The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family

by Peter Byrne

  FURRY:

  To me, the hard thing about it is that one must picture the world, oneself, and everybody else as consisting not in just a countable number of copies but somehow or another in an undenumerable number of copies, and at this my imagination balks. I can think of various alternative Furrys doing different things, but I cannot think of a non-denumerable number of alternative Furrys. (Podolsky chuckles.)

  EVERETT:

  I’d like to make one final remark here.

  What follows uses some technical terminology, but is mostly couched in ordinary language. It is worth quoting in its entirety as Everett never published a word on quantum mechanics after July 1957, and his Xavier comments shed considerable light on how he contrived his probability measure, and his view of the physical reality of the “splitting” worlds.

  Imagine a very large series of experiments made by an observer. With each observation, the state of the observer splits into a number of states, one for each possible outcome, and correlated to the outcome. Thus the state of the observer is a constantly branching tree, each element of which describes a particular history of observations.

  Now, I would like to assert that, for a ‘typical’ branch, the frequency of results will be precisely what is predicted by ordinary quantum mechanics [i.e. the Born rule]. Even more strongly, I would like to assert that, as the number of observations goes to infinity, almost all branches will contain frequencies of results in accord with ordinary quantum theory predictions. To be able to make a statement like this requires that there be some sort of a measure on the superposition of states. What I need, therefore, is a measure that I can put on a sum of orthogonal [i.e. separate, non-interfering] states. There is one consistency criteria which would be required for such a thing. Since my states are constantly branching, I must insist that the measure on a state originally [the probability distribution for an electron to be found at position X or Y or Z …] is equal to the sum of the measures on the separate branches after a branching process, [i.e. probability is conserved].22

  Now this consistency criterion can be shown to lead directly to the squared amplitude of the coefficient [Born probability], as the unique measure which satisfies this. With this unique measure, deduced only from a consistency condition, I then can assert: indeed, for almost all (in the measure theoretic sense) elements of a very large superposition, the predictions of ordinary quantum mechanics hold.

  Now I could draw a parallel here to statistical mechanics where the same sort of thing takes place. Here we like to make statements for almost all trajectories. They are ergodic [i.e. the influence of initial conditions is preserved over long runs of time] and things like that. Here also you can only make such a statement if you have some underlying measure that you regard as fundamental, since any such statements would be false if I take a measure that had only non-zero measure on the exceptional trajectories [i.e. my probability measure must apply to all physically possible events on the average].

  In both the original and edited versions of his thesis, Everett had made the mathematical argument that it is not necessary to postulate the Born rule in quantum mechanics, because there is a statistical equivalent to it in classical mechanics that emerges naturally as a measure of probability for observers confined to a single branch (our branch). But, for mathematical consistency, he needed to show how this measure conserves the seeds of probability in a universe in which everything that is physically possible happens. Stepping away from the quantum mechanical Born rule, he analogized a classical probability measure placed across sets of separate, non-collapsing branches after an interaction—as a measure of the total weight of the multiple results flowing from that interaction (adding up to 1, or 100 percent).

  He continued,

  In statistical mechanics it turns out there is uniquely one measure of the phase space [coordinate frame in which entire systems are represented by points] … being essentially the only measure giving the conservation of probability [i.e. the probabilities for the various positions of an electron at any given moment in all branches add up to 1, or 100 percent]. It is precisely this analogue that I use on the branching of the state function and I can therefore assert that the probabilistic interpretation of quantum mechanics can be deduced quite as rigorously from pure wave mechanics as the deductions of statistical mechanics.

  Although Everett’s explanation of his derivation of a measure that was equivalent to the Born Rule—thereby explaining why probability appears in “our” branch without the collapse postulate—was not totally convincing to panel members, it held enough promise that they did not outright scoff at his argument that we subjectively experience probability in a universe of universes in which everything happens—i.e. all elements of a superposition are equally “real,” even if they are not equally probable.

  When Everett was finished, Shimony said, “You eliminate one of the two alternatives I had in mind. You do associate awareness with each of these [branches].”

  EVERETT:

  Each individual branch looks like a perfectly respectable world where definite things have happened.

  SHIMONY:

  What, from the standpoint of any of these branches, is the difference within a branch, between your picture of the world and one in which there are stochastic [random, probabilistic] elements?

  EVERETT:

  None whatever. The whole point of this viewpoint is that a deduction from it is that the standard interpretation will hold for all observers. In addition, however, one can, within this viewpoint, get some hold on approximate measures and this type of thing.

  And with that, Everett sat down.

