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John Preskill's strange anti-quantum zeal

On his blog, I've had some exchanges with John Preskill concerned with the black hole information puzzle. He knows a lot about these matters and he has done some nontrivial research as well so much of the time, you're inclined to think that he agrees with the general rules of the game – the postulates of quantum mechanics and things like that.

But at some places, you get some suggestive evidence that it isn't the case. The first time I noticed some anti-quantum zeal inside John Preskill was in late 2014 when he hysterically celebrated John Bell. As far as I can say, John Bell hasn't done any important thing in the foundations of quantum mechanics in his life. He has just proposed another experimental setup in which classical physics and quantum mechanics gave different predictions. Well, classical and quantum physics give differing predictions at almost all times. The difference between classical and quantum physics is absolutely obvious and has been absolutely realized by everybody since the first moment when quantum mechanics was formulated. You don't need – or you shouldn't need – another example of that phenomenon every day to appreciate the difference.

His theorem was an inequality that only worked with the classical side of this comparison. So John Bell has never really applied the laws of quantum mechanics to calculate or explain anything. And if you look carefully, you will easily convince yourself that John Bell didn't believe quantum mechanics; and he didn't understand quantum mechanics. So while his theorem about the local classical theories was correct, he had no understanding of the laws of Nature beyond classical physics. He always assumed the world to be classical which is why he – absolutely incorrectly – interpreted his theorem as evidence of nonlocality in Nature.

OK, back to 2017. There are many interesting and OK things in Preskill's explanation of the recent advances in the black hole information puzzle. But I noticed at least two bizarre features:

  • He always seems to choose the language that indicates that he really believes that there is a paradox – a contradiction – in quantum gravity
  • He carefully avoids the standard terminology of quantum mechanics such as the word "observer"
Both points manifested themselves in his comments about the cloning in the presence of black holes. Concerning the first point, he likes to talk about scenarios that are obviously forbidden by the laws of physics – and often mathematics.

There's no unitary linear map on the Hilbert space that is bilinear at the same moment (that tensor squares vectors). So a map \(\ket\psi\to\ket\psi\otimes \ket\psi\) cannot be an approximation of any unitary quantum evolution. This statement is as obvious as the statement that linear and quadratic functions differ; these two statements are fundamentally the same. But we often hear about Alice and Bob who clone quantum objects and square the wave functions. Why? Aren't we adults who understand that those things can't happen?

I think that at the end, the motivation is to fool the listeners – and the speaker himself – to believe that there is really a logical contradiction in quantum gravity. And these examples of the contradictions are basically nothing else than a special case of very similar verbal exercises that want to claim that they have found a logical contradiction in quantum mechanics in general. Once the listeners get brainwashed into thinking that there is a big paradox, they may be led to the desire to apply a "big fix" of this contradiction. Modify the rules of quantum mechanics. Introduce the black hole firewall and cancel the black hole interior altogether. Or something like that.

Except that there is no real paradox in quantum gravity or quantum mechanics – or anywhere in physics, for that matter – which is why all the "big fixes" are only justified by tricks, by deceitful maneuvers designed to confuse the listeners and often the speaker himself.

Concerning the second point I listed, Preskill loves to avoid words such as "observer". You know, on the spacetime that contains an evaporating black hole, you may draw spacelike slices in which you may see all the infalling objects shortly before they are killed near the singularity; as well as almost all the Hawking radiation that the black hole emits over the lifetime. Because the radiation is thought of as "dependent" on the state of the matter inside the black hole, it looks like you have cloned – doubled the carriers of – the information.

But this is just an illusion because there's no valid evidence that the fields on the spacelike slice with the doubled information really commute with each other. To check whether two operators commute, you need an observer who can measure both. In other words, if you want to construct some statement or paradox involving two observables \(L,M\), it must be either be a full-blown mathematical statement about operators \(L,M\) on a space, or a physical argument dealing with observables. But a physical argument saying anything about observables needs the actual observer who may exist and make the observations.

