1. Exam 3 average: 65%. You will have all of class time on Thursday to do the group review. The response “Exams” will be on Learning Suite by Wed noon. They will be due Sat at noon. I will post your new scores by Sat night. The exams are in the boxes. With the group review the average will be raised to 80%. HW 26 (last one) will be up later today. It will be due Fri 11 pm.

2. General Relativity includes gravitation, acceleration
Einstein’s equivalence principle (postulate) The physics is exactly the same in a reference frame accelerating at g, or in a (nonaccelerating ) frame in a gravitational field g, pointing opposite.

3. Light in an accelerated reference frame
Light looks like it’s curved away from the acceleration vector, because the elevator speeds up

4. Light in a gravitational field
Let’s try Einstein’s equivalence principle!
So light is a gravitational field is curved toward the gravitational field vector.

5. Einstein predicted starlight would bend around our sun
Confirmed during solar eclipse in 1919!

6. Gravity as distorting space-time

7. Today called “gravitational lensing”
In the formation known as Einstein's Cross, four images of the same distant quasar appear around a foreground galaxy.

9. Same galaxy seen at six angles in the sky…light bent by other massive galaxies! 5 billion light years away

10. Acceleration and time Up-time increases.
If people in the elevator use light bouncing from the top and bottom in the accelerating elevator to build a photon clock, how does that clock run to an unaccelerated outside observer?
Up-time increases.
Down-time decreases, but not by as much! (because it’s always going faster)
So time goes slower compared to all unaccelerated (or less accelerated ) observers!!!

11. Acceleration and time: another view
The path light takes is longer for the curved path, but the speed of light is the same for all observers.
So time goes slower compared to all unaccelerated (or less accelerated) observers!

12. Gravity and time
By the equivalence principle, time in a gravitational field goes slower compared to observers in a weaker field.
Disclaimer: this equation is not quite right, but enough to be useful
M is the planet/star mass
r the distance from its center

13. We have clocks good enough see the difference
We have clocks good enough see the difference! And GPS is built for the difference.

14. Acceleration and light frequency
Mary (at the bottom), sends a light signal to Joe, who is at the top of the upward accelerating elevator.
P1. Joe sees a _____ frequency than Mary
higher
lower
Hint: Doppler: what is Joe’s motion compared to the motion of the source of the light when it was emitted?

15. Gravity and light frequency
“Fast” electron motion on the star (generating blue light frequency) is seen as “slower” away from the star (generating red-shifted light frequency) Light sent out of stronger gravity must “redshift”, and when going in must “blueshift”

16. Light frequency and photon energy
Light can’t be slower than c, but it does pick up energy as photon frequency increases going into a strong gravitational field. It loses energy going out.

17. Black holes
Events on the star’s surface (at R) appear to us (far away) to happen slower:
Suppose the star cools and gets smaller….what happens to that time factor?
If it collapses enough, and a black hole is born!
Classical analogy: occurs when the “escape velocity” equals the speed of light

18. Black hole artist's (mis)conception
The “event horizon” is at R given by The space inside is inscrutable, and disconnected from time as we know it: nothing can get out.
artist's (mis)conception

19. But the space around a black hole can be bright!

20. But the space around a black hole can be bright!
artist's conception

21. But the space around a black hole can be bright!

22. Black holes may slowly evaporate
Can turn their gravitational PE into photon and particle energy by creating particle- antiparticle pairs! One goes in, one escapes.

23. Black hole at the center of our galaxy
Observations over 5 years of stars near the center.
Our black hole has around a billion solar masses

24. History of the universe: Big Bang

25. History of the universe
Matter as we “know” it: No protons and neutrons before 100 sec. Atoms form after millions of years

26. Surprise! The universe is expanding and accelerating…how?
We don’t know what form most of the matter/energy is!

27. Plenty of room for faith
Universe is exquisitely balanced for life
Strength of strong force (determines fusion)
if 0.1% weaker: He is largest nucleus
if 0.1% stronger: no H left for stars today
Just Six Numbers. See Discover, Nov 2000
Strong vs gravitation force
if smaller, universe would be small, short-lived
Density of universe
too strong, universe collapses; too weak, no stars
Density fluctuations in universe
if smaller, no stars; if large, mostly black holes
Number of dimensions
if 2 or 4, no life
Balance of E/M, gravity, and weak force
Very narrow range allows for supernovae and panets

28. Secular vs Religious view
There might be infinite number of universes with random variations
We happen to be in one that happens to support life
God created a universe that can support life
Existence has a purpose
Neither view can be tested by science
We are left with a choice between two faiths, one secular, one religious