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The Dreams That Stuff Is Made Of by Stephen Hawking
Albert Einstein called the first discoveries that launched quantum physics “spooky," as they suggested a random universe that seemed to violate the laws of common sense. Now bestselling author and physicist Stephen Hawking introduces the nonscientific reader to this fascinating and befuddling world. This collection gathers together the most important papers on quantum physics, including the scholarship of Niels Bohr, Max Planck, Werner Heisenberg, Max Born, Ervin Schrodinger, and Richard Feynman. This is the first time all of these important works have been together in one volume—with an introduction by today’s greatest living scientist.
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First published March 22, 2011
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About the author
Stephen Hawking
245 books12.8k followersStephen William Hawking was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world.
Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD degree in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, paralysed him. After the loss of his speech, he communicated through a speech-generating device initially through use of a handheld switch, and eventually by using a single cheek muscle.
Hawking's scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Initially, Hawking radiation was controversial. By the late 1970s, and following the publication of further research, the discovery was widely accepted as a major breakthrough in theoretical physics. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.
Hawking achieved commercial success with several works of popular science in which he discussed his theories and cosmology in general. His book A Brief History of Time appeared on the Sunday Times bestseller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society, a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He died in 2018 at the age of 76, having lived more than 50 years following his diagnosis of motor neurone disease.
Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD degree in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, paralysed him. After the loss of his speech, he communicated through a speech-generating device initially through use of a handheld switch, and eventually by using a single cheek muscle.
Hawking's scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Initially, Hawking radiation was controversial. By the late 1970s, and following the publication of further research, the discovery was widely accepted as a major breakthrough in theoretical physics. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.
Hawking achieved commercial success with several works of popular science in which he discussed his theories and cosmology in general. His book A Brief History of Time appeared on the Sunday Times bestseller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society, a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He died in 2018 at the age of 76, having lived more than 50 years following his diagnosis of motor neurone disease.
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July 22, 2024
The Dreams That Stuff Is Made of: The Most Astounding Papers on Quantum Physics--and How They Shook the Scientific World, Stephen Hawking, 2011, 1071 pages, Dewey 530.12 D81d, ISBN 9780762434343
Thirty-three foundational papers, lectures, and book excerpts on quantum mechanics, by Planck, Einstein, Rutherford, Bohr, Heisenberg, Schrödinger, Dirac, Pauli, Born, Bohm, Bell, Oppenheimer, Bethe, Feynman, Gamow and others, selected and introduced by Stephen Hawking.
The bulk of the book is graduate-level quantum mechanics. One exception, pp. 966-1001, Excerpts from Thirty Years that Shook Physics, by George Gamow, is a clear, detailed, not-too-technical explanation of what was discovered (1900-1929) and how.
Textbooks and professors teach the current understanding as received wisdom. The author of the original paper proposing a new idea does not teach it this way. He admits what is /not/ known at the time; where the current understanding fails to explain observed phenomena; points out the observations that suggest a new view; explores various possible ways of understanding the phenomenon; gives reasons for arriving at his conclusions. Everything written later will omit that indecision, and give only the conclusion as established fact. Original papers are irreplaceable sources of understanding what, and how, we know.
For most of the articles, the reader is presumed to understand calculus, differential equations, orthogonal functions, Fourier transforms, Green's functions, eigenvectors and eigenvalues, statistics, combinatorics, Hilbert spaces, thermodynamics, classical electrodynamics, optics, acoustics, special and general relativity, calculus of variations, Lagrangian and Hamiltonian formulations of classical mechanics, and chemistry. These eggheads were writing primarily to each other.
Many typographical errors.
CHAPTER 1. ENERGY IS QUANTIZED. 1901-1909. pp. 1-48.
1801. [Yes, 1801.] Thomas Young's two-slit experiment shows that light behaves as a wave, making an interference pattern. p. 1.
***** 1901. On the Law of Distribution of Energy in the Normal Spectrum, Max Planck (1858-1947 p. 976), p. 5
Planck explains blackbody radiation by supposing light energy to be quantized. pp. 1-15.
This is the paper where he derives the fact that the energy of a photon is Planck's constant times the frequency. p. 12. And computes the values of Planck's constant and the Boltzmann constant (to be 6.55*10^-27 erg sec and 1.346*10^-16 erg/deg, respectively; the current values are 6.626*10^-27 erg sec and 1.381*10^-16 erg/deg, respectively). pp. 15, 841-844, 980.
Errata:
First line of p. 8: "energy E_N" should be "entropy S_N."
In the equation at the top of page 10, S^N should be S_N.
**** 1905. On a Heuristic Viewpoint Concerning the Production and Transformation of Light, Albert Einstein, p. 16
Einstein explains the photoelectric effect as a consequence of the quantization of light energy. pp. 3-4, 16-31.
Errata
p. 22 title 4. "FROM" should be "FORM."
**** 1909. The Atomic Theory of Matter, Max Planck, p. 32
Planck points out that anything with entropy must be quantized: radiant energy included. p. 37.
Each individual atom interacts with its fellow in a /reversible/ process. Yet a gas comprising myriad atoms undergoes irreversible processes. pp. 38-39.
The macro state is described only in mean values of the states of the myriad atoms. p. 40. Only the disordered states exist in nature. That gives us entropy. A single atom has no entropy. p. 41.
Two light rays never interfere, except when they originate in the same source of light. [See 1801, Thomas Young two-slit experiment.] p. 45.
Errata
p. 47, equation in mid-page, the phi should be a subscript.
CHAPTER 2. ATOMIC STRUCTURE. 1909-1922. pp. 49-147
**** 1911. The Scattering of Alpha and Beta Particles by Matter and the Structure of the Atom, Ernest Rutherford, p. 52
This is the paper where Rutherford reports that atoms have nuclei.
Rutherford and Geiger shone a beam of alpha particles (which were not then known to be helium nuclei) on gold foil 400 nanometers thick. About 1 in 20,000 were deflected an average of 90 degrees. This could happen only if the gold atoms had their positive charges clumped tightly together. At the time, the atomic numbers of the elements were unknown.
An alpha particle deflected by an atomic nucleus moves in a hyperbola with the nucleus as an external focus.
Errata
p. 56 drawing. SO should be longer than OA. S is the center of the nucleus, O the intersection of the asymptotes of the alpha particle's hyperbolic path, A the alpha particle's closest approach to the nucleus.
p. 56 equations. Every nu should be a v.
p. 56 first equation after "From conservation of energy," the minus sign should be a plus sign.
**** 1913. On the Constitution of Atoms and Molecules, Niels Bohr, p. 75
Bohr points out that by standard electrodynamics, an orbiting electron should radiate its energy away--and that this doesn't happen. pp. 78-79, 840. However by supposing electron energy quantized in whole-number multiples of Planck's constant times frequency, we get stable atoms that absorb and emit light of characteristic frequencies corresponding to the differences between the allowed electron energies. This explains the hydrogen spectrum. pp. 82-103, 841.
Errata
pp. 76, 94-95 random symbols are printed instead of accented letters.
p. 78 second paragraph "energy w" should be "energy W."
p. 79 third full paragraph, "bad" should be "had."
p. 80 there's no footnote corresponding to the asterisk.
pp. 80, 83-85, 88, 92, 97 all the A-hat characters should be deleted.
p. 80, first line after the central equations, -a should be a.
pp. 82-84, 86, 88, 90-91 "page 5" should be "page 80."
p. 87, central equation needs an end parenthesis after tau_1.
pp. 88, 90 "page 7" should be "pp. 82-83."
