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Consistent Histories Aren't Inconsistent

The prohibited inconsistency of histories inwards the formalism is synonymous with Bohr's complementarity

The de Broglie-Bohm airplane pilot moving ridge theory too the many worlds interpretation are the 2 most widespread "alternative axiomatic systems" that are claimed to compete with the proper, Copenhagen or neo-Copenhagen, quantum mechanics. The Ghirardi-Rimini-Weber "objective spontaneous random collapse" theories are a distant tertiary too other "frameworks" meant to supersede the postulates of quantum mechanics are pretty much incoherent fifty-fifty at the bird of the grammar.

Both the airplane pilot moving ridge theory too the many worlds are irrational too both of them ultimately contradict of import too well-established facts almost the physical world. Both of them are motivated past times the champions' attachment to "realism" – a euphemism for the observer-independent i.e. classical physics. If I had to choose, I would direct the Bohmists equally the much worse physicists with the two. They're inwards a much deeper denial of modern physics.

You know, i may dissever those confused (and/or bigoted) people's efforts to deviate from quantum mechanics equally formulated inwards Copenhagen into 2 levels:
  1. Dissatisfaction with the philosophical conceptual "words" that Heisenberg, Bohr, Pauli, Dirac, Wigner, von Neumann, too others direct maintain been didactics us
  2. Disagreement with some universal properties of the mathematical formalism of quantum mechanics
Both Bohmists too many-worldists endure from (1). But exclusively the Bohmists commit the sin expose (2). In practice, most many-worldists prefer to say that the mathematical foundations of quantum mechanics are right too hither to stay. They "just" believe that it may live too should live supplemented with some "more realist" laid upwardly of words too to a greater extent than visualized "ways to imagine" what's going on.




What arrive at I hateful past times the key mathematical properties of the quantum theory that the many-worldists commonly direct piece the Bohmists deny it?
  • Observables (and the development too other transformation operations) are represented past times linear but non-commuting operators.
  • The theory ultimately computes probabilities too complex probability amplitudes are an intermediate stride inwards the calculations. They are combined into sesquilinear expressions of the type \(c_1^*c_2\).
Many-worldists whom nosotros know commonly concur with these statements. Many of them are particle physics or condensed affair physics practical men who compute correlators of linear operators all the time. They don't really appear themselves to mess upwardly with the "complex linear" spirit of quantum mechanics.

They're just thinking (more precisely, they are victims of a wishful thinking) that all these expressions could live employed past times some other philosophy – supplemented past times different conceptual words – inwards which the observer wouldn't live needed, moving ridge functions wouldn't collapse inwards whatsoever sense, the moving ridge functions could live split into sums of many parts that comport equally "many worlds", too the probabilities could live interpreted equally some subjective belief almost "where nosotros are".




There exists no consistent way to satisfy these weather too the many worlds approach so fails equally shortly equally an intelligent somebody looks carefully. But at least, the many-worldists aren't inwards the total denial of the change of the spirit of calculations that was forced upon the people past times the quantum revolution.

On the other hand, Bohmists deny everything – non exclusively the "philosophical" demand for the observers, the intrinsically probabilistic description etc. But they also deny the importance of linear operators, complexity of some probability amplitudes inwards the mathematical formalism etc. They desire to furnish physics to the epoch of classical physics non exclusively when it comes to the philosophy, words, too concepts; but also when it comes to the sort of mathematical structures that should live used to calculate the physical predictions.

In the airplane pilot moving ridge theory, linearity of the operators – too the development of the moving ridge business office (rebranded equally the airplane pilot wave) – plays no role. It seems completely coincidental. The airplane pilot moving ridge is a classical champaign (a multilocal champaign inwards the instance of many particles) too classical fields generically evolve according to nonlinear equations. Bohmists should really acknowledge that they're predicting that the equations governing the development of the moving ridge business office should live nonlinear because it's infinitely unlikely that all the nonlinear damage vanish (there is no argue for such a vanishing inwards the Bohmian picture, too anything that tin dismiss tumble out volition happen). This prediction clearly contradicts the observations.

Moreover, the airplane pilot moving ridge theory postulates the objective existence of the Bohmian particle positions, existent classical degrees of liberty that are neither quantum nor complex. None of these degrees of liberty were ever useful to explicate whatsoever quantum phenomenon but the Bohmists don't care.

