Tuesday, April 07, 2015 ... //

Fallacious thinking in Hugh Everett's thesis

In Spring 1959, Hugh Everett traveled to Denmark in order to convince the Copenhagen school that he has found something important about the foundations of quantum mechanics. Did he succeed? Léon Rosenfeld, a close collaborator of Niels Bohr's, probably summarized not only his but also Bohr's and others' opinions when he said that Everett was "indescribably stupid and could not understand the simplest things in quantum mechanics".

Off-topic, Czech LHC: a neat article about the 2015 run, your humble correspondent is mentioned a few times, e.g. when it comes to my \$10,000 supersymmetric bet against Adam Falkowski. Use Google/Chrome Translate. BBC told us that the LHC is aroused and erect again, too.
I strongly believe that this appraisal was fair and accurate and I want to elaborate on some details by discussing the first eight pages of Everett's dissertation, the incorrect assumptions, and the intrinsically unscientific way of thinking that Everett and his fans symbolize.

Here we go again:
THE THEORY OF THE UNIVERSAL WAVE FUNCTION
Hugh Everett, III

I. INTRODUCTION

We begin, as a way of entering our subject, by characterizing a particular interpretation of quantum theory which, although not representative of the more careful formulations of some writers, is the most common form encountered in textbooks and university lectures on the subject.
This may be "a" way of entering a subject but Everett seems to admit that the goal of the thesis is not to answer the scientific questions in the most careful and accurate way but rather to popularize some myths, fight straw men, and defend the author's own wrong claim by pointing out that some other people sometimes make wrong claims, too.

Now, he gets closer to the physical topics:
A physical system is described completely by a state function $$\psi$$, which is an element of a Hilbert space, and which furthermore gives information only concerning the probabilities of the results of various observations which can be made on the system.
It's conceptually misleading to place the state vector $$\psi$$ at the center of quantum physics – it's the observables (Hermitian operators linked to quantities that may be measured) that play the central role – but OK, there's a sense in which $$\psi$$ contains all the information. Well, it's the case if the observer has maximum knowledge about the physical system. If he doesn't, he should use the density matrix $$\rho$$ instead of the pure state $$\psi$$.

These are not "sharp" mistakes of the text but it's a bad sign that the very first physics sentence of a thesis is so problematic. It quickly gets much worse, however.
The state function $$\psi$$ is thought of as objectively characterizing the physical system, i.e., at all times an isolated system is thought of as possessing a state function, independently of our state of knowledge of it. On the other hand, $$\psi$$ changes in a causal manner so long as the system remains isolated, obeying a differential equation. Thus there are two fundamentally different ways in which the state function can change:

Footnote: We use here the terminology of von Neumann [17].
The prominent appearance of the word "objectively" makes Everett's words highly problematic. In practice, two or many observers may use the same $$\psi$$ to describe a physical system (especially a microscopic one) if they extracted it from the same previous measurements. So in practice, the state vector may be "intersubjective" or "objective". But it is not "objective" in any fundamental way and no authoritative writer on quantum mechanics – in its proper, Copenhagen (or similar) interpretation – has ever emphasized the word "objective".

While different people may end up using the same $$\psi$$ for an electron in practice, there is no fundamental rule that would dictate such an "objectivity". In principle, quantum mechanics is a method to obtain new knowledge (probabilistic predictions) from previous knowledge (measurements) and knowledge is "subjective" in general.

Note that John von Neumann is quoted – much of the "unusual" way of talking about quantum mechanics that we find in Everett's thesis is taken from von Neumann who used it many years before Everett. So Everett gets most of this "originality" credit for something he didn't really invent. Moreover, John von Neumann's writing is problematic and it's more accurate not to count John von Neumann among the representatives of the "Copenhagen school" who defined the proper understanding of quantum mechanics, even though he was rather close to them.

Let's continue. Everett lists the two processes that change $$\psi$$:
Process 1: The discontinuous change brought about by the observation of a quantity with eigenstates $$\phi_1$$, $$\phi_2$$, ... in which the state $$\psi$$ will be changed to the state $$\phi_i$$ with probability $$\abs{(\psi,\phi_i)}^2$$.

Process 2: The continuous, deterministic change of state of the (isolated) system with time according to a wave equation $$\partial \psi / \partial t = U\psi$$, where $$U$$ is a linear operator.
Let me be maximally benevolent and assume that he only describes two mathematical transformations that indeed do take place when people use quantum mechanics and no potentially controversial "physical interpretation" is included above. In other words, let's postpone all criticism concerning the meaning of the two "processes".
The question of the consistency of the scheme arises if one contemplates regarding the observer and his object-system as a single (composite) physical system. Indeed, the situation becomes quite paradoxical if we allow for the existence of more than one observer. Let us consider the case of one observer $$A$$, who is performing measurements upon a system $$S$$, the totality $$(A + S)$$ in turn forming the object-system for another observer, $$B$$.
This only outlines the context where possible or hypothetical problems may emerge. The only objection I have is a sociological one. This thought experiment was invented by Eugene Wigner in 1935 (as an improvement of Schrödinger's cat) and it's been called "Wigner's friend". Because those musings should have been known to everyone who discusses similar aspects of the meaning of quantum mechanics (although Wigner only published the idea in the 1960s), it's very unfortunate that Wigner – the first author of this thought experiment – isn't being mentioned at all.
If we are to deny the possibility of $$B$$'s use of a quantum mechanical description (wave function obeying wave equation) for $$A + S$$, then we must be supplied with some alternative description for systems which contain observers (or measuring apparatus). Furthermore, we would have to have a criterion for telling precisely what type of systems would have the preferred positions of "measuring apparatus" or "observer" and be subject to the alternate description. Such a criterion is probably not capable of rigorous formulation.
This paragraph is redundant because its assumption is self-evidently flawed. Human beings are physical objects, too, and like all other physical objects, they can be described by the laws of quantum mechanics, too. So it is obvious that Wigner i.e. $$B$$ may use the quantum mechanical description for the whole system consisting of the inanimate object $$S$$ and his friend $$A$$.