*** 1922. The Structure of the Atom, Niels Bohr, p. 104. This was Bohr's Nobel lecture.
Physical and chemical properties of atoms depend on the electrons; radioactivity depends on the nucleus. p. 105. "Isotopes" share chemical properties but differ in radioactivity. Rutherford has changed one element into another by breaking its nucleus by bombardment with alpha particles. p. 106.
"Atomic number" is an (electrically neutral) atom's number of electrons. pp. 108, 840.
Light comes in particles. How to reconcile that with its wave nature, such as interference patterns, is a mystery as of 1922. p. 112.
Studying the absorption and emission spectra of the elements led to insights into atomic structure: electrons are arranged in successive "shells" around the nucleus. How full of electrons the outer shell is, controls the element's physical and chemical properties, and gives rise to the periodicity of the periodic table. pp. 884-896.
Errata
p. 111 first paragraph: "properties."
p. 114 (2), and again in bottom paragraph, v should be nu.
p. 115 first paragraph, delete hyphen.
p. 125, last paragraph, delete mid-sentence period.
p. 126 top, "WC" should be "we."
p. 126 penultimate paragraph, "we" should not be italicized.
p. 128 top, "d&rent" should be "different."
p. 132 last paragraph, delete hyphen.
CHAPTER 3. MATHEMATICAL FORMALISM (NON-RELATIVISTIC). 1926-1933. pp. 148-387.
The act of measurement alters the state of a system. p. 148. The more precisely we measure, the more we alter the state. p. 149.
**** 1929. Excerpts from The Physical Principles of the Quantum Theory, Werner Heisenberg, pp. 151-236.
"I have attempted to make the distinction between waves in spacetime and the Schrödinger waves in configuration space as clear as possible." p. 153.
Quantum theory doesn't divide the world into observer and observed, hence lacks clear causality. p. 156. To attribute an effect to a cause, we'd have to observe both without disturbing their interrelation. p. 203. It's not possible to distinguish an observed system from the observer's apparatus. They affect each other. p. 204.
Every experiment to determine some quantity renders the knowledge of others illusory. p. 156.
The most important concepts of atomic physics can be induced from five experiments:
(a) 1911. Wilson photographs of alpha and beta rays emitted by radioactive elements into supersaturated water vapor. The curvature of the tracks under electric and magnetic fields shows the mass and charge of the particles. pp. 157-158, 206-214.
(b) 1928. Diffraction of matter waves, Davisson and Germer. A beam of beta rays (electrons) passing through a crystal is diffracted as if it were a wave. The wavelength of a matter wave is Planck's constant divided by the momentum of the particle. pp. 158-159, 214-216.
(c) Diffraction of x-rays. The momentum of a photon is Planck's constant divided by its wavelength (Einstein 1905). Same as for matter waves. pp. 159-160, 214-216.
(d) 1925. Compton scattering. An x-ray photon, on collision with an electron, transfers kinetic energy and momentum to the electron, just as occurs in collisions between particles of matter. pp. 159-161, 226-228. https://en.m.wikipedia.org/wiki/Compt...
(e) 1913. Franck-Hertz experiment. An electron loses a quantized amount of energy in collision with an atom. The atom can absorb energy only in lumps of particular sizes. p. 161. https://en.m.wikipedia.org/wiki/Franc...
Light /sometimes/ behaves as a particle. Matter /sometimes/ behaves as a wave. Both are both things. p. 162.
Heisenberg's Uncertainty Principle: the product of the uncertainties of a particle's position and momentum must be greater than or equal to Planck's constant. Derived by considering the particle to be a wave packet. p. 165. Another derivation, pp. 166-168, yields the product of the uncertainties greater than or equal to Planck's constant divided by 2 pi. Page 246 gives the product of the two probable errors as greater than or equal to Planck's constant divided by 4 pi.
**** 1933. The Development of Quantum Mechanics, Werner Heisenberg, pp. 237-250.
*** 1928. Quantisation as an Eigenvalue Problem, Parts I-IV, Erwin Schrödinger, pp. 251-387
Errata:
p. 252 line 7. "is" should be "it."
p. 252 line 8. "junction" should be "function."
p. 252, second paragraph, penultimate sentence, the clause beginning "such that" needs a verb.
p. 252, 4th paragraph, line 2 should begin, "continuous."
CHAPTER 4. RELATIVISTIC QUANTUM MECHANICS. 1928-1946. pp. 388-444
*** 1928. The Quantum Theory of the Electron, Paul A.M. Dirac, p. 391
Relativistic quantum mechanics: Dirac equation replaces Schrödinger equation. Predicts that antimatter must exist. p. 394. Relativistic effects are the source of "spin." pp. 388, 391-408.
*** 1940. On the Connection between Spin and Statistics, Wolfgang Pauli, pp. 409-423.
Particles with half-integer spin, "fermions," obey Fermi-Dirac statistics: Pauli exclusion principle applies: only one particle of a given set of quantum numbers can be in one place at one time. This is why white dwarf stars don't collapse: their electrons can't get too near one another. pp. 388-389. Integer-spin particles, "bosons," obey Bose-Einstein statistics: any number of particles can be in the same quantum state. pp. 388-390.
**** 1946. Exclusion Principle and Quantum Mechanics, Wolfgang Pauli, p. 424-444
This was Pauli's Nobel lecture.
The periodic table has groups of 2, 8, 18, 32, …, 2*n^2 elements, n integer. p. 424.
Electrons, protons and neutrons all have spin 1/2. p. 434.
Matter/antimatter particle pairs can be generated and annihilated. pp. 439, 441.
Errata
p. 439 Delta x > c/v should be Delta x > c/nu.
CHAPTER 5. NONDETERMINISM. PROBABILITIES ONLY. 1921-1954. pp. 445-567.
Errata
p. 445 line 5 "is remain" should be "remains."
**** 1954. The Statistical Interpretation of Quantum Mechanics, Max Born, p. 448
This was Born's Nobel lecture.
Planck's constant is the quantum of action (= energy*time = momentum*distance). p. 448.
Position-coordinate q and its corresponding momentum p are not scalars but noncommuting matrices such that p*q - q*p = h/2*pi*i (where i^2 = -1 and h is Planck's constant).
Concepts corresponding to no conceivable observation should be eliminated from physics. --Einstein, Heisenberg. p. 459.
The determinism of classical physics is an illusion. pp. 458-459.
It is necessary to redefine what is meant by "a particle." p. 461.
Errata
p. 449-450 v should be nu in the formulas for energy h*nu, frequency nu, and momentum h*nu/c.
p. 454 Missing superscript in the text corresponding to the footnoted Schrödinger paper.
p. 455 "anew's" should be "anew."
p. 458 each nu should be v, referring to speed.