I was looking at diverse Bohmist sources inwards recent days. Ilja Schmelzer, a Bohmist who i time wrote a TRF invitee blog, had a discussion forum where he promoted Bohmian mechanics too reported every trial of the type "Luboš Motl wrote this too that which was critical of Bohmian mechanics". This forum was hijacked past times spamming machines. Every minute, a novel comment (with 0 views) is promoting some other production – commonly a pharmacological product. The transition of a Bohmist propagandist forum to an unregulated pile of spam is rather characteristic.

Also, I spent to a greater extent than fourth dimension past times reading Jean Bricmont's mass promoting Bohmism (which has appeared inwards previous weblog posts). More than before, I was amazed past times the amount of political ideology inwards the book. Bricmont is a Marxist defending all sort of far left things. That could live fine for a physicist if he could defend himself against beingness affected past times the ideological stuff. However, inwards his mass claiming to live almost quantum mechanics, the rootage "Marx" appears a whopping 33 times. Not bad for a political guy who died inwards 1883, 42 years earlier quantum mechanics was get-go formulated. ;-)

Among other things, Bricmont criticizes Leon Rosenfeld – a Marxist who was silent a unopen friend too soulmate of Bohr's too a fierce critic of Bohmian mechanics too the many worlds. One may meet inwards betwixt the lines that Bricmont considers comrade Rosenfeld a traitor. Marxists should live obliged to worship the Bohmist crap, shouldn't they?

Bricmont also attacks Margaret Thatcher at i betoken – because she liked to say "There Is No Alternative [to global capitalism]" (TINA). There are 2 problems: The truth values of Heisenberg's too Thatcher's statements aren't necessarily the same. And fifty-fifty if they were the same, it doesn't affair much because Bricmont is incorrect both almost politics+economics too almost quantum physics. There is just no damn option to global capitalism too Copenhagen quantum mechanics – too there's no other game inwards town than string theory, either. You should ameliorate used to these facts, comrades.

Finally, I am getting to the topic announced inwards the title

Florin Moldoveanu wrote a bizarre weblog post almost the claims that the "consistent histories" approach to quantum mechanics is inconsistent. This claim is to a greater extent than oftentimes than non copied from a newspaper past times Shelly Goldstein – a Bohmian philosopher at Rutgers whom I was seeing every calendar week piece he was writing the newspaper inwards the belatedly 1990s, too. Every skillful physicist should live able to meet what's incorrect with Goldstein's criticism of the consistent histories. Sadly, Bricmont too Moldoveanu aren't skillful physicists so they just can't meet anything.

Bricmont's mass describes the "Goldstein's proof of the inconsistency of consistent histories" around page 219. The setup chosen past times Goldstein is nada else than Hardy's paradox that I wrote almost inwards 2011 – or at most a tiny generalization of it.



In Hardy's paradox, the initial Earth is a singlet – or whatsoever maximally entangled Earth – of 2 qubits. I direct to interpret them equally 2 spins of spin-1/2 particles. Well, it's a singlet with an extra term that deforms it a lilliputian bit:\[

|\Psi\rangle = a |e_1\rangle|f_2\rangle + a|e_2\rangle|f_1\rangle - b |e_1\rangle|f_1\rangle

\] The normalization status is \(2|a|^2+|b|^2=1\). The get-go 2 damage are the commons "up down" minus "down up" states of the singlet that imply the perfect anticorrelation of the 2 spins (the sign or stage isn't equally good of import inwards this uncomplicated illustration but the Bohmists' persistent denial of the complexity of the amplitudes is a sign of their conflict with the mathematical apparatus of quantum mechanics that I mentioned above). The last, \(b\), term allows "up up" with a nonzero probability equally good but "down down" remains forbidden.



Fine, so the particle A's spin too the particle B's spin may live measured with honor to the vertical (unprimed) axis or some other (primed) axis. Now, inwards quantum mechanics, i time y'all mensurate the particle A's spin with honor to i axis, y'all alter the predictions for the other axis, so exclusively i of them may live measured during i repetition of the experiment if y'all desire to determine the pre-existing Earth of the spin.

