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Abstract
Parmenides’ Poem on Nature contains a proof that the world could not have come into being in time, because no explanation could be given for why it would do so at a given time. This same proof reappears in the Leibniz-Clarke Correspondence, where it is directed against Newtonian absolute time. Newtonians, Leibniz explains, believe that time is homogeneous and absolute, but this makes it inexplicable how God could have chosen to create the world on a given day. Similarly, in his correspondence with Schrödinger in the 1930s, Einstein suggests that certain quantum mechanical occurrences, such as the spontaneous decay of a radioactive atom, are absurd, because they cannot be assigned a definite location in time. In Schrödinger’s version on Einstein’s argument, we must say that the cat dies twice: first, inside the box; yet, second, when we open the box. But both accounts cannot be true. Since each of the authors discussed was aware of the approach of his predecessors, they share a structure. In this article, I develop a unified account of all three.
Acknowledgments
I am grateful to the Albert Einstein Archives at the Hebrew University of Jerusalem, in particular Or Burla and Dr. Roni Grosz, for permission to translate and reprint material from Einstein’s correspondence with Schrödinger, as well as for their extensive and friendly assistance during the archival research. For comments and criticisms on this text, I thank Heinz Lübbig. For generous answers to my questions while developing the project, I thank Don Howard, Vincent Renzi and Eric Winsberg. I owe a great debt to Stephen Gardner for many discussions, and for his deep grasp of the contemporary logical foundations of the principle of intersubstitutability salve veritate. Finally, I thank the organizers and audiences at the University of Ottawa’s colloquium series, and the Leibniz Centenary Colloquium at Carleton University, in particular Paul Rusnock, for valuable suggestions and criticisms. While I have not had occasion to use any particular paper of Richard Arthur’s copious work on Leibniz in this article, it has been a constant reference point over the years. The ideas presented here are of long gestation—I am indebted to Douglas Moggach and Graham Hunter for inducing me to finally write them down.
Notes
1. Some recent work in this direction would include Futch, Leibniz’s Metaphysics of Time and Space.
2. The discussion of Parmenides cannot aspire to the same quality, as I am not a classicist; however, since I have not found a discussion in that literature of the aspects of Parmenides’ work I emphasize, it is presented in the hope that those who possess the knowledge I lack may find something helpful, and perhaps rectify my worst mistakes.
3. For instance, Chester, “Is Symmetry Identity?”
4. See Section 18 B.8 of Diels, Die Fragmente der Vorsokratiker, 122.
5. The bulk of our fragment is found in the First Book of Simplicius, Commentarii, 17.
6. English translation from Tarán, Parmenides, 82–85.
7. The text and translation of the Theogony are from Hesiod, Homeric Hymns and Homerica, 85–87; For a general discussion of the connection between these two authors, see Diels, Parmenides Lehrgedicht, 10, and Dolin, “Parmenides and Hesiod,” 93–98.
8. For instance in Giulio Cesare Lagalla’s 1612 De Phenomenis in Orbe Lunae, one of the first publications to make use of Galileo’s telescopic observations, reprinted in Galileo, Le opere, vol. 3, specifically 260–61.
9. Descartes, Principles XXI, Meditations and Selections from the Principles, 140.
10. Newton, Mathematical Principles, 10–11.
11. That is to say, the accelerating ship will traverse greater distances in an absolute second, but relative to the accelerated clock (whose relative seconds are now “contracted”) the measured velocity will be the same, making the two cases the same with respect to the (vulgar) measurements performed.
12. Leibniz’s Second Paper, Clarke and Leibniz, Collection of Papers, 21.
13. “~x □→ ~y” is the standard formal notation of the counterfactual conditional, had x not happened, y would not have happened either.
14. See Hyder, “Kant and Einstein.”
15. That is to say, I might find it convenient to divide my gold-holdings into several accounts, and calculate assets and liabilities in any one account with respect to an arbitrarily chosen zero point, as do all banks, and most individuals. The latter sort of account was called, beginning in the Renaissance, a “giro” or “revolving” account—it keeps track of differences in my holdings, not their absolute quantity.
16. A large collection of such late-medieval standards and coins form part of the permanent collection of the German Historical Museum in Berlin.
17. Leibniz does not hold that the PII holds with logical necessity, for God could create indiscernible identicals if he chose to; nonetheless, it would be irrational for him to do so: “25. When I deny that there are Two Drops of Water perfectly alike, or any two other Bodies Indiscernible from each other; I don’t say, 'tis absolutely impossible to suppose them; but that 'tis a thing contrary to the divine Wisdom, and which consequently does not exist.” Leibniz’s Fifth Paper, Clarke and Leibniz, Collection of Papers, 177.
18. Ibid., 227.
19. Leibniz’s Third Paper, Clarke and Leibniz, Collection of Papers, 57–59.
20. This argument obviously struck Kant, since it reappears within his own argument of incongruent counterparts.
21. Leibniz’s Third Paper, Clarke and Leibniz, Collection of Papers, 61.
22. Leibniz’s Fifth Paper, Clarke and Leibniz, Collection of Papers, 219.
23. I say “perceived,” because Einstein himself recognized, and was bothered by, the remnant of absolute metrical structure that remained in Special Relativity in the form of its “inertial frames.” Nor has the physical community followed him in claiming that General Relativity eliminated this structure. For a discussion, see Norton, “Geometries in Collision” as well as the remark of Hermann Weyl’s at the end of the present article.
