Friday, December 31, 2021

Pairs of quantum observers generically agree to disagree

Pierfrancesco La Mura – whom I have known rather well in person for 2 decades (or at least 2 decades ago) in New Jersey and California – showed us their new paper in Nature,
Observers of quantum systems cannot agree to disagree
A very long text with 9 theorems purports to prove the very assertion in the title. The phrase agree to disagree means that two people sometimes rationally conclude that their statements about a situation are distinguishably different but they cannot sharply prove that the other person's position is wrong, so they tolerate the other person's position.

Folks in this whole "field" of writing would-be clever things about agreement and similar elementary things, often conflating them with sexy buzzwords such as quantum mechanics, like to quote the 1976 Aumann's agreement theorem (the paper is titled Agreeing to Disagree) which proves that in classical physics, 2 people cannot ever agree to disagree.

Pierfrancesco et al. just found it a good idea to write a bunch of strange propositions and formulae and claim that the theorem also works in quantum mechanics: quantum observers cannot agree to disagree. It seems obvious that these people find it obvious that everything that holds in classical physics also holds in quantum mechanics. Those who know at least EPSILON (greater than zero) about quantum mechanics know that this view is completely wrong and sort of breathtakingly dumb, and so is this paper.

Aumann's theorem really analyzes the simple situation in classical physics where
  1. all the knowledge about reality is a truncation or approximation of the precise truth which is fundamentally objective because it's classical physics
  2. two observers share their input data and reasoning (including the reasoning about reasoning and longer versions of this type)
OK, if the truth were fundamentally objective and two people were fully verifying how they think to find something about the truth, they are really doing the exact same thing, and they must end up with the same conclusions. The theorem deals not only with the individual thinkers' measurements and reasoning but also with their reasoning about the other person's reasoning.

But if you see it rationally, all the seemingly complex and multi-layered "I think how you think how I think..." stuff is just a tool to converge closer to a unified thinking. If the precise truth is fundamentally unique and objective and if you have two ways to approach it, knowing that they are some epsilon away from the truth, they must also be at most 2 epsilon away from each other. As far as I can say, the theorem is a lot of writing about a complete triviality. It just sounds cool because as kids, we were trained to say that it's cool to say "I wonder why. I wonder why I wonder why I wonder..." (that is also a poem by Feynman LOL). But with some simple mathematical arguments, it is easy to see that this "recursive" thinking about thinking doesn't make things very difficult because the space of possible propositions about reality (including other people's thinking) is still easily mathematically classified. You may think how the other person thinks how you think etc., but both of you are still thinking "inside the box" and everything "inside the box" may be analyzed in a way that is in principle straightforward. And in fact, trying to reach some "empathy" and/or "collective thinking" makes both of you think even more inside the box because classical physics has a box which encourages the collective and "objective" thinking.

In classical physics, it is obvious that two people must ultimately agree which reasoning is right and which is wrong and right argumentations cannot contradict one another. Is that true quantum mechanically? The answer is clearly a resounding No. In fact, the Complementarity Principle that Bohr meaningfully considered the defining principle of quantum mechanics may be meaningfully restated by the proposition "agreeing to disagree is omnipresent and essential in quantum mechanics".

This principle reflects the fact that unlike the maximally precise truth in classical physics, the maximally precise truth in quantum mechanics simply isn't objective. One observer measures (and perceives) some observables \(L_i\); another observer measures some other observables \(M_j\). The sets are distinct and cannot be calculated from each other. Each set may be maximal (impossible to add another one) and mutually commuting; but \(L_i\) and \(M_j\) are not commuting with each other.\[ [L_a,L_b]=0, \quad [M_c,M_d]=0, \quad [L_e,M_f]\neq 0. \] In the first example that was always quoted almost a century ago, the position and the momentum of a particle are complementary quantities. You cannot assign truth values to statements about them simultaneously. It is impossible to assume that \(X\) has a sharp value and \(P\) has another sharp value at the same moment. It was possible in classical physics – \((X,P)\) is just a point in the phase space and all other probabilistic assumptions are just probability distributions on phase spaces. But quantum mechanics just doesn't have any sharp possibilities, it doesn't have and doesn't allow a phase space. On the other hand, it doesn't mean that you may eliminate \(X\) and \(P\) from physics. Separately (and as building blocks for composite quantities), \(X\) and \(P\) are as needed as they were in classical physics! This is no contradiction, the "separate importance" combined with "the ban on combination" is what complementarity means.