Our initial Earth has the next iii implications for the predictions of the spin measurements:
  1. After the doubly unprimed measurements, \(A=+1\) too \(B=+1\) sometimes occurs
  2. After the mixed measurements, \(A=+1\) too \(B'=+1\) never occurs, too \(A'=+1\) too \(B=+1\) never occurs, either
  3. After the doubly primed measurements, \(A'=-1\) too \(B'=-1\) never occurs.
The get-go implication, i with the news "sometimes", follows from the \(b\) term inwards the state. The other implications follow from the special cast of the state, i.e. from the equality of the coefficients \(a\) for the get-go 2 term, too from the absence of the \(\ket{e_2}\ket{f_2}\) term.

In classical physics, the variables \(A,A',B,B'\) could live measured too their values would direct maintain to objectively be prior to the measurement. So these 4 observables would direct maintain to live numbers from the laid upwardly \(\{+1,-1\}\) that commute with each other. However, if y'all impose all the "never" weather from the list, y'all may deduce that \(A=+1\) too \(B=+1\) never occurs, either, contradicting the "sometimes" claim inwards our list.

Fine. All of us know why quantum mechanics allows these iii claims to live satisfied at the same moment: Quantum mechanics isn't classical physics, stupid. Mathematically, the betoken is that \(A,A',B,B'\) arrive at not commute with each other. In particular, \(A\) doesn't commute with \(A'\) too \(B\) doesn't commute with \(B'\) – similar different components of the spin \(\vec S\). The remaining commutators are null but these 2 nonzero commutators construct a difference.

The "never" claims may live written algebraically. Some "logical" expressions \(P_{2A},P_{2B},P_3\) involving the operators \(A,A',B,B'\) annihilate the initial Earth \(\ket\Psi\):\[

P_{2A}\ket\Psi =0, \quad P_{2B}\ket\Psi =0, \quad P_{3}\ket\Psi =0,

\] If the ket vectors were missing, too if the operators were commuting, similar inwards classical physics, y'all could occupation those equations to derive \(P_1=0\) equally well. But they don't commute too \(\ket\Psi\) isn't missing, so the implication (1) with "never" instead of "sometimes" doesn't follow from the remaining properties inwards quantum mechanics. You just can't derive \(P_1\ket\Psi=0\), the expected quantum counterpart of \(P_1=0\), using the algebraic manipulations from the iii displayed equations above.

Fine, simple, I spent to a greater extent than fourth dimension with this materials inwards the 2011 weblog post.

But now, inwards his heavily misguided "Quantum Theory Without Observers" [1997-98], Sheldon Goldstein claims that this Hardy's paradox implies that the consistent histories approach to quantum mechanics is inconsistent. Let me quote Goldstein equally reproduced on page 220 of Bricmont's book:
It is of import to appreciate that, for orthodox quantum theory (and, inwards fact, fifty-fifty for Bohmian mechanics), the 4 statements above, if used properly, are non inconsistent, because they so would refer but to the outcomes of 4 different experiments, so that the probabilities would refer, inwards effect, to 4 different ensembles. However, the whole betoken of DH is that such statements refer directly, non to what would tumble out were certainly experimental procedures to live performed, but to the probabilities of occurrence of the histories themselves, regardless of whether whatsoever such experiments are performed.
Goldstein sort of realizes that Heisenberg too pals would betoken out that \(A\) too \(A'\) cannot live measured inwards the same experiment (without changing i another), too similarly for \(B\) too \(B'\), so it's non a job that quantum mechanics implies that the get-go prediction may "sometimes" occur, piece it would live classically impossible.

But Goldstein claimed that inwards the decoherent (or consistent) histories, the contradiction does arise because the statements almost the variables \(A,A',B,B'\) direct maintain some probabilities to live truthful simultaneously.

Needless to say, Goldstein – too similarly Bricmont, Moldoveanu, too others who uncritically parrot him – is laughably wrong. It's the real betoken of the describing word decoherent or consistent inwards the phrase "decoherent histories" or "consistent histories" that these iii or 4 propositions cannot live discussed simultaneously. Just depository fiscal establishment check whatsoever basic introduction to consistent or decoherent histories, e.g. the introduction at Wikipedia, to meet that. One may say that the betoken of consistent or decoherent histories is exactly the contrary than the "main point" assigned to this approach past times Goldstein!

Consistent histories allow y'all to calculate the probabilities of some statements (about observables at many moments). These statements are branded equally "histories". But i time y'all calculate the probabilities of different histories inwards a set, this laid upwardly of histories must live consistent. The consistency of 2 histories is nada else than their orthogonality (well, a specific sesquilinear orthogonality of their "class operators"). And when y'all beak over histories that depend on the values of quantities \(A\) too \(A'\), the consistency or orthogonality is simply equivalent to the vanishing commutator of \(A\) too \(A'\).