But in the black hole spacetime, such an observer cannot exist. An observer who fell inside the black hole can never get out again so he can't measure most of the Hawking radiation. And the observer who has measured most of the Hawking radiation has seen that the black hole has already – mostly or completely – evaporated so he can't jump inside anymore. There's no black hole left to jump into.

This simple observation is enough to eliminate the would-be paradox. If no observer may see a paradox, then the paradox doesn't exist. The fact that I can reason in this way is the very point why the term "observer" was introduced in quantum mechanics: Its positivist underpinnings say that statements are only guaranteed to be physically meaningful to the extent to which they say something about actual observations performed by actual observers. We can move on and ask: How are exactly the field operators inside and outside represented on a Hilbert space and what sort of algebra and mutual commutators they obey? If you don't want to move from the childish "look, physics looks like it is self-contradictory" to "physics is consistent, let us see how it precisely works", it's probably you don't want to learn how it actually works.

Preskill avoids the word "observer". So his version of the argument above said that "there is no referee" who can see both the black hole interior as well as almost all the Hawking radiation. Great. But wait a minute. A referee? In physics, what I was talking about is called the observer. In classical relativity, an observer may mean someone who is making observations in an objectively real spacetime but who is associated with a world line in the spacetime. That world line constrains what he can see or observe at various stages of his life. In quantum mechanics, an observer is an essential entity that is needed to apply the laws of physics at all – the laws of physics are probabilistic predictions for future observations calculated from the results of the past observations.

In quantum gravity, the "observer" represents both. So he's needed to make the state vectors well-defined and to validate the predictions in the quantum mechanical sense. But he must still operate within the spacetime in some way so he's associated with a world line. In particular, the black hole singularity kills all observers. The state vector becomes meaningless after this death near the singularity because the brain or anything similar ceases to exist. If you agree that an observer actually needs some physical object (like the brain) that is macroscopic enough to decohere etc., this object depends on the surrounding geometry's being peaceful enough and not deadly. For an observer inside the black hole, the singularity is precisely lethal. He is killed along with all his hopes that he could establish a paradox.

For another observer who is outside the black hole, the situation may be different. He doesn't need to care whether a human being was killed inside the black hole. He may still analyze the behavior and radiation of the black hole with an arbitrary precision. So it's possible that the information about the infalling observer escaped in some way and the observer got "reincarnated" in some sense and the observer outside the black hole may find evidence for that. But the observer inside cannot. It's very important to appreciate that the "qualitative answers" may depend on which observer evaluates the situation. This dependence is really the point why the observer was introduced – to quantum mechanics but already to relativity 20 years earlier (where the choice of the inertial system affects simultaneity, lengths, duration, and most other things).

I think that Preskill used the new word "referee" instead of the "observer" in order for the story to sound muddy, in order for his listeners to be confused and view the whole discussion as fishy. He clearly wants people to remain confused about quantum mechanics. A listener may ask: WTF is a referee and where the rules that a referee is needed are coming from? But they're not new rules – they are exactly the same rules of quantum mechanics saying that have always said that to talk about observables, you need observers. I was assuming that the views about the foundations of quantum mechanics held by all the real practitioners in quantum computation had to be similar. And even Scott Aaronson is rather sensible in this topic. He realizes that quantum mechanics is a particular generalization of the classical probability distributions in which the probabilities are replaced with the complex probability amplitudes – which are half-baked products that may be added in various ways and squared to obtain probabilities of various things. But he surely understands that the wave function is something different than a classical field.

And it's a guy who thinks that all men should be chemically castrated for their sin of being male; and that we live in a computer simulation, aside from many other yummy things. Nevertheless, as a reader named Ruggs from Palo Alto has forced me to learn in recent hours, John Preskill is actually much more anti-quantum than e.g. Scott Aaronson. So I have mostly read the Section 3.6 in some Preskill's notes which is dedicated to the foundations of quantum mechanics.

