ASTRONOMY 9: HISTORY OF COSMOLOGY

Handout #18

J. E. Baker
UC Berkeley, Spring 2000

Physics Before the Twentieth Century

1.

The Nature of Light: Electromagnetism

• Cosmology depends on observations: light tells us about the universe
• Important to understand something about the nature of light
• How fast does it move?
  • Before 1650: infinite speed?
  • Ole Romer (1656)
    • Jupiter's moons seemed 11 minutes ``ahead of schedule'' when Earth is closer to Jupiter, ``behind schedule'' when farther
  • Aberration of starlight (see previous lecture notes)
  • From 1850: lab measurements by Fizeau, Michelson, and others using rotating wheels and mirrors
  • Note: today we can't measure the speed of light any more!
    • It is defined to be c=299,792,458 m/s
    • Note 1 second is defined using the frequency of a specific atomic transition (``atomic clock'')
    • Thus, c really defines the meter
    • Before 1960s, meter was a rod in Paris! Kilogram is still a lump of stuff there
    • Connection between French Revolution and metric units (1790s)
  • Implication of finite speed of light: looking out into space is looking back in time!
• What is light ``made of''?
  • Newton: ``corpuscles'' (particles)
  • Huygens, Hooke, Halley: waves
  • 1803: Thomas Young double-slit experiment
    • Pass light through two narrow slits in a plate
    • Get interference pattern
    • Seems to prove that light is a wave...
  • Electric Fields
    • 1789: Charles Coulomb shows two electric charges exert a force on each other:
      
      
      

    • Like gravity (1/r²), but charges can either attract or repel
    • Opposite (+/-) charges attract, like charges repel
    • Michael Faraday (1791-1867) suggests idea of field
    • Charges ``disturb'' space around them so that other charges feel a force
    • Direction of field lines = direction of force
    • Force is stronger when field lines close together
  • Magnetic Fields
    • Magnetism also attractive or repulsive: poles (N/S) instead of charges
    • Unlike electric charges, magnetic poles always seem to come in pairs: no one has found a magnetic monopole
    • Can also describe using concept of fields
    • Compass needle lines up with field lines
    • Magnetism and electricity seem like separate phenomena, but they are not!
  • Electromagnetism
    • 1820: Oersted discovers moving charges create magnetic field!
    • 1831: Faraday discovers moving magnets create electricity!
    • Electric and magnetic fields related by motion
    • 1862: James Clerk Maxwell unites electricity and magnetism together as electromagnetism
    • Maxwell predicts accelerating charges produce electric and magnetic fields
    • This pair of fields travels together through empty space at speed of light!
    • Light is therefore an electromagnetic wave
• Properties of waves
  • Amplitude: height of peak above midpoint
  • Wavelength ($\lambda$): distance between peaks (or troughs)
  • Frequency (f or $\nu$): Sit at a point and count the number of waves that go by per second
  • $\lambda = c/f$ (just like dist = speed $\times$ time)
  • Doppler Effect (1842, Christian Doppler, Austria)
    • Waves from a source moving towards or away from you change wavelength
    • Example: Pitch of train whistle higher when approaching than when receding
    • Approaching sources have shorter $\lambda$ (higher f), receding have longer $\lambda$ (lower f)
    • In Newtonian physics,
      
      
      
      $\Delta\lambda$ is the change in wavelength, $\lambda$ is the wavelength when the source is not moving, v is the speed of the source towards or away from the observer, and c is the speed of the waves (could be sound, light, or whatever)
  • Most waves require a medium to propagate through (e.g., sound in air, waves in water)
  • Light was thought to travel though some unknown ``ether''
  • Maxwell shows that light waves can actually propagate through empty space!

2.

