Welcome to Mr. Einstein’s Welcome to Mr. Einstein’s Amazing World!Amazing World!

The physics of RelativityThe physics of Relativity

Quick Overview…Quick Overview… Reading: Chapter 26Reading: Chapter 26 Historical Background…Historical Background… Measuring the Speed of Measuring the Speed of

Light and the Michelson-Morley Experiment (read Chp 22.2)Light and the Michelson-Morley Experiment (read Chp 22.2)

Galilean Relativity and Einstein’s Two Galilean Relativity and Einstein’s Two PrinciplesPrinciples

The problem of TimeThe problem of Time• SimultaneitySimultaneity• Time dilationTime dilation

Exploring the Special Theory of RelativityExploring the Special Theory of Relativity Extending the theory – General RelativityExtending the theory – General Relativity

Measuring the Speed of LightMeasuring the Speed of Light

September 1676 Ole Roemer announces to the Academy of Sciences in Paris that the eclipse of one of Jupiter's moons (Io) would not occur at 5:25:45 as predicted but would occur exactly 10 minutes late!!!

British astronomer James Bradley announces some puzzling observations of the star Gamma Draconis. During the course of 1 year the star "nods" back and forth by about 40" or arc (0.2 milli radians)

The French physicist - Fizeau - who had a passion for measuring the speed of light reflected light from a mirror 8.633 km away and determined the speed of light with unprecedented accuracy.

May 6, 1850 Focault and Fizeau successfully measured the speed of light in water using essentially the same technique. What did they find?

The American physicist Albert Michelson built a long and distinguished career around measuring the speed of light. His most famous experiment used a 35 km path from Mount Wilson to Mount San Antonio and back. The result c = 299, 796 +/- 4 km/s.Today: the velocity of light is 299, 792.458 +/- 0.001 km/s

The Michelson-Morley ExperimentThe Michelson-Morley Experiment

Designed to Designed to measure the speed measure the speed of earth through of earth through the etherthe ether

The most famous The most famous experiment that experiment that didn’t work!didn’t work!

Was a hint that Was a hint that something was something was wrong with wrong with physics!physics!

How the M&M Expt. Worked…How the M&M Expt. Worked…

Use the “row-boat Use the “row-boat analogy” – how does time analogy” – how does time rowing across a stream rowing across a stream and back compare to and back compare to rowing downstream and rowing downstream and back?back?

Do the math! Compare Do the math! Compare time for light to travel time for light to travel across the interferometer across the interferometer and and upstream/downstream. upstream/downstream. They should be different They should be different – right?– right?

Implications…Implications… Lorentz and Fitzgerald contraction Lorentz and Fitzgerald contraction

hypothesis: “things get shorter in the hypothesis: “things get shorter in the direction of motion”direction of motion”

or…or…

There is no ether!There is no ether!

The M&M experiment continued to be carried out around the The M&M experiment continued to be carried out around the world over the next 20 years – always showing a fringe shift world over the next 20 years – always showing a fringe shift much smaller than expected. After 1905, however, there much smaller than expected. After 1905, however, there far less interest in the experiment!far less interest in the experiment!

The Special Theory of RelativityThe Special Theory of Relativity

Two principles:Two principles:• The laws of Physics are the same for all The laws of Physics are the same for all

observers moving in inertial frames observers moving in inertial frames • All observers, regardless of their inertial All observers, regardless of their inertial

frame of reference, will measure the frame of reference, will measure the same value for the speed of lightsame value for the speed of light

Surprising ConsequencesSurprising Consequences

Simultaneity: in general, events Simultaneity: in general, events simultaneous in one inertial frame will simultaneous in one inertial frame will not be simultaneous in other inertial not be simultaneous in other inertial framesframes

Time dilation: time between events is Time dilation: time between events is dependent on one’s frame of reference.dependent on one’s frame of reference.

Neither simultaneity nor time rates are Neither simultaneity nor time rates are absolute – they are frame dependent.absolute – they are frame dependent.

The Twin ParadoxThe Twin Paradox

Two space-age twins, Bob Two space-age twins, Bob and Barb, separate on their and Barb, separate on their 2020thth birthdays. Bob travels birthdays. Bob travels to Vega, 25 light years to Vega, 25 light years away and returns 55 years away and returns 55 years later just in time to arrive later just in time to arrive at his sisters 75at his sisters 75thth birthday birthday party. How old is Bob? party. How old is Bob?

applet illustrating this

Resolving the ParadoxResolving the Paradox

If the situations for Bob and Barb If the situations for Bob and Barb were completely symmetrical then were completely symmetrical then they could never be reunited and no they could never be reunited and no paradoxparadox

If they are re-united one of them If they are re-united one of them must have changed frames of must have changed frames of reference (experienced a force, reference (experienced a force, acceleration, etc) – again no paradoxacceleration, etc) – again no paradox

Spacetime DiagramsSpacetime Diagrams

The spacetime diagram depicts an object’s The spacetime diagram depicts an object’s position (and motion) in space and time. position (and motion) in space and time.

If two objects, originally in the same frame, are If two objects, originally in the same frame, are separated and reunited – the one undergoing the separated and reunited – the one undergoing the greatest spatial change will have undergone the greatest spatial change will have undergone the smallest temporal changesmallest temporal change

applet illustrating this

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics and therein lies their strength. They are radical. Henceforth, space by itself and time by itself are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality.

Hermann Minkowski, 1908

The Lorentz TransformationsThe Lorentz Transformations

Galilean TransformationsGalilean Transformations Lorentz TransformationsLorentz Transformations

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Working with the Lorentz Working with the Lorentz TransformationsTransformations

Length contraction: Length contraction: Why did Bob’s trip only take Why did Bob’s trip only take 22.9 years in his frame? 22.9 years in his frame? Answer – because Vega was Answer – because Vega was only 10.4 ly away and not 25!only 10.4 ly away and not 25!

Addition of Addition of velocities: velocities: Suppose Suppose Bob launched a Bob launched a communication probe that communication probe that traveled with a speed of 0.95c traveled with a speed of 0.95c in his frame. How fast would in his frame. How fast would the same probe appear to the same probe appear to move from Barb’s frame?move from Barb’s frame?

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Roemer’s MethodRoemer’s Method

Demonstrates that Demonstrates that the speed of light the speed of light is not infiniteis not infinite

Huygen’s figured it Huygen’s figured it out!out!

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Bradley and Bradley and Draconis Draconis

Use the “snow-Use the “snow-storm” analogy. storm” analogy. When driving When driving through a snow through a snow storm, what’s storm, what’s “odd” about the “odd” about the way the snowflakes way the snowflakes fall?fall?

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