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[1]. This fundamental obscurity as well as QM are re- all others theories of physics, describes rather different sult of the proposal by young Werner Heisenberg [2] to phenomena than a unique reality. No description of phe- describe observables instead of beables, see these terms nomena should be universal if they are not considered as in the Bell’s paper [3]. This proposal to abandon any a universal manifestation of a unique reality. Therefore attempt to find a unified picture of objective reality had it is logical mistake to think that QM should describe provoked the battle between creators of quantum the- universally all quantum phenomena. Nevertheless QM ory. Bohr, Pauli, Dirac and others admitted the Heisen- was developed and interpreted up to now as a univer- berg’s proposal whereas Einstein, Schrodinger, de Broglie sal theory. General confidence predominates that only and others rejected the repudiation of the science aim as the positivistic Born’s interpretation but not the realistic the discovery of the real. Schrodinger interpreted his Schrodinger’s interpretation can be valid for description wave function as a real wave [4] and defended this real- of all quantum phenomena. istic interpretation [5]. He tried to replace particles by This confidence is obviously false. Richard Feynman wavepackets. ”But wavepackets diffuse” [6]. This diffuse- in the Section ”The Schrodinger Equation in a Classical ness contradicts numerous observation. Therefore the in- Context: A Seminar on Superconductivity” of his Lec- terpretation of the Schrodinger’s wave function as prob- tures on Physics [13] stated that Schrodinger ”imagined ability amplitudes proposed by Born was fully accepted incorrectly that |Ψ|2 was the electric charge density of the by most physicists. This positivistic interpretation corre- electron. It was Born who correctly (as far as we know) sponds to the Heisenberg’s proposal and just therefore it interpreted the Ψ of the Schrodinger equation in terms results to the fundamental obscurity and mass delusion. of a probability amplitude”. But further Feynman wrote Indeterminism, subjectivity, non-locality and vagueness that ”in a situation in which Ψ is the wave function for implied with this interpretation are enough obvious. But each of an enormous number of particles which are all in only few physicists, Einstein, Schrodinger, de Broglie and the same state, |Ψ|2 can be interpreted as the density of some others worried about these ”philosophical” prob- particles”. Thus, Feynman had pointed out that the pos- lems during a long time. Most physicists, as Bell said itivistic Born’s interpretation could be replaced with the ”stride through that obscurity unimpeded... sleepwalk- realistic Schrodinger’s interpretation at the description of ing?”, see p. 170 in [1]. Bell worried about this obscu- macroscopic quantum phenomena, at least. This fact has rity of positivistic QM but even he said: ”The progress fundamental importance because ”There are two funda- so made is immensely impressive. If it is made by sleep- mentally different ways in which the state function can walkers, is it wise to shout ’wake up’? I am not sure change” [14] according to the Born’s interpretation: the that it is. So I speak now in a very low voice”, see p. 170 discontinuous change at the observation (Process 1 ac- in[1]. cording to [14]) and the continuous deterministic change But now it is needed to shout ”wake up” [7]. There are of state of an isolated system with time according to some reasons why it is needed: 1) numerous false pub- a Schrodinger’s wave equation (Process 2 according to lications because of misunderstanding of QM [7–9]; 2) [14]). Hugh Everett noted correctly that because of the misunderstanding of the idea of quantum computation Process 1 ”No way is evidently be applied the conven- [10]; 3) some authors, because of their implicit belief in tional formulation of QM to a system that is not subject QM, claim already that it is possible to prove experi- to external observation” and that ”The question cannot mentally that ”The moon - a small moon, admittedly - be ruled out as lying in the domain of psychology” [14]. is not there” [11]; 4) on the other hand many physicists But only select few realized this fundamental obscurity in have already refused this implicit belief in QM. The most QM in that time. Feynman did not realized. Therefore striking illustration of the fourth reason is the Action he did not attach great importance to the replacement of of the European Cooperation in Science and Technology the Born’s interpretation by the Schrodinger’s interpre- ”Fundamental Problems in Quantum Physics” [12]. The tation. Feynman did not understand that the Process 1, first aim of research - observer-free formulation of QM and all fundamental problems connected with it, disap- witnesses to perception by numerous participants of the pear at this replacement. Action MP1006 that no subjectivity can be permissible Richard Feynman and Hugh Everett were doctoral stu- in any physical theory. But I should say that only this dents of the same doctoral advisor - John Archibald perception does not indicate that these scientists have Wheeler. But their conception of QM was fundamen- ’waked up’ completely. tally different. Such dissent marks out QM from other They have not realized for the present a primary logi- theories of physics. The dissent was from the very out- cal mistake of the sleepwalkers creating QM. Scientists set of QM. It was observed both between defenders of have in mind always that any physical theory should QM, for example Heisenberg and Bohr, and its critics, describe universally all its subject matters. For exam- for example Schrodinger and de Broglie. But now the ple, everyone believes that the Newton’s laws describe diversity of opinion is unusually wide. Einstein wrote universally the motion of all object with different mass, as far back as 1928 to Schrodinger [15]: ”The soothing from major planets to smallest particles. This belief may philosophy-or religion?-of Heisenberg-Bohr is so cleverly be justified with a universality of the laws governing a concocted that it offers the believers a soft resting pillow unique objective reality. Orthodox QM, in contrast to from which they are not easily chased away”, see the cite 3 on the page 99 of [16]. The diversity of opinion about QM electron some place the entire charge is there”. Feynman witnesses that Einstein’s words turned out prophetic: the was sure that this idea is correct because he did not raise dissent can be about a religion but our right comprehen- the question: ”How can the entire charge be there when sion must be unified. At least we must believe that it is an observer has found the electron some place?” Let con- possible. Otherwise no science could be possible. There- sider the electron in empty space, or better a fullerene, or fore first of all it is important to show that subjectivity, even a long biomolecule, quantum interference of which non-locality, indeterminism and vagueness of QM are de- was observed already [17, 18]. Quantum state of such duced unambiguously from the Born’s interpretation. It particle can be described with the wave-packets (1) in will be made in the next Section. This positivistic in- which the wave functions expi(pr − Et)/~ are deduced terpretation can be valid and understood correctly only from the Schrodinger’s wave equation [19] in a new Weltanschauung proposed by Heisenberg. This ∂Ψ ~2 new Weltanschauung will be considered shortly in the i~ = − ∇2Ψ+ U(r)Ψ (2) Section 3. Unfortunately only few scientists have re- ∂t 2m alized that the correct understanding of QM demands whereas the amplitudes A0(p) can be estimate only with the new Weltanschauung. Both mass delusion connected with this lack of understanding and mistakes made by help of an observation at a time t = 0. According to (2) E = p2/2m in empty space where U(r) = 0. It is possi- Heisenberg will be considered in the Section 4. Mistakes of other type connected with the misinterpretation of ble, for example with help of the scanning laser ionization detector used in [20], to observe at t = 0 that a fullerene, quantum mechanics an a universal theory will be con- for example, is localised in a space region ∆r near r = 0. sidered in the Section 5. The fundamental obscurities in quantum mechanics worrying Einstein, Schrodinger, Bell The result of this observation may be describe approx- imately with the probability density function Ψ(r) = and others disappear with the realistic interpretation of −1/4 −1/2 2 2 wave function proposed by Schrodinger. But other fun- (2π) σ exp(−r /4σ ) [13] where σ ≈ ∆r/3. The wave-packet (1) diffuses, Fig.1, because its amplitudes, damental obscurities appear with this realistic interpre- 1/4 1/2 2 2 ~2 tation. These fundamental obscurities of other type will equal A0(p) = (8π) σ exp(−p σ / ) at t = 0, change with time A(p,t) = (8π)1/4σ1/2exp(−p2σ2/~2 − be considered in the Section 6. ip2t/~2m). Because of this Process 2 [14] the probabil- ity to observe the particle in a space region near r = 0 2. WHAT IS IMPLIED WITH THE BORN’S decreases and far off r = 0 increases with time, Fig.1. INTERPRETATION OF THE WAVE FUNCTION? The Process 2 is continuous and is determined with the Schrodinger’s wave equation (2). But the discontinuous change of the probability |Ψ(r, t)|2 and the wave-packet Feynman wrote [13] when Schrodinger ”imagined in- 2 Ψ(r, t) at an observation, i.e. the Process 1 [14], can not correctly that |Ψ| was the electric charge density of the be described with this equation (2). electron He soon found on doing a number of problems The Process 1, at t = t1 for example, Fig.1, cannot be that it didn’t work out quite right”. Schrodinger had tried described outside the domain of psychology. Everett [14] to replace ’particles’ by wave-packets was right. No physical interaction of the particle with ∞ i i photons radiated with laser or any measuring device can Ψ(r)= dp[A0(p)exp − Et]exp pr (1) Z−∞ ~ ~ compact the wave-packet. It is quite obvious that ac- cording to the Born’s interpretation the wave-packet is But this wave-packets spreads in empty space, for exam- squeezed in a smaller volume because of the observation ple, when the energy E = p2/2m. Therefore the real by an observer the particle near, for example, r ≈ 8, wave-packets cannot explain the observations of parti- Fig.1. The observation changes first of all the mind of the cle localized in the space, for example particle tracks in observer. Before the observation at t

It could be clear from the very outset that according to the Born’s interpretation the observation should be inter- preted unambiguously as interplay between the quantum system and the mind of the observer. But Heisenberg and Bohr had convinced most physicists that we can consider the 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 not undeceive most physicists about this error up to now. Bell wrote in 1989 [24] about the paper ’Ten theorems about quantum mechanical measurements’, by NG van Kampen [26] ”This paper is distinguished especially by its robust common sense. The author has no patience with ’··· such mind-boggling fantasies as the many world interpretation ···’. He dismisses out of hand the notion of 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 arrives at such a conclusion does not seek the error in his argu- ment’”. There is important to remind that Everett had proposed the many world interpretation in order to de- scribe the Process 1, i.e. ’measurement’, as lying outside the domain of psychology [14]. But the believers in the soothing philosophy or religion of Heisenberg-Bohr reject flatly, as well as van Kampen [26], both the mind of the observer and the many world interpretation. Although it must be obvious that the attempt by Heisenberg and Bohr to propose the realistic substantiation of the un- certainty principle was false it is needed to explain again and again that EPR correlation and Bell’s inequalities have proved this obvious fact.

2.2. EPR correlation and the non-locality of the mind

Bell wrote in 1981 [27]: ”The philosopher in the street,

FIG. 1: The initial conditions, i.e. the amplitudes A0(p) of who has not suffered a course in quantum mechanics, the wave-packet (1) are determined with results of an external is quite unimpressed by Einstein-Podolsky-Rosen corre- observation at a time moment t = 0, i.e. during the Process lations. He can point to many examples of similar cor- 1, when the quantum state changes discontinuously under in- relations in everyday life. The case of Bertlmann’s socks fluence of an external observer (the upper picture). Quantum is often cited. Dr. Bertlmann likes to wear two socks of 2 mechanics can predict the probability |Ψ(r, t1)| per unit vol- different colours. Which colour he will have on a given ume of finding the particle in any space place r at any time foot on a given day is quite unpredictable. But when you moment t1 (the middle picture) using the initial conditions see that the first sock is pink you can be already sure that and the Schrodinger’s wave equation (2). But no physical the second sock will not be pink”. The last sentence de- interaction of the particle with an agency of observation de- scribed with the Schrodinger’s wave equation (2) can compact scribes the influence of the object (the first sock) on the the wave-packet (the bottom picture) and provide with new subject (the mind of the observer). Such influence can initial conditions. The initial conditions can be provided only astonish nobody because ”it is old almost also, as the the mind of the observer who has found the particle some science” [21]. Bell asked: ”And is not the EPR business place. just the same?” [27]. He considered a particular version of 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 mechanics describes the spin states of two separate particles with 5 two separate equations unambiguously from the Born’s interpretation as a con- sequence of non-locality of the mind. Heisenberg noted: ψA = αA|↑A (rA) > +βA|↓A (rA) > ”Since through the observation our knowledge of the sys- tem has changed discontinuously, its mathematical rep- resentation also has undergone the discontinuous change ψ = α |↑ (r ) > +β |↓ (r ) > (3) B B B B B B B and we speak of a ’quantum jump’” [31]. He justified the ’quantum jump’ with help of the fact that ”our knowl- where the probability amplitudes αA, βA, αB, βB depend on a free choice of a certain axis along which the compo- edge can change suddenly” [31], i.e. the obvious fact that 2 2 the knowledge of Alice, for example, changes at the in- nent of particle spin will be measured and |αA| +|βA| = 2 2 fluence of the object, the deflection of the particle, on 1, |αB| +|βB| = 1 always. The spin state of pair of two separate particle may be described also with the product the subject, her mind. Already before the observation the Alice knowledge about the probability of the deflec- of the equations (3) in which the amplitudes γ1 = αAαB, tion up or down of particles A and B is entangled. She γ2 = αAβB, γ3 = βAαB, γ4 = βAβB and as a conse- knows that if the deflection of one particle, for exam- quence γ1γ4 = αAαB βAβB = γ2γ3 = αAβBβAαB. The ple A, will be up than the deflection of other particle B EPR correlation takes place when γ1γ4 6= γ2γ3 and the spin states of the particles cannot be separated. Two should be down. Thus, the EPR correlation (4) describes particles in the singlet spin state the entanglement of the Alice knowledge about the spin state of two particles. Therefore, motivated [32] by EPR

