The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family
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Collapse, on the other hand, lops off all branches but one.
The role of consciousness
In his introduction, Everett examined the claim (later concretized by Wigner in a famous paper6) that human consciousness intervenes to collapse the wave function, discarding all possible futures but one. Everett thought it absurd to say that the consciousness of a single observer can collapse the wave function of a quantum system that includes other observers. Where would the “real” collapse occur then? Which conscious being is responsible for the collapse? To escape this problem of infinite regression, Wigner claimed that consciousness is non-physical and, therefore, not subject to the laws of quantum mechanics7 (von Neumann agreed with Wigner’s metaphysical interpretation).8
Disparaging the idea of consciousness as a determinant force in nature, Everett concluded,
It is now clear that the interpretation of quantum mechanics [i.e., von Neumann’s collapse postulate] with which we began is untenable if we are to consider a universe containing more than one observer.9
According to Everett, human consciousness plays no super-causal role in the microscopic realm, for, if it did, then the universe would be a creation of human consciousness (but whose?) He considered consciousness to be nothing more or less than a quantum system itself: the physical state of a brain with no claim to special powers. And he was keenly aware that the “observer” need not be human, although it had to be physical. The only requirement for scientific observation, he said, is that an event leave an impression or create a record in the environment, and that does not require human agency. A computer creates electronic and paper records; for that matter, a fission track fossilized in a mineral is a record. Following the necessity of explaining quantum arguments to human beings from the point of view of human observers, Everett focused on the branching memory state of the observer, e.g. the physical recording in the observer’s brain of the click made by a Geiger counter registering the presence of a particle. For instance, an observer retains a memory of a Geiger counter click at precisely 10:43 PM, but one of his copies recalls a click a second later, and so on. It is the observer who splits, and, in Everett’s scheme, memory states are evidence that a split occurred because they record only one result. But, and this is the important part: in nature, objects split regardless of the participation of humans.
Alternative interpretations
To buttress his argument, Everett listed several alternative ways of dealing with the paradoxical rule of perpetual externality.
One, he called the “solipsist” position: there is only one observer in the universe. With no one to tell him otherwise, the solipsist is content with the collapse theory because it privileges his observational power: the world exists because he sees it and his memory contains the only record of it. Everett rejected solipsism, because the universe contains more than one recording device (observer).
Another alternative was to simply declare that quantum mechanics does not apply to macroscopic observers (including the “servomechanisms” with which Everett cheerfully proposed to replaced scientists). He considered that notion to be absurd, as macroscopic objects are obviously composed of microscopic systems.
Bohm’s hidden variables interpretation tempted Everett, but it got rid of wave function collapse by adding terms to the Schrödinger equation, which Everett was not prepared to do. Unlike Bohm, Everett was committed to treating the universe as a purely quantum playing field in which all of the various properties of particles exist in superpositions of “equally real” possibilities described by a universal wave function that bypasses the need for a collapse theory.10
So, the best alternative, said Everett, was his own: “pure wave mechanics.” It required abandoning collapse as non-physical, as scientifically convenient, but ultimately nonsensical and explainable as an illusion. It required the entire universe to obey the Schrödinger equation at all times: All objects, from electrons to elephants, exist in superpositions that are constantly entangling with other objects in their environments. Each object continuously “splits” into copies of itself relative to the states of the objects with which it entangles (and which are entangling with it!). And each copy embarks upon a uniquely branching history inside a foliating multiverse encompassing all physically possible correlations and governed by a universal wave equation.
Everett noted that Schrödinger held the view that his wave equation was universally valid,11 (although he did not go as far as Everett in arguing for that view, and, later, backed away from it, largely because he feared jellyfishication). But Everett admitted that it was incumbent upon him to explain why do we not witness macroscopic superpositions—why collapse appears to obtain. (In experiments since Everett’s day, “mesoscopic” quantum systems have been witnessed in superpositions, but in 1954 that technology was far-off.)
He summarized his task:
This theory can be called the theory of the ‘universal wave function,’ since all of physics is presumed to follow from this function alone. There remains, however, the question of whether or not such a theory can be put into correspondence with our experience.12
Probability, information, and correlation
Everett was deeply influenced by how Wiener, von Neumann, and Shannon treated information itself as physical and probabilistic. Weiner conceptualized negentropy (information) as a measure: “Entropy and information are negatives of one another. Information measures order and entropy measures disorder.”13 For Weiner, the gathering of information reduced uncertainty and was, therefore, subject to the rules of probability.
