Relativity

Albert Einstein

Special Theory of Relativity

Speed of light

General Theory of Relativity

Special relativity + gravity

Newton's Theory of Gravity

Deals with low speeds

Einstein's special relativity reduces to Newton's theory of gravity at low speeds

Newton's World of Velocities

You are in a car going v=100 km/hr

You fire a bullet forward with v=1000 km/hr from the open window of the car

Your friend is on the sidewalk

What does your friend measure for the speed of the ball?

Addition of Velocities

v(bullet)=1100 km/hr

v(light)=c

Fig. MP22-1a

Measurement of Speed of Light

Michelson-Morley Experiment

They measured the speed of light

The speed of light is independent of the motion of the observer or the source of the light

Speed of light (in vacuum) is always c

When speeds are near c, they are termed relativistic speeds

Thought Experiment

Albert Einstein's Thought Experiment

A person is in a totally enclosed elevator, no windows, in the middle of outer space.

The person is weightless

Then, suddenly the person feels like he has weight

Fig. MP22-1b

Thought Experiment Cont.

On left, a person has weight because a planet has passed nearby providing a downward force on the person

On right, a person has weight because the elevator is moving upward, creating a force against his feet, which feels like weight

If you are the person in the elevator how do you tell which situation is occurring?

Fig. MP22-1b

General Relativity

A person in the elevator cannot tell the difference between the 2 situations

Thus gravity behaves just like acceleration

Gravity can be treated as a general acceleration of all particles

Fig. MP22-1b

Space-Time

Newton described gravitational "fields" to explain gravity

Einstein describes gravity as space-time

According to Einstein, mass causes space-time to warp!

2_D Example of Space-Time

(a) 2-D space

(b) 2-D space deformed by presence of mass

Fig. 22-14

Tests of General Relativity

General relativity is harder to measure than special

Need large gravitational fields to measure effects (when orbit speeds and escape velocities become relativistic)

Deflection of light by mass (aberration of starlight)

Precession of Mercury's perihelion

Gravitational redshift

And others to be discussed next semester

Aberration (Deflection) of Starlight

The path of light is affected by mass, just like particles with mass

Maximum deflection 1.75''

1919 solar eclipse- deflection observed

Fig. MP22-2a

Precession of Perihelion

General relativity predicts that orbits of planets should deviate from Keplerian orbits (Fig. MP 22-2a)

Effect is strongest closest to Sun- Mercury

Rotation rate of Mercury's orbit is 574''/ century- most due to perturbations from other planets

43''/ century due to relativity is predicted and seen

Gravitational Redshift

A photon loses energy moving out of a gravitational well

(Fig. MP 22-2b)

E=hf

So the frequency of an outgoing photon will be redshifted