* The Present Situation in Quantum Mechanics, Erwin Schrödinger, p. 462
Schrödinger's cat: Put a cat in a box with a vial of poison that equally probably will or won't be broken, based on whether a radioactive decay does or doesn't occur. Schrödinger says that quantum mechanics says the cat is simultaneously alive and dead, because the state of the cat hasn't been "measured." No, a tree falling in the forest makes a sound whether anyone hears it or not. The issue is whether radiation has or has not interacted with matter--not whether someone is aware of it. A particle or wave goes through both slits of the two-slit experiment--and makes a black dot in a particular spot on the glass plate, having hit a particular molecule of silver nitrate--whether anybody sees it or not.
* 1935. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Albert Einstein, Boris Podolsky, and Nathan Rosen, pp. 463-470.
Refuted by Bohr 1935. pp. 471-483.
***** 1935. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Niels Bohr, pp. 471-483.
Quantum-mechanical uncertainty is not merely our ignorance of the values of certain quantities, but the impossibility of unambiguously defining these quantities. p. 477.
Errata
p. 477 sacrifying should be sacrificing. https://www.oed.com/dictionary/sacrif...
p. 478 footnote. "a part" should be "apart."
p. 481 no accent on "agencies."
1952. A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, David Bohm, p. 484
Errata
p. 484 No accent on "leads."
p. 487. Superscript 1 should be superscript 10 for the footnote.
1964. On the Einstein-Podolsky-Rosen Paradox, John Bell. pp. 559-567.
CHAPTER 6. QUANTUM ELECTRODYNAMICS. 1927-1947. pp. 568-666.
*** 1927. The Quantum Theory of the Emission and Absorption of Radiation, Paul A.M. Dirac, p. 570
The light quantum (photon) has the peculiarity that it apparently ceases to exist when it is in one of its stationary states. p. 591.
Errata
pp. 571-572, 575, 593-596. h should be hbar, referring to h/(2*pi).
*** 1933. The Lagrangian Method in Quantum Mechanics, Paul A.M. Dirac, pp. 598-606.
The Lagrangian method uses coordinates and velocities; the Hamiltonian uses coordinates and momenta. pp. 598, 848.
*** 1927 (dated 1927 but cites papers through 1932). On Quantum Electrodynamics, Paul A.M. Dirac, V.A. Flock, and Boris Podolsky, p. 607-619.
Errata
p. 607 delete period after "and."
**** 1934. Foundations of the New Field Theory, Max Born and Leopold Infeld, p. 620-651.
Errata
p. 624. first equation. first x^2 should be x^1.
*** 1950. Electron Theory, J. Robert Oppenheimer, p. 652-666.
CHAPTER 7. QUANTUM ELECTRODYNAMICS "RENORMALIZED" TO REMOVE INFINITE ENERGY. 1947. pp. 667-679.
**** 1947. Fine Structure of the Hydrogen Atom by a Microwave Method, Willis Lamb and Robert Rutherford, p. 669-674.
**** The Electromagnetic Shift of Energy Levels, Hans Bethe, p. 675-679.
Errata
p. 675. Retherford should be Rutherford.
CHAPTER 8. RELATIVISTIC QUANTUM ELECTRODYNAMICS. 1946-1949. pp. 680-831.
A positron moving forward in time is an electron moving backward in time. p. 681.
*** 1946. On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields, Sin-Itiro Tomonaga, p. 682-698.
*** 1949. Space-Time Approach to Quantum Electrodynamics, Richard Feynman, p. 699-761.
Errata
p. 699 last paragraph "Co" should be "to."
p. 701 first paragraph, delete "7."
*** 1949. The Theory of Positrons, Richard Feynman, p. 762-794.
Errata
p. 762. No accent on "transition."
*** 1949. The Radiation Theories of Tomonaga, Schwinger and Feynman, Freeman Dyson, pp. 795-831.
Errata
p. 796. "simplexity" should be "simplicity."
CHAPTER 9. HISTORY. pp. 832-
General-relativistic quantum theory or quantum gravity is still an unsolved problem, as of 2011.
**** 1926. Problems of Atomic Dynamics, Max Born, p. 834-965.
A system of electric charges cannot be in stable equilibrium. p. 840.
Errata
p. 838 bottom, pointe should be points.
p. 841 m*nu^2 /2 should be m*v^2/2.
p. 931 top line should begin, "systems of"
***** Excerpts from Thirty Years That Shook Physics (Chapters I and IV), George Gamow, p. 966
Max Planck and light quanta (photons: blackbody radiation), 1900. pp. 967-980.
Einstein explains the photoelectric effect, 1905. pp. 980-985.
Compton Effect: photons have momentum and kinetic energy, 1923. pp. 985-990.
DeBroglie waves: electrons behave as waves, both in atomic orbits and in moving through space. 1925. Davisson and Germer verified it. Stern showed that atoms also diffract as waves. pp. 987-993.
Schrödinger's wave equation, 1926. Explains Bohr's quantum orbits. pp. 993-1001.
Some scattering of light by light must be expected because of virtual electron-pair formation. p. 974.
De Broglie could speak excellent English, but at home in Paris would speak only French to a visitor. p. 992.
Errata
p. 979. "hv" should be "h nu."
pp. 988-989. Every nu should be a v. These are all speeds, not frequencies.
**** Excerpts from Lectures on Quantum Mechanics, Paul A.M. Dirac, p. 1002
Thirty-three foundational papers, lectures, and book excerpts on quantum mechanics, by Planck, Einstein, Rutherford, Bohr, Heisenberg, Schrödinger, Dirac, Pauli, Born, Bohm, Bell, Oppenheimer, Bethe, Feynman, Gamow and others, selected and introduced by Stephen Hawking.
The bulk of the book is graduate-level quantum mechanics. One exception, pp. 966-1001, Excerpts from Thirty Years that Shook Physics, by George Gamow, is a clear, detailed, not-too-technical explanation of what was discovered (1900-1929) and how.
Textbooks and professors teach the current understanding as received wisdom. The author of the original paper proposing a new idea does not teach it this way. He admits what is /not/ known at the time; where the current understanding fails to explain observed phenomena; points out the observations that suggest a new view; explores various possible ways of understanding the phenomenon; gives reasons for arriving at his conclusions. Everything written later will omit that indecision, and give only the conclusion as established fact. Original papers are irreplaceable sources of understanding what, and how, we know.
For most of the articles, the reader is presumed to understand calculus, differential equations, orthogonal functions, Fourier transforms, Green's functions, eigenvectors and eigenvalues, statistics, combinatorics, Hilbert spaces, thermodynamics, classical electrodynamics, optics, acoustics, special and general relativity, calculus of variations, Lagrangian and Hamiltonian formulations of classical mechanics, and chemistry. These eggheads were writing primarily to each other.
Many typographical errors.
CHAPTER 1. ENERGY IS QUANTIZED. 1901-1909. pp. 1-48.
1801. [Yes, 1801.] Thomas Young's two-slit experiment shows that light behaves as a wave, making an interference pattern. p. 1.
***** 1901. On the Law of Distribution of Energy in the Normal Spectrum, Max Planck (1858-1947 p. 976), p. 5
Planck explains blackbody radiation by supposing light energy to be quantized. pp. 1-15.
This is the paper where he derives the fact that the energy of a photon is Planck's constant times the frequency. p. 12. And computes the values of Planck's constant and the Boltzmann constant (to be 6.55*10^-27 erg sec and 1.346*10^-16 erg/deg, respectively; the current values are 6.626*10^-27 erg sec and 1.381*10^-16 erg/deg, respectively). pp. 15, 841-844, 980.