The whole PDF document I linked to has 62 pages and a big portion of it is dedicated to the foundations of quantum mechanics. Let me begin with a funny, characteristic observation. I have measured the number of appearances of names of various thinkers in this long text (partly or mainly) about the foundations of quantum mechanics. The results are as follows:
  • Everett: 12
  • von Neumann: 6
  • Bell: 1
  • Plato: 1
  • Bohr: zero
  • Heisenberg: zero
  • Born: zero
  • Jordan: zero
  • Pauli, Dirac, ... : zero
I have chosen the word "zero" instead of 0 to avoid questions such as "what is the circle supposed to mean when the entries should indicate numbers". The text is about the foundations of quantum mechanics but none of the actual discoverers of the foundations of quantum mechanics – or their authentic ideas – are ever mentioned by Preskill! Thank God, at least von Neumann was allowed but he still couldn't compete with Hugh Everett. Even John Bell, a clueless crank, must have been so important according to Preskill that he has beaten Bohr, Heisenberg, Dirac, and all these people combined. In fact, Bell was so important that he is even quoted for having proposed that FAPP means "for all practical purposes". I was surprised that the PDF file didn't contain a picture with the important mummified excrement of John Bell that was sold to a driver of Tesla for $3 million at an auction in Pasadena.

(And no, the collapse of the wave function which is FAPP isn't just "for all practical purposes". Instead, it is "Fundamental According to the Person's Perceptions" – and those perceptions are needed to apply the laws of quantum mechanics.)

Preskill says lots of incredible things about Hugh Everett. Half a century ago, things were still OK so Everett didn't get a postdoc job simply because he claimed to be working on a set of problems – foundations of quantum mechanics – but he didn't understand this discipline. These days, it doesn't matter. So Everett is quoted as the guy who discovered that the evolution of quantum systems was unitary, the need for many worlds, and similar stuff. All these claims are absolutely idiotic, of course. The unitarity of the evolution operator was understood from the first moments of quantum mechanics of the 1920s. The unitarity – a property of a complex matrix – is only a property of the evolution (and other transformation) operators. Once you talk about the actual observed facts, they're not "unitary" in any sense, and no amount of worshiping of a crackpot named Everett may change the fact.

Another person who has trumped Bohr, Heisenberg, Jordan, Born, and others in the story about the foundations of quantum mechanics was Plato – probably because he was more progressive than Aristotle. Let me pick a part of the page about Platonism:
...Yet each time I look at a cat, it is always either dead or alive. Both outcomes are possible, but only one is realized in fact. Why is that?

Your answer to this question may depend on what you think quantum theory is about. There are (at least) two reasonable schools of thought.

Platonic: Physics describes reality. In quantum theory, the “wave function of the universe” is a complete description of physical reality.

Positivist: Physics describes our perceptions. The wave function encodes our state of knowledge, and the task of quantum theory is to make the best possible predictions about the future, given our current state of knowledge.

I believe in reality. My reason, I think, is a pragmatic one. As a physicist, ...
These paragraphs are pretty much the same garbage that hardcore anti-quantum zealots love to write. The rest of Preskill's document is mostly better than that but there are many claims that are comparably atrocious.

Let's answer his questions and correct the blunders hiding in the sentences above. First:
...Yet each time I look at a cat, it is always either dead or alive. Both outcomes are possible, but only one is realized in fact. Why is that?
Because quantum mechanics is a correct theory and it's exactly what quantum mechanics says. Quantum mechanics postulates that an observer can make an observation – a measurement – of a quantity. Every observation is associated with a Hermitian operator \(L\) acting on the Hilbert space.

Before he performs the observation, there are various possible results that can be identified with the eigenvalues of \(L\). The probabilities of different eigenvalues \(\ell_i\) may be calculated as \(|c_i|^2\), the squared absolute values of the amplitudes in front of the corresponding terms in the decomposition of \(\ket\psi\) into eigenstates.

Once the observation of \(L\) is completed, the observer learns about the actual eigenvalue \(\ell_i\) that has become a fact. Quantum mechanics says that it must be one of the eigenvalues \(\ell_i\) whose \(|c_i|^2\) was nonzero, the squared amplitudes are the probabilities – this principle is known as Born's rule.

