Bohmists' Inequivalence & Dishonesty

Off-topic, annoying: The Central Committee of Both F*cked-up as well as Non-F*cked-Up Feminist Whores at Advice for debaters inwards back upward of Bohmian mechanics (that's how the page is referred to at the primary page of the website).

Wow, this sounds precisely similar the 135 1 1000 m pages ;-) written past times Al Gore's disciples (and courses taught past times them) most how to manipulate your parents concerning the climate, how to deceive the Nobel peace prize committee, how to utter to a conservative, how to fool a denier, convince a neighbor, bag existent estate inwards Tennessee as well as California, as well as how to escape police delineate as well as express mirth at everyone. ;-)




I am lamentable but this non how an honest scientist behaves. On his "Advice for Bohmians" page, Taylor sensibly says that Bohmists won't convince anyone etc. But he also recommends them:

Assure them that at that spot are mathematical results for existence, uniqueness, agreement, extensions to whatever phenomena, etc.

This hugely differs from the advice that an honest scientist such as your humble correspondent would give to everyone – for discussions most foundations of quantum mechanics, string theory, climate, or whatsoever other scientific topic:

Tell the truth whether it supports 1 viewpoint or another. Try to move comprehensible as well as assure that the listener gets as accurate a flick of the available evidence, facts, as well as explanations as his or her abilities as well as noesis allow.

Unfortunately, Taylor's "how to brainwash" page isn't the entirely sign showing that the Bohmists are a deceitful, ideologically driven movement.




Ilja Schmelzer – who wrote a guest spider web log inwards 2013 – had to move banned a calendar week agone or so. It precisely happens that about at the same moment, lots of responses to myself appeared on his forum, along amongst novel users such as secur.

In 1 comment, secur tells us that he's the same somebody as the commenter "algore" who appeared on this blog. Influenza A virus subtype H5N1 prissy admission. Even to a greater extent than interestingly, I recall that at that spot exists nontrivial evidence that secur=algore as well as Ilja Schmelzer are truly the same person, too. Try to read all exchanges betwixt these 2 men on Ilja's forum. The bird of understanding betwixt them is amazing. It's precisely similar Amy's virtual friend inwards The Big Bang Theory. They're constantly on the same frequency, know the same things, usage the same not-quite-generic acronyms such as dBB, overuse the colon (;) relatively to almost everyone else, as well as so on. There may move other users on Ilja's forum who are Ilja's sock puppets, too.

Well, it's funny.

One of the other possible copies of Ilja's – as well as at least, a Bohmist – is user7348 who has posted lots of assorted pro-Bohmian stuff on the Physics Stack Exchange recently. (I also ran into some other obnoxious Bohmist crackpot named Timaeus over there.) Whoever user7348 is, he clearly plays a propaganda game, asks bogus enquiry whether Bohm's theory suffers from 1 work or another, as well as waits for someone to write a bogus respond – the people who respond may move the same person. But fifty-fifty if they're not, many of the answers are precisely wrong.

One omnipresent declaration made past times the Bohmists is that Bohmian mechanics is equivalent to quantum mechanics. That's manifestly completely wrong. Equivalent theories must give the same predictions. That's pretty much possible entirely if they involve an "equally large laid of degrees of freedom" that may move mapped to 1 another, that receive got the same physical meaning, as well as nada is added or replaced on either side.

Bohmian mechanics may reproduce the whole moving ridge role as well as Schrödinger's equation for its evolution. But Bohmian mechanics also adds additional "beables", such as the classical particle positions, as well as uses these novel classical degrees of liberty to create upward one's heed what volition occur inwards an experiment. At this moment, the theory is already obviously inequivalent to quantum mechanics where all the predictions are made from the moving ridge role – as well as never from some additional classical degrees of freedom.

The claim that such a modified theory is equivalent to QM is as ludicrous as the claim that communism is equivalent to the free-market economy. People receive got the same ingenious ideas precisely similar inwards capitalism – they precisely demand a postage stamp from the communist political party – so the communism is equivalent to capitalism, isn't it? Well, it's not. The communists screw everything skillful most capitalism, as well as analogously the beables as well as the incorrect interpretation of the moving ridge role screw everything skillful most quantum mechanics.

