1. Visual Guide to Special and General Relativity

2. This is about to get weird…

3.  Michelson-Morley contradicted Newton  Radioactivity (the energy released didn’t match up with the energy of the atoms)  Emission spectra of blackbodies  Atomic Emission Spectra

5.  There is no ether  Speed of light defies Newton’s predictions

12.  Applies to accelerated reference frames  The Principle of Equivalence All experiments conducted in a gravitational field and in an accelerated reference frame give identical results  This means that if you dropped a ball in an elevator, you would have no way of knowing if you were in a gravitational field or being accelerated through space

13.  Black Holes  Gravitational lensing  New perception of gravity  An idea well before its time!

14.  Equivalence of Physical Laws The laws of Physics are the same in all inertial frames of reference (An inertial reference frame is a reference frame with no acceleration)  Constancy of the speed of light The speed of light in a vacuum is the same in all reference frames, independent of the motion of the observer

15.  Specific Example: An object at rest with no forces acting on it will have zero acceleration in all reference frames

16.  All observers in all reference frames agree that light waves move at 3.00 x 10 8 m/s regardless of their own motion.  Example  If spaceship A, traveling close to the speed of light) flies past a stationary astronaut and fires a laser beam straight ahead as it passes, how fast will the laser beam travel according to the spaceship pilot? The astronaut?

17.  Nothing can move faster than light.  All observers in all reference frames agree.  In order for this to be true, Einstein posed that both time and space are relative!!

18.  As objects approach the speed of light, relativistic time dilation becomes significant.  Consider a plane flying very fast at a very high altitude.

19.  Time is not the same for all observers.  The faster an object moves, the slower time gets for that object (relative to a stationary observer)  An observer on the moving object, perceives time to move normally for him or herself

20.  It would travel back in time!!!  Tachyons are particles that do just that… We don’t know much about them

21. Time in inertial reference frame Velocity of the moving object Speed of light Time in moving reference frame (1 – v 2 /c 2 ) -1/2 can be written as γ (gamma) This is called the Lorentz Transformation

22. A space ship carrying a light clock moves with a speed of 0.500c relative to an observer on Earth. According to this observer, how long does it take for the spaceship’s clock to advance 1.00 s? Solution: Insert ∆t = 1.00 s and v = 0.500c into the equation and get:

23. Elephants have a gestation period of 21 months. Suppose that a freshly impregnated elephant is placed on a spaceship and sent toward a distant space jungle at v = 0.75c. How long will scientists on the distant planet have to wait until the spaceship lands exactly 21 months later? Solution: 31.7 months

24. Omar and Maurice are identical twins. Omar gets on a spaceship and travels at a high speed to a star far outside our solar system and returns to Earth while his twin brother Maurice remains at home. When they greet each other, Maurice will be very much older than Omar. How can this be?

25. Example: If Omar and Maurice are both 17.0 years old when Omar leaves on his space journey, and he travels at 0.990c to Vega (a star 26.4 ly distant), a) How long does the trip take from Maurice’s point of view?

26. Example problem: b) How much has Omar aged when he reaches Vega? **When Omar Reaches Vega, he is 20.77 years old; Maurice is 43.7 years old!

27.  Since time dilates for objects traveling at near light speed, Length must also contract  This prediction of Einstein’s that coincides with time dilation  Length only contracts in the direction of motion.  E.g. if the object is moving in the x direction, the height in the y direction is unaffected

28. http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/specrel/Lc.html

29. Proper Length Contracted Length Velocity Speed of light

30. Example: Find the speed for which the length of a meter stick is 0.500 m Solve for v: v 1.00 m 0.500 m

31. Suppose you are the pilot of a space shuttle in deep space, moving toward an asteroid with a speed of 25 mi/h. To signal a colleague on the asteroid, you activate a beam of light from the front of your shuttle. Classical physics predicts that the velocity of the light beam would be 25 mi/h + c. Relativity states this is impossible because nothing can travel with a speed greater than c. How fast then, does the beam of light travel? Is its speed different for you than it is for your colleague?

32. Classical (Newtonian) mechanics predicts that velocity can increase without limit. Einstein imposed a limit of 1.0c for the maximum speed 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 0 10 20 30 40 Speed, v/c Time Spent accelerating (arbitrary scale) Classical velocity addition Relativistic velocity addition

33. Speed of light Velocity of Moving object A (relative to a stationary observer) Velocity of Moving object B (relative to a stationary observer) Velocity of objects A & B relative to each other **Assume Object A is the spaceship, object B is the light beam, the colleague is the stationary observer

34. Example: Suppose the spaceship described in the previous example is approaching an asteroid with a speed of 0.750c. If the spaceship launches a probe toward the asteroid with a speed of 0.800c relative to the ship, what is the speed of the probe relative to the asteroid? Solution:

35. Not this too!!!???? Because of the ways that relativistic velocities add, momentum becomes relative as well (and thus mass) 0 0.2 0.4 0.6 0.8 1.0 Momentum, p Speed, v/c Classical momentum Relativistic momentum **Note the momentum increases to infinity as v approaches c**

36. Momentum Mass Velocity Speed of Light

37. Example: Find both the classical and relativistic momentum of a 2.4 kg mass moving with a speed of 0.81c. Solution: Relativistic momentum: Classical momentum

38. A useful way to apply relativistic momentum is in terms of a mass that increases with speed. We can suppose that an object has a fixed mass when at rest; we call this rest mass. Rest mass Relativistic mass **Note that m approaches infinity as v  c, thus a constant force generates less and less acceleration, a = F/m; thus the speed of light cannot be exceeded.

39.  You were just shown that an object’s mass increases as its velocity increases.  Thus, when work is done on an object, part of the work increases the object’s velocity, and part of the work increases the object’s mass.  Thus, mass is another form of energy!

40. Total Energy Rest Mass Relativistic Mass Velocity Speed of Light

41. Example: Show the expression for the rest energy of an object. That is the energy when the object’s speed is zero.

42. Example: Find the rest energy of a 0.12 kg apple. Compare this with the total yearly energy usage of the US… 10 20 J!!!!

43. Kinetic Energy Rest mass

44. 0 0.2 0.4 0.6 0.8 1.0 Kinetic Energy Speed, v/c Relativistic Kinetic Energy Classical Kinetic Energy

45.  It is impossible to exceed the speed of light  When approaching the speed of light, an object gains an infinite mass  An infinite amount of energy must be applied to allow the object to reach the speed of light.  This, no object with a mass can actually reach the speed of light