1. Special Relativity Einstein (1905): Three Nobel-Prize worthy publications On unrelated subjects: Brownian motion Photo-electric effect (Nobel prize) “On the electrodynamics of moving bodies”... ⇐

2. Special Relativity Requires only three assumptions: ★ The laws of physics are the same in every uniformly moving laboratory ★ (if I hit my head, an observer moving relative to me will also see me hitting my head) ★ Space is “homogeneous” and “isotropic” ★ (a yardstick at rest is exactly a yard long, regardless of where it is used and which way it is pointing) ★ The speed of light is constant and the same in every frame of reference (Maxwell’s equations are the same in every lab)

3. Radical changes... This implies that space and time are no longer independent. Space and time are interwoven into a fabric, called “spacetime”. Maxwell’s laws still hold, but Newton’s must be altered.

4. Frames A “frame” is really just an imaginary laboratory attached to some object or observer. A frame can be moving with some fixed velocity Such a frame is called an “inertial frame” Natural laws are formulated in inertial frames

5. Frames A “frame” is really just an imaginary laboratory attached to some object or observer. A frame can be accelerated Rotating frames are accelerated An accelerated frame is bad for formulating the laws of physics

6. Frames Each object has a “frame” that is attached to it In this frame it is not moving and not rotating That frame is called the “rest frame” of that object (because it is at rest in that frame).

7. Spacetime... Consider a flash of light Its rays will move outward on a sphere

8. Spacetime... Now add another observer, moving at some velocity (say, half the speed of light) Light flash is emitted when observers pass

9. Spacetime... Now consider the other observer... Light flash is emitted when observers pass

10. Spacetime... In our rest frame, the light arrives at the two outer clocks and the observer arrives at the inner clock at the same time

11. Spacetime... In “moving” frame, the light has already passed the right clock and not yet arrived at the left clock when the inner clock reaches him

12. Bye-bye simultaneity Things that happen simultaneous for one observer are not longer simultaneous for other observers in special relativity

13. Bye-bye simultaneity Things that happen simultaneous for one observer are not longer simultaneous for other observers in special relativity

14. Spacetime That means: separation in space between two things can turn into a separation in time and space ⇒ Space and time are now coupled to each other ⇒ 3 space dimensions + 1 time = 4 dimensions

15. Measuring a length Use a ruler (of course) Easiest when the car is at rest (of course) L

16. Measuring a length When the car is moving, measure both ends at the same time (of course) 15cm

17. Measuring a length From the point of view of the car: Right measurement before left measurement! ⇒ The ruler appears shorter than the car! ⇒ Moving objects are length contracted! ???

18. Length contraction By symmetry: moving car must also appear shorter Example: Car is 25cm long when it is at rest If it is moving along with velocity v=4/5c, how long do we measure the car to be? ★ Newton:25 cm ★ Einstein: 15 cm In other words: walking is slimming, but driving is even more slimming!

19. The best diet... The moving car is contracted

20. The best diet... To the car, the observer is contracted

21. Time “dilation” Now the car shines a light upward This takes a certain amount of time

22. Time “dilation” Now look at this when the car is moving The light has to travel a longer distance That means on our clock it takes longer How long it takes when the car is moving How long it takes when the car is at rest

23. Time “dilation” Moving clocks go slower! A clock moving at 80% of c moves 40% slower than a clock at rest

24. Time “dilation” Of course, from the point of view of the moving clock, it is our clock that is moving (backwards), so our clock is moving slower

25. Example: “Muons” created high in earth’s atmosphere from energetic particles from outer space Muons decay in 2 μ s Light travels 6 kilometers in 2 μ s But muans actually travel 30 kilometers down to us Their clocks go 5x slower ! 2μs2μs

26. Velocity addition Consider a train with some velocity v and car with velocity v ontop The looks is shortened Time is dilated Car is moving at less than v+v

27. Doppler shift The siren of a police car driving by sounds like it is getting lower when the car passes. This is the Doppler effect: The police car is catching up to the emitted sound waves Same thing happens with light Additional effect: Time dilation (slower clock)

28. “Beaming” Consider a photon emitted by a standing car

29. “Beaming” What happens when the car is moving? Light moves forward (also called aberration).

30. Doppler boosting Putting the Doppler shift and beaming together: Light bulb at rest

31. Doppler boosting Putting the Doppler shift and beaming together: Moving light bulb