by Peter Byrne
Branching diagram.
Back to information
Everett was confident that he had formally demonstrated that,
We have thus seen how pure wave mechanics, without any initial probability assertions, can lead to these notions on a subjective level, as appearances to observers.36
Subjectivity occurs because the wave function for each branching universe obviously contains less information than the amount of information embedded in the universal wave function (which is inaccessible to macroscopic observers consigned to single branches). So, the splitting process can be considered overall as entropic, as an objective loss of information to each copy of an observer, as a “decoupling” of one world from the set of all physically possible worlds—even though we one-branchers experience this process as an increase in information (a probability statement). The apparent increase is tied to the fact that after making an experimental measurement, we gain information about the chance that a repetition of the measurement will produce a particular result.
According to Everett, the experimental validity of the Born rule for obtaining a probability measure can be explained by information theory as an appearance generated by the ignorance of an observer trapped in a single history. It is worth remembering that the Born rule is itself a postulate, so, at the worst, Everett implicitly, if unknowingly, embedded it in his formal argument even as he claimed to be deriving it. Until the day he died, however, he firmly believed that he had shown why an observer would subjectively experience wave collapse, for all practical purposes.
The preferred basis problem
For Everett, macroscopic objects and, indeed, entire universes coalesce out of the quantum microworld by connecting in a way that is historically consistent with what is physically possible: “All laws are correlation laws.”
He explained causality as an effect of correlation:
Causality is a property of a model, and not a property of the world of experience.37
In other words, A does not cause B, A is correlated to B in as many branching universes as it takes to exhaust all physically possible correlations. Take heart: you did not necessarily lose your loved ones in some dark universe.38
But there is a related issue identified by both Everett’s supporters and critics as a major problem for the theory: It does not seem to provide a precise method for determining how the constantly splitting amoebas and cannonballs and brains keep their individual histories causal and consistent (correlated), so that the past does not contradict the present and turn us all into jellyfish. How does each universe keep track of its own history so that physical consistency—causality—is preserved as pieces of each universe split off into different universes? On what physical basis does one branch separate itself from the other branches? Along what specific fault lines of position or momentum or spin or time does a superposed object split? Why would an object split on a position “basis,” as opposed to a momentum basis?39 Why are some branches more stable or robust and enduring than others? How can we be sure that the “present” correlates to the “past” even when there are records? How do we know that finding the fossilized footprint of a dinosaur means that there once were dinosaurs? For that matter, why do we not see dinosaurs shopping on Fifth Avenue? And what about worlds where it is probable that the laws of probability do not apply?
This is called the preferred basis problem; it is suggested by some theorists that it is resolved by decoherence theory; others say it is not resolved. At any rate, in the Everett model the question of preferred basis is intimately tied to the problem of defining probability in a multiverse where everything happens.40 Everett seems to have had a blind spot on this question; he did not consider preferred basis to be a problem. He seems to have assumed that it was sufficient that the observer’s selection of an experimental apparatus determined the preferred basis (i.e. whatever physical properties the machine was rigged to measure). But his critics note that making preferred basis dependent upon an experimental set-up does not answer the burning question of how preferred basis is determined in nature independently of machines and observers! Therefore, “the preferred basis problem is just the original measurement problem in another guise.”41
This was a serious flaw in his formal argument, but, as we shall learn in a subsequent chapter, many modern theorists believe it is solved.
Bird’s eye view
Linking entropy, information, and probability in his long thesis, Everett showed that the universal wave function is intrinsically reversible (time can flow backwards, broken eggs reverse trajectories to reunite yolk and shell). But for us, the motion through time appears to be irreversible, said Everett:
Macroscopically irreversible phenomena are common to both classical and quantum mechanics, since they arise from our incomplete information concerning a system, not from any intrinsic behavior of the system.42
And in the handwritten draft:
Thus the apparent irreversibility of natural processes is understood also as a subjective phenomena, relative to observers who lose information in an essential manner, still within a determinate framework which is overall reversible (in which total information is conserved).
So, even though the universal wave function allows information to be transferred to a scientist who does not stand outside the system observed, his perspective is limited:
There are, therefore, fundamental restrictions to the knowledge that an observer can obtain about the state of the universe…. Any single observer can therefore possess knowledge only of relative state function (relative to his state) of any systems, which is in any case all that is of any importance to him.43
Physicist Max Tegmark uses the metaphor of a “birds-eye” view when conceptualizing the totality of Everett’s universal wave function as a superposition of all the separate branches.44 He reserves the “frogs-eye” point of view for a continually branching observer with incomplete information.