It's remarkable how dense the Bohmists may move when it comes to the simple signal that 1 either has an equivalent theory – so that he can't claim whatsoever improvement at all – or he changes something most the ways how things are predicted (or what tin move predicted), as well as this full general modify way that the theory volition construct dissimilar or novel predictions that are probable to disagree amongst the facts (given the fact that quantum mechanics agrees amongst all the facts).

It may move seen inwards millions of ways – conceptual as good as detailed "minor" examples – that Bohmian theory merely cannot move equivalent to quantum mechanics. As "algore" told us, Bohm & Hiley's 1993 majority (which both secur=algore as well as Ilja Schmelzer seem to know really good – I've never seen the majority as well as I recall that almost no physicist has) made it clear that the authors realized that at that spot can't move whatsoever valid Bohmian handling of bosonic fields as well as other things, due to their stress tensor's fifty-fifty number of indices etc. Bohm & Hiley realized that a disagreement amongst relativity/locality is unavoidable as well as that this disagreement is a lethal problem.

Bohmian mechanics incorporates both the moving ridge role (rebranded as the airplane pilot wave) as well as the actual positions. This right away raises the work that inwards general, nosotros don't know which of these 2 "copies of the information" is observed, which of them affects other things. In almost every exceptional situation, you lot may run across that every respond is a problem.

For example, receive got the simplest "relative success story" Bohmian theory for 1 electron as well as essay to inquire whether the electron emits electromagnetic radiation. The radiations is composed of photons which should also move associated amongst some "real trajectories" because the location of photons may move measured, too. OK, these photons are emitted whenever a accuse is accelerating.

An obvious enquiry arises: Should the "presence of acceleration" move decided according to the moving ridge role (pilot wave), or according to the Bohmian trajectory? And analogously, should the Bohmian photons amongst trajectories move created entirely nigh the Bohmian electrons, or nigh all the points where the moving ridge role (pilot wave) for the electrons is nonzero?

Both answers Pb to immediate disagreements amongst the observations. "Sometimes" (well, almost always), 2 attempts are merely non plenty to justice the right answer. If the photons may arise "anywhere" where the airplane pilot moving ridge is supported, 1 predicts the existence of the synchrotron radiations at points where no charged particle is truly found. On the other hand, if the synchrotron radiations (photons) are created nigh the Bohmian electron's trajectory, as well as then fifty-fifty a costless but self-interfering electron volition receive got to emit the radiations because the generic Bohmian trajectory is curved as well as accelerating inwards that case.

This is 1 of the signal of the 2014 newspaper past times Pisin Chen as well as Hagen Kleinert

Deficiencies of Bohmian Trajectories inwards View of Basic Quantum Principles

which also argues, next a newspaper past times blog post ruling out all realist "interpretations" past times seeing the depression rut capacity of atoms.

The declaration was already known to Dirac – as well as presented at the showtime of his textbook on quantum mechanics – as well as its meat is ultimately really simple, so if you lot yet haven't understood why it safely kills all Bohmian-like theories, I inquire you lot for some patience.

Quantum mechanics predicts as well as experiments confirm that the entropy of 1 atom is e'er comparable to \(k\), i.e. the Boltzmann constant, nigh room temperatures etc. This entropy may move measured from the rut capacity of the materials. In the units \(k=1\), the declaration is that the data carried past times 1 average atom at the room temperature is comparable to 1 bit. It may move a few bits but it's non too much higher.

The entropy is the logarithm of the number of microstates that are macroscopically indistinguishable, \(S=k \log W\), as Boltzmann's tomb proudly says. How is it possible that for an atom inwards QM, \(S\sim k\)? It's because the number of microstates \(W\), if I respectfully usage Boltzmann's notation, is of club one.

