Friday, July 12, 2019

MWI fans are collapse deniers, hypocritically assume collapse in the past, anyway

Ben asked me to refute the Many-Worlds Interpretation again.



I think that the first sentences of the Wikipedia article do a wonderful job in explaining what the typical people promoting the "MWI brand" actually want to believe, and one might argue that this is what Hugh Everett actually meant, too:
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics...
Too bad, these claims are self-evidently wrong and don't pass even the most elementary, 1-minute-long consistency checks, thus proving that the defenders of this indefensible position lack intelligence.



Just to be sure, proper quantum mechanics is a theoretical framework composed of some mathematics, including operators acting on the Hilbert space, and physical axioms saying how to connect this mathematical apparatus with the observations. All these axioms are known as the "universal postulates of quantum mechanics" but the deniers of quantum mechanics have renamed all the physical axioms as the "Copenhagen Interpretation" and they treat this name as a slur.



The deniers of quantum mechanics – and the "many-worlds champions" are a key subgroup – don't do any proper calculations or predictions because their belief system doesn't allow those. But they do everything they can to sling mud on these key axioms of modern physics. For example:


By the way, note how Einstein was spelled and compare it with this rule number eight.

As you can see, Sean Carroll not only refuses to use the standard term "universal postulates of quantum mechanics" or "axioms of quantum mechanics". Even the terms "heresies" or "blasphemies" look too generous to him. So in his mindless antiscientific propaganda, he calls those axioms a "coping mechanism".

Well, they're still the most important laws of Nature that were found in the 20th century science. In particular, the champions of MWI want to generously accept "some mathematics of QM" but refuse all the physical novelties and facts about QM, including the facts that
  • the results of QM experiments are random and only probabilities are calculable; physics has switched to the mode of probabilistic predictions
  • the decision whether there is a measurement depends on the observer, and that's why the values of the state vector (wave function) are observer-dependent, too
  • because the wave function has to be interpreted as a complex generalization of the subjective probability distributions, it collapses whenever the observer associated with the wave function completes the measurement and learns some new information about an observable (a generalization of Bayesian inference)
The three statements above are extremely important and extremely well-chosen physically. Just try to convert them to Yes/No questions for a while. They would be wonderful questions and quantum mechanics – i.e. the "Copenhagen Interpretation" – gives the Yes answers to all three of them.

But these three Yes answers aren't a matter of an artistic subjective taste – even though this is exactly how the quantum mechanics deniers are trying to interpret all the key rules in physics, as a multicultural paradise where everything goes and all opinions are created equal. They're well-defined questions about Nature and the Yes answers may be experimentally proven in complete analogy with any other answer given by science – e.g. the roundness of the Earth. First, the outcomes of experiments are said to be random in QM. You know, this is not an opinion, it's a measured fact. You measure some polarization of the spin along a different axis many times, sometimes you get "up", sometimes you get "down". It's random. Similarly, nuclei decay at random moments.

The MWI fans say, as Wikipedia honestly mentioned:
The existence of the other worlds makes it possible to remove randomness and...
Their theory "removes randomness". Note that they didn't say that they explained randomness differently. Their theory doesn't have randomness! The problem is that if that's so, then it is immediately ruled out by experiments because experiments demonstrably end up with random results! This is really one of the first facts that people learn about the quantum measurements – and MWI just gives a wrong prediction. Quantum mechanics deniers and MWI fans in particular don't like the randomness of our quantum world, and because they don't have the respect for who is in charge, Mother Nature, they just demand Nature to adapt to their beliefs instead of adapting their theories.

All of the mathematical calculations in QM are about the calculation of the probabilities and probability amplitudes for one outcome or another. MWI has absolutely no way to give the correct experimental interpretation to these numbers because one of the defining points of MWI is to deny randomness. If you assumed that all the "worlds" with different outcomes exist, there would exist no basis for saying that some of them are "more likely" and others are "less likely".