Preparing to write his thesis, Everett studied von Neumann’s influential paper, “The General and Logical Theory of Automata.”14 Here, von Neumann argued that the human brain is analogous to a machine, that living organisms are analogous to automata—part digital, part analogue—and that neurons are analogous to vacuum tubes, and that information obeys the laws of physics, especially thermodynamics. The article influenced Everett on several levels, including in his description of human observers of quantum events as information processing machines, as equivalent to “servomechanisms.”
Inspired by these pioneers of the information age, Everett strove, in his first chapter, “Probability, Information, and Correlation,” to develop a probability measure for a single quantum mechanical event emerging from the multiplicity of all physically possible quantum events without using the Born postulate. Using (classical) information theory, he claimed to have deduced an explanation for the apparent existence of probability in a quantum universe in which everything happens. He defined information as, “the negative of the entropy of a probability distribution as defined by Shannon.”15
For Everett, as for Shannon, information was subject to statistical analysis. For Everett, all information was physically encapsulated in the universal wave function: “This is the position proposed in the present thesis, in which the wave function itself is held to be the fundamental entity, obeying at all times a deterministic wave equation.”16
Wheeler later wrote in his companion article to Everett’s published dissertation:
Every attempt to ascribe probabilities to observables [properties of particles] is as out of place in the relative state formalism as it would be in any kind of quantum physics to ascribe coordinate and momentum to a particle at the same time. The word ‘probability’ implies the notion of observation from outside with equipment that will be described typically in classical terms. Neither these classical terms, nor observation from outside, nor a priori probability considerations come into the foundations of the relative state form of quantum theory.17
The trick was to deduce a probability measure from the point of view of an observer inside a branch of the universal wave function. This was problematic because the mathematical space (“Hilbert” space) in which quantum mechanics is calculated by the Schrödinger equation does not allow for a probability measure, as such. That is why wave function collapse (also called the “projection” postulate) proje
cts the description of a quantum system into a different mathematical space, one in which probability can be measured classically (“phase” space). Because we can calculate a measure of probability in “our” branch, Everett needed to show how such a phenomenon could occur, without postulating the Born rule, which he was trying to avoid, because it is tied umbilically to the collapse postulate. He claimed to show that a mathematical equivalent to the Born rule logically emerges from the quantum formalism without being assumed a priori.18
Instead of collapsing the wave function to find a probability (the Born rule method), Everett strove to measure the amount of information available after an event happened (e.g. an observer or cannonball split) and to equate the result to a probability statement. He put it thus:
The information is essentially a measure of the sharpness of a probability distribution.19
In Everett’s information-theoretic model, every measured event has a probability weight (information). And that weight is proportional to the sum of the weights of the events that split off (into separate universes) from the original event.20 Everett’s information-theoretic measure, conveniently, happens to be mathematically equivalent to the Born rule.21
To recapitulate, in Everett’s highly technical argument, he claimed to be able to obtain a classical probability measure over branching events without resorting to collapse that was the equivalent of using the Born rule with collapse. This explained, he thought, why an observer stuck in a single branch subjectively experiences probability in a multiverse in which all physically possible events occur. But his critics, and many of his supporters, note that developing an abstract mathematical equivalence is not the same thing as deriving a measure that can be experimentally shown to fit the actual dynamics of physical reality.22 His claim to have derived a probability measure from the formalism of quantum mechanics is often seen as unproven and it is the major theoretical weakness in his model. And yet it holds water.
Everett remained convinced until the day he died that he had succeeded in deriving probability from the formalism of quantum mechanics and that he had, therefore, solved the measurement problem: he was puzzled as to why many physicists he respected failed to agree with him. He blamed their incomprehension, at least partly, on the excision of the chapter on probability and information from the first published version of his thesis (the short thesis). In the 1973 publication of the long thesis, the missing chapter was restored.
Relative states
Deepening his argument in the next chapter, “Quantum Mechanics,” Everett translated his information theoretic model into a purely quantum mechanical model. Explaining the meaning of correlating information in quantum mechanics, Everett wrote: “If we say that X and Y are correlated, what we intuitively mean is that one learns something about one variable when he is told the value of the other.”23 For instance, if you know that the spin of one of two entangled electrons is “up,” then you may be confident that, simultaneously, the spin of the other electron is “down,” even if the two electrons are separated by 100 million light years.
As touched upon previously, entanglement is a very formal concept, which may be described as the experimentally verified fact that when two particles interact (exchange energy), they then share a quantum state described by a composite wave function: they are correlated, linked, entangled. Everett argued that entangled subsystems (such as X and Y in a composite system Z),
do not possess states independent of the states of the remainder of the system…. It is meaningless to ask the absolute state of a subsystem—one can only ask the state relative to a given state of the remainder of the system.24
After a measurement interaction, every element of the superposition of the measured object is entangled with a copy of the observer. Each copy exists relative to the state of the object observed and, also, to the state of the remainder of the branching universe with which both are correlated. And this process is going on everywhere:
So far as the complete theory is concerned all elements of the superposition exist simultaneously, and the entire process is quite continuous.25
Everett evoked the image of a cannonball correlated to an electron in a superposition of spin states.
