Postulates Of Quantum Mechanics Most Guide Follow From Experiments

Most of the ordinary people who take maintain tried to empathise modern physics discovery the novel logical framework of quantum mechanics challenging. Some of them take maintain acquire full-blown anti-quantum zealots which way that they scream "it cannot live on true", "physics must ultimately live on governed past times the logic of classical physics" – well, they love to utilisation different words but this is exactly what they mean.

Although many of these people may take maintain achieved diverse things, I discovery it impossible to consider these people intelligent. I take maintain explained the consistency of quantum mechanics (internal consistency too compatibility with observations) too the failure of whatsoever "realist" proposal to supersede quantum mechanics from many perspectives.

Here, I wishing to debate that it's pretty much obvious that sure experimental facts just cannot mayhap take maintain a different explanation than the precise framework of quantum mechanics.




Anti-quantum zealots love to separate the empirical noesis into tiny pieces. They ideally create something rattling specific – similar next Bell's recipe to entangle 2 spins inwards some way, stair out this too that (there is absolutely cypher exceptional or interesting nigh the item two-spin experiment discussed past times Bell) – too because it's thus specific, they fool themselves into thinking that at that spot must live on lots of theories different from the Copenhagen quantum mechanics that explains the observations every bit well.

They think that they just demand to acquire some mess for some randomness to arise, too there's a lot of mess everywhere, thus the work to explicate the "messy" observations must live on slow inside "realist" theories.




But this rattling methodology of thinking nigh every bit good item examples is just a stupid strategy to discovery the truth. It's really a deceitful method for those folks to delude themselves too others. Quantum mechanics isn't just a theory of Bell's two-spin experiment or 2 or iii or xx similar experiments. It's a theory of everything. Well, "a theory of everything" is normally meant to stand upwardly for quantum mechanics including the noesis of the dynamics ("the Hamiltonian" or whatever generalizes it). So maybe I should say that quantum mechanics is the framework for theories that explicate all experiments that take maintain ever been made – too most likely, all experiments that may live on done inwards the future, too.

And the randomness nosotros demand to explicate the information isn't just some "mess". In fact, it isn't whatsoever "mess" at all. It's a rattling item variety of randomness whose statistical features are exactly calculable from rattling prissy too elementary formulae inwards quantum mechanics. Outside quantum mechanics, yous take maintain no jeopardy to acquire the right formulae.

Why don't nosotros essay to theoretically explicate to a greater extent than full general empirical facts? What nigh the uncertainty principle? For \(x,p\), it says\[

\Delta x \cdot \Delta p \geq \frac\hbar 2.

\] But why don't nosotros verbalize nigh the doubtfulness regulation for 2 to a greater extent than full general observables \(A,B\) instead?\[

\sigma_A \sigma_B \geq \left| \frac{1}{2i}\langle[\hat{A},\hat{B}]\rangle \right| = \frac{1}{2}\left|\langle[\hat{A},\hat{B}]\rangle \right|.

\] You know, these \(A,B\) may live on functions of many observables such every bit \(x,p\) or fields, particles' spins, too other things. The inequality higher upwardly is an experimental fact that may live on verified on infinitely many choices of the pair \(A,B\) which may live on arbitrary functions or functionals of positions, momenta, spins, and/or fields.

Imagine yous take maintain zillions of graduate students. You split them into groups. Each grouping gets some selection of \(A,B\) too the business to minimize the production \(\sigma_A \cdot \sigma_B\). They volition piece of work hard. Because they're smart, their best i.e. minimized production volition live on exactly what the doubtfulness regulation requires. In some approximation, the commutator on the right manus side may live on approximated past times \(i\hbar\) times the classical Poisson bracket.

So there's some doubtfulness inwards Nature. Typically, if \(A\) is known accurately enough, almost all other quantities \(B\) take maintain to live on inaccurate. The outcomes of measurements of \(B\) are guaranteed to live on random too the distribution has a sure minimum variance that is calculable from the commutator of some operators – roughly from the Poisson bracket (times Planck's constant). Does it imply something big? You bet.