Quantum mechanics says that the post-measurement fact about the observable is one of the eigenvalues because this is an axiom – postulate – of quantum mechanics. This particular wisdom – that there is one particular fact resulting from a measurement – isn't even a new addition discovered along with quantum mechanics. It is a tautological consequence of the definition of the term probability. Even in the era of classical physics, the probability was a number that quantified which particular possibilities may become facts once the result is observed – once it becomes known.

If you don't understand this absolutely trivial fact that whenever probabilities are calculable, there are possibilities before the observation but a fact after the observation, you shouldn't use the word "probability" at all because you clearly don't have the slightest clue what the word means. And once I successfully prevent you from using this word that you don't understand, you can't talk about quantum mechanics, either – because the laws of quantum mechanics just cannot be expressed without the word "probability". Period.

What is Preskill's answer?
Your answer to this question may depend on what you think quantum theory is about. There are (at least) two reasonable schools of thought.
Well, it's a meta-answer. What Preskill doesn't seem to realize is that quantum mechanics and physics aren't arts or religions where answers about the laws are subjective. The laws of Nature are objective, some answers are right and some answers are wrong. So your answer may depend on many things but if it differs from the correct one as discovered 90 years ago, then you are just wrong – and probably a crackpot.

He gives you two "reasonable" options, the Platonic and positivist one. Quantum mechanics was discovered when the founding fathers carefully appreciated the importance of the positivist principles. So verbally, positivism is clearly the correct principle underlying the new, correct physics – quantum mechanics – while the Platonism in this particular sense is the outdated, falsified foundation that formed the foundations of the previous framework, that of classical physics.

However, if you study what Preskill means by "Platonism" and "positivism", you will find that both of them are wrong. While the simple sentence about positivism of quantum mechanics quoted above is correct (but Preskill chooses that "school" to be wrong), the following paragraphs make it clear that by "Platonism", Preskill means that \(\ket\psi\) is a wave whose general meaning is the same as that of classical fields \(\vec B(x,y,z,t)\), among other classical observables, while "positivism" is that the world may be captured by a particular probability distribution \(\rho(x,p,t)\) on some phase space.

The would-be philosophers trying to talk about the foundations of quantum mechanics use the words "ontic" and "epistemic" as synonyms for Preskill's "Platonic" and "positivist".

Well, none of these two possibilities is right. Both of them ultimately assume that there exists some objective reality as envisioned by classical physics. At the end, the difference between "ontic" and "epistemic" is just a matter of a description. Whenever there is an ontic description, there may be an epistemic description of the same laws of physics, and vice versa. But quantum mechanics is fundamentally different. It is neither ontic, nor epistemic – it is neither Platonic, nor positivist – in the sense understood by Preskill.

Quantum mechanics postulates – and the postulate is validated by the successful tests of quantum mechanics and the failures of all conceivable alternatives – that there is no objective state of Nature. Instead, the state of Nature must always be expressed relatively to a given observer who or that can make observations. And the laws predict the odds for outcomes of future measurements from the results of the past ones (that are used to construct a state vector or a density matrix which is evolved by the complex unitary evolution etc., and the squared matrix elements are interpreted as probabilities).

This is how the laws of Nature around us actually work and as long as you try to squeeze Nature into a straitjacket of the classical thinking where things were objective and observers were unnecessary, you will always fail. The change from classical physics to quantum mechanics wasn't a technical development that added a new field or a new \(1/r^5\) term to the potential energy or anything of the sort. It was a development that fundamentally changed the logic how predictions are made, that altered the relationship between observations and mathematical concepts in the theory.

OK, again, while Heisenberg et al. called themselves positivist, it was the actual positivism that acknowledged that the observations – an operational definition of a term – weren't optional. They were mandatory for a discussion to be meaningful in general. If you can't give me a procedure how to actually measure something – like the value of an observable before the observation – then it is totally OK to say that this operationally ill-defined quantity is scientifically meaningless. The previous sentence captures what "positivism" is actually about: it is ultimately the need for an operational definition of the concepts. What Preskill calls "positivism" isn't real positivism. It is really "epistemism" believed by those philosophers etc. whose brains are too small to really understand what the positivist thinking is.

