Special and General Relativity

1. Special and General Relativity Marcus Han 3O3 (!0)

2. Albert Einstein • 14 March 1879 – 18 April 1955 • Einstein was a theoretical physicist. • He used to work at a patent office – where he evaluated patent applications for electromagnetic devices. This helped him sharpen his physics skills. • Einstein came up with both the special and general relativity theories, when he was working in a patent office. • I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.

3. Principle of relativity • This was (not by Einstein) the basis for both special and general relativity. • The laws of nature are not affected by motion • Therefore you can never tell if you are stationary or moving at a constant speed since the laws of nature remain the same. • Kind of like saying, “Is the car more expensive than the boat or is the boat cheaper than the car?” It’s all relative!

4. Special relativity • States that space and time are deeply connected. • Applies only for objects travelling at a constant speed in a straight line. Thus the name ‘special relativity”. • Special relativity has the following effects:

5. Special relativity • There is no ‘absolute motion’. There is only ‘relative motion’. • Derived from the principle of relativity. As there is no way to tell if an object is moving at a constant speed in a straight line or stationary we can only say that it is moving relative to something.

6. Special Relativity • Example – A car is moving smoothly at 90km/h relative to the ground. • Or a car is moving smoothly at 40km/h relative to a truck, which is moving at 50km/h relative to the ground. 90km/h relative to ground 40km/h relative to truck 50km/h relative to ground

7. Special relativity • 2. As time passes at different rates depending on the speed of the observer, there is no way you can be sure that two things are happening at the same time.

8. Special Relativity 3. From an observer’s point of view, time slows down on an object moving past him. On the object, a person would notice time slowing down in the environment around him. (time dilation)

9. 3. Time dilation • Let’s say we have a light-clock. • We have a light ray in the clock moving straight, up and down. • The light ray is moving at the speed of light (obviously) • Each time the ray reaches the top or bottom it makes a tick, signifying that one unit of time has passed.

10. Now the clock itself is moving near the speed of light. Thus the ray is moving horizontally as well as vertically.

11. Since the speed of light is constant for everyone, the ray must take a longer time to make a tick as it must travel a longer distance.

12. Thus from an observer’s point of view, time slows down for an object in motion. • However since there is no way you can tell if you are moving at a constant speed or just stationary, a person travelling with the light-clock would not notice anything different about the clock so he does not notice time slowing down. Instead, he notices the environment around him slowing down.

13. Exploring time dilation • Video of time dilation: http://www.youtube.com/watch?v=ex6yzNJ5y64 • Amazing experiment involving time dilation: http://www.youtube.com/watch?v=DWKn_Punrjk • Applet of time dilation in spaceship http://www.walter-fendt.de/ph14e/timedilation.htm

14. Obtaining a formula • Now we want to get a formula that would tell us exactly how much time slows down (or dilates) for an object moving at a certain speed.

18. However for a person holding the clock and travelling with the clock, he would not notice the time dilation (Principle of relativity). • Instead he would see the ray moving up and down normally, like this 

21. Case study: Muons • Muons (symbol: μ) are a type of elementary particle, like photons and electrons. (Protons and neutrons are not) • Their mean lifetime is around 2.2×10−6 s, which means they only last for about 2 μs. Right: Standard Model of Elementary Particles

22. Case study: Muons • Muons are formed high (around 10km) above the surface of the Earth, when radiation splits atoms into elementary particles like muons. • Here’s the strange part: Lots of muons can be discovered hitting the Earth’s surface but they are only formed 10km away. • It seems that even the longest lasting muons (which can last for around 4μs) cannot hit the Earth’s surface. They would have to travel 10km in 4μs, which means they would need to have a speed of 2.5 x 109 m/s – more than 8 times the speed of light!

23. Case study: Muons • So how is this possible? • Muons travel at nearly the speed of light but not above (in fact, nothing can). The only answer is time dilation. If you travelled with a 4 μs-lasting muon only 4 μs would pass for you. However you were on the surface of the Earth around 40 μs would pass for you! • Which goes to show that time dilation is not just theoretical – it really exists!