This outcome of the many graduate students – I suppose that the beloved reader isn't too stupid to think that they volition really acquire incorrect answers i.e. that quantum mechanics really fails – says that Nature doesn't comprise just "some" doubtfulness too "some randomness". The products of the variances – which stair out the amount of randomness – are just linked to the expectation value of the commutator i.e. the Poisson bracket of \(A,B\).

You tin essay it at arbitrary examples of \(A,B\) inwards mechanics or land theory, polynomial inwards \(x,p\) or to a greater extent than complex ones. So clearly, if yous wishing to predict some experimentally measurable quantities – such every bit the minimum \(\Delta H5N1 \cdot \Delta B\) inwards a given nation prepared experimentally – yous volition discovery out that the Poisson bracket is sort of important. And indeed, yous may easily discovery out that yous demand to supersede the Poisson bracket past times the commutator.

For example, yous may consider \(A,B\) to live on components of the spin of a spin-1/2 particle along 2 axes given past times unit of measurement vectors \(\hat a,\hat b\) i.e. \[

H5N1 = \hat a \cdot \vec j, \quad B = \hat b \cdot \vec j.

\] You may ready whatsoever initial nation of the spin of the spinning particle too stair out \(\Delta A\cdot \Delta B\). The inequality volition live on obeyed. Well, inwards many cases such every bit the spin, it volition non live on possible to saturate the inequality. But inwards the continuous examples, it is possible to saturate the inequality.

In proper quantum mechanics, yous may bear witness the inequality for whatsoever \(A,B\) too whatsoever nation inwards which yous wishing to stair out these 2 observables. It's a straightforward proof too its existence implies that quantum mechanics explains all these inequalities. The proof is thus straightforward that the pieces of the proof aren't just sufficient. They seem pretty necessary, too. If yous alter whatsoever slice that matters, the proof volition interruption down.

The proof plant because all the quantities that are inwards regulation observable – such every bit functions of \(x,p\) or fields or components of the spin – must live on assigned the corresponding observables which are linear operators on a complex vector space. All the observable quantities – observables – really must be represented past times non-commuting operators. To explicate the experiments past times the zillions of your graduate students, yous only demand a theory where all functions of \(x,p\) etc. are described past times a linear operator on the Hilbert space. Similarly, yous demand the predictions to live on predictions of the outcomes of the measurements of the observables (operators) too these probabilities must live on calculated via Born's rule.

Just essay to imagine that yous wishing to explicate the full general doubtfulness regulation inwards a "realist" i.e. fundamentally classical theory. So an anti-quantum zealot volition in all probability acknowledge that the operators are "useful" inwards some way but they're just a caricature of some "deeper", classical theory. Now yous must ask: Can such a hypothetical classical theory take maintain a justification for the doubtfulness principle? H5N1 argue that implies that if \(A\) is accurately measurable inwards the prepared state, \(B\) must live on less accurate, too vice versa? And tin it acquire the right fountain for whatsoever selection of \(A,B\)?

In a "realist" theory, if the outcome of the measuring of \(A\) too \(B\) that you're going to acquire is knowable inwards advance, there's just no argue why at that spot should live on some unavoidable uncertainty. It doesn't affair what is the precise type of your "realist" theory – many worlds, Bohmian mechanics, objective collapse theory, too thus on.

All these theories are "realist" which way classical when it comes to their basic logic. It way that at that spot exists the "set \(S\) of possible states" at the given 2d – when the laid is a continuum, nosotros telephone band \(S\) the stage infinite too nosotros should utilisation this terminology for a full general \(S\), too. \(S\) may comprise elements that cry back all the information nigh the airplane pilot moving ridge every bit good every bit the "actual" seat of the Bohmian particles; or all the information nigh the reveal of worlds inwards which Adolf Hitler has won, too everything else, if yous verbalize nigh the many worlds, too all such things.

