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## The Story of the Quantum

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**The Story of the Quantum**量子的故事 張志義 Cheung, Chi-Yee 2007.10.13Academia Sinica**In the past century, the progress in physics is tremendous:**Elementary particles, atoms, nuclei, solid states, …, cosmology Physics Technologies Our lives World**Pillars of modern physics:**(1) Relativity (2) Quantum theory …**Theory of Relativity (1905, 1915):**Structure of space-time Motion at high speeds Well accepted by everybody! C = constant V < C event 3-d space + time = 4-d space-time**Physics of the microscopic world**Quantum Theory (1901-1930) Predictions are all correct, but … Underlying physics is controversial! “Wavefunction” g.s. ~ 0.1 nanometer ~**“Quantum mechanics: Real black magic calculus”**--- Albert Einstein (1879-1955, German, Swiss, US) Nobel Prize: 1921 (for photoelectric effect) 1999**"And anyone who thinks they can talk about**quantum theory without feeling dizzy hasn't yet understood the first thing about it." --- Niels Bohr(1885-1962, Danish) Nobel Prize: 1922 (for atomic model)**“I think I can safely say that no one understands**quantum mechanics” --- Richard Feynman (1918-1988, American) Nobel Prize: 1965 (for QED)**WHY did great physicists have trouble**with Quantum Theory? • NOT difficulties in mathematics (2) Didn’t know how to interpret the results**The Quantum Revolution:**Began 1901: Max Planck (German, 1858-1947) Nobel Prize: 1918 Ended 1930: Paul Dirac (English,1902-1984) Nobel Prize: 1933**George Gamow (1904-1968, Ukrainian, US)**1901-1930 1948: CMB T~ Expt. 2.7 K (1965) Alpha-Bethe-Gamow 1965**Physics at the end of 19th century**Issac Newton (1643-1727) 1687: Principia (Philosophiae Naturalis Principia Mathematica) Alexander Pope: “Nature and nature's laws lay hid in night; God said "Let Newton be" and all was light.”**Leonhard Euler**(1707-1783, Swiss) Joseph-Louis Lagrange (1736-1813, Italian French) Pierre-Simon Laplace (1749-1827, French) William Hamilton (1805-1865, Irish)**A mechanical, deterministic world view:**Laplace (~1800): A being equipped with unlimited computational power, and given complete knowledge of the positions and momenta of all particles at one instance of time, could use Newton’s equation to predict the future and retrodict the past of the whole universe with certainty.**Statistical mechanics:**Ludwig Boltzmann(1844-1906, Austrian) --- Boltzmann equation (1872) --- (1877) Willard Gibbs(1839-1903, American) --- Gibbs ensembles (1876)**James Maxwell (1831-1879)**“Treatise on Electricity and Magnetism” (1873) Maxwell’s equations (1864): --- Unification of Electricity and Magnetism --- Maxwell eq. wave equation wave velocity=speed of light Light is electromagnetic wave**Thus, at 1900, it seems that the classical theories of**Newton and Maxwell are able to explain everything on earth and in the sky. Well, almost … Cracks in classical physics: (1) Nature of light (2) Blackbody radiation (3) Spectrum of hydrogen**Nature of Light: Particle or wave?**Newton: Particle (1643-1727, English) Christiaan Huygens: Wave (1629-1695, Dutch)**Thomas Young (1773-1829, English)**“The last person who knows everything” • Double slit (1801) • Young’s Modulus • Vision of color • Translation of Rosetta stone (1819) http://en.wikipedia.org/wiki/Thomas_Young_%28scientist%29**Waves interfer:**(1) Flickr: naughton321 (2) Flickr: Mr. 7**Black-body radiation**A blackbody is a theoretical object which absorbs radiation of all wavelengths.(Reflects nothing, therefore black) (Jean-Rayleigh Ultraviolet catastrophe) Black-body Temp = T**Birth of the quantum**Max Planck (1858-1947, German) Nobel Prize: 1918 (1901, Berlin) So, light is also particles!**(2) Photoelectric effect**(first observed 1839 by Becquerel ) Critical frequency Below: no emission, no matter how intense Above: emission, even weak**Albert Einstein (1879-1955, German, Swiss, US)**• 1905 (annus mirabilis, year of wonders) • Brownian motion • Photoelectric effect • Special relativity Note: In 1905, he was a third-class examiner in the Patent Office in Berne, i.e., an amateur physicist!**Explanation of photoelectric effect**W = Work function = Minimum energy needed to kick out an electron Therefore, if E < W, no electron at all if E > W, some electrons, no matter how dim is the light Again, light is particles, not wave!**Spectrum of Hydrogen**Johann Balmer(1825-1898, Swiss) Bamler Series (1885): No one cared much about this result in 1885, because no one knew what atoms are!