Even though most of these texts await much to a greater extent than cryptic than necessary, I was repeatedly tempted to call upwards that he must ultimately empathize quantum mechanics. But at a sufficient frequency, he posts something that is as well as so self-evidently incorrect that the belief that he powerfulness endure to a greater extent than than exactly some other anti-quantum zealot evaporates almost instantly. These neverending bogus claims most "problems" inside quantum mechanics are the entirely affair that most of the "community" of the anti-quantum zealots calling themselves "researchers inward quantum foundations" keeps on producing.
That was also the illustration of Moldoveanu's recent text
Use as well as abuse of von Neumann measuring of the foremost kindin which he claimed that quantum mechanics with the "first sort measurement" – which, inward von Neumann's jargon (and von Neumann's measuring scheme), is basically the most ordinary canonical type of a measuring inward quantum mechanics, as I volition verbalize over – suffers from a "flaw" which agency that at to the lowest degree 1 of the 3 goodness features below must endure sacrificed:
- The moving ridge role of a organisation is complete.
- It evolves via a linear equation.
- Measurements yield acute outcomes.
What is this "first kind" stuff? In 1932, John von Neumann published a mass that contained some give-and-take of a "predecessor of decoherence". He discussed the quantum states of the measuring apparatus as well as the entanglement (without using this intelligence which was entirely coined inward 1935) betwixt the measured organisation as well as the apparatus, alongside other things.
Much of this materials is truly unnecessary to empathize whatever physical aspect of quantum mechanics but at least, von Neumann's formalism worked inside proper quantum mechanics. Many decades later, Everett as well as fifty-fifty Zurek as well as others receive got largely copied all the "good stuff" from von Neumann but Everett as well as his followers began to distort some of the rules as well as abandon quantum mechanics.
You may banking enterprise check this section at Wikipedia to larn some basics of von Neumann's measuring scheme.
The measured organisation is industrial plant life inward the lay down \(\ket\psi\) as well as may ever endure decomposed to the superposition\[
\ket\psi = \sum_n c_n \ket{\psi_n}
\] where \(\ket{\psi_n}\) are the eigenstates of the observable \(L\) that nosotros are going to measure. Now, the basics of quantum mechanics only say that \(P_n = |c_n|^2\) are the probabilities that nosotros volition mensurate the eigenvalue \(L=\ell_n\) as well as that the moving ridge role of the organisation of involvement collapses to \(\ket{\psi_n}\) after the measurement.
That's uncomplicated as well as it was known years earlier von Neumann began to play with these things – it was understood yesteryear the fathers of quantum mechanics, Heisenberg, Pauli, Jordan, Bohr, as well as perhaps Dirac. Von Neumann wanted to report some of the "modern" materials as well as so he also analyzed the moving ridge role of the measuring apparatus etc. – fifty-fifty though many of the "modern" people doing this materials call upwards that this aspect of their analyses makes them to a greater extent than "high brow" than the early on workers inward quantum mechanics.
Historically, this belief inward their superiority is indefensible. Macroscopic objects – including measuring apparatuses (but also lattices, metals, gases, molecules of whatever size etc.) – were existence described yesteryear the newly industrial plant life formalism of quantum mechanics since the real early on years of quantum mechanics. No serious physicist doubted that quantum mechanics described all of those things, non exactly private atoms etc.
OK, what happens if nosotros analyze the organisation of involvement as good as the measuring apparatus? The organisation of involvement (the object nosotros measure) is industrial plant life inward the moving ridge role \(\ket\psi\) earlier the measuring spell the apparatus is inward the lay down \(\ket\phi\). They're non entangled yet which is why the lay down of the "composite system" is only the tensor production \(\ket\psi \ket\phi\).
The apparatus is able to mensurate the observable \(L\) acting on the moving ridge role \(\ket\psi\). The measuring starts with allowing the organisation \(\ket\psi\) to influence or imprint itself to the apparatus \(\ket\phi\). So it agency that the composite organisation (originally described yesteryear a non-entangled lay down vector) unitarily evolves to the entangled lay down vector\[
\ket\Psi = \ket\psi \ket\phi \to \sum_n c_n \ket{\psi_n} \ket{\phi_n}.
\] In the concluding state, nosotros encounter that the states of the measured object as good as the apparatus are entangled. One is inward the \(n\)-th lay down vector if the other is inward the corresponding \(n\)-th lay down vector. The lay down vectors \(\ket{\psi_n}\) are eigenstates of \(L\).