ψEPR = γ2|↑A (rA) ↓B (rB ) > +γ3|↓A (rA) ↑B (rB ) > [24], Schrodinger coined [33, 33] the term ”entanglement (4) of our knowledge”: ”Maximal knowledge of a total sys- when γ1 = 0, γ4 = 0, and γ2 6= 0, γ3 6= 0 is called EPR tem does not necessarily include total knowledge of all pair. The axis along which the component of particle its parts, not even when these are fully separated from spin will be measured is the direction of a non-uniform each other and at the moment are not influencing each magnetic field produced by magnets of a Stern-Gerlach other at all”. Maximal knowledge of a total system in- analyzer [16]. The particles will deflect up in the state clude total knowledge of all its parts in the case (3) when |↑> and down in the state |↓>. The observers A (Alice) γ1γ4 = γ2γ3 but not in the case (4) when γ1γ4 6= γ2γ3. and B (Bob) can choose any direction of their analyzer’s axis. Whether either particle separately goes up or down In his last talk [35] Bell considered the question: ”What on a given occasion is quite unpredictable. But according can not go faster than light?” He said: ”The situation is to the basic principle of quantum mechanics formulated further complicated by the fact that there are things which by Dirac as far back as 1930 [29] ”··· a measurement al- do go faster than light. British sovereignty is the clas- ways causes the system to jump into an eigenstate of the sical example. When the Queen dies in London (may it dynamical variable that is being measured”. This Dirac long be delayed) the Prince of Wales, lecturing on modern jump, wave function collapse [30], or ”’quantum jump’ architecture in Australia, becomes instantaneously King, from the ’possible’ to the ’actual’” [31] must take place (Greenwich Mean Time rules here)” [35]. There is im- logically during the act of observation because Alice can- portant to define more exactly that the Prince of Wales not see that one particle deflects up and down simulta- becomes instantaneously King in the mind of witnesses of neously. When Alice sees that the particle deflects up in the Queen death. Like manner the spin state of the dis- her Stern-Gerlach analyzer directed along an axis n the tant particle B changes instantaneously from (4) to (5a) spin state of the EPR pair (4) changes discontinuously in the mind of Alice when she sees that her particle A has to the eigenstate deflected up. The analogue of the British sovereignty in the EPR correlation is the Dirac jump, or wave function ψ = |↑ (r ) ↓ (r ) > (5a) n A A B B n collapse, which should be at the Process 1. But there or to the eigenstate is a fundamental difference of the Dirac jump from the British sovereignty. The witnesses of the Queen death

ψn = |↓A (rA) ↑B (rB ) >n (5b) cannot have an influence on the Prince of Wales whereas Alice can govern the spin state of the distant particle B. when the particle deflects down. Thus, according to Each of the eigenstates (5a) and (5b) of the operator of the basic principles of quantum mechanics deduced logi- the spin component along n (this dynamical variable) is cally from the Born’s interpretation one particle A of the superposition of eigenstates of the spin component along EPR pair (4) goes up the other B always goes down and other direction (other dynamical variable) [19]. Suppose vice-versa when axis of two analyzers located at widely that initially Alice had chosen to orient the non-uniform separated points in space rA and rB is directed in the magnetic field of her Stern-Gerlach analyzer perpendic- same direction n. This EPR correlation should be non- ular to the line of flight of the approaching particle, the local because of the opportunity to observe the deflec- y-axis, and pointing vertically upward along the z-axis. tion of the particle A and the particle B at the same And Bob had oriented his non-uniform magnetic field time independently on the distance |rA − rB | between also perpendicular to the y-axis but at an angle ϕ to the the Stern-Gerlach analyzers. This non-locality is deduced z-axis. Than the EPR pair jumps discontinuously to the 6 state

ψz = |↑A,z↓B,z>= cos(ϕ/2)|↑A,ϕ↓B,ϕ> +

+sin(ϕ/2)|↓A,ϕ↑B,ϕ> (6a) when Alice will see that her particle has deflected up and to the state

ψz = |↓A,z↑B,z>= −sin(ϕ/2)|↑A,ϕ↓B,ϕ> +

+cos(ϕ/2)|↓A,ϕ↑B,ϕ> (6b) when her particle has deflected down. The operator of the turning round the y-axis [19] is used hear and below. Each of these states is the eigenstate of the operator cor- FIG. 2: Sketch of the EPR experiment (a) and experimental responding to the orientation on the Alice analyzer but apparatus for measurement of the probability Pθ+Pϕ− with it is superposition the eigenstates of the operator corre- help of a source of single electrons Se (b). In a case (a) one sponding to the orientation on the Bob analyzer. Alice of the electrons of each EPR pair flies from the EPR pairs can turn her Stern-Gerlach analyzer on an angle θ during source SEPR to the Stern-Gerlach analyzer A, and another to the flight of the particles of the EPR pair (4). This turn the analyzer B. The probabilities PAθ+ = NA+/(NA+ +NA−) changes the spin states of both her and Bob’s particle and PBϕ+ = NB+/(NB+ + NB−) are defined as the relation after her observation to of number NA+ (or NB+) of detection by detector DA+ (or DB+) to the sum NA+ + NA− (or NB+ + NB−) of detection by detectors DA+ and DA− (or DB+ and DB−). In a case ψθ = |↑A,θ↓B,θ>= cos((ϕ − θ)/2)|↑A,ϕ↓B,ϕ> + (b) electron flies from the source Se to the first Stern-Gerlach analyzer and gets in the second analyzer if it deflects up, and gets in the first detector D1− if it deflects down. After the +sin((ϕ − θ)/2)|↓A,ϕ↑B,ϕ> (7a) second analyzer electron gets in the detector D2+ or D2−. The if her particle has deflected up and to probability Pθ+Pϕ− = N2−/(N1− + N2+ + N2−) is defined as the relation of the number N2− of detection by detector D2+ to the sum N1− + N2+ + N2− of detection by all detectors ψθ = |↓A,θ↑B,θ>= −sin((ϕ − θ)/2)|↑A,ϕ↓B,ϕ> +

+cos((ϕ − θ)/2)|↓A,ϕ↑B,ϕ> (7b) definitely with help of the Bell’s inequalities [36]. Only condition used at the deduction of the Bell’s inequality if it has deflected down. Thus, the EPR correlation re- is ”the requirement of locality, or more precisely that the veals that quantum mechanics concedes that Alice can result of a measurement on one system be unaffected by change instantaneously the quantum state of the distant operations on a distant system” [36]. Bell had proposed particle with her will and her observation. According to in [27] a most simple example of this logical deduction. the Born’s interpretation she can act faster than light Bell started with an trivial inequality thanks to non-locality of her mind. P0+P45− + P45+P90− ≥ P0+P90− (8a)