If he wants to do physics, the observer must decide what he measured in the past and what he is going to measure (and perceive) momentarily. The measured quantities are associated with operators. The number of operators that an observer measures (and the fineness of the measurements) cannot be too high because he would be influencing (or damaging) the measured system too much. Recall that a measurement always influences the measured system and quantum mechanics simply bans the assignment of sharp classical truth values to propositions whose outcome couldn't have been perceived by any subject. For example, if an observer measures the location of each electron in your body with a better-than-0.1-nanometer precision, it will ionize most of the atoms in your body and your body instantly evaporates. So the frequency and precision of measurements must be "limited" to allow the measured system to survive; and there are infinitely many ways to choose how the "reasonable rate of reasonably imprecise measurements" is chosen. Two observers are almost guaranteed to do it differently, at least a little bit. So they generically end up with different stories that neither coincide – they cannot be consolidated into their shared truth – nor sharply disagree (because a well-informed observer knows that statements about the location don't sharply contradict statements about the momentum although the eigenstates of the two are totally different wave functions). In quantum mechanics, it always matters whether some value was measured or not – the measurement destroys the interference between the possible eigenstates that result from this measurement.

Bohr and Heisenberg defined the "Copenhagen school" which was named after the Danish capital where Bohr (a bit older "daddy" of all the big shots like Heisenberg) created a vibrant place to develop quantum mechanics in the early decade(s) of its existence. Heisenberg actually used the term "Copenhagen spirit" to refer to the new conceptual or philosophical principle of their framework in the late 1920s; and in the 1950s, he also coined the phrase "Copenhagen Interpretation" in a philosophical book he wrote in order to mock all the other "interpretations". This choice of words backfired badly (and Heisenberg was really sorry about this linguistic playfulness of him very soon: he actually knew it would backfire shortly before the book was printed) because it literally encouraged tons of cranks to invent their own new "interpretations". And of course Heisenberg agreed with me that all those interpretations were always pure rubbish. He wanted to end this obfuscation about quantum mechanics but he achieved the opposite. He invented a template for dozens of new "interpretations" that made it easier for crackpots to say nonsense about quantum mechanics. More than half a century later, we are drowning in the sea of feces created by the crackpots.

For years after 1925, Heisenberg and Bohr debated and one of the key questions was "what was the defining principle of quantum mechanics". Heisenberg favored the uncertainty principle; Bohr favored his complementarity. At the end, these are just two verbally different philosophical interpretations of the "nonzero commutators of operators that represent observables". Because the commutators of measurable quantities are nonzero for the first time in science, the total certainty and precision of "all observables" is impossible. At the same time, we need to choose some of them so we have one of the complementary ways of looking at the objects which are qualitatively different.

These things may be expressed by many sentences, ideas, and fables that sound totally different to the laymen but that ultimately convey the same mathematical properties of the new theoretical framework. But everyone who understands the beef and who gets familiar with the terms "complementary" and "agreeing to disagree" will find out that they are basically the exact same thing! Of course quantum mechanics allows "agreeing to disagree", it is the whole point of complementarity expressed in slightly different words!

Now, the paper in Nature doesn't mention the Complementarity Principle at all. It does refer to the "uncertainty relations" but it is completely clear that the authors don't really understand the new, quantum mechanical rules of them, either. They are imagining that these uncertainties work in the same way as they always did in classical physics. Well, they obviously don't. More generally, the paper claims to consolidate the logical framework of two observers into a collective one (pompous phrases for "epistemic programs" sound intimidating but the actual content of all these things is completely wrong and worthless) but that is clearly forbidden in quantum mechanics because in quantum mechanics, one can only make statements about truth values (and probabilities!) after a particular observer's perspective is chosen, after we insert the information about "what we considered the observations and what the perceived results were". If it were possible to consolidate two or many observers' perspectives into one (more universalist or even "collectivist") picture, the individual observers would become redundant and we could get rid of them. If all people or scientists were just figuring out the truth values of propositions that all of them share (and that may be assumed to be right or wrong for everyone), then the whole reasoning of each individual and each group would be just "straightforward classical logic and probability calculus". But according to quantum mechanics, it simply isn't the case. Quantum mechanics allows you to reason and calculate probabilities what "probabilities of what" is what the theory also determines (in particular, quantum mechanics says that the propositions with calculable probabilities are always observer-dependent), much like newer rules to actually calculate the probabilities (Born's rule etc.). Like always, when we talk to anti-quantum zealots: You just fudging cannot get rid of the individual observers or replaced their perspective by a more universal one, this is the main point of quantum mechanics.