In principle, the precise chemical element of \(S\) that describes the electrical current nation is knowable. So God may know the perfect values of \(x_i,p_i\) that parameterize the right betoken on the stage space. In practice, the precise betoken isn't known to a mortal too nosotros demand to push clit our noesis past times a probability distribution\[

\rho(x_i,p_i)

\] that is defined on the whole laid \(S\). OK, what is the minimum value of the production \(\Delta H5N1 \cdot \Delta B\) inwards a realist theory? Well, a realist theory admits God or a "super-observer" who just knows the right chemical element of \(X\in S\) earlier the measuring – regardless of the things that the imperfect human experimenters did at the showtime of the experiment when they were preparing the initial state. For that chemical element \(X\), at that spot are some values of \(A\) too \(B\) which God knows, thus He gets\[

\Delta H5N1 =0, \quad \Delta B = 0,\quad \Delta A\cdot \Delta B = 0.

\] In that world, graduate students don't take maintain whatsoever key obstruction that prevents them from approaching omniscient God increasingly closely, thus these graduate students may entirely derive a vacuous inequality\[

\Delta H5N1 \cdot \Delta B \geq 0.

\] Too bad, they acquire a much weaker inequality which way that they take maintain no explanation for the correct, stronger inequality – i that has a quantity proportional to \(\hbar\) on the right manus side.

This fatal affliction kills all realist theories, whether they were promoted past times David Bohm or whatsoever other fudging Bolshevik. All of these theories only predict that the minimum possible production of uncertainties is zero.

OK, if yous wishing him to fall, yous demand to shoot a Bolshevik thrice too hitting him with your hands, too. So these Bolsheviks volition protest. We are separated from God – whom they volition telephone band George Soros or Joseph Stalin. Let me utilisation the latter convention. So Joseph Stalin may know the precise \(X\in S\) with its value of \(A,B\) which way that His minimal \(\Delta H5N1 \cdot \Delta B\) is going to live on zero.

But the graduate students can't create sure things because their apparatuses are unavoidably messy, thus their \(\Delta A\cdot \Delta B\) volition live on the right fountain proportional to \(\hbar\).

Great theory, comrade. Now, all people are equal, right? What is it that allows Joseph Stalin to crush the uncertainties all the way to null piece the zillions of graduate students run across the fountain proportional to \(\hbar\) – a fountain that Joseph Stalin knows to live on spurious? Joseph Stalin is also equal to the students but he's fifty-fifty to a greater extent than equal, right?

Even if yous invented some qualitative story that "explains" that the students must live on expected to acquire a nonzero fountain on the uncertainties, it would live on just an infinitely minor percentage of the work that yous would take maintain to solve to justifiably claim that yous take maintain a feasible "realist" choice to (Copenhagen) quantum mechanics. To sensibly claim that yous take maintain an alternative, yous would really take maintain to offering a quantitative scheme that predicts the right lower fountain for whatsoever selection of \(A,B\). Even if the doubtfulness is just an artifact of the apparatuses' imperfection, these apparatuses are withal governed past times the laws of physics too the laws of physics must take maintain some explanation why their minimum doubtfulness ever seems to live on what the doubtfulness regulation claims, right?

This is an obvious yet huge business that none of the Bohms too similar stinky Bolsheviks has fifty-fifty attempted to solve. I think that all of them know that entirely the proper apparatus of quantum mechanics – inwards which the observables really are linear operators, too the calculable predictions really are subjective probabilities of outcomes – tin attain this triumph. The finish of the Bohmian, many-world, too similar theories is just to fake quantum mechanics – to "embed" quantum mechanics inwards some "realist" framework too claim that it's the improve one.

But there's a work with "faking". The things you're proposing are withal "fake". If the comrades essay to imitation the capitalist economic scheme but they impose all the Bolshevik constraints such every bit egalitarianism, they withal acquire just the communist economic scheme which totally sucks. The magic of capitalism too its prosperity strictly contradicts the communist axioms such every bit egalitarianism. You only can't imitation the capitalist economic scheme inside communism – too yous can't imitation quantum mechanics inside a "realist" theory.

