The quantum mechanics is a non-universal theory. The realistic Schrodinger's and positivistic Born's interpretation of the wave function
aa r X i v : . [ phy s i c s . h i s t - ph ] N ov The quantum mechanics is a non-universal theory.The realistic Schrodinger’s and positivistic Born’s interpretation of the wave function
Alexey Nikulov
Institute of Microelectronics Technology, Russian Academy of Sciences,142432 Chernogolovka, Moscow District, Russia E-mail: [email protected]
The controversies about quantum mechanics, in the old days and present-day, reveal an inconsis-tency of understanding of this most successful theory of physics. Therefore it is needed to set forthunambiguously what and how quantum mechanics describes in order to cut down the number ofthe fantasies trying to eliminate the fundamental obscurity in quantum mechanics. In this chapterreader’s attention is drawn first of all to a non-universality of quantum-mechanical descriptionsof different quantum phenomena. The realistic interpretation of the wave function proposed bySchrodinger is used at the description of most quantum phenomena whereas the controversies touchon the positivistic interpretation proposed by Born. These controversies are result, in the main, ofthe misinterpretation, proposed by Bohr, of the orthodox quantum mechanics. Most physicists, fol-lowing Bohr, did not want to admit that Born had assumed in fact a mutual causal relation betweenquantum system and the mind of the observer. The EPR correlation is non-local and quantummechanics predicts violation of the Bell’s inequalities because of non-locality of the mind of theobserver. The quantum postulate and complementarity proposed by Bohr are valid according torather hidden-variables theories than the orthodox quantum mechanics. Measurement is describedas process of interaction of quantum system with the measuring device in hidden-variables theoriesalternative of quantum mechanics. It is shown, that the mutual causal relation between ’res extensa’and ’res cogitans’, presupposed with the Born’s interpretation, results to a logical absurdity whichtestifies against the self-consistency of the orthodox quantum mechanic. This self-contradiction isa consequence of logical mistakes inherent in a new Weltanschauung proposed by Heisenberg for aphilosophical substantiation of quantum mechanics. Quantum mechanics is successful in spite ofthis absurdity and these mistakes because rather the realistic Schrodinger’s interpretation than thepositivistic Born’s interpretation is used at the description of the majority of quantum phenom-ena. The act of measurement and the fundamental obscurity connected with it are absent at thisdescription. But there are other fundamental obscurities which are considered in the last section.
Contents
1. Introduction2. What is implied with the Born’s interpreta-tion of the wave function?2.1. ’Measurement’ might be complete only inthe mind of the observer2.2. EPR correlation and the non-locality ofthe mind2.3. Violation of Bell’s inequalities uncovers theinfluence of subject on object2.4. What EPR intended to prove and whatthey have proved2.5. Hidden variables2.6. Indeterminism of quantum mechanics. Theentanglement of cat with atom states2.7. Whose knowledge and whose will?3. New Weltanschauung proposed by Heisen-berg3.1. Quantum mechanics rejects the Cartesianpolarity between ’res cogitans’ and ’res extensa’3.2. The notion of the ’thing-in-itself ’ by Kantand hidden-variables3.3. The Kantian a priori character of the lawof causality and quantum mechanics4. Fundamental mistakes by sleepwalkers4.1. The quantum postulate and complemen-tarity proposed by Bohr ’objectivate’ observation 4.2. The mass delusion and the idea of quantumcomputation4.3. Two principal mistakes of Heisenberg5. Fundamental mistakes because of the preju-dice of the QM universality5.1. The Aharonov - Bohm effects are describedboth with the ψ - functions and the wave function5.2. We can believe for the time being in realityof the moon6. Fundamental obscurity connected with wavefunction usage6.1. Puzzles generated with the quantum for-malism6.2. Experimental results which can not be de-scribe with help of the quantum formalism7. Conclusion
1. INTRODUCTION
Quantum mechanics (QM) is the most successful the-ory. It has given rise to revolutionary technologies ofthe XX century. The progress of physics of last centuryare fairly connected with the QM. But John Bell said inhis Introductory remarks ”Speakable and unspeakable inquantum mechanics” at Naples-Amalfi meeting, May 7,1984 that ”
This progress is made in spite of the funda-mental obscurity in quantum mechanics ”, see p. 170 in[1]. This fundamental obscurity as well as QM are re-sult of the proposal by young Werner Heisenberg [2] todescribe observables instead of beables, see these termsin the Bell’s paper [3]. This proposal to abandon anyattempt to find a unified picture of objective reality hadprovoked the battle between creators of quantum the-ory. Bohr, Pauli, Dirac and others admitted the Heisen-berg’s proposal whereas Einstein, Schrodinger, de Broglieand others rejected the repudiation of the science aim asthe discovery of the real. Schrodinger interpreted hiswave function as a real wave [4] and defended this real-istic interpretation [5]. He tried to replace particles bywavepackets. ”But wavepackets diffuse” [6]. This diffuse-ness contradicts numerous observation. Therefore the in-terpretation of the Schrodinger’s wave function as prob-ability amplitudes proposed by Born was fully acceptedby most physicists. This positivistic interpretation corre-sponds to the Heisenberg’s proposal and just therefore itresults to the fundamental obscurity and mass delusion.Indeterminism, subjectivity, non-locality and vaguenessimplied with this interpretation are enough obvious. Butonly few physicists, Einstein, Schrodinger, de Broglie andsome others worried about these ”philosophical” prob-lems during a long time. Most physicists, as Bell said ”stride through that obscurity unimpeded... sleepwalk-ing?” , see p. 170 in [1]. Bell worried about this obscu-rity of positivistic QM but even he said: ”The progressso made is immensely impressive. If it is made by sleep-walkers, is it wise to shout ’wake up’? I am not surethat it is. So I speak now in a very low voice” , see p. 170in[1].But now it is needed to shout ”wake up” [7]. There aresome reasons why it is needed: 1) numerous false pub-lications because of misunderstanding of QM [7–9]; 2)misunderstanding of the idea of quantum computation[10]; 3) some authors, because of their implicit belief inQM, claim already that it is possible to prove experi-mentally that ”The moon - a small moon, admittedly -is not there” [11]; 4) on the other hand many physicistshave already refused this implicit belief in QM. The moststriking illustration of the fourth reason is the Actionof the European Cooperation in Science and Technology”Fundamental Problems in Quantum Physics” [12]. Thefirst aim of research - observer-free formulation of QMwitnesses to perception by numerous participants of theAction MP1006 that no subjectivity can be permissiblein any physical theory. But I should say that only thisperception does not indicate that these scientists have’waked up’ completely.They have not realized for the present a primary logi-cal mistake of the sleepwalkers creating QM. Scientistshave in mind always that any physical theory shoulddescribe universally all its subject matters. For exam-ple, everyone believes that the Newton’s laws describeuniversally the motion of all object with different mass,from major planets to smallest particles. This belief maybe justified with a universality of the laws governing aunique objective reality. Orthodox QM, in contrast to all others theories of physics, describes rather differentphenomena than a unique reality. No description of phe-nomena should be universal if they are not considered asa universal manifestation of a unique reality. Thereforeit is logical mistake to think that QM should describeuniversally all quantum phenomena. Nevertheless QMwas developed and interpreted up to now as a univer-sal theory. General confidence predominates that onlythe positivistic Born’s interpretation but not the realisticSchrodinger’s interpretation can be valid for descriptionof all quantum phenomena.This confidence is obviously false. Richard Feynmanin the Section ”The Schrodinger Equation in a ClassicalContext: A Seminar on Superconductivity” of his Lec-tures on Physics [13] stated that Schrodinger ”imaginedincorrectly that | Ψ | was the electric charge density of theelectron. It was Born who correctly (as far as we know)interpreted the Ψ of the Schrodinger equation in termsof a probability amplitude” . But further Feynman wrotethat ”in a situation in which Ψ is the wave function foreach of an enormous number of particles which are all inthe same state, | Ψ | can be interpreted as the density ofparticles” . Thus, Feynman had pointed out that the pos-itivistic Born’s interpretation could be replaced with therealistic Schrodinger’s interpretation at the description ofmacroscopic quantum phenomena, at least. This fact hasfundamental importance because ”There are two funda-mentally different ways in which the state function canchange” [14] according to the Born’s interpretation: thediscontinuous change at the observation (Process 1 ac-cording to [14]) and the continuous deterministic changeof state of an isolated system with time according toa Schrodinger’s wave equation (Process 2 according to[14]). Hugh Everett noted correctly that because of theProcess 1 ”No way is evidently be applied the conven-tional formulation of QM to a system that is not subjectto external observation” and that ”The question cannotbe ruled out as lying in the domain of psychology” [14].But only select few realized this fundamental obscurity inQM in that time. Feynman did not realized. Thereforehe did not attach great importance to the replacement ofthe Born’s interpretation by the Schrodinger’s interpre-tation. Feynman did not understand that the Process 1,and all fundamental problems connected with it, disap-pear at this replacement.Richard Feynman and Hugh Everett were doctoral stu-dents of the same doctoral advisor - John ArchibaldWheeler. But their conception of QM was fundamen-tally different. Such dissent marks out QM from othertheories of physics. The dissent was from the very out-set of QM. It was observed both between defenders ofQM, for example Heisenberg and Bohr, and its critics,for example Schrodinger and de Broglie. But now thediversity of opinion is unusually wide. Einstein wroteas far back as 1928 to Schrodinger [15]: ”The soothingphilosophy-or religion?-of Heisenberg-Bohr is so cleverlyconcocted that it offers the believers a soft resting pillowfrom which they are not easily chased away” , see the citeon the page 99 of [16]. The diversity of opinion about QMwitnesses that Einstein’s words turned out prophetic: thedissent can be about a religion but our right comprehen-sion must be unified. At least we must believe that it ispossible. Otherwise no science could be possible. There-fore first of all it is important to show that subjectivity,non-locality, indeterminism and vagueness of QM are de-duced unambiguously from the Born’s interpretation. Itwill be made in the next Section. This positivistic in-terpretation can be valid and understood correctly onlyin a new Weltanschauung proposed by Heisenberg. Thisnew Weltanschauung will be considered shortly in theSection 3. Unfortunately only few scientists have re-alized that the correct understanding of QM demandsthe new Weltanschauung. Both mass delusion connectedwith this lack of understanding and mistakes made byHeisenberg will be considered in the Section 4. Mistakesof other type connected with the misinterpretation ofquantum mechanics an a universal theory will be con-sidered in the Section 5. The fundamental obscurities inquantum mechanics worrying Einstein, Schrodinger, Belland others disappear with the realistic interpretation ofwave function proposed by Schrodinger. But other fun-damental obscurities appear with this realistic interpre-tation. These fundamental obscurities of other type willbe considered in the Section 6.