Suppose, for example, that we coupled a spin measuring device to a cannonball, so that if the spin is up the cannonball will be shifted one foot to the left, while if the spin is down it will be shifted an equal distance to the right. If we now perform a measurement with this arrangement upon a particle whose spin is in a superposition of up and down, then the resulting total state will also be a superposition of two states, one in which the cannonball is to the left, and one in which it is to the right. There is no definite position for our macroscopic cannonball!26
It is all about entanglement: when you know something about the electron, you know something about the cannonball and vice versa.
Everett was aware that,
This behavior seems to be quite at variance with our observations, since macroscopic objects always appear to us to have definite positions.27
And indeed the cannonball does have a definite position in his model: exactly one position in each of the two universes that corresponds to the state of a cannonball relative to each possible spin state of the electron. Naturally, the cannonball could be simultaneously entangling with systems more complex than a single electron, and, therefore, automatically splitting into an uncountably infinite number of cannonballs, each in a different (non-communicating) branch of the multiverse.
Completely breaking with Bohr and von Neumann, Everett treated measurement as “a natural process within the theory of pure wave mechanics.” Eliminating any special role of an observer, he defined a measurement as “simply a special case of interaction between physical systems—an interaction which has the property of correlating a quantity in one subsystem with a quantity in another.”28
To split or not to split
“Split” appears thrice in the long dissertation; only once as a description of the observer state.29 But the word that made Wheeler so nervous appears numerous times in Everett’s notes, the handwritten draft, the mini papers, and in an important footnote added at the last minute to printer galleys of the short thesis. Limiting the use of the offensive verb did not eliminate the concept of splitting, which was embedded in Everett’s formalism.
Near the end of the long thesis, Everett referred to a comment made by Einstein at the Palmer Lab lecture in 1954 regarding the role of the observer in wave function collapse. Everett wrote,
He put his feeling colorfully by stating that he could not believe that a mouse could bring about drastic changes in the universe simply by looking at it.30
Everett explained, using italics,
However, from the standpoint of our theory, it is not so much the system which is affected by an observation as the observer, who becomes correlated to the system …. From the present viewpoint all elements of the superposition are equally ‘real.’ Only the observer state has changed, so as to become correlated with the state of the near system and hence naturally with that of the remote system also. The mouse does not affect the universe—only the mouse is affected [by the universe].31 But, given that multiple copies of the observer emerge: who is the observer? Everett noted (in a much-debated footnote):
At this point we encounter a language difficulty. Whereas before the observation we had a single observer state afterwards there were a number of different states for the observer, all occurring in a superposition. Each of these separate states is a state for an observer, so that we can speak of the different observers described by the different states. On the other hand, the same physical system is involved, and from this viewpoint it is the same observer, which is in different states for the different elements of the superposition (i.e. has had different experiences in the separate elements of the superposition). In this situation we shall use the singular when we wish to emphasize that a single physical system is involved, and the plural when we wish to emphasize the diffe
rent experiences for the separate elements of the superposition.32
That this statement needed to be made makes sense when considering how to trace the transtemporal—or transbranching—identity of an observer or object. In a sense, the splitting observers share an identity because they stem from a common ancestor, but they also embark on different fates in different universes. They experience different life-spans, dissimilar events (such as a nuclear war, perhaps), and at some point they are no longer the “same” person, even though they share certain memory records. As with the amoeba, Everett was not suggesting that the splitting of observers was not physical.33
In a handwritten note, he commented,
There is no question about which of the final observers corresponds to the initial one, since each of them possess the total memory of the first. (Which amoeba is the original one?) The successive memory sequences of an observer do not form a linear array, but a planar graph (tree): That is, the trajectory of an observer forms not a line but such a tree.34
And he made a diagram of the trajectory of an observer (or more precisely, the memory records of an observer).
Many years later, DeWitt recalled:
For [Everett], whether we (i.e. the universe and all that is in it) have an independent existence or are merely solutions of some super differential equation is irrelevant. If there is an isomorphism [direct correspondence] between one and the other they are interchangeable…. Under an isomorphism between formalism and the ‘real’ world, if something exists in the formalism then it ‘exists’ in the ‘real’ world. Does this make Everett a realist? In my opinion the views of both Everett and myself lie somewhere between realism and Platonic idealism. We both believe in the ‘reality’ of the many worlds but we also believe that ultimately the abstract idea, theory, wave function, or ideal form behind it all is the true reality.35