2.3. Violation of Bell’s inequalities uncovers the asserting that the probability P0+ of the deflection up at influence of subject on object the orientation of the Stern-Gerlach analyzer vertically o upward along the z-axis, i.e. at θ = 0 and the P45− Heisenberg justified [31] the discontinuous change con- of the deflection down at θ = 45o plus the probability o ceded quantum mechanics with the argument that our P45+ of the deflection up at θ = 45 and P90− - down o knowledge of the system changes discontinuously at any at θ = 90 is not less than the probability P0+ of the o o observation. But quantum mechanics represents not only deflection up at θ =0 and P90− - down at θ = 90 . The our knowledge. It predicts first of all the probability of inequality is obvious when all probabilities P0+, P45−, different outcomes of observations. For example, the re- P45+ and P90− are measured in the same spin state. lation (7) predicts that the probability to observe the de- Any particle in the same spin state which deflects up at flection up of the Bob’s particle equals |cos((ϕ − θ)/2)|2 θ =0o and down at θ = 90o (and so contributing to the 2 and down |sin((ϕ − θ)/2)| when the Alice particle has third probability P0+P90− in (8a)) can deflect either up deflected up. Thus, the Alice’s will and her observation at θ = 45o (and so contributes to the second probability o influence instantaneously on the outcome of observations P45+P90− in (8a)) or down at θ = 45 (and so contributes of the distant particle. This influence is revealed most to the first probability P0+P45− in (8a)). The inequality 7 is trivial but it can not be verified experimentally with subject and the probability of the observation changes measurements of single particles, as shown on Fig2b, be- because of the influence of subject on object. Thus, cause ”··· a measurement always causes the system to the EPR correlation and the Bell’s inequalities have con- jump into an eigenstate of the dynamical variable that is firmed the statement by Schrodinger that in the orthodox being measured” [29]. All particles flying from the first quantum mechanics ”··· the causal interconnection be- to the second Stern-Gerlach analyzer on Fig.2b should tween the subject and object is considered reciprocal. It is be in the state ’spin up’ because of this Dirac jump. The stated, that the unremovable and uncontrollable influence eigenstate ’spin up’ for this orientation of the first Stern- of the subject on the object takes place” [21]. Gerlach analyzer differs in common case from the initial spin state of the particles. Therefore it is impossible to measure the probabilities both P0+ and P45−, for ex- 2.4. What EPR intended to prove and what they ample, in the same spin state with the method shown have proved on Fig.2b. The probabilities at different orientation of the Stern-Gerlach analyzers θ and ϕ can be measured in EPR [24] denied any possibility of the EPR correla- the same state with help of the EPR pair if the require- tion. It was in conflict with the Einstein’s belief: ”But ment of locality is valid. The equality of the probabilities on one supposition we should, in my opinion, absolutely PAθ+ = PBθ− and PAθ− = PBθ+ must be observed be- hold fast: the real factual situation of the system S2 is cause of the EPR correlation when if one particle A of independent of what is done with the system S1, which is the EPR pairs (4) deflects up then the other B always spatially separated from the former” [37]. EPR intended deflects down and vice-versa. This equality is valid for to prove ”that the description of reality as given by a all orientation including θ = 45o and θ = 90o. The Bell’s wave function is not complete” [24]. Of course they had inequality in mind the wave function in the Born’s interpretation. It is stated in the abstract of the EPR paper [24]: ”In P 0+P 45+ + P 45+P 90+ ≥ P 0+P 90+ (8b) A B A B A B quantum mechanics in the case of two physical quantities is deduced from the obvious inequality (8a) at the sin- described by non-commuting operators, the knowledge of gle requirement: a turning of the Stern-Gerlach ana- one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function lyzer A located in a space region rA can not change in- stantaneously on the spin of the distant particle B lo- in QM is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem cated in a space region rB and vice-versa. The proba- bility to observe the deflection up in the Stern-Gerlach of making predictions concerning a system on the basis of measurements made on another system that had pre- analyzers A equals always the same value PAθ+ = 2 2 (|γ2| + |γ3| )/2=0.5 if Alice is first observer because viously interacted with it leads to the result that if (1) of the same probability for each particle of the EPR is false then (2) is also false”. Indeed, if Alice reveals pair (4) to flow toward Alice. Bob, as second observer, a real situation existing irrespective of any act of obser- should observe the deflection up with the probability vation when she sees that the particle has deflected up 2 in her Stern-Gerlach analyzer pointing vertically upward PBϕ+ = |sin((ϕ − θ)/2)| according to (7a). The re- 2 along the z-axis (6a) than all other spin components (7a) sult PAθ+PBϕ+ = 0.5|sin((ϕ − θ)/2)| gives the values 2 o or (7b) of her and Bob’s particles should exist before her PA0+PB45+ = PA45+PB90+ = 0.5sin (45 /2) ≈ 0.0732, 2 o observation. Alice can know any spin component (7a) PA0+PB90+ = 0.5sin (90 /2) ≈ 0.25. The inequality (8b) would then require or (7b) in the same spine state turning her analyzer in the respective axis. Therefore she can obtain the knowl- 0.1464 ≥ 0.25 (8c) edge about different spin component of the Bob’s par- ticle, | ↓B,z> and | ↓B,θ> for example, contrary to the which is not true. foundation of QM, if this knowledge about a real situa- This violation (8c) of the Bell’s inequality (8b) reveals tion existing irrespective of her mind. that quantum mechanics presupposes that a turning of Thus, QM is observably inadequate if it is interpreted the Stern-Gerlach analyzer can influence instantaneously as the description of reality. The description given by the on the distant particle because the Bell’s inequality (8b) wave function in QM can be adequate and complete only was deduced only from the requirement of impossibility of if two physical quantities described by non-commuting such non-local influence. According to the Born’s inter- operators does not have reality simultaneous before their pretation this non-local influence is actualized by means observation. QM can be valid only if physical quantities of the Alice’s mind. The probability that the Bob’s par- are rather created by the mind of the observer than mea- ticle will deflect up should equal PBϕ+ =0.5 until Alice sured at the observation. Just this absurdity of QM had has seen that her particle has deflected up. Thus the been proved by EPR [24]. Bell proposed ”to replace the probability of the observation ’spin up’ by Bob changes word ’measurement’” which misleads: ”When it is said 2 from PBϕ+ =0.5 to PBϕ+ = |sin((ϕ − θ)/2)| because of that something is ’measured’ it is difficult not to think the discontinuous change of the Alice’s knowledge. The of the result as referring to some pre-existing property knowledge changes because of the influence of object on of the object in question” [24]. The pre-existing prop- 8 erties revealed at measurement are in hidden-variables Bell, 1966, rediscovered the fact that von Neumann’s no- theory, alternative the orthodox QM using the Born’s in- variables-hidden proof was based on an assumption that terpretation. According to this theory, hidden variables can only be described as silly - so silly, in fact, that one is determine results of individual measurements and thus led to wonder whether the proof was ever studied by either eliminate subjectivity and indeterminism inherent QM. the students or those who appealed to it”. Von Neumann did not take into account that non-commuting opera- tors do not have simultaneous eigenvalues [43]. There is 2.5. Hidden variable more important to realize a physical mistake correspond- ing to this ’mathematical’ mistake. Eigenvalues non- commuting operators cannot be simultaneous measured Bell asserted ”that vagueness, subjectivity, and inde- according to the quantum postulate and complementar- terminism, are not forced on us by experimental facts, ity proposed by Bohr [23]. Bell noted [42] that additional but by deliberate theoretical choice” [38]. It is not ab- demands of the von Neumann’s proof are ”quite unrea- solutely so. The main reason of refusal of realism were sonable when one remembers with Bohr [40] ’the impos- problems with the realistic description of some quantum sibility of any sharp distinction between the behaviour phenomena, such as Stern-Gerlach effect [39]. Bohr wrote of atomic objects and the interaction with the measur- in 1949 [40], that ”as exposed so clearly by Einstein and ing instruments which serve to define the conditions un- Ehrenfest [41], it presented with unsurmountable difficul- der which the phenomena appear’”. In order to exhibit ties any attempt at forming a picture of the behaviour of of the error of the von Neumann’s proof Bell had con- atoms in a magnetic field”. And Bell wrote 32 years later: structed a hidden-variables model which reproduces all ”Phenomena of this kind made physicists despair of find- predictions of results of a single spin 1/2 measurement ing any consistent space-time picture of what goes on the given by QM. There is important to accentuate that Bell atomic and subatomic scale ··· Going further still, some used in this model the Bohr’s quantum postulate which asserted that atomic and subatomic particles do not have ”implies that any observation of atomic phenomena will any definite properties in advance of observation. There involve an interaction with the agency of observation not is nothing, that is to say, in the particles approaching to be neglected” [23]. According to the quantum postu- the magnet, to distinguish those subsequently deflected up late ”With or without hidden variables the analysis of the from those subsequently deflected down. Indeed even the measurement process presents peculiar difficulties” [42], particles are not really there” [27]. because no theory can describe an interaction with the As Bell wrote [42] ”To know the quantum mechani- agency of observation. Any result of this interaction may cal state of a system implies, in general, only statistical be assumed because of this vagueness. restrictions on the results of measurements”. The clas- sical statistical mechanics also describes only statistical In the Bell’s model [42] the interaction of single spin distribution of parameters. But these parameters are as- 1/2 with the agency of observation results to mea- sumed to exist irrespective of any act of observation and surement of the same value of spin component, as the mind of the observer. Just the negation of real ex- it is observed in the paradoxical Stern-Gerlach effect istence of parameters results to subjectivity and indeter- [39]. Thanks to the vague interaction the results of minism of QM. Therefore Bell was sure: ”It seems inter- observation can be described with the relation sn = esting to ask if this statistical element be thought of as 1/2cos(θ)/|cos(θ)| proposed by Bell in [27]. This rela- arising, as in classical statistical mechanics, because the tion describes an individual measurement of spin com- states in question are averages over better defined states ponent sn along n, as well as the superposition (3), but for which individually the results would be quite deter- has a fundamental advantage: θ is the angle between an mined. These hypothetical ’dispersion free’ states would axis n of Stern-Gerlach analyzer and an axis z + m of be specified not only by the quantum mechanical state vec- spin. Therefore results of an individual measurement is tor but also by additional ’hidden variables’-’hidden’ be- determined with the spin axis z + m and the mind of the cause if states with prescribed values of these variables observer can not influence on these results. In the Bell’s could actually be prepared, quantum mechanics would be model [42] z is a unit vector directed along the z-axis in observably inadequate” [42]. But most physicists did not the spin state ψz = | ↑z> and m is a random unit vec- take an interest in this problem fifty years ago and up to tor which plays the role of hidden variable. This model now many physicists underestimate the fundamental im- predicts the same probabilities of observation of positive portance of hidden variables. Few experts, who did find π/2 values Pθ+ =1/2+ θ dx2π sin x/4π = (1+cos θ)/2= the question interesting, believed that ”the question con- 2 θ cos (θ/2) and negativeR values P − = dx2π sin x/4π = cerning the existence of such hidden variables received an θ 0 2 R early and rather decisive answer in the form of von Neu- (1 − cos θ)/2= sin (θ/2) as orthodox QM. mann’s proof on the mathematical impossibility of such It predicts also that if one particle A of the EPR pair variables in quantum theory” [42]. goes up the other B always goes down and vice-versa But this belief was false. David Mermin writes in when axis of two analyzers is directed in the same di- the paper ”Hidden variables and the two theorems of rection n because if cos(θA) > 0 for the angle θA be- John Bell” [43]: ”A third of a century passed before John tween n and +(z + m) then cos(θB) < 0 for the an- 9 gle θB between n and −(z + m) and vice-versa. The agency of observation can change variables at observation hidden-variables model implies also the Dirac jump at but it can not create observed variables. Only the mind observation in order to correspond to the prediction of of the observer can create definite properties observed by QM. Therefore it also predicts violation of the trivial in- the observer if they were not definite with variables even equality (8a). Because of the vague interaction with the hidden in advance of observation. The EPR correlation agency of observation, i.e. with the first Stern-Gerlach and violation (8c) of the Bell’s inequality (8b) reveal that analyzer, shown on Fig.2b, the particle deflecting with an interaction rather with the mind of the observer than the probability Pθ+ = 0.5 to the second Stern-Gerlach with the agency of observation is implied in the orthodox analyzer jumps to the spin state ψθ = | ↑θ>. Therefore QM thanks to the non-locality of the first interaction and the particle will deflect down after the second analyzer the locality of the second one. 2 with the probability Pϕ− = |sin((ϕ − θ)/2)| . The total 2 probability Pθ+Pϕ− =0.5|sin((ϕ − θ)/2)| to hit the de- tector D2− predicts violation (8c) of the trivial inequality 2.6. Indeterminism of quantum mechanics. The 2 o (8a): P0+P45− = P45+P90− = 0.5sin (45 /2) ≈ 0.0732, entanglement of cat with atom states 2 o P0+P90− = 0.5sin (90 /2) ≈ 0.25. Thus, the hidden- variables model can reproduce almost all prediction of Von Neumann, Pauli, Wigner and also Heisenberg and QM. Among few predictions which it can not reproduce others were forced to note ”that ’measurement’ might be is violation of the Bell’s inequality (8b). The probability complete only in the mind of the observer” [24] because of observation both s = +1/2 and s = −1/2 of each n n of indeterminism of QM: if a cause of a definite result of particle of the EPR pairs is the same P + = P − = Aθ Aθ the observation is absent in nature then only the mind of P + = P − = 0.5 because the results of individual Bϕ Bϕ the observer can be the cause. Bohr reminder in 1949 [40] measurements are determined by the spin axis +(z + m) that during the Solvay meeting 1927 ”interesting discus- or −(z + m) and therefore the act of measurement of one sion arose also about how to speak of the appearance of particle can not influence on the result of observation of phenomena for which only predictions of statistical char- other particle. The corroboration of the Bell’s inequality acter can be made. The question was whether, as to the (8b) P 0+P 45+ + P 45+P 90+ =0.5 × 0.5+0.5 × 0.5= A B A B occurrence of individual effects, we should adopt a termi- 0.5 > P 0+P 90+ = 0.5 × 0.5=0.25 reveals that if A B nology proposed by Dirac, that we were concerned with a definite properties exist in advance of observation then choice on the part of ”nature” or, as suggested by Heisen- ’measurement’ might be complete without the mind of berg, we should say that we have to do with a choice on the the observer. part of the ’observer’ constructing the measuring instru- There is important to note that hidden variables re- ments and reading their recording”. Bohr wrote: ”Any place the mind of the observer with soulless agencies of such terminology would, however, appear dubious since, observation. This fact reveals that the quantum postu- on the one hand, it is hardly reasonable to endow nature late and complementarity proposed by Bohr [23] is valid with volition in the ordinary sense, while, on the other according to rather hidden-variables theories than the hand, it is certainly not possible for the observer to influ- QM based on the Born’s interpretation. Variables are ence the events which may appear under the conditions he hidden just because ”any observation of atomic phenom- has arranged” and advertised his complementarity: ”To ena will involve an interaction with the agency of obser- my mind, there is no other alternative than to admit that, vation not to be neglected” [23]. Bohr concluded from in this field of experience, we are dealing with individ- this statement implied with his quantum postulate that ual phenomena and that our possibilities of handling the ”an independent reality in the ordinary physical sense can measuring instruments allow us only to make a choice neither be ascribed to the phenomena nor to the agencies between the different complementary types of phenomena of observation” [23]. This conclusion misleads. A cel- we want to study” [40]. But this pet idea by Bohr can ebrated polymath who is quoted in [43] declared that not answer on the question: ”What or who can a defi- ”Most theoretical physicists are guilty of ··· fail[ing] to nite result of the observation determine?” It can result distinguish between a measurable indeterminacy and the and even had resulted [19] to the illusion that individual epistemic indeterminability of what is in reality deter- effects are chosen by the agency of observation, named minate. The indeterminacy discovered by physical mea- ”the ’classical object’ usually called apparatus” [19]. surements of subatomic phenomena simply tells us that This illusion is logically absurd. Nevertheless it pre- we cannot know the definite position and velocity of an dominated and predominates up to now among most electron at any instant of time. It does not tell as that physicists thanks to the followers [19] of Bohr. Bell had the electron, at any instant of time, does not have a def- called the spontaneous jump of a ’classical’ apparatus inite position and velocity. [Physicists] ··· convert what into an eigenstate of its ’reading’ as the LL jump, con- is not measurable by them into the unreal and the non- sidering in [24] Quantum Mechanics by L D Landau and existent” [44]. Bohr was among these most theoretical E M Lifshitz [19] as the first of the ’good books’ which physicists and had misled some generation of physicists mislead. The assumption [19] about the LL jump is ab- with his quantum postulate and complementarity. He surd first of all because a apparatus even ’classical’ is did not take into account that an interaction with the a part of nature as well as the cat in the famous para- 10 dox proposed by Schrodinger [33]. The Schrodinger’s cat +γ3|↓A (rA) ↑B (rB) > CatA,liv CatB,dead (11) paradox is well-known but pure understood. Therefore it is useful to reminder its text here: ”One can even with two types of entanglements: because of the con- set up quite ridiculous cases. A cat is penned up in a servation law (the EPR correlation) and because of the steel chamber, along with the following diabolical device condition of experiment proposed by Schrodinger [33]. (which must be secured against direct interference by the The results of observations will be cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour ΨEPR,cat = CatA,deadCatB,liv (12a) one of the atoms decays, but also, with equal probability, perhaps none; if it hap-pens, the [Geiger] counter tube or discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left ΨEPR,cat = CatA,livCatB,dead (12b) this entire system to itself for an hour, one would say when the axis of the Stern-Gerlach analysers are paral- that the cat still lives if meanwhile no atom has decayed. lel. Advocates of quantum mechanics justify the using of The first atomic decay would have poisoned it. The ψ- state superposition (11) with the absence of any cause of function of the entire system would express this by having the atom decay. They ”convert what is not measurable in it the living and the dead cat (pardon the expression) by them into the unreal and the non-existent” [44]. Let mixed or smeared out in equal parts” [33], see also p.185 imagine that we do not know why the observed states of in the book [16]. Schrodinger had entangled with the cats are correlated as well as we do not know the cause of ψ-function of the entire system atom decay. Then, to convert our lack of knowledge into

Ψcat = αAtdecayGyesFlyesCatdead+ the unreal we can describe the results of our observations of the cats state with superposition

