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QM: it is very dumb to deny the need for postulates related to the collapse

With the help of the omnipresent corrupt journalistic biomass, Sean Carroll's incorrect, unimaginative, unoriginal book successfully sells the ideology of the "Many Worlds Interpretation" to the uninformed, unintelligent laymen (if I avoid the overly technical term "imbeciles") – ideology that is simply a plain denial of the basic axioms of quantum mechanics (QM) and that has virtually nothing to do with science or its explanation of the observed phenomena.



The ideology basically says that the wave function is a set of classical degrees of freedom – it's not – and it evolves unitarily and never "collapses" – it does and it needs to. You're supposed to believe that the postulates related to the collapse are "not needed" – which is absolutely preposterous, of course.

In the summary of lethal defects of the revisionist claims about QM, I denoted the "Many Worlds Interpretation" as R2, the revisionism of the second type. You may search for R2 on that page. You will see that R2 predicts that it should be possible to measure \(\ket\psi\) – but experiments show that it is not possible. R2 predicts that the heat capacity of molecules should be huge in the units of \(k_B\) – because there are many bits that encode the state of the molecule via the degrees of freedom in the objectified \(\ket\psi\) – but the experiments show that the heat capacity is always of order \(k_B\).

R2, like other revisionist pictures, breaks the symmetry between observables that are treated by the same rules within proper QM. Instead, R2 makes some generally ill-defined "position" more important because it decides about "how to separate the wave function into the worlds". Also, no actual prescription "how to separate the state vector into worlds" has been written down – and no natural one can exist for elementary mathematical reasons.



Any such proposed detailed rules "when and how the state vector should be split to worlds" would ruin the mathematical symmetry of the theory and it would also depend on lots of new – almost certainly unphysical – parameters. Perhaps most importantly, the axioms of R2 say nothing about the probabilities which are the only actual quantities that QM may predict, along with their functions and densities. For this reason, R2 is capable of making precisely zero quantitative predictions. It is absolutely useless to do any science. It is a complete lie that it may emulate the successes of QM.



Needless to say, the inability to predict any probabilities boils down to the absence of any kind of Born's rule in R2. Without Born's rule, you have no axiom that would tell you how the magnitude of any probability is linked to the mathematical objects in the theory – including the wave function – and without an axiom that would link these two things, the link simply cannot ever arise.

Also, in a special blog post, I discussed the hypocrisy or inconsistency of the champions of R2 – namely the fact that they always assume a nice, controllable initial state in any experiment. But how could they ever get such a nice initial state in any experiment if such a nice and simple state can obviously result from a previous collapse only? They seem incapable of seeing this elementary stupidity in their story – and of course they never offer any justification for a nice, controllable initial state in their analysis of anything. According to the story that they actually want to sell, the initial state should already be some completely messy superposition of infinitely many unknown wave functions including the "irrelevant ones". So why don't they assume this kind of a state that they say to be the correct one? They assume the initial state that follows from proper QM – but that contradicts their crackpot alternative.

Proper QM is defined by universal postulates of quantum mechanics. They may be written as a variable number of "bullets" (and sometimes the bullets overlap, they're somewhat redundant) but the content is always the same. There are several postulates that directly address aspects of the measurement and the collapse – events that R2 tries to completely deny. Because the likes of Carroll want to "erase everything linked to the measurement and the collapse", they don't have the following axioms:

Measurements exist and are specified by an observable – which is mathematically represented by a Hermitian linear operator (any such operator) acting on the Hilbert space.

Eigenvalues of the operator label the allowed results of the measurement.

The probability of a particular outcome of the measurement is calculated by Born's rule, \(Prob=\sum_i |c_i|^2\), as the sum of all squared absolute values of the complex coefficients in front of all the (orthonormal) basis vectors with the right eigenvalue.

The state vector after the measurement of \(L\) must be an eigenstate of the measured observable corresponding to the actual obtained eigenvalue, i.e. it obeys\[

(L-\lambda_{\rm obtained}) \ket{\psi_{\text{post-measurement}}} = 0
\] The particular post-measurement state is obtained as an orthogonal projection of the pre-measurement one, \(\ket{\psi_{\text{post}}} = P_{L=\lambda,{\rm obtained}} \ket{\psi_{\text{pre}}}\), on the subspace with the right eigenvalue.
Great. Every sane undergraduate student who has played with quantum mechanics knows that these rules are needed in quantum mechanics. They're needed for turning the final state into predictions but they're also needed for preparing the initial state. QM envisions the world as a sequence of "evolve unitarily, collapse, evolve unitarily, collapse". Both steps are needed to make the physical system, the apparatus, and the brain "reusable" – just like when you load a gun and shoot, load, shoot, load, shoot.