Now, we're entirely truly interested inward the object described yesteryear the moving ridge functions denoted yesteryear the missive of the alphabet \(\ket\psi\) as well as so nosotros describe over the degrees of liberty of the apparatus to obtain the reduced density matrix of the object which happens to be\[
{\rm Tr}_{\phi} \ket\Psi \bra\Psi = \sum_n |c_n|^2 \ket{\psi_n} \bra{\psi_n}
\] The density matrix for the measured object has been diagonalized. Equivalently, spell the diagonal entries are the probabilities, the off-diagonal elements vanish because of the coupling with the apparatus. Note that this reduced density matrix differs from \(\ket\psi \bra \psi\); the latter isn't diagonal (it contains all the nonzero off-diagonal entries, too).
The coupling with the appropriate apparatus had the number of "forgetting" the relative phases betwixt \(c_n\). Only the squared absolute values \(|c_n|^2\) – the probabilities – are preserved after the "premeasurement". I haven't said it yet: the aforementioned coupling betwixt the object of involvement as well as the apparatus is referred to as the "premeasurement".
Our transition from the full general lay down \(\ket\psi \ket\phi\) to the reduced density matrix is sometimes called the "weak von Neumann projection" spell the "strong von Neumann projection" is the subsequent trial of the collapse, the actual measuring which abruptly changes the lay down vector to 1 of the vectors \(\ket{\psi_n}\).
For a degenerate spectrum of \(L\), nosotros must adopt a slight generalization of von Neumann's formulae above, namely the Lüders projection where \(|c_n|^2\) are summed over the degenerate lay down vectors or, using projection operators, the forgetting of the relative phases is non expressed as the previous "weak von Neumann projection" higher upwards but yesteryear the product\[
\rho \to \sum_n P_n \rho P_n
\] of projection operators \(P_n\) projecting onto the subspaces respecting the eigenvalues \(\ell_n\).
Simple. All of that is uncontroversial. It is truly non adding anything to quantum mechanics. We exactly report a composite organisation that contains the measured object as good as the apparatus. It doesn't allow us to brand quantum mechanics whatever less quantum. We notwithstanding demand an actual observer to perceive 1 of the states \(\ket{\phi_n}\) of the apparatus as well as thence 1 of the states \(\ket{\psi_n}\) of the object, too. And the apparatus wasn't what nosotros were truly interested in, either. The add-on of the "apparatus layer" to the give-and-take of the measuring (the add-on yesteryear von Neumann) was non essential from a physics viewpoint.
If there's the foremost sort measurement, at that spot should also endure the minute sort measurement, right? Yes, as well as at that spot is one. The minute sort measuring is 1 starting with a similar premeasurement evolution\[
\ket\psi \ket\phi \to \sum_n c_n \ket{\chi_n} \ket{\phi_n}
\] but inward this case, the vectors \(\ket{\chi_n}\) that nosotros receive got used for the object of involvement are not orthogonal to each other. (It also agency that they can't endure eigenstates of a Hermitian operator corresponding to differing eigenvalues.) They're to a greater extent than full general vectors.
The states \(\ket{\phi_n}\) of the apparatus are notwithstanding orthogonal to each other (and consequently, the private price inward the center describing the composite organisation are also orthogonal to each other) as well as so nosotros effectively mensurate some belongings of the apparatus again. But 1 time this belongings of the apparatus is measured, nosotros can't deduce a corresponding belongings of the "system of interest" inward such a way that the dissimilar outcomes would endure strictly mutually exclusive. The data nosotros larn most the measured object can't endure interpreted classically as well as this "second sort measurement" may also endure shown to create irreversibility because the post-collapse probabilities differ from the pre-collapse ones.
OK, as well as so the "first kind" measuring agency that the states of the object of involvement receive got to endure orthogonal to each other; they are non orthogonal to each other for the "second kind" measurement. Moldoveanu never mentions or discusses this "orthogonality" associated with the "first kind" at all. As far as I tin say, he can't perhaps know what the "first kind" describing word truly means. He entirely uses words because they audio fancy but he exactly doesn't know what he's talking about.
Now, the telephone commutation "negative" claim yesteryear Moldoveanu is that this "first sort measurement" as described yesteryear von Neumann cannot endure repeatable. This is an extremely bizarre controversy because this "first sort measurement" is the most ordinary, the simplest, the most problem-free, the most controllable development earlier the measuring as well as during the measuring that textbook quantum mechanics involves. Moldoveanu should know that what he claims most the "non-repeatability" is exactly land rubbish but he doesn't know it.
