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

The background The background to and essentials to and essentials

of special of special relativityrelativityRory Makielski, Sally Salvador

March 28, 2006

Albert EinsteinAlbert Einstein

1879 – 19551879 – 1955

Modern scientific geniusModern scientific genius

HumanitarianHumanitarian

The early yearsThe early years

Born in Ulm, GermanyBorn in Ulm, Germany Early education was too Early education was too

oppressiveoppressive Early interest in scienceEarly interest in science

Compass needleCompass needle ““Something deeply hidden had Something deeply hidden had

to be behind things.”to be behind things.” Euclidean geometryEuclidean geometry

““This lucidity and certainty This lucidity and certainty made an indescribable made an indescribable impression upon me.”impression upon me.”

AccomplishmentsAccomplishments 1900- earns degree 1900- earns degree

from Swiss Federal from Swiss Federal Polytechnic School in Polytechnic School in ZurichZurich

1901- claims Swiss 1901- claims Swiss citizenship, works as citizenship, works as patent examinerpatent examiner Michelangelo Besso Michelangelo Besso

(1873 – 1955)(1873 – 1955) 1905 – publishes 1905 – publishes

dissertation on dissertation on determining molecular determining molecular dimensions and four dimensions and four more papersmore papers

Annalen der PhysikAnnalen der Physik ““On a Heuristic Viewpoint Concerning the On a Heuristic Viewpoint Concerning the

Production and Transformation of Light”Production and Transformation of Light” Describes photoelectric effect based on Describes photoelectric effect based on

light quanta (Nobel Prize, 1921)light quanta (Nobel Prize, 1921) ““On the Movement of Small Particles On the Movement of Small Particles

Suspended in a Stationary Liquid Demanded Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat”by the Molecular Kinetic Theory of Heat” Brownian motion, existence of atomsBrownian motion, existence of atoms

““On the Electrodynamics of Moving Bodies”On the Electrodynamics of Moving Bodies” Special theory of relativitySpecial theory of relativity

““Does the Inertia of a Body Depend Upon Its Does the Inertia of a Body Depend Upon Its Energy Content?”Energy Content?” Equivalence of energy and matterEquivalence of energy and matter

Duality of personalityDuality of personality

Poor student, but interested in Poor student, but interested in sciencescience

passion for social justice but lacked passion for social justice but lacked personal relationships and state personal relationships and state loyaltyloyalty

Indifferent toward outside opinionIndifferent toward outside opinion

The HumanitarianThe Humanitarian Pacifist, democratic Pacifist, democratic

socialistsocialist ZionismZionism Used scientific prestige Used scientific prestige

to promote his social to promote his social causecause

Anti-Einstein groupsAnti-Einstein groups 1930’s, Hitler purges 1930’s, Hitler purges

universities of Jewsuniversities of Jews 1939, urges FDR to 1939, urges FDR to

develop atom bombdevelop atom bomb Civil Rights MovementCivil Rights Movement

Religious & Philosophical Religious & Philosophical InfluencesInfluences

"I believe in Spinoza’s God who reveals "I believe in Spinoza’s God who reveals himself in the orderly harmony of what himself in the orderly harmony of what exists, not in a God who concerns himself exists, not in a God who concerns himself with the fates and actions of human beings."with the fates and actions of human beings."

Logical positivismLogical positivism Free invention of mind + experiments = Free invention of mind + experiments =

general theoriesgeneral theories Hume, Mach, PoincaréHume, Mach, Poincaré

Skeptical, criticalSkeptical, critical

Skepticism on Classical Skepticism on Classical PhysicsPhysics

Maxwell, LorentzMaxwell, Lorentz Asymmetry between reference Asymmetry between reference

framesframes GedankenexperimentGedankenexperiment

““Simultaneity”Simultaneity”

Definition of Simultaneity based on Definition of Simultaneity based on round trip of light from A to Bround trip of light from A to B

Assumes constancy of cAssumes constancy of c

Leads to Lorentz transformations Leads to Lorentz transformations (discussed later)(discussed later)

Constant Speed of Light?Constant Speed of Light? The speed of light is defined as being The speed of light is defined as being

independent of the direction of independent of the direction of propagationpropagation

This is merely a convention, not provable This is merely a convention, not provable experimentallyexperimentally

Other possibilities exist (such as the Other possibilities exist (such as the speed being constant for round trip)speed being constant for round trip)

First AssumptionFirst Assumption

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

The laws of physics the same in all The laws of physics the same in all inertial framesinertial frames

Second AssumptionSecond Assumption

““Any ray of light moves in the Any ray of light moves in the “stationary” system of coordinates “stationary” system of coordinates with the determined velocity c, with the determined velocity c, whether the ray be emitted by a whether the ray be emitted by a stationary or by a moving bodystationary or by a moving body””

The speed of light has the same The speed of light has the same value for all observersvalue for all observers

Dilemma for Classical Dilemma for Classical MechanicsMechanics

Newton’s laws of Newton’s laws of motionmotion

Maxwell’s equationsMaxwell’s equations Classical concepts of Classical concepts of

space time space time Taken together, imply Taken together, imply

that it must be that it must be possible to determine possible to determine the velocity of an the velocity of an observer relative to observer relative to lightlight

Not consistent with Not consistent with Einstein’s postulatesEinstein’s postulates

Einstein’s ResolutionEinstein’s Resolution

Maxwell’s equations Maxwell’s equations correctcorrect

Classical mechanics Classical mechanics incorrect when v incorrect when v approaches capproaches c

No aether, no absolutesNo aether, no absolutes

1905 Relativity Paper1905 Relativity Paper

Profound and remarkable Profound and remarkable despite no references to despite no references to contemporary researchcontemporary research

Only acknowledgement Only acknowledgement to Bessoto Besso

Theory of principle Theory of principle (Einstein) vs. (Einstein) vs. constructive theories constructive theories (Lorentz)(Lorentz)

Time Dilation/Length Time Dilation/Length ContractionContraction

http://www.phys.unhttp://www.phys.unsw.edu.au/einsteinlisw.edu.au/einsteinlight/ght/

Proper times are Proper times are dilated- a clock dilated- a clock moving close to the moving close to the speed of light will speed of light will appear to run more appear to run more slowly to a slowly to a “stationary” “stationary” observerobserver

Moving objects will Moving objects will appear shorter appear shorter

Direct ConfirmationDirect Confirmation

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

Lorentz TransformationsLorentz Transformations

Used to transcribe an event in one Used to transcribe an event in one inertial frame to anotherinertial frame to another

When v/c <<1, Newtonian When v/c <<1, Newtonian transformation appliestransformation applies

x’= x’= γγ(x-vt) or x’=x-vt for Newton(x-vt) or x’=x-vt for Newtony’=yy’=yz’=zz’=zt’= t’= γγ(t-vx/c2) or t’=t for Newton(t-vx/c2) or t’=t for Newtonγγ = 1/(√1-(v/c)2), approaches 1 for = 1/(√1-(v/c)2), approaches 1 for low velocitieslow velocities

““I have no particular I have no particular talent, talent,

I am merely extremely I am merely extremely

inquisitive.”inquisitive.”