Chapter 16

Relativity

Momentum, mass, Energy, and

Gravity

Momentum

• Remember

• P=MV

• Momentum is mass times velocity

• Combine this with special relativity.

• Mass increases with increased velocity.

Relativistic Momentum

• Examine the extreme cases.

• V=0 momentum is just mv

• V=c momentum is infinite!

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P =mv

1− (v c)2

Einstein proposed a new

concept of momentum

The most Famous Equation

• Special Relativity gave us new insight into space, time, and how we(mass) interact with them.

• Through this he discovered a new idea.

Mass is EnergyEnergy is Mass

• Mass and energy are equivalent.

• Anything with mass also has energy.

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E = mc 2

General Relativity

• It took Einstein 10 years of hard work to come up with his next contribution to the world.

• He was thinking about gravity and acceleration.

• What is the acceleration due to gravity?

What Einstein thought• Imagine dropping two balls in a gravitational field. • They fall tothe ground (duh)

• Now imagine dropping two balls in a space ship accelerating upward.

The balls still falls to the ground!

The Principle of Equivalence

• You can not tell the difference between being accelerated and being in a gravitational field.

• The effects of gravity and the effects of acceleration are equivalent.

• This isn’t too crazy but what Einstein said next was revolutionary!

The Principle of Equivalence

• Einstein said

• The principle holds for all natural phenomena!

• This includes optical, electromagnetic, and mechanical phenomena.

• That is, it applies to light too

General Relativity

• Mass warps space-time.

• Gravity is a result of this bending of space-time.

Tests of General Relativity

• Why are we going to believe Einstein?

• Yes! We are not.

• Like all things, We must test the threory

Precession of Mercury

• Einstein predicted that the orbits of the planets, according to Newton, were wrong.

• Predicted that the orbits should wobble.• This is tough to observe for outer planets.• Astronomers observed and calculated the

precession of Mercury but could not account for why they were off by a small amount.

• Einstein’s theory accounted for the change.

The bending of light by Gravity

• Gravity bends light.

• This has been

• observed in every eclipse since 1919.

Gravity slows Time

• The more gravity, the slower time moves.

• From the top to the bottom of the tallest sky- scraper,

• the difference is very small. Only a few millionths of a second per decade

Tests of General Relativity