Your "realist" theory doesn't fundamentally associate the observable quantities with linear operators. So it's infinitely unlikely that the millions of bounds obtained past times the zillions of graduate students volition grip with the quantum mechanical right manus side, \(\langle [A,B] \rangle\). The probability isn't just infinitely small. It's really \[

P \approx \frac{1}{\infty^\infty}

\] because at that spot are infinitely many experiments or choices of \(A,B,\ket\psi\), too for each of them, your fundamentally non-operator theory should predict the right lower fountain on the production of uncertainties. An infinite amount of fine-tuning would live on necessary for yous to imitation quantum mechanics inwards a "realist" theory – but fifty-fifty an infinite amount of fine-tuning wouldn't live on sufficient because Joseph Stalin withal knows that \(\Delta H5N1 \cdot \Delta B = 0\).

So the principal message of my text is that yous should ask:

Has mortal ever asked why the Bohmian theory or whatsoever other "realist" theory predicts the doubtfulness regulation with the right right manus side?

And the reply is a resounding No. No i has ever made fifty-fifty the tiniest initiatory off steps towards that goal. "Realist" theories really predict that yous should ever live on able to cut the uncertainties farther i.e. closer to zero. But the experiment speaks inwards a clear language. The production of uncertainties just can't acquire beneath the fountain proportional to \(\hbar\). The "realist" theories are falsified.

There's i cute, almost equivalent, way to kill the "realist" theories. And it's the universality of \(\hbar\). Tell all your teams of graduate students – who hadn't known Planck's constant to start with – to write the minimum value of their \(\Delta A\cdot \Delta B\) every bit \(\hbar \cdot \{A,B\}\) where the braces are the Poisson bracket too \(\hbar\) is a novel coefficient. The fascinating thing is that regardless of their \(A,B,\ket\psi\), all of them volition acquire the same value of \(\hbar\)!

This universality of Planck's constant is also totally incompatible with any realist theory only because realist theories don't take maintain too can't take maintain whatsoever universal constant whose units are those of \(\hbar\). There's just no room for such a constant inwards classical or "realist" physics! The classical Hamiltonian dynamics is fully given past times the Hamiltonian \(H\) whose units are just joules, but \(H\) isn't a universal constant too the scaling of \(H\) doesn't impact the development equation at all, anyway. All other universal constants inwards classical physics are diverse coefficients defining diverse damage inwards \(H\) etc. too those apply differently to different degrees of liberty – they are not universal. For example, if some students essay to decide the energy-to-frequency ratio, \(\hbar\) from \(E=\hbar\omega\), "realist" theories predict that they must acquire different values of \(\hbar\) from different particle species etc. H5N1 universal value of \(\hbar\) would live on an infinite amount of fine-tuning because at that spot can't live on a argue for that inwards a "realist" theory.

So if many groups of graduate students essay to extract a constant with units of \(\hbar\) from their experiment, it's basically guaranteed that each grouping volition take maintain a different reply for \(\hbar\): "realist" theories predict that nonzero quantities with the units of \(\hbar\) only cannot live on universal constants of Nature! This is perfectly falsified past times Nature where \(\hbar\) may live on extracted from infinitely many different experiments (with particles or fields or strings or branes of whatsoever kinds, or whatsoever combinations of those) too it ever has the same value, despite the high precision of the modern experiments.

"Realist" failure to acquire quantized measured values

The doubtfulness regulation is just i famous, too almost defining, outcome of the basic rules of quantum mechanics. But at that spot are many others. Such every bit the quantized spectrum of the energy. The hydrogen atom entirely has (in the non-relativistic approximation) the liberate energy levels\[

E_n = -\frac{E_0}{n^2}, \quad n\in\ZZ.