Light and Astrophysics

• Newton: white light is a combination of all colors
• Can be split using a prism
• In modern astronomical instruments, diffraction grating (a flat surface with narrow grooves) replaces prism
• Spectrum: visible light is only a very small part! ( $\lambda \approx$ 300-700 nm, where nm = nanometer = 10^-9 m)
• Increasing wavelength: Radio, Infrared, Visible, Ultraviolet, X-ray, Gamma-ray
• Joseph Fraunhofer (1815): spectrum of sunlight has hundreds of narrow dark lines!
• Lines at these specific wavelengths must have been absorbed
• Bunsen and Kirchoff (1850s): light from burning different chemical elements produces unique sets of spectral lines (``fingerprint'')
• Allows identification of chemical composition of elements in the sun, stars, and nebulae
• Elements are the same as those found on Earth!
• Absorption spectra: dark lines against bright continuous spectrum
• Emission spectra: bright lines against dark
• Relationship between these not well understood until later...
• Using the ``fingerprints'', can use Doppler effect to measure speeds at which planets, stars, galaxies, etc. are moving towards or away from us!

3.

The Nature of Heat: Thermodynamics (19th Century)

• Tied to problems of Industrial Revolution: production of efficient mechanical engines
• First Law: conservation of energy
  • Energy can change into different forms, but is never created or destroyed
  • Energy of a closed system is constant
• Second Law: entropy does not decrease in a closed system
  • Entropy is a measure of
    • The disorder of a system
    • Generally, the more information something contains (or the more complex it is), the lower its entropy is
    • Probability: there are many more ways (``states'') to arrange something in a disordered way than in an ordered way
    • Example: monkeys at a typewriter: you have to wait almost forever (10<sup>122</sup> years) before they'll produce the works of Shakespeare!
  • No ``free lunch'': can't make a perpetual motion machine to produce energy for free
  • Note: only applies to closed systems; increasing complexity of life does not violate the Second Law
  • Connection with arrow of time: universe doesn't look the same if run backwards
  • May have implications for (im)possibility of life 100s of billions of years in future
• Somewhat depressing subject; Boltzmann committed suicide!
• Third Law: Absolute zero (0 K $\approx -273^\circ$ C $\approx -459^\circ$ F) results if all thermal motion stops
  • Heat is really the statistical jiggling of particles
  • Faster jiggling means higher temperatures
• Study of thermal radiation
  • Blackbody: an object that absorbs all radiation that hits it
    • Blackbodies are perfect absorbers (no light is reflected)
    • They are also perfect emitters!
  • Spectrum from such an object is very simple: only depends on temperature T (not composition or anything else)
  • Shape is always the same, but higher T means more light of all frequencies is emitted
  • Higher T also moves the peak to shorter $\lambda$ (higher f or ``bluer'' color)
  • Need to heat to several thousand degrees to get much visible light; room temp. gives infrared

4.

Problems at the End of the 19th Century

• Some people (e.g., Planck's teacher) claimed interesting problems in physics were all solved, mere details remaining!
• But these ``details'' led to revolutions in the 20th century...

(a)

Maxwell's electromagnetism inconsistent with Newtonian physics?

• Equations predict light is an EM wave with velocity c
• Galilean relativity: velocities simply add
• Imagine light shining forward from a train moving at speed v
• Observer on the ground would see speed c + v
• Which speed of light to use in Maxwell's eqns., c or c + v??
• Does ``ether'' define an absolute rest frame?

(b)

Michelson-Morley Experiment (1887)

• Purpose: find the mysterious ``ether'' which fills space
• Idea: if we consider Earth's motion through ether, light will seem to travel at different speeds in different directions
• Result: No difference!! Who is wrong: Maxwell or Newton??

(c)

The ``Ultraviolet Catastrophe''

• Study thermal radiation coming from a blackbody
• Classical physics predicts it will radiate an infinite amount of energy, most at short wavelengths
• Obviously absurd, what is going on??

(d)

First Cosmological ``Age Problem''

• Lord Kelvin and Helmholtz compute age of Sun is 100 million years
  • Assumed it only gets energy from gravitational contraction
  • Didn't know about nuclear physics (20th century): real source of energy is nuclear fusion and age is 5 billion years
• Geologists dating rocks found Earth is much older than 100 million years
• Darwin: also need a long time for species to evolve
• How could Earth be older than Sun?!?

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