Gravity as Curved Space Article

http://Video intro

Video Why?

Read Ch 15 Start # 1-15 p 230

Einstein’s Theory of Special Relativity

Einstein’s Theory of Special Relativity

Space and time exist inside the universe. Together, they make up what Einstein called “Space-time.”

Time is a 4th dimension in space-time.

Relativity?

• Frames of reference are “relative.”

• Video:classical relativity

• Einstein’s theory deals with motion nearing the speed of light.

Two fundamental postulates must be stated:

1. All the laws of nature hold true in uniformly moving frames of reference.

2. The speed of light is constant 3 x 108 m/s.

(Einstein also stated that no object can travel faster than the speed of light)

video explanation

At normal rates, we travel through time and space.

Example: If we drive to Wisconsin, we are travelinga distance in space and we are also traveling throughtime because time goes by in order to get there. Our watches show a later time when we get there.

BUT according to Einstein, as we travel faster and faster, we alter the rate at which time goes by. This is called “Time Dilation.”

If we travel as fast as the speed of light, for example, NOTIME will go by! We will be traveling only in space.

Picture this:

Clock reads 2 pm

If we are traveling at the same speed as the light that allows us to read the clock, the clock will read 2 pm when it gets to our eyes. But we will have traveled millions of miles through space by then.

Another way to look at it (p 219)

A light ray sentstraight up reflects on a mirror.

The same light ray observedfrom an observer outside musttravel a greater distance, and therefore, takes more time.

Einstein has an exact equation that helps verify this idea.

Tstationary = tobserver

1 – (v2/c2)

Let’s try it: Say we are traveling at a rate of one half the speed of light for one hour according to our watch.On earth, the time that passes will be greater. How much?

Try the equation again – this time, you are traveling at 0.9 times the speed of light.

Einstein’s Twin Trip Analogy

Two twins say “good bye” as one gets on a spaceship and travels through space at .99 times the speed of light.

The twin on earth records a time of 10 years when the second twin returns.

The twin on the spaceship returns after one year according to his watch.

See p.223 - 227

• https://www.youtube.com/watch?feature=player_detailpage&v=HpIoBw0yL0c

Motion through space also affects length, mass and the energy of moving objects.

Length contraction:

As motion gets closer and closer to the speed of light, the length of an object gets closer and closer to zero.

Einstein’s Equation for Length Contraction:

L = Lo 1 – ( v2/c2)

Try it!

What happens to the length if the object travels at the speed of light?

How long would a 30 cm football appear at .5 times the speed of light?

Relativistic Mass:

As the speed of any mass approaches the speed of light,the mass increases.

The mass of an object is called “rest mass.”

m = mo

1 – ( v2/c2)

Einstein’s Famous Equation:

E = mc2

If the kinetic energy of an object is measured by 1/2mv2,and the mass increases as it moves, then the kinetic energy also must increase. ( KE = 1/2mv2 )

This equation infers that energy and mass are interchangeable.

Mass can be converted to energy!

Nuclear power plants and atomic bombs are the resultof Einstein’s theory.