The Early History of Quantum Entanglement, 1905-1935 Don Howard Department of Philosophy and Program in History and Philosophy of Science University of Notre Dame TAM 2007 August 28, 2007 Einstein and Bohr ca. 1927 “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Entanglement is everywhere today. “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Schrödinger introduces the term, “entanglement,” and the quantum interaction formalism: Erwin Schrödinger. “Die gegenwärtige Situation in der Quantenmechanik.” Die Naturwissenschaften 23 (1935), 807-812, 823-828, 844-849. Erwin Schrödinger. “Discussion of Probability Relations Between Separated Systems.” Proceedings of the Cambridge Philosophical Society 31 (1935), 555-662. Erwin Schrödinger. “Probability Relations Between Separated Systems.” Proceedings of the Cambridge Philosophical Society 32 (1936), 446-452. “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Erwin Schrödinger. “Die gegenwärtige Situation in der Quantenmechanik.” Die Naturwissen- schaften 23 (1935), 807-812, 823-828, 844-849. If two separated bodies, about which, individually, we have maximal knowledge, come into a situation in which they influence one another and then again separate themselves, then there regularly arises that which I just called entanglement [ Verschränkung ] of our knowledge of the two bodies. Athe outset, the joint catalogue of expectations consists of a logical sum of the individual catalogues; during the process the joint catalogue develops necessarily according to the known law [linear Schrödinger evolution] . . . . Our knowledge remains maximal, but at the end, if the bodies have again separated themselves, that knowledge does not again decompose into a logical sum of knowledge of the individual bodies. “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Einstein ca. 1905 Einstein in the 1920s Einstein and Entanglement, 1905-1927 “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Albert Einstein. “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.” Annalen der Physik 17 (1905), 132-148. Monochromatic radiation of low density (within the domain of validity of Wien's radiation formula) behaves from a thermodynamic point of view as if it consisted of mutually independent energy quanta of the magnitude R ß í / N . If we have two systems S 1 and S 2 that do not interact with each other, we can put S 1 = ö 1 (W 1 ), S 2 = ö 2 (W 2 ). If these two systems are viewed as a single system of entropy S and probability W, we have S = S 1 + S 2 = ö (W) and W = W 1 � W 2 . The last relation tells us that the states of the two systems are mutually independent events. “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Einstein to H. A. Lorentz, 23 May 1909 (EA 16-419). I must have expressed myself unclearly in regard to the light quanta. That is to say, I am not at all of the opinion that one should think of light as being composed of mutually independent quanta localized in relatively small spaces. This would be the most convenient explanation of the Wien end of the radiation formula. But already the division of a light ray at the surface of refractive media absolutely prohibits this view. A light ray divides, but a light quantum indeed cannot divide without change of frequency. As I already said, in my opinion one should not think about constructing light out of discrete, mutually independent points. I imagine the situation somewhat as follows: . . . I conceive of the light quantum as a point that is surrounded by a greatly extended vector field, that somehow diminishes with distance. Whether or not when several light quanta are present with mutually overlapping fields one must imagine a simple superposition of the vector fields, that I cannot say. In any case, for the determination of events, one must have equations of motion for the singular points in addition to the differential equations for the vector field. “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Mieczys ³ aw Wolfke. “Antwort auf die Bemerkung Herrn Krutkows zu meiner Note: ‘Welche Strahlungsformel folgt aus den Annahme der Lichtatome?’” Physikalische Zeitschrift 15 (1914), 463-464. In fact the Einsteinian light quanta behave like the individual, mutually independent molecules of a gas . . . . However, the spatial independence of the Einsteinian light quanta comes out even more clearly from Einstein’s argument itself. From the Wien radiation formula Einstein calculates the probability W that all n light quanta of the same frequency enclosed in a volume v 0 find themselves at an arbitrary moment of time in the subvolume v of the volume v 0 . The expression for this probability reads: W = ( v / v 0 ) n . This probability may be interpreted as the product of the individual probabilities v / v 0 that an individual one of the light quanta under consideration lies in the subvolume v at an arbitrary moment of time. From the fact that the total probability W is expressed as the product of the individual probabilities v / v 0 , one recognizes that it is a matter of individual mutually independent events . Thus we see that, according to Einstein’s view, the fact that a light quantum lies in a specific subvolume is independent of the position of the other light quanta . “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Paul Ehrenfest and Heike Kamerlingh Onnes. “Simplified Deduction of the Formula from the Theory of Combinations which Planck Uses as the Basis of His Radiation-Theory.” Amsterdam Academy of Sciences. Proceedings . 17 (1914), 870-873. Appendix: “The Contrast between Planck’s Hypothesis of the Energy-Grades and Einstein’s Hypothesis of Energy- Quanta.” Planck does not deal with really mutually free quanta � , the resolution of the multiples of � into separate elements � , which is essential in his method, and the introduction of these separate elements have to be taken “cum grano salis”; it is simply a formal device . . . . The real object which is counted remains the number of all the different distributions of N resonators over the energy-grades 0, � , 2 � , . . . with a given total energy P . If for instance P = 3, and N = 2, Einstein has to distinguish 2 3 = 8 ways in which the three (similar) light-quanta A , B , C can be distributed over the space-cells 1, 2. A B C I 1 1 1 II 1 1 2 III 1 2 1 IV 1 2 2 V 2 1 1 VI 2 1 2 VII 2 2 1 VIII 2 2 2 “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
Paul Ehrenfest and Heike Kamerlingh Onnes. “Simplified Deduction of the Formula from the Theory of Combinations which Planck Uses as the Basis of His Radiation-Theory.” Amsterdam Academy of Sciences. Proceedings . 17 (1914), 870-873. Appendix: “The Contrast between Planck’s Hypothesis of the Energy-Grades and Einstein’s Hypothesis of Energy- Quanta.” [Continued] Planck on the other hand must count the three cases II, III, and V as a single one, for all three express that resonator R 1 is at the grade 2 � , R 2 at � ; similarly he has to reckon the cases IV, VI and VII as one; R 1 has here � and R 2 2 � . Adding the two remaining cases I ( R 1 contains 3 � , R 2 0 � ) and II ( R 1 has 0 � , R 2 3 � ) one actually obtains different distributions of the resonators R 1 , R 2 over the energy-grades. We may summarize the above as follows: Einstein’s hypothesis leads necessarily to formula ( ÷ ) for the entropy and thus necessarily to Wien’s radiation formula, not Planck’s. Planck’s formal device (distribution of P energy-elements � over N resonators) cannot be interpreted in the sense of Einstein’s light-quanta . “Early History of Quantum Entanglement,” TAM 2007, August 28, 2007
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