2. WHAT IS IMPLIED WITH THE BORN’SINTERPRETATION OF THE WAVE FUNCTION?
Feynman wrote [13] when Schrodinger ”imagined in-correctly that | Ψ | was the electric charge density of theelectron He soon found on doing a number of problemsthat it didn’t work out quite right” . Schrodinger had triedto replace ’particles’ by wave-packetsΨ( r ) = Z ∞−∞ dp [ A ( p ) exp − i ~ Et ] exp i ~ pr (1)But this wave-packets spreads in empty space, for exam-ple, when the energy E = p / m . Therefore the realwave-packets cannot explain the observations of parti-cle localized in the space, for example particle tracks intrack chambers. Because of this and other defectionsof the Schrodinger’s interpretation most physicists hadaccepted the Born’s interpretation. Most of they strideunimpeded through the nonsense that the wave-packetscan be localized only under influence of the mind of theobserver. Feynman wrote [13] that Born had proposed ”very dif-ficult idea that the square of the amplitude is not thecharge density but is only the probability per unit volumeof finding an electron there, and that when you do find the electron some place the entire charge is there” . Feynmanwas sure that this idea is correct because he did not raisethe question: ”How can the entire charge be there whenan observer has found the electron some place?” Let con-sider the electron in empty space, or better a fullerene, oreven a long biomolecule, quantum interference of whichwas observed already [17, 18]. Quantum state of suchparticle can be described with the wave-packets (1) inwhich the wave functions expi ( pr − Et ) / ~ are deducedfrom the Schrodinger’s wave equation [19] i ~ ∂ Ψ ∂t = − ~ m ∇ Ψ + U ( r )Ψ (2)whereas the amplitudes A ( p ) can be estimate only withhelp of an observation at a time t = 0. According to (2) E = p / m in empty space where U ( r ) = 0. It is possi-ble, for example with help of the scanning laser ionizationdetector used in [20], to observe at t = 0 that a fullerene,for example, is localised in a space region ∆ r near r = 0.The result of this observation may be describe approx-imately with the probability density function Ψ( r ) =(2 π ) − / σ − / exp ( − r / σ ) [13] where σ ≈ ∆ r/
3. Thewave-packet (1) diffuses, Fig.1, because its amplitudes,equal A ( p ) = (8 π ) / σ / exp ( − p σ / ~ ) at t = 0,change with time A ( p, t ) = (8 π ) / σ / exp ( − p σ / ~ − ip t/ ~ m ). Because of this Process 2 [14] the probabil-ity to observe the particle in a space region near r = 0decreases and far off r = 0 increases with time, Fig.1.The Process 2 is continuous and is determined with theSchrodinger’s wave equation (2). But the discontinuouschange of the probability | Ψ( r, t ) | and the wave-packetΨ( r, t ) at an observation, i.e. the Process 1 [14], can notbe described with this equation (2).The Process 1, at t = t for example, Fig.1, cannot bedescribed outside the domain of psychology. Everett [14]was right. No physical interaction of the particle withphotons radiated with laser or any measuring device cancompact the wave-packet. It is quite obvious that ac-cording to the Born’s interpretation the wave-packet issqueezed in a smaller volume because of the observationby an observer the particle near, for example, r ≈ t < t he conjecturedto see the particle in any space region with a probability | Ψ( r, t ) | . His knowledge changes discontinuously whenhe sees the particle near r ≈
8, Fig.1. Such change of theknowledge takes place at any observation. Schrodingernoted that ” · · · the simple statement, that each observa-tion depends both from the object and the subject which’are entangled’ by extremely complex manner is a state-ment which is hardly possible to consider new, it is oldalmost also, as the science” [21]. But according to QM ” · · · the causal interconnection between the subject andobject is considered reciprocal. It is stated, that the unre-movable and uncontrollable influence of the subject on theobject takes place” [21]. According to the Born’s inter-pretation both the observer knowledge and the quantumstate change at the observation. FIG. 1: The initial conditions, i.e. the amplitudes A ( p ) ofthe wave-packet (1) are determined with results of an externalobservation at a time moment t = 0, i.e. during the Process1, when the quantum state changes discontinuously under in-fluence of an external observer (the upper picture). Quantummechanics can predict the probability | Ψ( r, t ) | per unit vol-ume of finding the particle in any space place r at any timemoment t (the middle picture) using the initial conditionsand the Schrodinger’s wave equation (2). But no physicalinteraction of the particle with an agency of observation de-scribed with the Schrodinger’s wave equation (2) can compactthe wave-packet (the bottom picture) and provide with newinitial conditions. The initial conditions can be provided onlythe mind of the observer who has found the particle someplace. It could be clear from the very outset that according tothe Born’s interpretation the observation should be inter-preted unambiguously as interplay between the quantumsystem and the mind of the observer. But Heisenberg andBohr had convinced most physicists that we can considerthe act of the observation (measurement) as an interac-tion between quantum system and measuring instrument.The famous [16] Heisenberg uncertainty microscope [22],the quantum postulate and complementarity by Bohr [23]have misled some generations of physicists. Even the fa-mous EPR paper [24] and the Bell’s works [1] could notundeceive most physicists about this error up to now.Bell wrote in 1989 [24] about the paper ’Ten theoremsabout quantum mechanical measurements’, by NG vanKampen [26] ”This paper is distinguished especially byits robust common sense. The author has no patiencewith ’ · · · such mind-boggling fantasies as the many worldinterpretation · · · ’. He dismisses out of hand the notionof von Neumann, Pauli, Wigner - that ’measurement’might be complete only in the mind of the observer: ’. .. I find it hard to understand that someone who arrivesat such a conclusion does not seek the error in his argu-ment’” . There is important to remind that Everett hadproposed the many world interpretation in order to de-scribe the Process 1, i.e. ’measurement’, as lying outsidethe domain of psychology [14]. But the believers in thesoothing philosophy or religion of Heisenberg-Bohr rejectflatly, as well as van Kampen [26], both the mind of theobserver and the many world interpretation. Althoughit must be obvious that the attempt by Heisenberg andBohr to propose the realistic substantiation of the un-certainty principle was false it is needed to explain againand again that EPR correlation and Bell’s inequalitieshave proved this obvious fact.
Bell wrote in 1981 [27]: ”The philosopher in the street,who has not suffered a course in quantum mechanics,is quite unimpressed by Einstein-Podolsky-Rosen corre-lations. He can point to many examples of similar cor-relations in everyday life. The case of Bertlmann’s socksis often cited. Dr. Bertlmann likes to wear two socks ofdifferent colours. Which colour he will have on a givenfoot on a given day is quite unpredictable. But when yousee that the first sock is pink you can be already sure thatthe second sock will not be pink” . The last sentence de-scribes the influence of the object (the first sock) on thesubject (the mind of the observer). Such influence canastonish nobody because ”it is old almost also, as thescience” [21]. Bell asked: ”And is not the EPR businessjust the same?” [27]. He considered a particular versionof the EPR paradox [24], developed by David Bohm [28],i.e. the Einstein-Podolsky-Rosen-Bohm gedanken exper-iment with two spin 1/2 particles. Quantum mechanicsdescribes the spin states of two separate particles withtwo separate equations ψ A = α A | ↑ A ( r A ) > + β A | ↓ A ( r A ) >ψ B = α B | ↑ B ( r B ) > + β B | ↓ B ( r B ) > (3)where the probability amplitudes α A , β A , α B , β B dependon a free choice of a certain axis along which the compo-nent of particle spin will be measured and | α A | + | β A | =1, | α B | + | β B | = 1 always. The spin state of pair of twoseparate particle may be described also with the productof the equations (3) in which the amplitudes γ = α A α B , γ = α A β B , γ = β A α B , γ = β A β B and as a conse-quence γ γ = α A α B β A β B = γ γ = α A β B β A α B . TheEPR correlation takes place when γ γ = γ γ and thespin states of the particles cannot be separated. Twoparticles in the singlet spin state ψ EP R = γ | ↑ A ( r A ) ↓ B ( r B ) > + γ | ↓ A ( r A ) ↑ B ( r B ) > (4)when γ = 0, γ = 0, and γ = 0, γ = 0 is called EPRpair. The axis along which the component of particlespin will be measured is the direction of a non-uniformmagnetic field produced by magnets of a Stern-Gerlachanalyzer [16]. The particles will deflect up in the state | ↑ > and down in the state | ↓ > . The observers A (Alice)and B (Bob) can choose any direction of their analyzer’saxis. Whether either particle separately goes up or downon a given occasion is quite unpredictable. But accordingto the basic principle of quantum mechanics formulatedby Dirac as far back as 1930 [29] ” · · · a measurement al-ways causes the system to jump into an eigenstate of thedynamical variable that is being measured” . This Diracjump, wave function collapse [30], or ”’quantum jump’from the ’possible’ to the ’actual’” [31] must take placelogically during the act of observation because Alice can-not see that one particle deflects up and down simulta-neously. When Alice sees that the particle deflects up inher Stern-Gerlach analyzer directed along an axis n thespin state of the EPR pair (4) changes discontinuouslyto the eigenstate ψ n = | ↑ A ( r A ) ↓ B ( r B ) > n (5 a )or to the eigenstate ψ n = | ↓ A ( r A ) ↑ B ( r B ) > n (5 b )when the particle deflects down. Thus, according tothe basic principles of quantum mechanics deduced logi-cally from the Born’s interpretation one particle A of theEPR pair (4) goes up the other B always goes down andvice-versa when axis of two analyzers located at widelyseparated points in space r A and r B is directed in thesame direction n . This EPR correlation should be non-local because of the opportunity to observe the deflec-tion of the particle A and the particle B at the sametime independently on the distance | r A − r B | betweenthe Stern-Gerlach analyzers. This non-locality is deduced unambiguously from the Born’s interpretation as a con-sequence of non-locality of the mind. Heisenberg noted: ”Since through the observation our knowledge of the sys-tem has changed discontinuously, its mathematical rep-resentation also has undergone the discontinuous changeand we speak of a ’quantum jump’” [31]. He justified the’quantum jump’ with help of the fact that ”our knowl-edge can change suddenly” [31], i.e. the obvious fact thatthe knowledge of Alice, for example, changes at the in-fluence of the object, the deflection of the particle, onthe subject, her mind. Already before the observationthe Alice knowledge about the probability of the deflec-tion up or down of particles A and B is entangled. Sheknows that if the deflection of one particle, for exam-ple A , will be up than the deflection of other particle B should be down. Thus, the EPR correlation (4) describesthe entanglement of the Alice knowledge about the spinstate of two particles. Therefore, motivated [32] by EPR[24], Schrodinger coined [33, 33] the term ”entanglementof our knowledge” : ”Maximal knowledge of a total sys-tem does not necessarily include total knowledge of allits parts, not even when these are fully separated fromeach other and at the moment are not influencing eachother at all” . Maximal knowledge of a total system in-clude total knowledge of all its parts in the case (3) when γ γ = γ γ but not in the case (4) when γ γ = γ γ .In his last talk [35] Bell considered the question: ”Whatcan not go faster than light?” He said: ”The situation isfurther complicated by the fact that there are things whichdo go faster than light. British sovereignty is the clas-sical example. When the Queen dies in London (may itlong be delayed) the Prince of Wales, lecturing on modernarchitecture in Australia, becomes instantaneously King,(Greenwich Mean Time rules here)” [35]. There is im-portant to define more exactly that the Prince of Walesbecomes instantaneously King in the mind of witnesses ofthe Queen death. Like manner the spin state of the dis-tant particle B changes instantaneously from (4) to (5a)in the mind of Alice when she sees that her particle A hasdeflected up. The analogue of the British sovereignty inthe EPR correlation is the Dirac jump, or wave functioncollapse, which should be at the Process 1. But thereis a fundamental difference of the Dirac jump from theBritish sovereignty. The witnesses of the Queen deathcannot have an influence on the Prince of Wales whereasAlice can govern the spin state of the distant particle B .Each of the eigenstates (5a) and (5b) of the operator ofthe spin component along n (this dynamical variable) issuperposition of eigenstates of the spin component alongother direction (other dynamical variable) [19]. Supposethat initially Alice had chosen to orient the non-uniformmagnetic field of her Stern-Gerlach analyzer perpendic-ular to the line of flight of the approaching particle, they-axis, and pointing vertically upward along the z-axis.And Bob had oriented his non-uniform magnetic fieldalso perpendicular to the y-axis but at an angle ϕ to thez-axis. Than the EPR pair jumps discontinuously to thestate ψ z = | ↑ A,z ↓ B,z > = cos ( ϕ/ | ↑ A,ϕ ↓ B,ϕ > ++ sin ( ϕ/ | ↓ A,ϕ ↑ B,ϕ > (6 a )when Alice will see that her particle has deflected up andto the state ψ z = | ↓ A,z ↑ B,z > = − sin ( ϕ/ | ↑ A,ϕ ↓ B,ϕ > ++ cos ( ϕ/ | ↓ A,ϕ ↑ B,ϕ > (6 b )when her particle has deflected down. The operator ofthe turning round the y-axis [19] is used hear and below.Each of these states is the eigenstate of the operator cor-responding to the orientation on the Alice analyzer butit is superposition the eigenstates of the operator corre-sponding to the orientation on the Bob analyzer. Alicecan turn her Stern-Gerlach analyzer on an angle θ duringthe flight of the particles of the EPR pair (4). This turnchanges the spin states of both her and Bob’s particleafter her observation to ψ θ = | ↑ A,θ ↓ B,θ > = cos (( ϕ − θ ) / | ↑ A,ϕ ↓ B,ϕ > ++ sin (( ϕ − θ ) / | ↓ A,ϕ ↑ B,ϕ > (7 a )if her particle has deflected up and to ψ θ = | ↓ A,θ ↑ B,θ > = − sin (( ϕ − θ ) / | ↑ A,ϕ ↓ B,ϕ > ++ cos (( ϕ − θ ) / | ↓ A,ϕ ↑ B,ϕ > (7 b )if it has deflected down. Thus, the EPR correlation re-veals that quantum mechanics concedes that Alice canchange instantaneously the quantum state of the distantparticle with her will and her observation. According tothe Born’s interpretation she can act faster than lightthanks to non-locality of her mind. Heisenberg justified [31] the discontinuous change con-ceded quantum mechanics with the argument that ourknowledge of the system changes discontinuously at anyobservation. But quantum mechanics represents not onlyour knowledge. It predicts first of all the probability ofdifferent outcomes of observations. For example, the re-lation (7) predicts that the probability to observe the de-flection up of the Bob’s particle equals | cos (( ϕ − θ ) / | and down | sin (( ϕ − θ ) / | when the Alice particle hasdeflected up. Thus, the Alice’s will and her observationinfluence instantaneously on the outcome of observationsof the distant particle. This influence is revealed most FIG. 2: Sketch of the EPR experiment (a) and experimentalapparatus for measurement of the probability P θ + P ϕ − withhelp of a source of single electrons S e (b). In a case (a) oneof the electrons of each EPR pair flies from the EPR pairssource S EPR to the Stern-Gerlach analyzer A , and another tothe analyzer B . The probabilities P Aθ + = N A + / ( N A + + N A − )and P Bϕ + = N B + / ( N B + + N B − ) are defined as the relationof number N A + (or N B + ) of detection by detector D A + (or D B + ) to the sum N A + + N A − (or N B + + N B − ) of detectionby detectors D A + and D A − (or D B + and D B − ). In a case(b) electron flies from the source S e to the first Stern-Gerlachanalyzer and gets in the second analyzer if it deflects up, andgets in the first detector D − if it deflects down. After thesecond analyzer electron gets in the detector D or D − . Theprobability P θ + P ϕ − = N − / ( N − + N + N − ) is defined asthe relation of the number N − of detection by detector D to the sum N − + N + N − of detection by all detectors definitely with help of the Bell’s inequalities [36]. Onlycondition used at the deduction of the Bell’s inequalityis ”the requirement of locality, or more precisely that theresult of a measurement on one system be unaffected byoperations on a distant system” [36]. Bell had proposedin [27] a most simple example of this logical deduction.Bell started with an trivial inequality P P − + P P − ≥ P P − (8 a )asserting that the probability P of the deflection up atthe orientation of the Stern-Gerlach analyzer verticallyupward along the z-axis, i.e. at θ = 0 o and the P − of the deflection down at θ = 45 o plus the probability P of the deflection up at θ = 45 o and P − - downat θ = 90 o is not less than the probability P of thedeflection up at θ = 0 o and P − - down at θ = 90 o . Theinequality is obvious when all probabilities P , P − , P and P − are measured in the same spin state.Any particle in the same spin state which deflects up at θ = 0 o and down at θ = 90 o (and so contributing to thethird probability P P − in (8a)) can deflect either upat θ = 45 o (and so contributes to the second probability P P − in (8a)) or down at θ = 45 o (and so contributesto the first probability P P − in (8a)). The inequalityis trivial but it can not be verified experimentally withmeasurements of single particles, as shown on Fig2b, be-cause ” · · · a measurement always causes the system tojump into an eigenstate of the dynamical variable that isbeing measured” [29]. All particles flying from the firstto the second Stern-Gerlach analyzer on Fig.2b shouldbe in the state ’spin up’ because of this Dirac jump. Theeigenstate ’spin up’ for this orientation of the first Stern-Gerlach analyzer differs in common case from the initialspin state of the particles. Therefore it is impossible tomeasure the probabilities both P and P − , for ex-ample, in the same spin state with the method shownon Fig.2b. The probabilities at different orientation ofthe Stern-Gerlach analyzers θ and ϕ can be measured inthe same state with help of the EPR pair if the require-ment of locality is valid. The equality of the probabilities P Aθ + = P Bθ − and P Aθ − = P Bθ + must be observed be-cause of the EPR correlation when if one particle A ofthe EPR pairs (4) deflects up then the other B alwaysdeflects down and vice-versa. This equality is valid forall orientation including θ = 45 o and θ = 90 o . The Bell’sinequality P A P B + P A P B ≥ P A P B (8 b )is deduced from the obvious inequality (8a) at the sin-gle requirement: a turning of the Stern-Gerlach ana-lyzer A located in a space region r A can not change in-stantaneously on the spin of the distant particle B lo-cated in a space region r B and vice-versa. The proba-bility to observe the deflection up in the Stern-Gerlachanalyzers A equals always the same value P Aθ + =( | γ | + | γ | ) / . P Bϕ + = | sin (( ϕ − θ ) / | according to (7a). The re-sult P Aθ + P Bϕ + = 0 . | sin (( ϕ − θ ) / | gives the values P A P B = P A P B = 0 . sin (45 o / ≈ . P A P B = 0 . sin (90 o / ≈ .
