1900

Planck constant

• The energy of a phonon
• is related to its frequency
• by the Planck constant, h,
• as E = hf.
• Max Planck calculated h
• to explain the nature
• of black-body
• radiation,
• but in 1900
• Planck realized that h
• was the smallest unit
• of action—
• the basis of everything,
• not just photons,
• but all energy
• and all matter.

Planck units

• A natural unit of measurement
• is based on a property of nature.
• A property of nature like
• the least largest unit of motion.
• The dimensions of motion
• are energy and time,
• and its value can be expressed
• in joule-seconds, or in Plancks.
• Fundamental units
• for mass, length, and time,
• therefore, for all physical quantities,
• can be expressed in terms of
• ħ, the reduced Planck’s constant,
• G₀, Newton’s gravitational constant,
• k_e, Coulomb’s constant for electric force,
• k_B, Boltzmann’s constant for kinetic energy,
• and c, the velocity of light.
• These, with clever arrangements
• of powers and roots,
• give us natural units for
• Planck length,
• Planck mass,
• Planck time,
• Planck charge,
• and Planck temperature.

Gyroscope

• Even an imperfect gyroscope
• maintains its vertical to conserve
• angular momentum.
• If you could harness a perfect gyroscope,
• it could turn the hand of a clock
• once every day,
• but the harness would impair
• the gyroscope so that it would thus
• be imperfect.