In the Everett model, probability only has meaning for frog-like observers stuck inside one branch. They cannot see the whole picture, i.e. the multiverse in which everything physically possible happens. Everett equates the unavailability of information to each branching observer as the appearance of probability, as a measure of ignorance. For a frog, the determinist universe appears to be indeterminist. But the probability measure generated by the conceptual tool of wave function collapse is, nonetheless, informative: squaring the wave function works!
From the “bird’s eye view,” an omniscient observer accesses all of the information included in the universal wave function. Overall, Everett takes the bird’s eye view and tries to account for what the frogs see.45
In the last few paragraphs of the long thesis, Everett paid his dues to Wheeler’s quantum gravity project by commenting on the application of the universal wave function to general relativity. He boldly asserted that by eliminating quantum jumps—i.e. wave function collapse—his relative state theory allowed the field equations of general relativity to be “satisfied everywhere and every-when.”46 And it is this application that was to later catch the eye of cosmologists and power up the many worlds interpretation of quantum mechanics.
17 The Battle with Copenhagen, Part I
Bohr’s principle of complementarity is the most revolutionary scientific concept of this century and the heart of his fifty year search for the full significance of the quantum idea.
John Wheeler, 19571
In the beginning, Wheeler was Everett’s champion. The publication of his thesis in Reviews of Modern Physics was accompanied by his advisor’s glowing assessment:
It is difficult to make clear how decisively the ‘relative state’ formulation drops classical concepts. One’s initial unhappiness at this step can be matched but few times in history: when Newton described gravity by anything so preposterous as action at a distance; when Maxwell described anything as natural as action at a distance in terms as unnatural as field theory; when Einstein denied a privileged character to any coordinate syst
em, and the whole foundations of physical measurement at first sight seemed to collapse…. No escape seems possible from this relative state formulation…. [It] does demand a totally new view of the foundational character of physics.2
But the paper printed in Reviews of Modern Physics was drastically abridged from the original thesis submitted to Wheeler in January 1956. Everett was displeased by the final product. He never published another word on quantum mechanics.
Wheeler’s initial support for Everett was born of a scientific agenda: quantizing gravity. And for this project, Everett’s formulation of a universal wave function was useful, provided that its baggage—a non-denumerable infinity of branching worlds—could be, somehow, lightened. But Wheeler was not going to sign off on the thesis until Bohr had a chance to weigh in. And after Bohr rejected it, Wheeler insisted that Everett cut and rewrite it on pain of losing his degree. Under the professor’s close supervision, three-quarters of the original was excised or condensed. One of the first sentences to go was Everett’s dismissal of the Copenhagen interpretation as “developed by Bohr,” because it treated the wave function as “merely a mathematical artifice.” The basic critique of von Neumann’s collapse postulate remained intact, but metaphors of splitting cannonballs and observers vanished, leaving the concept of multiple universes in the formalism, but not in the language. And the entire chapter on information and probability disappeared, along with most of its argument.
When the thesis was revamped to Wheeler’s satisfaction, he waxed most eloquently, publicly comparing his student’s work to the achievements of Newton, Maxwell, and Einstein. Not everybody agreed with him, to say the least (especially not Bohr and his circle in Copenhagen). But as the many worlds interpretation gradually gained credence and popularity over the next few decades, Wheeler ceased advocating for, and eventually disparaged it.
American Bohr
Misner explains Wheeler’s dilemma:
John Wheeler got along with everybody. But in Hugh’s case, Wheeler had a very difficult time applying his usual tactics because he couldn’t just encourage Hugh to follow his ideas and present them as powerfully as possible since they ran contrary to Bohr’s ideas. And Wheeler regarded Bohr as his most important mentor.
He really adored Bohr and Bohr was a marvelous person. He had ways Wheeler somewhat copied of trying to encourage people and being very careful about getting the best possible people but then giving them a fairly free hand.
Wheeler’s theme for the previous several years had been something he called radical conservatism which means, and he was applying it to gravity, that if you’ve got a theory that you think is sound, you shouldn’t just use it to calculate the decimal point about things you understand, you should look at the theory and see if it’s telling you about anything you haven’t thought of. And that’s where he got these ideas of wormholes which evolved into black holes later and geons which were ways of thinking about really curved space time.
He would say, ‘Let’s push the equations and see if they don’t open up a new world.’ So Hugh had this dynamic conservatism of just taking the equations and looking to see what they would say. So here was Wheeler with Hugh following his own principles of physics, namely following the equations, and Bohr was his deepest emotional attachment in all of physics. He was a man he really respected and bowed to.