One thing to mention is that to describe most "collective" macroscopic aspects of human beings, classical physics is a good enough approximation so the full-fledged quantum mechanical description of $$A+S$$ is usually unnecessary in practice. But it is possible in principle – and untruncated quantum mechanics is undoubtedly the most correct framework for $$B$$ to discuss the system $$A+S$$ and the mutual interactions of $$A$$ and $$S$$.

As Everett correctly says, descriptions allowing to use quantum mechanical equations only to $$A$$ but not $$B$$, or vice versa, would depend on a sharp division of physical systems to "measuring apparatuses" (or "observers") and those that are not, and such a sharp division can't exist – more precisely, it cannot be unique, canonical, and objective. But it doesn't matter because the assumption of the whole paragraph is incorrect. Instead, the following paragraph has the correct assumption:
On the other hand, if we do allow $$B$$ to give a quantum description to $$A + S$$, by assigning a state function $$\psi^{A+S}$$, then, so long as $$B$$ does not interact with $$A + S$$, its state changes causally according to Process 2, even though $$A$$ may be performing measurements upon $$S$$. From $$B$$'s point of view, nothing resembling Process 1 can occur (there are no discontinuities), and the question of the validity of $$A$$'s use of Process 1 is raised. That is, apparently either $$A$$ is incorrect in assuming Process 1, with its probabilistic implications, to apply to his measurements, or else $$B$$'s state function, with its purely causal character, is an inadequate description of what is happening to $$A + S$$.
This paragraph correctly assumes that both Wigner $$B$$ and his friend $$A$$ are allowed to use the laws of quantum mechanics but Everett suggests that there must be a problem because the "collapse" (Process 1) that takes place early according to $$A$$ – when the friend measures $$S$$ – is postponed to a later moment according to $$B$$. So $$B$$ and $$A$$ i.e. Wigner and his friend disagree when or whether the "collapse" took place.

But this objection is clearly wrong. There is absolutely no paradox because the Process 1 is nothing else than the observer's act of learning something about the observed physical system. Process 1 (measurement) occurs at the beginning to find out the initial state, then Process 2 "takes place" which allows the observer to make predictions, and these predictions may be verified by a final measurement, another Process 1.

Everett's objection is that $$A$$ and $$B$$ disagree what (when) is the final measurement. But they indeed do. And it's totally logical that they have to. The measurement is an act by which the observer learns something about Nature. And learning is clearly a subjective thing. In general, every observer learns different things and he does so at different moments.

The very fact that there are "two different processes" is not unnatural in any way. The splitting to Process 1 and Process 2 only represents the not-so-shocking revelation that learning/measuring (Process 1) is a different process than predicting (Process 2). In classical physics, systems "objectively evolved" according to some (deterministic) dynamical equations and the observers only played a trivial role. Nothing really depended on observers. But quantum mechanics deals with information about the physical systems in a more general way that depends on the observer's perspective. So we have to talk about "learning", "predictions", and "verification", and they're different processes.

There is absolutely nothing logically contradictory about these things. The only appropriate adjective is that quantum mechanics works "differently" than classical physics did.
To better illustrate the paradoxes which can arise from strict adherence to this interpretation we consider the following amusing, but extremely hypothetical drama.

Isolated somewhere out in space is a room containing an observer, $$A$$, who is about to perform a measurement upon a system $$S$$. After performing his measurement he will record the result in his notebook. We assume that he knows the state function of $$S$$ (perhaps as a result of previous measurement), and that it is not an eigenstate of the measurement he is about to perform. $$A$$, being an orthodox quantum theorist, then believes that the outcome of his measurement is undetermined and that the process is correctly described by Process 1.

In the meantime, however, there is another observer, $$B$$, outside the room, who is in possession of the state function of the entire room, including $$S$$, the measuring apparatus, and $$A$$, just prior to the measurement. $$B$$ is only interested in what will be found in the notebook one week hence, so he computes the state function of the room for one week in the future according to Process 2. One week passes, and we find $$B$$ still in possession of the state function of the room, which this equally orthodox quantum theorist believes to be a complete description of the room and its contents. If $$B$$'s state function calculation tells beforehand exactly what is going to be in the notebook, then $$A$$ is incorrect in his belief about the indeterminacy of the outcome of his measurement. We therefore assume that $$B$$'s state function contains non-zero amplitudes over several of the notebook entries.
No, the claim that there is a physical inconsistency here is demonstrably incorrect.

$$A$$ immediately knows – and knowing is subjective knowledge – the result of the measurement he performed upon $$S$$. But $$B$$ i.e. Wigner doesn't know anything before he makes his own measurements a week later. Of course, both in principle and in practice, $$B$$ will calculate nonzero amplitudes for many different entries in the notebook.

If $$B$$ describes $$A+S$$ using a pure state $$\psi^{A+S}$$ and if $$S$$ undergoes some random process (like the radioactive decay we know from Schrödinger's cat), both $$S$$ as well as $$A$$ and his notebook will evolve into a superposition of macroscopically different states.

$$A$$ may write things like "the nucleus has decayed" or the "nucleus hasn't decayed yet" to his notebook. Because the outcome (the sentence in the notebook) depends on obviously random events (radioactive decay), $$B$$ will predict a nontrivial distribution that will assign nonzero probabilities to different outcomes.

As long as the objects, such as the notebook, may be approximately described in the framework of classical physics, this probability distribution will be nothing else than the usual probability distribution that we use when we throw dice or buy lottery tickets, before we learn what the result actually was. For such objects and their properties that are "in practice" classical, the nontrivial probabilistic distributions that result from quantum mechanics will be indistinguishable from the usual probabilistic distributions we know from the classical world.