25. The inequality(8b) would then require0 . ≥ .
25 (8 c )which is not true.This violation (8c) of the Bell’s inequality (8b) revealsthat quantum mechanics presupposes that a turning ofthe Stern-Gerlach analyzer can influence instantaneouslyon the distant particle because the Bell’s inequality (8b)was deduced only from the requirement of impossibility ofsuch non-local influence. According to the Born’s inter-pretation this non-local influence is actualized by meansof the Alice’s mind. The probability that the Bob’s par-ticle will deflect up should equal P Bϕ + = 0 . P Bϕ + = 0 . P Bϕ + = | sin (( ϕ − θ ) / | because ofthe discontinuous change of the Alice’s knowledge. Theknowledge changes because of the influence of object on subject and the probability of the observation changesbecause of the influence of subject on object. Thus,the EPR correlation and the Bell’s inequalities have con-firmed the statement by Schrodinger that in the orthodoxquantum mechanics ” · · · the causal interconnection be-tween the subject and object is considered reciprocal. It isstated, that the unremovable and uncontrollable influenceof the subject on the object takes place” [21]. EPR [24] denied any possibility of the EPR correla-tion. It was in conflict with the Einstein’s belief: ”Buton one supposition we should, in my opinion, absolutelyhold fast: the real factual situation of the system S isindependent of what is done with the system S , which isspatially separated from the former” [37]. EPR intendedto prove ”that the description of reality as given by awave function is not complete” [24]. Of course they hadin mind the wave function in the Born’s interpretation.It is stated in the abstract of the EPR paper [24]: ”Inquantum mechanics in the case of two physical quantitiesdescribed by non-commuting operators, the knowledge ofone precludes the knowledge of the other. Then either(1) the description of reality given by the wave functionin QM is not complete or (2) these two quantities cannothave simultaneous reality. Consideration of the problemof making predictions concerning a system on the basisof measurements made on another system that had pre-viously interacted with it leads to the result that if (1)is false then (2) is also false” . Indeed, if Alice revealsa real situation existing irrespective of any act of obser-vation when she sees that the particle has deflected upin her Stern-Gerlach analyzer pointing vertically upwardalong the z-axis (6a) than all other spin components (7a)or (7b) of her and Bob’s particles should exist before herobservation. Alice can know any spin component (7a)or (7b) in the same spine state turning her analyzer inthe respective axis. Therefore she can obtain the knowl-edge about different spin component of the Bob’s par-ticle, | ↓ B,z > and | ↓ B,θ > for example, contrary to thefoundation of QM, if this knowledge about a real situa-tion existing irrespective of her mind.Thus, QM is observably inadequate if it is interpretedas the description of reality. The description given by thewave function in QM can be adequate and complete onlyif two physical quantities described by non-commutingoperators does not have reality simultaneous before theirobservation. QM can be valid only if physical quantitiesare rather created by the mind of the observer than mea-sured at the observation. Just this absurdity of QM hadbeen proved by EPR [24]. Bell proposed ”to replace theword ’measurement’” which misleads: ”When it is saidthat something is ’measured’ it is difficult not to thinkof the result as referring to some pre-existing propertyof the object in question” [24]. The pre-existing prop-erties revealed at measurement are in hidden-variablestheory, alternative the orthodox QM using the Born’s in-terpretation. According to this theory, hidden variablesdetermine results of individual measurements and thuseliminate subjectivity and indeterminism inherent QM. Bell asserted ”that vagueness, subjectivity, and inde-terminism, are not forced on us by experimental facts,but by deliberate theoretical choice” [38]. It is not ab-solutely so. The main reason of refusal of realism wereproblems with the realistic description of some quantumphenomena, such as Stern-Gerlach effect [39]. Bohr wrotein 1949 [40], that ”as exposed so clearly by Einstein andEhrenfest [41], it presented with unsurmountable difficul-ties any attempt at forming a picture of the behaviour ofatoms in a magnetic field” . And Bell wrote 32 years later: ”Phenomena of this kind made physicists despair of find-ing any consistent space-time picture of what goes on theatomic and subatomic scale · · ·
Going further still, someasserted that atomic and subatomic particles do not haveany definite properties in advance of observation. Thereis nothing, that is to say, in the particles approachingthe magnet, to distinguish those subsequently deflected upfrom those subsequently deflected down. Indeed even theparticles are not really there” [27].As Bell wrote [42] ”To know the quantum mechani-cal state of a system implies, in general, only statisticalrestrictions on the results of measurements” . The clas-sical statistical mechanics also describes only statisticaldistribution of parameters. But these parameters are as-sumed to exist irrespective of any act of observation andthe mind of the observer. Just the negation of real ex-istence of parameters results to subjectivity and indeter-minism of QM. Therefore Bell was sure: ”It seems inter-esting to ask if this statistical element be thought of asarising, as in classical statistical mechanics, because thestates in question are averages over better defined statesfor which individually the results would be quite deter-mined. These hypothetical ’dispersion free’ states wouldbe specified not only by the quantum mechanical state vec-tor but also by additional ’hidden variables’-’hidden’ be-cause if states with prescribed values of these variablescould actually be prepared, quantum mechanics would beobservably inadequate” [42]. But most physicists did nottake an interest in this problem fifty years ago and up tonow many physicists underestimate the fundamental im-portance of hidden variables. Few experts, who did findthe question interesting, believed that ”the question con-cerning the existence of such hidden variables received anearly and rather decisive answer in the form of von Neu-mann’s proof on the mathematical impossibility of suchvariables in quantum theory” [42].But this belief was false. David Mermin writes inthe paper ”Hidden variables and the two theorems ofJohn Bell” [43]: ”A third of a century passed before John Bell, 1966, rediscovered the fact that von Neumann’s no-variables-hidden proof was based on an assumption thatcan only be described as silly - so silly, in fact, that one isled to wonder whether the proof was ever studied by eitherthe students or those who appealed to it” . Von Neumanndid not take into account that non-commuting opera-tors do not have simultaneous eigenvalues [43]. There ismore important to realize a physical mistake correspond-ing to this ’mathematical’ mistake. Eigenvalues non-commuting operators cannot be simultaneous measuredaccording to the quantum postulate and complementar-ity proposed by Bohr [23]. Bell noted [42] that additionaldemands of the von Neumann’s proof are ”quite unrea-sonable when one remembers with Bohr [40] ’the impos-sibility of any sharp distinction between the behaviourof atomic objects and the interaction with the measur-ing instruments which serve to define the conditions un-der which the phenomena appear’” . In order to exhibitof the error of the von Neumann’s proof Bell had con-structed a hidden-variables model which reproduces allpredictions of results of a single spin 1/2 measurementgiven by QM. There is important to accentuate that Bellused in this model the Bohr’s quantum postulate which ”implies that any observation of atomic phenomena willinvolve an interaction with the agency of observation notto be neglected” [23]. According to the quantum postu-late ”With or without hidden variables the analysis of themeasurement process presents peculiar difficulties” [42],because no theory can describe an interaction with theagency of observation. Any result of this interaction maybe assumed because of this vagueness.In the Bell’s model [42] the interaction of single spin1/2 with the agency of observation results to mea-surement of the same value of spin component, asit is observed in the paradoxical Stern-Gerlach effect[39]. Thanks to the vague interaction the results ofobservation can be described with the relation s n =1 / cos ( θ ) / | cos ( θ ) | proposed by Bell in [27]. This rela-tion describes an individual measurement of spin com-ponent s n along n , as well as the superposition (3), buthas a fundamental advantage: θ is the angle between anaxis n of Stern-Gerlach analyzer and an axis z + m ofspin. Therefore results of an individual measurement isdetermined with the spin axis z + m and the mind of theobserver can not influence on these results. In the Bell’smodel [42] z is a unit vector directed along the z-axis inthe spin state ψ z = | ↑ z > and m is a random unit vec-tor which plays the role of hidden variable. This modelpredicts the same probabilities of observation of positivevalues P θ + = 1 / R π/ θ dx π sin x/ π = (1 + cos θ ) / cos ( θ/
2) and negative values P θ − = R θ dx π sin x/ π =(1 − cos θ ) / sin ( θ/
2) as orthodox QM.It predicts also that if one particle A of the EPR pairgoes up the other B always goes down and vice-versawhen axis of two analyzers is directed in the same di-rection n because if cos ( θ A ) > θ A be-tween n and +( z + m ) then cos ( θ B ) < θ B between n and − ( z + m ) and vice-versa. Thehidden-variables model implies also the Dirac jump atobservation in order to correspond to the prediction ofQM. Therefore it also predicts violation of the trivial in-equality (8a). Because of the vague interaction with theagency of observation, i.e. with the first Stern-Gerlachanalyzer, shown on Fig.2b, the particle deflecting withthe probability P θ + = 0 . ψ θ = | ↑ θ > . Thereforethe particle will deflect down after the second analyzerwith the probability P ϕ − = | sin (( ϕ − θ ) / | . The totalprobability P θ + P ϕ − = 0 . | sin (( ϕ − θ ) / | to hit the de-tector D − predicts violation (8c) of the trivial inequality(8a): P P − = P P − = 0 . sin (45 o / ≈ . P P − = 0 . sin (90 o / ≈ .
25. Thus, the hidden-variables model can reproduce almost all prediction ofQM. Among few predictions which it can not reproduceis violation of the Bell’s inequality (8b). The probabilityof observation both s n = +1 / s n = − / P Aθ + = P Aθ − = P Bϕ + = P Bϕ − = 0 . z + m )or − ( z + m ) and therefore the act of measurement of oneparticle can not influence on the result of observation ofother particle. The corroboration of the Bell’s inequality(8b) P A P B + P A P B = 0 . × . . × . . > P A P B = 0 . × . .
25 reveals that ifdefinite properties exist in advance of observation then’measurement’ might be complete without the mind ofthe observer.There is important to note that hidden variables re-place the mind of the observer with soulless agencies ofobservation. This fact reveals that the quantum postu-late and complementarity proposed by Bohr [23] is validaccording to rather hidden-variables theories than theQM based on the Born’s interpretation. Variables arehidden just because ”any observation of atomic phenom-ena will involve an interaction with the agency of obser-vation not to be neglected” [23]. Bohr concluded fromthis statement implied with his quantum postulate that ”an independent reality in the ordinary physical sense canneither be ascribed to the phenomena nor to the agenciesof observation” [23]. This conclusion misleads. A cel-ebrated polymath who is quoted in [43] declared that ”Most theoretical physicists are guilty of · · · fail[ing] todistinguish between a measurable indeterminacy and theepistemic indeterminability of what is in reality deter-minate. The indeterminacy discovered by physical mea-surements of subatomic phenomena simply tells us thatwe cannot know the definite position and velocity of anelectron at any instant of time. It does not tell as thatthe electron, at any instant of time, does not have a def-inite position and velocity. [Physicists] · · · convert whatis not measurable by them into the unreal and the non-existent” [44]. Bohr was among these most theoreticalphysicists and had misled some generation of physicistswith his quantum postulate and complementarity. Hedid not take into account that an interaction with the agency of observation can change variables at observationbut it can not create observed variables. Only the mindof the observer can create definite properties observed bythe observer if they were not definite with variables evenhidden in advance of observation. The EPR correlationand violation (8c) of the Bell’s inequality (8b) reveal thatan interaction rather with the mind of the observer thanwith the agency of observation is implied in the orthodoxQM thanks to the non-locality of the first interaction andthe locality of the second one.