+βAtnoGnoFlnoCatliving (9) ΨEPR,cat = γ2CatA,deadCatB,liv + γ3CatA,livCatB,dead (13) cat state Catdead, Catliving with the states of the small which should collapse to (12a) or (12b) at each obser- flask of hydrocyanic acid Flyes, Flno, the Geiger counter tube Gyes, Gyes and radioactive atom Atdecay, Atno with vation. The absence of any cause of (12a) or (12b) in the experiment conditions. The act of observation of the advance of observation raises a question: ”What or who dead cat is described with the ψ - function (9) collapse makes a choice?” According to the concept of the spon- to taneous collapse of a macroscopic system into a definite macroscopic configuration [19], i.e. the LL jump [24], Ψcat = AtdecayGyesFlyesCatdead (10) the choice is made by a cat, which is a ’classical’ appara- tus in the Schrodinger’s paradox. But what cat A or B One can draw the conclusion that the cat is dead Cat dead would make a choice (12a) or (12b)? The collapse of the because the hammer has shattered the small flask of hy- superposition of cats states (13) must be instantaneous drocyanic acid Fl . The hammer has shattered it be- yes irrespective of a distance |r −r | between cats. Accord- cause the Geiger counter tube has discharged G . It A B yes ing to the principle of relativity by Einstein both the cat is has discharged because the atom has decayed At . decay A and the cat B may be observed first in the same case Till this each event had a cause. But the atom decay but in different frames of reference. Therefore it is im- is causless. There is no term to the right of At in decay possible to say the spontaneous collapse of what cat can (9). According to the assumption [19] about the LL jump choose the fate of other cat with help a mystical action the cat kills himself. Moreover one may demonstrate to of a distance. The absurdity of the LL jump assumed in combine two famous paradoxes, the EPR paradox and [19] is obvious even without this consideration of the cats the Schrodinger’s cat paradox, that the death of a cat fate. It must be obvious for any one that only a magical A can preserve life of a distant cat B and vice-versa. apparatus even ’classical’ can collapse spontaneously. Thereto one may substitute of the radioactive atom for the EPR pairs with two spin particles in the singlet state (4), as well as in the Bohm’s version [28] of the EPR 2.7. Whose knowledge and whose will? paradox. We will use also two Stern-Gerlach analysers, two Geiger counter tubes, two flasks of hydrocyanic acid Therefore von Neumann, Pauli, Wigner, Heisenberg and two cats CatA and CatB. The Geiger counter tubes will be located on the upper trajectory of each particle and others admitted ”that ’measurement’ might be com- after its exit from its Stern-Gerlach analyser, so it will plete only in the mind of the observer” and the Dirac discharge when spin up and will not discharge when spin jump is forced by an external intervention [24] which can down. The subsequent events will be as well as in the be only the mind of the observer. But a choice on the Schrodinger paradox [33]. This gedankenexperiment can part of the ’observer’ suggested by Heisenberg can not be described with the ψ-function deliver from a logical absurdity. According to the basic principle of QM formulated by Dirac ”··· a measurement ΨEPR,cat = γ2|↑A (rA) ↓B (rB ) > CatA,deadCatB,liv+ always causes the system to jump into an eigenstate of 11 the dynamical variable that is being measured” [29]. But majority who are ’indifferent’ rather believe than under- into which eigenstate should the system jump when two stand QM. The authors of the book [48] and other be- dynamical variables described by non-commuting oper- lievers do not want to understand that no experimental ators are measured at the same time? Alice may orient result can save QM because it is self-contradictory and her Stern-Gerlach analyser at an angle θ to the z-axis and vague. Because of its vagueness the contradictions were Bob may orient his Stern-Gerlach analyser at an other observed even between its creators, Heisenberg and Bohr, angle ϕ. Then Alice will be sure that her and Bob’s par- first of all about the role of the observer. Heisenberg ad- ticles jump to the spin state (7a) when she will see that mitted that ’measurement’ might be complete only in her particle has deflected up. But Bob will be sure that the mind of the observer. It is obvious, for example, his and Alice’s particles jump to the other state from his destructive criticism of Soviet scientists Alexan- drov and Blochinzev in the Section VIII ”Criticism and ψϕ = |↓A,ϕ↑B,ϕ>= −sin((θ − ϕ)/2)|↑A,θ↓B,θ> + Counterproposals to the Copenhagen Interpretation of Quantum Theory” of the Lectures 1955-1956 ”Physics +cos((θ − ϕ)/2)|↓A,θ↑B,θ> (14) and Philosophy” [31]. These Soviet scientists stated that ”Among the different idealistic trends of contemporary when he will see that his particle has deflected up. Thus, physics the so-called Copenhagen school is the most re- according to orthodox QM, knowledge of two observers actionary” [31] and rejected the role of the observer in of the same system can be various. Moreover, each of QM. Heisenberg quotes Alexandrov ”We must therefore them can impose her (or his) will on the distant particle. understand by ’result of measurement’ in quantum theory When Alice has oriented her Stern-Gerlach along the z- only the objective effect of the interaction of the electron axis the Bob’s particle should jump in the spin state (5a) with a suitable object. Mention of the observer must be or (5b) at her measurement. And when Bob has oriented avoided, and we must treat objective conditions and ob- his Stern-Gerlach at an angle θ to the z-axis the Alice’s jective and effects. A physical quantity is objective char- particle should jump in the spin state (6a) or (6b) at acteristic of phenomenon, but not the result of an ob- his measurement. Here it is impossible to solve, whose servation” and notes ”According to Alexandrov, the wave knowledge is correct, and whose will can win because of function in configuration space characterizes the objective the principle of relativity according to which Alice ob- state of the electron” [31]. Further Heisenberg explains serves her particle ahead of Bob in a frame of reference why the Alexandrov’s point of view is false: ”In his pre- whereas in an other frame of reference Bob observes his sentation Alexandrov overlooks the fact that the formal- particle ahead of Alice. ism of quantum theory does not allow the same degree of This absurdity of QM has became especially relevant objectivation as that of classical physics. For instance, after experimental evidence [45–47] of violation of the if a interaction of a system with the measuring appara- Bell’s inequalities. Before these experiments Bell ex- tus is treated as a whole according to QM and if both are pressed a hope that ”Perhaps Nature is not so queer as regarded as cut off from the rest of the world, then the quantum mechanics” [27] and rated a possibility of vio- formalism of quantum theory does not as a rule lead to lation of his inequalities as indigestible. One of the in- a define result; it will not lead, e.g., to the blackening of terpretations of this violation could be a conclusion that the photographic plate in a given point. If one tries to ”Apparently separate parts of the world would be deeply rescue the Alexandrov’s ’objective effect’ by saying that and conspiratorially entangled, and our apparent free will ’in reality’ the plate is blackened at a given point after would be entangled with them” [27]. The results of the the interaction, the rejoinder is the quantum mechani- experiments of the Aspect’s team [45–47] Bell appraised cal treatment of the closed system consisting of electron, as a fundamental problem of theory: ”For me then this measuring apparatus and plate is no longer being applied” is the real problem with quantum theory: the apparently [31]. essential conflict between any sharp formulation and fun- damental relativity. That is to say, we have an apparent This disproof by Heisenberg of the objectivation of QM incompatibility, at the deepest level, between the two fun- is doubtless. Its obviousness is illustrated in the Section damental pillars of contemporary theory” p. 172 in [1]. 2.1 and must be quite clear at consideration of the exam- As opposed to Bell contemporary believers in the sooth- ple shown on Fig.1: the wave-packet can be compacted ing philosophy or religion of Heisenberg-Bohr, for exam- only by the mind of the observer. In spite of this ob- ple the authors of the book [48] are sure that violation of viousness not only the Soviet scientists Alexandrov and the Bell’s inequalities has corroborated the correctness Blochinzev but most physicists including Bohr objectified of QM. Mermin wrote as far back as in 1985 [49]: ”In and objectify the matter of quantum mechanical treat- the question of whether there is some fundamental prob- ment. Bohr objectified it with his quantum postulate and lem with quantum mechanics signaled by tests of Bell’s complementarity [23] according to which the act of obser- inequality, physicists can be divided into a majority who vation is an interaction with the agency of observation. are ’indifferent’ and a minority who are ’bothered’”. Most physicists had followed rather Bohr than Heisen- This division observed up to now witnesses against berg because of their robust common sense according to QM as a consistent and transparent theory. The incon- which both the many world interpretation and the mind sistency the assessment discloses vagueness of QM. The of the observer are mind-boggling fantasies. QM seems 12 reasonable to most physicists only thanks to its misinter- the Section V ”The Development of Philosophical Ideas pretation. The following word by Heisenberg can explain Since Descartes in Comparison with the New Situation partly the cause of this mass delusion: ”Above all, we see in Quantum Theory” he stated: ”This reality was full of from these formulations how difficult it is when we try to life and there was no good reason to stress the distinc- push new ideas into an old system of concepts belonging tion between matter and mind or between body and soul” to an earlier philosophy - or, to use an old metaphor, [31]. This point of view by Heisenberg contradicts funda- when we attempt to put new wine into old bottles” [31]. mentally to the scientific Weltanschauung of the previous Therefore it is needed to give an account of the essence centuries and Heisenberg emphasizes that QM compels of a new bottle proposed by Heisenberg for QM. to change this Weltanschauung. He reminds: ”The first great philosopher of this new period of science was Rene Descartes who lived in the first half of the seventeenth 3. NEW WELTANSCHAUUNG PROPOSED BY century. Those of his ideas that are most important for HEISENBERG the development of scientific thinking are contained in his Discourse on Method” [31]. And then Heisenberg points QM had originated from the proposal by young Heisen- out on the importance of the Cartesian philosophy for berg ”to try to establish a theoretical quantum mechanics, the posterior development of natural science: ”While an- analogous classical mechanics, but in which only relations cient Greek philosophy had tried to find order in the in- between observable quantities occur” [2]. Only few scien- finite variety of things and events by looking for some tists, first of all Einstein, realized at that time and later fundamental unifying principle, Descartes tries to estab- on that this proposal presupposes a revolutionary revi- lish the order through some fundamental division ··· If sion of the aim of science and even a new Weltanschau- one uses the fundamental concepts of Descartes at all, it ung. The essence of this revolutionary revision was ex- is essential that God is in the world and in the I and it is pressed by Einstein in his explanation of ”reasons which also essential that the I cannot be really separated from keep he from falling in line with the opinion of almost the world. Of course Descartes knew the undisputable all contemporary theoretical physicists”: ”What does not necessity of the connection, but philosophy and natural satisfy me in that theory, from the standpoint of prin- science in the following period developed on the basis of ciple, is its attitude towards that which appears to me the polarity between the ’res cogitans’ and the ’res ex- to be the programmatic aim of all physics: the complete tensa’, and natural science concentrated its interest on description of any (individual) real situation (as it sup- the ’res extensa’. The influence of the Cartesian division posedly exists irrespective of any act of observation or on human thought in the following centuries can hardly substantiation)” [50]. The philosophical fundamentals of be overestimated, but it is just this division which we have QM, proclaimed by Heisenberg as far back as 1927 are: to criticise later from the development of physics in our subjectivity, ”I believe that one can fruitfully formulate time” [31]. the origin of the classical ’orbit’ in this way: the ’orbit’ The latter sentence clarifies in a greatest extent the comes into being only when we observe it” [22]; the nega- fundamental difference of QM from all other theories of tion of an objective reality, ”As the statistical character physics. All other theories concentrated their interest on of quantum theory is so closely linked to the inexactness the ’res extensa’, i.e. all objects of the Nature, existing of all perceptions, one might be led to the presumption irrespective of any act of observation and the mind of the that behind the perceived statistical world there still hides observer, i.e. the ’res cogitans’. Heisenberg points out on a ’real’ world in which causality holds. But such specula- a philosophical basis of these theories ”Since ··· the ’res tions seem to us, to say it explicitly, fruitless and sense- cogitans’ and the ’res extensa’ were taken as completely less. Physics ought to describe only the correlation of different in their essence, it did not seem possible that observations” [22]; indeterminism, ”One can express the they could act upon each other” [31]. He attacks this true state of affairs better in this way: Because all ex- basis ”Obviously this whole description is somewhat ar- periments are subject to the laws of quantum mechanics, tificial and shows the grave defects of the Cartesian par- and therefore to equation (1), it follows that quantum tition” but admits ”On the other hand in natural science mechanics establishes the final failure of causality” [22]. the partition was for several centuries extremely success- The equation (1) in [22] is the famous Heisenberg’s un- ful. The mechanics of Newton and all the other parts of certainty relation. Thus, the uncertainty principle results classical physics constructed after its model started from to indeterminism, according to its author. the assumption that one can describe the world without speaking about God or ourselves” [31]. Before the QM emergence ”This possibility soon seemed almost a nec- 3.1. Quantum mechanics rejects the Cartesian essary condition for natural science in general. But at polarity between ’res cogitans’ and ’res extensa’ this point the situation changed to some extent through quantum theory” [31]. Therefore Heisenberg comes ”to a Later on Heisenberg had developed his new Weltan- comparison of Descartes’s philosophical system with our schauung more neatly, in particular in his Lectures 1955- present situation in modern physics” [31]. 