So for 2 observables that y'all desire to mensurate at the same instant – too split the histories according to their values – the required "consistency" of the histories way nada else than the vanishing of the commutator of these 2 observables. So the "consistency" simply says exactly the same thing equally quantum mechanics ever does: noncommuting variables cannot live assumed to direct maintain some classical values at the same moment.

The consistent (=decoherent) histories approach to quantum mechanics just repackages the absolutely measure axioms too novelties of quantum mechanics into slightly different packages labeled with slightly different words. But the total "beef" contained inwards these packages is exactly the same equally it is inwards measure Copenhagen quantum mechanics. You just can't mensurate \(A\) too \(A'\) at the same instant – too analogously, y'all can't mensurate \(x\) too \(p\) at the same moment. It's non just y'all who can't mensurate it. No observer can. And an observer is needed to construct the values physically meaningful. So the values cannot simultaneously exist inwards the classical sense.

You know, I learned Consistent Histories from Roland Omnes who specifically admits that this approach to quantum mechanics is neo-Copenhagen – he realizes that the interpretation isn't really changing things or discovering whatsoever genuinely novel things beyond Copenhagen. It's just a way to reshuffle all the Copenhagen axioms too optimize them for predictions of properties of the physical organisation at many moments of time.

In private discussions, I've noticed that Jim Hartle too Murray Gell-Mann were to a greater extent than obscure almost the query whether they believe that that their interpretation is just a different repackaging of Copenhagen – too Griffiths, some other "consistent histories" guy, is obscure, too. I scream upwardly that none of them has ever said that "their interpretation has a qualitatively different pith than Copenhagen". But other people dear to propose so. In particular, y'all could direct maintain seen Goldstein who basically believes that "consistent histories" is some other endeavour to fully restore "realism" i.e. classical physics.

Sorry, it just can't live one.

In Bohr's Copenhagen jargon, nosotros may say that \(A\) too \(A'\) are complementary observables so they can't live assumed to direct maintain classical values simultaneously. In Heisenberg's or Pauli's or Dirac's Copenhagen jargon, nosotros notice that \(A\) too \(A'\) are non-commuting operators which direct maintain no simultaneous eigenstates so they can't live identified with \(c\)-number values at the same moment. So far so good, it's non difficult to meet that all the founders of quantum mechanics were really proverb the same thing fifty-fifty if the languages were a fleck different.

Consistent histories desire to alter the linguistic communication inwards a deeper way. We can't beak almost propositions that depend on \(A\) too \(A'\) because the splitting of the development to such histories would arrive at a laid upwardly of histories that aren't consistent with each other, too that's prohibited. Now, the previous judgement sounds different – too fifty-fifty when translated to equations, the equation looks different – but the message of the judgement is silent equivalent to the previous paragraph. One just can't mensurate complementary or non-commuting etc. observables inwards the same repetition of an experiment.

H5N1 reasonable many-worldist could really limited the same thought inwards completely different words, too. There is a splitting of the worlds when an experimenter decides whether he measures \(A\) or \(A'\) i.e. when he chooses the axis with honor to which the spin of a particle is measured. (Well, the reasonable many worlds are splitting when an experimenter decides what to measure, non when Nature decides what outcome he should get.) In some worlds, the experimenter close the particle H5N1 measures \(A\), inwards other worlds, he measures \(A'\), but in that location are no worlds inwards which he measures both \(A\) too \(A'\). Such worlds don't be too what happens inwards these non-existing worlds doesn't direct maintain to live discussed too doesn't demand to live "consistent". It's OK for the physical theory to prohibit the give-and-take of such things at the same moment.

The "reasonable many-worldist's story" conveys the same betoken equally Bohr's stories almost complementarity. Many-worlds champions are almost ever absolutely unreadable when it comes to key "detailed" questions – e.g. whether the worlds split when an experiment decides what he wants to mensurate or when Nature produces an outcome or both – but if a many-worldist is happy with the "splitting during the experimenter's decision" too proud almost the insight that "propositions almost measurements of \(A\) too \(A'\) don't direct maintain to live consistent with each other because they occur inwards different 'branches' of the many worlds", she should live sensible too respectful plenty to appreciate that this idea was realized past times Bohr too non Everett (or DeWitt) too has been known equally the Bohr complementarity earlier the idiotic anti-Copenhagen Marxist displace took off. You're just stealing the most precious ideas of scientific discipline if y'all claim that this insight due to Bohr was basically done past times Everett or someone else.