Errata:
First line of p. 8: "energy E_N" should be "entropy S_N."
In the equation at the top of page 10, S^N should be S_N.
**** 1905. On a Heuristic Viewpoint Concerning the Production and Transformation of Light, Albert Einstein, p. 16
Einstein explains the photoelectric effect as a consequence of the quantization of light energy. pp. 3-4, 16-31.
Errata
p. 22 title 4. "FROM" should be "FORM."
**** 1909. The Atomic Theory of Matter, Max Planck, p. 32
Planck points out that anything with entropy must be quantized: radiant energy included. p. 37.
Each individual atom interacts with its fellow in a /reversible/ process. Yet a gas comprising myriad atoms undergoes irreversible processes. pp. 38-39.
The macro state is described only in mean values of the states of the myriad atoms. p. 40. Only the disordered states exist in nature. That gives us entropy. A single atom has no entropy. p. 41.
Two light rays never interfere, except when they originate in the same source of light. [See 1801, Thomas Young two-slit experiment.] p. 45.
Errata
p. 47, equation in mid-page, the phi should be a subscript.
CHAPTER 2. ATOMIC STRUCTURE. 1909-1922. pp. 49-147
**** 1911. The Scattering of Alpha and Beta Particles by Matter and the Structure of the Atom, Ernest Rutherford, p. 52
This is the paper where Rutherford reports that atoms have nuclei.
Rutherford and Geiger shone a beam of alpha particles (which were not then known to be helium nuclei) on gold foil 400 nanometers thick. About 1 in 20,000 were deflected an average of 90 degrees. This could happen only if the gold atoms had their positive charges clumped tightly together. At the time, the atomic numbers of the elements were unknown.
An alpha particle deflected by an atomic nucleus moves in a hyperbola with the nucleus as an external focus.
Errata
p. 56 drawing. SO should be longer than OA. S is the center of the nucleus, O the intersection of the asymptotes of the alpha particle's hyperbolic path, A the alpha particle's closest approach to the nucleus.
p. 56 equations. Every nu should be a v.
p. 56 first equation after "From conservation of energy," the minus sign should be a plus sign.
**** 1913. On the Constitution of Atoms and Molecules, Niels Bohr, p. 75
Bohr points out that by standard electrodynamics, an orbiting electron should radiate its energy away--and that this doesn't happen. pp. 78-79, 840. However by supposing electron energy quantized in whole-number multiples of Planck's constant times frequency, we get stable atoms that absorb and emit light of characteristic frequencies corresponding to the differences between the allowed electron energies. This explains the hydrogen spectrum. pp. 82-103, 841.
Errata
pp. 76, 94-95 random symbols are printed instead of accented letters.
p. 78 second paragraph "energy w" should be "energy W."
p. 79 third full paragraph, "bad" should be "had."
p. 80 there's no footnote corresponding to the asterisk.
pp. 80, 83-85, 88, 92, 97 all the A-hat characters should be deleted.
p. 80, first line after the central equations, -a should be a.
pp. 82-84, 86, 88, 90-91 "page 5" should be "page 80."
p. 87, central equation needs an end parenthesis after tau_1.
pp. 88, 90 "page 7" should be "pp. 82-83."
*** 1922. The Structure of the Atom, Niels Bohr, p. 104. This was Bohr's Nobel lecture.
Physical and chemical properties of atoms depend on the electrons; radioactivity depends on the nucleus. p. 105. "Isotopes" share chemical properties but differ in radioactivity. Rutherford has changed one element into another by breaking its nucleus by bombardment with alpha particles. p. 106.
"Atomic number" is an (electrically neutral) atom's number of electrons. pp. 108, 840.
Light comes in particles. How to reconcile that with its wave nature, such as interference patterns, is a mystery as of 1922. p. 112.
Studying the absorption and emission spectra of the elements led to insights into atomic structure: electrons are arranged in successive "shells" around the nucleus. How full of electrons the outer shell is, controls the element's physical and chemical properties, and gives rise to the periodicity of the periodic table. pp. 884-896.
Errata
p. 111 first paragraph: "properties."
p. 114 (2), and again in bottom paragraph, v should be nu.
p. 115 first paragraph, delete hyphen.
p. 125, last paragraph, delete mid-sentence period.
p. 126 top, "WC" should be "we."
p. 126 penultimate paragraph, "we" should not be italicized.
p. 128 top, "d&rent" should be "different."
p. 132 last paragraph, delete hyphen.
CHAPTER 3. MATHEMATICAL FORMALISM (NON-RELATIVISTIC). 1926-1933. pp. 148-387.
The act of measurement alters the state of a system. p. 148. The more precisely we measure, the more we alter the state. p. 149.
**** 1929. Excerpts from The Physical Principles of the Quantum Theory, Werner Heisenberg, pp. 151-236.
"I have attempted to make the distinction between waves in spacetime and the Schrödinger waves in configuration space as clear as possible." p. 153.
Quantum theory doesn't divide the world into observer and observed, hence lacks clear causality. p. 156. To attribute an effect to a cause, we'd have to observe both without disturbing their interrelation. p. 203. It's not possible to distinguish an observed system from the observer's apparatus. They affect each other. p. 204.
Every experiment to determine some quantity renders the knowledge of others illusory. p. 156.
The most important concepts of atomic physics can be induced from five experiments:
(a) 1911. Wilson photographs of alpha and beta rays emitted by radioactive elements into supersaturated water vapor. The curvature of the tracks under electric and magnetic fields shows the mass and charge of the particles. pp. 157-158, 206-214.
(b) 1928. Diffraction of matter waves, Davisson and Germer. A beam of beta rays (electrons) passing through a crystal is diffracted as if it were a wave. The wavelength of a matter wave is Planck's constant divided by the momentum of the particle. pp. 158-159, 214-216.
(c) Diffraction of x-rays. The momentum of a photon is Planck's constant divided by its wavelength (Einstein 1905). Same as for matter waves. pp. 159-160, 214-216.
(d) 1925. Compton scattering. An x-ray photon, on collision with an electron, transfers kinetic energy and momentum to the electron, just as occurs in collisions between particles of matter. pp. 159-161, 226-228. https://en.m.wikipedia.org/wiki/Compt...
(e) 1913. Franck-Hertz experiment. An electron loses a quantized amount of energy in collision with an atom. The atom can absorb energy only in lumps of particular sizes. p. 161. https://en.m.wikipedia.org/wiki/Franc...
Light /sometimes/ behaves as a particle. Matter /sometimes/ behaves as a wave. Both are both things. p. 162.
Heisenberg's Uncertainty Principle: the product of the uncertainties of a particle's position and momentum must be greater than or equal to Planck's constant. Derived by considering the particle to be a wave packet. p. 165. Another derivation, pp. 166-168, yields the product of the uncertainties greater than or equal to Planck's constant divided by 2 pi. Page 246 gives the product of the two probable errors as greater than or equal to Planck's constant divided by 4 pi.