1956 ”Physics and Philosophy” [31]. In the beginning of His next remark demystifies the essence of his con- 13 tradictions with Einstein and other critics of QM: ”If 3.2. The notion of the ’thing-in-itself’ by Kant and one follows the great difficulty which even eminent sci- hidden-variables entists like Einstein had in understanding and accepting the Copenhagen interpretation of quantum theory, one According to the empiristic philosophy ”to be perceived can trace the roots of this difficulty to the Cartesian par- is identical with existence” [31]. Heisenberg admitted: tition. This partition has penetrated deeply into the hu- ”This line of argument then was extended to an extreme man mind during the three centuries following Descartes scepticism by Hume, who denied induction and causation and it will take a long time for it to be replaced by a really and thereby arrived at a conclusion which if taken se- different attitude toward the problem of reality” [31]. Ac- riously would destroy the basis of all empirical science” cording to Heisenberg an old-fashioned attitude toward [31] but he followed just this line when he rejected the the problem of reality may be called dogmatic realism ’thing-in-itself’ and the law of causality of the Kant’s and metaphysical realism [31]. He explains the essence philosophy. Heisenberg wrote: ”The disagreeable ques- of the first: ”Dogmatic realism claims that there are no tion whether ’the things really exist’, which had given statements concerning the material world that cannot be rise to empiristic philosophy, occurred also in Kant’s sys- objectivated ··· actually the position of classical physics tem. But Kant has not followed the line of Berkeley and is that of dogmatic realism. It is only through quantum Hume, though that would have been logically consistent. theory that we have learned that exact science is possible He kept the notion of the ’thing-in-itself’ as different from without the basis of dogmatic realism. When Einstein has the percept, and in this way kept some connection with criticised quantum theory he has done so from the basis of realism” [31]. He was right that ”Considering the Kan- dogmatic realism” [31]. Einstein said ”I like to think that tian ’thing-in-itself’ Kant had pointed out that we cannot the moon is there even if I don’t look at it”, explaining his conclude anything from the perception about the ’thing- dislike for QM. Heisenberg and Einstein did not agree but in-itself’” [31]. But his interpretation of the Kantian they discussed on the common language of European phi- ’thing-in-itself’ is very doubt: ”This statement has, as losophy. Therefore this controversy of they makes quite Weizsacker has noticed, its formal analogy in the fact clear the essence of dogmatic realism. There is important that in spite of the use of the classical concepts in all the also to know the essence of metaphysical realism accord- experiments a non-classical behaviour of the atomic ob- ing to Heisenberg: ”Metaphysical realism goes one step jects is possible. The ’thing-in-itself’ is for the atomic further than dogmatic realism by saying that ’the things physicist, if he uses this concept at all, finally a mathe- really exist’. This is in fact what Descartes tried to prove matical structure: but this structure is - contrary to Kant by the argument that ’God cannot have deceived us’” [31]. - indirectly deduced from experience” [31]. Heisenberg reminded above: ”On the basis of doubt and The Kantian ’thing-in-itself’ is rather a cause of our logical reasoning he [Descartes] tries to find a completely perceptions than a mathematical structure. Any math- new and as he thinks solid ground for a philosophical sys- ematical structure is a method of description and can- tem. He does not accept revelation as such a basis nor not belong to the percept or the perception. It can does he want to accept uncritically what is perceived by only describe they. Heisenberg and Weizsacker obscured the senses. So he starts with his method of doubt. He the obvious meaning of the Kantian ’thing-in-itself’ as a casts his doubt upon that which our senses tell us about cause of our perceptions because of their persuasion that the results of our reasoning and finally he arrives at his causality ”can have only a limited range of applicability” famous sentence: ’cogito ergo sum’. I cannot doubt my [31]. They rejected the ’thing-in-itself’ as the cause of existence since it follows from the fact that I am think- our perceptions as well as they rejected hidden-variables ing. After establishing the existence of the I in this way as the cause of an individual observation of quantum phe- he proceeds to prove the existence of God essentially on nomenon. the lines of scholastic philosophy. Finally the existence of the world follows from the fact that God had given me a strong inclination to believe in the existence of the world, 3.3. The Kantian a priori character of the law of and it is simply impossible that God should have deceived causality and quantum mechanics me” [31]. Soon after Descartes his faith that God can not deceive was call in question by representatives for The most doubt principle of QM and the new Weltan- early empiristic philosophy, Locke, Berkeley and Hume. According to Heisenberg: ”The criticism of metaphysical schauung by Heisenberg is indeterminism. Considering the law of causality Heisenberg wrote: ”Kant says that realism which has been expressed in empiristic philosophy is certainly justified in so far as it is a warning against whenever we observe an event we assume that there is a foregoing event from which the other event must fol- the naive use of the term ’existence’” [31]. low according to some rule. This is, as Kant states, the basis of all scientific work. In this discussion it is not important whether or not we can always find the forego- ing event from which the other one followed. Actually we can find it in many cases. But even if we cannot, noth- ing can prevent us from asking what this foregoing event 14 might have been and to look for it. Therefore, the law of example, disproving the claim by Alexandrov that ”Men- causality is reduced to the method of scientific research; tion of the observer must be avoided” (see above) Heisen- it is the condition which makes science possible. Since berg writes: ”Of course the introduction of the observer we actually apply this method, the law of causality is ’a must not be misunderstood to imply that some kind of priori’ and is not derived from experience” [31]. If the subjective features are to brought into the description of law of causality is the method of scientific research, as nature. The observer has, rather, only the function of Kant stated, then QM proposed by Heisenberg is obvi- registering decisions, i.e. processes in space and time, ously no-scientific theory. Heisenberg tried to prove that and it does not matter whether the observer is an appa- ”the scientific method actually changed in this very fun- ratus or a human being ···” [31]. Any apparatus be- damental question since Kant” [31]. longs to the ’res extensa’ whereas any human being is His first argument: ”We have been convinced by expe- the ’res cogitans’, at least according to Descartes. If rience that the laws of quantum theory are correct and, if the observer is an apparatus then the Cartesian division they are, we know that a foregoing event as cause for the should not be criticised ”from the development of physics emission at a given time cannot be found” [31]. The other in our time” [31] and Heisenberg rather follows than dis- argument: ”We know the foregoing event, but not quite proves Alexandrov stating that ”’result of measurement’ accurately. We know the forces in the atomic nucleus that in quantum theory only the objective effect of the interac- are responsible for the emission of the α-particle. But tion of the electron with a suitable object”, see above. The this knowledge contains the uncertainty which is brought new Weltanschauung by Heisenberg could be unaccept- about by the interaction between the nucleus and the rest able not only for most physicists but even for Heisenberg of the world. If we wanted to know why the α-particle was himself if it would be logically consistent. emitted at that particular time we would have to know the microscopic structure of the whole world including our- selves, and that is impossible” [31]. Both arguments are 4.1. The quantum postulate and complementarity doubt and have no relation to the fundamental question proposed by Bohr ’objectivate’ observation about the law of causality. If this law is ’a priori’ and is not derived from experience then its disproof can not be Heisenberg defines: ”The position to which the Carte- also derived from experience. At least, the arguments by sian partition has led with respect to the ’res extensa’ Heisenberg could not satisfy Schrodinger, proposing the was what one may call metaphysical realism. The world, cat paradox, Einstein and other critics of QM. Neverthe- i.e., the extended things, ’exist’” [31]. According to this less Heisenberg stated that ”Kant’s arguments for the a definition and the Cartesian division the dogmatic real- priori character of the law of causality no longer apply” ism claims that there are no statements concerning the [31]. Most believers in the soothing philosophy or religion ’res extensa’ that cannot be conceived outside of and in- of Heisenberg-Bohr overlook this philosophical statement dependently of the ’res cogitans’. Therefore according by Heisenberg. to Heisenberg the term ’to objectivate’ should signify to conceive any real situation outside of and independently of the mind of the observer. But he gives fundamentally 4. FUNDAMENTAL MISTAKES BY different definition: ”We ’objectivate’ a statement if we SLEEPWALKERS claim that its content does not depend on the conditions under which it can be verified” [31]. Heisenberg as well as Most sleepwalkers stride unimpeded, first of all, most theoretical physicists confuses here what is not mea- through the new Weltanschauung proposed by Heisen- surable with the unreal. Therefore his practical realism berg. Partly this carelessness may be explained with is very vague. ”Practical realism assumes that there are the inconsistency of Heisenberg. In the same paper [22] statements that can be objectivated and that in fact the Heisenberg refutes a ’real’ world in which causality holds largest part of our experience in daily life consists of such and substantiates his uncertainty relation with help of statements” [31]. If the term ’to objectivate’ signifies only the famous ’uncertainty microscope’ existing in this real independence on the conditions of verification than the world in which causality holds. Later on he criticises the Heisenberg’s practical realism can not make a distinc- Cartesian polarity between the ’res cogitans’ and the ’res tion between the orthodox QM and theories of hidden extensa’ and notes: ”In classical physics science started variables. This distinction can be made only with help from the belief - or should one say from the illusion? - of the philosophically true definition of the term ’to ob- that we could describe the world or at least parts of the jectivate’. We ’objectivate’ a statement if we claim that a world without any reference to ourselves” [31]. On the matter of its description (belonging to the ’res extensa’) other hand he states that ”in the Copenhagen interpre- exists outside of and independently of the mind of the ob- tation of quantum theory we can indeed proceed without server (belonging to the ’res cogitans’). According to this mentioning ourselves as individuals” [31]. Then, what definition hidden variables can be objectivated whereas is fundamental difference between the classical physics the uncertainty relation, the superposition of states, the and the Copenhagen interpretation? Heisenberg confuses Dirac jump and the act of observation in QM can not be constantly the ’res cogitans’ and the ’res extensa’. For objectivated. 15