But the very purpose of R2 is to deny all axioms and physics related to the measurement and its mathematical representation, the collapse. Theirs is a gun that is allowed to repeatedly load but it can never shoot. So in R2, there is actually no room for the observables – R2 is trying to totally incorrectly claim that everything is about the state vector. So there is also no special role played by their eigenvalues and eigenstates. There is no axiom – or a way to derive – that the post-measurement states are eigenstates of the measured operator (which is why R2 has no justification for decomposing \(\ket\psi\) along any particular basis). There is no Born's rule or a way to derive it. There is even no way to derive that mutually orthogonal states are mutually exclusive.

Everything that actually connects the mathematical apparatus of QM with the observed phenomena is banned in R2. It is really banned for stupid ideological reasons. It means that the mathematical objects and equations that are "generously allowed to survive" within R2 are completely disconnected from any kind of empirical science.

Carroll posted a hilarious blog post on the delayed choice quantum eraser (see the diagram of the experiment at the top of this page). He wanted to include this discussion in that book but it hasn't made the cut so the readers may see it on his blog.

I have posted several blog posts about the delayed choice quantum eraser – you may start with the oldest one in 2010. Don't forget some of these texts from 2018. Most of my texts about this experiment are meant to show that there is absolutely no "retrocausality", the ability of experimenters to change the past by pressing buttons. Popular articles are full of ludicrous claims about the alleged "retrocausality of this experiment".

It seems to me that Carroll basically agrees with this assertion – there is no evidence for retrocausality and there is no need to invoke retrocausality in the explanation of this experiment. So far so good. The only problem occurs when it comes to predicting what actually does happen in that experiment. Carroll hilariously pretends that he can do it – without using the postulates of proper QM – but it is spectacularly clear that he hasn't done it and he cannot do it.

Fine, so Carroll repeats some of the ludicrous ideological comments about the "many worlds" and on top of that, he writes several correct equations saying "the wave function is this or that" and "some basis vectors in one basis may be written as a combination of basis vectors from another basis". Well, a problem is that his assumption about the value of the initial \(\ket\psi\) contradicts the "many worlds" claims – his should be a superposition that is as messy as his thinking, not the nice "collapsed" eigenstate he wrote down. Also, he doesn't explain why the transformation of bases should be relevant for the problem at all – note that he has no axioms that would make the eigenstates of an observable more relevant for anything than any other state. So he is basically just copying some parts of the correct QM calculation of the problem without having the slightest justification within his own pet theory why he is doing what he is doing.

At some moment, he reposts an "unsurprising result from the Wikipedia" which is equivalent to these pictures of the probabilities or distributions:



I laughed out loud when I arrived to that place because it was a repetition of the classic cartoon:



In this joke, the man on the right is explaining something, and Step 2 says "then a miracle occurs". And the other guy who listens to the explanation objects: "I think you should be more specific about Step 2." This is a spot on cartoon describing the absolutely transparent shell game that Carroll is playing with his stupid readers.

He is first pouring tons of absolutely ludicrous ideological assertions about many worlds, the denial of the collapse, and the alleged evil of all related vital axioms of QM, then he writes some formulae for a wave function that are stolen from the correct QM calculation yet utterly insufficient to calculate anything, and... after the miracle occurs... he posts the resulting graphs for the distribution of the electrons.

Can you explain to us how the miracle occurred, Mr Carroll? How could the ideology plus the formulae for the complex wave function suddenly yield the graphs (distributions) that we actually wanted – which are clearly graphs of real functions of a real variable? There is nothing algebraically real about the wave functions – everything is complex. And you have no axiom that allows to calculate anything real from something complex. So it is spectacularly obvious that you cannot complete the actual calculation.

The subset of the formulae from the proper QM that you "generously accepted" is clearly insufficient to make the calculation and your ideology – the ban on most of the actual universal postulates of QM – makes it absolutely impossible for anyone to actually complete the calculation. Everyone who pretends that the charts follow from R2 is simply fooling his readers – and everyone else. It is exactly the same degree of deception (namely a complete one) as if a creationist claims that the Bible allows us to calculate details about the observed species' characteristics and their DNA. Surely everything that evolution can explain, a proper interpretation of the Bible can achieve, too. Hmmm, not really.

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