**** 1933. The Development of Quantum Mechanics, Werner Heisenberg, pp. 237-250.
*** 1928. Quantisation as an Eigenvalue Problem, Parts I-IV, Erwin Schrödinger, pp. 251-387
Errata:
p. 252 line 7. "is" should be "it."
p. 252 line 8. "junction" should be "function."
p. 252, second paragraph, penultimate sentence, the clause beginning "such that" needs a verb.
p. 252, 4th paragraph, line 2 should begin, "continuous."
CHAPTER 4. RELATIVISTIC QUANTUM MECHANICS. 1928-1946. pp. 388-444
*** 1928. The Quantum Theory of the Electron, Paul A.M. Dirac, p. 391
Relativistic quantum mechanics: Dirac equation replaces Schrödinger equation. Predicts that antimatter must exist. p. 394. Relativistic effects are the source of "spin." pp. 388, 391-408.
*** 1940. On the Connection between Spin and Statistics, Wolfgang Pauli, pp. 409-423.
Particles with half-integer spin, "fermions," obey Fermi-Dirac statistics: Pauli exclusion principle applies: only one particle of a given set of quantum numbers can be in one place at one time. This is why white dwarf stars don't collapse: their electrons can't get too near one another. pp. 388-389. Integer-spin particles, "bosons," obey Bose-Einstein statistics: any number of particles can be in the same quantum state. pp. 388-390.
**** 1946. Exclusion Principle and Quantum Mechanics, Wolfgang Pauli, p. 424-444
This was Pauli's Nobel lecture.
The periodic table has groups of 2, 8, 18, 32, …, 2*n^2 elements, n integer. p. 424.
Electrons, protons and neutrons all have spin 1/2. p. 434.
Matter/antimatter particle pairs can be generated and annihilated. pp. 439, 441.
Errata
p. 439 Delta x > c/v should be Delta x > c/nu.
CHAPTER 5. NONDETERMINISM. PROBABILITIES ONLY. 1921-1954. pp. 445-567.
Errata
p. 445 line 5 "is remain" should be "remains."
**** 1954. The Statistical Interpretation of Quantum Mechanics, Max Born, p. 448
This was Born's Nobel lecture.
Planck's constant is the quantum of action (= energy*time = momentum*distance). p. 448.
Position-coordinate q and its corresponding momentum p are not scalars but noncommuting matrices such that p*q - q*p = h/2*pi*i (where i^2 = -1 and h is Planck's constant).
Concepts corresponding to no conceivable observation should be eliminated from physics. --Einstein, Heisenberg. p. 459.
The determinism of classical physics is an illusion. pp. 458-459.
It is necessary to redefine what is meant by "a particle." p. 461.
Errata
p. 449-450 v should be nu in the formulas for energy h*nu, frequency nu, and momentum h*nu/c.
p. 454 Missing superscript in the text corresponding to the footnoted Schrödinger paper.
p. 455 "anew's" should be "anew."
p. 458 each nu should be v, referring to speed.
* The Present Situation in Quantum Mechanics, Erwin Schrödinger, p. 462
Schrödinger's cat: Put a cat in a box with a vial of poison that equally probably will or won't be broken, based on whether a radioactive decay does or doesn't occur. Schrödinger says that quantum mechanics says the cat is simultaneously alive and dead, because the state of the cat hasn't been "measured." No, a tree falling in the forest makes a sound whether anyone hears it or not. The issue is whether radiation has or has not interacted with matter--not whether someone is aware of it. A particle or wave goes through both slits of the two-slit experiment--and makes a black dot in a particular spot on the glass plate, having hit a particular molecule of silver nitrate--whether anybody sees it or not.
* 1935. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Albert Einstein, Boris Podolsky, and Nathan Rosen, pp. 463-470.
Refuted by Bohr 1935. pp. 471-483.
***** 1935. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Niels Bohr, pp. 471-483.
Quantum-mechanical uncertainty is not merely our ignorance of the values of certain quantities, but the impossibility of unambiguously defining these quantities. p. 477.
Errata
p. 477 sacrifying should be sacrificing. https://www.oed.com/dictionary/sacrif...
p. 478 footnote. "a part" should be "apart."
p. 481 no accent on "agencies."
1952. A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, David Bohm, p. 484
Errata
p. 484 No accent on "leads."
p. 487. Superscript 1 should be superscript 10 for the footnote.
1964. On the Einstein-Podolsky-Rosen Paradox, John Bell. pp. 559-567.
CHAPTER 6. QUANTUM ELECTRODYNAMICS. 1927-1947. pp. 568-666.
*** 1927. The Quantum Theory of the Emission and Absorption of Radiation, Paul A.M. Dirac, p. 570
The light quantum (photon) has the peculiarity that it apparently ceases to exist when it is in one of its stationary states. p. 591.
Errata
pp. 571-572, 575, 593-596. h should be hbar, referring to h/(2*pi).
*** 1933. The Lagrangian Method in Quantum Mechanics, Paul A.M. Dirac, pp. 598-606.
The Lagrangian method uses coordinates and velocities; the Hamiltonian uses coordinates and momenta. pp. 598, 848.
*** 1927 (dated 1927 but cites papers through 1932). On Quantum Electrodynamics, Paul A.M. Dirac, V.A. Flock, and Boris Podolsky, p. 607-619.
Errata
p. 607 delete period after "and."
**** 1934. Foundations of the New Field Theory, Max Born and Leopold Infeld, p. 620-651.
Errata
p. 624. first equation. first x^2 should be x^1.
*** 1950. Electron Theory, J. Robert Oppenheimer, p. 652-666.
CHAPTER 7. QUANTUM ELECTRODYNAMICS "RENORMALIZED" TO REMOVE INFINITE ENERGY. 1947. pp. 667-679.
**** 1947. Fine Structure of the Hydrogen Atom by a Microwave Method, Willis Lamb and Robert Rutherford, p. 669-674.
**** The Electromagnetic Shift of Energy Levels, Hans Bethe, p. 675-679.
Errata
p. 675. Retherford should be Rutherford.
CHAPTER 8. RELATIVISTIC QUANTUM ELECTRODYNAMICS. 1946-1949. pp. 680-831.
A positron moving forward in time is an electron moving backward in time. p. 681.
*** 1946. On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields, Sin-Itiro Tomonaga, p. 682-698.
*** 1949. Space-Time Approach to Quantum Electrodynamics, Richard Feynman, p. 699-761.
Errata
p. 699 last paragraph "Co" should be "to."
p. 701 first paragraph, delete "7."
*** 1949. The Theory of Positrons, Richard Feynman, p. 762-794.
Errata
p. 762. No accent on "transition."
*** 1949. The Radiation Theories of Tomonaga, Schwinger and Feynman, Freeman Dyson, pp. 795-831.
Errata
p. 796. "simplexity" should be "simplicity."
CHAPTER 9. HISTORY. pp. 832-
General-relativistic quantum theory or quantum gravity is still an unsolved problem, as of 2011.
**** 1926. Problems of Atomic Dynamics, Max Born, p. 834-965.
A system of electric charges cannot be in stable equilibrium. p. 840.
Errata
p. 838 bottom, pointe should be points.
p. 841 m*nu^2 /2 should be m*v^2/2.
p. 931 top line should begin, "systems of"
***** Excerpts from Thirty Years That Shook Physics (Chapters I and IV), George Gamow, p. 966
Max Planck and light quanta (photons: blackbody radiation), 1900. pp. 967-980.