But the true definition of the term ’to objectivate’ as a distance, only the first system could be supposed dis- well as the true essence of QM of Heisenberg-Bohr could turbed by the first measurement and yet definite predic- be unacceptable for most physicists. Therefore QM based tions become possible for the second system. Is Bohr just on the quantum postulate and complementarity by Bohr rejecting the premise - ’no action at a distance’ - rather had became the symbol of almost general faith in spite than refuting the argument?” Indeed, Bohr could save his of its self-contradiction. Bohr had objectivated the act quantum postulate and his complementarity only reject- of observation when he considered it as an interaction ing the premise - ’no action at a distance’. ”The quantum between quantum system and measuring instrument. It postulate implies that any observation of atomic phenom- must be obvious that the Dirac jump can not be described ena will involve an interaction with the agency of obser- by this way. Nevertheless most physicists including such vation not to be neglected” [23]. EPR had proposed a eminent one as Feynman [13] and Landau [19] had fol- method of the observation, for example, by Alice the spin lowed Bohr in his wrong belief. Bell wrote that ”Lan- state of the distant particle flying toward Bob at which dau sat at the feet of Bohr” [24]. Therefore Landau was no interaction between the agency of observation of Alice sure ”that, in speaking of ’performing a measurement’, and the Bob’s particle can be assumed without action at we refer to the interaction of an electron with a classical a distance between they. The Bohr’s complementarity ’apparatus’, which in no way presupposes the presence of can be valid also if only the premise - ’no action at a an external observer” [19] and could not understand the distance’ could be rejected. This action should be real logical absurdity of the LL jump. Even the EPR cor- because of the reality of an interaction with the agency of relation [24] could not shake the wrong belief of Bohr observation which belongs to the ’res extensa’, as well as and his followers. It must be obvious that non-locality any quantum object. The mind of Alice and Bob belong of the EPR correlation precludes any possibility to inter- to the ’res cogitans’. But the quantum postulate and pret the act of observation realistically as an interaction complementarity exclude an interaction with the mind with measuring instrument. Nevertheless Bohr tried to of the observer. Bohr and his followers objectivated (in save his quantum postulate and his complementarity. In the meaning of the true definition) the act of observation, his reply [51] on the EPR paper [24] Bohr criticizes the the Dirac jump and even the EPR correlation. The ob- EPR criterion of the existence of an element of physical jectiveness of the EPR correlation implies a real action reality: ”··· the wording of the above mentioned crite- at a distance between the ’res extensa’ contradicting to rion ··· contains an ambiguity as regards the meaning of the relativity. The neglect by sleepwalkers this essential the expression ’without in any way disturbing a system’. conflict ”between the two fundamental pillars of contem- Of course there is in a case like that just considered no porary theory” has resulted to mass delusion. question of a mechanical disturbance of the system under investigation during the last critical stage of the measur- ing procedure. But even at this stage there is essentially 4.2. The mass delusion and the idea of quantum the question of an influence on the very conditions which computation define the possible types of predictions regarding the fu- ture behaviour of the system ··· their argumentation does This mass delusion shows itself, in particular, in the not ’justify their conclusion that quantum mechanical de- idea of quantum computation enjoying wide popularity scription is essentially incomplete ··· This description now [48]. The widespread interest in this idea seems quite may be characterized as a rational utilization of all pos- valid. The minimal sizes of nanostructures come nearer sibilities of unambiguous interpretation of measurements, to atomic level and subsequent miniaturization will not compatible with the finite and uncontrollable interaction be possible in the near future. Therefore exponential in- between the objects and the measuring instruments in the crease of calculating resources with number of quantum field of quantum theory”. bits has provoked almost boundless enthusiasm. This This criticism is very obscure and Bell quoting it writes exponential increase seems possible thanks to the princi- in [27]: ”Indeed I have very little idea what this means. I ple of superposition of states, interpreted as the cardinal do not understand in what sense the word ’mechanical’ is positive principle of the QM [19]. Feynman [52] proposed used, in characterising the disturbances which Bohr does universal simulation, i.e. a purpose-built quantum sys- not contemplate, as distinct from those which he does. tem which could simulate the physical behaviour of any I do not know what the passage means - ’an influence other, noting that the calculation complexity of quantum on the very conditions ···’. Could it mean just that system increases exponentially with number N of its ele- N different experiments on the first system give different ments. Indeed, the number gN =2 − 1 of independent kinds of information about the second? But this was just variables γj describing, for example, the spin 1/2 states one of the main points of EPR, who observed that one of N particle could learn either the position or the momentum of the second system. And then I do not understand the final ψ = γ1| ↑↑↑ ... ↑> +γ2| ↑↑↑ ... ↓> +... reference to ’uncontrollable interactions between measur- ing instruments and objects’, it seems just to ignore the essential point of EPR that in the absence of action at +γgN−1| ↓↓↓ ... ↑> +γgN | ↓↓↓ ... ↓> (15) 16 increases exponentially with the number of these particles the number of quantum bits N ≈ 2303, when the ob- thanks to the EPR correlation. server observes the spine state only one particle. The Feynman’s idea of simulation was based on his be- Our mind, in a certain relation, is much more rich than lief in QM as an universal theory. But this belief is false. our empirical knowledge. We can write any big number, 1000 10000000 1000000000 The idea of universal quantum computer was proposed for example 10 , 10 , 10 , and even to by David Deutsch ”as a way to experimentally test the set yourself a task to factorized it on multipliers with help ’Many Universes Theory’ of quantum physics - the idea of the Shor’s algorithm. But it does not mean, that this that when a particle changes, it changes into all possible task can be solved with help of a real device, quantum forms, across multiple universes” [53]. There is impor- computer, in a reality of one universe. It could be possi- tant to remind that the concept of multiple universes was ble only if a real action on distance, violating relativistic proposed by Hugh Everett [14] in order to describe the causality, could be possible. The violations [45–47] of Process 1, i.e. the act of observation out the domain of the Bell’s inequalities give experimental evidence of ”a psychology, i.e. without the mind of the observer. In the gross violation of relativistic causality”, p. 171 in [1], for early 1990’s several authors sought computational tasks results of observations. The EPR correlation describes which could be solved by a quantum computer more effi- just this violation. But the experimental results [45–47] ciently than any classical computer. Shor has described and any others can not give evidence that the EPR cor- in 1994 [54] an algorithm which was not only efficient relation describes a real action on distance between the on a quantum computer, but also addressed a central ’res extensa’, existing outside of and independently of the problem in computer science: that of factorising large ’res cogitans’, i.e. the mind of the observer. Authors of integers. This possibility has provoked mass enthusiasm. numerous publications about quantum computation ob- But most authors of numerous publication on quantum jectivate without hesitation quantum bits and quantum computation ignore the statement of the author of this gates doing not suspect about conflict with relativistic idea that quantum computer can be real only in multiple causality and even with the Copenhagen interpretation universes. Deutsch writes in his book [55]: ”For whose of quantum theory. In the Section ”The Copenhagen who still thinks that there is only one universe I offer Interpretation of Quantum Theory” of [31] Heisenberg the following problem: to explain a principle of action of stated ”that certainly our knowledge can change suddenly the Shor’s algorithm. I do not request to predict that it and that this fact justifies the use of the term ’quantum will work, as for this purpose it is enough to solve some jump’”. Just this sudden change of our knowledge at ob- consistent equations. I ask you to give an explanation. servation results to non-locality of the EPR correlation When the Shor’s algorithm has factorized number, hav- and the conflict between the Copenhagen interpretation ing involved about 10500 computing resources which can be of quantum theory with relativistic causality. Heisenberg seen where this number was factorized on multipliers? In noted also in this Section that ”there is no description whole visible universe exists in all about 1080 atoms, the of what happens to the system between the initial obser- number is insignificant small in comparison with 10500. vation and the next measurement” [31]. Thus, according Thus, if the visible universe was a whole physical reality, to the Copenhagen interpretation QM can not describe the physical reality even is remote would not contain re- a process of quantum computation which should be just sources, sufficient for factorization on multipliers of such before the next measurement. Both the EPR correlation big number”. and quantum computation can not be possible accord- ing to hidden-variables theories. Deutsch is quite right This contradiction between the author of the idea of that quantum computer can be real only in a reality of quantum computation and numerous authors of publica- multiple universes. tions about quantum computation is consequence of the robust 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- 4.3. Two principal mistakes of Heisenberg thodox QM ”cannot be ruled out as lying in the domain of psychology” [14] and only the idea of multiple universes The Heisenberg’s point of view was inconsistent. On can deliver from this nonsense. In contrast to Deutsch the one hand he understood that ”if a interaction of a and Everett most authors believing Heisenberg and Bohr, system with the measuring apparatus is treated as a whole who had obscured the logically obvious fact, spurn such according to quantum mechanics and if both are regarded mind-boggling fantasies as both the many world interpre- as cut off from the rest of the world, then the formalism of tation and the mind of the observer having an influence quantum theory does not as a rule lead to a define result” on quantum system at observation. The belief in the [31]. But on the other hand he did not want to admit soothing philosophy or religion of Heisenberg-Bohr is so the presence of subjectivity in his pet quantum mechan- thoughtless that believers refuse to admit that the nu- ics. Although the subjectivity follows logically and in- merous independent variables γj in the EPR correlation evitably from his understanding that ’quantum jump’ of (15) describe the knowledge of an observer. It must be the measuring apparatus can not be spontaneous. Try- N obvious from the fact that the huge number gN =2 − 1 ing to deny subjective features of QM Heisenberg was decreases twice, for example approximately on 101000 at forced to use obscure declarations, for example: ”The 17 observer has, rather, only the function of registering de- what is ’observable’. I think he was right - ’observation’ is cisions, i.e. processes in space and time, and it does not a complicated and theory-laden business. Then that no- matter whether the observer is an apparatus or a human tion should not appear in the formulation of fundamental being; but the registration, i.e. the transition from the theory” [24]. Einstein and Bell asserted fairly that the ’possible’ to the ’actual’ is absolutely necessary here and offer by Heisenberg to describe only observable parame- can not be omitted from the interpretation of quantum ters rather has complicated than has simplified the task theory. At this point quantum theory is intrinsically con- of theory. The description of observation results can not nected with thermodynamics in so far as every act of ob- be complete without a description of the act of observa- servation is by its very nature an irreversible process; it is tion. Therefore it is easier to create a theory describing only through such irreversible processes that the formal- ”real situation (as it supposedly exists irrespective of any ism of quantum theory can be consistently connected with act of observation or substantiation)” [50] than a theory actual events in space and time” [31]. This explanation is describing observation results. The vagueness of the no- very obscure! Any apparatus belongs to the ’res extensa’ tion about observation (measurement) is principal cause whereas a human being belongs to the ’res cogitans’. An of the fundamental obscurity in quantum. Bell was right answer on the question ”What or who is the observer, the when he stated that ”On this list of bad words from good ’res extensa’ or the ’res cogitans’?” should be decisive for books, the worst of all is ’measurement’”. Heisenberg the essence of QM. But Heisenberg ignores this question proposing to describe observation results could not even because he understands that no apparatus can induce the formulate enough clear what is observation. transition from the ’possible’ to the ’actual’. This tran- This logical mistake is result of other fundamen- sition can be only in the mind of a human being. But tal mistake concerning his conception of human think- Heisenberg did not want to admit this subjective feature ing. Heisenberg noted: ”This basis of the philosophy of QM. of Descartes is radically different from that of the an- The proclaim resemblance of QM and thermodynamics cient Greek philosophers. Here the starting point is not distracts the attention from the principal problem and a fundamental principle or substance, but the attempt of has misled many physicists, in particular Landau [19]. a fundamental knowledge. And Descartes realises that The principal problem was raised by Bell in his paper what we know about our mind is more certain than what ”On the problem of hidden variables in quantum me- we know about the outer world” [31]. But Heisenberg chanics” [42]: ”To know the quantum mechanical state of himself seems to do not realise that our knowledge about a system implies, in general, only statistical restrictions our mind is more certain than about the outer world. on the results of measurements. It seems interesting to Only therefore he could contest the logical conclusion by ask if this statistical element be thought of as arising, Kant that the law of causality is a priori form of our as in classical statistical mechanics, because the states in mind and the basis of all scientific work. The vagueness question are averages over better defined states for which and self-contradiction of QM prove that rather Kant than individually the results would be quite determined”. Bell Heisenberg was right. Considering the law of causality in this work had given the answer of the principal ques- Heisenberg wrote: ”Kant says that whenever we observe tion ”What or who is the observer?” If all quantum phe- an event we assume that there is a foregoing event from nomena can be described using better defined states for which the other event must follow according to some rule” which individually the results would be quite determined, [31]. This conclusion by Kant about human thinking i.e. ’hidden variables’ than the observer is an apparatus. is confirmed with an interesting discussion between cre- But in this case the orthodox QM proposed by Heisen- ators of quantum mechanics at the Solvay meeting 1927, berg is observably inadequate. It may be adequate if which Bohr remembered in 1949 [40]: ”On that occasion ”atomic and subatomic particles do not have any definite an interesting discussion arose also about how to speak properties in advance of observation” [27]. In this case of the appearance of phenomena for which only predic- the observer must be the mind of a human being because tions of statistical character can be made. The question no apparatus can create definite properties when they do was whether, as to the occurrence of individual effects, not exist in advance of observation. Any apparatus can we should adopt a terminology proposed by Dirac, that only change properties and make they hidden. we were concerned with a choice on the part of ’nature’ The vagueness of QM is a consequence of logical or, as suggested by Heisenberg, we should say that we mistakes made by young Heisenberg. Einstein warned have to do with a choice on the part of the ”observer” against one of they. Heisenberg remembered [56] that af- constructing the measuring instruments and reading their ter his talk at the Berlin university in 1926 Einstein has recording. Any such terminology would, however, appear told him that ”from the fundamental point of view the in- dubious since, on the one hand, it is hardly reasonable to tention to create a theory only on observable parameters endow nature with volition in the ordinary sense, while, completely ridiculously. Because in the real all is quite on the other hand, it is certainly not possible for the ob- the contrary. Only the theory can decide what exactly server to influence the events which may appear under can be observable. As you can see, observation, generally the conditions he has arranged”. speaking, is very complicated process”. In 63 years later Here three principal creators of QM discuss what is Bell wrote: ”Einstein said that it is theory which decides the cause of the appearance of phenomena. None of they 18 state the absence of the cause, even Heisenberg. Almost when the Dirac jump is absent. 30 years later Heisenberg calls in question that the Kant’s conclusion ”Since we actually apply this method, the law of causality is ’a priori’ and is not derived from expe- 5.1. The Aharonov - Bohm effects are described rience” [31] may be true in atomic physics. Heisenberg both with the ψ - functions and the wave function considers a radium atom, which can emit an α-particle states ”The time for the emission of the α-particle cannot For example, the Dirac jump is used for the descrip- be predicted” [31]. Next he asks ”But why has the scien- tion of the two-slit interference experiment demonstrat- tific method actually changed in this very fundamental ing particle - wave duality at observation. The interfer- question since Kant?”, gives two answers one of they is ence pattern, for example electrons observed on a detect- ”We have been convinced by experience that the laws of ing screen [57], testifies to that electrons pass through quantum theory are correct and, if they are, we know that the double-slit as a wave with the de Broglie wave- a foregoing event as cause for the emission at a given time length λdeB = 2π~/mv. But the same electrons man- cannot be found” and concludes ”Therefore, Kant’s argu- ifest itself as particles at they arrival at the detecting ments for the a priori character of the law of causality no screen [57], see also Fig.1-3 in the book [16]. QM de- longer apply” [31]. This Heisenberg’s conclusion is abso- scribes this observed duality with help of the ψ func- lutely ill-founded because he considers the ’res extensa’ tion ΨB =ΨB1 +ΨB2 which is the superposition of two iϕ1 iϕ2 whereas Kant considered the ’res cogitans’, human mind. ψ - functions ΨB1 = A1e ,ΨB2 = A2e describing The Kant’s conclusion that the law of causality is ’a pri- two possible path L1, L2 of electrons through the first ori’ is ’a priori’. Therefore neither experience nor theory and second slits with the amplitudes A1 and A2 of the describing correctly this experience can call this conclu- arrival probability at the point y of a particle passing sion in question. The negation of a cause in ’nature’, i.e. through the first and second slit. Then, the probability 2 the terminology proposed by Dirac results inevitably to P (y) = |ΨB| of the electron arrival at a point y of the the suggestion by young Heisenberg that the ’observer’ is detecting screen, Fig.3, the cause of the occurrence of individual effects. Just this 2 2 suggestion results to the EPR paradox, the Schrodinger’s P (y)= A1 + A2 +2A1A2 cos(∆ϕ1 − ∆ϕ2) (16) cat paradox, the questions ”Whose knowledge and whose will?”, considered above, and other nonsense. should depend on the phase difference ∆ϕ1 − ∆ϕ2. Y. Aharonov and D. Bohm had noted more than fifty years ago [58] that this phase difference ∆ϕ1 − y y y ∆ϕ2 = dr1(p/~) − dr2(p/~) = dr1(mv/~) − 5. FUNDAMENTAL MISTAKES BECAUSE OF S S S y R ~ R ~ R THE PREJUDICE OF THE QM UNIVERSALITY S dr1(mv/ ) + dr(eA/ ) = 2π(L1 − L2)/λdeB + R2πΦ/Φ0 and consequentlyH the probability (16) should change with magnetic flux Φ inside the closed contour The fundamental obscurity in QM discussed during al- S − L1 − y − L2 − S, Fig.1, because of the relation most ninety years is connected with the vague notion p = mv + qA between canonical momentum p and elec- about the act of observation, i.e. the Process 1 accord- tron q = e velocity v in the presence of a magnetic vector ing to Everett [14]. The description of the Process 1 potential A. The interference pattern shift with the flux should lie in the domain of psychology [14]. Therefore Φ change was corroborated by many experiments [59]. it is very important to draw reader’s attention that the The value of the probability (16) oscillates with the pe- act of observation is absent at the description of most riod equal the flux quantum Φ0 =2π~/q. quantum phenomena. It was noted in the Introduction The periodicity because of the Aharonov - Bohm effect that already Feynman had become aware of the appli- [59], i.e. because of the relation ~∇ϕ = p = mv + qA, cability of the realistic interpretation of wave function are observed also in normal metal [60] and superconduc- proposed by Schrodinger for description of macroscopic tor [62, 63, 75] loops. But this effect differs in essence quantum phenomena. But he did not understand the from the case of the two-slit interference experiment. fundamental importance of this fact. Anyone can easy The periodical dependencies in magnetic flux Φ with pe- see that not only macroscopic quantum phenomena are riod Φ0 = 2π~/q are observed in the mesoscopic rings described with the Schrodinger interpretation, i.e. with- [60, 62, 63, 75] because of the quantization of velocity out the Process 1, the mind of the observer and other circulation mysticism. Schrodinger had introduced the term ’wave function’ for his interpretation and used, as well as Ein- 2π~ Φ stein [50], the term ’ψ - function’ [33] for the positivistic dlv = (n − ) (17) Il m Φ0 interpretation proposed by Born. The terms ’wave func- tion’ ΨSh and ’ψ - function’ ΨB will be used below in the The quantization (17) is deduced from the requirement same sense. It would be useful to categorise the quan- that the complex wave function must be single-valued tum phenomena described the ’wave function’ and the ’ψ ΨSh = |ΨSh| exp iϕ = |ΨSh| exp i(ϕ + n2π) at any point. - function’. QM uses the ’ψ - function’ when the Dirac Because of this requirement, the phase ϕ must change by jump is used at the description and the ’wave function’ integral n multiples of 2π following a complete turn along 19