OK, in practice, the MWI advocates
  • want to pick the same Hilbert space and Schrödinger's equation as in quantum mechanics (the fact that they only "allow" Schrödinger's picture, and only for the pure state, not the mixed state, shows that they don't really understand the mathematical portion of the theory, either)
  • completely deny that the probabilities are fundamentally needed for anything
  • completely deny that the wave function is observer-dependent
  • completely deny that the wave function ever collapses
It's so ingenious. The rest of the work waiting for an MWI champion is to persuade the world that he is ingenious and physics may work perfectly even with these three denials. Well, it cannot work at all. The randomness of the results is an experimentally observed fact – it's so basic and universal that almost every experiment is good enough to prove it.

The observer-dependence may be seen e.g. in the Wigner's friend setup. Wigner observes a friend who observes an elementary particle. They will unavoidably have a different description because the friend collapses the wave function after his measurement, while Wigner hasn't made any measurement by that time, and describes the whole lab as an entangled state of the friend and the particle. So Wigner and his friend clearly use a different wave function.

But in the previous paragraph, I assumed that there is a collapse. It's really illegitimate in the "Wikipedia" MWI because there's no collapse there. It's simple what they say. There is an objective wave function – an analogy of a classical field, exactly what all good physicists learned very early on that is the completely wrong way to interpret the wave function – and this wave function just evolves into superpositions.

According to the MWI people, it's no problem because the terms contributing to the wave function such as\[

\ket\psi = \frac{ \ket{{\text {I see} } \uparrow} \ket{\uparrow} + \ket{\text{I see }\downarrow} \ket{\downarrow} }{\sqrt{2}}

\] may peacefully co-exist. The observer finds himself "in one of the parts of the wave packet", as indicated above, and everyone is happy. Well, there's no way to derive the probabilities given by Born's rule – and the calculation of these probabilities is what the whole mathematical apparatus of quantum mechanics is good for, so they completely deny the usefulness of the bulk of mathematics, too – and there's also no algorithm to divide a generic state vector or density matrix into terms, "the worlds", so none of these things makes any sense once you ask the next question.

Quantum mechanics needs a user who knows what he is doing – what he is measuring and how the wave function should be divided to the terms (eigenstates of the measured observable). It's plain stupid to deny that this is a precondition for every application of the quantum mechanical apparatus.

But as the title indicated, I wanted to focus on the claim that the "wave function never collapses". You just use the entangled superposition of all the possibilities. Why not, the MWI folks will ask? Well, because it gives totally silly results.

In the example above, I used the final wave function for a composite system – an observer plus a spinning particle – and wrote down the final state. A problem with my story is that it is only correct if the initial state is assumed to be something like\[

\ket{ \psi_{\rm initial} } = \ket{\text{observer preparing}} \zav{ a_\uparrow \ket\uparrow+ a_\downarrow \ket\downarrow }.

\] So in the initial state, the observer is just preparing for some measurement and he isn't entangled with the particle yet. Meanwhile, the particle's spin is in a particular pure state, a superposition of "up" and "down". This state is very simple, isn't it? Now, the key question of this blog post is the following:
How did it happen that the initial state is this simple? Shouldn't it be some complicated entangled superposition as well? One that also includes a term in which the observer is just accepting a job from President Hillary Clinton?
You bet it should be! Almost all MWI fans share the belief that the Universe has existed for billions of light years. For a very long time, their "universal wave function" – a classical wave in a highly multi-dimensional space – has evolved into increasingly complex and entangled superpositions that contain almost all possible states, including a victorious Hillary in 2016 who undergoes a surgery in 2017 and goes to Jeffrey Epstein's island along with his [sic] husband.

A complete mess.

So if any of the MWI ideologue were actually taking the statement about the "non-existence of the collapse" seriously, he just couldn't ever possibly use any simple wave function like one above, not even for the initial state, because it would clearly not be the right universal wave function, not even for the initial state of the experiment – which is still the final result of 13.8 billion years of evolution.

If you actually took these axioms of MWI seriously (there is no collapse!), and if you wanted to determine the initial state, you would obviously not be able to ever determine it with any certainty. You know, the state at the initial moment almost certainly includes a term (contribution to the wave function) in which Hillary won in 2016. And all other terms for all the possible evolutions that could have taken place in the previous 13.8 billion years but didn't.

