by Peter Byrne
15 DeWitt, B. and Graham, N. eds. (1973). 15.
16 Ibid. 115; compare to handwritten draft thesis, version #2, 6: “The theory is thus completely determinate and regards the wave function itself as the fundamental physical quantity.”
17 Wheeler. J. A. (1957). 152.
18 He used the “Lebesque” measure that Wiener had used previously to put a measure on an infinite set of trajectories. Wiener had demonstrated a close connection between the Lebesque measure and probability theory. Heims, S. J. (1980). 63.
19 DeWitt, B. and Graham, N. eds. (1973). 16.
20 Quantum measurements enable predictions of future events that can be recorded. Think about a particle that could be found at 10 different positions, A … J. Say that a measurement gives us a probability of D recurring as 0.7 or 70 percent. The Schrödinger equation does not deal in ratios. And if we believe in the Everett interpretation, we could say that each event, A … J, will occur in some universe with a probability of 1 (100 percent). So why, then, do we get probabilities out of measurements in our universe? What Everett seemed to be saying was that although there is not necessarily a determinate number of universes post-branching, probability weights can be assigned to sets of results. In this model, information and probability are conserved and the Born rule (or its equivalent) serves to weight the number of universes in which the event (D) has occured (a weight of 0.7) over a larger set of post-measurement branching universes that encompasses all results A … J, and that the weights of all such results sum to unity (100 percent). So, the fact that we experience one result is not contradicted by multiple observers experiencing all possible results. Finding the particle at D is recorded in 70 percent of the set of the post-measurement branching worlds (which can be uncountably infinite).
21 In 1962, Everett explained (somewhat enigmatically) to a conference of prominent physicists meeting at Xavier University in Ohio, that, “Since my states are constantly branching, I must insist that the measure on a state originally is equal to the sum of the measures on the separate branches after a branching process.” Xavier transcript, TUES AM, 21.
22 Everett was not the first nor the last scientist to try and extract the Born rule from the formal mathematics of quantum mechanics: In 1957, Andrew Gleason of Harvard University published a highly abstract proof that the Born rule emerges from quantum logic. And many other attempts have been made. But Everett and Gleason added certain formal conditions to the quantum logic, seemingly natural conditions that were necessary to support their conclusions that the Born rule emerges from the operation of the Schrödinger equation. Philosopher Jeffrey Barrett remarks, “Deriving a probability measure from the formalism plus a set of stipulated conditions falls short of justifying the use of the measure to assign probabilities to physical events. Neither Everett’s nor Gleason’s arguments are quite circular. Their arguments just do what they do—namely, they show that if one adds a few conditions to the quantum formalism, then there is just one probability measure that satisfies the conditions. One might argue that the necessary conditions are natural, but one still needs to add them to the theory in order to derive anything.” Private communication, Barrett, 2009. See Gleason, Andrew M. (1957).
23 DeWitt, B. and Graham, N. eds. (1973). 17.
24 Ibid. 43. In a handwritten notation: “Relativity Principal [sic]: In any composite system there is, in general, no state for a subsystem, but only a relative state, relative to some (arbitrary) specification of the state of the remainder. Sort of parallel to usual Relativity principle since denies absolute significance to subsystem state.” Source: “Random Notes on QM thesis.”
25 Ibid. 60.
26 Ibid. 146.
27 Ibid. 61.
28 Ibid. 53; In a handwritten note: “The ‘quantum-jumps’ exist in our theory as relative phenomena—the states of an object system relative to chosen observer states show this effect, while the absolute states change quite causally.” Source: “Footnotes.”
29 “As soon as the observation is performed, the composite state is split into a superposition for which each element describes a different object-system state and an observer with (different) knowledge of it. Only the totality of these observer states, with their diverse knowledge, contains complete information about the original object-system state - but there is no possible communication between the observers described by these separate states. Any single observer can therefore possess knowledge only of the relative state function (relative to his state) of any systems, which is in any case all that is of any importance to him.” Ibid. 98–99.
30 Ibid. 116.
31 Ibid. 116–117; see handwritten note from “Random notes on QM thesis”: “Note, the mouse does not affect the universe, only the universe affects the mouse!”.
32 Ibid. 68.
33 Some proponents of “many minds” interpretations of Everett see the footnote as substantiating a claim that Everett did not view the splits as physically real, but, in my opinion, this argument fails in the face of such statements as: “The theory is thus completely determinate and regards the wave function itself as the fundamental physical quantity.” Handwritten draft thesis, version #2, 6.
34 Everett explained further: “We see that the predictions of an observer have fundamental limitations. These limitations arise, however, not from the fact that there is no unique correspondence from initial to final system states, but because there is no unique observer state for an initial state.” Source: “Random Notes on QM thesis.”
35 DeWitt, B. S. (2008A). 5.
36 DeWitt, B. and Graham, N. eds. (1973). 78.
37 Ibid. 137.
38 In the handwritten draft, Everett wrote that “classical mechanics is an approximate law regarding the correlations in such systems. Can be seen most easily from Feynman point of view which shows that one classical configuration leads to nearly the corresponding result at later time since this case has largest amplitude over the histories.” “Random Notes on QM thesis.”
