Friday, August 23, 2019

Talking to a potential wall

These dialogues look like scenes from Václav Havel's absurd theater plays. Many years ago, however, I experienced one in reality. For a while, I thought that the person was joking and pretending to be an extraordinary moron. Or at least, it was an extremely unlikely anomaly that appears once in a century. But then I was sucked into the second discussion, third discussion of the same format. I haven't counted them but I believe there have been dozens of almost identical exchanges with different people who feel uncomfortable with quantum mechanics – and, incidentally, they seem totally retarded, illiterate, deaf, and identical to each other, too. The discussions similar to the idealized one below seem to be the rule rather than exceptions.

My comments are written in bold face, to be distinguished from the remarks by the polite and polished person who "feels uneasy" about quantum mechanics. Here is the dialogue.

In 1925, physics has switched to a new framework in which the laws of physics may only be applied by an observer who is able to assign values to observables (represented by operators on the Hilbert space) by observations that the observer rightfully trusts. Again, the observer is an irreducible ingredient in quantum mechanics that is necessary to verify any well-defined quantum mechanical calculation.

It's such a nice essay, Luboš. I particularly like that the interpretation that you have outlined is used in all of physics. In particular, it's very important to get rid of the observer because he's a creep watching breasts on the beach through his binoculars and such men have no place in physics. In fact, no men should be allowed in physics.

Quantum mechanics is a more mathematically well-defined framework that was built on (and respects the theses of) positivism, the dominant late 19th century direction in the philosophy science. Positivism, a refined modern variation of the empirical schools of philosophy, emphasized that all certain knowledge is derived from sensory experience, possibly supplemented by reason, logic, and calculations.

Luboš, I particularly liked your observations that the sensory experience plays absolutely no role in fundamental physics. Why don't we improve your nice essay by erasing the observers and replacing them with interacting vertebrates who can then be deleted as well? In this way, you have helped to make physics great and clear again, by erasing all the nonsense that was added in the 20th century.

Before any observations of the detailed temperature variations of the CMB were made, none of the a priori possible COBE-like maps was "preferred" in any scientifically meaningful sense.

Luboš, it is great that you have confirmed my belief that the CMB map objectively existed before it was observed by any humans!

COBE's publication is therefore associated with the collapse of the wave function or the density matrix to the COBE-like map.

Thank God that the wave function was already collapsed billions of years before COBE, Luboš.

When two COBE-like experiments on different planets observe the CMB at roughly the same time, their images will be seen – and QM predicts them to be seen – to be compatible but none of them may be objectively considered to be "the big deal" that has changed the Universe while the other didn't. After all, for spacelike-separated publications, even the chronology of the two events depends on the inertial frame. From an impartial perspective of a third observer, both of these observations should be considered conceptually on par.

It's so wonderful that one of the observations is the key one and the other was just observing a reality that already objectively existed.

Similarly, in Bell's experiments, the two measurements of the spin are anticorrelated but it is wrong to say that one of the measurements was the "cause" of the result of the other measurement. After all, again, they may be spacelike-separated – so the communication between them is prohibited and the ordering is inertial-frame-dependent. The actual cause of the anticorrelation and of any correlation in Nature is always further in the past, in the moments when the two spins were in contact or when they were jointly created.

It's so nice that one of these measurements is the cause of the other, that the action at a distance and the superluminal influence was discovered, thus confirming the wonderful proof by John Bell that the world is nonlocal.

The most complete theory of non-gravitational phenomena in Nature, quantum field theory, says that the word is precisely local. All operators at point P and time \(t_1\) may be written as functionals of operators at an earlier time \(t_0\) where it's enough to use the \(t_0\) operators inside the past light cone of P. It follows that all predictions are local – phenomena can't be affected by any choice made in the spacelike-separated regions. The valid version of Bell's proof only proves that the word is either non-classical or non-local and the correct conclusion, using the help from other pieces of evidence, says that the world is local but non-classical.

I like our world because it's so non-local. And it's obviously classical. In fact, it's so obvious that it's classical that, as you said, we should only say "realist" instead of classical, and as you said, we shouldn't distinguish realist theories at all because all sensible theories are realist. Thanks for confirming that John Bell has proven that the world is non-local.

