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Tree of quantum_mechanics2

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Tree of quantum_mechanics2

  1. 1. The Tree of Quantum Mechanics The Tree of Quantum Mechanics by J.THAMBAJI The Roots Electromagnetic Theory 1860 Scientific Method ~1614 The Trunk Hydrogen Atom Model 1913 Blackbody Studies 1859 Branches & Leaves Theory of Everything Electrons are Waves 1923
  2. 2. The Tree of Quantum Mechanics - Overview Often, at this museum, I have used our Spectroscopy Cart to explain to the public how we know what the sun and stars are made of. The explanation involves showing the spectra of a few elements; and explaining that the lines of each are different; so we can tell them all apart. Occasionally, some brash kid (and a few adults) might ask, “why are there lines?”. When I replied that the answer lies within quantum mechanics, the bulk of my audience would plead urgent business somewhere else, and melt away. It’s as if those 2 words somehow caused their critical faculties to shut down, much as “calculus” did a generation or 2 back. To those few who remained, I would offer a historical summary of the main ideas, and those who advanced them. Many thanked me profusely for so opening their eyes.
  3. 3. The Tree of Quantum Mechanics - Overview As most of today’s physics, chemistry, and molecular biology depends on quantum mechanics, as well as many of our gaudiest consumer goods, I felt that a Museum of Nature and Science should attempt to convey the core ideas to the public. The problem is that the field is essentially mathematical; and only a few of our museum staff have the necessary training. This presentation grew out of many discussions between us on what to present, and how. Only you can judge how well we have succeeded. What you will see is in the form of an historical tree, with roots stretching back to Galileo, a trunk embodying the development of the main ideas, and branches and leaves containing modern developments and possible future trends.
  4. 4. The Tree of Quantum Mechanics - Overview Expect no mathematics. On the Tree Menu each box with red text cites a critical development or insight; and is identified by a number on the bottom right. Boxes with green text lead to explanatory and biographical material. The numbers are in a rough historical sequence. Within the text slides you will see arrows to navigate forward through the slides for each topic. To return to the main “Tree” menu click on the tree icon on the bottom right of every slide. Red and green text will link to their corresponding slides in the presentation. We recommend a quick forward stroll through the red boxes, followed by meandering through those green details that pique your interest. Dave Sonnabend and the Museum Staff
  5. 5. Scientific Method ~1614 1 Particle theory of light 1666 2 Conservation of energy 5 Thermodynamics, Statistical mechanics 1824 6 Wave theory of Light 1678 3 Interference 1801 4 Electromagnetic Theory 1860 7 Huyghens Young Faraday Who of Thermodynamics Newton Laws of Physics Galileo Blackbody Studies 8 Ultraviolet Catastrophe ~1880 10 Discrete Energy Levels 1900 12 Photoelectric Effect 1905 13 Hydrogen Atom Model 1913 15 Spectroscopy 1859 9 Discovery of Electrons 1897 11 Discovery of Nucleus 1913 14 Bunsen Thomson Rutherford Kirchhoff Rayleigh Planck Einstein Bohr Electrons are waves 1923 16 Matrix, Wave Mechanics 1925 17 Statistical Interpretation ~1926 19 Quantum Electrodynamics 21 Quantum Chromodynamics 27 Electron Diffraction 1927 18 Modern Chemistry, Molecular Biology 22 Solid State Theory: Semiconductors, Superconductors 23 Astrophysics 24 Weirdness 25 Theory of Everything 28 Periodic Table Gell-Mann, Ne’eman De Broglie Heisenberg Born Feynman, et. al. Special Relativity 1920 20 Nuclear Physics 26 Nuclear Medicine, Weapons, Cyclotrons Click on text to select Who of Statistical Mechanics Maxwell Newton Schrodinger Pauli Dirac Click on text to select
  6. 6. The Tree of Quantum Mechanics If this were a history of science, we would begin millennia earlier, and fill many more pages. However, as quantum mechanics is our theme, we have chosen to begin our story with the intellectual revolution started by Galileo. The road leads through the birth of physics with Newton, the first tentative steps to understanding how the world ticks in the 17th and 18th centuries, and the major leaps forward in the 19th. The direct path to quantum mechanics began with the researches of Gustav Kirchhoff; and if impatience rules your soul, you may skip directly to 8 Blackbody Studies. Else, we recommend a more leisurely stroll through the main growth of physics. 1: The Scientific Method - The Roots
  7. 7. The Tree of Quantum Mechanics 1: The Scientific Method What is today called “The Scientific Method” was first introduced by Galileo. In his several writings, beginning around 1610, he argued that no theory should be accepted without supporting observational evidence. Put differently, if your measurements or observations conflict with your theory, you should modify or reject the theory. You might then hope to find a better theory, consistent with all known measurements and observations. This intellectual philosophy largely arose from his telescopic astronomical observations, which strongly contradicted the thinking of Aristotle (384 BC – 322 BC), as expounded in the “Almagest” of Claudius Ptolemy (~100 – ~170), around 150 AD. - The Roots Portrait of Galileo by Giusto Sustermans, 1636
  8. 8. The Tree of Quantum Mechanics 1: The Scientific Method He found 4 satellites of Jupiter, which plainly didn’t go around the earth. He saw that Venus had phases like the Moon, coinciding with its apparent path near the sun – it clearly orbited the sun. He found mountains on the moon, showing that it wasn’t a “perfect” body. Finally, the sun has spots which come and go, contrary to Aristotle’s view that the heavens are unchanging. All this was a big problem for the Catholic Church, which had slowly adopted Aristotle’s views as dogma, following the persuasive writings of Saint Thomas Aquinas (1224/5 – 1274) in his “Summa Theologica” published over the years 1265 – 1273. - The Roots Observations of Jupiter's moons Phases of Venus
  9. 9. The Tree of Quantum Mechanics - The Roots 1: The Scientific Method Galileo’s thinking was quickly adopted by the intellectual community in Europe, in large part because they were mostly out of the reach of the Catholic Church. While much valuable work had come before, the real flowering of science began here. That the scientific method could spread so easily was, in part, due to the Reformation, begun in 1517, with the publication of the writings of Martin Luther (1483 – 1546). Return to Main Menu Dialogo di Galileo GalileiGalileo discovering the principle of the pendulum
  10. 10. The Tree of Quantum Mechanics - The Roots 1: Galileo Galileo Galilei (1564 – 1642) was born in Pisa, Italia. His early education was at the Monastery of Santa Maria at Vallombrosa, and then at the University of Pisa in medicine in 1581. Lacking interest in this, He left without a degree in 1585, to study privately in philosophy and mathematics. His first discovery was that the period of a pendulum is independent of its amplitude, if it doesn’t swing too far. This finding was to dominate clock design for centuries thereafter. In 1589 he was appointed professor of mathematics at the University of Pisa. His researches there on falling bodies showed that Aristotle’s belief that heavier bodies fall faster was incorrect; but the tale that he demonstrated this by dropping weights from the leaning tower of Pisa isn’t well substantiated. By challenging Aristotle in this and other ways he earned the ire of most of the faculty; and in 1592 he wasn’t reappointed. He left to take up the chair of mathematics at the University of Padua, where he remained till 1610.
  11. 11. The Tree of Quantum Mechanics 1: Galileo The Copernican heliocentric theory had been published in 1543 (De revolutionibus orbium celestium, banned as heretical by the Catholic Church); and by 1595 Galileo was leaning toward it. However, it was the supernova of 1604 that really sparked his interest in astronomy. The invention of the telescope is generally attributed to Hans Lipperhey (1587 – 1619), a Dutch lens maker, in 1608. When Galileo heard of this in the next year, he built his own device, and turned it to the heavens. He was the first to see 4 moons of Jupiter, the rings of Saturn, mountains on the moon, sunspots, and the phases of Venus – all generally incompatible with the teachings of Aristotle (384 – 322 bc) and Claudius Ptolemy (~100 – ~170). He published these findings in The Starry Messenger, which became immensely popular throughout Europe. Cover page from Sidereus Nuncius - The Roots
  12. 12. The Tree of Quantum Mechanics - The Roots 1: Galileo While most intellectuals sided with Galileo, some powerful enemies caused the matter to be referred to the Inquisition. This body held that, as Church doctrine had accepted Aristotle’s teaching, the telescopic evidence was irrelevant, and convicted Galileo of heresy. In 1633 they sentenced him to life imprisonment, more or less enforced until his death. During that period, he wrote Dialogue Concerning the Two Chief World Systems, in which his 3 characters argued for and against heliocentrism, without taking an explicit position. However, Pope Urban VIII saw Simplicio, Galileo’s defender of Aristotle, as himself. The book was banned, and all copies ordered burned. It was smuggled out of Italy, and published in Holland in 1638. As a postscript, the Church formally apologized to Galileo in 1992. While he made several important inventions, and contributed greatly to mechanics, the scientific method and his astronomical discoveries were to remake the world. Return to Main Menu Galileo facing the Roman Inquistion by Cristiano Banti (1857).
  13. 13. The Tree of Quantum Mechanics - The Roots 2: Light is Particles What is light? Many ancients attributed light to particles moving at some extreme speed. But whether these particles originated in the eye, or in the object viewed, was unresolved. In 1666, Isaac Newton allowed sunlight to pass through a small hole in a blind, and fall on a glass prism. It was bent (refracted) there, and again at a second face of the prism. It then fell on a screen, and showed a rainbow of colors (see figure). The setup may be regarded as the first spectroscope. This separation of white light into its many colors is called “dispersion”. Newton thought that light consisted of particles; though why “blue” should bend more in the prism than “green”, and these more than “red”, he couldn’t say. Another difficulty lacking explanation was why intersecting light beams didn’t interact. After all, 2 beams of particles ought to bounce off each other. Not until the 20th century, would these issues be clarified, and in such a way as would have astounded even such an intellect as Newton. Return to Main Menu
  14. 14. The Tree of Quantum Mechanics - The Roots 2: The Laws of Physics That the science of mechanics could be founded on an axiomatic basis was the central accomplishment of Isaac Newton’s illustrious career (see 2: Newton). Part of his inspiration was “Kepler’s Laws” of planetary motion. Johannes Kepler (1571 – 1630), by analyzing the planetary observations of Tycho Brahe (1546 – 1601), certainly the most accurate of the time, determined that elliptical orbits best fit the data. He eventually published his findings as 3 laws: 1. Each planet moves in an ellipse, with the sun at one focus. 2. The radius vector of each planet sweeps out equal areas in equal times. 3. The square of the period of revolution of each planet is proportional to the cube of the mean distance of the planet from the sun. Johannes Kepler , 1610
  15. 15. The Tree of Quantum Mechanics Unlike Newton’s laws to follow, these were purely phenomenological – i.e., they were a straight generalization of Tycho’s observations. As these observations were of the apparent paths of the planets against the background stars as seen from a moving earth, Kepler’s insight was extraordinary. In his early days at Trinity College, Newton collected the known work on mechanics, in large part the writings of Galileo (see 1 Galileo), and formulated his 3 laws of motion. In modern language these are: 1. Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by forces to change that state. 2.Change of motion is proportional to the force and takes place in the direction of the straight line in which the force acts. 3.To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed along the same straight line. - The Roots 2: The Laws of Physics
  16. 16. The Tree of Quantum Mechanics - The Roots 2: The Laws of Physics In addition, his law of gravitation may be stated as, “Between any 2 bodies, there is an attractive force proportional to the product of their masses, and inversely proportional to the square of the distance between them”. Newton published all this in his monumental Philosophiae Naturalis Principia Mathematica, arguably, the most important scientific treatise of all time. Where did he get it? In later life, he said that it came to him while watching an apple fall from a tree. In the book, he used a long set of geometrical arguments based on Kepler’s Laws. However, it’s more likely that he used his own method of fluxions (calculus) to prove it in a few steps from Kepler’s Laws. Sir Isaac Newton's own first edition copy of his Philosophiae Naturalis Principia Mathematica. The book can be seen in the Wren Library of Trinity College, Cambridge.