Von Neumann, Pauli, Wigner and also Heisenberg andothers were forced to note ”that ’measurement’ might becomplete only in the mind of the observer” [24] becauseof indeterminism of QM: if a cause of a definite result ofthe observation is absent in nature then only the mind ofthe observer can be the cause. Bohr reminder in 1949 [40]that during the Solvay meeting 1927 ”interesting discus-sion arose also about how to speak of the appearance ofphenomena for which only predictions of statistical char-acter can be made. The question was whether, as to theoccurrence of individual effects, we should adopt a termi-nology proposed by Dirac, that we were concerned with achoice on the part of ”nature” or, as suggested by Heisen-berg, we should say that we have to do with a choice on thepart of the ’observer’ constructing the measuring instru-ments and reading their recording” . Bohr wrote: ”Anysuch terminology would, however, appear dubious since,on the one hand, it is hardly reasonable to endow naturewith volition in the ordinary sense, while, on the otherhand, it is certainly not possible for the observer to influ-ence the events which may appear under the conditions hehas arranged” and advertised his complementarity: ”Tomy mind, there is no other alternative than to admit that,in this field of experience, we are dealing with individ-ual phenomena and that our possibilities of handling themeasuring instruments allow us only to make a choicebetween the different complementary types of phenomenawe want to study” [40]. But this pet idea by Bohr cannot answer on the question: ”What or who can a defi-nite result of the observation determine?” It can resultand even had resulted [19] to the illusion that individualeffects are chosen by the agency of observation, named ”the ’classical object’ usually called apparatus” [19].This illusion is logically absurd. Nevertheless it pre-dominated and predominates up to now among mostphysicists thanks to the followers [19] of Bohr. Bell hadcalled the spontaneous jump of a ’classical’ apparatusinto an eigenstate of its ’reading’ as the LL jump, con-sidering in [24] Quantum Mechanics by L D Landau andE M Lifshitz [19] as the first of the ’good books’ whichmislead. The assumption [19] about the LL jump is ab-surd first of all because a apparatus even ’classical’ isa part of nature as well as the cat in the famous para-0dox proposed by Schrodinger [33]. The Schrodinger’s catparadox is well-known but pure understood. Thereforeit is useful to reminder its text here: ”One can evenset up quite ridiculous cases. A cat is penned up in asteel chamber, along with the following diabolical device(which must be secured against direct interference by thecat): in a Geiger counter there is a tiny bit of radioactivesubstance, so small that perhaps in the course of one hourone of the atoms decays, but also, with equal probability,perhaps none; if it hap-pens, the [Geiger] counter tubedischarges and through a relay releases a hammer whichshatters a small flask of hydrocyanic acid. If one has leftthis entire system to itself for an hour, one would saythat the cat still lives if meanwhile no atom has decayed.The first atomic decay would have poisoned it. The ψ -function of the entire system would express this by havingin it the living and the dead cat (pardon the expression)mixed or smeared out in equal parts” [33], see also p.185in the book [16]. Schrodinger had entangled with the ψ -function of the entire systemΨ cat = αAt decay G yes F l yes
Cat dead ++ βAt no G no F l no Cat living (9)cat state
Cat dead , Cat living with the states of the smallflask of hydrocyanic acid
F l yes , F l no , the Geiger countertube G yes , G yes and radioactive atom At decay , At no withthe experiment conditions. The act of observation of thedead cat is described with the ψ - function (9) collapseto Ψ cat = At decay G yes F l yes
Cat dead (10)One can draw the conclusion that the cat is dead
Cat dead because the hammer has shattered the small flask of hy-drocyanic acid
F l yes . The hammer has shattered it be-cause the Geiger counter tube has discharged G yes . Itis has discharged because the atom has decayed At decay .Till this each event had a cause. But the atom decayis causless. There is no term to the right of At decay in(9). According to the assumption [19] about the LL jumpthe cat kills himself. Moreover one may demonstrate tocombine two famous paradoxes, the EPR paradox andthe Schrodinger’s cat paradox, that the death of a cat A can preserve life of a distant cat B and vice-versa.Thereto one may substitute of the radioactive atom forthe EPR pairs with two spin particles in the singlet state(4), as well as in the Bohm’s version [28] of the EPRparadox. We will use also two Stern-Gerlach analysers,two Geiger counter tubes, two flasks of hydrocyanic acidand two cats Cat A and Cat B . The Geiger counter tubeswill be located on the upper trajectory of each particleafter its exit from its Stern-Gerlach analyser, so it willdischarge when spin up and will not discharge when spindown. The subsequent events will be as well as in theSchrodinger paradox [33]. This gedankenexperiment canbe described with the ψ -functionΨ EP R,cat = γ | ↑ A ( r A ) ↓ B ( r B ) > Cat A,dead
Cat
B,liv + + γ | ↓ A ( r A ) ↑ B ( r B ) > Cat A,liv
Cat
B,dead (11)with two types of entanglements: because of the con-servation law (the EPR correlation) and because of thecondition of experiment proposed by Schrodinger [33].The results of observations will beΨ
EP R,cat = Cat
A,dead
Cat
B,liv (12 a )or Ψ EP R,cat = Cat
A,liv
Cat
B,dead (12 b )when the axis of the Stern-Gerlach analysers are paral-lel. Advocates of quantum mechanics justify the using ofstate superposition (11) with the absence of any cause ofthe atom decay. They ”convert what is not measurableby them into the unreal and the non-existent” [44]. Letimagine that we do not know why the observed states ofcats are correlated as well as we do not know the cause ofatom decay. Then, to convert our lack of knowledge intothe unreal we can describe the results of our observationsof the cats state with superpositionΨ EP R,cat = γ Cat
A,dead
Cat
B,liv + γ Cat
A,liv
Cat
B,dead (13)which should collapse to (12a) or (12b) at each obser-vation. The absence of any cause of (12a) or (12b) inadvance of observation raises a question: ”What or whomakes a choice?” According to the concept of the spon-taneous collapse of a macroscopic system into a definitemacroscopic configuration [19], i.e. the LL jump [24],the choice is made by a cat, which is a ’classical’ appara-tus in the Schrodinger’s paradox. But what cat A or B would make a choice (12a) or (12b)? The collapse of thesuperposition of cats states (13) must be instantaneousirrespective of a distance | r A − r B | between cats. Accord-ing to the principle of relativity by Einstein both the cat A and the cat B may be observed first in the same casebut in different frames of reference. Therefore it is im-possible to say the spontaneous collapse of what cat canchoose the fate of other cat with help a mystical actionof a distance. The absurdity of the LL jump assumed in[19] is obvious even without this consideration of the catsfate. It must be obvious for any one that only a magicalapparatus even ’classical’ can collapse spontaneously. Therefore von Neumann, Pauli, Wigner, Heisenbergand others admitted ”that ’measurement’ might be com-plete only in the mind of the observer” and the Diracjump is forced by an external intervention [24] which canbe only the mind of the observer. But a choice on thepart of the ’observer’ suggested by Heisenberg can notdeliver from a logical absurdity. According to the basicprinciple of QM formulated by Dirac ” · · · a measurementalways causes the system to jump into an eigenstate of the dynamical variable that is being measured” [29]. Butinto which eigenstate should the system jump when twodynamical variables described by non-commuting oper-ators are measured at the same time? Alice may orienther Stern-Gerlach analyser at an angle θ to the z-axis andBob may orient his Stern-Gerlach analyser at an otherangle ϕ . Then Alice will be sure that her and Bob’s par-ticles jump to the spin state (7a) when she will see thather particle has deflected up. But Bob will be sure thathis and Alice’s particles jump to the other state ψ ϕ = | ↓ A,ϕ ↑ B,ϕ > = − sin (( θ − ϕ ) / | ↑ A,θ ↓ B,θ > ++ cos (( θ − ϕ ) / | ↓ A,θ ↑ B,θ > (14)when he will see that his particle has deflected up. Thus,according to orthodox QM, knowledge of two observersof the same system can be various. Moreover, each ofthem can impose her (or his) will on the distant particle.When Alice has oriented her Stern-Gerlach along the z-axis the Bob’s particle should jump in the spin state (5a)or (5b) at her measurement. And when Bob has orientedhis Stern-Gerlach at an angle θ to the z-axis the Alice’sparticle should jump in the spin state (6a) or (6b) athis measurement. Here it is impossible to solve, whoseknowledge is correct, and whose will can win because ofthe principle of relativity according to which Alice ob-serves her particle ahead of Bob in a frame of referencewhereas in an other frame of reference Bob observes hisparticle ahead of Alice.This absurdity of QM has became especially relevantafter experimental evidence [45–47] of violation of theBell’s inequalities. Before these experiments Bell ex-pressed a hope that ”Perhaps Nature is not so queer asquantum mechanics” [27] and rated a possibility of vio-lation of his inequalities as indigestible. One of the in-terpretations of this violation could be a conclusion that ”Apparently separate parts of the world would be deeplyand conspiratorially entangled, and our apparent free willwould be entangled with them” [27]. The results of theexperiments of the Aspect’s team [45–47] Bell appraisedas a fundamental problem of theory: ”For me then thisis the real problem with quantum theory: the apparentlyessential conflict between any sharp formulation and fun-damental relativity. That is to say, we have an apparentincompatibility, at the deepest level, between the two fun-damental pillars of contemporary theory” p. 172 in [1].As opposed to Bell contemporary believers in the sooth-ing philosophy or religion of Heisenberg-Bohr, for exam-ple the authors of the book [48] are sure that violation ofthe Bell’s inequalities has corroborated the correctnessof QM. Mermin wrote as far back as in 1985 [49]: ”Inthe question of whether there is some fundamental prob-lem with quantum mechanics signaled by tests of Bell’sinequality, physicists can be divided into a majority whoare ’indifferent’ and a minority who are ’bothered’” .This division observed up to now witnesses againstQM as a consistent and transparent theory. The incon-sistency the assessment discloses vagueness of QM. The majority who are ’indifferent’ rather believe than under-stand QM. The authors of the book [48] and other be-lievers do not want to understand that no experimentalresult can save QM because it is self-contradictory andvague. Because of its vagueness the contradictions wereobserved even between its creators, Heisenberg and Bohr,first of all about the role of the observer. Heisenberg ad-mitted that ’measurement’ might be complete only inthe mind of the observer. It is obvious, for example,from his destructive criticism of Soviet scientists Alexan-drov and Blochinzev in the Section VIII ”Criticism andCounterproposals to the Copenhagen Interpretation ofQuantum Theory” of the Lectures 1955-1956 ”Physicsand Philosophy” [31]. These Soviet scientists stated that ”Among the different idealistic trends of contemporaryphysics the so-called Copenhagen school is the most re-actionary” [31] and rejected the role of the observer inQM. Heisenberg quotes Alexandrov ”We must thereforeunderstand by ’result of measurement’ in quantum theoryonly the objective effect of the interaction of the electronwith a suitable object. Mention of the observer must beavoided, and we must treat objective conditions and ob-jective and effects. A physical quantity is objective char-acteristic of phenomenon, but not the result of an ob-servation” and notes ”According to Alexandrov, the wavefunction in configuration space characterizes the objectivestate of the electron” [31]. Further Heisenberg explainswhy the Alexandrov’s point of view is false: ”In his pre-sentation Alexandrov overlooks the fact that the formal-ism of quantum theory does not allow the same degree ofobjectivation as that of classical physics. For instance,if a interaction of a system with the measuring appara-tus is treated as a whole according to QM and if both areregarded as cut off from the rest of the world, then theformalism of quantum theory does not as a rule lead toa define result; it will not lead, e.g., to the blackening ofthe photographic plate in a given point. If one tries torescue the Alexandrov’s ’objective effect’ by saying that’in reality’ the plate is blackened at a given point afterthe interaction, the rejoinder is the quantum mechani-cal treatment of the closed system consisting of electron,measuring apparatus and plate is no longer being applied” [31].This disproof by Heisenberg of the objectivation of QMis doubtless. Its obviousness is illustrated in the Section2.1 and must be quite clear at consideration of the exam-ple shown on Fig.1: the wave-packet can be compactedonly by the mind of the observer. In spite of this ob-viousness not only the Soviet scientists Alexandrov andBlochinzev but most physicists including Bohr objectifiedand objectify the matter of quantum mechanical treat-ment. Bohr objectified it with his quantum postulate andcomplementarity [23] according to which the act of obser-vation is an interaction with the agency of observation.Most physicists had followed rather Bohr than Heisen-berg because of their robust common sense according towhich both the many world interpretation and the mindof the observer are mind-boggling fantasies. QM seems2reasonable to most physicists only thanks to its misinter-pretation. The following word by Heisenberg can explainpartly the cause of this mass delusion: ”Above all, we seefrom these formulations how difficult it is when we try topush new ideas into an old system of concepts belongingto an earlier philosophy - or, to use an old metaphor,when we attempt to put new wine into old bottles” [31].Therefore it is needed to give an account of the essenceof a new bottle proposed by Heisenberg for QM.
