Helgoland by Rovelli, Erica (ebook reader below 3000 .txt) 📗

contented himself with studying the nonrelativistic limit, and this worked.

17. Erwin Schrödinger, “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinem,” Annalen der Physik 384, no. 5 (1926), 734–56.

18. Throughout the book I call ψ the “wave function,” that is, the quantum state in the base position is the abstract quantum state, represented by a vector in a Hilbert space. For the considerations that follow, the distinction is not relevant.

19. George Uhlenbeck, quoted in A. Pais, “Max Born’s Statistical Interpretation of Quantum Mechanics,” Science 218 (1982), 1193–98.

20. Cited in Manjit Kumar, Quantum: Einstein, Bohr and the Great Debate about the Nature of Reality (London: Icon Books, 2008), 155.

21. Kumar, Quantum, 220.

22. Erwin Schrödinger, Nature and the Greeks and Science and Humanism (Cambridge, UK: Cambridge University Press, 1996).

23. Max Born, “Quantenmechanik der Stossvorgänge,” Zeitschrift für Physik 38 (1926), 803–27.

24. The squared modulus of ψ (x) gives the density of probability that the particle will be observed at point x rather than anywhere else.

25. They have changed the rules, and it is now illegal.

26. In the same way, Heisenberg’s theory gives the probability that we will see something, given the previous observations.The Granularity of the World: Quanta

27. B=2hv3c−2 / (ehv/kT−1). Max Planck, “Über eine Verbesserung der Wienschen Spectraleichung,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2 (1900), 202–4.

28. E = hv.

29. Albert Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 322, no. 6 (1905), 132–48.

30. This is the effect on which photoelectric cells are based: on certain metals the light produces a small electric current. The strange thing is that this does not happen for light of low frequency, independently of the intensity of the light. Einstein understood that the reason is that—regardless of how many there are—the photons of lower frequency are less energetic and do not have sufficient energy to extract electrons from atoms.

31. Niels Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine and Journal of Science 26 (1913), 1–25.

32. Subsequently published in Niels Bohr, “The Quantum Postulate and the Recent Development of Atomic Theory,” Nature 121 (1928), 580–90.

33. P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford: Oxford University Press, 1930).

34. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Berlin: Springer, 1932).

35. J. Bernstein, “Max Born and the Quantum Theory,” American Journal of Physics 73 (2005), 999–1008.II. A CURIOUS BESTIARY OF EXTREME IDEASSuperpositions

36. P. A. M. Dirac, I principi della meccanica quantistica (Turin: Bollati Boringhieri, 1968); L. D. Landau and E. M. Lisfits, Meccanica quantistica (Rome: Editori Riuniti, 1976); R. Feynman, La fisica di Feynman: The Feynman Lectures on Physics, vol. 3 (London: Addison-Wesley, 1970); La fisica di Berkeley, vol. 4, Fisica quantistica (Bologna: Zanichelli, 1973); A. Messiah, Quantum Mechanics, vol. 1 (Amsterdam: North Holland, 1967).

37. Cited in A. Pais, Ritratti di scienziati geniali. I fisici del XX secolo (Turin: Bollati Boringhieri, 2007), 31.

38. Erwin Schrödinger, “Die gegenwärtige Situation in der Quantenmechnik,” Naturwissenschaften 23 (1935), 807–12.

39. This is why we do not become aware of quantum mechanics in our daily lives. We do not see the effects of interference and therefore can replace the quantum superposition between cat-awake and cat-asleep with the simple fact that we do not know whether the cat is asleep or not. The suppression of interference phenomena for objects that interact with a large number of variables is well understood. It is called “quantum decoherence.”Taking ψ Seriously: Many Worlds, Hidden Variables and Physical Collapses

40. Many books reconstruct this historic discussion in more detail. For instance, see the excellent Quantum by Manjit Kumar and more recently La realtà al tempo dei quanti by Federico Laudisa. Laudisa is sympathetic to Einstein’s intuition; I follow more in the footsteps of Bohr and Heisenberg.

41. David Kaiser, How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival (New York: W. W. Norton, 2012).

42. For a recent defense of this interpretation, see Sean Carroll, Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime (New York: Dutton, 2019).

43. It is not enough to know the ψ wave and Schrödinger’s equation in order to define and use quantum theory: we need to specify an algebra of observables, otherwise we cannot calculate anything and there is no relation with the phenomena of our experience. The role of this algebra of observables, which is extremely clear in other interpretations, is not at all clear in the Many Worlds interpretation.

44. A presentation and a defense of Bohm’s theory can be found in David Z. Albert, Quantum Mechanics and Experience (Cambridge, MA, and London: Harvard University Press, 1992).

45. The way in which we interact with the particle is quite subtle, and often not very clear in presentations of the theory. The wave of an instrument of measurement interacts with the wave of the electron, but the dynamic of the equipment is guided by the value of the common wave determined by the position of the electron, and hence its evolution is determined by where the electron actually is.

46. There is another possibility: that quantum mechanics is only an approximation, and the hidden variables effectively reveal themselves in some other regime. For now, these modifications of the predictions of quantum mechanics, however, cannot be seen.

47. The space of the configurations of the set of particles.

48. There are different versions of these theories, all somewhat artificial and incomplete. There are two that are better known: a concrete mechanism designed by the Italian physicists Giancarlo Ghirardi, Alberto Rimini and Tullio Weber; and Roger Penrose’s hypothesis that the collapse is induced by gravity when the quantum superposition between different configurations of space-time exceeds a threshold value.Accepting Indeterminacy

49. C. Calosi and C. Mariani, “Quantum Relational Indeterminacy,” Studies in History and Philosophy of Science. Part B: Studies in History and Philosophy of Modern Physics 71 (2020), 158–69.

50. More precisely, the quantity ψ is like the Hamilton’s function S (the solution of the Hamilton–Jacobi equation) in classical mechanics: a calculation tool, not an entity to be considered real. As evidence of this, observe that Hamilton’s S function is effectively the classical limit of the wave