  17. 17. The Tree of Quantum Mechanics - The Roots 2: The Laws of Physics Later, using only his laws of mechanics and gravitation, Newton proved Kepler’s laws. If this set of advances seems circular, keep in mind that Kepler’s insight was purely phenomenological, i.e., it was based solely on Tycho’s observations. Anyway, the science of physics was firmly underway, and may be said to have begun with the publication of the Principia in 1687. As a postscript, Henry Cavendish (1731 – 1810), in 1798, in an elegant laboratory experiment, managed to measure the constant of proportionality G in Newton’s law of gravitation, thus determining the mass of the sun, earth, and those planets with moons. As we’ll later see, “force” is a concept of classical physics; quantum mechanics views motion quite differently. Return to Main Menu Drawing of torsion balance apparatus used by Henry Cavendish in the 'Cavendish Experiment' to measure the gravitational constant in 1798. This is a vertical section through the apparatus, including the building that housed it.
  18. 18. The Tree of Quantum Mechanics - The Roots 2: Newton Isaac Newton (1642 – 1727) was born at Woolsthorpe Manor, some 100 km northwest of Cambridge. After a rather unhappy, fatherless childhood, his intellectual prowess was noted; and his mother, reluctantly, allowed him to further his education. In 1661, he entered Trinity College, Cambridge, as a “subsizar”, the bottom of their totem pole. He got free board and tuition, in exchange for menial service. In the next year, his first exposure to 17th century mathematics began. In his notebooks, he speculated on many subjects. Perhaps the most forward looking was his geometrical proof of what today is called “the fundamental theorem of the calculus” – essentially that derivatives and integrals, that is, slopes of a curve, and the area under that curve, are inverses of each other; a truly remarkable insight, on which he would later expand. Newton in a 1702 portrait by Godfrey Kneller
  19. 19. The Tree of Quantum Mechanics The years 1664 – 1666 were perhaps the most productive, when he formulated the laws of mechanics and gravitation (see 2: Laws of Physics). In 1665 he graduated with a Bachelor of Arts degree. Also in that year, the bubonic plague reached Cambridge; the University was closed; and Newton returned to Woolsthorpe. There, he performed a number of experiments on the refraction of sunlight in a prism (see 2 Particle Theory of Light). Back in Cambridge, he was elected a minor fellow of Trinity College, which allowed him to remain. A year later he received a Master of Arts, and was elected a major fellow. In 1668, Newton’s professor, Isaac Barrow retired as the first Lucasian Chair of Mathematics, to join the ministry, and recommended Newton to succeed him. Newton held this chair for nearly 30 years. - The Roots 2: Newton
  20. 20. The Tree of Quantum Mechanics - The Roots 2: Newton Just prior to this appointment, Newton designed and built the first reflecting telescope. For the same resolution and light gathering power, it’s much shorter than the Galilean equivalent, which is built entirely of lenses. Lens based instruments suffer from chromatic aberration – variation of focal length with wavelength or color. Today we know that the speed of light in glass, and thus refraction, varies with wavelength. The effect is partly corrected in achromats, doublet lenses made of 2 different kinds of glass, or better (and more expensive) anachromats (triplets). Mirrors aren’t subject to chromatic aberration (see our Telescope Exhibit). Eyepiece Primary Mirror Diagonal Mirror Newtonian Telescope
  21. 21. The Tree of Quantum Mechanics - The Roots 2: Newton Today, most amateur telescopes are based on Newton’s design. Together with other advantages, telescopes with large mirrors have entirely supplanted lens based designs in modern astronomical instruments. In 1671, Barrow took Newton’s telescope to the Royal Society in London. It was so admired, that Newton was promptly elected a fellow. Much later, in 1703, Newton was elected President of the Society, which he ruled with an iron hand. A replica of Isaac Newton's telescope of 1672
  22. 22. The Tree of Quantum Mechanics - The Roots 2: Newton Newton’s advances in mathematics began about this time, including original work on infinite series, and the invention of the binomial theorem and “the method of fluxions”, later called “calculus”. He had started by devouring the works of René Descartes (1596 – 1650), Blaise Pascal (1623 – 1662), and others. Descartes had pioneered coordinate (analytic) geometry, although Newton’s taste later drifted back to the Greek view of the subject. Much later, Karl Friedrich Gauss (1777 – 1855), “The Prince of Mathematicians” referred to Newton as “The First Geometer of His Age”, high praise indeed. Newton in a 1702 portrait by Godfrey Kneller
  23. 23. The Tree of Quantum Mechanics - The Roots 2: Newton Exposure to the larger scientific community brought out the contentious side of Newton – temper; he couldn’t take criticism. Robert Hooke (1635 – 1703) sent him up the wall by disagreeing with his ideas on optics. Later, it went from bad to worse, when Hooke claimed that Newton had stolen some of his ideas, causing Newton to have a complete nervous breakdown. Somewhere around 1675, both Newton and Gottfried Wilhelm Leibnitz (1646 – 1716) developed the differential and integral calculus, leading to further controversy over who was first. Charges of plagiarism went back and forth for several years, adding to Newton’s paranoia. Scholars today are generally agreed that Newton was first; but Leibnitz was first to publish. Isaac Newton, 1689 Gottfried Wilhelm Leibnitz, 1700
  24. 24. The Tree of Quantum Mechanics Of Newton’s many achievements, today we would regard the publication of Philosophiae Naturalis Principia Mathematica in 1687 as number one. This work covered his studies in optics, laid an axiomatic foundation for the science of physics, introduced the law of gravitation, and derived Kepler’s laws of planetary motion (see 2 Laws of Physics). Newton had been quite reluctant to publish his many notes covering this material, but was strongly urged to do so by the astronomer Edmond Halley (1656 – 1742), who corrected the proofs, and saw to its publication. Incidentally, Halley didn’t discover the comet named for him; but he computed its orbit, and accurately predicted its return in 1758. He also showed how to size the solar system through multiple observations of transits of Mercury and Venus across the sun. The method was applied to transits of Venus in 1761 and 1769. - The Roots 2: Newton Return to Main Menu
  25. 25. The Tree of Quantum Mechanics In 1678, Christian Huyghens (1629 – 1695) (see 3 Huyghens) advanced the idea that light consisted of waves. He argued that light traveled slower in glass than in air, with blue light slower than red. This concept of refraction is illustrated in the figure, using the marching men analogy. Rows of soldiers replace the wave fronts of light. At the top, they march on an easy road (air); while at the bottom they slog more slowly through mud (glass). Short soldiers can keep up on the left by taking shorter steps than tall; but have more difficulty in the mud, go slower, and thus diverge from their faster brethren. The distance between wave fronts is the wavelength, shorter in glass and for short soldiers. - The Roots 3. Light is Waves
  26. 26. The Tree of Quantum Mechanics Waves avoid the corpuscle problem of crossing beams. After all, water waves pass through each other without interaction. On the other hand, waves of what? Light reaches us from the sun and stars; so, presumably, there must be something in space to wave. Following Huyghens (and the Greeks), this stuff was called the “ether”, or more pompously, “the luminiferous aether”. Like sound waves, and surface waves in water, light was assumed to be very rapid displacements of the ether. The conflict between waves and particles persisted until 1801 (see 4 Interference), when waves won out. However, a century later, equally compelling evidence favored particles (see 13 Photoelectric Effect); and we had to face the mind wrenching notion that light is both. - The Roots 3. Light is Waves Return to Main Menu
  27. 27. The Tree of Quantum Mechanics Christian Huyghens (1629 – 1695), was a Dutch polymath. He was born in Holland, but spent much of his life in France, even during its war with Holland (1672 – 1678). One of his first achievements was the design and construction of the first truly accurate pendulum clock. Galileo had shown that a pendulum had a quite stable period, provided the amplitude was small (see 1 Galileo). Huyghens showed that by restraining the upper part of the suspending wire by a pair of cycloidal surfaces, the period would be stable over much wider swings. This was analyzed and described in his Horologium Oscillatorium in 1656. - The Roots 3: Huyghens Huyghens in a 1671 portrait by Caspar Netscher
  28. 28. The Tree of Quantum Mechanics His astronomical contributions began by finding an improved method of grinding lenses, somewhere around 1654. He used this to build an improved telescope, with which he discovered Titan, the largest moon of Saturn in 1655; and in 1659, he showed that Saturn’s rings are truly circular. As a postscript, the European spacecraft Huyghens was carried to Saturn by the NASA spacecraft Cassini, where it landed on Titan, greatly improving our knowledge of that body. Huyghens is probably best known for his studies of light, which, unlike Newton, he regarded as made up of waves. In this view, each point on an expanding wave front is the source of a spherically expanding wavelet; the envelope of the wavelets is the wave front. Following the discovery of interference (see 4 Interference) by Thomas Young (see 4 Young) in 1801, this view was to dominate physics until quantum mechanics came along a century later. - The Roots 3: Huyghens Return to Main Menu
  29. 29. The Tree of Quantum Mechanics - The Roots 4: Interference In 1801, Thomas Young (1773 – 1829) (see 4 Young) performed an experiment that essentially demolished Newton’s corpuscular theory of light. In his original setup, he allowed sunlight to fall on a screen with a pinhole. Light passing through the pinhole then impinged on a second screen with 2 pinholes. Finally, light from the second screen struck a third screen, where a complicated set of colored fringes appeared. This made no sense from the corpuscular viewpoint.