The problem to determine the initial state of an experiment in this setup is a reverse problem, a textbook example of the Bayesian inference. In this MWI setup, the wave function is a classical wave and two wave functions, even if they're arbitrarily close, are mutually exclusive (unless they are complex multiples of each other). So to learn something about the initial wave function for a spin measurement, you need some classical probability distribution on the Hilbert space\[

\rho (\ket\psi).

\] It is a real density on the Hilbert space which must give the same values for "renormalized" state vectors so it obeys\[

\rho (\ket\psi) =|K|^\gamma\cdot \rho (K \ket\psi), \quad K\in \CC.

\] I allowed a power law rescaling with the exponent \(\gamma\). The most natural exponent, one borrowed from proper quantum mechanics, is \(\gamma=2\) – the probabilities should scale like the squared absolute value of the amplitudes and it's natural to extrapolate this rule to non-normalized wave functions, too.

But we have a complete mess here. We need to start with some prior classical probability distribution \(\rho\) on the Hilbert space (modulo normalizations), and use some observations to constrain it and replace the prior \(\rho\) with a posterior \(\rho\). Needless to say, we can't really probe the "part of the wave function where Hillary won", so we can learn nothing about the values of \(\rho\) at the "parts of the Hilbert space" that correspond to a completely different "world" than ours.

Now, try to complete the theory so that it is actually usable for any calculations. You need to define
  • which parts of the Hilbert space correspond to "different worlds" that are undetermined
  • in our part, you still need some rules to choose sensible priors, and some dictionary that translates some measurements to "evidence" in the usual classical Bayesian evidence.
It is very clear that there cannot exist any coherent, simple or unique enough theory that would bring any precision to these two things. Which parts of the wave function may classify as "different worlds" is clearly a matter of taste. Even if you chose some conventions about "how different the two terms in a wave function must be", these conventions would be no good because the relevant operational distance depends on what you will do with the wave function later!

In particular, it is not true that pieces of a wave packet that are "sufficiently far from one another" will never interfere with each other. This assumption would clearly be wrong. You can measure the interference – the relative phases – between the photons of the LIGO beams that are many miles away. So the assumption that there is some universal definition of "how to divide the wave function into separate worlds", independently of the future processing of the wave function, is clearly wrong.

On top of that, this whole exercise is totally useless. We're not really interested in the "other world where Hillary has won" because we know that she hasn't. So all the values of \(\rho(\ket\psi)\) for the wave function \(\ket\psi\) in the "region" of the Hilbert space where Hillary has won are completely useless for us. Even if we had some rules how to choose the priors and how to interpret the measurements as "evidence" to replace the priors by the posteriors, the "victorious Hillary" part of the wave function will still be unphysical gibberish for us!

On the other hand, we need to make measurements to learn about "our world". But the problem is that whenever a measurement is made, "our world" splits. That's why you cannot really ignore the "other worlds" completely because if you did ignore them, you would be totally unable to apply the Bayesian inference to a measurement by which you want to update your opinions about the probabilities of different values of the universal wave function, \(\rho (\ket\psi)\).

Note that these insurmountable messy obstacles are just the MWI's counterpart of the simple task of preparing the initial state. Proper Copenhagen QM allows you to measure a complete set of commuting observables which simply determine the initial state uniquely, up to the arbitrary complex normalization. That's it! In MWI, you have to deal with functions on infinite-dimensional spaces describing probabilities of different possible outfits of President Hillary Clinton etc. and their separation from the "world" that you're willing to consider "yours" although it is clearly impossible to pinpoint any particular boundary between them. You can't prepare a simple initial state (i.e. a controllable experiment) in MWI because... there's no collapse. What is marketed as a virtue is clearly a lethal bug.

None of the MWI advocates has ever run into these calculations because none of them has ever done even the most elementary 1-minute consistency check of the claim that they have found a seed of a new framework to do quantum mechanics. One minute is completely enough for an intelligent person to see that it is a non-starter.