Obviously, there's no uncomplicated contradiction (as promoted past times Goldstein too his parrots) inwards the consistent histories approach to quantum mechanics. The real betoken of the interpretation is that i isn't allowed to beak over the truth value (or probability) of diverse propositions that are inconsistent – outcome from non-commuting, non-decoherent observables – at the same moment. My to a greater extent than full general betoken is that most people don't empathize quantum mechanics which also way that when y'all limited the same thought using 2 slightly different choices of the words, they're lost. They just can't meet that the ideas expressed inwards 2 languages (perhaps fifty-fifty inwards Dirac's English linguistic communication too Heisenberg's German) are the same.

There's some other "linguistic" divergence betwixt Copenhagen too consistent histories that the "realists" just desire to misunderstand, too it's the existence of the observers. In Copenhagen, y'all desire to emphasize that every application of a quantum mechanical theory requires an observer who chooses what he or she or it measures, perceives, too considers to live a measurement. Consistent histories seemingly avoid the words "observer", "observation", too "measurement" altogether.

Does it hateful that consistent histories are returning us to the epoch inwards physics inwards which observers aren't needed at all, inwards which they play no role?

If you're exclusively doing comparative literature too meet that the words "observer" direct maintain been eliminated from many consistent histories papers, y'all could say "Yes, the consistent histories direct maintain achieved this destination to eliminate observers again". But if y'all really empathize the pregnant of the claims almost physics too the implications of all the equations too mathematical propositions, y'all know that the morally right answer is "No".

Consistent histories may direct maintain eliminated the identification of an observer equally a subset of the physical objects inwards an experiment. But the consistent histories approach hasn't eliminated the demand for someone to determine what should live considered an observation i.e. what observables should live used equally sources of some ordinary, "classical" data that may live discussed or predicted. Whoever decides which laid upwardly of consistent histories y'all desire to beak over is the observer. They play exactly the same role. They are needed for quantum mechanics to live applied to whatsoever actual physical situation.

The selection of the "set of the consistent histories" isn't uniquely determined inwards general. Someone has to determine how the "pie" is split to the different histories. And the somebody or entity doing this conclusion is the observer. OK, y'all may imagine that it's some external somebody who isn't sitting inwards the lab at all too just writes equations. You may say that he's non the same guy equally the Copenhagen observer. So permit me clarify what I said: As long equally the laws of physics are beingness verified inwards whatsoever way, the somebody who is splitting the 100% pie into the private "consistent histories" is the same somebody equally the Copenhagen observer. It's the guy who really perceives the results of the measurements that ship the data which of the consistent histories has taken place.

The human linguistic communication wasn't optimized to beak almost quantum mechanics effectively too accurately. So it shouldn't live surprising that the attempts to interpret quantum mechanics to the human linguistic communication (or, if y'all wish, to the linguistic communication of journalists or philosophers) atomic number 82 to confusions, inaccuracies, equally good equally redundancies. The same thing may seemingly live said inwards many different ways that appear completely different to a linguist. But a physicist must empathize the pith of the principles too claims. It basically way that he must know how to occupation the rules inwards the most full general situations too meet why it's ever the same rules that are beingness applied. He doesn't demand to refine the "human language" needed to beak almost the physics – although I am too others are trying to refine it, anyway.

People should halt arguing – too physicists direct maintain basically stopped arguing – almost the selection of the "best words" when it seems real probable that 2 such physicists hateful the same "beef". Only philosophers debate almost different words whose pregnant is oftentimes undefined – too inwards particular, their differences are oftentimes undefined.

But in that location be disagreements almost physics that are sharper. For example, equally I mentioned, Bohmists desire to deny that the right underlying theory that most accurately describes the phenomena inwards the microscopic Earth uses linear operators too exactly linear operators too equations. And that the predictions are made inwards the cast of probabilities that are computed from complex probability amplitudes. When the disagreement gets this deep, the proponents of the "alternative interpretation" – Bohmists, inwards this instance – must acknowledge that they're trying to promote a totally different theory. And it's i that has absolutely no direct chances to compete against the right theory, quantum mechanics (defined past times the universal Copenhagen or equivalent postulates).

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