The novel feature that quantum mechanics adds are the nonzero commutators and therefore the potential for constructive and destructive interference which predicts probabilities that may not be "emulated" by any classical model (or at least not any local or relativistic classical model etc.). For no good meritocratic reason, Bell's inequality is the most popular example showing that generic quantum predictions for complex enough observables (and correlations) can be "emulated" by no (local) classical "model". But if we only study observables that behave "basically" classically, not to understand why different observers, $$A$$ and $$B$$, use different probability distributions after $$A$$ learns about his measurement (but $$B$$ doesn't) means not to understand the very meaning of the word "probability", even in the classical context.
At this point, $$B$$ opens the door to the room and looks at the notebook (performs his observation). Having observed the notebook entry, he turns to $$A$$ and informs him in a patronizing manner that since his ($$B$$'s) wave function just prior to his entry into the room, which he knows to have been a complete description of the room and its contents, had non-zero amplitude over other than the present result of the measurement, the result must have been decided only when $$B$$ entered the room, so that $$A$$, his notebook entry, and his memory about what occurred one week ago had no independent objective existence until the intervention by $$B$$. In short, $$B$$ implies that $$A$$ owes his present objective existence to $$B$$'s generous nature which compelled him to intervene on his behalf. However, to $$B$$'s consternation, $$A$$ does not react with anything like the respect and gratitude he should exhibit towards $$B$$, and at the end of a somewhat heated reply, in which $$A$$ conveys in a colorful manner his opinion of $$B$$ and his beliefs, he rudely punctures $$B$$'s ego by observing that if $$B$$'s view is correct, then he has no reason to feel complacent, since the whole present situation may have no objective existence, but may depend upon the future actions of yet another observer.
But this argument between the two men doesn't indicate any physical contradiction. The argument has occurred only because $$B$$ – whom I will refer to as Everett because Wigner wouldn't behave in this way – is a jerk (and, incidentally, a totally failed husband and father) who completely misinterprets the character of information available to him and the meaning of $$\psi^{A+S}$$.

What actually happened when $$B$$ opened the door and made the measurement of $$A+S$$ was that $$B$$ has learned about some properties of $$A+S$$, especially about the words written in the notebook. The consequence of this process – of learning – is the change of the information available to $$B$$ which is stored somewhere in $$B$$'s brain but more importantly and more generally, it is clearly subjective.

So there is absolutely no reason why $$A$$ should be grateful to $$B$$ or something of the sort. The "collapse" (Process 1) induced by the decision of $$B$$ to open the door has only made an important change for the $$B$$'s subjective knowledge about $$A+S$$ – it was a measurement, after all. The fact that before he opened the door, $$B$$ was using a nontrivial probabilistic distribution for computed from $$A+S$$ that allowed "all realistic outcomes" doesn't mean that $$A$$ had fuzzy feelings about his brain or his notebook. It only means that $$B$$ didn't know the properties of $$A+S$$ with any certainty.

The fact that two observers may use different pure states $$\psi$$ or density matrices $$\rho$$ or different probability distributions resulting from either isn't an automatic contradiction. If two different quantum states aren't orthogonal to each other, they are not mutually exclusive. There is no contradiction. A contradiction only occurs if a measurement yields an outcome (or if a prediction guarantees an outcome) that is totally impossible according to a different way of making the prediction! This is clearly not the case here.

(I could design such an experiment where a sharp contradiction could occur but only if $$A$$ failed to be a macroscopic quantum system well-approximated by classical physics and if I exploited the interference in some very fine way. All disagreements could then be blamed on the fuzziness of $$A$$'s brain and the error that his fuzzy perceptions were interpreted as sharp classical truth values. As long as the observers may be approximated by classical objects or, more precisely, as long as their perceptions are decoherent histories, no sharp contradiction may ever occur.)

Everett's observation that $$A$$ and $$B$$ use different probability distributions right after $$A$$'s measurement only means the innocent and obvious fact that different people know different things at a given moment. What a big deal. To make a big deal or a PhD thesis out of this trivial fact is indescribably stupid, indeed.

By now, we have hit statements in the thesis that are "sharply idiotic", and this pretty much guarantees that the thesis is going down the hill from these pages. And it surely does.
It is now clear that the interpretation of quantum mechanics with which we began is untenable if we are to consider a universe containing more than one observer. We must therefore seek a suitable modification of this scheme, or an entirely different system of interpretation. Several alternatives which avoid the paradox are:
You see that he indeed does want to use the previous totally wrong interpretation of the wave functions in the experiment involving $$A+S$$ and $$B$$ as the basic "justification" of all the subsequent incoherent musings. But he hasn't found any contradiction at all.
Alternative 1: To postulate the existence of only one observer in the universe. This is the solipsist position, in which each of us must hold the view that he alone is the only valid observer, with the rest of the universe and its inhabitants obeying at all times Process 2 except when under his observation.

This view is quite consistent, but one must feel uneasy when, for example, writing textbooks on quantum mechanics, describing Process 1, for the consumption of other persons to whom it does not apply.
Quantum mechanics in no way requires to deny the right of other humans to use the same theory. After all, evolution theory can be deduced from quantum mechanics applied to an initial state with seeds of life and this theory due to Darwin (and therefore quantum mechanics) "disproves" solipsism by showing the common ancestry and qualitative similarity between all human beings (and other organisms).

The probability distributions encoding one's "knowledge" are always subjective – probabilities have always been subjective, even in classical physics, bookmaking, or anywhere else – but their being subjective in no way means that there only exists "one subject" in the world. The subjective character of probabilities only means that we must specify a subject if we want to talk about the values of the probabilities and they will depend on the subject (observer).
Alternative 2: To limit the applicability of quantum mechanics by asserting that the quantum mechanical description fails when applied to observers, or to measuring apparatus, or more generally to systems approaching macroscopic size.

