Special and General RelativityMarcus Han 3O3 (!0)

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.

Principle of relativity

• This was 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.

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:

Special relativity

1. 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.

• 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, moving at 50km/h relatve to the ground.

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.

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)

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.

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

• 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.

• 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.

• Video of time dilation: http://www.youtube.com/watch?v=ex6yzNJ5y64

• Amazing experiment involving time dilation:http://www.youtube.com/watch?v=DWKn_Punrjk

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.

•

•

•

• 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

•

•

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

• 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

• 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

•

Summary of Special Relativity

All of the following are applicable only to objects moving at a constant speed and in a straight line.1. 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.

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.

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.

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.

•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.

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.

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.

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?

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.

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.

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.

• 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)

• 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.

References• http://upload.wikimedia.org/wikipedia/en/5/5b/Time-dilation-001.s

vg• http://upload.wikimedia.org/wikipedia/en/a/a5/Time-dilation-002.s

vg• 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

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