Einstein explains the photoelectric effect, 1905. pp. 980-985.
Compton Effect: photons have momentum and kinetic energy, 1923. pp. 985-990.
DeBroglie waves: electrons behave as waves, both in atomic orbits and in moving through space. 1925. Davisson and Germer verified it. Stern showed that atoms also diffract as waves. pp. 987-993.
Schrödinger's wave equation, 1926. Explains Bohr's quantum orbits. pp. 993-1001.
Some scattering of light by light must be expected because of virtual electron-pair formation. p. 974.
De Broglie could speak excellent English, but at home in Paris would speak only French to a visitor. p. 992.
Errata
p. 979. "hv" should be "h nu."
pp. 988-989. Every nu should be a v. These are all speeds, not frequencies.
**** Excerpts from Lectures on Quantum Mechanics, Paul A.M. Dirac, p. 1002
June 5, 2013
This book makes me cry tears of joy, nothing is more rewarding than being able to read the seminal authors of the quantum age in their own words, and in a way that illuminates the topic. Do I understand it?, don't get wise, but it takes a lot of work to dig through anything that took some of these people years and decades to prepare, so bring your open comportment , don't be afraid to re re re read things, and take it in the spirit it's given, "I'm bored, I'll read a paper by Julian Schwanger tonight" don't be uncomfortable with uncertainty and you will be ok, and don't forget, the proper response to assertions about dice playing gods is " Stop Telling God What To Do" just like Bohr did, it's the irreverent thing to do!
July 8, 2012
Having all of these groundbreaking papers put in order is very illuminating, especially in seeing how the ideas that are now quite strictly defined developed over time and experimentation. One oddity is that Einstein's first paper is inexplicably full of typos, including the equations! However, the rest of the papers are relatively typo-free. Especially interesting were the "hidden variables" and controversy papers and the final introductory university lectures by Born, Gamow and Dirac, which not only quickly and concisely introduce the full theory but then attempt to apply it to curved spacetime. It would be excellent for any advanced undergraduate to read.
August 31, 2013
Quantum physics has never been more topical. Schrodinger's "dead and alive" cat has become part of popular folklore, parallel universes have emerged from science fiction to become part of serious scientific speculation, and quantum computers offer the prospect of a leap forward from the classical computer as great as the leap from the abacus to the classical computer itself. Quantum physicists have even achieved teleportation -- although as yet, only of photons, not people. So the time is very much ripe for a collection such as this, pulling together many of the great scientific papers of the twentieth century that together comprised the quantum revolution. There have been similar collections before (notably John Wheeler & Wojciech Zurek, editors, Quantum Theory and Measurement, Princeton UP, 1983); but with Stephen Hawking's name attached to it, the latest version is likely to reach a much wider audience than its predecessors, especially following the success of the same team’s Einstein collection, A Stubbornly Persistent Illusion.
That prospective audience should be warned, though, that the papers collected here are not for the faint hearted. They are the real nitty gritty, written by such luminaries as Max Planck, Albert Einstein, Werner Heisenberg and Erwin Schrodinger, more or less as published in the scientific journals of the time. There has been some judicious editing (and some I regard as injuducious), but there is very little here that would be an easy read for anyone with less than a degree in physics. That said, if you have either the stamina to plough through the whole story, or the inclination to dip in for favourite nuggets, this is the place to find the truth behind many of the stories making headlines today.
The story starts with Planck’s discovery at the beginning of the twentieth century of the mathematical law that describes radiation from a hot body (bizarrely known as “black body” radiation) and proceeds through Einstein’s proof that the “particles of light”, photons, are real, to the application of these ideas to atomic physics and the discovery in the 1920s that the quantum world is stranger than anything that had been imagined. The discovery of wave-particle duality (de Broglie) and quantum uncertainty (Heisenberg) made quantum physics as much a branch of philosophy as science, stirring arguments that continue to the present day about how to interpret what the equations are telling us. Is it really possible that quantum systems -- perhaps even cats -- exist in a state of unreality until we look at them ands “collapse the wave function”? Or are there many, perhaps infinitely many, different realities, in which all possible outcomes of quantum choices are carried out? Is it possible that instantaneous communications link quantum entities across vast spaces, what Einstein called “spooky action at a distance”? (The answer to the last question, by the way is “yes”; experiments, not included here, have proved it.)
Against this philosophical debating, hard core physicists such as Richard Feynman, who is included here, ignored the philosophy and got on with solving the equations (after they had found the right ones to solve!), coming up with a complete description of everything in the Universe except gravity. Including gravity in the quantum fold remains the Holy Grail of physicists, but that story is beyond the scope of Hawing’s book.
There are two serious omissions from the book, which shows signs of having been put together hastily, and one bizarre inclusion. Louis de Broglie's paper introducing the idea that electrons could be treated as waves (which impressed Einstein and led Schrodinger to his Nobel-prize winning breakthrough) is conspicuous by its absence, as is the paper by Hugh Everett which made the "many worlds" idea, which remains the best resolution of the Schrodinger's cat puzzle, part of mainstream science. Of course, something has to give even in a volume this size, but space for these ideas could have been found by leaving out the extract from a popular book by George Gamow, which no more deserves a place here than an extract from, say, A Brief History of Time. It is also inexcusable in as book of this kind to have no index, and no guide to further reading. And I may be a pedant but if you are going to use a Shakespeare quotation in the title of a book, you should get it right!
That said, on balance The Dreams that Stuff is Made Of is a welcome addition to the quantum library, and pulls together in one place a lot of material that it would otherwise take a while to track down. At $30, it is also remarkably good value; but do not be sucked in by the publisher’s claim that it “introduces the nonscientific reader to the mind-bending world of quantum physics.” Approach this with no knowledge of science and your mind may well get bent, but you are unlikely to get much insight into what is going on.
This review first appeared in the Wall Street Journal.
FYI:
Prospero: Our revels now are ended. These our actors, As I foretold you, were all spirits, and Are melted into air, into thin air: And like the baseless fabric of this vision, The cloud-capp'd tow'rs, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve, And, like this insubstantial pageant faded, Leave not a rack behind. We are such stuff As dreams are made on; and our little life Is rounded with a sleep.
The Tempest Act 4, scene 1, 148–158
September 5, 2017
This wonderful anthology from Stephen Hawking is something I have used as a reference text for almost a year now and greatly enjoyed. As many have noted, this is not for the layman as it contains genuine papers from important periods in the development of the study of quantum physics written for physicists and physics students. If you don't know that language then this will seem to be an alien language. I can see this being used effectively for an undergraduate course on the history of physics in the 20th century or some related topic. Rarely do you have such an anthology presented by a complete all-star in the field such as Stephen Hawking and his choice of material presents a potent narrative of increasing clarity and understanding (though obviously incomplete) of the quantum world.
December 20, 2012
A collection of scientific papers on the development of quantum mechanics. Not sure how interesting this stuff is to normal folk, but to the physics community it's pure gold. I'll put it on my bookshelf between my autographed copy of Principles of Quantum Mechanics (Dirac) and the Centennial Edition of the Astrophysical Journal, a similar volume published by the American Astronomical Society in 1999.