**Note:**Electron (1897): J. J. Thomson (1856-1940, English) Nobel prize: 1906 Nucleus(1911): Ernest Rutherford (1871-1937, NZ, English) Nobel prize: 1908 (Chemistry - chemistry ofradioactive substances)**plum pudding**Atomic models Electron: J. J. Thomson, 1897 Nucleus: E. Rutherford, 1911 Problem: circulating electron radiates! How does one stablize the atom?**--- Niels Bohr(1885-1962, Danish)**Nobel Prize: 1922 (for atomic structure) The Bohr atom (1913) Semi-classical model of H atom: rules, not theory!**1914, Bohr became famous after the success of his atomic**model, and the Royal Danish Academy of Science gave him financial support to set up an Physics Institute. The fund was actually donated by Carlsberg Brewery (beer)! The Institute quickly became the center of quantum science in the 1920s and 1930s, due to Bohr’s genius and his personality.**Birth of Quantum Theory (1925)**Werner Heisenberg (1901-1976, German) Nobel Prize: 1932 Matrix Mechanics: Matrices: p and x are represented as matrices of infinite dimension Then he was able to explain the spectrum of hydrogen!**Wave Mechanics(precursor)**1924: Louis de Broglie(1892-1987, French) Nobel Prize: 1929 Ph.D. thesis: Electron as wave If undulating light has particle nature, may be particles like electrons have wave properties too!**Wave Mechanics (1926)**(a few months after Heisenberg) Erwin Schrodinger (1887-1961, Austrian) Nobel Prize: 1933 Schrodinger Equation: The state of a particle is represented by a “wavefunction” which satisfies Where H(p,x) It was also able to explain the spectrum of hydrogen!**The state of a particle is represented by a wavefunction**called It contains everything you can know about the particle However, from the existence of “i”, we know that cannot be a real wave (like water waves). It is only a tool for predicting experimental results!**Note:**• 1925: Heisenberg was recuperating in a North Sea island after an severe attack of hay fever. (summer, 1925) • 1926: Schrodinger was recuperating in Arosa (a Swiss 1700m alpine resort) due to suspected tuberculosis, in the company of a girlfriend. (Christmas, 1925- early 1926) (The identity of the lady of Arosa was never known.)**Max Born (1882-1970, German)**Nobel Prize: 1954 Paul Dirac(1902-1984, English) Nobel Prize: 1933 Theories of Heisenberg and Schrodinger are in fact equivalent!**Relativistic quantum mechanics**(Schrodinger equation + special relativity) Paul Dirac (1928) Dirac equation --- for electron, not photon --- gives the correct magnetic moment But… It had negative energy solutions!**Dirac:**All the negative levels have already been occupied by other electrons! Pauli principle then excludes other electrons from these levels. (1) One-body becomes many-body… (2) Is the negative electron sea observable?**Dirac said yes!**Dirac: hole = proton (In the old days, physicists are much more conservative at proposing new particles.) In 1932 Carl Anderson found positron (1905-1991; Nobel prize: 1936)**Later we found that “Dirac sea” is actually not**necessary! So, sometimes one could get the right answer for the wrong reason! (That is, if you are clever enough!)Story: Dirac and fish**Nobel Prizes:**1932: W. Heisenberg "for the creation of QM…" 1933: E. Schrodinger and P. Dirac "for the discovery of new productive forms of atomic theory" Prizes conferred in the same year 1933 (no prize given in 1931 and 1932)**W. Pauli: Heisenberg over Schrodinger**• Matrix mechanics precedes wave mechanics. • Matrix mechanics is more original, for wave mechanics relies on the idea of de Broglie. • Einstein: Schrodinger over Heisenberg “I have the impression that the concepts created by him (Schrodinger) will extend further than those of Heisenberg.”**Heisenberg:**Schrodinger: Given the choice, which would you choose?**As we shall see, the physical principle presented by QM is**so revolutionary that it totally changed our understanding of nature forever! Deterministic vs Probabilistic (classical) (quantum)**Quantum mechanics so successful that**it can explain all quantum phenomena! Superposition Principle However, QM itself needs an interpretation itself!Why? What is ???**What is this thing called wavefunction?**Copenhagen Interpretation (1927): Max Born Heisenberg Bohr**Remember: Newtonian mechanics**is deterministic! Probability occurs in Newtonian mechanics Too, but in a different context, e.g. dice • = Probability density Probability = (2) Measurement (or disturbance) causes wavefunction collapse.