Copenhagen
An appetizer of physics and history
"The heart of Copenhagen
 is how we know why
 people do what they do,
 and even how one knows
 what one does oneself."
   ...
4 Big Physics Ideas in
       the Play

Uncertainty — Heisenberg

Complementarity — Bohr

Relativity — Einstein

Measureme...
“Yes, Heisenberg, but...”
Development of QM

Ideal gas

Equipartition   all molecules eventually end
up in distribution around same kinetic energy

...
Ultraviolet catastrophe
Max Planck
Postulated quantization of
energy in 1900

Radiant energy only comes in
packets of size hν

With this restricti...
Development of QM

Thomson separates electrons from ions in
1897, “plum pudding” model of atom
Development of QM


Bohr, 1911: quantize energy of electrons, too
  kicked out of Thomson’s group, joins
Rutherford, who h...
Development of QM
Bohr model, 1913: stable atoms, hydrogen
spectrum
Development of QM

de Broglie waves, 1925

Pauli exclusion principle, 1925

Goudsmit and Uhlenbeck, spin, 1925
Development of QM

Schrödinger, 1926: wave mechanics

Heisenberg, 1926: matrix mechanics

Give same results, but conceptua...
Uncertainty
Uncertainty for bullets
 ΔpΔq ≃ h = 6.6 x 10-34 J s = 6.6 x 10-34 kg m2 s-1

 Mass of bullet is about 0.010kg, so for bull...
Uncertainty for atoms
Mass of electron is 10-30 kg

Thus ΔvΔq ≃ 6.6 x 10-4 m2 s-1

For electron confined in atom of size Δq...
Complementarity

An object has both wave and particle
properties, but both cannot be observed at
the same time

Double sli...
Double slit experiment
History

Bohr, Fermi in Washington in 1939 at conference

News came to Bohr by telegram of Frisch and
Meitner’s discovery ...
History
Results of Manhattan Project — enough     235U   to build a bomb,
Trinity test in NM, Hiroshima, Nagasaki

Germans...
History
Bohr’s 11 draft letters
to Heisenberg, 1957-62,
released in 2002 (after
Copenhagen written)

Bohr says Heisenberg
...
History

Heisenberg took many trips for Cultural
Division of German Foreign Service, not just
to visit Bohr

Told Dutch co...
German project failed — why?

  Heisenberg sabotaged it?

  Heisenberg was only a theorist, and could not do the
  mammoth...
Uncertainty?
Still at the heart of history, as well as at the
             heart of Copenhagen!
Copenhagen, Michael Frayn, with Postscript, 1998

Thirty Years That Shook Physics, George Gamow, 1966

The Making of the A...
Copenhagen Presentation 100225
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  • Bohr godfather of quantum mechanics, Bohr model of atom, leader of group that developed quantum mechanics. “Copenhagen interpretation” because it was developed at his Institute in Copenhagen, from approximately 1924-27.

    Heisenberg known as very fast thinker and worker--almost too fast for his own good. Story in play of Heisenberg doing uncertainty while Bohr skiing in Norway and submitting the paper before Bohr returned—Bohr very upset.

    Bohr known as slow and plodding, but got through to every implication of the work. Famous for innumerable drafts of his papers, all typed by Margrethe. Bohr kidded in play about how slowly he skis, and about drafts.




















