by Peter Byrne
Why doesn’t our observer see a smeared out needle? The answer is quite simple. He behaves just like the apparatus did. When he looks at the needle (interacts) he himself becomes smeared out, but at the same time correlated to the apparatus, and hence to the system…. The observer himself has split into a number of observers, each of which sees a definite result of the measurement…. As an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba does not have a life line, but a life tree. The question of the identity or non identity of two amoebas at a later time is somewhat vague. At any time we can consider two of them, and they will possess common memories up to a point (common parent) after which they will diverge according to their separate lives thereafter.9
In this model, each copy of the amoeba is correlated to an element in the wave function of the apparatus, which, in turn, reflects the quantum state of the particle (a superposition): “The apparatus itself ‘smears out’ and is indefinite, no matter how large or ‘classical’ it is.”10 Relative to the quantum state of the apparatus, the amoeba is in a superposition of states. After splitting, each copy of the amoeba shares a common history with its immediate ancestor. And after each split, the quantum mechanical amoeba keeps on splitting as it continuously interacts with its changing environment in accord with the Schrödinger equation. Most importantly, the wave function of the smeared amoeba never collapses because each of its possible states becomes concrete in a “branch” of what Everett called a universal wave function. He later used the metaphor of a branching tree to show how the branches were separate, but linked by the past to a common root.
Wheeler wrote in the margin of the paper that the amoeba “analogy seems to be quite capable of misleading readers in a very subtle point. Suggest omission.”
Regarding the use of the word, “split,” Wheeler noted: “Split? Better words needed. Do first on unconscious object to show ideas more objectively.”
Everett observed of his own theory,
It can lay claim to a certain completeness, since it applies to all systems, of whatever size, and is still capable of explaining the appearance of the macroscopic world. The price, however, is the abandonment of the concept of uniqueness of the observer, with its somewhat disconcerting philosophical implications.11
Unlike the conventional collapse interpretation, his non-collapse model, he claimed, explained the emergence of classical objects from microscopic superpositions:12
It is this phenomenon which accounts for the classical appearance of the macroscopic world, the existence of solid bodies, etc. since we ourselves are strongly correlated to our environment. Even though it is possible for a macroscopic object to ‘smear out’, … we would never be aware of it due to the fact that the interactions between the object and our senses are so strong that we become correlated to it almost instantly. We now see that the wave mechanical description is really compatible with our ideas about the definiteness on a classical level, due to the existence of strong correlations.13
Everett’s analysis of how classical phenomena emerge from the quantum substrate raised questions of the type that were later more successfully addressed by decoherence theory, i.e. the technical description of how a microscopic system starts to behave macroscopically as it irreversibly entangles with its environment.14 What emerges from decoherence is either a single, macroscopic, classical world, or a “quasi-classical” component of a multiple universe system—depending on one’s interpretive stance.
Everett explained the ontology of his non-collapse interpretation:
The physical ‘reality’ is assumed to be the wave function of the whole universe itself. By properly interpreting the internal correlations in this wave function it is possible to explain the appearance of the macroscopic world to us, as well as the apparent probabilistic aspects.15
At the end of the mini paper, Wheeler wrote,
Have to discuss questions of know-ability of the universal ψ function – and latitude with which we can ever determine it…. Question of whether new view has any practical consequence. Also its implications for machinery of the world. Any special simplicity to be expected for the wave fun[ction]? If not, why not? If so, what kind of simplicity? Any explanation then why world doesn’t look so simple?
Wheeler’s remarks were certainly reasonable, as the universal wave function is not observable. But he viewed the universal wave function as necessary to building a theory of quantum gravity which must apply to the universe as a whole.16 Wheeler needed a theory that allowed quantum interactions to include the observer in a wave function describing the whole universe, as it is not possible for an observer to be outside the universe, as would be required by the legislated externality of the observer in both the collapse postulate and the Copenhagen interpretation. Everett’s concept of a universal wave function included the observer, along with everything else in a multitude of branching universes. The price was that the observer became many observers, and the universe, many universes.
In September 1955, Wheeler wrote to Everett,
I am frankly bashful about showing [“Probability in Wave Mechanics”] to Bohr in its present form, valuable and important as I consider it to be, because of parts subject to mystical misinterpretations by too many unskilled readers.17
Wheeler was more positive about the second mini paper “Quantitative Measure of Correlation.” Here, Everett utilized information theory to measure the amount of correlation (entanglement) between two quantum variables in terms of a probability distribution. Everett defined the measure as “learn[ing] something about one variable when [told] the value of the other,” which was germane to what he later called the “relative state formulation,” i.e. a single quantum state is only describable relative to the states with which it correlates (entangles).18
In the third mini paper, “Objective vs. Subjective Probability,” Everett argued that in the standard interpretation of quantum mechanics a particular probability must be both subjective and objective, and that this dichotomy is “untenable.” Everett argued that the Born rule probabilities are not objective. On the contrary, he said, the Born rule is really a measure of the ignorance of the observer:
A subjective probability refers to an estimate by a particular observer which is based upon incomplete information, and as such is not a property of the system being observed, but only of the information of the observer.