If we try to limit the applicability so as to exclude measuring apparatus, or in general systems of macroscopic size, we are faced with the difficulty of sharply defining the region of validity. For what $$n$$ might a group of $$n$$ particles be construed as forming a measuring device so that the quantum description fails? And to draw the line at human or animal observers, i.e., to assume that all mechanical aparata obey the usual laws, but that they are somehow not valid for living observers, does violence to the so-called principle of psycho-physical parallelism, [Footnote 2] and constitutes a view to be avoided, if possible. To do justice to this principle we must insist that we be able to conceive of mechanical devices (such as servomechanisms), obeying natural laws, which we would be willing to call observers.

Footnote 2: In the words of von Neumann ([17], p. 418): ..... it is a fundamental requirement of the scientific viewpoint - the so-called principle of the psycho-physical parallelism - that it must be possible so to describe the extra-physical process of the subjective perception as if it were in reality in the physical world - i.e., to assign to its parts equivalent physical processes in the objective environment, in ordinary space."
Quantum mechanics allows us to describe brains and human beings, too. This "alternative" is wrong, too. Psycho-physical parallelism is in no way violated. But probabilities are subjective in general and they have always been (even before quantum mechanics) because different people know different things or at least are differently certain about them.
Alternative 3: To admit the validity of the state function description, but to deny the possibility that $$B$$ could ever be in possession of the state function' of $$A + S$$. Thus one might argue that a determination of the state of $$A$$ would constitute such a drastic intervention that $$A$$ would cease to function as an observer.

The first objection to this view is that no matter what the state of $$A + S$$ is, there is in principle a complete set of commuting operators for which it is an eigenstate, so that, at least, the determination of these quantities will not affect the state nor in any way disrupt the operation of $$A$$. There are no fundamental restrictions in the usual theory about the knowability of any state functions, and the introduction of any such restrictions to avoid the paradox must therefore require extra postulates. The second objection is that it is not particularly relevant whether or not $$B$$ actually knows the precise state function of $$A + S$$. If he merely believes that the system is described by a state function, which he does not presume to know, then the difficulty still exists. He must then believe that this state function changed deterministically, and hence that there was nothing probabilistic in $$A$$'s determination.
Like the previous two, this "alternative" is obviously wrong, too. In principle, $$B$$ may measure a complete set of commuting observables describing $$A+S$$ just like any other external physical system. The argument from Everett's story in no way makes this wrong "alternative" inevitable, either.

In the paragraph above, Everett also keeps on repeating that there exists a contradiction because the two observers use different probabilities in a period of time. I have already explained that this is no contradiction and I will try not to be as stupidly repetitive as Everett.
Alternative 4: To abandon the position that the state function is a complete description of a system. The state function is to be regarded not as a description of a single system, but of an ensemble of systems, so that the probabilistic assertions arise naturally from the incompleteness of the description.

It is assumed that the correct complete description, which would presumably involve further (hidden) parameters beyond the state function alone, would lead to a deterministic theory, from which the probabilistic aspects arise as a result of our ignorance of these extra parameters in the same manner as in classical statistical mechanics.
Like the previous three, this "alternative" is also wrong. The wave function is a complete description of the physical system. To describe a system by a pure vector means to have a maximum allowed knowledge about it. But even in that case, all the predictions are only probabilistic and the uncertainty principle guarantees that most of the statements about the observables will have probabilities strictly between 0 and 100 percent. And in general, these probabilities are subjective – dependent on the observer – because different people may know different things. They may often use the same data from the measurements and translate them to the same pure states for "smaller systems" (and these pure states therefore become "effectively objective") but in complete generality, they don't.

There are no hidden variables and many theorems that have been written down demonstrate this claim, with some more or less mild assumptions, rigorously. If we allow the non-rigorous evidence that is omnipresent in natural sciences, the case against hidden variables – and in favor of the intrinsically and unavoidably probabilistic description – is overwhelming.
Alternative 5: To assume the universal validity of the quantum description, by the complete abandonment of Process 1. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his object-system, and which at all times obeys the wave equation (Process 2).

This brief list of alternatives is not meant to be exhaustive, but has been presented in the spirit of a preliminary orientation. We have, in fact, omitted one of the foremost interpretations of quantum theory, namely the position of Niels Bohr. The discussion will be resumed in the final chapter, when we shall be in a position to give a more adequate appraisal of the various alternate interpretations. For the present, however, we shall concern ourselves only with the development of Alternative 5.

It is evident that Alternative 5 is a theory of many advantages. It has the virtue of logical simplicity and it is complete in the sense that it is applicable to the entire universe. All processes are considered equally (there are no "measurement processes" which play any preferred role), and the principle of psycho-physical parallelism is fully maintained. Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense 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 whether or not such a theory can be put into correspondence with our experience.

The present thesis is devoted to showing that this concept of a universal wave mechanics, together with the necessary correlation machinery for its interpretation, forms a logically self consistent description of a universe in which several observers are at work.

We shall be able to Introduce into the theory systems which represent observers. Such systems can be conceived as automatically functioning machines (servomechanisms) possessing recording devices (memory) and which are capable of responding to their environment. [...]
Perhaps even more so than the previous four, this "alternative" is completely wrong. Quantum mechanics can't be defined without any reference to a measurement (Process 1) because that's the one and only way by which observers obtain information about the physical world and everything that quantum mechanics does is to describe probabilistic patterns in results of various measurements. To pretend that Process 1 (measurement) doesn't exist at all means to "ban" all inputs and outputs of a quantum mechanical calculation.

Also, it's completely wrong to suggest that quantum mechanics can be formulated "without any statistical assertions", as Everett explicitly wrote. Every prediction one can make in modern physics – which has switched to the framework of quantum mechanics – may be formulated as a function of calculable probability distributions. As far as modern physics is concerned, to "ban" probability distributions (and/or not to care about the values of these probabilities) means to ban all predictions and all explanations i.e. to ban all of science. Nothing would be left!