In fact, for \(T\to 0\) kelvins, the entropy of an atom obeys \(S\to 0\), something that was known as the "third law of thermodynamics" long earlier quantum mechanics was born. Why is it truthful that the entropy of all regular materials goes to null when the temperature goes to null kelvins? It's because at null kelvins, 1 doesn't receive got plenty unloosen energy to excite whatsoever bird of freedom, as well as inside the interval of energies comparable to \(kT\), the Earth earth of the atom (or a crystal etc.) is unique!

It's unique, so Boltzmann's number \(W=1\) as well as its logarithm is zero, giving \(S=0\) for \(T=0\).

For somewhat higher, e.g. room, temperatures, it becomes possible to excite some electrons into higher orbitals (it's easier to excite them inwards molecular orbitals etc., atomic orbitals demand much higher energies i.e. much higher temperatures). But nosotros yet receive got \(W\sim \O(1)\) as well as thus \(S\sim \O(k)\) for an atom.

How is it possible that nosotros receive got a unique Earth earth as well as \(W=1\) at really depression temperatures? It's because the Earth earth moving ridge role is counted as \(W=1\) state. But cannot you lot receive got "nearby" moving ridge functions? Cannot the Earth earth moving ridge role move deformed "infinitesimally"?

Yes, you lot tin consider \(\ket{\psi_0}+\epsilon\ket\phi\), but that's plenty to increase \(W\) e.g. to \(W=2\), allow lonely higher. Why? Because inwards quantum mechanics, non-orthogonal states are merely non mutually exclusive. Instead, the probability that a normalized vector \(\ket\alpha\) is "totally physically equivalent" to \(\ket\beta\) is given past times the Born rule, \[

P = \abs{\bra \alpha \beta \rangle}^2

\] If you lot demand to increase the number of states from \(W=1\) to \(W=2\) inwards quantum mechanics, you lot demand to bring out a novel Earth that is orthogonal to the Earth state, as well as is thus really dissimilar (and non precisely infinitesimally different) from the Earth state.

This is the miraculous fob past times which quantum mechanics achieves something that is totally impossible inwards whatsoever classical theory: It precisely freezes all the degrees of liberty at the depression temperatures – as well as yet freezes almost all of them at room temperatures. The unloosen energy spectrum is discrete. And what makes this declaration of import is that the states that are non unloosen energy eigenstates, e.g. min deformations of the Earth state, merely cannot move counted as new, mutually exclusive states that increase the value of \(W\) because quantum mechanics boldly says that they're "almost certainly" identical to the Earth state!

The indistinguishability of these nearby moving ridge functions is a manifestation of the incertitude principle. If your moving ridge role is too closed to the Earth state, you lot can't move whatsoever sure that it is a dissimilar moving ridge role because all of its physical properties are the same inside the fault margins.

The province of affairs is really dissimilar inwards whatsoever classical theory – a synonym of a "realist theory" or a "theory without observers". Bohmian mechanics is 1 of them. In these theories, all the configurations are inwards regulation totally distinguishable: they are mutually exclusive. So the Earth earth moving ridge role \(\ket{\psi_0}\) is reinterpreted as a classical "pilot wave".

Its min deformations \(\ket{\psi_0}+\epsilon\ket\phi\) are distinguishable, different, mutually exclusive states, so they must move counted as novel states that increase the value of \(W\), the number of classically indistinguishable microstates. Clearly, at that spot is a continuous infinite so you lot larn \(W\to \infty\) fifty-fifty if you lot trammel yourself to the states that are closed to the Earth state. So the entropy is \(S/k\to \infty\), too.

This work has e'er existed inwards classical physics. The entropy was entirely well-defined upward to a universal additive shift \(\Delta S\) inwards classical physics. The 3rd law of thermodynamics didn't truly say that \(S\to 0\) for \(T\to 0\). It said that \(S\to S_0\) for \(T\to 0\) where the constant entropy \(S_0\) was undetermined.

All these problems of classical thermodynamics boiled downward to the fact that the number of states inwards the stage infinite was truly infinite (as the number of points inwards whatsoever continuum), so its logarithm \(S/k\) was infinite, too. This infinite additive constant had to move removed from \(S\) – basically past times assuming that the precision amongst which all the stage infinite variables may move measured was express – as well as that's how a finite \(S\) could receive got been restored.

