Here are some notes from Nov 18 and 20.
Other notes covering the material from those dates can be found
 just below this link on the page on level up from this one.

Note: You're not responsible for Section 8 of Chapter 9 in Wheeler,
except to know the difference between the 2 types of stellar-mass
black holes.

Principle of Equivalence:

Here's another way to describe the Principle of Equivalence, again
quoted from Abell's book: "For example, suppose a brave boy and girl
simultaneously jump into a bottomless chasm from opposite sides of its
banks. If we ignore air friction, while they fall they accelerate
downward together and feel no external force acting on them. They can
throw a ball back and forth between them, aiming always in a straight
line, as if there were no gravitation, and the ball, falling along
with them, would move directly to its target... Because our freely
falling boy, girl, and ball are all falling together, we could enclose
them in a large box falling with them. Inside that box, no one can be
aware of any gravitational force; nothing falls to the ground, or
anywhere else, but moves in a straight line in the most simple natural
way, obeying Newton's Laws. By having our box fall with the boy and
girl, we have removed the force of gravitation by selecting a
coordinate system that is accelerating at just the right rate to
compensate for gravitation. HERE IS THE PRINCIPLE OF EQUIVALENCE- A
FORCE OF GRAVITATION IS EQUIVALENT TO AN ACCELERATION OF THE
COORDINATE SYSTEM OF THE OBSERVER, and such a force can be completely
compensated for by an appropriate choice of an accelerated coordinate
system. Einstein himself pointed out how a rapidly descending elevator
seems to reduce our weight and a rapidly ascending one increases it.
In a FREELY FALLING elevator, with no air friction, we would lose our
weight altogether... Thus the [space station] provides an excellent
example of the principle of equivalence- how local effects of
gravitation can be removed by a suitable acceleration of the
coordinate system. To the astronauts it was as if they were far off in
space, remote from all gravitating objects [but they weren't, they
were close to the earth, and falling towards the earth in an orbit].
But what if astronauts WERE in remote space, and were to activate the
engines of their ship, producing acceleration. The ship would then
push up against their feet, giving the impression of a gravitational tug. If
one were to drop a small coin and a hammer, the floor of the ship would move up
to meet both objects at the same time; to the astronauts, though,
it would seem that the hammer and coin fell to the ground together...
In other words, an acceleration of one's local environment produces
exactly the same effect as a gravitational attraction; the two are
indistinguishable- again, the principle of equivalence."

So the really important part of this thought experiment (which CAN be verified
experimentally) is that IF the principle of equivalence is correct,
then you can't set up an experiment with light to tell if you're
accelerating or not. So LIGHT MUST BE BENT IN A GRAVITATIONAL FIELD.
Gravity bends light.

The fact that gravity bends (and redshifts) light has been apmply
experimentally verified. We have the apparent new position of stars seen
in an eclipse, we have the change of communication time from distant
spacecraft as the signal passes close to the Sun, we have lensing of
distant objects by nearer objects (most impressive in clusters of
galaxies). Look at the figures on the figures page!

There are also experiments that can be done in labs here on earth,
even though Earth's gravity is PUNY. There is a way to make gamma rays
of exacting wavelength. You can fire a "gamma ray gun" up from the
basement to the top of a building and see that the wavelength of the
gamma rays has changed (gotten redshifted). You can send atomic clocks
on plane flights and see that the clocks left behind on earth move
slower than the clocks in the airplane (clocks run slower in stronger
gravity). You can send masers on rocket flights.

We have also measured the GRAVITAIONAL REDSHIFT of white dwarfs in
binary systems. Imagine a binary system at rest with respect to us
(the center of mass is at rest). The individual objects orbit
the center of mass, but over one orbit their velocities average
to ZERO (half the time they're coming towards us, half the time
they're moving away). Well, that works for stars, but for white dwarfs,
the average velocity is about 40 kilometers per second, which
is the gravitational redshift of the white dwarf. This measurement
was first made in the 1950s.

The BINARY PULSAR is a great source of tests of General Relativity.
So far, General Relativity, and the "weird" effects it predicts,
are exactly as Nature chooses to behave.

Another aspect of relativity is that THERE IS NO PREFERRED REFERENCE FRAME.
Humans, used to small objects like Earth, with small gravities, think
of simultaneity as something built into the Universe. But that's only
because the Earth is so small that the speed of light is EFFECTIVELY 
infinite. Look at the figure with the trains to understand that
one person's view of which event happened first is just as valid
as the other person's view. All that matters is when you receive the
information (the signal). 

So warped space is Einstein's changing view of Newton's "action at a
distance" or force. the sun isn't pulling on the Earth. The Earth is
just taking the shortest path in a curved space, and this path happens
to be a closed path.

Now, for Black Holes... At some point near a black hole, space is so curved
that nothing, not even light, can climb out of that curved space.

See the "notes from 2 years ago" for more writeups and more information on
things we've talked about.

Finally, FLICKERING. How quickly an object can change its brightness
depends on its size. Another way of thinking about that is that the
different parts of the "star" need to talk to each other.  The thought
experiment that we did in class is that someone in the front row blows
a horn. When you, in whatever row you're in, hear the horn, you blow
your horn. Clearly, if the speed of sound were infinite, you'd all
blow your horns at the same time, and the sound would go from none to
loud instantly. But if the speed of sound is finite, it takes a finite
amount of time for the back row to know that someone is blowing a
horn, so the sound level rises more slowly. And, the bigger the room,
the longer it takes for the front to communicate with the back.

So, small objects can change their brightness more quickly than big objects.
This is part of the reason that people knew that pulsars cannot
be white dwarfs!

So, what we'll say next class is that the inner part of the accretion
disk around a black hole flickers much more quickly than the inner
edge of the accretion disk around a neutron star or a white dwarf.
DO WE SEE THIS FLICKERING OBSERVATIONALLY?