Probabilities quantitatively predicted by a theory must either be intrinsic, like in quantum mechanics (the most elementary and irreducible objects that the theory predicts are probability distributions); or particular values of probabilities may emerge from a classical system combined with huge symmetries or the ergodic hypothesis (which is effectively a symmetry between all points of the phase space). No other theory in which probabilities are not fundamentally incorporated can ever make or reproduce quantitative probabilistic predictions (the apparently correct ones are the reason why we consider quantum mechanics to be a verified theory) which means that there can be no non-quantum, non-classical competitor to quantum mechanics. For other reasons, there can be no classical viable alternative to quantum mechanics, either. Everett's program is a search for such a demonstrably non-existent alternative theory. A minute of thought fully clarified in this paragraph is enough to see that this program cannot ever succeed.

Needless to say, "Alternative 5" is meant to describe Everett's thinking and the rest of the thesis writes tons of additional nonsense about these "servomechanisms". This is how the broadest Everett's framework is defined. So you may want to look at the description of this "Alternative 5" again: as the summary of this "founding father" of this pseudoscientific movement makes explicit, every Everett-based interpretation is supposed to eliminate all statistical assertions from physics; and not to use the change of the wave function and/or probability distributions that are normally induced by a measurement.

It is totally obvious that nothing like that can work (replace quantum mechanics). With Process 2 only, wave functions spread to superpositions of virtually all conceivable states and if you don't interpret the wave function probabilistically, there won't be any relationship with anything we have ever observed.

He has listed five alternatives but sadly enough, he has omitted the correct one, namely "Alternative 0: quantum mechanics". In quantum mechanics, one may have many observers; the theory may be used to describe any and all physical systems, including humans; properties of every physical system may be measured in principle; the quantum description is the complete one and there can't be any hidden variables. But probabilities have to be used and they have to be dealt with according to the correct rules. In particular, probabilities depend on the observer in general (they have always depended) and they do change abruptly when an observer learns something.

In comments below the last "Alternative 5", Everett admits that he has omitted Bohr's view (Copenhagen interpretation). He was probably later forced to add this comment (I would guess that that his original, raw draft was much more offensively stupid and distorting quantum mechanics than the final text of the thesis). The Copenhagen interpretation – the proper framework to use and understand quantum mechanics – is then briefly mentioned only on page 110, after the "popular" interpretation and before three or so "realist" interpretations. On that obscure place, Everett admits (probably because he was forced to admit) that the Copenhagen interpretation doesn't view $$\psi$$ as an objective property of reality. But it's very clear from the ordering and proportions of the text that he has spent almost no time in his life by thinking about the actual rules of quantum mechanics, how Nature works according to modern physics.

At the beginning, Everett listed Process 1 and Process 2. Process 2 is the quantum counterpart of the dynamical laws in classical physics. Process 1 has to be added in quantum mechanics because of its intrinsically similar character. Every theory dealing with probability distributions (even in classical statistical physics or bookmaking) has to admit the abrupt change of probabilities when new evidence (from a measurement) becomes available to the observer! Process 1 is nothing else than this change of the knowledge. So the addition of the extra "bullet point" doesn't make quantum mechanics more contrived; this bullet point only says that quantum mechanics is intrinsically probabilistic. Classical physics is not – the degrees of freedom are to be interpreted in the same way by all observers – so classical physics contains a different (usually implicitly omitted) version of the "bullet one". Quantum mechanics and classical physics are equally simple, in this sense. They differ in one bit of information – quantum mechanics is intrinsically probabilistic, classical physics is not. (There are senses in which quantum mechanics is simpler than classical physics. For example, the answers – probability amplitudes – may always be written down as an explicit expression, one involving Feynman's path integral. There is no counterpart of that in classical physics. Also, the formula for the commutator $$[F,G]=FG-GF$$ is simpler than the formula for the corresponding Poisson brackets, and so on.)

To summarize this essay again, I wanted to elaborate upon the reasons why I agree with the appraisal by the folks around Bohr that Everett was "indescribably stupid and could not understand the simplest things in quantum mechanics" and why I cannot hold any intellectual respect for the apologists of this breathtaking junk who still exist today.

And that's the memo.

snail feedback (45) :

Brave Lubos! It's quite interesting to see the influence of those great distorters of quantum mechanics in Princeton, Einstein and von Neumann. And all the more remarkable that Wheeler's most famous student, Feynman, did understand QM despite this influence, as you reminded us in some previous post!

Lubos - Again?! I'm tempted to write a few encouraging and sympathetic words, but given your relentless and indefatigable assault on this sort of stupidity, you obviously have no need for them.
Cheers!!!

In any well defined application of quantum mechanics, there MUST be some heavy objects which are "outside the description", which define the situation and the possible phenomena that can appear. This classically described situation is specified by the classically defined parameters like X that enter into the Schrodinger differential equation. The large mass of the measuring bodies implies that ΔX ~ 0, and so statements like the "probability of finding a particle at X on the photographic plate" make sense. The fact that these measuring bodies can also be subjected to measurement only implies that there must be additional heavy bodies which must be introduced relative to which these measurements take place. There is no objective "classical" vs "quantum" cut, but in any application of qm, there must be some bodies which are taken to be outside the description, without which the parameters entering into the schrodinger equation would not make any sense.

Dear RAF, thanks - it was slightly original because I think that the "Holy Scripture" of this movement hasn't ever been debunked this explicitly, a sentence after another.

Exactly. To make any old-fashioned sharp statements about Nature, one always need an apparatus or an observer with some properties (not necessarily position of any sort) that behave like classical information, and (quantum) physics reduces to the analysis of the influence of everything else on these properties.

The place of the Heisenberg cut isn't mandatory or canonical. But if we placed some interfering, quantum observables on the classical side of the cut, we would neglect some interference and got wrong predictions; and if we placed absolutely everything on the quantum side of the cut, we would never have any measurements or information that may be compared to the laws of physics.

Upvote!