September 24, 2013
Lots of reviews point out the errors in equations. Almost too glaring of an oversight that the first equation of the first paper (by Einstein no less) had glaring errors that would be obvious even to a lay person, left me wondering if that error in particular could even be an intentional signal by the authors not to take for granted the entirety of the content. I could be reading too much into it though.
September 28, 2020
This is an excellent survey of foundations of quantum physics, and directly helped me in some graduate work.
October 22, 2024
A MARVELOUS PRESENTATION OF THE “KEY” PAPERS ESTABLISHING QUANTUM THEORY
Hawking wrote in his Introduction to this 2011 book, “The success of quantum theory, and its interpretation, raised many philosophical issues because quantum theory is non-deterministic, meaning that when a system starts in a given state, the results of measurements on its future state cannot in general be precisely predicted… The development of quantum theory meant the end of the idea that science could in principle predict all future events given enough information about the system at present… Today, thanks to Richard Feynman, we know that quantum theory means that a physical system doesn’t have a single history, but rather has many histories, each associated with a different probability… As this volume traces all these developments we are reminded of Bertrand Russell’s words, ‘We all start from ‘naïve realism,’ i.e., the doctrine that things are what they seem… But physics assures us that the greenness of grass, the hardness of stones, and the coldness of stones are not… that we know in our experience, but something very different…’ It is these dreams that stuff is made of.”
Niels Bohr observes, “Thus the length of the year is not determined by the masses of the sun and the earth alone, but depends also on the conditions that existed during the formation of the solar system, of which we have very little knowledge. Should a sufficiently large foreign body some day traverse our solar system, we might among other effects expect that from the day the length of the year would be different from its present value.” (Pg. 108-109)
Werner Heisenberg states, “it is seen that both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time---the two concepts are too different. It is true that it might be postulated that two separate entities, one having all the properties of a particle, and the other all the properties of wave motion, were combined in some way to form ‘light.’ But such theories are unable to bring about the intimate relation between the two entities which seems required by the experimental evidence.
"As a matter of fact, it is experimentally certain only that light sometimes behaves as if it possessed some of the attributes of a particle, but there is no experiment which proves that it possesses all the properties of a particle; similar statements hold for matter and wave motion. The solution of the difficulty is that the two mental pictures which experiments lead us to form---the one of particles, the other of waves---are both incomplete and have only the validity of analogies which are accurate only in limiting cases… Light and matter are both single entities, and the apparent duality arises in the limitations of our language.” (Pg. 161-162)
Hawking explains Heisenberg’s Uncertainty Principle: “A measurement of position will alter the original state. Taking a measurement of speed afterward will be on this altered state, and so will produce a different answer than if it were taken on the original state. The more precisely we measure the particle’s speed, the more we alter the state, and consequently the less we can know about its original velocity. It is impossible to get a complete measurement of both simultaneously… The impossibility comes not from our inability to design a clever enough experiment, but seems is inherent in the physical laws of nature as formalized in the Heisenberg Uncertainty Principle.” (Pg. 149)
Heisenberg himself explains it thusly: “The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not restrict, for example, the exactness of a position measurement alone or a velocity measurement alone… This may be expressed in concise and general terms by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments. This formulation makes it clear that the uncertainty relation does not refer to the past; if the velocity of the electron is at first known and the position then exactly measured, the position for times previous to the measurement may be calculated.” (Pg. 169)
Heisenberg says, “Many of the abstractions that are characteristic of modern theoretical physics are to be found discussed in the philosophy of past centuries. At that time these abstractions could be disregarded as mere mental exercises by those scientists whose only concern was with reality, but today we are compelled by the refinements of experimental art to consider them seriously.” (Pg. 205)
Erwin Schrodinger suggests, “we can never assert that the electron at a definite instant is to be found on any definite one of the quantum paths, specialized by the quantum conditions… All these assertions systematically contribute to the relinquishing of the ideas of ‘place of the electron’ and ‘path of the electron.’ If these are not given up, contradictions remain. This contradiction has been so strongly felt that it has even been doubted whether what goes on in the atom could ever be described within the scheme of space and time. From the philosophical standpoint, I would consider a conclusive decision in this sense as equivalent to a complete surrender. For we cannot really alter our manner of thinking in space and time, and what we cannot comprehend within it we cannot understand at all. There ARE such things---but I do not believe that atomic structure is one of them.” (Pg. 285)
Hawking again explains, “The standard interpretation of quantum mechanics … has been named as the ‘Copenhagen interpretation.’ Two fundamental postulates of the Copenhagen interpretation are that we should only be concerned with what is actually observed and that the quantum wave function or state vector of a system contains all possible information for that system. These two postulates seem very reasonable, but they lead to many strange results… How do we interpret the wave function?
"The most widely accepted answer comes Max Born. He argued that the wave function… represents the probability that an event will occur. In this sense, quantum mechanics is non-deterministic. In a deterministic theory, when a system starts out with a given initial state, its final state can be calculated from the theory at all times. But in quantum mechanics this is not the case. Identical experiments with identical starting conditions can produce different results. All we can do is calculate the PROBABILITY that a system will end in a certain final state.” (Pg. 445)
Max Born states, “I should like only to say this: the determinism of classical physics turns out to be an illusion, created by overrated mathematico-logical concepts. It is an idol, not an ideal in scientific research and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.” (Pg. 459)
Schrodinger gives his famous “cat paradox”: “One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device… in a Geiger counter there is a tiny bit of radioactive substance, so small, that PERHAPS in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left his entire system to itself for an hour, one would say that the cat still lives IF meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat… mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be RESOLVED by direct observation. That prevents us from so naively accepting as valid a ‘blurred model’ for representing reality.” (Pg. 462)
Hawking suggests, “The search for a quantum theory that is consistent with general relativity or a quantum gravity theory is still an unsolved problem in physics. Finding this theory is, perhaps, the primary goal of theoretical physics. Currently the most favored type of quantum gravity theory is known as string theory, but it still remains to be shown if string theory is an accurate description of reality. It will be fascinating to see in the coming years which quantum gravity theory best describes out universe, because once this theory is found, we will for the first time have a fundamental understanding of all known physical laws.” (Pg. 833)
This book is based on what I consider to be an excellent idea: Present the ACTUAL “original” technical papers that were important for the development of quantum theory, along with an excellent “commentator” (Hawking, in this case) who is able to put the technical details into comprehensible English. Some readers will relish digging into the complexities and mathematics of the original papers; while others (such as myself) may simply breeze past the math, and simply relish the actual words of the FOUNDERS of theory, rather than the third-and fourth-hand paraphrases of their ideas that we get in too many books about the development of quantum theory
Hawking wrote in his Introduction to this 2011 book, “The success of quantum theory, and its interpretation, raised many philosophical issues because quantum theory is non-deterministic, meaning that when a system starts in a given state, the results of measurements on its future state cannot in general be precisely predicted… The development of quantum theory meant the end of the idea that science could in principle predict all future events given enough information about the system at present… Today, thanks to Richard Feynman, we know that quantum theory means that a physical system doesn’t have a single history, but rather has many histories, each associated with a different probability… As this volume traces all these developments we are reminded of Bertrand Russell’s words, ‘We all start from ‘naïve realism,’ i.e., the doctrine that things are what they seem… But physics assures us that the greenness of grass, the hardness of stones, and the coldness of stones are not… that we know in our experience, but something very different…’ It is these dreams that stuff is made of.”