The locality of predictions in QFT mathematically boils down to the vanishing (graded) commutators of fields at spacelike-separated points. The Heisenberg equations of motion are manifestly Lorentz-covariant. Also, Feynman wrote down his path integral approach to QFT in order to make the Lorentz invariance and special theory of relativity of all predictions manifest.

Good you mentioned the Lorentz symmetry which is clearly violated in Nature, by all the communication that guarantees the correlations in Bell's experiment, as you surely know, Luboš. Bell has proven the violation of locality and relativity – and disproved the fallacies by that guy, what was his name, Einstien or Epstein or something like that – and didn't need to assume almost anything except for completely obvious trivialities, e.g. that physics must respect the principles from the 17th century. Where we would live if we violated them?

In general, each observer may have his own wave function. That's why most detailed questions about the timing of the collapse etc. are just subjective choices that have no valid observer-independent interpretations. The wave function isn't a classical wave or a set of observer-independent degrees of freedom – in this sense, the wave function isn't universal.

Good that you mentioned this important property, that the wave function is universal, as nicely discovered by Hugh Everett. The word "universal" sounds so nice and eliminates all the strange things about non-universal phenomena or observer dependence from quantum mechanics. I love you for having eliminated those observers.

The Wigner's friend is the simplest arrangement in which two observers use a different wave function. The internal observer's wave function collapses when he measures an object. The external observer doesn't use any collapse in his description – because he hasn't learned about any result of a measurement yet. Instead, he just describes the behavior as a unitary evolution with an interaction that has entangled the internal observer with the underlying object (the relative phase is measurable in principle but not practice). That entangled wave function is only collapsed when the external observer makes his observations. There is nothing inconsistent about observers' having different wave functions.

Yup, it's really so nice that the wave function is universal and everyone has the same one! It would surely be a contradiction – and it would violate fairness and egalitarianism – if there were some differences between two observers' wave functions.

A version of Born's rule implies that two nearby, non-orthogonal, normalized elements of the Hilbert space \(\ket\psi\) and \(\ket\phi\) describe situations that aren't reliably distinguishable from each other, not even in principle. The squared inner product \(|\langle\phi\ket\psi|^2\) quantifies the probability that \(\ket\psi\) will unavoidably produce exactly the same results of a complete set of observables as \(\ket\phi\) and vice versa.

We can't overemphasize the fact that when two wave functions differ, even by a small epsilon, they correspond to completely different physical realities. This is what makes us, the physicists, such wonderfully precise scientists.

An argument to disprove the distinguishability of nearby wave functions is a thermodynamic one: all molecules have the measured heat capacity of order \(k_B\) which means that they only carry \(O(1)\) bits of information that may be reliably distinguished. Quantum mechanics agrees with that by greatly reducing the information carried by a molecule at room temperatures – the only information is one that decides whether the molecule is in the ground state or one of the few low-lying excited states (energy eigenstates). Hidden variables – the pilot wave viewed as a classical one, the precise values of extra beables, occupation numbers for worlds in many worlds etc. – would greatly increase the heat capacity of molecules. All alternatives to quantum mechanics that try to add lots of new real information are in conflict with the thermodynamic experiments.

Luboš, finally someone has pointed out that thermodynamics doesn't belong to fundamental physics and no one should be allowed to talk about it. We can just ignore it, it's so nice. I have always found thermodynamics dirty and squalid.

The objective collapse of Ghirardi-Rimini-Weber would localize each elementary particle roughly once in time \(T\), with the post-collapse precision of position \(R\). Both \(T,R\) must be low enough to predict any significant change of physics (needed to make the wave function "look" less fuzzy and to avoid "unwanted" superpositions) but then the theory predicts frequent ionization-like or radioactive-decay-like phenomena (each time \(T/N\) where \(N\) is the number of particles) of ionization (kicks with momentum \(\hbar/R\)) which are clearly not seen in the huge water tanks, so the Ghirardi-Rimini-Weber theory is ruled out.