39 Technically, “basis” refers to a “vector” in Hilbert space, which holds an infinite number of vectors, i.e. directions and magnitudes of change.
40 Henry Stapp poetically asks how the Schrödinger equation can pick our particular history when it must treat them all as viable: “The essential point is that if the universe has been evolving since the big bang in accordance with the Schrödinger equation, then it must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilities. Indeed, the planet Earth would not have a well-defined location, nor would the rivers and oceans, nor the cities built on their banks. Due to the uncertainty principle, each particle would have a tendency to spread out. Thus various particles with various momenta would have been able to combine and condense in myriads of ways into bound structures, including measuring devices, whose centers, orientations, and fine details would necessarily be smeared out over continua of possibilities…. But the normal rules for extracting well-defined probabilities from a quantum state require the specification, or singling out, of a discrete set of [separate] subspaces, one for each set of alternative possible experientially distinguishable observations.” Stapp is a proponent of Von Neumann’s wave collapse postulate and links it to a concept of human consciousness as causal. He criticizes theorists who “claim that decoherence completely resolves” the preferred basis problem; and they criticize him for idealism. Stapp, H. (2002).
41 Barrett (1999), 176; see 173–179 for an informative discussion of preferred basis problem in Everett.
42 DeWitt, B. and Graham, N. eds. (1973). 99.
43 Ibid. 99.
44 Tegmark, M. (2008). 10.
45 In a handwritten note to himself about the global superposition, Everett wrote, “(Emphasize that non-interference of mixtures of combined system holds for operators on a subsystem, not on total.)”
46 DeWitt, B. and Graham, N. eds. (1973). 119.
1 “No Fugitive and Cloistered Virtue,” speech delivered on
October 24, 1957 in Washington D.C. ceremony presenting Bohr with Atoms for Peace Award. Wheeler. J. A. (1957A).
2 DeWitt, B. and Graham, N. eds. (1973). 152: DeWitt later told Wheeler: “It always amused me to read in your assessment of Everett’s theory how highly you praised Bohr, when the whole purpose of the theory was to undermine the stand which he had for so long taken!” DeWitt to Wheeler, 4/20/67.
3 Misner interview, 2007.
4 Wheeler, J. A. (1956).
5 Ibid. 49.
6 Ibid. 48–49.
7 Quantizing gravity (a cosmological project) requires that the universe as a whole be (in theory) measurable. But it is impossible to take a measurement from outside the universe.
8 And he was not in error. Despite his rhetoric against Bohr, in the basement file “Random notes on QM thesis” Everett wrote: “Complementarity contained in general form in present scheme.” But Bohr believed complementarity was universal, and not subsumable into a more comprehensive scheme.
9 He brought with him there Misner (working on wormholes), Joseph Weber (working on gravitational waves), and was visited there by Tullio Regge (working on the stability of what Wheeler later named “black holes”), all projects impacting the Chapel Hill conference the next spring. Misner private communication, 2009.
10 A paper trail detailing the stages of a fierce struggle between Everett and Wheeler and members of Bohr’s inner circle emerged, not only from the basement archive, but also at the Niels Bohr Archive in Copenhagen, the American Philosophical Society in Philadelphia, and at the American Institute of Physics in College Park, Maryland. Some of these records were unearthed by Professor Olival Freire Jr. of the Universidade Federal da Bahia, Salvador, Brazil, Anja Jacobsen of the Niels Bohr Archive, Stefano Osnaghi of the Centre de Recherche en Epistémologie Appliquée, Ecole Polytechnique, Paris, France and Fabio Freitas of the Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil. With assistance from the author, a study of these records, “The Origin of the Everttian Heresy,” appeared in Studies in History and Philosophy of Modern Physics, 2009.
11 Wheeler to Everett-1, 5/22/56.
12 Wheeler to Everett-2, 5/22/56.
13 Stern to Wheeler, 5/20/56.
14 Stern is an interesting character; for starters, he was horrified by the increasingly industrial and social nature of scientific research. For decades, he had earned his living as a civil engineer in Brooklyn, New York, while pursuing his avocation: quantum physics. From the 1930s to the early 1960s, he contributed thoughtful articles on quantum foundations to Physics Today and a wide range of papers to scientific, technical and philosophical journals. He was a firm believer that science should not be professionalized: “The growing socialization of science involves serious dangers [to freedom of scientific thought]. One must be alert and guard against scientific research degenerating into rubber, oil, textile, military research…. The pure science of physics … may disappear. The desire to get at the nature of things would give place to the desire to make ‘better things.’ Thus, the age of scientific enlightenment and culture may be succeeded by an age of technology, where comfort replaces culture.” Stern, A. (1945). Stern agitated against government control of science, which, he wrote, must remain ‘an intellectual activity—its very nature is not practical.’ Stern, A. (1944). As a frequent visitor to Bohr’s institute, Stern did not question the Dane’s ideological authority, and he actively promoted use of the philosophy of complementarity. But he encouraged physicists to keep an open mind, quoting the American humorist Artemus Ward, ‘It is not what people don’t know that makes them ignorant, it is what they do know that isn’t so.’ Stern, A. (1953).