Quantum mechanics doesn't deal with this mess about the "distribution on the victorious Hillary region of the Hilbert space". Quantum mechanics is a recipe to deal with propositions about observables. When you know some statements about the observables, usually about the initial state, quantum mechanics allows you to calculate the probabilities of other propositions, usually about the final state. That's how it works and it works flawlessly. You may assume that "Hillary lost" is a true statement and it has consequences. You don't need to include unknown wave packets supporting the claim "Hillary won" in your calculations because those are just physically wrong according to you!

But in MWI, almost all the work is about inventing probability distributions for states in the Hilbert space that you actually know to be wrong, just like you know that Hillary is actually crooked. It's not only pointless to invent distributions on the space of falsehoods. There clearly cannot exist any well-defined mathematical system to make this procedure quantitative. There can't be any preferred priors on the wrong parts of the Hilbert space (unless you really evolve the initial wave function from some Hartle-Hawking state vector). And the conversion of the measurements into the Bayesian evidence is also impossible to be quantified because the "other worlds" aren't ever canonically separated from "ours".

Even if you imagined that the world were run by some "universal wave function" like in MWI, that theory would be incomplete as a predictive scheme and you would need rules how to do all the calculations with the priors and posteriors to make actual probabilistic predictions. The correct "effective" theory would clearly be Copenhagen QM, anyway. Even if you downgraded proper QM to an "effective" theory, it would still rather clearly be the only correct one you could find. It avoids the priors etc. completely – and any theory that uses the priors is bound to be unequivalent and worse than proper QM.

Also, the MWI demagogues love to say that they have thrown away all "the ugly parts of QM". The ugly parts of quantum mechanics are... all the physical axioms that actually connect the mathematical apparatus with the physical experiments! They have clearly thrown the baby out with the bath water. But as we saw, they not only threw away all the good physical stuff. They also created the need to introduce lots of extremely ugly and unphysical stuff, like the probability distribution on the sector of the Hilbert space that is compatible with the description "victorious Hillary". If a predictive theory requires one to choose priors or divide the worlds to pieces, when no canonical separation exists, it's a huge contribution to the ugliness and ill-definedness of the theory.

I must also say that the very object\[

\rho( \ket\psi)

\] – which we showed to be unavoidable if you actually wanted to make any calculations and take the MWI axioms (especially the non-existence of the collapse) seriously – is an extremely mathematically ugly and unnatural object. It is a generic real function on the Hilbert space (modulo complex normalizations, i.e. on the space of "rays").

What is similar in proper QM? If we don't know the precise pure vector in proper (i.e. Copenhagen) quantum mechanics, we describe it by the density matrix \(\hat \rho\) - I added the hat just locally, to distinguish it from the classical function above. And if you want to calculate the probability that the physical system described by the density matrix \(\hat \rho\) finds itself in a pure state \(\ket\psi\), well, the probability is given by (a potentially misleading formula, you have to be careful what all the pieces mean)\[

P = \bra\psi \hat \rho \ket\psi.

\] This is the formula that produces \(\gamma=2\) in the aforementioned sense. The real point is that all the probabilities in quantum mechanics are bilinear functions of the state vectors describing the statements. Bilinear functions on the Hilbert space are highly restricted. They are completely expressed by a matrix. If it is a density matrix, it must be Hermitian, the trace must be one, and all the eigenvalues must be non-negative.

But the probability distribution that we need in the MWI picture – where \(\ket\psi\) is assumed to be a classical wave – is not bilinear in general. It's a general real function on the Hilbert space. The whole pretty "linear [or bilinear] algebra" character of the mathematics of quantum mechanics is thrown out of the window as well.

So the MWI is just a bunch of wrong statements with zero chance to ever become well-defined (when the splitting occurs, how, why, what are all the priors, and links between apparatuses and evidence that affects the probability distribution on the Hilbert space), zero chance to be compatible with Born's rule (let alone to derive it). These wrong statements are motivated by pure ideology – the MWI demagogues simply have a psychological problem with quantum mechanics – and they are enabled by these demagogues' inability to honestly evaluate even the most basic consistency checks of their proposed alternative to quantum mechanics.

Last April, I discussed a version of the many worlds that "works" because it's chosen as a bizarre encapsulation of the Copenhagen rules. But that version is not what most of the MWI people have in mind. Their MWI – simply a denial of the randomness, probabilistic character of predictions, observer dependence of the wave function, and the collapse – doesn't work at all.