  30. 30. The Tree of Quantum Mechanics - The Roots 4: Interference What was going on may be seen more clearly from a later modification of Young’s experiment. As shown in the figure (not to scale), light from a source L goes through a filter F, passing only a single color. It then strikes a screen S with a single slit, running out of the plane of the figure. Light from S then lands on a second screen T with 2 slits parallel to the slit in S. Light from these 2 slits lands on a final screen P, where one sees a wavy pattern of intensity, as shown. That this is due to interference is shown by covering one of the slits in T, when the wavy final pattern on P is replaced by a single intensity peak.
  31. 31. The Tree of Quantum Mechanics Measurements on P show that at any peak such as C, the distances to the 2 slits in T differ by an integral number of wavelengths of the color passed by F; while at a null in intensity such as D, the difference in distance is an odd number of half wavelengths. Experiments such as this “established” the wave nature of light, and also pinned down the wavelength associated with each color. All this was turned on its head with the arrival of quantum mechanics, early in the 20th century. For a modern reinterpretation of the Young experiment, see 19 Statistical Interpretation. - The Roots 4: Interference Return to Main Menu
  32. 32. The Tree of Quantum Mechanics - The Roots 4: Thomas Young Thomas Young (1773 – 1829) was another polymath. He was educated at the universities of Edinburgh, Göttingen, and Cambridge; receiving an MD from Göttingen in 1796; and opened a practice in 1799 in London. In 1798, while still a medical student, he worked out how we focus on nearby objects by reshaping the lens in the eye; and in 1801, found that astigmatism also depended on lens shape. Portrait of Dr. Thomas Young (1773 – 1829)
  33. 33. The Tree of Quantum Mechanics Also in that year, he performed the interference experiment (see 4 Interference) that transformed physics. In 1817, he anticipated Maxwell (see 7 Electromagnetic Theory) by suggesting that light is a transverse, rather than longitudinal wave like sound1 . The phenomenon of polarization thus began to make sense; but, as the physics of this is rather deep, we will not pause here to explain it. Prior to Young, it was thought that there were separate receptors in the eye for each color; but he showed that 3 receptors – red, green, and blue – are sufficient. Finally, he made considerable progress in deciphering the Rosetta Stone, a task completed around 1821 by Jean-François Champollion. - The Roots 4: Thomas Young Return to Main Menu 1 In a sound wave, successive zones of compression and rarefaction advance in the direction of motion of the wave. In a transverse wave, something changes from side to side, perpendicular to the direction of the wave. The changes are confined to a “plane of polarization”.
  34. 34. The Tree of Quantum Mechanics In studying the motions of the planets (see 2 Laws of Physics), physicists found it convenient to define the potential energy of a body as the product of the negative of G (the universal gravitational constant) and the body’s mass, divided by the distance to another body pulling on it. They also defined the kinetic energy as half the mass of the body times the square of its speed. It was found that the sum of all the potential and kinetic energies of all the bodies is fixed. This result is easily shown to follow directly from Newton’s combined laws of motion and gravity. - The Roots 5: Conservation of Energy The gravitational constant G is a key element in Newton's law of universal gravitation.
  35. 35. The Tree of Quantum Mechanics - The Roots 5: Conservation of Energy If one hangs a mass at the end of a spring, and disturbs it, another potential energy can be defined as proportional to the changing stretch of the spring. Here too, the sum of the kinetic energy of the mass, and the potential energy of the spring was found to be constant, independent of the motion of the mass. If the mass is hung vertically from the spring in the earth’s gravity field, then the sum of the kinetic energy and the 2 potential energies is now fixed, in spite of any 3 dimensional motions. This conservation of energy holds whatever the nature of the spring. Gradually, this invariant total energy was viewed as having a life of its own. It will be expanded in the next box, and later will play a central role in quantum mechanics and relativity. Return to Main Menu
  36. 36. The Tree of Quantum Mechanics - The Roots 6: Thermodynamics and Statistical Mechanics By the late 18th century, heat was recognized as a form of energy, in that it could cause matter to change temperature, or change state (melting or boiling, or the reverse). Previously, heat was regarded as a material substance, “caloric”, which could be added to something to raise its temperature. Caloric was abandoned in favor of the idea that heat was some form of vibration. This led to the notion that mechanical energy and heat are related. Indeed, careful experiments showed that when mechanical energy was converted to heat through friction, or the reverse in a steam engine, the total is conserved. The concept of the conservation of energy had been greatly expanded, and became known as “the 1st law of thermodynamics”. Joule’s Water-Churning Apparatus Engraving of Joule's apparatus for measuring the mechanical equivalent of heat.
  37. 37. The Tree of Quantum Mechanics One statement of the First Law of thermodynamics is that there is no process by which heat may be moved from one reservoir to another at a higher temperature, without adding energy. This was first clearly stated by Nicolas Léonard Sadi Carnot (1796 – 1832), who established the maximum efficiency of an engine that converts heat to mechanical energy, and is sometimes called the Father of Thermodynamics. Many others contributed to its development (see 6 The Who of Thermodynamics). In general, a heat engine is a device that transfers heat from a high temperature reservoir to a lower one, while diverting some of the energy as mechanical, electrical, chemical, or other usable form. - The Roots 6: Thermodynamics and Statistical Mechanics Heat engine diagram - where heat flows from a high temperature TH furnace through the fluid of the "working body" (working substance) and into the cold sink TC, thus forcing the working substance to do mechanical work W on the surroundings, via cycles of contractions and expansions.
  38. 38. The Tree of Quantum Mechanics - The Roots 6: Thermodynamics and Statistical Mechanics Central to the 2nd law of thermodynamics is a mysterious concept called “entropy”. First, absolute temperature. In 19th century physics, this is where all atomic and molecular motion would cease. Absolute temperature is measured in kelvins (K). 0 K corresponds to -273 C, or -459 F. So water freezes at 273 K. Now to entropy. In any heat transfer process, in or out, a tiny change of entropy is given by the corresponding tiny transfer of heat, divided by the absolute temperature of the reservoir. A different statement of the 2nd law is that, if you count both the source of heat and the sink, the sum of the entropy changes is always positive; i.e., total entropy never decreases.
  39. 39. The Tree of Quantum Mechanics - The Roots 6: Thermodynamics and Statistical Mechanics Viewed somewhat differently, if you add 2 fluids at different temperatures, you get a mixture at some intermediate temperature; and the total entropy increases. The 2nd law says there is no way to unmix them, as this would decrease the entropy. In the static universe of the 19th century, this meant that everything would head toward a single uniform temperature, known then as “the heat death of the universe”. Well, physicists have argued over this for 150 years, with the waters muddied by relativity and quantum mechanics; so we aren’t going to settle it here. A waggish expression of these laws is: 1. You can’t get something for nothing; and 2. You can’t even break even.
  40. 40. The Tree of Quantum Mechanics - The Roots 6: Thermodynamics and Statistical Mechanics Statistical mechanics had its beginning in the researches of Robert Boyle (1627 – 1691). Boyle’s law states that, at constant temperature, the pressure and volume of a gas are inversely related. In Newtonian mechanics, if you can specify the position and velocity of each of a set of spherical particles, you can, in principle, determine their future motions till the end of time. Since this is plainly impractical, the idea of treating a rich ensemble statistically gained credence, albeit reluctantly. Portrait of Robert Boyle, c. 1689
  41. 41. The Tree of Quantum Mechanics The 1st real success along this line was by James Clerk Maxwell (1831 – 1879) (see 7 Maxwell). He was able to derive the distribution of velocities of a large ensemble of spherical gas molecules, colliding with one another in 3 dimensions, and how it depended on temperature (see figure on the next slide; there’s much to be gleaned from it; but, if this is your first look, don’t spend too much time on it). This development became the basis for understanding such properties as diffusion and heat transport in gasses. Significant improvements were introduced by Ludwig Boltzmann (1844 - 1906); so we now call this development the Maxwell – Boltzmann statistics. Several others contributed to the development of statistical mechanics, including Josiah Willard Gibbs (1839 – 1903) (see 6 The Who of Statistical Mechanics). Besides laying the groundwork for a much better understanding of the behavior of gasses, statistical mechanics caused a revolution in thought – physicists now started to look at the universe in probabilistic terms. - The Roots 6: Thermodynamics and Statistical Mechanics Return to Main Menu
  42. 42. The Tree of Quantum Mechanics - The Roots What’s plotted is the probability distribution function of molecular speeds, shown for hydrogen gas at 3 different Kelvin temperatures. The peak of each curve is the most likely speed. As each molecule has some speed, the total probability (area) under each curve is 1. Maxwell’s Molecular Speed Distribution in Gasses Return to Main Menu
  43. 43. The Tree of Quantum Mechanics Several people played star roles in the development of thermodynamics in the 19th century. Of these, arguably the first was Nicolas Léonard Sadi Carnot (1796 - 1832). Born in France, he entered the École Polytechnique in 1812, and graduated in 1814. After years in the French army, he turned to physics and chemistry, and became interested in steam engines. Although others worried mostly about the mechanical details, Carnot was able to show that the maximum efficiency of a heat engine (the fraction of heat passing from hot to cold, convertible to useful energy) depends only on the temperatures of the hot and cold reservoirs. No heat engine, of whatever design, can exceed the Carnot efficiency. Carnot published this analysis in 1824; but it got little attention till 1834 when Émile Clapeyron, a railroad engineer extended his result. In 1850, Rudolf Julius Emanuel Clausius (1822 – 1888), a German physicist generalized this idea further to what is now known as the 2nd Law of Thermodynamics (see 6 Thermodynamics & Statistical Mechanics). Many others, including Wilhelm Wien (1864 – 1928), and Hermann von Helmholtz, (1821 – 1894) contributed to thermodynamics. - The Roots 6: The Who of Thermodynamics Return to Main Menu
  44. 44. The Tree of Quantum Mechanics The loudest guns in statistical mechanics were James Clerk Maxwell (1831 – 1879) (see 7 Maxwell), Ludwig Eduard Boltzmann (1844 – 1906), and Josiah Willard Gibbs (1839 – 1903). Boltzmann received a doctorate from the University of Vienna in 1866, and later held professorships in Vienna, Graz, Munich, and Leipzig. Probably his main contribution to Physics was to show that the 2nd law of thermodynamics could be derived from statistical mechanics. He also showed that gasses tended toward thermodynamic equilibrium because it is by far the most probable state. This work was widely misunderstood and criticized, presumably leading to his later depression and suicide. Thereafter, considerable experimental work led to his vindication. - The Roots 6: The Who of Statistical Mechanics Ludwig Eduard Boltzmann (1844-1906)
  45. 45. The Tree of Quantum Mechanics - The Roots 6: The Who of Statistical Mechanics Statistical mechanics also profited greatly from the studies of Gibbs, an American chemist and theoretical physicist. He was educated at Yale and in Europe; and was appointed Professor of Mathematical Physics at Yale in 1871, a position he held until his death. He applied the newly emerging statistical mechanics to physical and chemical processes, and gave the whole field a more rigorous mathematical foundation. Gibbs was awarded the Copley medal of the Royal Society of London, a sign that science in Europe was well ahead of the U. S. at the time. Return to Main MenuLudwig Eduard Boltzmann (1844-1906)
  46. 46. The Tree of Quantum Mechanics By the beginning of the 19th century, mechanics had come a long way; but electric and magnetic phenomena were still a disconnected jumble of observations. Shuffle your feet on a carpet, and you might draw sparks, and attract bits of paper. Lodestones attracted bits of iron, and coils of wire carrying an electric current did the same. Along came Michael Faraday (1791 - 1867), (see 7 Faraday). He introduced the ideas of lines of force, and electric and magnetic fields. He showed that 2 current carrying wires exerted forces on each other; and he demonstrated that a current change in one wire would generate a current change in another. These findings are the basis of all of today’s transformers, motors, and generators. - The Roots 7: Electromagnetic Theory
  47. 47. The Tree of Quantum Mechanics What Faraday lacked in formal mathematical training, James Clerk Maxwell (1831 - 1879), (see 7 Maxwell) possessed in abundance. Gathering what was known of electric and magnetic phenomena (mostly from Faraday’s work), he produced a set of equations covering the lot. Realizing that the set appeared incomplete, he made an inspired guess. Since magnetic field changes induced electric effects, he supposed that electric field changes would induce magnetic fields. In mathematical clothes, the complete set is now known as The Maxwell Equations, familiar to every physicist, and electrical and electronic engineer. - The Roots 7: Electromagnetic Theory
  48. 48. The Tree of Quantum Mechanics - The Roots 7: Electromagnetic Theory In free space, and lacking any charges or currents, these equations reduce to separate electric and magnetic disturbances, moving in lockstep. Each field creates the other as it goes. Technically, such relations are known as “wave equations”, employed at the time to describe water and sound waves. You will encounter them again as we get into quantum mechanics, but in entirely different clothes. Could all this be real? In both wave equations, the speed of propagation is readily calculated from then known properties of static electric and magnetic fields. This speed came out to be about 300,000 kilometers per second – the speed of light! Light is an electromagnetic wave! When all this appeared in various publications in the 1860’s and 1870’s, the door was opened to today’s technology.
