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Constructor theory: Deutsch and Marletto are just vacuously bullšiting

I can't stand pompous fools, people who are completely dumb but who like to pretend how wonderfully smart they are. So it is not hard for you to guess that I was rather upset when I was forced to read a new preprint by David Deutsch and Chiara Marletto and the associated hype in Scientific American:
Constructor Theory of Information (arXiv)

A New “Theory of Everything”: Reality Emerges from Cosmic Copyright Law (SciAm)
If you happen to forget similar factoids, Deutsch is one of the philosophical babblers who likes to say ludicrous things about the allegedly unavoidable naive many-worlds interpretations of quantum mechanics, and so on. What is this constructor theory? It's a sequence of worthless would-be smart sentences sold as a "theory of everything" and a "unifying theory of classical and quantum physics" and "all information in them" which also "defines all forms of information" and transforms all of our knowledge to "claims that some tasks are impossible".



"Where is the beef?" the ladies would surely ask in this case, too. If you try to find any content inside these texts, you will inevitably fail. There is no content. It's just a stupid game with words and a couple of mathematical symbols.




For example, we're told to change our wording used to describe the energy conservation law. Ms Marletto tells us about her wonderful new idea that clarifies what the conservation law is:
“You simply say that the task of creating energy from nothing is impossible.”
How simple, deep, and useful. More seriously, first of all, this statement doesn't accurately express the conservation law – which also says that destroying the energy into nothing is impossible. Second of all, the contrived language above tells us nothing about the validity of the energy conservation law. Third of all, the law is exactly valid whenever the background or the effective laws of physics are time-translational symmetric; however, the law is violated in cosmology which helpfully allowed cosmic inflation to create the whole visible Universe out of (almost) nothing.




At any rate, their musings have nothing to do with the actual technical questions or the truth value of the energy conservation law – or any other scientific question, for that matter.

Their "work" is all about imposing a meaninglessly contrived language upon people. Moreover, Ms Marletto's understanding of energy – dominated by the question whether it can be obtained for free – is exactly the same childish misunderstanding of the concept that Feynman would humiliate in his text Judging Books By Their Covers. "Energy makes it go" was written as an answer to all questions in the book. Feynman pointed out that the children wouldn't learn a damn thing. They could have written "Wakalixes make it go" just as well. Moreover, the statements aren't really true because energy isn't what makes things go. It's just being converted from one form to another etc.

Some of the most experienced readers already know that
a kettle may heat water.
Fortunately, the authors allow us to formulate even such statements in a more "natural" and more "profound" way:
For instance, a kettle with a power supply can serve as a constructor that can perform the task of heating water.
LOL, it's a constructor. Who would have thought? One would think that a kettle isn't constructing anything – in the same sense as cranes do. But if you want to become so high that you confuse construction workers with cooks, it may be a great idea to unify cranes with kettles. And raindrops on roses and whiskers on kittens. Bright copper kettles and warm woolen mittens. Brown paper packages tied up with strings. These are a few of my favorite things. Engineers and cooks are the same thing, after all. They are constructors.

OK, what is a constructor? You study the paper and you find out that it is a meaningless word that may represent anything and that may be inserted into any sentence for pompous fools to look even "smarter". Instead of saying that X does Y, you must say that X is a constructor that is prohibited to do things different than Y. It isn't really quite the same thing and the whole expansion of the sentence is bringing you nothing of value but you don't care. I can't resist to compare these awkward sentences to yet another quote by Feynman who was reading some "smart" texts by participants of an interdisciplinary conference.
The individual member of the social community often receives his information via visual, symbolic channels.
He didn't know what the first sentence of a text could have possibly meant. He must have been stupid! However, he didn't give up and finally figured out what the sentence meant.
People read.
There was a longer paragraph which could have been translated as
Sometimes people read, sometimes they listen to the radio.
And so on. The Deutsch-Marletto texts are made uselessly contrived in the very same sense as the sentence involving visual, symbolic channels. There is no point of talking about a "constructor". This redundant concept doesn't help your understanding of anything in Nature or mathematics.

But equally importantly, the comments they are making about things like quantum information are just totally wrong.

They want to "unify classical physics and quantum mechanics" and the concepts of information in them. But this is complete nonsense. The frameworks can't be unified because they contradict one another. More clearly, quantum mechanics is right in Nature around us while classical physics is wrong. Classical physics is a limit of quantum mechanics – classical physics is approximately valid in some extreme enough situations accurately described by quantum mechanics – but not the other way around. One should never try to unify a thing that is right with a thing that is wrong. It's like pouring gasoline on the fire – and I won't even tell you which of these two elements is right and which of them is wrong.

Moreover, the information has always meant the same thing "in" classical physics or quantum mechanics. Information is independent. The concept of information exists independently of particular theories in physics. However, particular theories in physics differ in what they say about the form that information can take and how the information about the past that we already know is linked to the information about the future that we may only predict.