What drives me up the wall about all the garbage like MWI with lots of deluded champions – and there are many examples – is the sense of arrogance and entitlement that is seen in statements such as this (quoted by Ben):
It [MWI] does not make any new predictions beyond the Copenhagen rules.
The implicit assumption is that MWI can do "at least as well as Copenhagen, everyone can". Except that this statement is completely and totally wrong. The Copenhagen rules – i.e. proper axioms of quantum mechanics – are the most important scientific discovery of the 20th century and the ultimate scientific gold that always perfectly works. On the other hand, MWI is an example of utter and complete bullšit whose every "new" aspect is totally and completely wrong, useless, and hopeless.

The idea that "every piece of šit is valuable at least as gold or more" is just totally wrong – yet it seems to be one of the most widespread beliefs in mankind today. The fact that people are willing to repeat this incredible statement boils down to the immense propaganda promoting garbage – which is possible because "everyone feels entitled", by our de facto socialist countries, to always possess some "minimum", and the Copenhagen rules of quantum mechanics have apparently been labeled a part of this "minimum".

But they're no minimum that everyone gets. They're a maximum in the people's understanding of the Universe and at least 99.99% of the people on Earth do worse and usually much worse than quantum mechanics in their description or understanding of the quantum mechanical experiments. All interpretations of quantum mechanics that are neither Copenhagen nor neo-Copenhagen in any sense are worse than Copenhagen – simply because they don't work well enough to incorporate the Standard Model (and usually not even much simpler systems).

I will digress but the same comments are being said about string theory – every crackpot assumes that he is "at least as good as a string theorist" – or very different things from the real world such as Tesla Inc.:
Perhaps, in the most catastrophic scenario, Tesla Inc is just another average car company.
Well, it's not. An average car company makes a profit and gives everyone a promise to keep on producing some profit in the future. On the other hand, Tesla Inc is a Ponzi scheme that has generated a loss in each of the 15 years and the losses seem to be growing exponentially. Tesla Inc is clearly much worse than the average car company. But this kind of a conclusion is literally a blasphemy within a religious cult – like the Tesla cult. In the Tesla cult – or any cult – negative numbers don't exist at all when it comes to the evaluation of "our holy cows". Tesla fans basically add the absolute value to the profits and treat the growing losses as a great sign of the growth! And the MWI cult is analogous. Needless to say, Tesla Inc at least produces some cars, although they are sold at a loss. MWI is worse because nothing works about it at all.

The MWI fairy-tales are among the top reasons why I lost my respect for many physicists who have done some nontrivial technical things. But they're just lousy thinkers if they can't figure out the lethal problems with the MWI above – in fact, they seem unable to figure out even 5% of those things. How much smarter the founding fathers of quantum mechanics were. They were able not only to understand them but to discover them in the first place – which is an achievement greater than a mere understanding, by many orders of magnitude.

P.S.: The Wikipedia page on MWI also correctly states that the MWI fans claim that they need to get rid of the non-locality, and they do so by the ban on the collapse. This is what the MWI fans really say. But as I argued, by throwing away the collapse, they threw away all the physics, too. Meanwhile, proper quantum mechanics as understood in Copenhagen is local because the wave function is not an objectively real object. Instead, it is a collection of numbers describing the observer's knowledge about the world. When it collapses, it is not automatically an influence modifying all things in the Universe (although a measurement does unavoidably change the state of some observables according to QM – there is no non-intrusive measurement in QM). The collapse only modifies the probabilities of observables that you measured, and those that don't commute with them. But because the observables in faraway regions (another subsystem) commute with the observable you measured, the probabilities of statements about the faraway system may be shown to be completely unchanged by your choice of the type of the measurement. The probabilities don't change by any observer's willful decisions which is why there is no action at a distance in quantum mechanics, despite the fact that proper QM needs the observer to acknowledge the collapse. The observed correlations exist – but correlation isn't causation. The cause of the correlation resulting from any entanglement is always the contact of the subsystems in the past or their joint birth.

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