  49. 49. The Tree of Quantum Mechanics From planetary and solar magnetic fields to cell phones, radio and TV, and microwave ovens, the Maxwell Equations are all around you. Moreover, the wave theory of light, so beautifully demonstrated by Thomas Young’s experiments (see 4 Interference), had been given new meaning. The unification of electric and magnetic phenomena was the second great coalescence in physics, after the widening of the conservation of energy. Read on; there will be others. There was one loose end – waves of what? When the luminiferous aether was demolished in the Michelson – Morley experiment of 1887 (see 20 Special Relativity), it was recognized that none of the supposed properties of the ether appeared in the Maxwell Equations; so the equations were saved, if not the sanity of physicists. - The Roots 7: Electromagnetic Theory Return to Main Menu
  50. 50. The Tree of Quantum Mechanics - The Roots 7: Michael Faraday Son of a blacksmith, Michael Faraday (1791 – 1867) was born south of London. With little schooling, he was apprenticed to a bookbinder, which gave him the opportunity to read books brought in for rebinding. An article on electricity in the third edition of the Encyclopædia Britannica particularly fascinated him; and led him to simple experiments with electricity and electrochemistry. When offered a ticket to a lecture by Sir Humphrey Davy (1778 – 1829), a chemist with a considerable reputation, Faraday went, took extensive notes, and was greatly impressed. Faraday bound his various notes and sent them off to Davy, along with a request for a job. When a position opened eventually, Davy hired him as a Laboratory Assistant in 1812. Later, when asked what was his greatest discovery, Davy promptly replied, “Michael Faraday”. This second apprenticeship gave Faraday a solid grounding in chemistry, but ended in 1820. Portrait of Michael Faraday, c. 1820
  51. 51. The Tree of Quantum Mechanics Davy had discovered chlorine by dissociating hydrochloric acid, thus showing that acids didn’t necessarily contain oxygen. Faraday went on to produce compounds of carbon and chlorine (C2Cl4 and C2Cl6), and was the first to find and describe benzene (C6H6). We’ll return to benzene when we touch on its peculiar quantum behavior in 22 Modern Chemistry & Molecular Biology. Following his stint with Davy, Faraday was hired by the Royal Society in London, lived there, married Sarah Barnard, carried out important research on steel alloys and high refractivity optical glass, and showed that the latter slightly expels magnetic fields (diamagnetism). He then returned to electrical phenomena. In 1820, Hans Christian Ørsted (1777 – 1851) found that a magnetic compass always pointed widdershins (counterclockwise) around a current carrying wire. On hearing of this, André-Marie Ampère (1775 – 1836) quickly developed a mathematical theory, which Faraday turned into the first electric motor. - The Roots 7: Michael Faraday
  52. 52. The Tree of Quantum Mechanics - The Roots The principle involved is called electromagnetic induction, where a varying magnetic field causes a varying current in a conductor, or vice versa. It is the basis for all electric motors, generators, and transformers; all of which, Faraday was the first to construct. In the latter, Faraday wound 2 coils of wire on the same iron ring; a varying current in one coil caused a varying current in the other. The current and voltage in the 2nd coil depends on the ratio of the number of turns in the 2 coils. In 1831, Faraday worked with Charles (later Sir Charles) Wheatstone (1802 – 1875) to investigate sound waves in plates. If one excites the plate with a violin bow to create transverse waves in the plate, and sprinkles powder on the plate, the particles will cluster in groups known as Chladni figures. Moreover, a nearby plate could be excited with similar figures, by sound transmission through the air. These effects gave rise to Faraday’s induction experiments mentioned above. 7: Michael Faraday
  53. 53. The Tree of Quantum Mechanics In 1832, he turned to electrochemistry, and found the laws that apply; first, that the amount of material removed from one plate in a conductive solution, and deposited on another, depended directly on the current passed through the solution. Second, if the solution is dissociated, the amount deposited at each plate is in the ratio of their chemical equivalents (number of atoms divided by valence). In later years, he carefully experimented on the magnetic properties of various materials. He found that some slightly enhanced the ambient field, which he labeled “paramagnetic”, and some that slightly expelled the ambient field, which he called “diamagnetic”, terms we use to this day. He also developed the idea that electric and magnetic fields permeated space, ideas that were to inspire James Clerk Maxwell (1831 – 1879) to dress them in mathematical clothes that were to revolutionize physics (see 7 Maxwell). - The Roots Return to Main Menu 7: Michael Faraday Michael Faraday, c. 1861
  54. 54. The Tree of Quantum Mechanics - The Roots 7: James Clerk Maxwell James Clerk (pronounced Clark, as in Kent) Maxwell (1831 – 1879), was born in Edinburgh, Scotland. At age 16 he entered the University of Edinburgh, but transferred to Cambridge in 1850. Because of his father’s poor health, he returned to Scotland, and was appointed professor of natural philosophy at Marischal College, Aberdeen. In 1858, he married Katherine Mary Dewar. Alas, in 1860, Marischal merged with King’s College, and became the University of Aberdeen. Maxwell was rejected for tenure, and was required to leave, an event the University has never lived down. He left behind a laboratory of great quality for its day; but, unlike the DMNS, it’s short of explanations, and closed to the public. After this fiasco, Maxwell was appointed professor of natural philosophy and astronomy at King's College, London. Following the death of his father in 1865, he returned to Scotland, where he buried himself in research. In 1871, he moved to Cambridge, as the first professor of experimental physics. He set up the Cavendish Laboratory there in 1874. He continued in this position until 1879, when illness forced him to resign.
  55. 55. The Tree of Quantum Mechanics In 1849, his earliest scientific work showed that Thomas Young’s hypothesis that 3 color receptors in the eye are sufficient, is correct (see 4 Young). He did this by spinning disks with red, green, and blue pie segments, showing that he could produce everything the eye can see with varying segments of each. Also, in 1861, he produced what was essentially the 1st color photo, by exposing the same scene through red, green, and blue filters, and projecting them simultaneously on the same screen. During the period 1855 – 9, Maxwell studied the dynamics of Saturn’s rings. He found that both solid and liquid rings would be gravitationally unstable. He concluded that they must be icy or rocky rubble, as there were no other viable options. The Pioneer and Voyager fly-bys of Saturn in the 1970s and 1980s proved him right. - The Roots 7: James Clerk Maxwell The first permanent color photograph, taken by James Clerk Maxwell in 1861. Subject is a Tartan ribbon.