5.2. We can believe for the time being in reality of the moon

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 of what goes on the atomic and subatomic scale” [27]. ”For example [67], Bohr once declared when asked whether the quantum mechanical algorithm could be considered as somehow mirroring an underlying quantum reality: FIG. 3: The Ahronov-Bohm effects in the two-slit interference ’There is no quantum world. There is only an abstract experiment (on the left) and in in normal metal or supercon- quantum mechanical description. It is wrong to think that ductor ring (on the right) are consequence of the magnetic flux the task of physics is to find out how Nature is. Physics

Φ influence on the phase difference ∆ϕ1 − ∆ϕ2 = Hl dl∇ϕ. In concerns what we can say about Nature’” [27]. The cre- the first case the difference ∆ϕ1 − ∆ϕ2 of the phase changes ators of QM disclaimed reality only on the atomic and between S and y points along upper L1 way ∆ϕ1 and lower L2 subatomic scale. Recently this scepticism about realism way ∆ϕ2 should not be divisible by 2π (∆ϕ1 − ∆ϕ2 6= n2π) was expanded to macroscopic level [11]. The authors since the ψ function collapses at the observation of the elec- [11] quoting the known remark by Albert Einstein ”I like tron arrival in a point y of the detector screen. In contrast to think that the moon is there even if I don’t look at it” to the interference experiment the Ahronov-Bohm effects in mesoscopic ring (for instance the persistent current) are ob- claims that some experimental results obtained on super- conducting circuit [68] could refute this trust by Einstein served because of the requirement ∆ϕ1 − ∆ϕ2 = n2π since the wave function, describing this case, can not collapse in objective reality even on the macroscopic level. This scandalized claim bears a direct relation to the problem of a possibility of superconducting quantum bits [69]. A small moon, which is not there according to [11], is a the path of integration, yielding dl ▽ ϕ = dlp/~ = l l magnetic flux inside a superconducting loop [70] which ~ ~ H H l dl(mv + qA)/ = m l dlv/ +2πΦ/Φ0 = n2π. is considered as flux qubit in numerous publications [69] H This requirement isH violated at the description of the including the one [71] of the author of the scandalized two-slit interference experiment because of the collapse claim [11]. The authors [11] believes paradoxically that of the ψ - function (the Dirac jump) at the observa- QM can prove that nothing is there but it is possible to tion of the electron arrival in a point y of the detector create anything, superconducting quantum bits [71] for y screen. The phase difference ∆ϕ1 − ∆ϕ2 = S dr1∇ϕ − example, using this nothing. Ironically, quantum bits can y R S dr2∇ϕ = l dr∇ϕ and the probability (16) can change be created indeed only if quantum systems do not have uninterruptedlyR H with the coordinate y and magnetic flux any definite properties in advance of observation. Φ thanks to the collapse. This uninterrupted variation Only basis both of the doubt in macroscopic reality provides the interference pattern (16) and its shift with [11] and of the reality of superconducting quantum bits Φ. Thus, although the both Aharonov - Bohm effects re- [69, 71] is the Leggett-Garg inequality referred to as a sult from the Φ influence on the phase variation along a Bell’s inequality in time [11, 68]. A.J. Leggett and A. closed path l dr∇ϕ they differ fundamentally: the first Garg [70] have concocted the contradiction with real- one should beH described with the ψ - function whereas the ism extremely unsuccessful. The doubt about reality of second one should be described with the wave function macroscopic magnetic flux in rf SQUID, i.e. a supercon- [64]. ducting loop interrupted by Josephson junction, is pro- The ignorance about this fundamental difference pro- voked in [70] only because of ψ - function usage in ad- vokes mistakes. For example, the authors [65] have con- ditional to the wave function describing superconducting cluded that electrons can be reflected because of mag- state. ψ - function can apply speculatively for description netic flux Φ in the Aharonov-Bohm ring, in defiance of of any macroscopic object, for example the cat [33] or the the law of momentum conservation [8]. The contradic- moon [49]. But realism must not be called in question tion in such scandalous form is absent in the Aharonov - without irrefutable empirical evidence obtained on the Bohm effect [58], although there is a problem with non- base of no-hidden-variables theorem (or, vulgarly, ’no-go local force free momentum transfer [16, 66]. In spite of theorem’) [43]. the change in the interference pattern no overall deflec- The superconducting loop interrupted by Josephson tion of electrons is observed in the Aharonov-Bohm effect junction, considered in [70], has two permitted states because of magnetic flux [16]. The transmission (reflec- with the same minimal energy and opposite directed su- 2 2 tion) probability Ptr = dyP (y) = dx(A1 + A2)=1 perconducting current (the persistent current Ip), when can not depend at all onR magnetic fluxR Φ contrary to the external magnetic flux inside its loop is divisible by half erroneous theoretical result shown on Fig.2 in [65]. The Φ = (n+0.5)Φ0 of the flux quantum Φ0 =2π~/q, see the mistake [65] is one of consequences of the prejudice of the relation (17). Imitating Bell, A.J. Leggett and A. Garg QM universality [7]. [70] have offered inequalities which experimental check 20 should prove the contradiction with any realistic theory 6.1. Puzzles generated with the quantum and the necessity of the positivistic description with help formalism of superposition of states, which should collapse at obser- vation. The no-go theorem by A.J. Leggett and A. Garg The real situation, described with the wave function [70] is false because of some reasons. First of all there is ΨSh = |ΨSh| exp iϕ, can not change because of our look, not a well-grounded motive to call macroscopic realism in but it can alter with help of a real physical influence. question because rather the realistic Schrodinger’s than For example, we can decrease the density of Cooper pairs 2 positivistic Born’s interpretation of the wave function is |ΨSh| = ns = ns,0(1 − T/Tc) down to ns = 0 at a time valid for description of macroscopic quantum phenom- t = ton, overheating a loop segment B above supercon- ena. The authors [70] as well many others [69, 71, 73] ducting transition T >Tc, for example with help of laser liken superconducting loop to spin 1/2 and assume su- beam, Fig.4. The electric field E = −▽ V ≈ VB /(l − lB) perposition of its two permitted states, described as the of the potential voltage superposition of the spin states ψ = α| ↑> +β| ↓>. This likening is obviously false because of some reasons. t − ton VB = RBI(t)= RBIp exp − (18) First of all because superconducting loop is flat and the τRL magnetic moment M = I S of the current I circu- m p p appeared because of a non-zero resistance R > 0 of lating in it anticlockwise or clockwise and the angular B the B segment in normal state, will decrease the veloc- momentum of Cooper pairs M = (2m /e)I S are one- p e p ity of Cooper pairs from the quantum value (17), equal dimensional. The assumption [69–71, 73] of superposi- v = −2π~/lm4 at the magnetic flux inside the loop tion of states with different value of the one-dimensional Φ=Φ0/4, down to zero v = 0, during the relaxation angular momentum contradicts to formalism of QM [19] time τ = L/R . I = s2en v is the persistent current even if the one-dimensional angular momentum is micro- RL B p s observed because of the quantization (17); s = hw is the scopic. Therefore it is very strange that A.J. Leggett loop section; L is the inductance of the loop with a length and A. Garg [70] and other authors [69, 71, 73] could as- l. This velocity change occurs in accordance with the sume superposition of states with macroscopically differ- Newton’s second law mdv/dt =2eE, under the influence ent ∆M ≈ 105 ~ angular momentum. This assumption p of the real force F = 2eE acting on each Cooper pair. contradicts obviously to the fundamental law of angular E According to the universally recognised quantum formal- momentum conservation [72] and is much more incon- ism the velocity in all loop segment, including the A one, ceivable than superposition of the cat’s states, at least of Fig.4, must return to the initial value v = −2π~/lm4 the Schrodinger’s cat (9). Besides the authors [70] repeat corresponding the permitted state (17) with minimum virtually the mistake [42, 43] of the von Neumann’s no- 2 energy ∝ (n − Φ/Φ0) after turning off of the laser beam hidden-variables proof. Thus, the doubt in macroscopic at a time t and the cooling of the B segment down realism [11, 70] is absolutely baseless and was provoked off to the initial temperature T

The wave function describes a real situation (as it sup- Vdc ≈ RBIp; at ωswτRL ≫ 1 (19b) posedly exists irrespective of any act of observation or substantiation) in accordance with the programmatic aim of the voltage (12) should be observed at repeated switch- of all physics upheld by Einstein [50]. Therefore the fun- ing with a frequency ωsw of the B segment, Fig.4, be- damental obscurity connected with the Born’s interpre- tween superconducting and normal states, because of the tation is absent at the description of macroscopic and returning of the loop to the same state n at each B cool- some other quantum phenomena. But there is different ing [74]. The sign and value of the dc voltage (19) should fundamental obscurity, more real than the one connected vary periodically with magnetic flux Vdc(Φ/Φ0) like the with violation of the Bell’s inequalities. In spite of this persistent current Ip(Φ/Φ0) [75], because of the change obscurity, the universally recognised quantum formalism of the quantum number n corresponding to minimum en- 2 describes almost all effects observed in superconductor ergy ∝ (n − Φ/Φ0) atΦ=(n +0.5)Φ0 [76]. Such quan- structures. But some experimental results obtained re- tum oscillations of the dc voltage Vdc(Φ/Φ0) ∝ Ip(Φ/Φ0) cently contradict to its predictions. were observed on segments of asymmetric aluminium 21

was called in [83] ”quantum force” Fq: Φ dlFq =2π~(n − )ωsw (20) Il Φ0

at ωsw ≪ 1/τRL. The quantum force l dlFq takes the place of the Faraday’s voltage −dΦ/dt Hwhich maintains IRl = −dΦ/dt a conventional current I circulating in a loop and describes why the persistent current can not

