Welcome to Mr. Einstein’s Amazing World! The physics of Relativity

Quick Overview… Reading: Chapter 26 Reading: Chapter 26 Historical Background… Measuring the Speed of Light and the Michelson-Morley Experiment (read Chp 22.2) Historical Background… Measuring the Speed of Light and the Michelson-Morley Experiment (read Chp 22.2) Galilean Relativity and Einstein’s Two Principles Galilean Relativity and Einstein’s Two Principles The problem of Time The problem of Time SimultaneitySimultaneity Time dilationTime dilation Exploring the Special Theory of Relativity Exploring the Special Theory of Relativity Extending the theory – General Relativity Extending the theory – General Relativity

Measuring 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 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, / km/s

The Michelson-Morley Experiment Designed to measure the speed of earth through the ether Designed to measure the speed of earth through the ether The most famous experiment that didn’t work! The most famous experiment that didn’t work! Was a hint that something was wrong with physics! Was a hint that something was wrong with physics!

How the M&M Expt. Worked… Use the “row-boat analogy” – how does time rowing across a stream and back compare to rowing downstream and back? Use the “row-boat analogy” – how does time rowing across a stream and back compare to rowing downstream and back? Do the math! Compare time for light to travel across the interferometer and upstream/downstream. They should be different – right? Do the math! Compare time for light to travel across the interferometer and upstream/downstream. They should be different – right?

Implications… Lorentz and Fitzgerald contraction hypothesis: “things get shorter in the direction of motion” Lorentz and Fitzgerald contraction hypothesis: “things get shorter in the direction of motion”or… There is no ether! There is no ether! The M&M experiment continued to be carried out around the world over the next 20 years – always showing a fringe shift much smaller than expected. After 1905, however, there far less interest in the experiment!

The Special Theory of Relativity Two principles: Two principles: The laws of Physics are the same for all observers moving in inertial framesThe laws of Physics are the same for all observers moving in inertial frames All observers, regardless of their inertial frame of reference, will measure the same value for the speed of lightAll observers, regardless of their inertial frame of reference, will measure the same value for the speed of light

Surprising Consequences Simultaneity: in general, events simultaneous in one inertial frame will not be simultaneous in other inertial frames Simultaneity: in general, events simultaneous in one inertial frame will not be simultaneous in other inertial framessimultaneous Time dilation: time between events is dependent on one’s frame of reference. Time dilation: time between events is dependent on one’s frame of reference. Time dilation Time dilation Neither simultaneity nor time rates are absolute – they are frame dependent. Neither simultaneity nor time rates are absolute – they are frame dependent.

The Twin Paradox Two space-age twins, Bob and Barb, separate on their 20 th birthdays. Bob travels to Vega, 25 light years away and returns 55 years later just in time to arrive at his sisters 75 th birthday party. How old is Bob? Two space-age twins, Bob and Barb, separate on their 20 th birthdays. Bob travels to Vega, 25 light years away and returns 55 years later just in time to arrive at his sisters 75 th birthday party. How old is Bob? applet illustrating this

Resolving the Paradox If the situations for Bob and Barb were completely symmetrical then they could never be reunited and no paradox If the situations for Bob and Barb were completely symmetrical then they could never be reunited and no paradox If they are re-united one of them must have changed frames of reference (experienced a force, acceleration, etc) – again no paradox If they are re-united one of them must have changed frames of reference (experienced a force, acceleration, etc) – again no paradox

Spacetime Diagrams The spacetime diagram depicts an object’s position (and motion) in space and time. The spacetime diagram depicts an object’s position (and motion) in space and time. If two objects, originally in the same frame, are separated and reunited – the one undergoing the greatest spatial change will have undergone the smallest temporal change If two objects, originally in the same frame, are separated and reunited – the one undergoing the greatest spatial change will have undergone the smallest 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 Transformations Galilean Transformations Lorentz Transformations

Working with the Lorentz Transformations Length contraction: Why did Bob’s trip only take 22.9 years in his frame? Answer – because Vega was only 10.4 ly away and not 25! Length contraction: Why did Bob’s trip only take 22.9 years in his frame? Answer – because Vega was only 10.4 ly away and not 25! Addition of velocities: Suppose Bob launched a communication probe that traveled with a speed of 0.95c in his frame. How fast would the same probe appear to move from Barb’s frame? Addition of velocities: Suppose Bob launched a communication probe that traveled with a speed of 0.95c in his frame. How fast would the same probe appear to move from Barb’s frame?

Roemer’s Method Demonstrates that the speed of light is not infinite Demonstrates that the speed of light is not infinite Huygen’s figured it out! Huygen’s figured it out!

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