General Theory of Relativity (Part 2)

1. General Theory of Relativity(Part 2)

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.

3. 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

4. Gravity vs Acceleration

6. II. Equivalence Principle

7. III. Einstein redefines Gravity Einstein rejects 250yrs of Newtonian gravity.

8. 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.

9. 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

10. If spaceship accelerates past person on outside of ship, what is observed according to outside and inside RF?

11. How come we don’t notice light falling/bending like a cannonball shot from cannon?

12. 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.

13. 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.

14. Bending of star light • Light actually follows the curve in space created by massive objects like the Sun.

15. How light ‘bends’ or is attracted by ‘gravity’ • Photons are affected by gravitational fields not because photons have mass, but

16. 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

17. 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?

18. 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?

19. 3 2 1 Clock 1 states that 3 is slow due to ? Clock 2 says that 3 is slow due to ?

20. Gravitational Time Dilation

21. The effect is so small that it would add just 90 billionths of a second to a 79 year life span. The extraordinary experiment - published today in the respected journal Science - demonstrates one of the strangest consequences of Einstein's theories of relativity. In 1907 his General Theory of Relativity showed that clocks run more quickly at higher altitudes because they experience a weaker gravitational force than clocks on the surface of the Earth. It's taken a century but scientists have finally prove that Albert Einstein was right - time really does past more quickly if you stand on a step ladder. In a bizarre experiment using the most accurate atomic clocks ever invented, researchers showed that clocks run faster if they are raised by just 12 inches. However, anyone hoping that a lifetime living in a basement is the secret to longevity will be disappointed.

22. 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

23. 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.

25. 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.

26. 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

27. Simply stated: Mass 1 tells space-time how to curve. Curved space-time tells Mass 2 how to move.