Relativity

Einstein’s solution: Two principles

Principle of Relativity:

All of the laws of physics are the

same for any two observers

moving at constant relative speed

Principle of Constancy of Speed of Light:

All observers see the same speed of light, no matter their relative

velocities.

Requires re-thinking of basic physics from the ground up

Requires re-thinking of nature of time and space

Time moves at different rates for different observers

Quantum Mechanics

The other great theory of modern physics

Deals with very small objects

Electrons, atoms, molecules

Grew out of problems that seemed simple

Black-body radiation

Photoelectric Effect

Atomic Spectra

Produces some very strange results…

Blackbody Radiation Light emitted by hot object

Depends only on temperature

Characteristic spectrum of light

Blackbody Radiation

Max Planck, 1900

Developed mathematical formula for spectrum

Problem: Derivation of formula required a mathematical trick

Introduced idea of “quantum” of energy

Completely overturned classical physics

Blackbody Model Imagine object as box with “oscillators” in walls

Small amount of light leaks out blackbody spectrum

What radiation exists in box?

“Standing wave” integer number of half-wavelengths

fit across the length of the box

(Rayleigh-Jeans approach; slightly different than Planck, but simpler)

Add up all allowed modes to get total spectrum

Divide thermal energy of object among possible modes

Standing Waves

Ultraviolet Catastrophe

Problem: Lots and lots of ways to get short wavelengths

Wavelength (box length)

0.0 0.2 0.4 0.6 0.8 1.0

Nu

mb

er

0

20

40

60

80

100

120

200 modes, 0.02L bins Predicts huge

amount of light at very

short wavelengths

Quantum Hypothesis

Planck’s trick:

Each mode has a minimum energy depending on frequency

Can only contain an integer multiple of fundamental energy

Modes with very short wavelength would need more than their

share of thermal energy

Amount of radiation drops off very sharply at short wavelength

Energy Partition

6 quanta

3 quanta

2 quanta

1 quanta

0 quanta

Blackbody Spectrum

Photoelectric Effect

Shine light on some object,

electrons come out

Discovered by Heinrich Hertz, 1887

Simple model: Shaking electrons

Predict: 1) Number of ejected electrons depends on intensity

2) Energy of ejected electrons depends on intensity

3) No obvious dependence on frequency

Photoelectric Effect: Experiment Observations:

1) Number of electrons

depends on intensity

2) Energy of electrons DOES

NOT depend on intensity

3) Cut-off frequency:

minimum frequency to get

any emission

4) Above cut-off, energy increases linearly

with frequency

Photoelectric Effect: Einstein Einstein, 1905: “Heuristic Model” of PE Effect

Particle model: “Light quanta” with energy

Some minimum energy to remove electron:

“Work Function”

Energy of emitted electron:

Take’s Planck’s “trick” seriously, runs with the idea

Photoelectric Effect: Einstein Observations:

1) Number of electrons depends on intensity

2) Energy of electrons DOES NOT depend

on intensity

3) Cut-off frequency: minimum frequency

to get any emission

4) Above cut-off, energy increases linearly

with frequency

Higher intensity More quanta

Only one photon to eject

Einstein in 1921

Nobel Prize portrait

Cited for PE Effect

Atomic Spectra

Atoms emit light at discrete, characteristic frequencies

Observed in 1860’s, unexplained until 1913

Bohr Model 1913: Neils Bohr comes up with “solar system” model

1) Electrons orbit nucleus in certain “allowed states”

2) Electrons radiate only when moving between allowed states

3) Frequency of emitted/absorbed light determined by Planck rule

Works great for hydrogen, but no reason for ad hoc assumptions

Matter Waves

Louis de Broglie: Particles are Waves

Electrons occupy standing wave orbits

Orbit allowed only if integral number of

electron wavelengths

Wavelength determined by momentum h

p

Same rule as for light…

Matter Waves

de Broglie Waves:

Why don’t we see this?

Planck’s Constant is tiny

h = 6.626 10 –34 J-s

145 g baseball, 40 m/s

= 1.1 10 –34 m

Insignificant for macroscopic objects

More significant for single atoms

87Rb, 200 m/s

= 0.02 nm

Still small, but can

start to see effects

h

p

Electron Diffraction

Image and video from Hitachi:

http://www.hitachi.com/rd/research/em/doubleslit.html

Send electrons at two slits in a barrier:

Fullerene Diffraction

http://commons.wikimedia.org/wiki/

File:Fullerene-C60.png

Fig. 7 in the paper, "Quantum interference experiments with large molecules,"

by Nairz, Arndt, and Zeilinger (Am. J. Phys 71, 319 (2003)).

Big Molecules

430 ATOMS

Light as a Clock

Light: Electromagnetic wave

Extremely regular oscillation

No moving parts

Use atoms as a reference:

Performance: Lose 1s in 100,000,000 years