At any rate, Preskill chooses his answer to be
Platonic: Physics describes reality. In quantum theory, the “wave function of the universe” is a complete description of physical reality.
The wave function is a complete description in the sense that it's not emergent and there can't be anything "more accurate" than the wave function. A non-pure density matrix always has "more uncertainty" in it than a pure state vector. However, even a pure state vector has uncertainty about most observables – which cannot be eliminated, not even in principle. However, the way how the wave function describes Nature is absolutely different from the way how the value of the magnetic field \(\vec B(x,y,z,t)\) does so. The wave function contains the probability amplitudes – complex generalizations of probability distributions – associated with a particular observer who has done some particular observations.

If you don't describe the precise rules how you use the wave function to make predictions, I can't tell you whether you understand it. Saying that the state vector is a "complete description" is too vague a statement to be of any value. What is essential is that there is fundamental difference between the "completeness of the description" by a classical field \(\vec B(x,y,z,t)\) and by the wave function \(\ket{\psi(t)}\). What is it?

If you know that at \(t=0\), the magnetic field is \(\vec B(x,y,z)\), and you ask what is the probability that the magnetic field is some other function \(\vec B'(x,y,z)\), then the answer is either zero or one. It's one if and only if the two functions are exactly the same,\[

B(x,y,z) = B'(x,y,z),

\] otherwise the probability is exactly zero. However, it's completely different with wave functions. If Nature or a physical object is brought to the state \(\ket\psi\) and you ask whether it's in the state \(\ket\phi\) – let us assume \(\langle \psi\ket\psi=\langle\phi\ket\phi=1\) – then the answer is that you usually can't answer with certainty.

Instead, the answer is that there is some probability that Nature in the state \(\ket\psi\) is in the state \(\ket\phi\), and some probability that it is not. The probability that the physical object in the state \(\ket\psi\) is (also) in the state \(\ket\phi\) is given by\[

P(\psi=\phi) = \abs{ \langle \psi \ket\phi }^2

\] It's just Born's rule. Non-orthogonal states are simply not mutually exclusive in quantum mechanics. If you consider two very close profiles of a classical magnetic field \(B(x,y,z)\) which are not equal, you may sharply say that if Nature is in the first, it is not in the second. But for two nearby vectors in the Hilbert space, you just can't do it. The probability that they're the same is \(\cos^2 \gamma\) where \(\gamma\) is the angle in between them.

You can't distinguish nearby states in the Hilbert space. This statement is just another formulation of the Heisenberg uncertainty principle. States \(\ket\psi\) and \(\ket\phi\) that are too similar just can't be distinguished by a measurement – if you can only repeat the situation once.

(The nearby states \(\ket\psi\) and \(\ket\phi\) may be sharply distinguished as mathematical objects – or brains or computers with the memory remembering these two states may be sharply distinguished. But the memory or an idea isn't the same thing as the object it refers to. The ideas or knowledge about \(X\) held by two people may differ but it may still be the same \(X\) – and vice versa.)

If you insist on using the phrase "complete description of physical reality", what is the answer to the question whether a wave function is one? Well, because of the reasons above, the correct answer is that
a wave function is an overcomplete description of physical reality.
The wave function contains more mathematical degrees of freedom than the number of physical degrees of freedom in reality. For example, \(M\) qubits (the wave function for their possibilities) contain "more mathematical stuff" than \(M\) bits, the results of a measurement of these qubits (i.e. the facts). Note that this correct answer is clearly none of the "two reasonable possibilities" allowed by Preskill. His Platonism means that the mathematical degrees of freedom in the wave function match the physical degrees of freedom in reality; while his positivism means that the wave function only captures a subset of the degrees of freedom in reality – the complete reality has much more stuff, perhaps some hidden variables (or histograms showing the demographics of many worlds), and the wave function is an effective, truncated description.