Quantum mechanics solved the work past times making \(W\) literally finite (at to the lowest degree for whatsoever collection of particles inwards a box as well as at a finite temperature). But \(W\) is no longer the total number of moving ridge functions – which is yet infinite. Instead, \(W\) is the dimension of the Hilbert infinite of states whose macroscopic appearance is the desired one. Only because nosotros utter most the dimension – i.e. because nosotros don't consider nearby ket vectors to move dissimilar i.e. because nosotros entirely count the pose down vectors inwards a pose down – nosotros may construct \(W\) finite for an atom. In other words:

The incertitude regulation logically identifying nearby states as "in regulation indistinguishable" (no repetition of the province of affairs is allowed) is a necessary status for the finite (and low) entropy or rut capacity per 1 atom!

Bohmian mechanics denies the incertitude regulation – it says that the nearby forms of the "pilot wave" are inwards regulation distinguishable – so it doesn't reproduce this clever fob of quantum mechanics. Consequently, Bohmian mechanics implies \(W\to \infty\) as well as thus \(S/k\to \infty\), too (for 1 atom). Even amongst some regularizations as well as truncations you lot could suggest as a fix, nosotros volition unavoidably receive got \(S\gg k\).

I wouldn't allow a pupil who can't larn these unproblematic things to transcend a course of educational activity that includes quantum statistical physics. This is no research-level physics. It's most basics of statistical physics.

By the way, the Bohmian mechanics has other problems likewise \(S\gg k\). One of them is that the entropy isn't extensive. If you lot receive got \(N\) atoms, the entropy should scale as \(N\). If you lot add together \(M+N\) atoms, the entropies should add together as \(S(M)+S(N)\), too. Mutual interactions betwixt the subsystems volition move neglected.

In feasible theories of classical physics, this upshot arises because the stage infinite of a composite organisation is the Cartesian product \(PS=PS_A\times PS_B\). Its majority is thus \(V(PS)=V(PS_A)V(PS_B)\). This multiplicative behaviour is a simple generalization of the formula for the surface area of a rectangle. Note that Boltzmann's \(W\) obeys \(W\sim PS\) as well as thus \(\log W\) is additive (the logarithm of the production is the total of logarithms).

In quantum mechanics, the same logic holds but at nowadays \(W={\rm dim}\HH\). You entirely count the pose down vectors of the Hilbert space. Influenza A virus subtype H5N1 composite organisation has the Hilbert infinite described past times the tensor production of the subsystems' Hilbert spaces as well as its dimension obeys \(d=d_A d_B\). That translates to \(\log d = \log d_A + \log d_B\) as well as consequently, the entropy exhibits the same additive behavior.

It works. However, Bohmian mechanics is a foreign hybrid: it is conceptually classical but tries to recycle the mathematical objects of quantum mechanics. The Hilbert infinite \(\HH_A\otimes \HH_B\) (or the laid of "rays" inwards it – this number doesn't construct much difference) must move considered a "phase space" of the Bohmian theory – the laid of all in-principle distinguishable, mutually exclusive states. But the number of points inwards this \(\HH_A\otimes \HH_B\) tensor production infinite is inwards no mode a "product" of factors from \(A\) as well as \(B\) – it's much higher than that because \(\HH_A\otimes \HH_B\) is a "much bigger space" than \(\HH_A\times \HH_B \equiv \HH_A\oplus \HH_B\) – so you lot merely couldn't larn whatsoever additivity for the entropy of a organisation inwards Bohmian mechanics.

The totally basic things such as the additivity of rut capacity neglect to piece of work inwards Bohmian mechanics.

These totally elementary, lethal bugs are never discussed past times the Bohmians because they're inconvenient. Formally, they receive got never gotten "this far" because they haven't described what's happening amongst all their airplane pilot waves as well as beables when a macroscopic organisation tries to ambit an equilibrium Earth etc. However, a min of a careful reasoning is plenty to run across that independently of whatsoever details, it is absolutely guaranteed that no theory based on the Bohmian epitome may ever reproduce the extensive entropy or the entropy that is comparable to \(S\sim k\) for 1 atom. Every intelligent pupil should receive got understood the proof above. Nothing is truly missing inwards it.

