Download Unit Review D – General Relativity

Unit Review D – General Relativity
Modern Physics
Mr. Youker |
1. The Principle of Equivalence is the founding principle for Einstein’s General
Theory of Relativity. How would the occupants of the following frames of
reference witness the following scenarios:
a. An occupant of a deep-space probe releases a ball from his hand as he coasts
along at constant velocity.
b. An occupant of a deep-space probe releases a ball from his hand as he
accelerates “upward” in a straight line.
c. An occupant of a free-falling elevator on Earth’s surface releases a ball from
her hand as she falls.
d. An occupant of a rotating room places a ball on the floor and releases it from
her hand.
2. Does light travel in a straight line when it passes by massive objects?
3. Why did Sir Eddington need to mount a pair of expeditions to far-flung places on
the Earth’s surface in order to conduct a test of Einstein’s light-bending effect?
4. What happens to the observed light emitted from a laser when the laser is lifted to
an elevation higher than the observer? What about when it is placed at a lower
elevation? What if the observer then goes down to where the light source is? What
causes these effects?
5. What determines the outcome of any given star’s evolutionary lifetime?
6. What are ‘binary pulsars’ and in what ways do they provide excellent test subjects
for experimental confirmation of General Relativity?
7. Why are black-holes black? State two reasons.
8. If the Sun were to suddenly and instantaneously disappear, what would happen to
the orbit of the Earth? Consider both the Newtonian model of gravity and the
Einstein model.
9. According to Einstein’s General Theory of Relativity is the Earth’s surface larger,
smaller, or equal to 4r2 (where r is the radius of the Earth measured from its
center)? Assume the Earth to be a perfect sphere.
10. Describe what the following experiments were designed to test: Pound-Rebka,
Gravity Probe B, LIGO.
Unit Review D – General Relativity
Modern Physics
Mr. Youker |
1. The Principle of Equivalence is the founding principle for Einstein’s General
Theory of Relativity. How would the occupants of the following frames of
reference witness the following scenarios:
a. An occupant of a deep-space probe releases a ball from his hand as he coasts
along at constant velocity.
At constant velocity (in deep space) is identical to being free of any
gravitational influence. The ball will remain motionless near the person’s
hand (as it continues to inertially move along with the ship).
b. An occupant of a deep-space probe releases a ball from his hand as he
accelerates “upward” in a straight line.
By accelerating “upward” the motion of the ship creates the equivalent of a
gravitational field in a “downward” direction. The released ball will “fall”
downward. (It will continue to move forward at the speed at which it was
released and the ship will accelerate “up” to meet it.)
c. An occupant of a free-falling elevator on Earth’s surface releases a ball from
her hand as she falls.
Motion in free-fall is identical to being free of any gravitational influence. The
ball will remain motionless near the person’s hand (as it falls at the same rate
as the individual).
d. An occupant of a rotating room places a ball on the floor and releases it from
her hand.
By rotating... there is an inward acceleration (centripetal acceleration) which
creates the equivalent of a gravitational field in an “outward” direction. The
released ball will “fall” outward… this will be mistaken for a “centrifugal
force”. (It will continue to move tangentially at the speed at which it was
released eventually meeting up with the wall of the room.
2. Does light travel in a straight line when it passes by massive objects?
Yes and no. Light will follow the shortest path between two events in spacetime.
So if we define a straight line as the shortest path between two points… then yes.
The warping of spacetime by massive objects redefines what is straight. From our
Euclidean perspective, the light will curve and bend due to gravity.
3. Why did Sir Eddington need to mount a pair of expeditions to far-flung places on
the Earth’s surface in order to conduct a test of Einstein’s light-bending effect?
To observe the bending of starlight as it grazed past the surface of the Sun, it was
necessary to take photographic images of the stars during a total solar eclipse.
These do not happen often and occur only over limited geographical regions
during any singular eclipse (once in 375 years for any given location).
4. What happens to the observed light emitted from a laser when the laser is lifted to
an elevation higher than the observer? What about when it is placed at a lower
elevation? What if the observer then goes down to where the light source is? What
causes these effects?
When coming from higher locations, the light’s frequency will be higher (blueshifted) whereas when coming from lower locations, the light’s frequency will be
lower (red-shifted). This is due to gravitational time-dilation. An observer in a
stronger gravitational field will perceive time to be moving more rapidly within
frames of references elevated at higher locations (weaker gravity) whereas an
observer in a weaker gravitational field will perceive time to be moving more
slowly within frames of references depressed at lower locations (stronger gravity).
5. What determines the outcome of any given star’s evolutionary lifetime?
The mass of a star determines its outcome. Depending on the mass, the star’s
collapsed core will either end up as a white dwarf (<1.1 solar masses), a neutron
star/pulsar, or a blackhole (>3 solar masses).
6. What are ‘binary pulsars’ and in what ways do they provide excellent test subjects
for experimental confirmation of General Relativity?
Binary pulsars are rapidly spinning neutron stars that orbit each other in close and
fast proximity. The strong gravity and high speeds affects the rate of pulsing in
easily observable and measurable ways. Both time dilation, orbital precession,
and gravitational radiation are easily tested.
7. Why are black-holes black? State two reasons.
First, no light (or other electromagnetic radiation) can pass outwardly through the
event horizon. Second, any light emitting object moving inward toward the event
horizon will experience infinite time dilation (relative to an outside observer) at
the event horizon and therefore “stop” emitting light.
8. If the Sun were to suddenly and instantaneously disappear, what would happen to
the orbit of the Earth? Consider both the Newtonian model of gravity and the
Einstein model.
According to Newton, gravity operates instantaneously across space. When the
Sun disappeared, the force of gravity would go to zero and the Earth would
immediately start moving in a straight line. On the other hand, special relativity
dictates that no signals can propagate at faster than the speed of light, and indeed,
general relativity predicts that the flattening of spacetime that would occur with
the disappearance of the Sun would move outwardly at the speed of light… taking
eight minutes to reach Earth. We would continue to orbit the “dimple” that would
exist where the Sun used to be for a while.
9. According to Einstein’s General Theory of Relativity is the Earth’s surface larger,
smaller, or equal to 4r2 (where r is the radius of the Earth measured from its
center)? Assume the Earth to be a perfect sphere.
Due to the warping of spacetime, the distance from the surface of the planet to the
core is greater than one would expect in a Eucliden space. So the surface area of
the Earth is smaller than one would get using the relativistic radius of the planet.
10. Describe what the following experiments were designed to test:
Pound-Rebka – gravitational time dilation.
Gravity Probe B – inertial frame dragging and the geodetic effect.
LIGO – gravitational waves or radiation.