You wrote it so nicely and clearly that one may always switch to a new interpretation, like the GRW that adds the objective collapses. Nothing bad can happen because it's just an interpretation. The more intepretations, the better! Good to have you in our team. We need as many interpretations as possible, especially as soldiers to defeat the unphysical, blasphemous comments about observers and probabilities that don't belong to science.

The uncertainty represented e.g. by the error margin \(\Delta X\) in the uncertainty principle is observer-dependent but real in the sense that the observer really cannot assume that the precise \(X\) is known. When it comes to all doable experiments, probabilities may be computed from the density matrix via \(Prob ={\rm Tr}(\rho \Pi)\) with a projection operator \(\Pi\) – note that for pure states, \(\rho=\ket\psi\bra\psi\) – and one can't generally attribute which part of the uncertainty is due to "pure states" and which is from "mixed states". One can write a generic density matrix \(\rho\) as a sum of "squared pure states" in many ways but they produce exactly identical predictions for all doable experiments – so no decomposition to the sum is "more true" than others. The uncertainty is qualitatively always the same concept, an observer has to be chosen – which makes uncertainties quantifiable – and no "perfect observer" who would avoid the uncertainties or the uncertainty principle is possible, not even in principle.

It's so nice you have also mentioned that the uncertainty, e.g. in the width of a wave packet \(\Delta X\), is just an illusion. Someone ultimately knows the precise \(X\) and/or \(P\), anyway, right? So the uncertainty and other claims discussed in quantum mechanics textbooks are just illusions. Like the uncertainty principle. I always laugh out loud when I hear it. Someone has an inaccurate apparatus, what a big deal. Uncertainties are illusions. For example, in Wigner's friend setup, the internal experiment has already measured something, so the result just cannot be uncertain, even if the external observer is uncertain what the result is! ;-)

The superposition principle – the statement that the space of allowed states is a complex linear vector space i.e. any complex superposition of allowed states is equally allowed – is an essential universal postulate of quantum mechanics, usually listed as the #1 postulate. There is no way to avoid it, superpositions are the generic and omnipresent states that are unavoidable especially whenever the values of observables may change with time. In particular, the superpositions of states with \(N=2\) and \(N=3\) photons are allowed and legitimate, much like the superpositions of states with dead and alive cats. The superpositions mean just "the value is this OR that" (not "this AND that") except that the relative phase between the probability amplitudes becomes physically relevant in quantum mechanics, while it didn't exist classically, and it affects the probabilities of statements including non-commuting or "off-diagonal" observables. Those always exist in principle (and they often have very natural and fundamental interpretations like velocities or spins along other axes) although they may only be measured in practice in the absence of decoherence.

Good that you mentioned the superpositions, Luboš, they are so ludicrous, indeed. I have always disliked them. How can something be "this AND that" at the same moment? They're a clear inconsistency. The only consistent quantum mechanics is one that prohibits such superpositions, e.g. classical physics. That's what all of us need to fight for. The wave function is real and on top of that, it must be prevented from evolving into all those superpositions that I don't like. We may finally define the pure, no-nonsense, fully quantum mechanical theory where all the bad stuff is eliminated – like observers, superpositions, probabilities, commutators, matrices, complex numbers (why complex? It's so artificial, let's be real), Heisenberg the German, Bohr who was so unclear, and other things. Only the purely quantum deterministic and objectively and algebraically real motion of planets within the phlogiston around them will be left.

And it goes on and on and on. I can make almost any statement – and they say the exact opposite and they even pretend that I just said what they did. Repeat the discussion above 10 times to approximate an average debating partner who is uncomfortable about quantum mechanics. Multiply this increased discussion by a factor of 100 – the approximate number of similar people who have "talked" to me in this way. It's just insane and unmanageable to be "talking" to an ocean of agents that uniformly look as completely deaf and brain-dead zombies.

I just can't understand how this almost perfect approximation of a brain-dead zombie can occur in the real world – and so frequently. It totally baffles me. Maybe all the people are just some NPCs who have been programmed to parrot several anti-quantum slogans randomly and periodically, regardless of anything you try to tell them. This is the best theory explaining the phenomenon that I have right now.

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