15 Wheeler to Stern, 5/25/56.
16 Ibid.
17 Ibid.
18 Wheeler to Everett, 5/25/56.
19 Wheeler to Shenstone, 5/28/56.
20 Wheeler to Dees, 5/24/56.
21 Wheeler to Bohr, 5/24/56.
22 Petersen to Wheeler, 5/26/56.
23 Petersen to Everett, cable and letter, 5/28/56.
24 Everett to Petersen, circa June 1956.
25 Cocktail party tape, 1977.
1 London, F. & Bauer, E. (1939). 219–220.
2 Everett to NSF, Fellowship Report for 1955–56, 6/24/57.
3 Wheeler to Everett, 9/17/56.
4 Bohr to Wheeler, 4/12/57.
5 Petersen to Everett, 4/24/57.
6 Ibid.
7 Everett to Petersen, 5/31/57. Italics added.
8 Groenewold to Everett, 4/11/57.
9 The “Schrödinger’s cat” example of macroscopic superposition appears in Schrödinger, E. (1935A). Everett’s solution to the cat paradox was that it was supple in one universe, stiff in another.
10 Everett, H III. (1957) in DeWitt, B. and Graham, N. eds. (1973). 149; Everett thought his theory made the EPR paradox irrelevant as pairs of non-locally entangled particles would correlate their spin states as “spin up-spin down” in one universe, and “spin down-spin up” in another universe regardless of the speed of information transfer. Jeffrey Barrett brings up the point that this explanation may violate relativity, as “The question ‘when does the universe split’ cannot have an inertial frame independent answer as required by relativity.” Barrett, private communication, July 2009.
11 Margenau to Everett, 4/8/57.
12 Wiener to Wheeler and Everett, 4/9/57. It is worth noting that in 1950, Wiener observed of physics, “One interesting change that has taken place is that in a probabilistic world we no longer deal with quantities and statements which concern a specific, real universe as a whole but ask instead questions which may find their answers in a large number of similar universes. Thus chance has been admitted, not merely as a mathematical tool for physics, but as part of its warp and weft.” Wiener, N. (1950).11.
13 In a handwritten comment on a copy of Wiener’s letter, Misner wrote: “[Everett] uses a true Lebesque measure. It is a meas. on sequences of outcomes of observations. This seems to be a more reasonable place to want a probability than in Hilbert space, where there can be none.” And Everett scrawled on another copy of the letter, “I do not need Leb. measure in Hilbert space. Whole problem neatly avoided by my treatment. My measure on trajectories, i.e. sup[erposition] of orthog. states, not entire H[ilbert] space.” Everett wrote to Wiener, “I would like to correct any impression that my theory requires a Lebesque measure on Hilbert space. The only measure which I introduced was a measure on the [trajectories of] orthogonal states which are superposed to form another state … and not a measure of Hilbert space itself, the difficulties of which I am fully aware.”
14 Wiener to Wheeler and Everett, 4/9/57.
15 Everett, H III to Wiener, 5/31/57. In July 1957, Wheeler wrote to Everett saying he and Wiener agreed that Everett needed to explain his probability measure better, so he asked if he would, “write up a 7-typewritten page draft of a possible note on the subject for submission to him and me with the idea it would go in Phys. Rev. after it had been modified to meet all objections? Perhaps there is more you’d like to add – but is there any issue outstanding that’s more central to the future discussion that will occur on your paper? Like basketball so here I believe the way to win is to keep every player covered!” Wheeler to Everett, H III, 7/23/57. There is no record of Everett complying with Wheeler’s request.
16 Jaynes, E. T. (1957).
17 Jaynes to Everett, H III, 6/17/57. Found in the basement was Jaynes’ letter, two papers by Jaynes with Everett’s comments in the margins, and Everett’s handwritten draft of a letter to Jaynes critiquing his papers.
18 See Zurek, W. H. ed. (1990).
19 Frank, P. (1954).
20 “In a famous paper written in 1907, [Frank] made the original suggestion that the law of causality is a convention. How do we know when an experiment has been repeated ‘under the same conditions?’ Frank argued that there is no exact method except to find out whether it yields the same result. Hence he concluded that the law of causality
is not a statement about observable physical facts but is a definition of the expression ‘under the same conditions.’” Whitrow, G. T. and Bondi, H. (1954). 275.
21 Frank, P. (1949). 144.
22 Frank, P. (1954). 12–13.
23 Everett to Frank, 5/31/57.
24 Ibid.
25 Frank, P. (1954). 9.
26 Frank to Everett, H III, 8/3/57.
27 DeWitt to Wheeler, 5/7/57.
28 DeWitt, B. S. (2008A).
29 DeWitt-Morette interview by Kenneth Ford, 2/28/95.
30 Rockman to Everett, 3/2/57.
31 Dissertation acceptance memo, Everett Princeton student file. 4/15/57. Mudd.