But the correct answer is the third one: the number of physical degrees of freedom is much smaller than the number of numbers stored in the wave function. This fact is also responsible for the ability of quantum mechanics to predict the observed, very low heat capacities of atoms and molecules. No "Platonic" let alone "positivist" theory in Preskill's sense could do it.

If you phrase the whole discussion in terms of the comparison of the "number of mathematical variables in the wave function" and the "number of actual physical degrees of freedom", there are clearly three possible outcomes of the comparison. Either they're equal, or the first is greater than the second, or the first is smaller than the second. And among his "two reasonable schools of thoughts", Preskill has simply omitted the correct answer – the third one although it should clearly be the first one.

So his – and not only his – story is basically isomorphic to the following:
The circumference of the circle of radius \(R\) is said to be equal to \(2\pi R\). It's strange. You walk for the distance \(2\pi R\) and you end up being at the same place where you were at the beginning. Why is that? If you walk, shouldn't you move on?

There are two reasonable schools of thought about this mysterious circumference \(2\pi R\):

Platonism: You end up at the same place because \(2 \pi\) is actually zero.
Positivism: The value of \(2 \pi\) is negative so walking the distance \(2\pi R\) is so counterproductive that you really can't get anywhere.

I, Preskill, choose Platonism, \(\pi=0\), because I am really smart and wise...
OK, sorry but none of these "schools of thoughts" is reasonable and you're not smart or wise if you promote them. \(2\pi\) is neither zero nor negative. It is positive and the actual reason why you end up at the same place follows from the definition of a circle and it's much more elementary or axiomatic than any numerical estimate of the value of \(2\pi\).

Note that this clone of Preskill has also used an illogical name, positivism, for the second "reasonable" school of thought. It would be much more accurate to call this school claiming \(\pi\lt 0\) "negativism". ;-) This negativism, i.e. fake positivism, has hijacked the brand from the true positivism – and only the true positivism (just like the statement that \(\pi\) is positive) contains the valid answer to questions about the character of the knowledge and the wave function in Nature.

The situations really are isomorphic. Preskill – and other people making similar weird statements – are simply omitting the correct answers to all the questions from the very beginning even though the existence of the correct answer is as obvious as the existence of positive numbers, and even though it is clear that the correct explanations for their "mysteries" have nothing whatever to do with their proposed explanations. They just omit the correct explanation even in their lists of options – just like they omit the names of discoverers of this most profound revolution in the history of physics.

If you're teaching a course on quantum mechanics or anything that depends on the postulates, couldn't you please eliminate all the post-modern garbage that was added to it – and that distorted the logic of the theory – in the recent 60 years or so? Many more things were messed up than those that were improved. When e.g. Dirac was writing his textbook in 1930, he understood all the principles much better than you do today, despite your ludicrous games pretending that you have made some progress and "someone else than Heisenberg et al." really discovered the basic rules underlying modern physics. You are only adding chaos, fog, redundant babbling, and outright lies to the talk about the principles of quantum mechanics.

Bonus: A few words about the final paragraphs of Preskill's Section 3.6
In summary then: Physics should describe the objective physical world, and the best representation of physical reality that we know about is the quantum-mechanical wave function. Physics should aspire to explain all observed phenomena as economically as possible – it is therefore unappealing to postulate that the measurement process is governed by different dynamical principles than other processes. Fortunately, everything we know about...
Physics should explain our observations. The assumption that laws of physics are compatible with an objective physical world is a hypothesis and by 1925, this hypothesis was unquestionably and irrevocably falsified whether anti-quantum zealots like this fact or not, and whether or not they have been "fast" enough to have noticed these fundamental changes in the "engine of physics" in these 90 years. Physics doesn't describe the objective physical world.