3. NEW WELTANSCHAUUNG PROPOSED BYHEISENBERG
QM had originated from the proposal by young Heisen-berg ”to try to establish a theoretical quantum mechanics,analogous classical mechanics, but in which only relationsbetween observable quantities occur” [2]. Only few scien-tists, first of all Einstein, realized at that time and lateron that this proposal presupposes a revolutionary revi-sion of the aim of science and even a new Weltanschau-ung. The essence of this revolutionary revision was ex-pressed by Einstein in his explanation of ”reasons whichkeep he from falling in line with the opinion of almostall contemporary theoretical physicists” : ”What does notsatisfy me in that theory, from the standpoint of prin-ciple, is its attitude towards that which appears to meto be the programmatic aim of all physics: the completedescription of any (individual) real situation (as it sup-posedly exists irrespective of any act of observation orsubstantiation)” [50]. The philosophical fundamentals ofQM, proclaimed by Heisenberg as far back as 1927 are:subjectivity, ”I believe that one can fruitfully formulatethe origin of the classical ’orbit’ in this way: the ’orbit’comes into being only when we observe it” [22]; the nega-tion of an objective reality, ”As the statistical characterof quantum theory is so closely linked to the inexactnessof all perceptions, one might be led to the presumptionthat behind the perceived statistical world there still hidesa ’real’ world in which causality holds. But such specula-tions seem to us, to say it explicitly, fruitless and sense-less. Physics ought to describe only the correlation ofobservations” [22]; indeterminism, ”One can express thetrue state of affairs better in this way: Because all ex-periments are subject to the laws of quantum mechanics,and therefore to equation (1), it follows that quantummechanics establishes the final failure of causality” [22].The equation (1) in [22] is the famous Heisenberg’s un-certainty relation. Thus, the uncertainty principle resultsto indeterminism, according to its author. Later on Heisenberg had developed his new Weltan-schauung more neatly, in particular in his Lectures 1955-1956 ”Physics and Philosophy” [31]. In the beginning of the Section V ”The Development of Philosophical IdeasSince Descartes in Comparison with the New Situationin Quantum Theory” he stated: ”This reality was full oflife and there was no good reason to stress the distinc-tion between matter and mind or between body and soul” [31]. This point of view by Heisenberg contradicts funda-mentally to the scientific Weltanschauung of the previouscenturies and Heisenberg emphasizes that QM compelsto change this Weltanschauung. He reminds: ”The firstgreat philosopher of this new period of science was ReneDescartes who lived in the first half of the seventeenthcentury. Those of his ideas that are most important forthe development of scientific thinking are contained in hisDiscourse on Method” [31]. And then Heisenberg pointsout on the importance of the Cartesian philosophy forthe posterior development of natural science: ”While an-cient Greek philosophy had tried to find order in the in-finite variety of things and events by looking for somefundamental unifying principle, Descartes tries to estab-lish the order through some fundamental division · · ·
Ifone uses the fundamental concepts of Descartes at all, itis essential that God is in the world and in the I and it isalso essential that the I cannot be really separated fromthe world. Of course Descartes knew the undisputablenecessity of the connection, but philosophy and naturalscience in the following period developed on the basis ofthe polarity between the ’res cogitans’ and the ’res ex-tensa’, and natural science concentrated its interest onthe ’res extensa’. The influence of the Cartesian divisionon human thought in the following centuries can hardlybe overestimated, but it is just this division which we haveto criticise later from the development of physics in ourtime” [31].The latter sentence clarifies in a greatest extent thefundamental difference of QM from all other theories ofphysics. All other theories concentrated their interest onthe ’res extensa’, i.e. all objects of the Nature, existingirrespective of any act of observation and the mind of theobserver, i.e. the ’res cogitans’. Heisenberg points out ona philosophical basis of these theories ”Since · · · the ’rescogitans’ and the ’res extensa’ were taken as completelydifferent in their essence, it did not seem possible thatthey could act upon each other” [31]. He attacks thisbasis ”Obviously this whole description is somewhat ar-tificial and shows the grave defects of the Cartesian par-tition” but admits ”On the other hand in natural sciencethe partition was for several centuries extremely success-ful. The mechanics of Newton and all the other parts ofclassical physics constructed after its model started fromthe assumption that one can describe the world withoutspeaking about God or ourselves” [31]. Before the QMemergence ”This possibility soon seemed almost a nec-essary condition for natural science in general. But atthis point the situation changed to some extent throughquantum theory” [31]. Therefore Heisenberg comes ”to acomparison of Descartes’s philosophical system with ourpresent situation in modern physics” [31].His next remark demystifies the essence of his con-3tradictions with Einstein and other critics of QM: ”Ifone follows the great difficulty which even eminent sci-entists like Einstein had in understanding and acceptingthe Copenhagen interpretation of quantum theory, onecan trace the roots of this difficulty to the Cartesian par-tition. This partition has penetrated deeply into the hu-man mind during the three centuries following Descartesand it will take a long time for it to be replaced by a reallydifferent attitude toward the problem of reality” [31]. Ac-cording to Heisenberg an old-fashioned attitude towardthe problem of reality may be called dogmatic realismand metaphysical realism [31]. He explains the essenceof the first: ”Dogmatic realism claims that there are nostatements concerning the material world that cannot beobjectivated · · · actually the position of classical physicsis that of dogmatic realism. It is only through quantumtheory that we have learned that exact science is possiblewithout the basis of dogmatic realism. When Einstein hascriticised quantum theory he has done so from the basis ofdogmatic realism” [31]. Einstein said ”I like to think thatthe moon is there even if I don’t look at it” , explaining hisdislike for QM. Heisenberg and Einstein did not agree butthey discussed on the common language of European phi-losophy. Therefore this controversy of they makes quiteclear the essence of dogmatic realism. There is importantalso to know the essence of metaphysical realism accord-ing to Heisenberg: ”Metaphysical realism goes one stepfurther than dogmatic realism by saying that ’the thingsreally exist’. This is in fact what Descartes tried to proveby the argument that ’God cannot have deceived us’” [31].Heisenberg reminded above: ”On the basis of doubt andlogical reasoning he [Descartes] tries to find a completelynew and as he thinks solid ground for a philosophical sys-tem. He does not accept revelation as such a basis nordoes he want to accept uncritically what is perceived bythe senses. So he starts with his method of doubt. Hecasts his doubt upon that which our senses tell us aboutthe results of our reasoning and finally he arrives at hisfamous sentence: ’cogito ergo sum’. I cannot doubt myexistence since it follows from the fact that I am think-ing. After establishing the existence of the I in this wayhe proceeds to prove the existence of God essentially onthe lines of scholastic philosophy. Finally the existence ofthe world follows from the fact that God had given me astrong inclination to believe in the existence of the world,and it is simply impossible that God should have deceivedme” [31]. Soon after Descartes his faith that God cannot deceive was call in question by representatives forearly empiristic philosophy, Locke, Berkeley and Hume.According to Heisenberg: ”The criticism of metaphysicalrealism which has been expressed in empiristic philosophyis certainly justified in so far as it is a warning againstthe naive use of the term ’existence’” [31]. According to the empiristic philosophy ”to be perceivedis identical with existence” [31]. Heisenberg admitted: ”This line of argument then was extended to an extremescepticism by Hume, who denied induction and causationand thereby arrived at a conclusion which if taken se-riously would destroy the basis of all empirical science” [31] but he followed just this line when he rejected the’thing-in-itself’ and the law of causality of the Kant’sphilosophy. Heisenberg wrote: ”The disagreeable ques-tion whether ’the things really exist’, which had givenrise to empiristic philosophy, occurred also in Kant’s sys-tem. But Kant has not followed the line of Berkeley andHume, though that would have been logically consistent.He kept the notion of the ’thing-in-itself ’ as different fromthe percept, and in this way kept some connection withrealism” [31]. He was right that ”Considering the Kan-tian ’thing-in-itself ’ Kant had pointed out that we cannotconclude anything from the perception about the ’thing-in-itself ’” [31]. But his interpretation of the Kantian’thing-in-itself’ is very doubt: ”This statement has, asWeizsacker has noticed, its formal analogy in the factthat in spite of the use of the classical concepts in all theexperiments a non-classical behaviour of the atomic ob-jects is possible. The ’thing-in-itself ’ is for the atomicphysicist, if he uses this concept at all, finally a mathe-matical structure: but this structure is - contrary to Kant- indirectly deduced from experience” [31].The Kantian ’thing-in-itself’ is rather a cause of ourperceptions than a mathematical structure. Any math-ematical structure is a method of description and can-not belong to the percept or the perception. It canonly describe they. Heisenberg and Weizsacker obscuredthe obvious meaning of the Kantian ’thing-in-itself’ as acause of our perceptions because of their persuasion thatcausality ”can have only a limited range of applicability” [31]. They rejected the ’thing-in-itself’ as the cause ofour perceptions as well as they rejected hidden-variablesas the cause of an individual observation of quantum phe-nomenon.
The most doubt principle of QM and the new Weltan-schauung by Heisenberg is indeterminism. Consideringthe law of causality Heisenberg wrote: ”Kant says thatwhenever we observe an event we assume that there isa foregoing event from which the other event must fol-low according to some rule. This is, as Kant states, thebasis of all scientific work. In this discussion it is notimportant whether or not we can always find the forego-ing event from which the other one followed. Actually wecan find it in many cases. But even if we cannot, noth-ing can prevent us from asking what this foregoing event might have been and to look for it. Therefore, the law ofcausality is reduced to the method of scientific research;it is the condition which makes science possible. Sincewe actually apply this method, the law of causality is ’apriori’ and is not derived from experience” [31]. If thelaw of causality is the method of scientific research, asKant stated, then QM proposed by Heisenberg is obvi-ously no-scientific theory. Heisenberg tried to prove that ”the scientific method actually changed in this very fun-damental question since Kant” [31].His first argument: ”We have been convinced by expe-rience that the laws of quantum theory are correct and, ifthey are, we know that a foregoing event as cause for theemission at a given time cannot be found” [31]. The otherargument: ”We know the foregoing event, but not quiteaccurately. We know the forces in the atomic nucleus thatare responsible for the emission of the α -particle. Butthis knowledge contains the uncertainty which is broughtabout by the interaction between the nucleus and the restof the world. If we wanted to know why the α -particle wasemitted at that particular time we would have to know themicroscopic structure of the whole world including our-selves, and that is impossible” [31]. Both arguments aredoubt and have no relation to the fundamental questionabout the law of causality. If this law is ’a priori’ and isnot derived from experience then its disproof can not bealso derived from experience. At least, the arguments byHeisenberg could not satisfy Schrodinger, proposing thecat paradox, Einstein and other critics of QM. Neverthe-less Heisenberg stated that ”Kant’s arguments for the apriori character of the law of causality no longer apply” [31]. Most believers in the soothing philosophy or religionof Heisenberg-Bohr overlook this philosophical statementby Heisenberg.
4. FUNDAMENTAL MISTAKES BYSLEEPWALKERS
Most sleepwalkers stride unimpeded, first of all,through the new Weltanschauung proposed by Heisen-berg. Partly this carelessness may be explained withthe inconsistency of Heisenberg. In the same paper [22]Heisenberg refutes a ’real’ world in which causality holdsand substantiates his uncertainty relation with help ofthe famous ’uncertainty microscope’ existing in this realworld in which causality holds. Later on he criticises theCartesian polarity between the ’res cogitans’ and the ’resextensa’ and notes: ”In classical physics science startedfrom the belief - or should one say from the illusion? -that we could describe the world or at least parts of theworld without any reference to ourselves” [31]. On theother hand he states that ”in the Copenhagen interpre-tation of quantum theory we can indeed proceed withoutmentioning ourselves as individuals” [31]. Then, whatis fundamental difference between the classical physicsand the Copenhagen interpretation? Heisenberg confusesconstantly the ’res cogitans’ and the ’res extensa’. For example, disproving the claim by Alexandrov that ”Men-tion of the observer must be avoided” (see above) Heisen-berg writes: ”Of course the introduction of the observermust not be misunderstood to imply that some kind ofsubjective features are to brought into the description ofnature. The observer has, rather, only the function ofregistering decisions, i.e. processes in space and time,and it does not matter whether the observer is an appa-ratus or a human being · · · ” [31]. Any apparatus be-longs to the ’res extensa’ whereas any human being isthe ’res cogitans’, at least according to Descartes. Ifthe observer is an apparatus then the Cartesian divisionshould not be criticised ”from the development of physicsin our time” [31] and Heisenberg rather follows than dis-proves Alexandrov stating that ”’result of measurement’in quantum theory only the objective effect of the interac-tion of the electron with a suitable object” , see above. Thenew Weltanschauung by Heisenberg could be unaccept-able not only for most physicists but even for Heisenberghimself if it would be logically consistent.