In fact, almost all the credible texts using the phrase "first sort measurement" explicate that those are "repeatable" (for discrete spectra) almost immediately. You may let on a proof inward the third chapter of Max Jammer's book. (Or banking enterprise check this page yesteryear Pechenkin to encounter that "first kind" as well as "repeatable" are basically synonymous.) Jammer's mass has been the #1 source of wisdom most the foundations of quantum mechanics for other serious authors, e.g. for Zurek as well as Wheeler who wrote their mass most the discipline inward 1983.
Alternatively, opened upwards this Busch-Lahti 1996 paper as well as search for the intelligence "repeatable". You volition let on it at xiv places (and "first kind" at 10 places) as well as larn that "repeatable" as well as "first kind" are pretty much equivalent for discrete spectra. Repeatable measurements are of the foremost kind. Problems occur with continuous spectra – the eigenstates aren't normalized – as well as since the 1930s, at that spot receive got been discussions most the possibility to occupation the "first kind" formalism for continuous spectra etc. Also, if yous desire to mensurate 2 non-commuting observables, yous volition let on a conflict with repeatability – a way to clit the uncertainty principle.
But for the province of affairs inward which nosotros truly bargain with discrete spectra – as well as thence with the sums – at that spot can't endure whatever contradiction betwixt "first kind" as well as "repeatable". You may banking enterprise check Moldoveanu's detailed propositions most the conflict as well as encounter that they're exactly land stupid. He asserts that at that spot exists no unitary map that could map\[
\eq{
|\psi_A\rangle \otimes |M_0 \rangle &\rightarrow |\psi_A \rangle \otimes |M_A \rangle \\
|\psi_B\rangle \otimes |M_0 \rangle &\rightarrow |\psi_B \rangle \otimes |M_B \rangle \\
(c_A|\psi_A\rangle + c_B|\psi_B\rangle)\otimes |M_0\rangle &\rightarrow c_A|\psi_A\rangle \otimes |M_A\rangle +\\
&+ c_B|\psi_B\rangle \otimes |M_B\rangle
}
\] Oh, really? Why should such a unitary operator endure forbidden? The 3rd status follows from the foremost 2 as well as linearity – it's exactly a damn superposition of them. So nosotros may manifestly ignore it because nosotros await for a linear operator, anyway.
And the foremost 2 weather condition only say that 2 particular normalized, mutually orthogonal vectors \(\vec v_1,\vec v_2\) are mapped to 2 particular normalized, mutually orthogonal (you may banking enterprise check all the adjectives) vectors \(f(\vec v_1),f(\vec v_2)\). Does a unitary operator or a unitary matrix with these properties exist? You bet. The weather condition only order us what 2 rows of the matrix are. The norms as well as inner production of both vectors \(\vec v_1,\vec v_2\) are preserved yesteryear \(f\) as well as so there's no conflict with unitarity here. And the remaining rows of the matrix (if other outcomes likewise \(A,B\) exist) may endure completed yesteryear an "orthogonalization process".
To misunderstand these claims agency to neglect an essay inward the foremost or minute semester of an undergraduate linear algebra course. What Moldoveanu says most the non-existence of the unitary operator isn't exactly wrong; it is utterly idiotic. It is idiotic from the viewpoint of soul who has mastered the basics of linear algebra. It is as idiotic from the viewpoint of soul who is thinking most quantum mechanics because if yous call upwards inward price of quantum mechanics, every damn observation of the lay down nosotros ever exercise (at to the lowest degree when it comes to discrete spectra, as well as due to limitations on accuracy etc., nosotros ever mensurate discrete spectra, strictly speaking) starts with a unitary transformation that Moldoveanu claims non to exist.
The mathematical claim most the non-existence of the "first sort measurement" unitary operator is dumb. I've said that the real usage of "first sort measurement" yesteryear Moldoveanu was exactly a snobbish ritual because Moldoveanu didn't occupation the divergence betwixt "first kind" as well as "second kind" (about the orthogonality) at all – the describing word was inserted exactly to brand his texts await to a greater extent than incomprehensible. But at that spot are other aspects of his weblog postal service that evidence that he is only non thinking most physics quantum mechanically.
At the beginning, he talks most the states of the apparatus\[
\ket{M_0},\quad \ket{M_A}, \quad \ket{M_B}
\] where \(\ket{M_A}\) as well as \(\ket{M_B}\) play the role of the states \(\ket{\phi_n}\) I mentioned previously as well as they clit the lay down of the apparatus that has detected the corresponding eigenvalue inward the discrete spectrum. But as yous tin see, Moldoveanu has added 1 to a greater extent than lay down of the apparatus, \(\ket{M_0}\), which he describes as the "apparatus ready for measurement".