On top of that, it's nonsensical to say that "the wave function is the best representation of physical reality". One needs a whole theory – in this case quantum mechanics – and not just isolated objects from the theory to represent physical reality. Also, even if one could tear the objects from the theory, the wave function wouldn't be a "representation" of a physical reality. It is a mathematical encapsulation of what the observer associated with the wave function knows about physical reality. The numbers in the wave function are probability amplitudes which are close cousins of probabilities. They say not "what is out there" but "what an observer knows or can say about the world out there".

The following sentence is wrong as well. The measurement process isn't governed by any dynamical principles. The dynamical evolution is a phrase describing the continuous evolution of the observables or probability amplitudes in time. The measurement isn't a dynamical evolution, it is a process leading to the observer's learning of new information whose existence is automatically guaranteed by the very notion of "probability". The need for observations doesn't add any dynamical structure, let alone an "ugly" or "unappealing" structure, to the theory whatsoever.

The claim that quantum mechanics is "unappealing" because it involves observations isn't a justifiable statement. It is just an expression of the speaker's prejudice and his absolute incompatibility with the fundamental postulates of modern physics – exactly for the same reasons as a creationist's statement that "evolution is unappealing because it requires the animals' brutal competition and moreover, it suppresses the people's belief in God". Whether or not a believer likes these fundamental features of evolution, they are elegant, highly predictive, and amazingly verified by the evidence. So the comments that they are "ugly" are just a stupid propaganda by an ignorant, ideologically prejudiced speaker. The comments about the "unappealing" character of a theory depending on observations are exactly analogous.
...Fortunately, everything we know about physics is compatible with the hypothesis that all physical processes (including measurements) can be accurately modeled by the unitary evolution of a wave function (or density matrix). When a microscopic quantum system interacts with a macroscopic apparatus, decoherence drives the “collapse” of the wave function “for all practical purposes.”...
It is an utterly ludicrous statement if someone says that measurements are "modeled by unitary evolution". A measurement cannot be a unitary evolution because it is not even a map. A map is something that assigns a unique well-defined result \(f(\psi_i)\) to the argument – in this case the initial state – \(\psi_i\). The measurement ends up with a random result so it is obviously not even a map, let alone a linear unitary map. Only the probability amplitudes in the state vector, and not the measured facts, are evolving in a unitary way.

Statements such as "the measurement is a unitary map" are exactly as ludicrous as "an elephant is a truck", "the Earth is flat", or "the DNA is determined by the people's behavior towards minorities". A completely ignorant person may buy these propositions and these propositions may play some role in strengthening some weird propaganda but everyone who has a clue understands that they're ludicrously wrong.

Decoherence doesn't drive any collapse. Decoherence is only an effective evolution of a reduced density matrix of a subsystem – when the environmental degrees of freedom have been traced over. When it's done, one learns that the reduced density matrix rapidly converges to a diagonal form in a certain basis. But the probabilities – the diagonal entries of the density matrix – are generally nonzero, all of them, so all possibilities are still allowed after decoherence and there's just no collapse. The collapse only happens when the observer actually learns about a result. The result is random and quantum mechanics may only calculate probabilities. There is nothing deeper or "composite" – and there cannot be anything deeper or "composite" – about this event of learning.

As I just said, the collapse of a wave function is a subjective process analogous to (and generalizing) the update of probabilities in Bayesian inference which is however fundamental for any application of the laws of quantum mechanics. It is completely wrong to marginalize the measurement as something emergent or something that only exists "for all practical purposes". The observation is absolutely fundamental and irreducible in any application of quantum mechanical theories.
If we eschew measurement as a mystical primitive process, and we accept the wave function as a description of physical reality, then we are led to the Everett or “many-worlds” interpretation of quantum theory.
If you "eschew" measurement as a primitive process, then you have no chance to correctly describe or understand how quantum mechanics works. Measurement is a fundamental, irreducible process in any quantum mechanical theory. But it is not a "mystical" one. The measurement is just about someone's "learning". "Learning" is the transition from "not knowing" to "knowing". Verbs "to learn" and "to know" are as clear, simple, and well-defined as verbs such as "to be". Every kid knows them. To call these verbs "mystical" is just pure stupidity.