Heisenberg defines: ”The position to which the Carte-sian partition has led with respect to the ’res extensa’was what one may call metaphysical realism. The world,i.e., the extended things, ’exist’” [31]. According to thisdefinition and the Cartesian division the dogmatic real-ism claims that there are no statements concerning the’res extensa’ that cannot be conceived outside of and in-dependently of the ’res cogitans’. Therefore accordingto Heisenberg the term ’to objectivate’ should signify toconceive any real situation outside of and independentlyof the mind of the observer. But he gives fundamentallydifferent definition: ”We ’objectivate’ a statement if weclaim that its content does not depend on the conditionsunder which it can be verified” [31]. Heisenberg as well asmost theoretical physicists confuses here what is not mea-surable with the unreal. Therefore his practical realismis very vague. ”Practical realism assumes that there arestatements that can be objectivated and that in fact thelargest part of our experience in daily life consists of suchstatements” [31]. If the term ’to objectivate’ signifies onlyindependence on the conditions of verification than theHeisenberg’s practical realism can not make a distinc-tion between the orthodox QM and theories of hiddenvariables. This distinction can be made only with helpof the philosophically true definition of the term ’to ob-jectivate’. We ’objectivate’ a statement if we claim that amatter of its description (belonging to the ’res extensa’)exists outside of and independently of the mind of the ob-server (belonging to the ’res cogitans’). According to thisdefinition hidden variables can be objectivated whereasthe uncertainty relation, the superposition of states, theDirac jump and the act of observation in QM can not beobjectivated.5But the true definition of the term ’to objectivate’ aswell as the true essence of QM of Heisenberg-Bohr couldbe unacceptable for most physicists. Therefore QM basedon the quantum postulate and complementarity by Bohrhad became the symbol of almost general faith in spiteof its self-contradiction. Bohr had objectivated the actof observation when he considered it as an interactionbetween quantum system and measuring instrument. Itmust be obvious that the Dirac jump can not be describedby this way. Nevertheless most physicists including sucheminent one as Feynman [13] and Landau [19] had fol-lowed Bohr in his wrong belief. Bell wrote that ”Lan-dau sat at the feet of Bohr” [24]. Therefore Landau wassure ”that, in speaking of ’performing a measurement’,we refer to the interaction of an electron with a classical’apparatus’, which in no way presupposes the presence ofan external observer” [19] and could not understand thelogical absurdity of the LL jump. Even the EPR cor-relation [24] could not shake the wrong belief of Bohrand his followers. It must be obvious that non-localityof the EPR correlation precludes any possibility to inter-pret the act of observation realistically as an interactionwith measuring instrument. Nevertheless Bohr tried tosave his quantum postulate and his complementarity. Inhis reply [51] on the EPR paper [24] Bohr criticizes theEPR criterion of the existence of an element of physicalreality: ” · · · the wording of the above mentioned crite-rion · · · contains an ambiguity as regards the meaning ofthe expression ’without in any way disturbing a system’.Of course there is in a case like that just considered noquestion of a mechanical disturbance of the system underinvestigation during the last critical stage of the measur-ing procedure. But even at this stage there is essentiallythe question of an influence on the very conditions whichdefine the possible types of predictions regarding the fu-ture behaviour of the system · · · their argumentation doesnot ’justify their conclusion that quantum mechanical de-scription is essentially incomplete · · · This descriptionmay be characterized as a rational utilization of all pos-sibilities of unambiguous interpretation of measurements,compatible with the finite and uncontrollable interactionbetween the objects and the measuring instruments in thefield of quantum theory” .This criticism is very obscure and Bell quoting it writesin [27]: ”Indeed I have very little idea what this means. Ido not understand in what sense the word ’mechanical’ isused, in characterising the disturbances which Bohr doesnot contemplate, as distinct from those which he does.I do not know what the passage means - ’an influenceon the very conditions · · · ’. Could it mean just thatdifferent experiments on the first system give differentkinds of information about the second? But this was justone of the main points of EPR, who observed that onecould learn either the position or the momentum of thesecond system. And then I do not understand the finalreference to ’uncontrollable interactions between measur-ing instruments and objects’, it seems just to ignore theessential point of EPR that in the absence of action at a distance, only the first system could be supposed dis-turbed by the first measurement and yet definite predic-tions become possible for the second system. Is Bohr justrejecting the premise - ’no action at a distance’ - ratherthan refuting the argument?”
Indeed, Bohr could save hisquantum postulate and his complementarity only reject-ing the premise - ’no action at a distance’. ”The quantumpostulate implies that any observation of atomic phenom-ena will involve an interaction with the agency of obser-vation not to be neglected” [23]. EPR had proposed amethod of the observation, for example, by Alice the spinstate of the distant particle flying toward Bob at whichno interaction between the agency of observation of Aliceand the Bob’s particle can be assumed without action ata distance between they. The Bohr’s complementaritycan be valid also if only the premise - ’no action at adistance’ could be rejected. This action should be realbecause of the reality of an interaction with the agency ofobservation which belongs to the ’res extensa’, as well asany quantum object. The mind of Alice and Bob belongto the ’res cogitans’. But the quantum postulate andcomplementarity exclude an interaction with the mindof the observer. Bohr and his followers objectivated (inthe meaning of the true definition) the act of observation,the Dirac jump and even the EPR correlation. The ob-jectiveness of the EPR correlation implies a real actionat a distance between the ’res extensa’ contradicting tothe relativity. The neglect by sleepwalkers this essentialconflict ”between the two fundamental pillars of contem-porary theory” has resulted to mass delusion.
This mass delusion shows itself, in particular, in theidea of quantum computation enjoying wide popularitynow [48]. The widespread interest in this idea seems quitevalid. The minimal sizes of nanostructures come nearerto atomic level and subsequent miniaturization will notbe possible in the near future. Therefore exponential in-crease of calculating resources with number of quantumbits has provoked almost boundless enthusiasm. Thisexponential increase seems possible thanks to the princi-ple of superposition of states, interpreted as the cardinalpositive principle of the QM [19]. Feynman [52] proposeduniversal simulation, i.e. a purpose-built quantum sys-tem which could simulate the physical behaviour of anyother, noting that the calculation complexity of quantumsystem increases exponentially with number N of its ele-ments. Indeed, the number g N = 2 N − γ j describing, for example, the spin 1/2 statesof N particle ψ = γ | ↑↑↑ ... ↑ > + γ | ↑↑↑ ... ↓ > + ... + γ gN − | ↓↓↓ ... ↑ > + γ gN | ↓↓↓ ... ↓ > (15)6increases exponentially with the number of these particlesthanks to the EPR correlation.The Feynman’s idea of simulation was based on his be-lief in QM as an universal theory. But this belief is false.The idea of universal quantum computer was proposedby David Deutsch ”as a way to experimentally test the’Many Universes Theory’ of quantum physics - the ideathat when a particle changes, it changes into all possibleforms, across multiple universes” [53]. There is impor-tant to remind that the concept of multiple universes wasproposed by Hugh Everett [14] in order to describe theProcess 1, i.e. the act of observation out the domain ofpsychology, i.e. without the mind of the observer. In theearly 1990’s several authors sought computational taskswhich could be solved by a quantum computer more effi-ciently than any classical computer. Shor has describedin 1994 [54] an algorithm which was not only efficienton a quantum computer, but also addressed a centralproblem in computer science: that of factorising largeintegers. This possibility has provoked mass enthusiasm.But most authors of numerous publication on quantumcomputation ignore the statement of the author of thisidea that quantum computer can be real only in multipleuniverses. Deutsch writes in his book [55]: ”For whosewho still thinks that there is only one universe I offerthe following problem: to explain a principle of action ofthe Shor’s algorithm. I do not request to predict that itwill work, as for this purpose it is enough to solve someconsistent equations. I ask you to give an explanation.When the Shor’s algorithm has factorized number, hav-ing involved about computing resources which can beseen where this number was factorized on multipliers? Inwhole visible universe exists in all about atoms, thenumber is insignificant small in comparison with .Thus, if the visible universe was a whole physical reality,the physical reality even is remote would not contain re-sources, sufficient for factorization on multipliers of suchbig number” .This contradiction between the author of the idea ofquantum computation and numerous authors of publica-tions about quantum computation is consequence of therobust common sense intrinsic not only the authors [26]but almost all physicists. Deutsch, as well as Everett,understands that the problem of ’observation’ in the or-thodox QM ”cannot be ruled out as lying in the domainof psychology” [14] and only the idea of multiple universescan deliver from this nonsense. In contrast to Deutschand Everett most authors believing Heisenberg and Bohr,who had obscured the logically obvious fact, spurn suchmind-boggling fantasies as both the many world interpre-tation and the mind of the observer having an influenceon quantum system at observation. The belief in thesoothing philosophy or religion of Heisenberg-Bohr is sothoughtless that believers refuse to admit that the nu-merous independent variables γ j in the EPR correlation(15) describe the knowledge of an observer. It must beobvious from the fact that the huge number g N = 2 N − at the number of quantum bits N ≈ , 10 , 10 , and even toset yourself a task to factorized it on multipliers with helpof the Shor’s algorithm. But it does not mean, that thistask can be solved with help of a real device, quantumcomputer, in a reality of one universe. It could be possi-ble only if a real action on distance, violating relativisticcausality, could be possible. The violations [45–47] ofthe Bell’s inequalities give experimental evidence of ”agross violation of relativistic causality” , p. 171 in [1], forresults of observations. The EPR correlation describesjust this violation. But the experimental results [45–47]and any others can not give evidence that the EPR cor-relation describes a real action on distance between the’res extensa’, existing outside of and independently of the’res cogitans’, i.e. the mind of the observer. Authors ofnumerous publications about quantum computation ob-jectivate without hesitation quantum bits and quantumgates doing not suspect about conflict with relativisticcausality and even with the Copenhagen interpretationof quantum theory. In the Section ”The CopenhagenInterpretation of Quantum Theory” of [31] Heisenbergstated ”that certainly our knowledge can change suddenlyand that this fact justifies the use of the term ’quantumjump’” . Just this sudden change of our knowledge at ob-servation results to non-locality of the EPR correlationand the conflict between the Copenhagen interpretationof quantum theory with relativistic causality. Heisenbergnoted also in this Section that ”there is no descriptionof what happens to the system between the initial obser-vation and the next measurement” [31]. Thus, accordingto the Copenhagen interpretation QM can not describea process of quantum computation which should be justbefore the next measurement. Both the EPR correlationand quantum computation can not be possible accord-ing to hidden-variables theories. Deutsch is quite rightthat quantum computer can be real only in a reality ofmultiple universes. The Heisenberg’s point of view was inconsistent. Onthe one hand he understood that ”if a interaction of asystem with the measuring apparatus is treated as a wholeaccording to quantum mechanics and if both are regardedas cut off from the rest of the world, then the formalism ofquantum theory does not as a rule lead to a define result” [31]. But on the other hand he did not want to admitthe presence of subjectivity in his pet quantum mechan-ics. Although the subjectivity follows logically and in-evitably from his understanding that ’quantum jump’ ofthe measuring apparatus can not be spontaneous. Try-ing to deny subjective features of QM Heisenberg wasforced to use obscure declarations, for example: ”The observer has, rather, only the function of registering de-cisions, i.e. processes in space and time, and it does notmatter whether the observer is an apparatus or a humanbeing; but the registration, i.e. the transition from the’possible’ to the ’actual’ is absolutely necessary here andcan not be omitted from the interpretation of quantumtheory. At this point quantum theory is intrinsically con-nected with thermodynamics in so far as every act of ob-servation is by its very nature an irreversible process; it isonly through such irreversible processes that the formal-ism of quantum theory can be consistently connected withactual events in space and time” [31]. This explanation isvery obscure! Any apparatus belongs to the ’res extensa’whereas a human being belongs to the ’res cogitans’. Ananswer on the question ”What or who is the observer, the’res extensa’ or the ’res cogitans’ ?” should be decisive forthe essence of QM. But Heisenberg ignores this questionbecause he understands that no apparatus can induce thetransition from the ’possible’ to the ’actual’. This tran-sition can be only in the mind of a human being. ButHeisenberg did not want to admit this subjective featureof QM.The proclaim resemblance of QM and thermodynamicsdistracts the attention from the principal problem andhas misled many physicists, in particular Landau [19].The principal problem was raised by Bell in his paper”On the problem of hidden variables in quantum me-chanics” [42]: ”To know the quantum mechanical state ofa system implies, in general, only statistical restrictionson the results of measurements. It seems interesting toask if this statistical element be thought of as arising,as in classical statistical mechanics, because the states inquestion are averages over better defined states for whichindividually the results would be quite determined” . Bellin this work had given the answer of the principal ques-tion ”What or who is the observer?” If all quantum phe-nomena can be described using better defined states forwhich individually the results would be quite determined,i.e. ’hidden variables’ than the observer is an apparatus.But in this case the orthodox QM proposed by Heisen-berg is observably inadequate. It may be adequate if ”atomic and subatomic particles do not have any definiteproperties in advance of observation” [27]. In this casethe observer must be the mind of a human being becauseno apparatus can create definite properties when they donot exist in advance of observation. Any apparatus canonly change properties and make they hidden.The vagueness of QM is a consequence of logicalmistakes made by young Heisenberg. Einstein warnedagainst one of they. Heisenberg remembered [56] that af-ter his talk at the Berlin university in 1926 Einstein hastold him that ”from the fundamental point of view the in-tention to create a theory only on observable parameterscompletely ridiculously. Because in the real all is quitethe contrary. Only the theory can decide what exactlycan be observable. As you can see, observation, generallyspeaking, is very complicated process” . In 63 years laterBell wrote: ”Einstein said that it is theory which decides what is ’observable’. I think he was right - ’observation’ isa complicated and theory-laden business. Then that no-tion should not appear in the formulation of fundamentaltheory” [24]. Einstein and Bell asserted fairly that theoffer by Heisenberg to describe only observable parame-ters rather has complicated than has simplified the taskof theory. The description of observation results can notbe complete without a description of the act of observa-tion. Therefore it is easier to create a theory describing ”real situation (as it supposedly exists irrespective of anyact of observation or substantiation)” [50] than a theorydescribing observation results. The vagueness of the no-tion about observation (measurement) is principal causeof the fundamental obscurity in quantum. Bell was rightwhen he stated that ”On this list of bad words from goodbooks, the worst of all is ’measurement’” . Heisenbergproposing to describe observation results could not evenformulate enough clear what is observation.This logical mistake is result of other fundamen-tal mistake concerning his conception of human think-ing. Heisenberg noted: ”This basis of the philosophyof Descartes is radically different from that of the an-cient Greek philosophers. Here the starting point is nota fundamental principle or substance, but the attempt ofa fundamental knowledge. And Descartes realises thatwhat we know about our mind is more certain than whatwe know about the outer world” [31]. But Heisenberghimself seems to do not realise that our knowledge aboutour mind is more certain than about the outer world.Only therefore he could contest the logical conclusion byKant that the law of causality is a priori form of ourmind and the basis of all scientific work. The vaguenessand self-contradiction of QM prove that rather Kant thanHeisenberg was right. Considering the law of causalityHeisenberg wrote: ”Kant says that whenever we observean event we assume that there is a foregoing event fromwhich the other event must follow according to some rule” [31]. This conclusion by Kant about human thinkingis confirmed with an interesting discussion between cre-ators of quantum mechanics at the Solvay meeting 1927,which Bohr remembered in 1949 [40]: ”On that occasionan interesting discussion arose also about how to speakof the appearance of phenomena for which only predic-tions of statistical character can be made. The questionwas whether, as to the occurrence of individual effects,we should adopt a terminology proposed by Dirac, thatwe were concerned with a choice on the part of ’nature’or, as suggested by Heisenberg, we should say that wehave to do with a choice on the part of the ”observer”constructing the measuring instruments and reading theirrecording. Any such terminology would, however, appeardubious since, on the one hand, it is hardly reasonable toendow nature with volition in the ordinary sense, while,on the other hand, it is certainly not possible for the ob-server to influence the events which may appear underthe conditions he has arranged” .Here three principal creators of QM discuss what isthe cause of the appearance of phenomena. None of they8state the absence of the cause, even Heisenberg. Almost30 years later Heisenberg calls in question that the Kant’sconclusion ”Since we actually apply this method, the lawof causality is ’a priori’ and is not derived from expe-rience” [31] may be true in atomic physics. Heisenbergconsiders a radium atom, which can emit an α -particlestates ”The time for the emission of the α -particle cannotbe predicted” [31]. Next he asks ”But why has the scien-tific method actually changed in this very fundamentalquestion since Kant?” , gives two answers one of they is ”We have been convinced by experience that the laws ofquantum theory are correct and, if they are, we know thata foregoing event as cause for the emission at a given timecannot be found” and concludes ”Therefore, Kant’s argu-ments for the a priori character of the law of causality nolonger apply” [31]. This Heisenberg’s conclusion is abso-lutely ill-founded because he considers the ’res extensa’whereas Kant considered the ’res cogitans’, human mind.The Kant’s conclusion that the law of causality is ’a pri-ori’ is ’a priori’. Therefore neither experience nor theorydescribing correctly this experience can call this conclu-sion in question. The negation of a cause in ’nature’, i.e.the terminology proposed by Dirac results inevitably tothe suggestion by young Heisenberg that the ’observer’ isthe cause of the occurrence of individual effects. Just thissuggestion results to the EPR paradox, the Schrodinger’scat paradox, the questions ”Whose knowledge and whosewill?”, considered above, and other nonsense.