What you think then about the views if David Deutsch? BTW, excellent review: I never read Everett's original work.

Oh Lubos, you lost me at "John von Neumann's writing is problematic"

Thanks, Kiril! I think that Deutsch should be responded in a similar detailed analysis of individual paragraphs of a reasonable review-like text I will find somewhere, but there are indeed many mistakes in his assumptions, reasoning, and conclusions.

Dear Gail, sorry to hear. I didn't want to question he was a genius. He surely was.

But he didn't represent the Copenhagen interpretation of QM (neither by his location and people he interacted with; nor by the content), some of his additions were in disharmony with it, and even some of his totally orthodox work on QM wasn't quite right, like his no-go theorem against the hidden variables which overlooked the seemingly possible loopholes that are being addressed separately today (like the pilot wave theory).

http://plato.stanford.edu/entries/qm-everett/

Everett offers no empirical experiment consistent with prior observation contradicting Copenhagen. Quantum gravitation offers no empirical experiment consistent with prior observation contradicting general relativity. Uncle Al offers an empirical experiment consistent with prior observation but selectively contradicting general relativity (Equivalence Principle) and quantum mechanics (sourced Milgorm acceleration). Test spacetime geometry with pure geometry in existing apparatus with commercial materials over 90 days.

A mature science says "bullšit" to falsification. Newton got over it (GR, QM). A synchrotron is not a cyclotron plus perturbation theory. Look.

Self-professed positivist Stephen Hawking describes Everett as "trivially true". Pity the poor lay reader...

The analytic philosopher William Lane Craig, who you have written about, frequently claims that 'at least ten different physical interpretations of quantum mechanics' fit what we know about reality and thus that there is no way to prove which one of them is the true interpretation. Not understanding or (at the moment) being capable of understanding quantum mechanics, I've always wondered whether Craig is manifestly wrong on this point. Is he?

On second thoughts, I guess they wouldn't/don't really mind that. They've already got it so that each "world" is accompanied by an uncountably infinite number of almost-identical worlds, so what's a Cartesian product of uncountable infinities between friends... :D :D

He is manifestly wrong and hopelessly confused. When he describes the “Copenhagen” interpretation as unintelligible he is confessing to his own lack of intelligence for, if he does not comprehend Bohr’s view, he does not grasp the basics at all and should just shut up.
Interpreting quantum mechanics is a fools game. This has been pointed out many times on TRF, Mike. The only way to really get it is to stop trying to interpret it and look at the world from within QM.

And in one of those worlds there is some version of Lubos, which is female, writing articles about . err Eotvos experiment in MWI ;)

Feynman was truly remarkable and would have been unable to reformulate it without his profound grasp of quantum mechanics. A guy like Feynman comes along once in a lifetime. Of course he was still subject to human fallibility but his insights were breathtaking.

Dear Lubos, I just have one question that should clarify your position to me clearly. Do you object to an "explanation" of QM(i.e. two places at one time) as to any explanation amounts to a "classical" picture. Or do think an explanation is not necessary whatsoever. Or do you think that an explanation might be there which we can arrive at sometime in the future, and do you have any guess or hint. Thanks.

Nature is not truly classical. Nature is quantum. She simulates classical mechanics in some exclusive conditions.

Fortunately, Nature beautifully permit us, sons of these exclusive conditions to understand and assess her quantum nature. Unfortunately, only a few physicist are able to put your arrogance down and appreciate her.

In uncountable infinity of Everett worlds there must be one Uncle Al who is making some sense.

Dear Qsa, the first thing I object in your comment is the implicit suggestion that proper quantum mechanics as outlined by Bohr and pals is not an explanation. It surely is one. It is the best, deepest, and most accurate explanation of all observations in Nature we have ever made.

If the propositions and logic are used in the conventional way, quantum mechanics strictly says that two orthogonal states - for example, a particle in two disjoint, distant region - are mutually exclusive. So they obviously *cannot* happen at the same time. Either one is realized, or the other is realized, and quantum mechanics allows one to calculate the probabilities of each answer in every situation. But the fact that all the probabilities in a distribution are nonzero doesn't mean that two mutually exclusive options occur at the same time. It means that the answer is not known in advance - it only becomes known when the measurement is made and when the probability distribution has to be updated (collapsed).

One more focused comment what's so wrong about the kind of talking that your comment represents. You ask me whether an "explanation amounts to a classical picture". This is a bizarre question because the term "explanation" as you used it is much less well-defined than classical picture. So it is completely irrational to be asking the question about the "explanation" instead of the much more meaningful question about the classical picture.

The insights made almost a century ago imply that any classical picture is wrong. So depending on what your loaded term "explanation" means or doesn't mean, one may determine whether such an "explanation" is *a* classical picture, and if such an "explanation" is a classical picture, then we know that such an "explanation" is a wrong theory of Nature because we know that the classical picture, any classical picture, is wrong. There is no reason to write the word classical in quotes because we know exactly what it is. It is a theory that identifies the state of the physical system with some objectively existing values of observable - some classical information - and dictates (usually deterministic) laws how these objective quantities evolve in time. These evolving objective quantities that take values in the phase space (which may be conventional or less conventional, it's technicality) determine the observations of all observers. For 90 years, we have known that any such theory of the Universe around us is just wrong.

It is not really right to talk about "objections". Science is about claims that are right or wrong. Bohr's statements are right, your or Everett's are wrong. Trying to hide this simple fact in the fog and ill-defined words such an "explanation" (while you indicate that you won't allow QM to be recognized as the right explanation) is just a stupid propaganda by which you keep yourself unable to understand the basic framework in which Nature operates.

Right. You meant the coefficients sqrt(0.2) and sqrt(0.8), with possible phases.

These values - probability amplitudes and/or probability distributions calculable from them - are the "universal information" that we extract from physical theories. All modern physics' predictions and explanations of Nature boil down to the values of these probability amplitudes (or probabilities). Not to care about their precise values or how they arise means not to care about science - to kill all of science.

