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

51. In the sense of Johann Gottlieb Fichte, Friedrich Schelling and G. W. F. Hegel.III. IS IT POSSIBLE THAT SOMETHING IS REAL IN RELATION TO YOU BUT NOT IN RELATION TO ME?Relations

52. For a technical introduction to the relational interpretation of quantum mechanics, see the entry “Relational Quantum Mechanics” in Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, https://plato.stanford.edu/archives/win2019/entries/qm-relational/.

53. Niels Bohr, The Philosophical Writings of Niels Bohr (Woodbridge, CT: Ox Bow Press, 1998), vol. 4, 111.

54. The properties I am referring to are those that are variables: that is, those described by functions on the phase space, not the invariant properties such as the nonrelativistic mass of a particle.

55. An event is real with respect to a stone if it acts on it, if it modifies it. An event is not real with respect to the stone if its fall implies that interference phenomena that occur do not occur.The Rarefied and Subtle World of Quanta

56. An event e1 is “relative to A, but not to B,” in the following sense: e1 acts on A, but there is an event e2 that can act on B which would be impossible if e1 had acted on B.

57. The first person to realize the relational character of the ψ wave was a young American doctoral student in the mid-1950s, Hugh Everett III. His doctoral thesis, “The Formulation of Quantum Mechanics Based on Relative States,” has a had a big influence on discussions of quanta.

58. Anthony Aguirre, Cosmological Koans: A Journey to the Heart of Physical Reality (New York: W. W. Norton, 2019), chap. 44.

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

60. Carlo Rovelli, Che cos’è la scienza. La rivoluzione di Anassimandro (Milan: Mondadori, 2011).IV. THE WEB OF RELATIONS THAT WEAVES REALITYEntanglement

61. Juan Yin et al., “Satellite-Based Entanglement Distribution over 1200 Kilometers,” Science 356 (2017), 1140–44.

62. John S. Bell, “On the Einstein–Podolsky–Rosen Paradox,” Physics Physique Fizika 1 (1964), 195–200.

63. Bell’s argument is subtle, very technical, but solid. An interested reader can find it, with extensive detail, in Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/bell-theorem/.

64. If ψ1 is the Schrödinger wave for an object and ψ2 is the wave of a second object, our intuition tells us that we only need to know ψ1 and ψ2 in order to predict everything that it is possible to observe about the two objects. But this is not the case. Schrödinger’s wave for two objects is not the same as the two individual waves. It is a more complicated one that contains other information. The information on possible quantum correlations cannot be written with the two ψ1 and ψ2 waves alone. Formally, the state of two systems does not live in the tensor sum of two Hilbert H1 ⊗ H2, but rather in their tensor product H1 ⊗ H2. The general form of the wave function of two systems in any base is not ψ12(x1,x2) = ψ1(x1)ψ2(x2) but a generic function ψ12(x1,x2), which can be a quantum superposition of terms of the form ψ12(x1,x2) = ψ1(x1)ψ2(x2); that is, it includes entangled states.

65. In the language of analytic philosophy, the relation does not supervene on the state of the single objects. It is necessarily external, not internal.The Dance for Three That Weaves the Relations of the World

66. The reason is that in the entangled state |A⟩ ⊗ |OA⟩ + |B⟩ ⊗ OB⟩ where A and B are the observed properties and OA and OB are the observer’s variables correlated with these, a measurement of A collapses the system to the state |A⟩ ⊗ |OA⟩, and therefore a later measure of the observer’s variables yields OA.

67. The tensorial structure of the Hilbert spaces of the subsystems.Information

68. This is the definition of “relative information” given by Claude Shannon in the classic work that introduced the theory of information: Claude E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal 27 (1948), 379–423. Shannon insisted that his definition has nothing mental or semantic about it.

69. These postulates were introduced in Carlo Rovelli, “Relational Quantum Mechanics,” International Journal of Theoretical Physics 35 (1996), 1637–78, https://arxiv.org/abs/quant-ph/9609002.

70. The phase space of which has finite Liouville volume. Every physical system can be approximated appropriately with a phase space of finite volume.

71. For example, if you measure the spin of a particle of ½ spin along two different directions, the result of the second measurement renders the result of the first irrelevant for predicting the results of future measurements of spin.

72. Ideas similar to those introduced in Rovelli, “Relational Quantum Mechanics,” have appeared independently in Anton Zeilinger, “On the Interpretation and Philosophical Foundation of Quantum Mechanics,” Vastakohtien todellisuus: Festschrift for K. V. Laurikainen, ed. U. Ketvel et al. (Helsinki: Helsinki University Press, 1996); Časlav Brukner and Anton Zeilinger, “Operationally Invariant Information in Quantum Measurements,” Physical Review Letters 83 (1999), 3354–57.

73. More precisely: no degree of freedom of any physical system can have its state localized in its phase space with precision greater than ħ (the constant ħ has the dimensions of a volume in phase space).

74. Werner Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Zeitschrift für Physik 43 (1927), 172–98.

75. At first Heisenberg and Bohr interpreted in a concrete way the fact that to measure one variable altered another: because of granularity, no measurement—they thought—could be sufficiently delicate to not modify the object observed. But Einstein, with insistent criticism, forced them to recognize that things were more subtle. Heisenberg’s principle does not mean that position and velocity have definite values and that we cannot know both because to measure one modifies the other. It means that a quantum particle is something that never has perfectly determined position and velocity. They are determined only in an interaction, at the price of rendering one or the other indeterminate.

76. The observables form a noncommutative algebra.

77. This fact is clarified well by the phenomenon of “quantum decoherence,” whereby quantum interference phenomena are not seen in an environment with many variables.

78. This point is clarified in the