you approach the black hole the difference in
the gravitational pull on your head compared to your
feet (known as tidal forces) would rip you apart
(spaghettification)
• If people from Earth were watching your journey into a
black hole they would never see you cross the event
horizon. As you approach a black hole your time slows
down (stronger gravity) and light is redshifted.
• The closer you get to the black hole the more you
appear to be in slow motion as seen by Earth.
Eventually you appear to be frozen in time as you cross
the event horizon. You would notice nothing different
whatsoever. We would not see the person cross it.
• Person moving towards event horizon would see
events on earth as occurring at an extremely fast
pace…not the same as STOR where you can turn it
around. GTOR is different RF’s with different
accelerations, not necessarily the same.
Einstein unseats Newton’s gravity
• The instantaneous gravitational force proposed
by Newton is replaced by the curvature of
spacetime. There is NO gravitational force.
• Moving a mass causes ripples to form in this
curvature, and these ripples travel with the
same speed as light….meaning if the sun
were to disappear, it would take 8 minutes
for that ripple to reach us. These are called
gravitational waves
Simply stated:
Mass 1 tells space-time how to curve.
Curved space-time tells Mass 2 how to
move.