24. Einstein, “Physik und Realität,” 342.
25. Despite the apparently natural connection of the two principles through those holding classically between momentum and energy, and between spatial and temporal position, there is no self-adjoint time-operator in quantum mechanics, meaning that “energy and time cannot be treated in formal analogy to momentum and position.” Busch, “On the Energy-Time Uncertainty Relation” (1990), 5. See also Busch, “The Time-Energy Uncertainty Relation” (2008), 75f.
26. Because there is no operator for time in quantum mechanics, the parallelism in question has proven difficult to formulate over the years. Since we are, at present, considering historical debates, we will set aside the subtleties, and approach the question using the same “semi-classical” terminology that was employed by Bohr, Schrödinger, and Einstein.
27. Bohr, “Discussions with Einstein,” 225–26.
28. “In this sense Bohr’s answer shows that energy and event time are complementary quantities, since their precise determinations involve mutually exclusive experimental arrangements.” (Busch, “On the Energy-Time Uncertainty Relation” [1990], 22). Busch’s striking treatment of the role of time in quantum mechanics merits greater discussion than I have place for here.
29. Einstein was not only responsible for introducing the concept of spontaneous emission, but he devoted considerable energy, during the 1920s, to the problems it raised:
In his first more extensive paper on the theory of radiation, about which he gave a lecture in 1916 at the Physical Society of Berlin, Einstein had constructed a connection between the concepts of Bohr’s atomic model and Planck’s radiation law. For this purpose he treated the interaction between the atom and the electromagnetic field using statistical methods and introduced the idea of spontaneous emission. The latter is the emission of a photon, triggered by a quantum jump of the electron after a short time spent at a higher energy level, without any external reason. (Hübener and Lübbig, A Focus of Discoveries, 121)
30. Einstein, Podolsky, and Rosen, “Can Quantum-Mechanical Description.”
31. Einstein to Schrödinger, August 8, 1935. Translated and reprinted with the permission of the Albert Einstein Archive.
32. See Fine, The Shaky Game, 78.
33. Here I follow his presentation as published in November of (1935).
34. Schrödinger, “Die gegenwärtige Situation,” 812. My translation.
35. For a full account, see Fine, “Schrödinger’s Cat and Einstein’s: The Genesis of a Paradox,” chap. 5 of The Shaky Game, and Howard, “Einstein on Locality.”
36. Schrödinger, “Die gegenwärtige Situation,” 812.
37. Bohr described this thought-experiment has having been proposed at the 1930 Solvay Conference:
As an arrangement suited for such purpose, Einstein proposed the device indicated in Fig. 7, consisting of a box with a hole in its side, which could be opened or closed by a shutter moved by means of a clock-work within the box [schematic of clock connected to shutter]. If, in the beginning, the box contained a certain amount of radiation and the clock was set to open the shutter for a very short interval at a chosen time, it could be achieved that a single photon was released through the hole at a moment known with as great accuracy as desired. Moreover, it would apparently also be possible, by weighing the whole box before and after this event, to measure the energy of the photon with any accuracy wanted, in definite contradiction to the reciprocal indeterminacy of time and energy quantities in quantum mechanics.” (Bohr, “Discussions with Einstein,” 225)
38. Thus, I disagree slightly with Fine’s characterization of the relation, namely that the gunpowder and cat cases “are…arguments for incompleteness that bypass the need for an additional premise having to do with locality (or separation).” (Fine, The Shaky Game, 6). In my view, both EPR and the later paradoxes target the quasi-causal nature of the measurement-operation, but only the first (EPR) provides a complete demonstration: the two arguments under consideration here attempt to show that spontaneous events cannot be given a precise temporal location, which seems absurd on the macro-scale; the EPR-paradox exploits the instantaneous passion-at-a-distance of the “effects” of the operation in order to derive a contradiction with SR and the Locality it requires. That is to say, Fine’s extra premise was, from Einstein’s point of view, one half of the contradiction in EPRs’ reductio, whereas the two experiments under consideration do not generate any theoretical contradiction, only one with intuition. They illustrate aspects of the core argument, but should not be considered to achieve more.
39. Einstein used the term “telepathisch,” which is the same concept expressed in Greek. It need have no particular connection to psychic processes, as in contemporary colloquial usage.
40. Busch, “On the Energy-Time Uncertainty Relation” (1990), 3ff.
41. “The coordinate system is the unavoidable residue of the destruction of the ego [Ich-Vernichtung] in the geometrico-physical world, which reason peels out of intuition under the norm of ‘objectivity’—the last faded signpost [dürftiges Wahrzeichen], in this objective sphere, that existence is only, and can only be given as the intentional content of the conscious experiences of a pure, signifying I.” (Weyl, Das Kontinuum, 72). Weyl wrote these words while developing his first version of what is now called “gauge theory.” The phenomenological language is due to the close relations between his wife Helene (née Joseph) and the school around Husserl in Göttingen. This phenomenology of time antedates the better-known version due to Husserl’s student, Martin Heidegger, by many years, and does not, quite obviously, share in the latter’s antipathy towards mathematics.
42. In Einstein’s words from 1955, “for us believing physicists, the division between past, present and future has only the significance of a persistent illusion.” (Besso and Einstein, Correspondence, 538–38).