  Rosen reflected that in the light of these interpretive problems, quantum mechanics was incomplete and physicists should either “reformulate” it, or “look for a different theory.” Clearly referring to Bohr and his inner circle, he said,

  I am sometimes a little annoyed at the attitude of some quantum mechanicians because of a certain dogmatism that they display in these discussions. There is an old saying that the revolutionary of yesterday is the conservative of today. Some people even refuse to consider the possibility that there can be any other valid point of view than that which corresponds to the orthodox interpretation. Of course, nobody here in this discussion is considered to be guilty.

  The rest of the morning was spent discussing (and largely dismissing) Bohm’s theory of hidden variables, which does not allow for superpositions and eliminates the measurement problem.

  Parallel interpretations

  That afternoon, questions from the audience were entertained. One question pinpointed the contradiction at the heart of the Copenhagen interpretation: “Is it justified to make a theory ignoring at the outset questions of the measuring process, and then expect to obtain, by means of that theory, a description of the measurement process?”23 Restating the problem: because the Copenhagen interpretation posits a moveable boundary between the quantum and classical worlds, and because there is no definite place in the chain of interactions and correlations for a definite measurement (the “cut”) to occur, quantum mechanics cannot say exactly what a measurement is, nor why one result rather than another emerges, nor exactly when a wave function collapses. And, yet, it is incumbent upon any coherent interpretation of quantum mechanics to explain why measurements work (they have predictive power).

  Wigner opined that the collapse, “takes place only through the act of cognition.” Rosen disagreed, saying that a machine could carry out a measurement. Wigner tried, but could not explain why only human consciousness could collapse a wave function and a machine could not. Furry, Rosen, and Podolsky mocked Wigner (politely) for his failure to explain.

  Furry said he thought there was something to be said for considering entangled, interfering quantum systems as “coherent,” and that they lose that coherence at the macroscopic level of interaction, becoming “incoherent.”24 He was struggling to find a physical process underlying wave reduction that was not populated by hidden variables
or multiple universes. Aharonov remarked that in a closed quantum system [such as Everett’s] there is no such thing as collapse and that all possibilities would exist at the same time. It was more or less agreed that without the necessity of explaining how observers observe, quantum mechanics would be consistent.

  A member of the audience said that everyone seemed to agree that quantum mechanical systems are multi-valued [superposed], but “where we disagree is, if we can select out one of these values, and when the selection is made.” Wigner commented that Everett’s position was that no selection is made. When asked if he would like to comment, Everett said, “Yes. Well, what he said pretty much covers it.” If he had anything more to add, the page that contained his further response is unfortunately missing from the transcript and cannot be recovered.

  At one point an audience member asked Podolsky, “What is reality?” He answered, “Something more than just subjective information.”

  Furry then loudly and furiously attacked Wigner for his subjectivity:

  I’m really too old to believe in the branching that Mr. Everett believes in—in the parallel universes of Mr. Everett and things like that. But for instance, if I were to take cosmic rays that come down right through the air of this room rather frequently—they are leaving trails of ionized molecules. The fact that we haven’t set up the right conditions of super-saturated vapor to render them visible doesn’t mean they aren’t really there. But according to the point of view that puts all the emphasis on cognition, they aren’t even in the cloud chamber unless you take a picture! (Furry shouts) And they are not even in the cloud chamber or in the picture then unless you look at it! (Furry shouts until Wigner finally speaks again.)

  WIGNER:

  It is done. It is surely agreed that it is done. We will surely admit that it is done.

  FURRY:

  I can’t go that far, somehow.

  The conference adjourned for the day.

  A big bang

  On the third day, Dirac spoke. Famously taciturn, he had refrained from entering the philosophical debates. He made a highly technical presentation on relativistic quantum mechanics, and the tone of the conference cooled.

  On the fourth day, Shimony brought the topic back to philosophy. Returning to the measurement problem, he suggested, as had Everett in his thesis, that solipsism would be a solution, albeit an “unhappy” one.25

  Puzzled, Dirac asked, “What are solipsists?”

  Shimony kindly explained, and the panel members joked about how solipsists could kill each other and it would not matter since each was a product of the other’s imagination. Shimony concluded that if the quantum formalism was to be kept intact, “there are many, many blind alleys; and I, for one, do not see a way out.”

  The conversation returned to Everett’s theory. Shimony pointed out that an observer in one of Everett’s branches would experience one reality—even though “ultimately the universe has one state, and its propagation is governed by the Schrödinger equation.”

  SHIMONY:

  [Everett’s] claim is that the theory he is proposing is more logical. Well, I don’t know what this means. I think that if you have two statistical theories each equally consistent, you can’t claim one is more logical than the other. It seems to me that in some sense these are equivalent ways of talking about the same thing.