Dear Mike, talking about ten interpretations and, in this way, pretending that there is chaos in the foundations of physics is just a demagogic (in this case religious) attempt to undermine the foundations of science.

But such "undermining" is not backed by the scientific facts. In reality, there is just one perfectly well-defined, internally consistent, and with experiments unbelievably agreeing theoretical framework, namely quantum mechanics. It has some basic axioms - due to Bohr, Heisenberg, Born, and others - how to collect data, make predictions, and verify them by experiments, and it works. One may use slightly different words in describing quantum mechanics (and reorganize the information, or focus on different aspects of it) but the beef is always the same.

If someone's comments about "the" theory contradict the beef of what Bohr and Heisenberg and pals wrote as "quantum mechanics", then it's wrong. So there may exist a dozen of incompatible "philosophies" about such things but these things are wrong and the existence of lots of wrong "alternative" theories doesn't mean that there are gaps in the scientific understanding of the corresponding questions.

Ha ha - I'm glad I don't live there then.. :D :D

Let me see if I get your position straight. Quantum mechanics is about predicting probabilities of subjective experiences aka qualia, or is it about knowledge? Knowledge and experience are two different things.

A drunk hydrogen atom might have hallucinatory experiences, but what does "she" have a knowledge about?

Are qualia objective or subjective? Is it fair to claim that for me, you're not conscious, but for you, I'm not conscious?

You do realize you could be reversed, and interfered with yourself in principle, don't you?

Awesome.. :-)

I still don't get what you mean by "experiences". You claim that hydrogen atoms have experiences, and now, you claim only agents intelligent to use and understand quantum mechanics may count as observers. Does that mean there were no observers before 1926, and even nowadays, most humans are not eligible to be observers?

Your objections about any basis being as good as any other applies just as well to human brains as to hydrogen atoms. Are there no preferred bases for human brains then? Or do measurements make the difference, but in that case, what exactly is a measurement? Do hydrogen atoms measure the presence of neighboring atoms via van der Waal's interactions?

If I can make predictions of the alleged subjective experiences of a hydrogen atom, does that mean "she" is conscious? Or does consciousness require a working knowledge of quantum mechanics? Were you unconscious before you learned quantum mechanics?

Human brains are very fallible recording and memory devices. Can your philosophy accommodate fallible observers? Observers so fallible they may be Dutch booked and violate Baye's rule in their actions?

At any rate, to even make the claim that an observer's subjective probability predictions might be incorrect presupposes an external objective frame of reference, doesn't it?

The word "experience" is one of the most elementary, simplest, and most fundamental words that may be used when explaining the foundations of quantum mechanics.

So the word "experience" can't be explained in terms of anything simpler. There is nothing simpler. Experience is what one feels by living and perceiving the world, seeing etc.

Understanding of one's experience is a necessary condition for an agent to use or meaningfully talk about or verify the laws of quantum mechanics. If you don't have any experiences, you can't use quantum mechanics, but it is not quantum mechanics' fault. It is your fault.

Your last question is related to questions about the Sleeping Beauty Problem.
A Hobbesian answer and explanation of them all, in terms of 'centred epistemic possibilities' can be found here: http://ace.mu.nu/Windows-Live-Writer/34740215485e_1105A/too_true_8_2.jpg.

You know, I was going to object, but, if Von Neumann had thought introducing locality in order to close that loophole, he would have come up with Haag duality.

An excellent quote, RAF. It sounds funny but it really does have a very serious and important point.

Physics or science is only "obliged" to produce explanations for those who can actually perceive things, look for such explanations, and verify them.

So a necessary condition for an "agent" to meaningfully use quantum mechanics is that he or she or it or they can perceive something, remember it with a sufficient capacity and reliability of the memory, think sufficiently so that he can deduce the predictions, and the person's memory or senses shouldn't be tampered with or his freedom shouldn't be crippled and so on.

If any of these conditions is violated, it becomes meaningless for him to look for the "right laws of Nature", or one may say that they don't exist.

So whether the hydrogen atom, or a DNA molecule, or an ant, or a chimp, or a feminist - to enumerate a couple of bound states that are increasingly close to a human being - has some consciousness is insufficient for the question what are the laws of physics from her viewpoint.

The nearly dead people, for example, may have some perceptions, but their connection to the external observables is limited, so they're not solid enough "subjects" to learn and verify the laws of quantum mechanics.

However, these nearly dead bodies are still good subjects, so their reactions may be evaluated by other, more healthy and intelligence and alive observers, just like if they were any other physical object.

Yes, I wanted to write the superposition without specifying any phases.

Of course I wasn't seriously trying to suggest that MWI could be fixed by positing that there are also copies of the worlds, with 4 times as many world-copies in the 0.8 "branch" compared to the 0.2 one, it's rather silly. The idea was more to point out how absurd the whole argument is! :-)

In a classical theory where probabilities don't appear to be "intrinsic", it's more careful to say that they're just implicit, because we have a very special case where maximal knowledge allows all possible observations to be assigned probability either 0 or 1.

Ergodicity/Liouville's theorem then gives us an unambiguous way of assigning a probability distribution on a classical phase-space as a way of representing imperfect knowledge.

In the quantum case where not all observables commute it's a more general case, where maximal knowledge still isn't sufficient to ascribe probability 0 or 1 to all possible observations, so that the probabilities are no longer implicit and it's now inherently unavoidable to talk about them.

It seems pretty clear that in that case there's clearly going to have to be an unambiguous explicit postulate as to how to compute them, and that trying to surgically remove that postulate is going to destroy any predictive power of the theory!

Even if it *were* somehow possible to cook-up a scheme with some kind of ergodicity postulate, a suitable world-ensemble with world-copies to reproduce weights and a friendly anthropic consciousness-injection genie to guide observers down a typical "branch" so that they could somehow make reasonable Bayesian inferences etc - wouldn't the result still be an outrageously fugly mess compared to standard QM and not "more simple and beautiful" as claimed?