In Everett’s developing scheme the Born rule is subjective, because in a branching quantum universe where everything happens there can be no such thing as objective probability. The observer is trapped in a single, classical world and does not have access to all the information in the universal wave function, only to the partial information encoded in his particular branch of it. Therefore, the statistical measure he extracts through experiment is subjective—a measure of his ignorance of the content of the universal wave function.19
Hence, what an observer views as the indeterministic collapse of a wave function is not a collapse, but simply a loss of information to him in an otherwise deterministic universe governed by a non-collapsing wave equation. Everett argued that each copy of a branching observer will subjectively experience determinism (everything happens) as indeterminism (chance rules), because each copy accesses only partial information about the total quantum environment.
Philosophical monstrosity
By January 1956, when he turned in his typed thesis to Wheeler, Everett had abandoned the amoeba metaphor, but he did not shy away from painting pictures of superposed, bifurcating observers, cannonballs, and splitting mice. Nor was Everett the least bit bashful about criticizing the prevailing interpretations of quantum mechanics. He said that the “popular” (von Neumann) interpretation, including its postulate of wave function collapse, was “untenable.” Speaking directly of the Copenhagen Interpretation, “developed by Bohr,” Everett declared,
While und
oubtedly safe from contradiction, due to its extreme conservatism, it is perhaps overcautious. We do not believe that the primary purpose of theoretical physics is to construct ‘safe’ theories at severe cost in the applicability of their concepts, which is a sterile occupation, but to make useful models which serve for a time and are replaced as they are outworn.20
Lest there be any misunderstanding about the depth of Everett’s disenchantment with Bohr, here is what he wrote to Bryce DeWitt in May of 1957.
The Copenhagen Interpretation is hopelessly incomplete because of its a priori reliance on classical physics (excluding in principle any deduction of classical physics from quantum theory, or any adequate investigation of the measuring process), as well as a philosophical monstrosity with a ‘reality’ concept for the macroscopic world and denial of the same for the microcosm.21
But in a handwritten note in the basement file of his thesis materials called “Random Notes,” he wrote: “Complementarity contained in general form in present scheme.” In other words, he was not throwing away what he called Bohr’s “plausibility arguments to support QM [quantum mechanical] conclusions.” His main objection to complementarity was that it precluded the deduction of the classical world from pure wave mechanics. He saw Bohr’s partition between the classical and quantum realms as an unnecessary impediment to understanding. So, he held that his own “scheme” included (and improved upon) Bohr’s dualistic model by explaining how the classical world is contained within the quantum realm.
In the long thesis, Everett concluded,
Our theory in a certain sense bridges the positions of Einstein and Bohr, since the complete theory is quite objective and deterministic … and yet on the subjective level … it is probabilistic in the strong sense that there is no way for observers to make any predictions better than the limitations imposed by the uncertainty principle.22
He added,
The constructs of classical physics are just as much fictions of our own minds as those of any other theory; we simply have a great deal more confidence in them.23
The picture of smeared observers, and the biting critique of Bohr, were features in the long thesis of January 1956. Those features were excised from the final dissertation as approved by Wheeler and published in 1957. Decades later, in an unpublished referee report, DeWitt commented,24
I know that John Wheeler admires brevity and probably urged Everett to try and ‘sum up in a nutshell’ the essential points of his new interpretation of quantum mechanics. It is also possible that Wheeler was reluctant to support a more blatant statement because it would mean setting himself into direct opposition to his hero, Niels Bohr.
What is sure is that Wheeler long ago abandoned his support for Everett. What is equally sure is that if the Urwerk [the original, unedited 137 page thesis that DeWitt published in 1973] had been published [in 1957], Everett would not have been ignored for so long.
16 Tour of Many Worlds
I can safely say that nobody understands quantum mechanics…. Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain,’ into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
Richard Feynman, 19651
Now that the main ideas of the many worlds interpretation have been introduced, we take an informational tour of the long thesis. Leaving out the mathematics, we explain how Everett argued for his main idea in ordinary language that does not require any special training to follow. We talk about the influences of Wiener, von Neumann, Shannon, Schrödinger, Einstein, Bohr, Bohm, and others on the development of the theory. We go where no one has ever gone before, using handwritten drafts and research notes discovered in the basement that illuminate Everett’s inner thoughts.