So he was really torn and I think he kept trying to play both sides of that tension by trying to get Hugh to tone down the thesis so it wouldn’t be quite so needling to people, and then writing a comment on it himself to publish along side of it to try and smooth things over a bit.3
In classical antiquity, a “sibyl” was a woman who uttered prophecies of the gods: an oracle. Among Everett’s basement papers is a copy of “A Septet of Sibyls,” seven essays on the nature of truth written by Wheeler for American Scientist in 1956.4 The article was inscribed: “Hugh Everett from J. A. W.” It must have given Everett a chill to read the article, in which Wheeler treated Bohr as a living god.
Wheeler’s rhetorical habit was to juxtapose opposites, and he took this model directly from Bohr’s philosophy as he summed it up in Septet:
Complementarity … represents … the most revolutionary philosophical conception of our day…. We say, ‘The use of certain concepts in the description of nature automatically excludes the use of other concepts, which however in another connection are equally necessary for the description of phenomenon.’5
He lauded Bohr’s method of unifying old and new physics:
His judgment and courage, his daring conservatism, carried him to wonderful conclusions…. That human truth is defined, not by text books, but by the battles of men and ideas that have brought us where we are, is a lesson appreciated least of all by those we call cranks and nuts, knowing well that we are all in some measure cranks and nuts…. What a wonderful sorter-out of ideas is the principle that new ideas must correspond to old ones, must include them, but must transcend them!6
That statement highlights Wheeler’s problem: he was not satisfied with the collapse postulate, nor Bohr’s partition between the quantum and classical realms—both rules stood in the way of quantizing gravity.7 Yet, it was not a wise career move to question Bohr on such a fundamental issue as the usefulness of complementarity. So, he set out to convince Bohr that Everett’s theory was not a refutation of complementarity, but a refinement of it.8
The battle is joined
Mid-May 1956 found Wheeler in Copenhagen discussing Everett’s work with Bohr and Petersen (Wheeler was teaching that semester at University of Leiden, Netherlands).9 Bohr had a copy of Everett’s long thesis, which contained overt criticisms of the Copenhagen interpretation. Wheeler was hoping that Bohr and his circle would concentrate on understanding Everett’s formalism, and not be too put-off by the loaded language.10
He wrote to Everett,
After my arrival the three of us had three long and strong discussions about [your thesis]…. Stating conclusions briefly, your beautiful wave function formalism of course remains unshaken; but all three of us feel that the real issue is the words that are to be attached to the quantities of the formalism. We feel that complete misinterpretation of what physics is about will result unless the words that go with the formalism are drastically revised.11
Wheeler urged Everett to struggle it out in Copenhagen directly with Bohr. And he warned Everett that he would not schedule his final exam “until this whole issue of words is straightened out.”
A few hours later, Wheeler wrote Everett another letter, this time enclosing a copy of the notes he had taken of his meetings with Bohr and Petersen. He penned,
Much of what is said in objection to your work is irrelevant. Much is relevant: The difficulty of expressing in everyday words the goings on in a mathematical scheme that is about as far removed as it could be from the everyday description; the contradictions and misunderstandings that will arise; the very very heavy burden and responsibility you have to state everything in such a way that these misunderstandings can’t arise.
This appallingly difficult job I feel you (among the very few in this world) have the ability in thinking and in writing to accomplish, but it is going to take a lot of time, a lot of heavy arguments with a practical tough minded man like Bohr, and a lot of writing and rewriting. The combination of qualities, to accept corrections in a humble spirit, but to insist on the soundness of certain fundamental principles, is one that is rare but indispensable; and you have it. But it won’t do much good unless you go and fight with the greatest fighter.
Frankly, I feel about 2 more months of nearly solid day by day argument are needed to get the bugs out of the words, not out of the formalism.
Wheeler offered to pay half of Everett’s steamship fare to Denmark and said Bohr would cover the rest.12
According to Wheeler’s notes, Petersen said that Everett should have paid more attention to “Bohr’s way,” which did not recognize a problem with measurement. He said that the measuring apparatus simpl
y could not be included in the wave function of the object observed: “Silly to say apparatus has a wave function.”
Everett scribbled several caustic remarks on his copy of Wheeler’s notes. Next to a comment made by Petersen that wave functions do not make sense outside of viewing experimental results, Everett wrote: “Nonsense!”
Then Petersen argued that formalisms must be constructed on a foundation of communicable meaning:
Math can never be used in physics until [we] have words. [We] aren’t comparing [our]selves with servomechanisms. What [we] mean by physics is what can be expressed unambiguously in ordinary language.