But the dishonest ideologues' self-respect depends on their misunderstanding of similar unproblematic arguments so you lot tin move sure that these ideologically driven crooks volition move "confused" most these unproblematic matters for centuries to come upward – fifty-fifty though all these arguments were absolutely clear to Dirac (and others) earlier 1930.

Influenza A virus subtype H5N1 bonus: Ilja Schmelzer added the next respond concerning the Bohmian rut capacities:

One should distinguish hither de Broglie-Bohm theory for the full general province of affairs exterior the equilibrium, as well as that for quantum equilibrium. Entropy is defined as commons past times \(H=-\int \rho \ln \rho dq\). Outside the quantum equilibrium it is useful to dissever it into the entropy relative to the quantum equilibrium \(H=-\int \rho \ln (\rho/|\psi|^2) dq\). This relative entropy has been used past times Valentini to essay a "subquantum H-theorem" that a full general initial distribution volition tend toward quantum equilibrium, run across for example, http://arxiv.org/abs/1103.1589 for details.

In quantum equilibrium, nosotros receive got \(\rho=|\psi|^2\), so that the formula becomes \(H=-\int |\psi|^2 \ln (|\psi|^2) dq\), thus, the criterion quantum-mechanical one. After this, you lot tin apply criterion quantum theory.

That's cracking that he wrote it inwards this mode because everyone familiar amongst the basics of quantum statistical physics knows that the foremost formula as good as the concluding formula (Schmelzer's equilibrium formula for the entropy) totally disagrees amongst the actual entropy inwards quantum mechanics. Instead, the entropy is \(S=0\) for whatsoever pure Earth \(\ket\psi\) piece for a mixed state, nosotros must usage the von Neumann entropy\[

southward = -{\rm Tr}(\rho \log \rho).

\] At really depression temperatures, \(\rho\approx \ket{\psi_0}\bra{\psi_0}\) which implies \(S/k \ll 1\), something that neither formula of Schmelzer's tin ever give. At the same temperatures, Schmelzer's formula gives a large value of \(H\) (which is meant to move \(S\)) so the theory is clearly falsified. You may run across that Schmelzer doesn't sympathise statistical physics (and belike quantum mechanics) at all. He confuses pure states as well as mixed states (mixed states are absolutely needed to meaningfully hash out whatsoever nonzero values of entropy etc.) as well as does many other stupid things.

But as I receive got shown above, all these airheaded things are non precisely artifacts of his personal misunderstanding of basic physics. Instead, at that spot can't be whatsoever "fix" of Bohmian mechanics that would imply \(S/k\ll 1\) for 1 atom at \(T\to 0\). This remarkably depression entropy requires the incertitude regulation (fundamental indistinguishability of states that are too closed to each other, which is why entirely the pose down vectors are counted into \(W\)) as well as the Bohmian mechanics denies this regulation when it declares \(\ket\psi\) to move an objective reality (distinct from other values of \(\ket\psi\)).

(I was beingness extremely generous. Schmelzer's formula for \(H\) wasn't fifty-fifty dimensionally right because \(\psi(\vec r)\) is dimensionful as well as the logarithms of dimensionful arguments receive got ill-defined units. Moreover, Schmelzer's upshot should receive got included 2 terms, 1 from the Bohmian particle as well as 1 from the Bohmian airplane pilot wave. But fifty-fifty his "maximally QM-like sketch" must larn inwards clear to every reader who has a clue that regardless of whatsoever "details", the Bohmian upshot for the entropy has nada whatsoever to practice amongst the correct, experimental or quantum mechanical, answer.)

Again, because the depression rut capacities are experimentally verified, 1 may say that nosotros receive got an experimental proof of the incertitude regulation – an experimental falsification of all theories that contradict this principle. And Bohmian mechanics is precisely an illustration of those dead hypotheses.