He was not writing for lay people; he presupposed a professional knowledge of quantum mechanics for his readers. So, it is safe to say that this tour for the general reader does not fully explicate the difficult theory (even with the mathematics it is not fully explained!). Rather, we focus on the role played by “information as physical” and Everett’s struggle with language as he left the realm of the intuitive.
Some physicists and philosophers of science are attracted to the simplicity of the many worlds interpretation, i.e. that everything that is physically possible happens inside a non-collapsing wave function. Some agree with Everett and DeWitt that the branching worlds are physically real,2 some treat them as useful idealizations. For convenience, we employ a term that Everett did not use—“multiverse”—to describe the sum of branching universes described by the universal wave function, real or not.3
No collapse!
Inside one of the basement files, there is an undated scrap of paper upon which Everett penciled:
Theory of UWF [universal wave function] is above all a precise, clear, unmystical way to understand just those assertions (rules of thumb of engineers) which are made by Bohr and called ‘complementarity’ without having a wide, gaping vacuum by denying the very possibility of ever understanding functioning of class[ical] descrip[tion] of meas[uring] app[aratus]! … Theory acts as a whole to explain phenomena … [There is] no necessity that elements behave ‘independently’ [of Schrödinger equation].
It is clear from this scrap and his much more substantial writings that Everett started with the assumption that the universe is completely quantum mechanical. Psyching himself up to overthrow the prevailing interpretations, he conceived of inventing a theory as a competitive game4 and noted to himself:
Activate – PUTTING OTHER FELLOW ON DEFENSIVE – If we have a rule that keeps us from using QM [quantum mechanics] on a system that contains an observer
or rather put other fellow on spot – he has to invent some alternative law – Complete history of the universe wherein all systems are physical systems subject to same laws – There should be no mystical sets of observations separate from theory.
The “rule” was the externalization of the observer by Bohr’s ontological partition coupled to von Neumann’s paradoxical collapse postulate. In best military practice, Everett immediately went on the offensive, declaring at the outset that the rule prevents us from understanding quantum mechanics. He declared his intention to solve the measurement problem by ignoring the rule, and treating the Schrödinger equation as universally valid.
A wave function, said Everett, “objectively characterizes the physical system,” provided that the system is “isolated,” i.e. considered as not interacting with an external system. His big idea was that as the only truly isolated system is the universe, no subsystem of the universe is forever isolated: every subsystem, every object, can be described as existing relative to the remainder of the universe.
Saying this was one thing, proving it was another.
Building the case for a universal wave function, Everett commenced by explaining the measurement problem as the contradiction between the Schrödinger equation and the collapse postulate. He carefully noted that he intended for his theory to conform with von Neumann’s “principle of psycho-physical parallelism,” which requires that a scientific formalism must be able to describe a real, physical world. And he set out to show why, in a multiverse in which all physically possible events occur, we experience only one of those events at a time on our particular branch of the universal wave function.
As was and is commonly accepted, the Schrödinger equation documents the continuous, causal evolution of quantum systems as they change through time. The seeds of possibilities are superposed within the wave equation. This phenomenon can be tested by experiment, i.e. the Schrödinger equation accurately computes the set of positions (or momentums, energies, etc.) at which an electron can be found. We use the collapse postulate and the Born rule to assign a probability measure to each of these positions. But according to Everett, the Schrödinger equation ruthlessly evolves everything in a huge number of universes through stages of causal change regardless of how static or disconnected thi
ngs may appear to be to humans—and the collapse postulate and the Born rule are but useful illusions generated by human ignorance.
In the handwritten draft, Everett explained how observers correlate or entangle with macroscopic objects that, like the microsystems of which they are composed, also exist in superpositions5:
Even though the wave function for such an object may be spread over a large region, interaction with an observer will immediately correlate him to the object, so that he will perceive the object in a definite position, that is, after the interaction there will be a superposition of states, each of which will contain the definite object in a definite position, and an observer who perceives this.
And, like the amoeba, each copy of the splitting observer embarks upon its own future as “it” splits again and again like a branching tree, mirroring the superpositions with which it incessantly entangles. And all copies of the observer can be traced backwards through time to common ancestors, as the foliating branches at the top of a tree can all be traced to a common trunk. It is not the universe that splits, per se, but the observer, and in doing so he correlates with a causally connecting branch of the multiverse within the global superposition described (in theory) by the universal wave function.
