Relatively EinsteinRelatively Einstein2005 has been chosen as the World Year of Physics to

celebrate the 100th anniversary of Einstein’s Miraculous Year. In this presentation, we will explore

both his special and general theories of relativity.

Related by Rideout and McGourty

Special Relativity(SR,1905)

Two postulates:

• All inertial reference frames are equivalent.– There is no experiment you can do to determine

your own absolute velocity.– There is no absolute reference frame. All

velocities must be measured relative to something.

• All observers will measure same speed of light, c. – The speed of light in outer space is a constant.

Even if the source of the light itself is traveling, the light emitted goes the same speed as from a stationary source.

What does this mean?

• Simultaneity is relative:– Different inertial observers will not agree on which

events are simultaneous.

Click here to see a demo.

Defining Relativity

• All measurements are “relative” to your velocity.• As you speed up (v), length contracts and time dilates

according to the gamma (γ) factor.

2

2

1

1

cv

Defining Relativity

• Relative length:

• Relative time interval:

0L

L

0TT

Defining Relativity

• Since length and time are fundamental units, most other kinematic expressions also need to be adjusted to fit with SR.– Relativistic mass: m = γ m0

– Relativistic momentum: p = γ p0

• The most famous Einstein equation of them all came from his relativistic correction to kinetic energy….

E = mc2

– This equation contains both kinetic energy and the “rest energy” (m0c2)

That’s crazy talk!Can you prove it?

1. Michelson-Morley Interferometer (1885)

That’s crazy talk!Can you prove it?

2. Atomic clocks flown around the world (1972, Haefele & Keating)

2. Subatomic muons (half-life of 2.197 μs) traveling close to the speed of light live “too long” according to a stationary observer (1941, Rossi and Hall)

SR in Radio Astronomy

• Synchrotron Radiation– A charged particle moving in a curved path

experiences a centripetal acceleration.– This acceleration causes the particle to radiate

energy.– As particle speed approaches the speed of light, the

radiation pattern is distorted by relativistic effects and changes to a narrow cone of radiation.

Forming a Narrow Cone of Radiation

General Relativity(GR, 1916)

• Equivalence Principle:- Acceleration due to gravity is equivalent to

acceleration due to motion.

-Gravitational mass is

equivalent to inertial mass.

Equivalence Principle

– Therefore, being in a gravity field is the same as constantly accelerating upward.

– See this wicked cool demo

Light

• Light appears to bend in gravity!

• Since light from point p would appear to “bend” to Observer A (due to his motion), the same must be true for Observer B on Earth because of the Equivalency Principle.

Gravity

• Gravity is the actual bending of space-time caused by mass and energy.

More crazy talk!Can you prove it?

• Four experiments have tested GR:

1. Precession of perihelion of Mercury (existing data)

1. Bending of light passing near the sun (1919 eclipse)

More crazy talk!Can you prove it?

3. Red shifting as photonloses energy leaving a gravitational well (1960, Harvard)

4. Change in time for light to travel by the sun (1966, Haystack, “the fourth test of GR”)

So, are there any practical uses for this stuff?

• Global Positioning System (GPS)– The satellites are moving faster than the Earth’s

surface, so SR corrections of 7 μs/day are needed.

– Satellites are high enough (subject to weaker gravity) for GR corrections of 45 μs/day.

– Without these corrections, GPS would drift by 10 km/day!