\] That tin live on seen inwards the emission or absorption spectra. The photons entirely take maintain liberate energy \(E_n - E_{n'}\). Great. Can a "realist" theory really predict the discrete liberate energy spectrum of atoms?

You may embed the mathematics of the moving ridge functions inwards your "realist" theory. But the interpretation of the moving ridge percentage volition live on incorrect – the moving ridge percentage volition live on misinterpreted every bit a classical moving ridge – too this misinterpretation has far-reaching consequences.

One of them is that every observable that yous tin stair out volition take maintain a continuous spectrum.

The argue is utterly simple. If yous translate the moving ridge percentage every bit a classical wave, your stage infinite \(S\) is a connected, infinite-dimensional continuum. It's every bit continuous every bit yous tin get. If your apparatus ends upwardly measuring the liberate energy of a photon, \(E_\gamma\), yous know that a priori, all positive values of the liberate energy of a full general photon must live on allowed. If the transformation mapping the initial nation to the concluding nation is continuous inwards whatsoever way, it's obvious that yous may perturb the desired concluding value of \(E_\gamma\), run the development backwards, too discovery an appropriately perturbed initial nation that leads to this non-quantized value of the photon's energy.

Bohm's theory can't live on constructed for relativistic particles such every bit photons (Quantum Electrodynamics) but a Bohmist would sure enough say that they explicate the measured quantized liberate energy because the airplane pilot moving ridge gets reduced to several beams too the existent Bohmian particle is inwards i of them. Great but this sleight-of-hand won't piece of work if yous stair out other observables that aren't reduced to positions – such every bit the voltages inwards our encephalon which is how nosotros really perceive things at the end.

All "realist" theories are inwards serious, too generally fatal, tension with the quantized spectrum of many observables.

There are many to a greater extent than rudimentary, universal, empirical facts nigh the globe governed past times quantum mechanics that really directly kill all "realist" theories. But iii is plenty for today thus allow me advert the concluding one:

Another fact nigh quantum mechanics: If yous brand a measuring of the observable \(L\) too the moving ridge percentage collapses to an eigenstate \(\ket\psi\) of that observable, all the parts of the moving ridge percentage that "existed" (outcomes that were possible) earlier the measuring completely disappear too they take maintain exactly zero impact on anything afterward the measuring of \(L\).

Now, this is an extremely full general empirical fact – i.e. a fact that yous may experimentally banking concern check inwards millions of different situations involving thousands of different physical systems, particles of all types, with or without spins, fields, strings, branes, whatever yous like.

Prepare the electron with its spin along some axis \(\hat n\). Measure \(j_z\). You volition acquire "up". Then all the probability distributions are fully calculable from the novel initial nation "up". The erased parts of the collapsed moving ridge functions are totally eradicated, totally forgotten. You may create anything to your experiment, essay ingenious methods to persuade your clever apparatus to "remember" or "recall" the erased parts of the moving ridge function. But your clever apparatuses volition non live on able to say anything nigh the reveal \(a\) that defined the nation earlier the collapse\[

\ket \psi = \frac{ \ket\uparrow + a \ket\downarrow }{\sqrt{1+|a|^2}}

\] Once yous know that the spin is "up", the coefficient \(a\) is laid to zero. Precisely too genuinely. No kidding.

If yous think nigh it for a second, this footling fact totally contradicts whatsoever natural (not fine-tuned) "realist" theory. Take Bohmian mechanics every bit an example. In that "realist" theory, there's the objective airplane pilot wave, a classical field/wave whose numerical values are chosen to imitation the quantum mechanical moving ridge function, too and thus at that spot are the objective "real" positions of the particles.

Now, the airplane pilot moving ridge guides the "real" particle somewhere, too yous may stair out the existent particle too say something nigh the spin – Bohmian mechanics doesn't allow the spin direct thus the spin measuring has to live on reduced to some measuring of the position. So the Bohmian particle is known to live on at the house corresponding to "up". However, the airplane pilot moving ridge withal exists inwards the part that would agree to "down", too.