Niels Bohr observes, “Thus the length of the year is not determined by the masses of the sun and the earth alone, but depends also on the conditions that existed during the formation of the solar system, of which we have very little knowledge. Should a sufficiently large foreign body some day traverse our solar system, we might among other effects expect that from the day the length of the year would be different from its present value.” (Pg. 108-109)
Werner Heisenberg states, “it is seen that both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time---the two concepts are too different. It is true that it might be postulated that two separate entities, one having all the properties of a particle, and the other all the properties of wave motion, were combined in some way to form ‘light.’ But such theories are unable to bring about the intimate relation between the two entities which seems required by the experimental evidence.
"As a matter of fact, it is experimentally certain only that light sometimes behaves as if it possessed some of the attributes of a particle, but there is no experiment which proves that it possesses all the properties of a particle; similar statements hold for matter and wave motion. The solution of the difficulty is that the two mental pictures which experiments lead us to form---the one of particles, the other of waves---are both incomplete and have only the validity of analogies which are accurate only in limiting cases… Light and matter are both single entities, and the apparent duality arises in the limitations of our language.” (Pg. 161-162)
Hawking explains Heisenberg’s Uncertainty Principle: “A measurement of position will alter the original state. Taking a measurement of speed afterward will be on this altered state, and so will produce a different answer than if it were taken on the original state. The more precisely we measure the particle’s speed, the more we alter the state, and consequently the less we can know about its original velocity. It is impossible to get a complete measurement of both simultaneously… The impossibility comes not from our inability to design a clever enough experiment, but seems is inherent in the physical laws of nature as formalized in the Heisenberg Uncertainty Principle.” (Pg. 149)
Heisenberg himself explains it thusly: “The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not restrict, for example, the exactness of a position measurement alone or a velocity measurement alone… This may be expressed in concise and general terms by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments. This formulation makes it clear that the uncertainty relation does not refer to the past; if the velocity of the electron is at first known and the position then exactly measured, the position for times previous to the measurement may be calculated.” (Pg. 169)
Heisenberg says, “Many of the abstractions that are characteristic of modern theoretical physics are to be found discussed in the philosophy of past centuries. At that time these abstractions could be disregarded as mere mental exercises by those scientists whose only concern was with reality, but today we are compelled by the refinements of experimental art to consider them seriously.” (Pg. 205)
Erwin Schrodinger suggests, “we can never assert that the electron at a definite instant is to be found on any definite one of the quantum paths, specialized by the quantum conditions… All these assertions systematically contribute to the relinquishing of the ideas of ‘place of the electron’ and ‘path of the electron.’ If these are not given up, contradictions remain. This contradiction has been so strongly felt that it has even been doubted whether what goes on in the atom could ever be described within the scheme of space and time. From the philosophical standpoint, I would consider a conclusive decision in this sense as equivalent to a complete surrender. For we cannot really alter our manner of thinking in space and time, and what we cannot comprehend within it we cannot understand at all. There ARE such things---but I do not believe that atomic structure is one of them.” (Pg. 285)
Hawking again explains, “The standard interpretation of quantum mechanics … has been named as the ‘Copenhagen interpretation.’ Two fundamental postulates of the Copenhagen interpretation are that we should only be concerned with what is actually observed and that the quantum wave function or state vector of a system contains all possible information for that system. These two postulates seem very reasonable, but they lead to many strange results… How do we interpret the wave function?
"The most widely accepted answer comes Max Born. He argued that the wave function… represents the probability that an event will occur. In this sense, quantum mechanics is non-deterministic. In a deterministic theory, when a system starts out with a given initial state, its final state can be calculated from the theory at all times. But in quantum mechanics this is not the case. Identical experiments with identical starting conditions can produce different results. All we can do is calculate the PROBABILITY that a system will end in a certain final state.” (Pg. 445)
Max Born states, “I should like only to say this: the determinism of classical physics turns out to be an illusion, created by overrated mathematico-logical concepts. It is an idol, not an ideal in scientific research and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.” (Pg. 459)
Schrodinger gives his famous “cat paradox”: “One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device… in a Geiger counter there is a tiny bit of radioactive substance, so small, that PERHAPS in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left his entire system to itself for an hour, one would say that the cat still lives IF meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat… mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be RESOLVED by direct observation. That prevents us from so naively accepting as valid a ‘blurred model’ for representing reality.” (Pg. 462)
Hawking suggests, “The search for a quantum theory that is consistent with general relativity or a quantum gravity theory is still an unsolved problem in physics. Finding this theory is, perhaps, the primary goal of theoretical physics. Currently the most favored type of quantum gravity theory is known as string theory, but it still remains to be shown if string theory is an accurate description of reality. It will be fascinating to see in the coming years which quantum gravity theory best describes out universe, because once this theory is found, we will for the first time have a fundamental understanding of all known physical laws.” (Pg. 833)
This book is based on what I consider to be an excellent idea: Present the ACTUAL “original” technical papers that were important for the development of quantum theory, along with an excellent “commentator” (Hawking, in this case) who is able to put the technical details into comprehensible English. Some readers will relish digging into the complexities and mathematics of the original papers; while others (such as myself) may simply breeze past the math, and simply relish the actual words of the FOUNDERS of theory, rather than the third-and fourth-hand paraphrases of their ideas that we get in too many books about the development of quantum theory
June 3, 2019
A not-so-little anthology of scientific wonder. I have to say, not the easiest read. It took me months to finally finish it; But digging in to understand the equations and concepts is part of what makes it such an enjoyable read. Recommended for the relentless science lovers.
May 31, 2015
This book... was extremely good. Explaining many things confused in general about quantum physics, and makes it clear or even more confusing!
December 15, 2017
Los papers importantes para entender la mecánica cuántica.
November 27, 2020
The book The stuff that dreams are made of by stephen hawking is a fantastic compilation to the principles papers of quantum mechanics for an advanced levellevel person in this field. This book is a comprehensive walk through all of the principles of cosmology from the big bang to an introduction to quantum mechanics. This book does not include math, and is extremely principle heavy, so it is comprehensible to someone who doesn’t have a background in calculus or advanced theoretical physics. I would recommend this book to anyone who wants a more advanced and in depth analysis and description of cosmological principles than the brief history of time by stephen hawking offers, but not as advanced as a full on cosmology tesxtbook. This book was enjoyable for me to read because I already have a mathematical background in these areas that the little book of cosmology covered, so it helped me visualize these abstract concepts better than I previously had. Overall, I really enjoyed this book and it was an extremely fun book to read
Currently reading
April 3, 2020This is a difficult book to get through, so putting it aside for now, and will come back to read the occasional chapter
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February 16, 2021Collection of scientific papers with little to no elucidation for the layman by the great Stephen Hawking, so no, unfortunately not for me...
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February 22, 2023A thick read if you like that stuff and hard to understand. It covers a lot of ground.
March 30, 2023
Una joyita en cuanto a textos de física. No solo es denso teóricamente, sino que da interesantes detalles del contexto en el cual se van haciendo los descubrimientos. Difícil de seguir por la naturaleza de las ecuaciones, pero tengo la esperanza de que en un futuro no tal lejano sea capaz de comprenderlo a profundidad.
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