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".
Here we go again:
Now, he gets closer to the physical topics:
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.
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 \(\psi\):
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:
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.
\(A\) 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.
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.
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).
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.
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.
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.
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 FUNCTIONThis 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.
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.
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: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".
Footnote: We use here the terminology of von Neumann [17].
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 \(\abs{(\psi,\phi_i)}^2\).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".
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.
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 Schr̦dinger'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 Рthe first author of this thought experiment Рisn'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.No, the claim that there is a physical inconsistency here is demonstrably incorrect.
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.
\(A\) 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.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).
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.
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.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.
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."
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.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.
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.
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.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.
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.
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).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.
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. [...]
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.
Fallacious thinking in Hugh Everett's thesis
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April 07, 2015
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