The betoken is that this "wrong percentage of the airplane pilot wave" hasn't been cleaned or forgotten. This airplane pilot moving ridge is coupled to other degrees of liberty inwards the physical organization thus inwards principle, it should live on observable. However, experiments clearly say that whatever yous do, yous just can't discovery this "wrong percentage of the moving ridge function". To avoid the contradiction with the basic empirical facts, the Bohmian mechanics really needs some "janitors" that take away the zombie parts of the airplane pilot moving ridge at places where the particle wasn't seen.

It's non just some aesthetic requirement for David Bohm to hire the illegal Mexican comrades. He really fudging needs it because if that mess isn't cleaned, his theory predicts that the mess volition almost certainly demo upwardly inwards some doable measurements. This mess is coupled to the degrees of liberty remembering particles "genuine" seat thus whatever is done, this mess volition live on imprinted into some time to come measurements – which is non observed.

To say the least, the janitor hired past times David Bohm has to brand the development irreversible because cleaning is irreversible. You know, inwards quantum mechanics, there's absolutely cypher incorrect nigh the irreversibility of the measurement. Measurements are fundamentally irreversible because the learning of the novel information (just similar inwards the classical Bayesian inference – too the collapse of the moving ridge percentage is just a complex, non-commuting generalization of Bayesian inference) has a logical arrow of time. Schrödinger's equation governing the development of the moving ridge percentage – the probability aAmplitude – is withal perfectly reversible.

However, if the moving ridge percentage is "faked" too misinterpreted every bit some classical wave, all hell breaks loose. Your laws of physics take maintain to include the irreversible janitors which brand the key classical transformations – the percentage of your theory that is governed past times analogous differential equations every bit Schrödinger's equation – irreversible. That's also bad because the reversibility of Nature at the key aeroplane is another experimental fact.

In quantum mechanics, all the irreversibility entirely exists at the subjective or psychological level. "Realist" imitations of quantum mechanics don't take maintain whatsoever subjective or psychological level. So they either include janitors which violate the experimental fact nigh the key reversibility of all unobserved processes inwards Nature; or they violate the experimental fact that the "not realized" percentage of the moving ridge percentage is perfectly forgotten.

The "realists" don't bother to enjoin yous which of these 2 failures they prefer. They don't hash out their janitors. That's rattling ironic because these janitors are totally essential to take maintain a coherent theory of the measurement. Quantum mechanics has a coherent story nigh the measuring – it's a percentage of the universal postulates. The anti-quantum zealots didn't similar something nigh the "measurement theory" inwards quantum mechanics (because it differs from the classical physics' story nigh the measuring which is the entirely "acceptable" i for them) too that was their excuse to pursue "realist" theories inwards the initiatory off place. But because they say cypher nigh the janitors – non fifty-fifty whether they should be – they acquire inwards clear that the anti-quantum zealots take maintain cypher to say nigh the measuring at all!

Whatever they would essay to say nigh the cleaning of the not-realized portions of the moving ridge function, it just doesn't piece of work too it doesn't affair at all into which sect of the anti-quantum zealots – Bohmian, many-worlds etc. – a given Bolshevik belongs. (Well, inwards "many worlds", some information may live on totally forgotten past times beingness thrown away into a "different world" but the irreversibility – why yous cannot furnish dorsum from a different globe – remains unexplained too if it holds, a massive fine-tuning has to live on present. Moreover, if it's really impossible for the "different world" to influence yours again, that "different world" should live on considered unphysical according to the empirical or operational rules.)

The "realist" theories are just old-fashioned classical theories which fundamentally contradict the doubtfulness principle, the universality of Planck's constant, the quantization of liberate energy too other observables, too the elimination of the non realized parts of the moving ridge percentage and/or the reversibility of all unobserved processes inwards Nature – with other key facts that I discussed elsewhere. And all the people persistently (in 2018) trying to negate the basic rules of the game every bit articulated inwards Copenhagen are morons – sadly, inwards most cases, pompous morons.

And that's the memo.