  56. 56. The Tree of Quantum Mechanics Around 1860, Maxwell turned to the kinetic theory of gasses. In 1857, Rudolf Clausius (1822 – 1888) had shown that the molecules of a gas are in motion, continually bouncing off each other, and had determined the mean free path – the average distance between collisions. Maxwell looked deeper, and was able to work out the probability distribution function of molecular speeds (see figure in 6 Thermodynamics & Statistical Mechanics). This function is the probability dP that the speed v will lie in a very small range dv, as a function of v. The function depends only on the molecular properties, and on the absolute temperature of the gas. This was the beginning of statistical mechanics. 8 years later, Ludwig Boltzmann (1844 – 1906) (see 6 The Who of Statistical Mechanics) extended Maxwell’s result to cover the conduction of heat in gasses. Today, these works together are called the Maxwell–Boltzmann statistics – they caused a revolution in physicist’s view of the universe. - The Roots 7: James Clerk Maxwell
  57. 57. The Tree of Quantum Mechanics Maxwell is best known today as the father of electromagnetic field theory (see 7 Electromagnetic Theory). That electric and magnetic fields are related was known to Michael Faraday (1791 – 1867) (see 7 Faraday), who had shown that a changing magnetic field could induce an electric field in a conductor. Over several years, starting in 1855, Maxwell found concise mathematical descriptions of Faraday’s results; but felt that something was missing. He decided that symmetry demanded that a changing electric field would create magnetic field changes. On stating this mathematically, his complete set of relations are known today as “The Maxwell Equations”. Wave solutions of these equations turned out to describe light, radio waves, X-rays; indeed, the whole electromagnetic spectrum – if you are now in Space Odyssey, perhaps a third of the exhibits pertain to aspects of electromagnetic phenomena. - The Roots 7: James Clerk Maxwell
  58. 58. The Tree of Quantum Mechanics - The Roots Return to Main Menu 7: James Clerk Maxwell Maxwell is generally considered the greatest theoretical physicist of the 19th century. In 1931, on the 100th anniversary of Maxwell's birth, Einstein described the change in the conception of reality in physics that resulted from Maxwell's work as “the most profound and the most fruitful that physics has experienced since the time of Newton”. James Clerk Maxwell in his 40’s
  59. 59. The Tree of Quantum Mechanics Till now, our story has concerned the development of physical ideas through the middle of the 19th century. That something was seriously wrong with this structure first emerged with the research of Gustav Robert Kirchhoff (1824 – 1887) (see 8 Kirchhoff). He had chosen to investigate the properties of “blackbodies”. In physics, a black body is defined as something that perfectly absorbs all incident radiation, and perfectly reemits it. No such stuff exists; but a close approximation is achieved by holding a hollow box at some uniform temperature. Radiation from the inner wall impinges on other parts of the wall, is absorbed and reradiated, until some sort of equilibrium is reached. If a tiny hole is drilled in the box, some radiation will escape; and its spectrum may be measured. A spectrum is the distribution of energy, as a function of wavelength. It typically rises to a peak as wavelength increases, and then falls off. - The Trunk 8: Blackbody Studies
  60. 60. The Tree of Quantum Mechanics Kirchhoff showed, experimentally, that the peak, and the shape of the distribution depends only on the temperature, and not on the box properties, such as size, shape, or the materials it was made of. Calling attention to this, he suggested that there must be something very fundamental about blackbody radiation. Little did he know that he had started a revolution in physics, and in our view of the universe. Many others followed his lead, confirming his results, and leading to the unsuccessful theoretical investigations in 10 Ultraviolet Catastrophe. - The Trunk 8: Blackbody Studies Return to Main Menu
  61. 61. The Tree of Quantum Mechanics Gustav Robert Kirchhoff (1824 – 1887) was born in Königsberg, Prussia (now Kaliningrad, Russia). In 1845 he first announced Kirchhoff's laws, for the calculation of the currents and voltages of electrical networks. Extending the theory of the German physicist Georg Simon Ohm (1789 – 1854), he generalized the equations describing current flow to the case of networks in three dimensions. In further studies he demonstrated that current flows through a conductor at nearly the speed of light. In 1847 Kirchhoff became Privatdozent (unsalaried lecturer) at the University of Berlin and three years later accepted the post of extraordinary professor of physics at the University of Breslau. In 1854 he was appointed professor of physics at the University of Heidelberg, where he joined forces with Robert Wilhelm Bunsen (see 9 Bunsen) and founded spectrum analysis (see 9 Spectroscopy). Applying this new research tool, they discovered two new elements, cesium (1860) and rubidium (1861). - The Trunk 8: Kirchhoff
  62. 62. The Tree of Quantum Mechanics - The Trunk Kirchhoff went further to apply spectrum analysis to study the composition of the sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated. He used this principle to explain the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. That discovery marked the beginning of a new era in astronomy. In 1875 Kirchhoff was appointed to the chair of mathematical physics at the University of Berlin. 8: Kirchhoff Return to Main Menu Spectroscope of Kirchhoff and Bunsen
  63. 63. The Tree of Quantum Mechanics The science of spectroscopy may be said to have begun with Newton (see 2 Particle Theory of Light). With a prism, he spread out sunlight into a rainbow, and showed that it contained all the colors we can see. Newton’s instrument was improved by William Hyde Wollaston (1766 – 1828), who in 1802 glimpsed dark lines superimposed on the rainbow. However, Joseph von Fraunhofer (1787 – 1826) really made it take off. In 1814 he added a telescope following the prism, and began to map the lines in the solar spectrum. In 1819, he managed to rule many parallel fine lines on a plate of glass, to produce what is now called a “diffraction grating”. Much like the Young 2 slit experiment (see 4 Interference), the grating causes each wavelength to concentrate at a different spot on a final screen, where the contributions from each grating line add up in phase. The grating took over in spectroscopy when Henry Augustus Rowland (1848 – 1901) in 1882 developed a ruling engine that could produce large, precise, and very densely scribed gratings. You can view various atomic spectra through diffraction gratings at our Spectroscopy Exhibit. - The Trunk 9: Spectroscopy
  64. 64. The Tree of Quantum Mechanics An essential contribution was made by Gustav Robert Kirchhoff (1824 – 1887) (see 8 Kirchhoff) and Robert Wilhelm Bunsen (1811 – 1899) (see 9 Bunsen). Around 1859, they showed that, if an element is vaporized, and heated to incandescence, its spectrum contained a number of bright lines, unique to each element. Moreover, if a transparent tube, containing a cool gaseous element is placed before a white light source, dark lines appeared at the same wavelengths as in that element’s emission spectrum. This showed that the lines seen by Wollaston and von Fraunhofer in sunlight are caused by absorption and scattering in the atmospheres of the sun and earth. - The Trunk 9: Spectroscopy
  65. 65. The Tree of Quantum Mechanics Kirchhoff and Bunsen developed techniques for analyzing spectra from unknown sources, and sorting out the lines to determine the source elements, and their relative proportions. Thus, they were the first to determine the composition of the sun. Later, improvements in instruments, and the use of large telescopes to gather sufficient light, allowed spectroscopy to be applied to the stars (see 24 Astrophysics). Today, we have millions of stellar spectra, showing a huge range of compositions. Many of these were taken with instruments in space, to avoid absorption and scattering in the earth’s atmosphere, which blocks much of the spectrum. Most of what we know of stellar structure and dynamics comes from spectroscopy. - The Trunk 9: Spectroscopy Return to Main Menu
  66. 66. The Tree of Quantum Mechanics Robert Wilhelm Bunsen (1811 – 1899) received a Ph.D. in chemistry at the University of Göttingen in 1830, and taught at the universities of Marburg and Breslau, and at Heidelburg from 1852 until his death. During his career, he was responsible for many developments in chemical instrumentation; though, oddly, probably not for the burner that bears his name. Most important for science was his collaboration with Gustav Kirchhoff (see 8 Kirchhoff). They found that heating a gas to incandescence caused it to emit a set of wavelengths, or colors, unique to each gas. Moreover, when a cool gas was placed in front of a white light source, it absorbed or scattered the same set of wavelengths. This was the true beginning of the science of spectroscopy (see 9 Spectroscopy). By these means, they discovered the elements cesium and rubidium, both of which were to play important roles in the development of atomic clocks. - The Trunk 9: Bunsen Return to Main Menu
  67. 67. The Tree of Quantum Mechanics Theoreticians attempted to derive the blackbody spectrum from the Maxwell Equations (see 7 Electromagnetic Theory) and thermodynamics (see 6 Thermodynamics & Statistical Mechanics). In 1893, Wilhelm Wien (1864 – 1928) came up with a formula, based on thermodynamic arguments, that described the peak and short wavelengths, but failed at long wavelengths. A different approach from the Maxwell equations by Lord Rayleigh (John William Strutt 1842 – 1919) (see 10 Rayleigh), and later by James Jeans (1877 – 1946), failed completely at short wavelengths. The Rayleigh-Jeans formula had the intensity going off to infinity at the violet end, suggesting that the blackbody was emitting infinite energy – plainly false. Something was clearly awry with 19th century physics and maybe the Maxwell Equations; the problem became known as “The Ultraviolet Catastrophe”. Of course, what was in trouble was physics. The fix would require another revolution – stay tuned. - The Trunk 10: The Ultraviolet Catastrophe Return to Main Menu
  68. 68. The Tree of Quantum Mechanics John William Strutt, 3rd Baron Rayleigh (1842 – 1919) was born in Langford Grove, Maldon, Essex, England. In 1861 he entered Trinity College, Cambridge, from which he graduated with a B.A. in 1865. In his first paper, published in 1869, he gave a lucid exposition of some aspects of the electromagnetic theory of James Clerk Maxwell (see 7 Maxwell) in terms of analogies that the average person would understand. An attack of rheumatic fever in 1871 threatened his life for a time. On a recuperative trip up the Nile, he began work on his great book, “The Theory of Sound”, in which he examined questions of vibrations and the resonance of elastic solids and gases. The first volume appeared in 1877, followed by a second in 1878, concentrating on acoustical propagation in material media. After some revision during his lifetime and successive reprintings after his death, the work has remained the foremost monument of acoustical literature. - The Trunk 10: Rayleigh
  69. 69. The Tree of Quantum Mechanics - The Trunk Perhaps his most significant early work was his theory explaining the blue color of the sky as the result of scattering of sunlight by small particles in the atmosphere. The Rayleigh scattering law, which evolved from this theory, has since become classic in the study of all kinds of wave propagation. In the period 1879–84, he served as the second Cavendish professor of experimental physics at Cambridge, after Maxwell. Later he became secretary of the Royal Society, a post he held for 11 years. Rayleigh's greatest contribution to science, with William Ramsey (1852 – 1916), is generally considered his discovery and isolation of argon in 1895, which makes up about 1% of the atmosphere. 10: Rayleigh Return to Main MenuJohn William Strutt, 3rd Baron Rayleigh