  Aharonov said he didn’t see any inconsistencies in Everett’s theory; and Shimony could not pinpoint any. Shimony fell back on a stance that is often used by Everett’s critics: “I think one should evoke Occam’s razor: Occam said that entities ought not to be multiplied beyond necessity. And my feeling is that among the entities which aren’t to be multiplied unnecessarily are histories of the universe. One history is quite enough.”

  The discussion circled back to the central questions of the conference—whether the mathematics of quantum mechanics suffices to describe the real world, is the world observer-independent, or is it a figment of the imagination of a solipsist? Nothing was resolved.

  A few minutes before the conference ended, the recorder noted: “(There is an extremely loud explosion outside; Bang!!! followed by fifteen seconds of silence.)”

  AHARONOV:

  Are we all agreeing that there was something, an explosion here, or (laughter) … Is everybody here on this same branch (referring to Everett’s theory)?

  The problem of probability

  The transcript does not reveal Everett’s coordinates at the moment of the explosion, but 11 years later he talked about the Xavier conference in the letter to Max Jammer:

  The unwillingness of most physicists to accept this theory, I believe, is [due] to the psychological distaste which the theory engenders … Thus the theory was not so much criticized, as far as I am aware, but simply dismissed.

  Subsequent to the publication of the paper, I had informal discussions with a number of physicists concerning the subject (including Bohr and Rosenfeld in Copenhagen, in 1959, Podolski [sic] and Wigner and a number of others active in the field at a conference at Xavier University several years later). I was somewhat surprised, and a little amused, that none of these physicists had grasped one of what I considered to be the major accomplishments of the theory–the ‘rigorous’ deduction of the probability interpretation of quantum mechanics from wave mechanics alone. This deduction is just as ‘rigorous’ as any of the deductions of classical statistical mechanics, since in both areas the deductions can be shown to depend upon an ‘a priori’ choice of measure on the space. In classical statistical mechanics this measure is standard Lebesque measure on the phase space whereas in quantum mechanics this measure is the [Born Rule].

  What is unique about the choice of measure and why it is forced upon one is that in both cases it is the only measure that satisfies a law of conservation of probability through the equations of motion. Thus, logically in both classical statistical mechanics and in quantum mechanics, the only possible statistical statements depend upon the existence of a unique measure which obeys this conservation principle.26

  There are physicists and philosophers, today, who think that Everett was on or very close to the mark with his derivation of probability. Physicist Max Tegmark agrees with Everett’s derivation as presented in the long thesis.27 And philosopher Simon Saunders says

  If you assume it is legitimate to talk about probability, given you have all these branches, and the question is ‘what is the right probability measure over branches,’ then Everett’s derivation of the Born rule is pretty good, in my opinion. Maybe he did nail it. Probability is no worse off in Everett than it is in any other physical theory (and its fine just to inductively infer the Born Rule).28

  But physicist Dieter Zeh, whose work on quantum decoherence has been inspired by Everett, points out that physical facts cannot be derived from mathematics alone:

  Pointing out the existence of a mathematical structure of a ‘measure’ is certainly far from giving a proof of its physical meaning. Apparently, Everett hoped to find a justification for the probability interpretation (and perhaps the Born rule) in the mathematics. This would be a typical mistake of a young scientist. The formal rules for probabilities were derived or postulated to describe classical ensembles. In particular, the correlations he is discussing in this connection are mostly those characterizing classical ensembles (incomplete information). The main problem of measurement is precisely the transition from entangled superpositions to (apparent) ensembles. So it would not suffice to point out some formal similarities.

  Zeh views Everett’s argument as justifying his probability measure, but not as having derived it: “However, one must also expect that he was in some state of confusion, which is normal when you start thinking about a completely novel idea that has strange consequences. Just compare it with the inconsistent claims of the founding fathers of quantum theory!”29

  28 Death’s Other Kingdoms

  These are those who have passed through our modern materialistic, ultra-rational dream world, with their ey
es directed upon death’s other-world kingdom. These are those who have retained faith in the face of our modernism and have the ability to see reality, through our illusory world. To them we, who outwardly appear satisfied of our own self-sufficiency and ostentatiously are in need of no God, appear as hollow men, as stuffed men.

  Herbert O. Horn1

  The cold spot

  While Everett was in Cincinnati, his mother lay dying. Katharine chronicled her battle with cancer in a letter to one of her nurses, written shortly before she died.2

  Her doctor had discovered a lump in her left breast shortly before she vacationed in Europe with Hugh and Nancy in 1959. But she could not feel the lump herself, so, regrettably, she did nothing about it. Eighteen months later, her left arm swelled up, and the nipple of her left breast ulcerated. Six months later, she went for a physical. The doctor said she had a tumor.

  She checked into George Washington University hospital for a biopsy, or so she thought.

  However, the following morning I was operated on and woke up after 5 hours in the operating room to find out that they had performed a radical left mastectomy with skin graft.