We may have some information about the spin of the electron a second ago and predict some measurement of the spin we perform the next second. This is true both in classical physics and quantum mechanics. The two frameworks radically differ by the "spectrum" of possible values that the spin can take (and similarly other observables). And they also fundamentally differ in the way how we make predictions about the future measurements – about the information that the measurements will yield (it's the very same thing) – from the information that the past experiments have already yielded. The laws of quantum mechanics are probabilistic and involve all the linear Hermitian operators acting on a Hilbert space (or density matrices which are also operators on the Hilbert space).

The engine that connects some pieces of information (e.g. ones about the initial state) with some others (e.g. those about the final state) is completely different in classical theories and in quantum theories. But the information is ultimately the very same thing. We make a measurement and we learn some information from that procedure. Information is whatever distinguishes one's state of ignorance (or knowing less) from the state of knowledge (or knowing more). In general classes of situations, information may be quantified, too. But there's no point in trying to decompose the words "information" or "know" to words that are more elementary. There are no words that would be more elementary. One must understand at least some words if she wants to be able to say anything about anything. Attempts to "define" words like "know" inevitably end as a ludicrous worse-than-circular game that "decomposes" simple enough words into words that are much more complex, contrived, or subtle – or several of these adjectives at the same moment.

Claude Shannon developed some theory of classical information based on logarithms that is useful especially whenever one is quantifying how many bits may be transmitted through one communication channel or another. Ask Shannon in the comment section if you want to know details. ;-) Do we have corresponding things for a Universe governed by a quantum mechanical theory? You bet. After all, our world is a quantum world so if Shannon's classical theory of information works, we must have an explanation for that. And we have one, of course. Shannon's information is linked to the entropy – and this logarithm-based formula has a completely natural quantum counterpart, the so-called von Neumann entropy.\[

S = -{\rm tr}(\rho \ln\rho)

\] Here, \(\rho\) is the density matrix. In a basis where \(\rho\) is diagonal, the formula directly reduces to the classical one. In this sense, the new aspect of information in quantum mechanics is that the state vector (or density matrix) may be sliced in many inequivalent ways – by measuring one set of mutually commuting observables; or another set of mutually commuting observables that however refuse to commute with those in the first set.

But once we measure something in a quantum world, you obtain the same "classical" information that you obtain by a measurement in a classical world that happens to have the same number of potential outcomes (the same spectrum). You may know something or not to know something; you may extract \(n\) bits from the measurements or another number. You may use more natural units of information, nats. One may also measure continuous observables. Such measurements naively yield an infinite amount of information (because there were infinitely many potential outcomes a priori) but due to some unavoidable errors, the effective information is actually finite. All these things are true in classical physics as well as quantum mechanics.

We have this extra term "qubit" or "quantum bit" to describe a unit of information in quantum mechanics. Does it prove that the information means something completely different in quantum physics? Well, yes and no. To have the information \(n\) qubits means to describe the physical system as a vector in a \(2^n\)-dimensional complex linear Hilbert space \(\HH\). Or a density matrix in the corresponding space of density matrices – pretty much in \(\HH\otimes \HH\). But you must understand that this state vector isn't classical information yet. It's just an auxiliary tool to predict information – to predict information that you may call classical.

At the end, you measure some observables such as the spin \(s_z\) or anything else and the state vector tells you the probabilities of individual outcomes. Once you get the outcome, like \(s_z=-1/2\), you have the same information – you may call it classical information – that you have in classical physics. There is no difference. What is completely different is "just" the way how physics predicts what will (or may) actually happen.

Before a measurement, the state vector or the density matrix describe the state of your subjective knowledge about the physical system. Whether you call it "information" or not is up to you. But whatever you do, the meaning of the density matrix in particular is the same as the meaning of its classical counterpart, namely the probability distribution on the phase space. It's straightforward to see that the probability distribution on the classical phase space is what one may get out of the density matrix in the classical, \(\hbar\to 0\) limit, assuming that we plan to measure the observables that are coordinates on the phase space. (In the classical limit, it doesn't matter much what we plan to measure because the commutators of the observables we care about go to zero: they are proportional to \(\hbar\).)

Would you describe the probability distribution on a classical phase space by the word "information"? Well, it's up to you. I would say that the distribution encodes one's subjective knowledge about a physical system that is only useful for predicting the actual information – the results of some measurements. I would personally only use the word "information" for something that changes your subjective knowledge – either measurements or someone's telephone call etc. about something he or she has measured (i.e. found out). One may also talk about the "amount of information" and there are formulae that allow us to quantify this concept as a function of the probability distribution in classical physics; or as a function of the density matrix in quantum mechanics. The essence of the formulae is the same in classical physics and quantum mechanics. It is no coincidence. The information is the same thing, something that changes our knowledge about something. Physical theories and frameworks differ in the "a priori spectrum" of the options that may be distinguished by the information; and in the actual methods to calculate some information about physical objects from other information (and they differ in the results of these methods, of course, i.e. in the actual predictions).