5. FUNDAMENTAL MISTAKES BECAUSE OFTHE PREJUDICE OF THE QM UNIVERSALITY
The fundamental obscurity in QM discussed during al-most ninety years is connected with the vague notionabout the act of observation, i.e. the Process 1 accord-ing to Everett [14]. The description of the Process 1should lie in the domain of psychology [14]. Thereforeit is very important to draw reader’s attention that theact of observation is absent at the description of mostquantum phenomena. It was noted in the Introductionthat already Feynman had become aware of the appli-cability of the realistic interpretation of wave functionproposed by Schrodinger for description of macroscopicquantum phenomena. But he did not understand thefundamental importance of this fact. Anyone can easysee that not only macroscopic quantum phenomena aredescribed with the Schrodinger interpretation, i.e. with-out the Process 1, the mind of the observer and othermysticism. Schrodinger had introduced the term ’wavefunction’ for his interpretation and used, as well as Ein-stein [50], the term ’ ψ - function’ [33] for the positivisticinterpretation proposed by Born. The terms ’wave func-tion’ Ψ Sh and ’ ψ - function’ Ψ B will be used below in thesame sense. It would be useful to categorise the quan-tum phenomena described the ’wave function’ and the ’ ψ - function’. QM uses the ’ ψ - function’ when the Diracjump is used at the description and the ’wave function’ when the Dirac jump is absent. ψ - functions and the wave function For example, the Dirac jump is used for the descrip-tion of the two-slit interference experiment demonstrat-ing particle - wave duality at observation. The interfer-ence pattern, for example electrons observed on a detect-ing screen [57], testifies to that electrons pass throughthe double-slit as a wave with the de Broglie wave-length λ deB = 2 π ~ /mv . But the same electrons man-ifest itself as particles at they arrival at the detectingscreen [57], see also Fig.1-3 in the book [16]. QM de-scribes this observed duality with help of the ψ func-tion Ψ B = Ψ B + Ψ B which is the superposition of two ψ - functions Ψ B = A e iϕ , Ψ B = A e iϕ describingtwo possible path L , L of electrons through the firstand second slits with the amplitudes A and A of thearrival probability at the point y of a particle passingthrough the first and second slit. Then, the probability P ( y ) = | Ψ B | of the electron arrival at a point y of thedetecting screen, Fig.3, P ( y ) = A + A + 2 A A cos(∆ ϕ − ∆ ϕ ) (16)should depend on the phase difference ∆ ϕ − ∆ ϕ .Y. Aharonov and D. Bohm had noted more thanfifty years ago [58] that this phase difference ∆ ϕ − ∆ ϕ = R yS dr ( p/ ~ ) − R yS dr ( p/ ~ ) = R yS dr ( mv/ ~ ) − R yS dr ( mv/ ~ ) + H dr ( eA/ ~ ) = 2 π ( L − L ) /λ deB +2 π Φ / Φ and consequently the probability (16) shouldchange with magnetic flux Φ inside the closed contour S − L − y − L − S , Fig.1, because of the relation p = mv + qA between canonical momentum p and elec-tron q = e velocity v in the presence of a magnetic vectorpotential A . The interference pattern shift with the fluxΦ change was corroborated by many experiments [59].The value of the probability (16) oscillates with the pe-riod equal the flux quantum Φ = 2 π ~ /q .The periodicity because of the Aharonov - Bohm effect[59], i.e. because of the relation ~ ∇ ϕ = p = mv + qA ,are observed also in normal metal [60] and superconduc-tor [62, 63, 75] loops. But this effect differs in essencefrom the case of the two-slit interference experiment.The periodical dependencies in magnetic flux Φ with pe-riod Φ = 2 π ~ /q are observed in the mesoscopic rings[60, 62, 63, 75] because of the quantization of velocitycirculation I l dlv = 2 π ~ m ( n − ΦΦ ) (17)The quantization (17) is deduced from the requirementthat the complex wave function must be single-valuedΨ Sh = | Ψ Sh | exp iϕ = | Ψ Sh | exp i ( ϕ + n π ) at any point.Because of this requirement, the phase ϕ must change byintegral n multiples of 2 π following a complete turn along9 FIG. 3: The Ahronov-Bohm effects in the two-slit interferenceexperiment (on the left) and in in normal metal or supercon-ductor ring (on the right) are consequence of the magnetic fluxΦ influence on the phase difference ∆ ϕ − ∆ ϕ = H l dl ∇ ϕ . Inthe first case the difference ∆ ϕ − ∆ ϕ of the phase changesbetween S and y points along upper L way ∆ ϕ and lower L way ∆ ϕ should not be divisible by 2 π (∆ ϕ − ∆ ϕ = n π )since the ψ function collapses at the observation of the elec-tron arrival in a point y of the detector screen. In contrastto the interference experiment the Ahronov-Bohm effects inmesoscopic ring (for instance the persistent current) are ob-served because of the requirement ∆ ϕ − ∆ ϕ = n π sincethe wave function, describing this case, can not collapse the path of integration, yielding H l dl ▽ ϕ = H l dlp/ ~ = H l dl ( mv + qA ) / ~ = m H l dlv/ ~ + 2 π Φ / Φ = n π .This requirement is violated at the description of thetwo-slit interference experiment because of the collapseof the ψ - function (the Dirac jump) at the observa-tion of the electron arrival in a point y of the detectorscreen. The phase difference ∆ ϕ − ∆ ϕ = R yS dr ∇ ϕ − R yS dr ∇ ϕ = H l dr ∇ ϕ and the probability (16) can changeuninterruptedly with the coordinate y and magnetic fluxΦ thanks to the collapse. This uninterrupted variationprovides the interference pattern (16) and its shift withΦ. Thus, although the both Aharonov - Bohm effects re-sult from the Φ influence on the phase variation along aclosed path H l dr ∇ ϕ they differ fundamentally: the firstone should be described with the ψ - function whereas thesecond one should be described with the wave function[64].The ignorance about this fundamental difference pro-vokes mistakes. For example, the authors [65] have con-cluded that electrons can be reflected because of mag-netic flux Φ in the Aharonov-Bohm ring, in defiance ofthe law of momentum conservation [8]. The contradic-tion in such scandalous form is absent in the Aharonov -Bohm effect [58], although there is a problem with non-local force free momentum transfer [16, 66]. In spite ofthe change in the interference pattern no overall deflec-tion of electrons is observed in the Aharonov-Bohm effectbecause of magnetic flux [16]. The transmission (reflec-tion) probability P tr = R dyP ( y ) = R dx ( A + A ) = 1can not depend at all on magnetic flux Φ contrary to theerroneous theoretical result shown on Fig.2 in [65]. Themistake [65] is one of consequences of the prejudice of theQM universality [7]. Even macroscopic realism was called in question be-cause of this prejudice. Bell noted that creators of QM ”despair of finding any consistent space-time picture ofwhat goes on the atomic and subatomic scale” [27]. ”Forexample [67], Bohr once declared when asked whetherthe quantum mechanical algorithm could be consideredas somehow mirroring an underlying quantum reality:’There is no quantum world. There is only an abstractquantum mechanical description. It is wrong to think thatthe task of physics is to find out how Nature is. Physicsconcerns what we can say about Nature’” [27]. The cre-ators of QM disclaimed reality only on the atomic andsubatomic scale. Recently this scepticism about realismwas expanded to macroscopic level [11]. The authors[11] quoting the known remark by Albert Einstein ”I liketo think that the moon is there even if I don’t look at it” claims that some experimental results obtained on super-conducting circuit [68] could refute this trust by Einsteinin objective reality even on the macroscopic level. Thisscandalized claim bears a direct relation to the problemof a possibility of superconducting quantum bits [69]. Asmall moon, which is not there according to [11], is amagnetic flux inside a superconducting loop [70] whichis considered as flux qubit in numerous publications [69]including the one [71] of the author of the scandalizedclaim [11]. The authors [11] believes paradoxically thatQM can prove that nothing is there but it is possible tocreate anything, superconducting quantum bits [71] forexample, using this nothing. Ironically, quantum bits canbe created indeed only if quantum systems do not haveany definite properties in advance of observation.Only basis both of the doubt in macroscopic reality[11] and of the reality of superconducting quantum bits[69, 71] is the Leggett-Garg inequality referred to as aBell’s inequality in time [11, 68]. A.J. Leggett and A.Garg [70] have concocted the contradiction with real-ism extremely unsuccessful. The doubt about reality ofmacroscopic magnetic flux in rf SQUID, i.e. a supercon-ducting loop interrupted by Josephson junction, is pro-voked in [70] only because of ψ - function usage in ad-ditional to the wave function describing superconductingstate. ψ - function can apply speculatively for descriptionof any macroscopic object, for example the cat [33] or themoon [49]. But realism must not be called in questionwithout irrefutable empirical evidence obtained on thebase of no-hidden-variables theorem (or, vulgarly, ’no-gotheorem’) [43].The superconducting loop interrupted by Josephsonjunction, considered in [70], has two permitted stateswith the same minimal energy and opposite directed su-perconducting current (the persistent current I p ), whenexternal magnetic flux inside its loop is divisible by halfΦ = ( n + 0 . of the flux quantum Φ = 2 π ~ /q , see therelation (17). Imitating Bell, A.J. Leggett and A. Garg[70] have offered inequalities which experimental check0should prove the contradiction with any realistic theoryand the necessity of the positivistic description with helpof superposition of states, which should collapse at obser-vation. The no-go theorem by A.J. Leggett and A. Garg[70] is false because of some reasons. First of all there isnot a well-grounded motive to call macroscopic realism inquestion because rather the realistic Schrodinger’s thanpositivistic Born’s interpretation of the wave function isvalid for description of macroscopic quantum phenom-ena. The authors [70] as well many others [69, 71, 73]liken superconducting loop to spin 1/2 and assume su-perposition of its two permitted states, described as thesuperposition of the spin states ψ = α | ↑ > + β | ↓ > .This likening is obviously false because of some reasons.First of all because superconducting loop is flat and themagnetic moment M m = I p S of the current I p circu-lating in it anticlockwise or clockwise and the angularmomentum of Cooper pairs M p = (2 m e /e ) I p S are one-dimensional. The assumption [69–71, 73] of superposi-tion of states with different value of the one-dimensionalangular momentum contradicts to formalism of QM [19]even if the one-dimensional angular momentum is micro-scopic. Therefore it is very strange that A.J. Leggettand A. Garg [70] and other authors [69, 71, 73] could as-sume superposition of states with macroscopically differ-ent ∆ M p ≈ ~ angular momentum. This assumptioncontradicts obviously to the fundamental law of angularmomentum conservation [72] and is much more incon-ceivable than superposition of the cat’s states, at least ofthe Schrodinger’s cat (9). Besides the authors [70] repeatvirtually the mistake [42, 43] of the von Neumann’s no-hidden-variables proof. Thus, the doubt in macroscopicrealism [11, 70] is absolutely baseless and was provokedwith misinterpretation of QM as a theory describing uni-versally all quantum phenomena. We can believe as be-fore in reality of the moon.
6. FUNDAMENTAL OBSCURITY CONNECTEDWITH WAVE FUNCTION USAGE
The wave function describes a real situation (as it sup-posedly exists irrespective of any act of observation orsubstantiation) in accordance with the programmatic aimof all physics upheld by Einstein [50]. Therefore the fun-damental obscurity connected with the Born’s interpre-tation is absent at the description of macroscopic andsome other quantum phenomena. But there is differentfundamental obscurity, more real than the one connectedwith violation of the Bell’s inequalities. In spite of thisobscurity, the universally recognised quantum formalismdescribes almost all effects observed in superconductorstructures. But some experimental results obtained re-cently contradict to its predictions.