  70. 70. The Tree of Quantum Mechanics - The Trunk Imagine a glass tube as in the figure, containing 2 electrodes, and a very low pressure gas. If a potential is applied between the plates, a current will flow, and a green glow will appear on most of the glass inner surface. This was first done around 1854 by Johann Heinrich Wilhelm Geissler (1814 - 1879), who had devised a pump capable of reaching a low enough pressure. The tube was improved by Sir William Crookes (1832 - 1919). He established that the glow came from something emitted from the negative electrode or cathode. He did this by introducing various kinds of obstacles in the tube, which showed that the “cathode rays”, whatever they were, traveled in straight lines. Since the rays could be deflected by a magnet, it was evident that they carried a charge, and from the direction of bending, that the charge is negative. With his modifications, the device became known as a “Crookes tube”. 11: Discovery of the Electron
  71. 71. The Tree of Quantum Mechanics In 1897, Sir Joseph John Thomson (1856-1940) (see 11 Thomson) added another pair of electrodes, orthogonal to those in the figure, and again deflected the cathode rays. Between these observations, he was able to show that the rays are particles, around 2000 times less massive than hydrogen atoms, and are now called “electrons”. That this was a distinct particle was demonstrated because cathode rays from many different cathode materials are identical. Since electrons appeared to be constituents of matter, Thomson advanced the “plum pudding” model – they were embedded in a much heavier ball of positively charged stuff, a model that was to survive only 16 more years. Thomson received the Nobel Prize for physics for this work in 1906. - The Trunk 11: Discovery of the Electron
  72. 72. The Tree of Quantum Mechanics From the deflection of cathode rays in electric or magnetic fields, Thomson and others could only determine the ratio of charge to mass of the electrons. However, around 1910, Robert Andrews Millikan (1868 – 1953) found a truly clever way to accurately measure the charge alone, thus determining the mass as well. A fine spray of oil drops is introduced into an upper chamber of the apparatus. The spray is stopped when one drop falls through a small hole into a lower chamber. There, a bright light both illuminates the drop, and charges it through the photoelectric effect in the air surrounding the drop (there’s more on this in 13 Photoelectric Effect). The top and bottom of this lower chamber are plates to which voltages may be applied. A microscope looks into the chamber horizontally. The drop is alternately allowed to drop freely, and is pulled upward by a positive voltage on the upper plate; and its terminal velocity in air is measured. The radius of the drop, and thus its mass, is determined from the free fall speed; after which its charge is found from the upward velocity. - The Trunk 11: Discovery of the Electron
  73. 73. The Tree of Quantum Mechanics - The Trunk The number of electrons clinging to the drop is initially unknown; but the measured charge is always close to a multiple of a charge e, the charge of the electron. Millikan received the Nobel Prize in Physics in 1923. 11: Discovery of the Electron Return to Main Menu
  74. 74. The Tree of Quantum Mechanics - The Trunk Sir Joseph John Thomson (1856 - 1940), was born near Manchester, England, and educated at Owens College (now part of Victoria University of Manchester) and Trinity College, University of Cambridge. At Cambridge he taught mathematics and physics, served as Cavendish Professor of Experimental Physics, and was Master of Trinity College (1918 - 40). He was also president of the Royal Society (1915 - 20) and Professor of Natural Philosophy at the Royal Institute of Great Britain (1905 - 18). For experiments on cathode ray tubes around 1897, he is regarded as the discoverer of electrons, as the carrier of electrical charge. Thomson was awarded the 1906 Nobel Prize in physics for his work on the conduction of electricity through gases, and was knighted in 1908. 11: Thomson Return to Main MenuPortrait of physicist J.J. Thomson
  75. 75. The Tree of Quantum Mechanics It may be argued that quantum mechanics originated with the researches of Gustav Kirchhoff (see 8 Kirchhoff) into the properties of black bodies (see 8 Blackbody Studies). But it’s quite unlikely that Kirchhoff, a giant of 19th century physics, had even an inkling of what was to come. To recapitulate, a formula expressing the black body spectral distribution, and derived from thermodynamic arguments by Wilhelm Wien (1864 – 1928), failed at long wavelengths; and the Rayleigh – Jeans formula, based on Maxwell’s Equations, went off to infinity at short wavelengths, clearly impossible. Many wrestled with this “ultraviolet catastrophe”, without success (see 10 Ultraviolet Catastrophe). - The Trunk 12: Discrete Energy Levels
  76. 76. The Tree of Quantum Mechanics Max Planck (1858 – 1947) (see 12 Planck) carefully considered both arguments; and noted that the Wien formula fit the known spectral data very well at short wavelengths; while the Rayleigh – Jeans formula did very well at long wavelengths. After several years, Planck came up with a formula that fit all the data over the whole range of measured temperatures. The problem was that it had no physical justification. In classical mechanics, an oscillator e.g., a pendulum, a mass hanging from a spring, etc., may have only a single or a set of natural frequencies; but any amplitude and thus any energy. However, in 1900, Planck suggested that, at any given frequency ν any such energy must be restricted to a value hν, or any of its harmonics, for some then unknown constant h – today, Planck’s constant. That we had never noticed this was because h is a really teensy number; so the allowable energies are very closely spaced. - The Trunk 12: Discrete Energy Levels
  77. 77. The Tree of Quantum Mechanics - The Trunk Applying this notion to the atoms making up the inside of a black box, he argued that radiation emission or absorption could only change the oscillator from one allowed energy to another. Thus, if the atoms of the inside of the box are capable of resonating at some frequency ν, then the radiation flying around inside the box must be composed of chunks with energies which are multiples of hν. He called each such chunk a “quantum”, a name that has stuck. Suppose n and m are positive integers, n greater than m. Then, if an atom has an energy nhν, it can emit a quantum of energy (or photon) (n – m)hν and drop to the lower energy mhν. This photon can then be absorbed by a different atom, and raise its energy by the same amount. Note that Planck’s hypothesis wouldn’t have worked if the allowed energy levels weren’t evenly spaced. Also note that emission of a photon doesn’t change the resonant frequency ν. 12: Discrete Energy Levels
  78. 78. The Tree of Quantum Mechanics On applying this restriction to the Maxwell Equations, Planck found that he could derive his previously found formula for the black body spectrum that precisely matched the measurements at any given temperature – provided he used the right value of h. So h was determined in this way; and it has a truly teensy value: 6.626 × 10-34 joule seconds1 . This result also showed why the black body spectrum doesn’t depend on the physical and geometric properties of the box. The quantum revolution had begun; but no one knew where it was headed. Around 1925, one of the first results of the emerging wave mechanics was this quantization of oscillator energies (see 17 Matrix & Wave Mechanics). Today, we know that these quantized energy levels correspond to atomic rotation and vibration states; but it took many years to work it all out. - The Trunk 12: Discrete Energy Levels Return to Main Menu 1 A joule is the unit of energy in the International System of units. It is the energy consumed by a 1 watt light bulb in 1 second.
  79. 79. The Tree of Quantum Mechanics - The Trunk Max Karl Ernst Ludwig Planck (1858 – 1947), although a gifted musician, chose to study physics over music and more classical studies at the age of 17. In 1874 he attended the University of München, transferring to the University of Berlin in 1877. Returning to München, he received his doctoral degree in 1879, with a dissertation on the 2nd law of thermodynamics; and in the next year, became a Lecturer there. In 1885, he went on to the University of Kiel, as Associate Professor. In 1889, he moved back to the University of Berlin, where he was promoted to Full Professor in 1892. 12: Planck Max Planck
  80. 80. The Tree of Quantum Mechanics All through this period, Planck saw the 2nd law of thermodynamics in absolute classical terms. However, as the idea of the quantization of energy levels began to take hold (see 12 Discrete Energy Levels) he found it necessary to see it statistically, following Boltzmann (see 6 Thermodynamics & Statistical Mechanics). This was quite wrenching for Planck, as for most others. As one biographer put it, Planck was a reluctant revolutionary. Planck received the Nobel Prize in physics in 1918. That it took so long (18 years) is a measure of how slow physicists were to accept the quantum hypothesis. - The Trunk 12: Planck Return to Main Menu
  81. 81. The Tree of Quantum Mechanics Although Max Planck’s blackbody spectrum formula fit the data better than anything else, physicists were slow to accept its quantum basis (see 12 Discrete Energy Levels). They argued that some other ideas for atomic structure might be found that would produce a similar formula, and be consistent with classical physics. Clearly, more evidence was needed. It wasn’t long in coming. The photoelectric effect – that light or ultraviolet radiation falling on a metallic surface in vacuum causes electrons to be emitted – was likely first noted by Heinrich Hertz (1857 – 1894) in 1887. On studying this effect in greater detail, Philipp Eduard Anton Lenard (1862 – 1947), in about 1902, found that the intensity of the incident radiation affected only the electron emission rate, not the velocity of the emitted electrons. Moreover, for each metal, there was a maximum wavelength, beyond which no electrons were emitted. Within the well established wave theory of light, to say nothing of the Maxwell Equations, this made no sense. That more intense light should generate more electrons was fine; but long wavelength radiation should have been just as effective. - The Trunk 13: The Photoelectric Effect
  82. 82. The Tree of Quantum Mechanics It remained for Albert Einstein (1879 - 1955) (see 13 Einstein) to, ah, shine light on this mystery. In 1905, in one of 4 papers he submitted to the journal The Annals of Physics, he suggested going back to Newton’s corpuscular theory of light (see 2 Particle Theory of Light), as well as Planck’s quantum theory (see 12 Discrete Energy Levels). In the latter, the energy of the incident quanta (or photons) is hν, where ν is the frequency of the light, and h is Planck’s constant. (In any wave, the frequency ν of passing wave peaks is the speed of propagation divided by the wavelength1 .) Einstein hypothesized that there is a minimum energy P needed to pry an electron out of any given surface; so the kinetic energy of the emitted electron is hν minus P. This neatly accounts for the wavelength limit found by Lenard. - The Trunk 13: The Photoelectric Effect 1 This may be easier to see as the speed of propagation is the frequency times the wavelength.