There is really nothing else that can be said about these matters and that is both true and fundamental. These concepts require one to think a bit and to be smart enough but all these conceptual insights are compact and once you learn these principles, you know them. The amount of stuff one may learn about the meaning of information in physics is finite. It is limited. Once you learn it, and you should learn it before you get your undergraduate degree, you know everything about it. Extra babbling about the information is guaranteed to be meaningless or vacuous. Or untrue. Or some combination of these adjectives.

Deutsch and Marletto also write kilotons of bullšit about the meaning of entanglement (they want to say that it's not mysterious but their babbling is only meaningful if you are ready to think that it is mysterious, so the goals of their "explanations" are internally logically inconsistent) and the "reasons" why quantum mechanics prohibits cloning (founders of quantum mechanics surely knew that the evolution in quantum mechanics is given by a linear evolution operator and because a copying is a tensor square, a quadratic operation, it clearly cannot result from the linear evolution). Why would they write lots of confusing šit about these matters that are in principle trivial?

So we're also exposed to the standard anti-quantum propaganda that entanglement is a borderline crime and it shouldn't happen unless – and the rest of the sentence is their "contribution" – you have some powerful constructors inside kettles to heat water and to beat other constructors, or whatever. It's just batšit crazy.



A Deutsch-Marletto constructor.

There is nothing mysterious about entanglement. Entaglement is just the most general description of correlations between two subsystems of a physical system – roughly speaking, between two physical objects – that is allowed by the laws of quantum mechanics. Conceptually, the "mutual relationships" between the two objects that are summarized by entanglement is the "same thing" as the usual correlation in classical physics. However, the degree of correlation or the number of ways in which it may get manifested is different in quantum mechanics than it is in classical physics simply because they're two inequivalent frameworks. Every quantum mechanical theory is inequivalent to every classical theory. So of course that they should be expected to give different predictions about the degree of correlation between two objects or the number of ways in which correlations may get manifested. But the interpretation of the result is exactly the same. Entanglement implies that the probability distribution for pairs of quantities measured on the systems A,B isn't the simple product of two distributions,\[

\rho_{AB}(\vec x_A, \vec x_B) \neq \rho_A (\vec x_A) \cdot \rho_B(\vec x_B).

\] Whenever this inequality holds, there is some correlation. Entanglement means that there is a correlation, using the language of quantum mechanics. An entangled state in combination with the laws of quantum mechanics produces or predicts correlations in various quantities that couldn't be extracted from any classical model. But that shouldn't be shocking. Classical physics is a fundamentally different kind of a theory so it gives fundamentally different predictions than quantum mechanics does. So there is absolutely no reason to expect that their predictions should agree with the other side, that one framework should be easily "emulated" by the other. Quantum mechanics cannot be emulated by classical physics; classical physics may be just approximately emulated by quantum mechanics in a classical limit.

Their wording – e.g. the constant repetition of the meme that entanglement is "spooky" – makes it very clear that they're just two more people who have decided to never understand quantum mechanics – because they have vowed in front of the other members of the Satanist Cult to never give up the efforts to look for a classical model beneath quantum mechanics. But there ain't a valid classical model. Classical physics has been falsified. It's wrong. It's dead. It's kaput. Falsification is irreversible. You can never resuscitate it again. Quantum laws are the correct ones and the linearity of evolution and the existence and basic properties of entanglement are no mysteries or contradictions within quantum mechanics. They're elementary building blocks of all quantum mechanical theories. If you have trouble to comprehend that entanglement is completely natural and doesn't need any constructors or unification with classical physics or kettles to boil water, then you are exactly in the same situation as a person who is trying to read English but can't possibly swallow E,T,A,I,N,O,S.

Just like these 7 letters are the most frequent letters in English texts, entangled states and linear operators are virtually omnipresent in quantum mechanics and anything and everything linked to it. If you haven't learned E,T,A,I,N,O,S, then you are illiterate. If you feel uncertain about the existence of entanglement or linearity of all operators, you are illiterate in quantum mechanics. If you are waiting for a kettle or for Sherlock Holmes to reduce E,T,A,I,N,O,S or entanglement or linearity of operators to something that you already know, e.g. how to make poops, then you are a baby who has a long way to go before you learn the basic things. This conclusion is addressed to Mr Deutsch and Ms Marletto, too. She is attractive and he is... sorry, I can't think of a positive adjective now..., but they are totally deluded about modern physics.

I will kindly avoid the discussion of some additional concepts they use such as the "superinformation medium". Those things are bullšit on steroids. Reality does in no way emerge from a "cosmic copyright law" and their mixing of buzzwords from classical and modern physics with the words from everyday life such as "kettles" and "copyright laws" and "Sherlock Holmes" or with sensationally sounding redundant new clichés such as "constructors" or "superinformation medium" or "subsidiary theories" or "output attributes of substrates" (no kidding) is beyond the pale. All these things are used by them not only to mask that they're complete morons but even to look as smart folks in the eyes of people who are even more hopeless morons than themselves. I just can't stand such games that are all about people's pretense.
Constructor theory: Deutsch and Marletto are just vacuously bullšiting Constructor theory: Deutsch and Marletto are just vacuously bullšiting Reviewed by MCH on May 27, 2014 Rating: 5

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