The real situation, described with the wave functionΨ Sh = | Ψ Sh | exp iϕ , can not change because of our look,but it can alter with help of a real physical influence.For example, we can decrease the density of Cooper pairs | Ψ Sh | = n s = n s, (1 − T /T c ) down to n s = 0 at a time t = t on , overheating a loop segment B above supercon-ducting transition T > T c , for example with help of laserbeam, Fig.4. The electric field E = − ▽ V ≈ V B / ( l − l B )of the potential voltage V B = R B I ( t ) = R B I p exp − t − t on τ RL (18)appeared because of a non-zero resistance R B > B segment in normal state, will decrease the veloc-ity of Cooper pairs from the quantum value (17), equal v = − π ~ /lm /
4, down to zero v = 0, during the relaxationtime τ RL = L/R B . I p = s en s v is the persistent currentobserved because of the quantization (17); s = hw is theloop section; L is the inductance of the loop with a length l . This velocity change occurs in accordance with theNewton’s second law mdv/dt = 2 eE , under the influenceof the real force F E = 2 eE acting on each Cooper pair.According to the universally recognised quantum formal-ism the velocity in all loop segment, including the A one,Fig.4, must return to the initial value v = − π ~ /lm ∝ ( n − Φ / Φ ) after turning off of the laser beamat a time t off and the cooling of the B segment downto the initial temperature T < T c , see the left picture onFig.4. The pair velocity in the segment A should changewithout a real force at the change of the real situation inthe spatially separated segment B , Fig.4, because of theprohibition (17) of the zero velocity v = 0 at Φ = n Φ .The quantum formalism can not explain this non-localforce-free momentum transfer. It can only describe phe-nomena connected with it.The direct component V dc = 1Θ Z Θ dtV B ( t ) ≈ Lω sw I p ; at ω sw τ RL ≪ a ) V dc ≈ R B I p ; at ω sw τ RL ≫ b )of the voltage (12) should be observed at repeated switch-ing with a frequency ω sw of the B segment, Fig.4, be-tween superconducting and normal states, because of thereturning of the loop to the same state n at each B cool-ing [74]. The sign and value of the dc voltage (19) shouldvary periodically with magnetic flux V dc (Φ / Φ ) like thepersistent current I p (Φ / Φ ) [75], because of the changeof the quantum number n corresponding to minimum en-ergy ∝ ( n − Φ / Φ ) at Φ = ( n + 0 . [76]. Such quan-tum oscillations of the dc voltage V dc (Φ / Φ ) ∝ I p (Φ / Φ )were observed on segments of asymmetric aluminium1 FIG. 4: Superconducting loop can be switched between thestates with different connectivity of the wave function Ψ Sh = | Ψ Sh | exp iϕ with a real physical influence, for example turn-ing on (the right picture) and turning off (the left picture) ofthe laser beam heating the loop segment B above T c . The per-sistent current, equal I p = − s en s (2 π ~ /lm
4) in a symmetricloop l with the same section s and pair density n s along thewhole l , flows at the magnetic flux Φ = Φ / l whenthe wave function is closed (the left picture). The current cir-culating in the loop should decay during the relaxation time τ RL = L/R B after the transition in the state with unclosedwave function because of a non-zero resistance R B > B segment in the normal state (the right picture). The photoof a real aluminum loop is used in order to exhibit that thegedankenexperiment can be made real. rings when the switching take place because of noise[77–80] or ac current [62, 81]. The experimental results[78, 79] give unequivocal evidence that the persistent cur-rent can flow against the dc electric field E = − ▽ V .This puzzle may be connected with the other one: theobservations [62, 63, 75, 78, 79, 82] of the persistent cur-rent I p (Φ / Φ ) at a non-zero resistance R l >
0. An elec-tric current should decay during a very short relaxationtime τ RL = L/R l < − s without Faraday’s voltage − d Φ /dt = 0 in the aluminium ring, used in [75, 78, 79],with radius r ≈ µm , the inductance L ≈ − H , atresistance R l > .
01 Ω. In defiance of this the persistentcurrent does not decay [75, 78, 79].This puzzles can be described in the limits of the quan-tum formalism taking into account that the angular mo-mentum H l dlp = H l dl ( mv +2 eA ) = m H l dlv +2 e Φ of eachCooper pair should change from 2 e Φ to n π ~ becauseof the quantization at each closing of superconductingstate in the ring. This change of pair momentum p ina time unit at repeated switching with a frequency ω sw was called in [83] ”quantum force” F q : I l dlF q = 2 π ~ ( n − ΦΦ ) ω sw (20)at ω sw ≪ /τ RL . The quantum force H l dlF q takes theplace of the Faraday’s voltage − d Φ /dt which maintains IR l = − d Φ /dt a conventional current I circulating in aloop and describes why the persistent current can notdecay I p R l = H l dlF q / e in spite of the power dissipation I p R l . Under equilibrium condition the I p = 0 at R l > T ≈ T c [75, 78, 79], wherethermal fluctuations can switch loop segments betweensuperconducting n s > R = 0 and normal n s = 0, R >
B < B c , completely expels the field from the supercon-ducting material except for a thin layer λ L ≈ nm =5 10 − m at the surface. The quantum formalism de-scribes the Meissner effect as the particular case n = 0of the flux quantization Φ = n Φ = 0 [64] but can notexplain the puzzle. In the case, considered on Fig.4, theangular momentum change of single pair n π ~ − e Φ =2 π ~ ( n − Φ / Φ ) ≤ π ~ . l = 2 πr radius r and the Φ = Bπr value.At the Meissner effect observed at any radius r of su-perconductor and any B < B c , this change is macro-scopic 2 π ~ ( − Φ / Φ ) = 2 π ~ ( − Bπr / Φ ) ≈ − ~ atthe first critical field B c ≈ . T and the superconduc-tor radius r = 1 m . This obscurity is macroscopic intruth because of the angular momentum change of all N s = n s πr h > pairs in a cylindrical superconduc-tor. Jorge Hirsch wonders fairly that ”the question ofwhat is the ’force’ propelling the mobile charge carriersand the ions in the superconductor to move in directionopposite to the electromagnetic force in the Meissner ef-fect was essentially never raised nor answered” [85]. Heproposes an explanation of the Meissner effect puzzle [85].But some consequences of this explanation, for examplethe electric field inside the superconductor, the relation(23) in [85], seem unacceptable.According to the point of view by Hirsch [86] the force-free momentum transfer indicates a fundamental problemwith the conventional theory of superconductivity [87]. Ithink that it indicates a fundamental problem rather withQM as a whole than with a theory of superconductivity[88]. The persistent current I p = 0 is observed at R > a familiar analog in atomic physics: a currentcirculating around the atom although the exponential de-crease of the persistent current amplitude with temper-ature increase, Fig.3 in [60], testifies against this analogand to fundamental differences between application ofsome quantum principles on atomic and mesoscopic lev-els [90]. Igor Kulik, who has described the possibility of I p = 0 at R > ”time-reversal symmetry shouldforbid a current choosing one direction over the otheraround the ring” [89]. According to [60, 89] ”A magneticflux Φ threading the ring will break time-reversal sym-metry, allowing the PC to flow in a particular directionaround the ring” [60]. But the I p [60, 75] and E = −▽ V p [78, 79] direction changes not only with the Φ directionbut also with its value at Φ = n Φ and Φ = ( n + 0 . .Each physicist must understand that the observation ofthe direction change with the value change is a puzzlewhich may have a fundamental importance [93–95]. Suchpuzzle was not observed on the atomic level because ofthe inaccessibly high magnetic fields Φ /πr B ≈ G needed for this. According to the criterion of demarcation betweenwhat is and is not genuinely scientific by Karl Popper:a theory should be considered scientific if and only if itis falsifiable. Therefore any experimental results contra-dicting to the quantum formalism should be at the centreof attention. I would like to draw reader’s attention totwo of such results. According to the quantum formalism(17) two permitted states n and n + 1 of superconductingloop should be observed at Φ = ( n + 0 . at the single-shot measurement. Some experimental results [96, 97]corroborate this prediction but other one [97] contradictto it. The χ -shaped crossing observed in [97] and mis-interpreted [98] by the authors as the single-shot read-out of macroscopic quantum superposition of ’flux qubit’[69, 71] states challenges the quantum formalism forbid-ding the state with v = 0 (17) at Φ = ( n + 0 . . Otherchallenge has been revealed at measurements of magneticdependencies of the critical current of asymmetric super-conducting rings [62, 99–101]. According to the quan-tum formalism (17) the critical current anisotropy shouldappear in the asymmetric ring because of a change of the functions describing its magnetic dependencies, seeFig.19 [62] and Fig.3 [100]. But the measurements haverevealed that the asymmetry appears because of changesin the arguments of the functions rather than the func-tions themselves [62, 99, 100].
7. CONCLUSION
The history of QM demonstrates clearly that nosuccessfulness of a theory can guarantee its accuracy.Most physicists believed in QM and disregarded thepointed criticism of Einstein, Schrodinger, Bell and oth-ers who tried to explain that the proposal of Heisen-berg to describe observables instead of beables and theBorn’s interpretation of the wave function are inade-quate. They strode unimpeded through the fundamentalobscurity and non-universal validity quantum principles.Schrodinger pointed out, for example, the non-universalvalidity of the complementarity and uncertainty princi-ples. According to Bohr ”the study of the complementaryphenomena demands mutually exclusive experimental ar-rangements” [40] But the method of momentum p = mv measurement, learned in the primary school, disprovesthis statement. According to this method the momentum p = m ( z − z ) / ( t − t ) is measured with help of mea-surement of the time t and t when the particle passespoints z and z . Thus, the experimental arrangementsfor the measurement of position and momentum are notmerely mutually non-exclusive but are the same. Thevelocity value v z = z/t can be measured with the uncer-tainty ∆ v z ≈ v z (∆ z/z + ∆ t/t ) at z = z − z ≫ ∆ z , t = t − t ≫ ∆ t . Consequently, we can make the prod-uct of the velocity ∆ v z and position ∆ z uncertainties∆ z ∆ v z ≈ ∆ zv z (∆ z/z + ∆ t/t ) how any small, contraryto the Heisenberg uncertainty relation ∆ z ∆ v z > ~ / m ,increasing the distance z = z − z and the time t = z/v z .The mass delusion concerning quantum mechanic is aconsequence of the optimistic point of view that the his-tory of science is the history of progress. But it is alsothe history of wrong belief. In the beginning of his talk”Speakable and unspeakable in quantum mechanics” p.169 in [1] Bell cites a quotation from A. Koestler’s book’The Sleepwalkers’ about of the Copernican revolution: ” · · · the history of cosmic theories may without exagger-ation be called a history of collective obsessions and con-trolled schizophrenias; and the manner in which some ofthe most important individual discoveries were arrived atreminds one of a sleepwalker’s performance ··· .” . Accord-ing to Bell and Koestler Copernicus, Kepler, and Galilei ”were not really aware of what they were doing · · · sleep-walkers” p. 169 in [1]. This sleepwalking in the historyof QM is more evident. QM is the most successful the-ory but it is also most obscure theory. The cause of thisobscurity is obvious and some experts denoted it, for ex-ample Jaynes [102]: ”From this, it is pretty clear whypresent quantum theory not only does not use - it doesnot even dare to mention - the notion of a ’real physical situation’. Defenders of the theory say that this notionis philosophically naive, a throwback to outmoded ways ofthinking, and that recognition of this constitutes deep newwisdom about the nature of human knowledge. I say thatit con-stitutes a violent irrationality, that somewhere inthis theory the distinction between reality and our knowl-edge of reality has become lost, and the result has morethe character of medieval necromancy than science” seep. 231 in the book [16].But most physicists continue to believe in QM. No sci-ence can be possible without a faith. Scientists should,at least, believe in the human capability to perceive theouter world. But the belief should not be implicit. Weshould understand that the EPR correlation and viola-tion of the Bell’s inequalities rather cast doubt on theour capability to perceive the outer world than give newopportunities, for example quantum computation. Suchsensible view of things hardly may be possible withoutthe comprehension epistemological basic of science. Ein-stein emphasised this: ”The reciprocal relationship ofepistemology and science is of noteworthy kind. Theyare dependent upon each other. Epistemology withoutcontact with science becomes an empty scheme. Sciencewithout epistemology is - insofar as it is thinkable at all- primitive and muddled. However, no sooner has theepistemologist, who is seeking a clear system, fought hisway through to such a system, than he is inclined to in-terpret the thought-content of science in the sense of hissystem and to reject whatever does not fit into his sys-tem. The scientist, however, cannot afford to carry hisstriving for epistemological systematic that far. He ac- cepts gratefully the epistemological conceptual analysis;but the external conditions, which are set for him by thefacts of experience, do not permit him to let himself betoo much restricted in the construction of his conceptualworld by the adherence to an epistemological system. Hetherefore must appear to the systematic epistemologist asa type of unscrupulous opportunist: he appears as real-ist insofar as he seeks to describe a world independentof the acts of perception; as idealist insofar as he looksupon the concepts and theories as the free inventions ofthe human spirit (not logically derivable from what is em-pirically given); as positivist insofar as he considers hisconcepts and theories justified only to the extent to whichthey furnish a logical representation of relations amongsensory experiences. He may even appear as Platonistor Pythagorean insofar as he considers the viewpoint oflogical simplicity as an indispensable and effective tool ofhis research” [50].The logical simplicity can not be attributable to QM.Moreover this theory is remarkable for logical inconsis-tency and non-universality. Even its fundamental obscu-rities are no-universal. The fundamental obscurity un-masked by Einstein, Schrodinger, Bell and other oppo-nents of the positivism may be connected with the repu-diation of realism. But even realistic description of manyquantum phenomena with help of the Schrodinger’s in-terpretation of the wave function has fundamental obscu-rities. We must conclude that a consistent and universaltheory of quantum phenomena is absent now. ”Couldsuch theory be created in principle?” is the question re-quiring an answer first of all. TURES: Physics and Technology”, Belarus, Minsk, In-stitute of Physics NAS, p. 87 (2009); arXiv: 0910.5172[64] Nikulov A. V. 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