  83. 83. The Tree of Quantum Mechanics Einstein’s paper lent much credence to Planck’s quantum theory; but the question remained – how could light be both waves and particles, or as some wag later put it, wavicles? Well, hang in here till 19 Statistical Interpretation, and you’ll find a resolution, of sorts. Einstein received the Nobel Prize for Physics in 1921 for this work; no one got it for relativity. - The Trunk 13: The Photoelectric Effect Return to Main Menu
  84. 84. The Tree of Quantum Mechanics - The Trunk Albert Einstein (1879 – 1955) was born in Ulm, Germany of middle class Jews. He has written that 2 things influenced his early years: a magnetic compass at age 5 that started a fascination with invisible forces, and a geometry book at age 12, which he “devoured”. In 1894, his father’s business failed; and his parents left for Milan, Italy to find work, leaving young Albert in a Boarding House, to finish his schooling. Facing military conscription at 16, he bolted, and found his way to Milan. As a school dropout and draft dodger, his prospects were poor indeed. 13: Einstein Albert Einstein, 1921
  85. 85. The Tree of Quantum Mechanics - The Trunk Fortunately, Einstein could apply directly to the Swiss Federal Polytechnic School (later the Swiss Federal Institute of Technology) in Zürich without the equivalent of a high school diploma if he passed its stiff entrance examinations. His marks showed that he excelled in mathematics and physics, but he failed at French, chemistry, and biology. Because of his exceptional math scores, he was allowed into the polytechnic on the condition that he first finish his formal schooling. He went to a special high school in Aarau, Switzerland, and graduated in 1896. He also renounced his German citizenship at that time. He was stateless until 1901, when he was granted Swiss citizenship. 13: Einstein
  86. 86. The Tree of Quantum Mechanics - The Trunk Einstein would recall that his years in Zürich were some of the happiest of his life. He met many students who would become loyal friends, such as Marcel Grossmann, a mathematician, and Michele Besso, with whom he enjoyed lengthy conversations about space and time. He also met his future wife, Mileva Maric, a fellow physics student from Serbia. He graduated from the Swiss Federal Polytechnic School in 1900. He and Mileva had a daughter, Lieserl, in 1902, whose fate is unknown. This was the nadir of Einstein’s life. His parents objected to marriage with Mileva, who he couldn’t support without a job; and his professor wouldn’t recommend him for employment. His father’s business again went under, and became seriously ill; but, before dying, he gave consent for marriage with Mileva. He did some tutoring of children; but even this didn’t last long. 13: Einstein
  87. 87. The Tree of Quantum Mechanics Things turned up when Grossmann’s father recommended him for a job in the Swiss Federal Patent Office in Bern. With a small, but steady income, he married Mileva in 1903. Their children, Hans Albert and Eduard, were born in Bern in 1904 and 1910, respectively. 1905 is often called Einstein's “miracle year” - he published 4 papers in the Annalen der Physik, each of which would alter the course of modern physics: 1. Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”), which applied quantum ideas to light in order to explain the photoelectric effect (see 13 Photoelectric Effect). This paper won the Nobel Prize for 1921. - The Trunk 13: Einstein
  88. 88. The Tree of Quantum Mechanics 2. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen (“On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat”), in which Einstein offered the first experimental proof of the existence of atoms. By analyzing the motion of tiny particles suspended in still water, called Brownian motion, he could calculate the size of the jostling atoms and Avogadro's number, the number of molecules in a mass of the water corresponding to its molecular weight. 3. Zur Elektrodynamik bewegter Körper (“On the Electrodynamics of Moving Bodies”), in which Einstein laid out the mathematical theory of special relativity (see 20 Special Relativity). - The Trunk 13: Einstein
  89. 89. The Tree of Quantum Mechanics 4. Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (“Does the Inertia of a Body Depend Upon Its Energy Content?”), submitted almost as an afterthought, which showed that relativity theory led to E = mc2 . This provided the first mechanism to explain the energy source of the Sun and other stars. Einstein also submitted a paper in 1905 for his doctorate at the Swiss Federal Polytechnic School, on the sizes of molecules. There has never been a year like 1905, in the whole history of physics. At first Einstein's 1905 papers were ignored. This began to change after he received the attention of just one physicist, perhaps the most influential physicist of his generation, Max Planck (see 12 Planck). - The Trunk 13: Einstein
  90. 90. The Tree of Quantum Mechanics Soon, owing to Planck's comments, and to experiments that gradually confirmed his theories, Einstein was invited to lecture at international meetings, and he rose rapidly. He was offered a series of positions at increasingly prestigious institutions, including the University of Zürich, the University of Prague, the Swiss Federal Institute of Technology, and finally the University of Berlin, where he served as director of the Kaiser Wilhelm Institute for Physics from 1913 to 1933. In 1915, Einstein completed his General Theory of Relativity, extending the Special Theory to cover accelerated systems and gravitation. Unfortunately, while General Relativity is the best theory of things in the large, available to physics at this writing, it’s incompatible with quantum mechanics; so we won’t offer a discussion of it in this program; but there will be some further mention of it in 28 Theory of Everything. - The Trunk 13: Einstein
  91. 91. The Tree of Quantum Mechanics - The Trunk Einstein's work was interrupted by World War I. A lifelong pacifist, he was only one of 4 intellectuals in Germany to sign a manifesto opposing Germany's entry into war. Disgusted, he called nationalism “the measles of mankind”. He would write, “At such a time as this, one realizes what a sorry species of animal one belongs to”. There are many good sources of information on the remainder of Einstein’s life; but, as he made few further contributions to quantum mechanics, we’ll keep it short. After the bending of starlight as it passes the sun was experimentally confirmed in 1919, Einstein was universally acclaimed. Sir Arthur Eddington, who led the expedition to measure this, was later interviewed by a media person, who said that he’d heard that there were only 3 people in the world who understood Einstein; to which Eddington, no shrinking violet, promptly replied, “Who’s the third?”. 13: Einstein
  92. 92. The Tree of Quantum Mechanics - The Trunk Inevitably, Einstein's fame and the great success of his theories created a backlash. The rising Nazi movement found a convenient target in relativity, branding it “Jewish physics” and sponsoring conferences and book burnings to denounce Einstein and his theories. The Nazis enlisted other physicists, including Nobel laureates Philipp Lenard and Johannes Stark, to denounce Einstein. One Hundred Authors Against Einstein was published in 1931. When asked to comment on this denunciation of relativity by so many scientists, Einstein replied that to defeat relativity one did not need the word of 100 scientists, just one fact. In December 1932 Einstein decided to leave Germany - he would never go back. It became obvious to Einstein that his life was in danger. A Nazi organization published a magazine with Einstein's picture and the caption “Not Yet Hanged” on the cover. There was even a price on his head. So great was the threat that Einstein split with his pacifist friends and said that it was justified to defend yourself with arms against Nazi aggression. To Einstein, pacifism was not an absolute concept but one that had to be re-examined depending on the magnitude of the threat. 13: Einstein
  93. 93. The Tree of Quantum Mechanics - The Trunk Einstein settled at the newly formed Institute for Advanced Study at Princeton, N.J., which soon became a mecca for physicists from around the world. Newspaper articles declared that the “pope of physics” had left Germany and that Princeton had become the new Vatican. To his horror, during the late 1930s, physicists began seriously to consider whether his equation E = mc2 might make an atomic bomb possible. In 1920 Einstein himself had considered, but eventually dismissed the possibility. However, he left it open, if a method could be found to release the power of the atom. Then in 1938–39 Otto Hahn, Fritz Strassmann, Lise Meitner, and Otto Frisch showed that vast amounts of energy could be unleashed by the splitting of the uranium atom. The news electrified the physics community. 13: Einstein
  94. 94. The Tree of Quantum Mechanics - The Trunk In July 1939 physicist Leo Szilard asked Einstein if he would write a letter to U.S. President Franklin D. Roosevelt urging him to develop an atomic bomb. Following several translated drafts, Einstein signed a letter on August 2 that was delivered to Roosevelt by one of his economic advisers, Alexander Sachs, on October 11. Roosevelt wrote back on October 19, informing Einstein that he had organized the Uranium Committee to study the issue. 13: Einstein Scan of the letter sent to U.S. President Franklin D. Roosevelt on August 2, 1939
  95. 95. The Tree of Quantum Mechanics - The Trunk Einstein was granted permanent residency in the United States in 1935 and became an American citizen in 1940, although he chose to retain his Swiss citizenship. During the war, Einstein's colleagues were asked to journey to Los Alamos, N.M., to develop the first atomic bomb for the Manhattan Project. Einstein, the man whose equation had set the whole effort into motion, was never asked to participate. Voluminous declassified FBI files, numbering several thousand, reveal the reason: the U. S. government feared Einstein's lifelong association with peace and socialist organizations. FBI director J. Edgar Hoover went so far as to recommend that Einstein be kept out of America by the Alien Exclusion Act, but he was overruled by the U.S. State Department. Instead, during the war Einstein was asked to help the U.S. Navy evaluate designs for future weapons systems. Einstein also helped the war effort by auctioning off priceless personal manuscripts. In particular, a handwritten copy of his 1905 paper on special relativity was sold for $6.5 million. It’s now located in the Library of Congress. 13: Einstein Return to Main Menu
  96. 96. The Tree of Quantum Mechanics - The Trunk The early years of the 20th century were to shake physics to its core. Major palpitations were caused by Ernest Rutherford, 1st Baron Rutherford of Nelson and Cambridge (1871 - 1937). Radioactivity had been discovered by Henri Becquerel (1852 – 1908) in 1896. It was found to be composed of 3 kinds of radiation, called alpha, beta, and gamma. Beta radiation was found to be Thomson’s electrons; and gamma was eventually identified as extremely short wavelength electromagnetic radiation. In 1909, Rutherford placed some radioactive material inside a thin walled evacuated glass tube, surrounded by another thicker wall, also evacuated. The inner wall stopped the electrons; but the alphas penetrated to the space between the walls. An electric discharge in that space caused a weak glow which showed the spectral lines of helium. Since alphas would bend in a magnetic field, they were identified as helium atoms, with their 2 electrons removed. 14: Discovery of the Nucleus
  97. 97. The Tree of Quantum Mechanics In 1913, he set one of his students to measure alpha scattering by a thin platinum foil. To their great surprise, about one in 8000 was deflected by more than 90 degrees. As he put it, “it was almost as incredible as if you had fired a 15-inch shell at a piece of tissue-paper and it came back and hit you”. What hit physics was that the “plum pudding” model of the atom (see 11 Discovery of Electrons) had just expired. What grew up in its place was a hard positively charged core, now called the nucleus, containing almost all of the atom’s mass, surrounded by a bunch of electrons. For his earlier work, he was awarded the Nobel Prize in Chemistry. - The Trunk 14: Discovery of the Nucleus Top: Expected results: alpha particles passing through the plum pudding model of the atom undisturbed. Bottom: Observed results: a small portion of the particles were deflected, indicating a small, concentrated positive charge.