  • Copenhagen Presentation 100225

    1. 1. Copenhagen An appetizer of physics and history
    2. 2. "The heart of Copenhagen is how we know why people do what they do, and even how one knows what one does oneself." Michael Frayn
    3. 3. 4 Big Physics Ideas in the Play Uncertainty — Heisenberg Complementarity — Bohr Relativity — Einstein Measurement
    4. 4. “Yes, Heisenberg, but...”
    5. 5. Development of QM Ideal gas Equipartition all molecules eventually end up in distribution around same kinetic energy “Gas” of radiant energy “UV catastrophe”
    6. 6. Ultraviolet catastrophe
    7. 7. Max Planck Postulated quantization of energy in 1900 Radiant energy only comes in packets of size hν With this restriction, you get the observed distribution!
    8. 8. Development of QM Thomson separates electrons from ions in 1897, “plum pudding” model of atom
    9. 9. Development of QM Bohr, 1911: quantize energy of electrons, too kicked out of Thomson’s group, joins Rutherford, who has discovered nucleus Nucleus + orbiting electrons + classical EM radiation atom lifetime of ~10-8 seconds
    10. 10. Development of QM Bohr model, 1913: stable atoms, hydrogen spectrum
    11. 11. Development of QM de Broglie waves, 1925 Pauli exclusion principle, 1925 Goudsmit and Uhlenbeck, spin, 1925
    12. 12. Development of QM Schrödinger, 1926: wave mechanics Heisenberg, 1926: matrix mechanics Give same results, but conceptually very different In 1927 Schrödinger proved they are identical!
    13. 13. Uncertainty
    14. 14. Uncertainty for bullets ΔpΔq ≃ h = 6.6 x 10-34 J s = 6.6 x 10-34 kg m2 s-1 Mass of bullet is about 0.010kg, so for bullet ΔvΔq ≃ 6.6 x 10-32 m2 s-1 Muzzle velocity of bullet is about 1000 m s-1 (~2200 miles per hour), so if we know the bullet velocity to a part in 1012 (~±1mm per century!), Δv = 10-9 m s-1 Δq ≃ 6.6 x 10-23 m Atomic nucleus is ~10-15 m across, so uncertainty is insignificant for macro-sized objects
    15. 15. Uncertainty for atoms Mass of electron is 10-30 kg Thus ΔvΔq ≃ 6.6 x 10-4 m2 s-1 For electron confined in atom of size Δq ≃ 10-10 m, Δv ≃ 6.6 x 106 m s-1 This gives ΔKE of ~ 10 eV, or on the order of the electron’s binding energy! Orbits along lines are nonsensical — don’t know where electron is going next
    16. 16. Complementarity An object has both wave and particle properties, but both cannot be observed at the same time Double slit experiment — Heisenberg’s “Swerve left? Swerve right? Or think about it and die? In your head you swerve both ways...”
    17. 17. Double slit experiment
    18. 18. History Bohr, Fermi in Washington in 1939 at conference News came to Bohr by telegram of Frisch and Meitner’s discovery of fission by fast neutrons Gamow says implications discussed and understood by all at conference Einstein writes to Roosevelt, 1939 Manhattan Project, Robert Oppenheimer, 1941-45
    19. 19. History Results of Manhattan Project — enough 235U to build a bomb, Trinity test in NM, Hiroshima, Nagasaki Germans working on Pu bomb, heavy water moderated reactor for Pu production German team captured, held at Farm Hall in England, recorded — they heard of Hiroshima while in captivity Heisenberg describes Hiroshima bomb, 235U critical mass to Gerlach, apparently for first time Farm Hall transcripts support the “we didn’t want to succeed” version, but they are after the fact and after the horror of Hiroshima
    20. 20. History Bohr’s 11 draft letters to Heisenberg, 1957-62, released in 2002 (after Copenhagen written) Bohr says Heisenberg sure of German victory, and that if the war lasted long enough it would be decided by nuclear weapons
    21. 21. History Heisenberg took many trips for Cultural Division of German Foreign Service, not just to visit Bohr Told Dutch colleagues in 1943 that either Germany or Russia would dominate Europe, and Germany would be better for them
    22. 22. German project failed — why? Heisenberg sabotaged it? Heisenberg was only a theorist, and could not do the mammoth engineering required? Heisenberg was too cocky, and didn’t do the calculations? Germany pursued jets and rockets instead? Heisenberg used fission as a means to a prestige appointment, then moved back to doing basic physics?
    23. 23. Uncertainty? Still at the heart of history, as well as at the heart of Copenhagen!
    24. 24. Copenhagen, Michael Frayn, with Postscript, 1998 Thirty Years That Shook Physics, George Gamow, 1966 The Making of the Atomic Bomb, Richard Rhodes, 1987 The Feynman Lectures on Physics, 3 volumes, Richard Feynman, 1965 “Werner Heisenberg and the Uncertainty Principle”, http://www.aip.org/history/heisenberg Bohr’s draft letters, http://nba.nbi.dk/papers/ introduction.htm

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