Einstein and the Development of Relativity

Light- The Gateway to Relativity

The Field Concept of Light Around 1850, Foucault (foo koh’) measured the speed of light to be about 3 x 10

8

meters/second.

Michael Faraday – magnetism creates electricity and electricity creates magnetism.

James Clark Maxwell – light cycles with a magnetic field creating an electronic field and an electronic field creating a magnetic field.

Maxwell’s 8 equations unify magnetism and electricity while describing electromagnetic radiation.

Problems With Prevailing Theory Seemingly endless supply of energy from radium.

Several problems with aether, a transparent, hard, elastic solid, that offered no resistance to the movement of matter through it.

Maxwell’s equations showed light was the same speed for all reference systems.

Ernst Mach challenged ideas that could not be proved such as: Atoms Aether Absolute motion (he said that all motion was relative) Absolute time

Absolute space All of Newtonian mechanics, because it assumed absolute time and space.

Michelson’s and Morley’s “failed” experiments

Michelson’s and Morley’s “failed” experiment Using mirrors, he split a single light beam into two identical beams and sent them out ninety degrees to each other.

The light beam sent in the direction of the earth’s motion should travel faster than light sent at right angels to the earth’s motion.

The beams traveled the same speed regardless of orientation to the movement of the earth.

Impossible Result If we were moving away from light at ¼ the speed of light, the light

should

only strike us at ¾ the normal speed of light. If we were traveling towards the light at ¼ the speed of light, the light

should

strike us at 1¼ times the normal speed of light.

The Michelson-Morley experiment proved that light strikes us at the same speed, regardless of our motion relative to the light source. The Galileo/Newton/common sense view of velocity must be wrong.

Could Newtonian Physics be saved?

Lorentz-Fitzgerald contraction – proposal that an object became shorter in the direction of travel (the math worked perfectly to explain the result).

This preserved the concepts of aether and of absolute space and time.

Einstein didn’t agree with this interpretation- the theory had no basis, and was not testable.

Einstein’s Explanation Time is different for different observers, like the clock tower – time changes with speed.

Lightning strikes a train – not simultaneous for different frames of reference.

As relative velocity increases, time and distance both decrease by the same percentage; therefore… The speed of light (ratio of distance/time does not change)

Special Theory of Relativity Equations If v=80% the speed of light, 1 m becomes .6m, 1 kg becomes 1.67 kg, and 10 sec become 16.7 sec.

The Space-time Arrow Arrow length = speed through space + speed through time.

Length of arrow never changes.

If you’re stationary, all of your speed is through time.

As you approach the speed of light, the speed through space section increases and the speed through time decreases and slows.

The length of arrow is the speed of light.

E = mc 2 E is energy in Joules, m is mass in kg, c is the speed of light (3 x 10

8

m/sec). 1 Joule = 1 kg m

2

/sec

2

Energy and mass are interchangeable, different forms of the same thing.

The total energy of an object is given by its mass.

Published 3 months after the Special Theory of Relativity.

New paradigm The universe is no longer a rigid grandfather clock ticking away.

It is dynamic, elastic, and dependent on the reference frame of the observer.

Time, distance, velocity, and even mass are no longer absolute “It’s all relative!”

Difficulty in accepting theory Relativity is difficult to accept because it lies outside our range of experience.

It violates our “common sense.” Einstein quote: “Common sense is that prejudice learned before the age of eighteen.”

1905 – Einstein’s miracle year Explained photoelectric effect – start of Quantum Theory.

Explained Brownian Motion – first hard evidence for atoms.

Special Theory of Relativity – replaced Newtonian Mechanics.

Problems with Special Relativity It only dealt with constant velocities.

Did not cover acceleration.

Did not cover gravity.

Newton’s gravity was instantaneous, while Einstein’s universe had a speed limit.

General Relativity Just as the speed of light was the springboard for Special Relativity… Gravity would be the springboard for General Relativity.

Freefall did not feel like acceleration (like being accelerated in a car).

Equivalence Principle Situations that felt the same and acted the same, in terms of physics, were the same.

Freefall was equivalent to weightlessness.

Acceleration was equivalent to gravity.

Gravity bends light Rocket ship – light thought experiment As the rocket ship is accelerated, light will bend as it travels.

Since acceleration is equivalent to gravity, gravity will also bend light.

Gravity slows time Two clock – rocket thought experiment The clock at the rear is being accelerated towards the light ray image of the front clock.

The front clock appears to be running faster than the rear clock.

Conclusion – acceleration slows time.

Therefore, gravity also slows time.

Minkowski’s Space-Time 4-dimensional coordinate system (3 space and 1 time).

Reworked the Pythagorean Theorem into four dimensions.

Absolute interval – The shortest line in space-time.

All observers can agree on the absolute interval.

World line – line of person or object during existence.

Curved space-time Imagine a spinning vinyl record.

The outer edge covers more distance per revolution than the center.

The velocity of the outer edge is greater than the center, therefore it will shrink more than the center.

The record becomes dome shaped as it rotates very fast.

Swirling galaxies, etc. must curve space.

Geometry for curved space Euclidean Geometry only held for flat space.

Math for curved space is differential geometry (tensor calculus), developed by George Friedrich Riemann in the 1850s.

Einstein did not have these math skills, so he asked his former classmate Grossman for help.

Math of curved space is applied to universe Einstein and Grossmann reworked Minkowski’s four dimensional, linear space-time into curved space-time.

The amount of mass and energy determines curvature at that location.

True nature of gravity The gravitational field does not pull objects, it simply curves space-time as determined by the amount of mass and energy. Objects moving towards the earth are simply following the shortest space time path as determined by the curvature of space.

Newton had it backwards: Objects in free-fall are not being acted on by a force, which is why we feel no force in free-fall.

Not following the natural space-time path requires a force and is an acceleration.

You are undergoing acceleration by simply standing on the earth because the earth is holding you back from the path.

General Relativity’s Final Form Einstein completed the final form of this theory in 1915.

It explained the wobble in Mercury’s orbit.

The 1919 solar eclipse also supported the theory.

In it’s simplest form, Guv = 8πTuv The left side defines the universe’s shape.

The right side tells matter-energy (all that the universe contains) how to move.

Strengths of Relativity It explains the constant speed of light.

It preserves Newton’s equations for everyday type situations while also including extraordinary mass, velocity, and energy situations.

Shows the equivalence of (relationship between) mass and energy, and time and space.