Riding on aLight Beam

Einstein’s SpecialTheory of Relativity

Last time … Discovery of electromagnetism Light as an electromagnetic wave

Frequency, wavelength, amplitude C = f * λ

Spectral lines in light Emission and absorption lines

– Fingerprints of chemical elements Quantum explanation of the lines (Bohr atom)

Light as energy packets (photons) Astrophysics of 1890s

Solar and stellar spectral photography & analysis

Newton and Einstein Both experienced a “Great Year” Both non-typical personalities Both famous during lifetime Both developed new styles of doing

science Both helped define new worldview for

physics and culture more generally

“Classical” reality rejected bythe “moderns” Absolute time and space Measurement unproblematic Deterministic, causal laws Continuously varying processes Objective world, independent of

observer

Albert Einstein (1879-1955) Son of failed businessman Carefree youth in Italy, failed exams Studied physics at ETH Zurich Bern patent officer, 1902-9 Professor in Prague, Zurich, Berlin 1921 Nobel Prize and growing anti-Semitism Emigration to Princeton, 1933 Search for deterministic unified field theory Guru of pacifism, Zionism, A-bomb

See virtual exhibit, “Einstein’s Revolution,” AmericanMuseum of Natural History (www.amnh.org/exhibitions/einstein/revolution/index.php)

The first 1905 paper“On a heuristic viewpoint regarding the

production and transformation of light”(the light quanta paper)

Applied old theory (Planck’s) to old data (Hertz’sphotoelectric effect)

Heuristic = aid to solving a problem, not otherwisejustifiable (makes light quantized particle, not wave)

Controversial challenge to wave theory, not widelyaccepted until 1915 (earns Nobel Prize, 1921)

Frequency of light

E of

ele

ctro

nThreshold

metal

Light Electrons

The second 1905 paperBrownian motion

– Old theory (heat is motion) applied to old data(botanist Robert Brown’s “jumping” pollenparticles, 1827)

– Used statistics to derive atomic parametersfrom measurements of visible motions ofparticles

– Proved existence of atoms (contra Mach’s“positivism”)

Asks simple, yet profound questions

The third 1905 paper (SR) Theory of measurement and how we know,

not a theory about nature Not general relativity (later, 1907-16) Continues style of asking simple, profound

questions Contributions from Mileva Maric?

– “When you’re my dear little wife we’ll diligently workon science together so we won’t become old philistines,right?” Einstein to Maric, 1901

Newton’s implicit theory ofmeasurement

Abolute time and space Instantaneous communicationVelocities addGalileo’s ‘principle of relativity’ (same

physics in inertial reference frames)

Vtrain

vball

Vball = Vtrain + vball

Sue

Joe

“Aether drift” problem, 1880s(do light velocities add?)

Ve = 3 x 104 m/s

c = 3 x 108 m/s

VJan measured = c + Ve?

VJun-measured = c - Ve?

Assume aetherfixed wrt stars

Two ad-hoc solutions to measured “null” result--Earth drags aether around sun?--Length contraction against aether wind?

Sun

Jan

Jun

(longer ruler?)

(shorter ruler?)

Einstein’s “Electrodynamcisof Moving Bodies” (1905) Asymmetries in Maxwell equations

no absolute rest with with respect to an aether

Begins with two postulates I. Principle of relativity

Physics invariant in inertial reference frames

II. Invariance of speed of light Predicted by Maxwell’s equations

Einstein calls theory the “invariance of light” Planck coined term “relativity” in 1906

Consequences of 2 postulatesElectrodynamics without an aetherNew theory of measurement because

simultaneity becomes relative– Simultaneous = Same time and same place– Arrival of train at 7 means “the pointing of the

small hand on my watch to 7 and the arrival ofthe train [beside me] are simultaneous events”

Moving clocks, lengths, masses change!Holds only for inertial motion (General

Relativity is for accelerated motion)

Relativity of simultaneity

Simultaneity always relative to reference frame!

Thunderbolt 1 Thunderbolt 2

Joe fixed on the landscape (1, 2 same time)

Sue moving on train (first 2, then 1)

Mirrors

Start Later

Time dilation (moving clocksslow down)

VStationary clock, Ts Moving clock, Tm

d

Time = Distance/VelocityTs = 2d/c

Tick

Tock

Let Ts = 1 secIf V = 0.6c, Tm = 1.3 secIf V = 0.8c, Tm = 1.7 secIf V = 0.99c, Tm = 7.1 sec

d

Mirror

!

Tm =Ts

1" v2/c

2

Some algebra yields:

Moving lengths contract

Tick

Tock

V

Stationary length

Movinglength

Ls

Lm

… and moving masses increase:

!

Mm =Ms

1" v2/c

2

!

Lm = Ls 1" v2/c

2 … a little algebra yields:

More consequences of SR E = mc2

“Events” happen in a given place at agiven time (“spacetime”)

Light beamt

xPast

FutureNow

One-Dimensional Spacetime (Minkowski)

“My future”