Now, experience gratis to verbalize most this lay down of the apparatus. If the apparatus has a display, \(A\) as well as \(B\) may clit letters that may appear on the display spell the display may also endure showing nothing, specially earlier the measuring is completed, as well as so at that spot is some other lay down of the apparatus. There isn't whatever corresponding lay down of the measured object. What corresponds to \(\ket{M_0}\) is "ignorance" most the measured object.
Influenza A virus subtype H5N1 funny affair is that the right give-and-take of the "first sort measurement" doesn't include whatever \(\ket{M_0}\). After the successful measurement, we're guaranteed non to acquire the lay down \(\ket{M_0}\). If nosotros got this state, it would hateful that we're notwithstanding ignorant most the lay down of the measured object. In other words, it would hateful that the measuring hasn't taken house or hasn't been successful!
And if the right manus side of the "premeasurement" contained some extra term\[
c_0 \ket{\psi_0}\ket{M_0}
\] with a nonzero aAmplitude (Moldoveanu suggests that this term isn't there, \(c_0=0\)), nosotros would run to the next problem: What is \(\ket{\psi_0}\)? We don't receive got that many lay down vectors inward the Hilbert infinite of the measured object because the label \(0\) shouldn't endure associated with whatever particular eigenvalue. As nosotros said, this "ready for measurement" is associated with "ignorance" most the measured object.
So this term would either endure an immediate contradiction. Or nosotros would receive got to define \(\ket{\psi_0}\) as a superposition of the actual eigenstates \(\ket{\psi_n}\). That would hateful that \(\ket{\psi_0}\) fails to endure orthogonal to all the vectors \(\ket{\psi_n}\) as well as the premeasurement would thence endure of the minute kind, non the foremost kind! At whatever rate, there's no way to "undo" our previous proof that at that spot ever exists the "first kind" unitary operator governing repeatable measurements that Moldoveanu claims non to exist.
I call upwards there's the well-known fallacious argue why he added the lay down \(\ket{M_0}\) to the listing of states of the apparatus. He doesn't similar quantum mechanics as well as so he wants to acquire rid of the observers. He wants to "objectivize" the query whether an observation has taken house or non as well as all his states either incorporate \(\ket{M_0}\) or \(\ket{M_A},\ket{M_B}\) which say "No" as well as "Yes", respectively. But quantum mechanics ever depends on observers as well as superpositions of all states – including the states "the apparatus has detected something" as well as "the apparatus hasn't detected anything yet" – are ever allowed yesteryear the universal superposition postulate. You don't gain whatever clarity yesteryear adding \(\ket{M_0}\). As I said, after a successful measurement, such "ambiguous" lay down vector must receive got the probability zero, anyway.
These anti-quantum zealots are exactly obnoxious. Now, to a greater extent than than xc years after the nascence of quantum mechanics, they volition overflowing your Internet as well as journals with arbitrarily preposterous claims most alleged "problems" of quantum mechanics, claims that intelligent undergraduate freshmen receive got to let on laughable. This "community" allows (and maybe encourages) itself to emit arbitrarily dumb statements as long as they are used to say that at that spot is some job with quantum mechanics. Such people should endure instantly stripped of their physics or mathematics degrees. Instead, what happens is that they evidence their membership inward the community of "researchers" inward the quantum foundations.
Like the creationist movement, it's a bunch of cranks. The deterioration of that "community" was gradual. Von Neumann started this give-and-take of the entangled states involving the apparatus etc. It was redundant but basically right – as well as if an fault appeared, it was admitted as well as corrected. EPR wrote to a greater extent than oftentimes than non incorrect things most quantum mechanics but the people allowed to telephone telephone themselves "experts inward foundations of QM" agreed that EPR were wrong. In 1927, experts dismissed the airplane pilot moving ridge theory as well as fifty-fifty its Bohm's revival inward the 1950s was considered "not fifty-fifty wrong" yesteryear Pauli (and all other large shots of that time). When Everett wrote his bizarre thesis, it was notwithstanding the illustration that the experts agreed he was wrong, specially all the suggestions that quantum mechanics had a flaw or needed to endure "fixed" inward some way, as well as Everett was rightfully denied a postdoc job. In the 1970s, the land belonged to folks similar Max Jammer who were notwithstanding writing right things. In the 1980s, the modern decoherence scheme was born along with consistent histories etc. as well as most of the experts influencing that land notwithstanding understood quantum mechanics correctly. Since the terminate of the 1980s, the number of incompetent hacks who exactly aren't capable of agreement quantum mechanics grew as well as they're the bulk of that land today.
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