  98. 98. The Tree of Quantum Mechanics The fallout from this discovery was to be profound; for it presented physics with an enduring mystery – what holds nuclei together? The simplest atom, hydrogen, consists of one positive proton, with one electron orbiting about it. The next, helium, has an atomic weight about 4 times larger, and was assumed to consist of 4 protons, plus 2 electrons in the nucleus, and 2 more orbiting about it, thus creating a neutral atom. More massive nuclei were assumed to be built up around the same plan. So, now dressed in more elaborate clothes, what holds nuclei together? All but hydrogen ought to fly apart. Physicists of the time posited a “strong force” did the job; but this term only labeled their ignorance. In 26 Nuclear Physics, we’ll take this up again. - The Trunk 14: Discovery of the Nucleus Return to Main Menu
  99. 99. The Tree of Quantum Mechanics - The Trunk Ernest Rutherford, 1st Baron Rutherford of Nelson and Cambridge (1871 - 1937) was born in Brightwater, New Zealand. In 1887 he won a scholarship to Nelson College, a secondary school. He won prizes in history and languages as well as mathematics. Another scholarship allowed him to enroll in Canterbury College, Christchurch, from which he graduated with a B.A. in 1892 and an M.A. in 1893 with first-class honors in mathematics and physics. Financing himself by part-time teaching, he stayed for a fifth year to do research in physics, studying the properties of iron in high-frequency alternating magnetic fields. He found that he could detect the electromagnetic waves, newly discovered by Heinrich Hertz (1857 – 1894), even after they had passed through brick walls. Two substantial scientific papers on this work won for him an “1851 Exhibition” scholarship, which provided for further education in England. 14: Rutherford
  100. 100. The Tree of Quantum Mechanics On his arrival in Cambridge in 1895, Rutherford began to work under J. J. Thomson (see 11 Thomson), professor of experimental physics at the university's Cavendish Laboratory. Toward the end of the 19th century many scientists thought that no new advances in physics remained to be made. Yet within 3 years Rutherford succeeded in marking out an entirely new branch of physics called radioactivity. He soon found that thorium or its compounds disintegrated into a gas that in turn disintegrated into an unknown “active deposit”, likewise radioactive. - The Trunk 14: Rutherford Ernest Rutherford
  101. 101. The Tree of Quantum Mechanics - The Trunk Rutherford and a young chemist, Frederick Soddy (1877 – 1956), then investigated 3 groups of radioactive elements: radium, thorium, and actinium. They concluded in 1902 that radioactivity was a process in which atoms of one element spontaneously disintegrated into atoms of an entirely different element, which also remained radioactive. This interpretation was opposed by many chemists who held firmly to the concept of the indestructibility of matter; the suggestion that some atoms could tear themselves apart to form entirely different kinds of matter was to them a remnant of medieval alchemy. Nevertheless, Rutherford's outstanding work won him recognition by the Royal Society, which elected him a fellow in 1903 and awarded him the Rumford medal in 1904. 14: Rutherford
  102. 102. The Tree of Quantum Mechanics - The Trunk In 1898 Rutherford was appointed to the chair of physics at McGill University in Montreal, Canada. In 1907 he returned to England to accept a chair at the University of Manchester, where he continued his research on the alpha particle. With the ingenious apparatus that he and his research assistant, Hans Geiger (1882 – 1945), had invented, they counted the particles as they were emitted one by one from a known amount of radium; and they also measured the total charge collected, from which the charge on each particle could be detected. 14: Rutherford Johannes (Hans) Wilhelm Geiger
  103. 103. The Tree of Quantum Mechanics - The Trunk Combining this result with the rate of production of helium from radium, determined by Rutherford and the American chemist Bertram Borden Boltwood (1870 – 1927), Rutherford was able to deduce Avogadro's number (the constant number of molecules in the molecular weight in grams of any substance) in the most direct manner conceivable1 . With his student Thomas D. Royds he proved in 1908 that the alpha particle really is a helium atom, by allowing alpha particles to escape through the thin glass wall of a containing vessel into an evacuated outer glass tube and showing that the spectrum of the collected gas was that of helium. Almost immediately, in 1908, came the Nobel Prize—but for chemistry, for his investigations concerning the disintegration of elements. As Rutherford put it, “It was very unexpected, and I am startled by my metamorphosis into a chemist”. 14: Rutherford 1 About this time, Einstein found an entirely different way to measure Avogadros number, see 13 Einstein.
  104. 104. The Tree of Quantum Mechanics - The Trunk In 1911 Rutherford made his greatest contribution to science with his nuclear theory of the atom. He had observed in Montreal that fast-moving alpha particles, on passing through thin plates of mica, produced diffuse images on photographic plates; whereas a sharp image was produced when there was no obstruction to the passage of the rays. He considered that the particles must be deflected through small angles as they passed close to atoms of the mica; but calculation showed that an electric field of 100,000,000 volts per centimeter was necessary to deflect such particles traveling at 20,000 kilometers per second, a most astonishing conclusion. This phenomenon of scattering was found in the counting experiments with Geiger; Rutherford suggested to Geiger and a student, Ernest Marsden, that it would be of interest to examine whether any particles were scattered backward—i.e., deflected through an angle of more than 90 degrees. 14: Rutherford
  105. 105. The Tree of Quantum Mechanics - The Trunk To their astonishment, a few particles in every 10,000 were indeed so scattered, emerging from the same side of a gold foil from where they had come. After a number of calculations, Rutherford came to the conclusion that the intense electric field required to cause such a large deflection could occur only if all the positive charge in the atom, and therefore almost all the mass, were concentrated on a very small central nucleus some 10,000 times smaller in diameter than that of the entire atom. The positive charge on the nucleus would therefore be balanced by an equal charge on all the electrons distributed somehow around the nucleus. This theory of atomic structure is known as the Rutherford atomic model. 14: Rutherford
  106. 106. The Tree of Quantum Mechanics - The Trunk During World War I he worked on the practical problem of submarine detection by underwater acoustics. He produced the first artificial disintegration of an element in 1919, when he found that on collision with an alpha particle an atom of nitrogen was converted into an atom of oxygen and an atom of hydrogen. The same year he succeeded Thomson as Cavendish professor. His influence on research students was enormous. In the second Bakerian Lecture he gave to the Royal Society in 1920, he speculated upon the existence of the neutron and of isotopes of hydrogen and helium; 3 of them were eventually discovered in the Cavendish Laboratory. His service as president of the Royal Society (1925 – 1930), and as Chair of the Academic Assistance Council, helped almost 1,000 university refugees from Germany, but increased the claims upon his time. Whenever possible he worked in the Cavendish Laboratory, where he encouraged students, probed for the facts, and always sought an explanation in simple terms. In 1931, he was made a Peer. 14: Rutherford Return to Main Menu
  107. 107. The Tree of Quantum Mechanics If physics was in shambles, following the work of Planck and Einstein, the discovery of the atomic nucleus by Rutherford and his students (see 14 Discovery of the Nucleus) managed to make matters worse. If the electrons are outside the nucleus, shouldn’t they be drawn in by the attraction between opposite charges? Yes, but they could avoid this fate if they are in orbit around the nucleus, much like the planets around the sun. After all, electrostatic attraction between charges is an inverse square force, just like gravity; so circular or elliptical orbits would make sense. The fly in this ointment is that, in any Keplerian orbit, there is a force on the orbiting body to keep it from flying off on a straight line. Thus, an orbiting body is being constantly accelerated. However, the Maxwell Equations say that any accelerated charge must radiate electromagnetic waves; so the electrons would lose energy, and spiral into the nucleus. As atoms appear to be stable, there must be something wrong with this picture. - The Trunk 15: Bohr Hydrogen Atom
  108. 108. The Tree of Quantum Mechanics It fell to Niels Henrik David Bohr (1885 - 1962) (see 15 Bohr) to lead the way to a solution. An essential clue came from spectroscopy (see 9 Spectroscopy) – lines in the spectrum of every element showed that atoms were only capable of emitting or absorbing energy at a discrete set of wavelengths. From the new quantum viewpoint, this suggested that the electrons in an atom could only exist in a finite set of energy states; and that emission or absorption of a photon implied that an electron had jumped from one allowed state to another. The simplest atom is hydrogen, consisting of a single electron, and a nucleus of equal and opposite charge. From the work of Johann Jakob Balmer (1825 - 1898), and Johannes Robert Rydberg (1854 – 1919), the lines of the hydrogen spectrum were known to obey a simple formula involving 2 integers and a constant R, now called the Rydberg constant. From analysis of the spectrum, the value of R was known. - The Trunk 15: Bohr Hydrogen Atom
  109. 109. The Tree of Quantum Mechanics - The Trunk Bohr assembled the above arguments, added a bit of arm waving, derived the Balmer-Rydberg formula, and demonstrated that R could be calculated from several known physical constants, including the mass and charge of the electron and Planck’s constant h. This tour de force was published in a set of papers between 1913 and 1915. With the help of Arnold Johannes Wilhelm Sommerfeld (1868 - 1951), Bohr generalized this scheme somewhat to build up a picture of what more complex atoms looked like. As Bohr saw it, hydrogen’s electron had to occupy one of a set of energy states, signified by a set of integers 1, 2, 3, . . . When emission or absorption occurred, and the electron jumped between 2 of these states; the corresponding integers are those appearing in the Balmer-Rydberg formula. A diagram of these energy states, and transitions between them, is shown below, and may be helpful. 15: Bohr Hydrogen Atom
  110. 110. The Tree of Quantum Mechanics - The Trunk 15: Bohr Hydrogen Atom
  111. 111. The Tree of Quantum Mechanics Some confirmation of this picture came from helium, an atom with 2 electrons, and for which no relation corresponding to the Balmer-Rydberg formula is known. However, if one of these electrons is somehow removed (ionized in the vernacular), the spectrum of the resulting atom looks like that of hydrogen, though displaced in wavelength. Moreover, it obeys the Balmer-Rydberg formula, with a different value of R, calculable from Bohr’s theory. The trouble with this “old quantum theory”, as it’s now called, is that it had no firm theoretical underpinning. Arguments raged everywhere about what all this meant, with Bohr leading the way from his institute in Kobenhavn; but it would be another decade before a more comprehensive quantum theory would begin to take shape. Please don’t jump to 17 Matrix & Wave Mechanics until we throw in some more confusion. - The Trunk 15: Bohr Hydrogen Atom Return to Main Menu
  112. 112. The Tree of Quantum Mechanics Niels Henrik David Bohr (1885 - 1962) was born in Kobenhavn of Jewish parents. He attended the university there, where he earned a doctorate in 1911. He then went to work for J. J. Thomson (see 11 Thomson) at Cambridge, and then Ernest Rutherford (see 14 Rutherford) in Manchester. It was there that he developed his theory of the hydrogen atom (see 15 Hydrogen Atom Model). Bohr returned to Kobenhavn from Manchester in 1912, married Margrethe Nørlund, and continued to develop his new approach to the physics of the atom. The work was completed in 1913. - The Trunk 15: Bohr Niels Henrik David Bohr
  113. 113. The Tree of Quantum Mechanics - The Trunk In 1916, after serving as a lecturer in Kobenhavn, and then in Manchester, Bohr was appointed to a professorship in his native city. The university created for Bohr a new Institute of Theoretical Physics, which opened its doors in 1921; he served as director for the rest of his life. Somewhere around 1920 he developed what he called the “correspondence principle” – essentially that, in reactions involving radiation, the frequencies calculated from quantum ideas should approach a classical electrodynamics limit, as the number of atoms involved increases; i.e., that everyday behavior should evolve directly from quantum behavior at the atomic level. Bohr's institute soon became an international center for work on atomic physics and quantum theory. He also urged physicists to view atomic phenomena from the standpoint of what he called the “principle of complementarity”, that is, whether you see waves or particles depends on how you choose to look at them; but you never see both at once. A complete understanding of what’s going on requires you to consider both viewpoints. 15: Bohr

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