If you look this paper and thousands of similar papers in this "industry of interpretations" rationally, you must agree that none of the co-authors actually understands quantum mechanics at all. They are thinking classically 100% of the time (just read the paper one sentence after another and try to find a counterexample!) and they are 100% unable to even admit that it could be wrong, they just can't imagine that their 17th century understanding of the world could be invalid or incomplete in any way. The word "quantum" is used as a purely P.R. trick for them to sound more modern and more sexy but the beef is utterly 17th century in its beliefs. This Nature paper is a textbook example of an anti-quantum paper and you can see it in basically every sentence. The first sentences of the introduction read:
Quantum mechanics famously made its creators uncomfortable. It is highly counterintuitive...
No, although this statement became a "consensus" in the popular books and lousy research that just copies the popular books into a would-be scholarly environment, it just fudging didn't. Quantum mechanics took years to be discovered because it was so qualitatively different from the previous framework of basic assumptions about Nature but once it was found, it made perfect sense and it made the early quantum physicists feel very comfortable. Instead, it made the critics of quantum mechanics feel uncomfortable. The first ones included Albert Einstein, the most famous name, but also, to one extent or another, Erwin Schrödinger and Louis de Broglie as two men who also made important observations that allowed the theory to be quickly developed. But Einstein, Schrödinger, and de Broglie were not really creators of the theory that was called quantum mechanics since the 1920s. They didn't ever accept it and they arguably didn't ever properly understand it. Consequently, they did nothing to truly advance the theory and to find its additional implications, either; they just made some early contributions that had to be "polished" by someone who actually knew what he was doing in order to construct a full theory that actually works. They and their much less famous followers have been promising alternatives and serving confusing social critiques for more than 96 years and nothing valuable has ever come out of it.

The paper in Nature, and thousands of similar papers, isn't a physics paper elaborating on the vital discoveries by the creators of quantum mechanics and 4-5 generations of physicists who were standing on the creators' shoulders. Instead, it is clearly another branch in the meaningless tree of the obfuscation created by the critics of quantum mechanics. Even this self-evident point about the "identity of the field where the paper belongs" is being obfuscated, perhaps because the authors honestly don't understand that a different theory than classical physics is possible at all.

But I think that most of this deception in similar anti-quantum papers must be absolutely intentional. Why? I see many inconsistencies in their stories that they must see because they don't require any understanding of modern physics at all. The question whether "creators of quantum mechanics were feeling uncomfortable" is a great example of a question that must make them realize the utter inconsistency of their writing. On one hand, we read that "the creators were feeling uncomfortable". On the other hand, pretty much the exact same authors like to whine that the creators didn't allow "geniuses" like Hugh Everett to express their own discomfort. Surely if the creators felt uncomfortable themselves, they would allow other people who felt uncomfortable. But they didn't. The creators felt totally fine and they realized that the writing by critics like Hugh Everett has never made any sense. That's why Hugh Everett couldn't have gotten a postdoc job. He just sucked as a theoretical physicist, was unable to comprehend some very basic things that make a perfect sense. All the people who were any close to the actual creators of quantum mechanics – Bohr, Heisenberg, Dirac, Pauli, Wigner, Jordan, ... and also the next generation including Feynman, Gell-Mann, Schwinger... agreed about the basic proposition that quantum mechanics was a satisfactory, consistent, complete theory of reality.

Science depends on the elimination of hypotheses that have been falsified (proven invalid with the help of the empirical data). It has worked rather well and much of the process took place in the science departments. But the humanity departments were always running an alternative environment where you don't have to abandon the falsified theories (and you are not really expected to know the state-of-the-art promising theories, either) because hyping some statements and ideas by misleading catchy words and demagogy is considered a good replacement of careful valid science (if not better). This "innocent" alternative has always been nothing else than a direct attack against the basic structures of science. Once the elimination of the wrong theories is labeled an evil that should be "compensated" by some affirmative action, you end up in a system where the truth doesn't matter. So when you get hundreds of scholars writing about quantum mechanics who don't actually understand quantum mechanics at all, the scholarly environment is messed up and may be described as a noisy cesspool. What is really bad is that these humanities people were allowed to hijack the terms like science, quantum mechanics... so although everything they do is the exact opposite of science or quantum mechanics, they get away with lying. Of course, there are still people who do actual science and who simply ignore nonsensical critiques of science written by the humanities types. But the social dynamics is likely to drive them to extinction. You just can't afford to ignore the proliferation of nonsense sold as science or quantum mechanics.

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