24. Special relativity • 4. An object moving past you decreases in length. • Imagine a train. We want to find out the length of the train, when it moves past you. • When it is stationary, it is 1m long. TRAIN

25. Now the train is moving, near the speed of light. We have two people on the train, one at the front and one at the back. The one at the front fires a ray (yellow) at the person at the back. On the ground, a super-accurate stopwatch is started upon firing the ray. TRAIN

26. The stopwatch is stopped when the ray hits the other person. However by the time the ray hits the other person the train would have moved a fair bit and the time taken for the ray to hit him would be shortened. TRAIN

28. Summary of Special Relativity All of the following are applicable only to objects moving at a constant speed and in a straight line. • There is no ‘absolute motion’. There is only ‘relative motion’. 2. As time passes at different rates depending on the speed of the observer, there is no way you can be sure that two things are happening at the same time.

29. 3. From an observer’s point of view, time slows down on an object moving past him. On the object, a person would notice time slowing down in the environment around him. (time dilation) 4. An object moving past you decreases in length.

30. General Relativity • Einstein was unhappy with his Special Relativity theory, as he soon discovered it did not cover acceleration and was only applicable to objects travelling in a straight line. • He wanted a general theory – one that would be applicable to all cases and explain the real world – for the real world was full of acceleration and multi-directional motion.

31. General relativity • Einstein knows he needs to explain space, time and gravity for his theory to apply to all cases. • At the patent office he imagined a man working on the roof of a building. He imagined the man falling off the roof. He had a vision that the man would not be feeling his own weight. • Thus he knew that there was no such thing as gravitational pull.

32. What then was making him fall to the ground? Einstein said that the Earth curved space around the man and that space was pushing him to the ground.

33. General Relativity • A. Gravity slows time down • He realised acceleration makes light curve. • Since gravity is acceleration, gravity makes light curve. • Gravity ends up slowing down light, too. • This means gravity slows down light-clocks. • Which means gravity slows time down.

34. General Relativity • B. Matter bends space. • Imagine a bicycle wheel, spinning near the speed of light. The tyre must get shorter since it is moving so quickly.

35. General Relativity • A shorter tyre should mean shorter spokes but the spokes are just moving sideways – they would just get narrower, not shorter. • Does this mean general relativity is wrong?

36. General Relativity • No! Acceleration and gravity affect space as well as time. • Space is bent such that there is more in the wheel, so that the spokes have more room.

37. General Relativity • So Albert found that matter bends space and slows time down – it warps space-time. • Light and matter cannot go straight – like they normally do – when space-time is curved by huge masses like planets. • C. Light and matter follow the shape of space-time.

38. General Relativity • D. Einstein came up with an equation that described the shape of the universe: • Where lambda (Λ) was the cosmological constant. • The cosmological constant was put in the equation for it to make sense. • If there was no cosmological constant, the universe would collapse onto itself as stars attracted one another due to gravity.

39. However in 1929 Edwin Hubble discovered that the universe was expanding. • Thus Einstein realised there was no need for a cosmological constant to prevent the universe to collapse onto itself. • (Although recently there has been some evidence that the constant may not have been so unnecessary)

40. E. Einstein also figured out that the faster an object is, the heavier it is. • When we rush towards a star it looks brighter the faster we rush towards it. To get the extra brightness Albert realised the energy source was the star’s mass. • He realised that mass and brightness are related and soon… • F. From this he figured out E=mc2, one of the world’s most famous equations.

41. References • http://upload.wikimedia.org/wikipedia/en/5/5b/Time-dilation-001.svg • http://upload.wikimedia.org/wikipedia/en/a/a5/Time-dilation-002.svg • http://en.wikipedia.org/wiki/Time_dilation • http://en.wikipedia.org/wiki/Special_relativity • http://www.youtube.com/watch?v=x2vx_UOaiRY&feature=related • Einstein and his inflatable universe. (2010). London, UK: Scholastic. • Albert Einstein. (2010). The History Channel website. Retrieved 9:21, September 11, 2010, from http://www.history.com/topics/albert-einstein. • http://image.ec21.com/image/qdyf/oimg_GC00101323_CA03527291/Wheel_Barrow_Wheel.jpg • http://upload.wikimedia.org/wikipedia/commons/7/78/Einstein1921_by_F_Schmutzer_4.jpg • http://en.wikipedia.org/wiki/Muon • http://en.wikipedia.org/wiki/Elementary_particle • http://www.carforums.net/reviews/makes/pictures/acura07.jpg • http://images.search.yahoo.com/search/images;_ylt=A0geuiPRiI9M5HQBHzpXNyoA?ei=UTF-8&p=truck&fr2=tab-web&fr=moz35

42. Thank you! • “I do not know how the Third World War will be fought, but I can tell you what they will use in the Fourth—rocks!” – Albert Einstein