The background to and essentials of special relativity Rory Makielski, Sally Salvador March 28, 2006

Albert Einstein 1879 – – 1955 Modern scientific genius Modern scientific genius Humanitarian Humanitarian

The early years Born in Ulm, Germany Born in Ulm, Germany Early education was too oppressive Early education was too oppressive Early interest in science Early interest in science Compass needle Compass needle “Something deeply hidden had to be behind things.” “Something deeply hidden had to be behind things.” Euclidean geometry Euclidean geometry “This lucidity and certainty made an indescribable impression upon me.” “This lucidity and certainty made an indescribable impression upon me.”

Accomplishments earns degree from Swiss Federal Polytechnic School in Zurich earns degree from Swiss Federal Polytechnic School in Zurich claims Swiss citizenship, works as patent examiner claims Swiss citizenship, works as patent examiner Michelangelo Besso (1873 – 1955) Michelangelo Besso (1873 – 1955) 1905 – publishes dissertation on determining molecular dimensions and four more papers 1905 – publishes dissertation on determining molecular dimensions and four more papers

Annalen der Physik “On a Heuristic Viewpoint Concerning the Production and Transformation of Light” “On a Heuristic Viewpoint Concerning the Production and Transformation of Light” Describes photoelectric effect based on light quanta (Nobel Prize, 1921) Describes photoelectric effect based on light quanta (Nobel Prize, 1921) “On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat” “On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat” Brownian motion, existence of atoms Brownian motion, existence of atoms “On the Electrodynamics of Moving Bodies” “On the Electrodynamics of Moving Bodies” Special theory of relativity Special theory of relativity “Does the Inertia of a Body Depend Upon Its Energy Content?” “Does the Inertia of a Body Depend Upon Its Energy Content?” Equivalence of energy and matter Equivalence of energy and matter

Duality of personality Duality of personality Poor student, but interested in science Poor student, but interested in science passion for social justice but lacked personal relationships and state loyalty passion for social justice but lacked personal relationships and state loyalty Indifferent toward outside opinion Indifferent toward outside opinion

The Humanitarian Pacifist, democratic socialist Pacifist, democratic socialist Zionism Zionism Used scientific prestige to promote his social cause Used scientific prestige to promote his social cause Anti-Einstein groups Anti-Einstein groups 1930’s, Hitler purges universities of Jews 1930’s, Hitler purges universities of Jews 1939, urges FDR to 1939, urges FDR to develop atom bomb Civil Rights Movement Civil Rights Movement

Religious & Philosophical Influences "I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings." "I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings." Logical positivism Logical positivism Free invention of mind + experiments = general theories Free invention of mind + experiments = general theories Hume, Mach, Poincaré Hume, Mach, Poincaré Skeptical, critical Skeptical, critical

Skepticism on Classical Physics Maxwell, Lorentz Maxwell, Lorentz Asymmetry between reference frames Asymmetry between reference frames Gedankenexperiment Gedankenexperiment

“Simultaneity” Definition of Simultaneity based on round trip of light from A to B Definition of Simultaneity based on round trip of light from A to B Assumes constancy of c Assumes constancy of c Leads to Lorentz transformations (discussed later) Leads to Lorentz transformations (discussed later)

Constant Speed of Light? The speed of light is defined as being independent of the direction of propagation The speed of light is defined as being independent of the direction of propagation This is merely a convention, not provable experimentally This is merely a convention, not provable experimentally Other possibilities exist (such as the speed being constant for round trip) Other possibilities exist (such as the speed being constant for round trip)

First Assumption “The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion” “The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion” The laws of physics the same in all inertial frames The laws of physics the same in all inertial frames

Second Assumption “Any ray of light moves in the “stationary” system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body” “Any ray of light moves in the “stationary” system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body” The speed of light has the same value for all observers The speed of light has the same value for all observers

Dilemma for Classical Mechanics Newton’s laws of motion Newton’s laws of motion Maxwell’s equations Maxwell’s equations Classical concepts of space time Classical concepts of space time Taken together, imply that it must be possible to determine the velocity of an observer relative to light Taken together, imply that it must be possible to determine the velocity of an observer relative to light Not consistent with Einstein’s postulates Not consistent with Einstein’s postulates

Einstein’s Resolution Maxwell’s equations correct Maxwell’s equations correct Classical mechanics incorrect when v approaches c Classical mechanics incorrect when v approaches c No aether, no absolutes No aether, no absolutes

1905 Relativity Paper Profound and remarkable despite no references to contemporary research Profound and remarkable despite no references to contemporary research Only acknowledgement to Besso Only acknowledgement to Besso Theory of principle (Einstein) vs. constructive theories (Lorentz) Theory of principle (Einstein) vs. constructive theories (Lorentz)

Time Dilation/Length Contraction u.au/einsteinlight/ u.au/einsteinlight/ u.au/einsteinlight/ u.au/einsteinlight/ Proper times are dilated- a clock moving close to the speed of light will appear to run more slowly to a “stationary” observer Proper times are dilated- a clock moving close to the speed of light will appear to run more slowly to a “stationary” observer Moving objects will appear shorter Moving objects will appear shorter

Direct Confirmation Bruno Rossi confirms time dilation for high speed radioactive particles in 1941 Bruno Rossi confirms time dilation for high speed radioactive particles in 1941

Lorentz Transformations Used to transcribe an event in one inertial frame to another Used to transcribe an event in one inertial frame to another When v/c <<1, Newtonian transformation applies When v/c <<1, Newtonian transformation applies x’= γ(x-vt) or x’=x-vt for Newton y’=yz’=z t’= γ(t-vx/c2) or t’=t for Newton γ = 1/(√1-(v/c)2), approaches 1 for low velocities

“I have no particular talent, “I have no particular talent, I am merely extremely inquisitive.”