Also, it is complete nonsense that there exists any valid argument that leads to the "Everett or many-worlds interpretation of quantum theory". These are just marketing slogans and there exists no actual theory that would be able to make scientific predictions according to rules that might actually be written down. Everett or many-worlds "interpretation" is just a nonsensical new age religion with no genuine relationship to modern physics.
In this view, all possible outcomes of any “measurement” are regarded as “real” — but I perceive only a specific outcome because the state of my brain (a part of the quantum system) is strongly correlated with the outcome
The a priori possible outcomes that are not realized are not real. The previous sentence is really tautologically true – so Preskill's statement is tautologically false – because the verb "realize" simply means "become real". If something doesn't become real, it just isn't real after the event! So Preskill's statement about those unreal outcomes' being real is exactly on par with the statement that "the truth is the same thing as a lie". It just can't be true and you don't even need to know anything to see that it's untrue.

On the other hand, the correlation between the brain and the result of the measurement is true regardless of an interpretation. An organ such as the human brain that is able to detect information is one that – by the definition of detection – becomes correlated with the quantity that it is detecting. So the statement that the observer's brain is correlated with whatever was observed is surely true. But the statement that this correlation points to Everett's theory is just utterly ludicrous. Moreover, the correlation between the brain and the observed object may only be seen from the viewpoint of yet another observer. So none of these correlations between apparatuses or brains on one side and the measured system on the other side helps to "clarify" anything about the measurement at all. These comments are just adding new redundant links in the explanatory chain.
Although the evolution of the wave function in the Everett interpretation is deterministic, I am unable to predict with certainty the outcome of an experiment to be performed in the future – I don’t know what branch of the wavefunction I will end up on, so I am unable to predict my future state of mind.
Proper quantum mechanics isn't making particular deterministic predictions. It is predicting probabilities of outcomes. But it is predicting something. When many unlikely events are combined, one may say that their combination is impossible (or its negation is guaranteed) and quantum mechanics can make such predictions.

On the other hand, when some ideas can't make any predictions at all, not even probabilistic ones, or if they can't say how to connect the mathematical objects with the observations, they just don't belong to science. From the viewpoint of science, their value is exactly zero. The fact that the complex numbers in the wave function are connected with probabilities of subjective perceptions of measurements is absolutely fundamental and by removing it, one kills the whole quantum mechanics as a physical theory. Nothing would be left if you omitted these fundamental pillars of quantum mechanics.
Thus, while the “global” picture of the universe is in a sense deterministic, from my own local perspective from within the system, I perceive quantum mechanical randomness.
If you perceive that the results are random but the theory predicts that they are deterministic, then this disagreement between your perceptions and your candidate theory has falsified the theory – it has proven it to be false. In science, theories are being chosen according to their agreement with our observations. Do I really have to explain this trivial point? It's pathetic.

A viable theory cannot be deterministic because the experimental data clearly prove that the outcomes of observations are not uniquely determined by the initial state. So any deterministic theory simply belongs to the trash can.
My own view is that the Everett interpretation of quantum theory provides a satisfying explanation of measurement and of the origin of randomness, but does not yet fully explain the quantum mechanical rules for computing probabilities.
Everything that quantum mechanics predicts is basically a collection of probabilities. So if you remove "probabilities" from the successes of a physical theory based on the same objects as quantum mechanics, then what is left has exactly zero scientific value.
A full explanation should go beyond the frequency interpretation of probability — ideally it would place the Bayesian view of probability on a secure objective foundation.
This is just another tautologically nonsensical statement. Bayesian probability is by definition subjective – Bayesian and subjective are really synonymous adjectives – so "making Bayesian probability objective" is exactly as nonsensical as "proving that white is black".

It seems to me that every sentence in this summary – even every half-sentence and every sentence implicitly hiding behind every other adjective and every third inserted word – is totally wrong. I was stunned enough by it so that I removed "softcore" from the title. Preskill is obviously another full-blown anti-quantum zealot who doesn't understand the basics of the discipline in which he is working.

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