As I've seen Susskind (and plenty of others) point out, probabilities and statistics are not some afterthought or secondary consideration in science - they're fundamental to the core meaning of observation and the empirical method right across the board, and there's no scientific discussion or knowledge without them.

There's a similar sense in which Statistical Mechanics/Thermodynamics is equally fundamental compared to Particle Physics or any other "foundational" branch of physics - in that any conceivable toy-model universe that could contain interesting non-trivial phenomena without being immediately subject to some kind of ultraviolet catastrophe, is guaranteed to have some kind of theromodynamics/stat-mech in there, regardless of the details of the "fundamental" building blocks of the toy model, (classical fluids, cellular automata, particles, strings etc).

So it shouldn't be seen as a "problem" to have an explicitly statistical postulate in our fundamental theory! It's just a natural extension of what's implicitly already there anyway, (even in the classical case) and a recognition that our universe doesn't admit the special case where maximal knowledge is equivalent to statistical certainty.

Lubos - Thanks. I really do appreciate it when someone understands that my jokes are serious criticisms.
I am afraid that these controversies will not disappear until universities stop awarding degrees to people after taking vast sums of money from them and 'educating' them well beyond their ability to understand their chosen subjects.

Cheers!!!

This was a great read, thanks for the excellent post. I wish someone in the know from the Many Worlds fan camp would respond in detail. Will you let us know if there's such a response from the "quantum crackpot" camp? :)

Thanks for your kind words. If you collided with a quantum realist believer whose answer you are looking forward to, I will publish it.

But so far, I've had the impression that the proposed responses were just the same myths improved at most by an even thicker layer of fog and nonsense than Everett's original thesis.

I totally agree with everything!

Probabilities are intrinsic to thinking about the world and they should be viewed as natural in this sense. Even if an ancient hunter was hunting for an animal, he was thinking in terms of chances, and maximizing the chances that he will survive the winter etc.

In statistical physics, it's unavoidable. In classical physics, one could assume an auxiliary hypothetical "perfect God's perspective" where all statements have probability 0 or 1. But the assumption that such a "perfect" viewpoint exists wasn't ever necessary for anything important in science that was found, and the uncertainty principle of quantum mechanics made it impossible.

So the opposition to the intrinsically probabilistic thinking is just some excessive emotional attachment to something that didn't quite deserve the status of a dogma, that people could live with before etc. because they never had access to the "perfect omniscient God's perspective", anyway.

Concerning the 4 worlds vs 1 world. Right, this is the most obvious attempt to bring unequal probabilities to the "many worlds illustration" (it is a more accurate word than interpretation).

However, this still contradicts some fundamental problems. First, there is no reason to assume that all the worlds should be equally likely. After all, there is no (thermalizing/ergodic) jumping in between them, so the ergodic justification can't be used. Also, and it's related, there is no exact symmetry between them - the future with a dead cat is different than one with the alive cat - so there is no reason to treat the "uniform" distribution as better than other distributions.

Also, one couldn't ever get irrational probabilities - and most correct probabilities that quantum mechanics predicts are irrational.

Also, this "illustration with different number of MWI copies" could only deal with continuous variables. It would become ill-defined for measurements of observables with continuous (or mixed) spectra.

But even if some miracle solved all these problems, or one would ignore them, the explanation would still be vastly more contrived than standard intrinsically probabilistic quantum mechanics. It would be clear from the description of the theory that it's a rationalization of some philosophy that was "determined as a dogma" a priori, and those who rationalize it don't care whether their explanations sound very awkward or extremely awkward.

Upvote!

Upvote! 2

Thanks for the reply. I think everybody agrees that QM explains nature, the question is what explains QM's unfamiliar features.The electron in the hydrogen atom is characterized as a cloud and the solution is time independent, so the electron seem to have no defined position until it is measured and you do not find that puzzling, it is the way nature is, that is it. No need for further inquiry into the nature of QM, is that correct?

Yes, it's the final answer, there is nothing wrong with it, and additional "inquiries" are both irrational and scientifically dishonest.

The shape of the orbitals isn't a cloud in the same sense as the water vapor clouds above is. It describes probability amplitudes whose only meaning is to predict the probabilities that the electron will be seen here or there.

The relative phases also matter - they're important for the predictions of all observables that don't commute with the position (and almost all of them don't commute, indeed).

Just the usual objection against your second (introductory) sentence

I think everybody agrees that QM explains nature, the question is what explains QM's unfamiliar features.

You can see that you are a victim of your extremely sloppy language and that this confusion of yours is a self-inflicted wound, can't you?

The problem is that you are using the word "explain" in two totally different meanings.

In the first part of the sentence, you use it for a theory's ability to calculate the results past (and future, i.e. predict) observations.

In the second part of the sentence, you use the word "explain" in the sense of a pedagogic effort. Some people find something "unfamiliar" - you used this word yourself! - so they have to be "explained" something.

But this need for "explanation" in the second sense is purely up to people's ignorance - their "unfamiliarity" with some principles and mechanisms, if I use your word, and this pedagogic effort has nothing whatever to do with the theory's explanations of phenomena.

The first part of your sentence uses the word "explain" but talks about science and research; while the second part uses the seemingly identical word "explain" but talks about teaching. Can't you see that? Can't you realize that science and research is something else than teaching? How can you conflate these totally different things?

On the bright side Lubos, you're not alone if you look at Prof Arnold Neumaier's view on Everett's thesis and its proponents:

http://www.mat.univie.ac.at/~neum/physfaq/topics/manyworlds

Yes, you have said it over a thousand times. I just wanted to hear it in a clear way.

Strangely enough, Neumaier claims that string theorists are the 1st group that supports the MWI.

The two most common elements in the universe are hydrogen and stupidity. :-)

-Harlan Ellison