Goal: To get to know the ins and outs of relativity (relatively speaking)

1. Goal: To get to know the ins and outs of relativity (relatively speaking) Objectives: To understand how Black holes compare to space-time To learn about General Relativity To learn about Special Relativity

2. Black Hole • A black hole is an object that is either so massive or so dense that the escape velocity on its surface is greater than the speed of light. • As Einstein discovered nothing can travel faster than the speed of light. • Therefore NOTHING, not even light can escape from a black hole!

3. No escape! • The radius at which the escape velocity is exactly the speed of light is called the Schwarzschild radius. • The Schwarzschild radius is an event horizon. • An event horizon is a surface where if something were to pass through it, it is gone (event horizon = goodbye forever).

4. But there’s more! • Mass warps space. Time is relative to space. Therefore masses warp time also! • Tobject = Tuniversal * (1 – rs / r)1/2 • Where rs is the Schwarzschild radius (the radius of the event horizon of a black hole) • rs = 1.5 km * Mass of object / Mass of our sun

5. Black hole astrophysics • What would happen if we swapped our sun for a black hole of exact equal mass? • A) The earth would be sucked into the black hole • B) Time on the earth would slow down • C) The earth would be slingshot out of the solar system • D) Nothing would happen to the orbit of the earth or the clocks on earth.

6. Black hole astrophysics • What would happen if we swapped our sun for a black hole of exact equal mass? • D) Nothing would happen to the orbit of the earth or the clocks on earth. • Black holes are not vacuum cleaners. They obey gravity just like everything else. • In fact it is harder to run into a black hole because it is so frikkn small (diameter of 3 km for one the mass of out sun).

7. Journey into a black hole • Is it possible or advisable? • The answer to the first is NO • Time stops for you before you can make it into the black hole • So, the black hole has to come to you. • Is it advisable, talk about that during black hole lecture 

8. Is that all? • Nope (but that is all for black holes for now, sorry). • Special Relativity • Clocks progress at a rate RELATIVE to their position in space. • Velocity slows the progress of an object’s clock so that: • Tobject = Tuniverse / gamma • Gamma = 1 / (1 – v2/c2)1/2

9. Lorenz contraction • Also, the sizes of moving objects are also RELATIVE to their velocities in space. • Linmotion = Lrest / gamma • Gamma = 1 / (1 – v2/c2)1/2 • So (in the direction they are moving) their length appears to shrink. • However their other dimensions stay the same. • A sphere for example would appear as a saucer…

10. Also • From the perspective of anyone on the ship they are at rest (so ship is normal length). • However, in the direction of “motion” the rest of the universe appears to be the one in motion • Therefore the entire universe shrinks in the one direction and everything in it. • So, the earth would look like a saucer as well.

11. But what happens… • If you are traveling a fraction of the speed of light and something flies by you? • First, a conceptual question, suppose light goes by you when you are traveling 90% of the speed of light. • What velocity does the light appear to be traveling?

12. But what happens… • If you are traveling a fraction of the speed of light and something flies by you? • First, a conceptual question, suppose light goes by you when you are traveling 90% of the speed of light. • What velocity does the light appear to be traveling? • - the speed of light! Light always appears to go the speed of light in a vacuum! • This is why lengths contract and time slows down. • If earth was watching though, they would see light move past you at 0.1 c faster than you…

13. Some other famous stuff • You have probably heard that E = mc2 • Too bad it is not completely correct… • This is only the rest energy of matter. • Yes, this means that matter is a form of energy!

14. However • The total energy is E = Gamma mc2 • And the kinetic energy is: • KE = (Gamma – 1) mc2 • And momentum is: • p = gamma * mv • So, most of relativity is multiplying or dividing by gamma!

15. That is all cool, but • Why is it important? • Space travel! • We can go long distances – and in the lifetime of the astronauts. • A 1000 light year trip at a gamma of 1000 would only take 1 year!

16. But what is the catch? • The catch is 1000 years passes by for the universe and for the Earth.

17. How do we know relativity is real? • 1) Particles created in the upper atmosphere make it to the surface even though their lifetimes are much shorter than the time it takes them to get to the Earth • The time dilation allows them to live longer in our time frame as their half lives are for their time frame

18. 2) Mercury • By the early 20th century it was known that Mercury seemed to lag 37 arcseconds behind in its orbit per century from what the Kepler model predicted. • The faster orbit and being closer to the sun make its clock run a little slower • Relativity was the cause of this

19. 3) Satellites • Since they are further out of Earth’s gravity well their clocks run a tiny bit slower • So, their clocks have to be adjusted by about a millisecond per year. • All as predicted by relativity.

20. Conclusion • Relativity is strange but cool, and not as much math as you might think. • You basically just have to know how to find gamma, and apply that to everything.