decay IpRl = l dlFq/2e in spite of the power dissipation 2 H Ip Rl. Under equilibrium condition the Ip 6=0 at Rl > 0 is observed only in a narrow temperature region near superconducting transition T ≈ Tc [75, 78, 79], where thermal fluctuations can switch loop segments between superconducting ns > 0, R = 0 and normal ns = 0, R> 0 states [83]. The first experimental evidence of the force-free an- gular momentum transfer was obtained as far back as 1933 when Meissner and Ochsenfeld [84] observed first that a superconductor, placed in a weak magnetic field FIG. 4: Superconducting loop can be switched between the B 0 of the perconductor and any B 10 pairs in a cylindrical superconduc- tor. Jorge Hirsch wonders fairly that ”the question of what is the ’force’ propelling the mobile charge carriers rings when the switching take place because of noise and the ions in the superconductor to move in direction [77–80] or ac current [62, 81]. The experimental results opposite to the electromagnetic force in the Meissner ef- [78, 79] give unequivocal evidence that the persistent cur- fect was essentially never raised nor answered” [85]. He rent can flow against the dc electric field E = −▽ V . proposes an explanation of the Meissner effect puzzle [85]. This puzzle may be connected with the other one: the But some consequences of this explanation, for example observations [62, 63, 75, 78, 79, 82] of the persistent cur- the electric field inside the superconductor, the relation rent Ip(Φ/Φ0) at a non-zero resistance Rl > 0. An elec- (23) in [85], seem unacceptable. tric current should decay during a very short relaxation According to the point of view by Hirsch [86] the force- −9 time τRL = L/Rl < 10 s without Faraday’s voltage free momentum transfer indicates a fundamental problem −dΦ/dt = 0 in the aluminium ring, used in [75, 78, 79], with the conventional theory of superconductivity [87]. I −11 with radius r ≈ 1 µm, the inductance L ≈ 10 H, at think that it indicates a fundamental problem rather with resistance Rl > 0.01 Ω. In defiance of this the persistent QM as a whole than with a theory of superconductivity current does not decay [75, 78, 79]. [88]. The persistent current Ip 6= 0 is observed at R> 0 not only in superconductor [75, 78, 79] but also in normal This puzzles can be described in the limits of the quan- metal rings [60]. In order to dodge the obvious puzzle the tum formalism taking into account that the angular mo- authors [60] and the author [89] claim that the electric mentum l dlp = l dl(mv+2eA)= m l dlv+2eΦ of each current can flow in realistic normal metal rings contain- Cooper pairH shouldH change from 2eΦH to n2π~ because ing atomic defects, grain boundaries, and other kinds of of the quantization at each closing of superconducting static disorder without dissipating energy. They do not state in the ring. This change of pair momentum p in try even to explain how a dissipationless current of elec- a time unit at repeated switching with a frequency ωsw trons can be possible at electron mean free path shorter 22 than the circle length of their rings [60]. The authors the functions describing its magnetic dependencies, see [60] find a pretext for the dropping of the obvious puz- Fig.19 [62] and Fig.3 [100]. But the measurements have zle using a familiar analog in atomic physics: a current revealed that the asymmetry appears because of changes circulating around the atom although the exponential de- in the arguments of the functions rather than the func- crease of the persistent current amplitude with temper- tions themselves [62, 99, 100]. ature increase, Fig.3 in [60], testifies against this analog and to fundamental differences between application of some quantum principles on atomic and mesoscopic lev- 7. CONCLUSION els [90]. Igor Kulik, who has described the possibility of I 6= 0 at R > 0 as far back as 1970 both in supercon- p The history of QM demonstrates clearly that no ductor [91] and normal metal rings [92] made forty years successfulness of a theory can guarantee its accuracy. ago reasonable statement that the taking into account of Most physicists believed in QM and disregarded the a dissipation should not result in the disappearance of pointed criticism of Einstein, Schrodinger, Bell and oth- the persistent current. The observation [78, 79] of the ers who tried to explain that the proposal of Heisen- persistent current flowing against dc electric field con- berg to describe observables instead of beables and the firms the Kulik’s statement and makes meaningless [78] Born’s interpretation of the wave function are inade- the preposterous claim by the authors [60, 89]. quate. They strode unimpeded through the fundamental The authors [60, 89] turn a blind eye also to the other obscurity and non-universal validity quantum principles. puzzle. It is known that ”time-reversal symmetry should Schrodinger pointed out, for example, the non-universal forbid a current choosing one direction over the other validity of the complementarity and uncertainty princi- around the ring” [89]. According to [60, 89] ”A magnetic ples. According to Bohr ”the study of the complementary flux Φ threading the ring will break time-reversal sym- phenomena demands mutually exclusive experimental ar- metry, allowing the PC to flow in a particular direction rangements” [40] But the method of momentum p = mv around the ring” [60]. But the Ip [60, 75] and E = −▽Vp measurement, learned in the primary school, disproves [78, 79] direction changes not only with the Φ direction this statement. According to this method the momentum but also with its value at Φ = nΦ0 and Φ = (n +0.5)Φ0. p = m(z2 − z1)/(t2 − t1) is measured with help of mea- Each physicist must understand that the observation of surement of the time t1 and t2 when the particle passes the direction change with the value change is a puzzle points z1 and z2. Thus, the experimental arrangements which may have a fundamental importance [93–95]. Such for the measurement of position and momentum are not puzzle was not observed on the atomic level because of 2 9 merely mutually non-exclusive but are the same. The the inaccessibly high magnetic fields Φ0/πr ≈ 5 10 G B velocity value v = z/t can be measured with the uncer- needed for this. z tainty ∆vz ≈ vz(∆z/z + ∆t/t) at z = z2 − z1 ≫ ∆z, t = t2 − t1 ≫ ∆t. Consequently, we can make the prod- uct of the velocity ∆vz and position ∆z uncertainties 6.2. Experimental results which can not be ∆z∆vz ≈ ∆zvz(∆z/z + ∆t/t) how any small, contrary describe with help of the quantum formalism to the Heisenberg uncertainty relation ∆z∆vz > ~/2m, increasing the distance z = z2 −z1 and the time t = z/vz. According to the criterion of demarcation between The mass delusion concerning quantum mechanic is a what is and is not genuinely scientific by Karl Popper: consequence of the optimistic point of view that the his- a theory should be considered scientific if and only if it tory of science is the history of progress. But it is also is falsifiable. Therefore any experimental results contra- the history of wrong belief. In the beginning of his talk dicting to the quantum formalism should be at the centre ”Speakable and unspeakable in quantum mechanics” p. of attention. I would like to draw reader’s attention to 169 in [1] Bell cites a quotation from A. Koestler’s book two of such results. According to the quantum formalism ’The Sleepwalkers’ about of the Copernican revolution: (17) two permitted states n and n+1 of superconducting ”··· the history of cosmic theories may without exagger- loop should be observed at Φ = (n+0.5)Φ0 at the single- ation be called a history of collective obsessions and con- shot measurement. Some experimental results [96, 97] trolled schizophrenias; and the manner in which some of corroborate this prediction but other one [97] contradict the most important individual discoveries were arrived at to it. The χ-shaped crossing observed in [97] and mis- reminds one of a sleepwalker’s performance ···.”. Accord- interpreted [98] by the authors as the single-shot read- ing to Bell and Koestler Copernicus, Kepler, and Galilei out of macroscopic quantum superposition of ’flux qubit’ ”were not really aware of what they were doing ··· sleep- [69, 71] states challenges the quantum formalism forbid- walkers” p. 169 in [1]. This sleepwalking in the history ding the state with v =0(17)atΦ=(n +0.5)Φ0. Other of QM is more evident. QM is the most successful the- challenge has been revealed at measurements of magnetic ory but it is also most obscure theory. The cause of this dependencies of the critical current of asymmetric super- obscurity is obvious and some experts denoted it, for ex- conducting rings [62, 99–101]. According to the quan- ample Jaynes [102]: ”From this, it is pretty clear why tum formalism (17) the critical current anisotropy should present quantum theory not only does not use - it does appear in the asymmetric ring because of a change of not even dare to mention - the notion of a ’real physical 23 situation’. Defenders of the theory say that this notion cepts gratefully the epistemological conceptual analysis; is philosophically naive, a throwback to outmoded ways of but the external conditions, which are set for him by the thinking, and that recognition of this constitutes deep new facts of experience, do not permit him to let himself be wisdom about the nature of human knowledge. I say that too much restricted in the construction of his conceptual it con-stitutes a violent irrationality, that somewhere in world by the adherence to an epistemological system. He this theory the distinction between reality and our knowl- therefore must appear to the systematic epistemologist as edge of reality has become lost, and the result has more a type of unscrupulous opportunist: he appears as real- the character of medieval necromancy than science” see ist insofar as he seeks to describe a world independent p. 231 in the book [16]. of the acts of perception; as idealist insofar as he looks But most physicists continue to believe in QM. No sci- upon the concepts and theories as the free inventions of ence can be possible without a faith. Scientists should, the human spirit (not logically derivable from what is em- at least, believe in the human capability to perceive the pirically given); as positivist insofar as he considers his outer world. But the belief should not be implicit. We concepts and theories justified only to the extent to which should understand that the EPR correlation and viola- they furnish a logical representation of relations among tion of the Bell’s inequalities rather cast doubt on the sensory experiences. He may even appear as Platonist our capability to perceive the outer world than give new or Pythagorean insofar as he considers the viewpoint of opportunities, for example quantum computation. Such logical simplicity as an indispensable and effective tool of sensible view of things hardly may be possible without his research” [50]. the comprehension epistemological basic of science. Ein- The logical simplicity can not be attributable to QM. stein emphasised this: ”The reciprocal relationship of Moreover this theory is remarkable for logical inconsis- epistemology and science is of noteworthy kind. They tency and non-universality. Even its fundamental obscu- are dependent upon each other. Epistemology without rities are no-universal. The fundamental obscurity un- contact with science becomes an empty scheme. Science masked by Einstein, Schrodinger, Bell and other oppo- without epistemology is - insofar as it is thinkable at all nents of the positivism may be connected with the repu- - primitive and muddled. However, no sooner has the diation of realism. But even realistic description of many epistemologist, who is seeking a clear system, fought his quantum phenomena with help of the Schrodinger’s in- way through to such a system, than he is inclined to in- terpretation of the wave function has fundamental obscu- terpret the thought-content of science in the sense of his rities. We must conclude that a consistent and universal system and to reject whatever does not fit into his sys- theory of quantum phenomena is absent now. ”Could tem. The scientist, however, cannot afford to carry his such theory be created in principle?” is the question re- striving for epistemological systematic that far. He ac- quiring an answer first of all.

[1] Bell J.S. Speakable and Unspeakable in Quantum Me- posium ”NANOSTRUCTURES: Physics and Technol- chanics. Collected Papers on Quantum Philosophy. ogy”, Russia, St. Petersburg, Ioffe Physical-Technical Cambridge University Press, Cambridge, 2004. Institute p. 145-146 (2011); arXiv: 1108.2628 [2] Heisenberg W. Uber quantentheoretische Umdeu- [11] Mooij J.E. Quantum mechanics: No moon there. Nature tung kinematischer und mechanischer Beziehungen. Physics 6, 401-402, (2010) Zeitschrift fur Physik 33, 879-893 (1925). [12] The COST Action MP1006 ”Fundamental Problems in [3] Bell J.S. The theory of local beables. Epistemological Quantum Physics”. http://www.equantum.eu/ Letters, March 1976; p. 52-62 in [1] [13] Feynman R.P., Leighton R.B., Sands M. The Feynman [4] Schrodinger E. An Undulatory Theory of the Mechan- Lectures on Physics, Addison-Wesley Publishing Com- ics of Atoms and Molecules. Phys. Rev. 28, 1049-1070 pany, Reading, Massachusetts, 1963. (1926) [14] Everett H. ’Relative State’ Formulation of Quantum [5] Schrodinger E. Are there Quantum Jumps? Brit. J. Mechanics. Rev. Mod. Phys. 29, 454-462 (1957) Philos. Sci. 3, 233-242 (1952). [15] A. Einstein, letter to E. Schrodinger, 31 May 1928, [6] Bell J.S. Are there quantum jumps? In Schrodinger. reprinted in Letters on Wave Mechanics, ed. M. Klein Centenary of a polymath. Cambridge University Press (New York: Philosophical Library, 1967). (1987); p. 201-212 in [1]. [16] Greenstein G. and Zajonc A. The Quantum Challenge. [7] Nikulov A.V. It is needed to shout ’wake up’. arXiv: Modern Research on the Foundations of Quantum Me- 1008.5389 (2010) chanics, 2nd edn. Jones and Bartlett, Sudbury 2006 [8] Nikulov A.V. Comment on ’Coherent Detection of Elec- [17] Hackermuller L., Uttenthaler S., Hornberger K., Reiger tron Dephasing’, arXiv: 1006.5662 (2010) E., Brezger B., Zeilinger A., and Arndt M. Wave Nature [9] Nikulov A.V. Comment on ’Probing Noise in Flux of Biomolecules and Fluorofullerenes, Phys. Rev. Lett. Qubits via Macroscopic Resonant Tunneling’. arXiv: 91, 090408 (2003). 0903.3575 (2009) [18] Gerlich S., et al. A Kapitza-Dirac-Talbot-Lau interfer- [10] V.V. Aristov and A.V. Nikulov, The fundamental ob- ometerfor highly polarizable molecules. Nature Physics scurity in quantum mechanics. Why it is needed to shout 3, 711 - 715 (2007). ”wake up”, Proceedings of 19th International Sym- [19] Landau L. D. and Lifshitz E. M. Quantum Mechanics: 24

Non-Relativistic Theory. Volume 3, Third Edition, El- mechanics. Rev. Mod. Phys. 38, 447-452 (1966); p.1 in sevier Science, Oxford, 1977. the book [1]. [20] Nairz O., Arndt M., Zeilinger A. Experimental verifica- [43] Mermin N.D. Hidden variables and the two theorems of tion of the Heisenberg uncertainty principle for fullerene John Bell. Rev. Mod. Phys. 65, 803-815 (1993) molecules. Phys. Rev. A 65, 032109 (2002). [44] Adler Mortimer J. Natural Theology, Chance, and God. [21] Schrodinger E. Science and Humanism. Physics in Our In The Great Ideas Today. Encyclopedia Britannica, Time. Cambridge: University Press, 1952. Chicago, p. 300, 1992. [22] Heisenberg W. The Physical Content of Quantum Kine- [45] Aspect A., Grangier P., and Roger G. Experimental matics and Mechanics. Zeilschrift fur Physik, 43, 172- Tests of Realistic Local Theories via Bell’s Theorem. 198 (1927). Phys. Rev. Lett. 47, 460-463 (1981) [23] Bohr N. The Quantum Postulate and the Recent Devel- [46] Aspect A., Dalibard J., and Roger, G. Experimental opment of Atomic Theory. Nature, 121, 580-90 (1928). Test of Bell’s Inequalities Using Time - Varying Ana- [24] Einstein A., Podolsky B. and Rosen N. Can quantum- lyzers. Phys. Rev. Lett. 49, 1804-1807 (1982). mechanical description of physical reality be considered [47] Aspect A., Grangier P., and Roger G. Experimental Re- complete? Phys. Rev., 47, 777-780 (1935) alization of Einstein-Podolsky-Rosen-Bohm Gedanken- [25] Bell J S, Against ’measurement’. in the proceedings of experiment: A New Violation of Bell’s Inequalities. 62Years of Uncertainty (PlenumPublishing, New York Phys. Rev. Lett. 49, 91 - 94 (1982). 1989); p. 213 in the book [1]. [48] Nielsen M.A. and Chuang I.L. Quantum Computa- [26] van Kampen N.G. Ten theorems about quantum me- tion and Quantum Information. Cambridge University chanical measurements. Physica A 153, 97-113 (1988) Press, 2000. [27] Bell J.S. Bertlmann’s socks and the nature of reality. [49] Mermin N.D. Is the moon there when nobody looks? Journal de Physique, 42, 41-61 (1981); p. 139 in the Reality and the quantum theory. Physics Today, 38, 38- book [1]. 47 (1985). [28] Bohm D. Quantum Theory. New York: Prentice-Hall, [50] Einstein A. Remarks concerning the essays brought to- 1951. gether in this co-operative volume. in Albert Einstein [29] Dirac A.M. Quantum Mechanics. Oxford University philosopherscientist, ed. by P.A. Schillp, Evanston, Illi- Press, 1930. nois, pp. 665-688, 1949. [30] von Neumann J. Mathematische Grundlagen der Quan- [51] Bohr N. Can Quantum-Mechanical Description of Phys- tenmechanik. Berlin: Springer, 1932; Mathematical ical Reality be Considered Complete? Phys. Rev. 48, Foundations of Quantum Mechanics. Princeton Univer- 696-702 (1935) sity Press, 1955. [52] Feynman R. P. Int. J. Theor. Phys. 21 467 (1982) [31] Heisenberg W. Physics and Philosophy. George Allen [53] Norton Q. The Father of Quantum Computing. and Unwin Edition, 1959. http://www.wired.com/science/discoveries/news/2007/02/72734 [32] Brukner C., Zukowski M., Zeilinger A., The essence of [54] Shor P. W. Algorithms for quantum computation: Dis- entanglement. arXiv: quant-ph/0106119 crete logarithms and factoring. in Proceedings of the [33] Schrodinger E. The present situation in quantum me- 35th Annual Symposium on Foundations of Computer chanics. Naturwissenschaften 23, 844-849 (1935); En- Science, IEEE Computer Society Press, Los Alamitos, glish translation published in Quantum Theory and CA, pp. 124-134; E- print: quantph/ 9508027 Measurement edited by J.A. Wheeler and W.H. Zurek, [55] Deutsch D. The Fabric of Reality. The Penguin Press, Princeton University Press, Princeton, p. 152-167 1997. (1983). [56] Heisenberg W. Der Teil und das Ganze. Gesprache im [34] Schrodinger E. Discussion of probability relations be- Umkreis der Atomphysik. Munchen, 1969 tween separated systems. Proc. Cambridge Phil. Soc. [57] Tonomura A., Endo J., Matsuda T., Kawasaki T., and 31, 555-563 (1935). Exawa H. Demonstration of single-electron buildup of [35] Bell J.S. La nouvelle cuisine. in Between Science and an interference pattern. Amer. J. Phys. 57, 117-120 Technology, (eds. A. Sarlemijn and P. Kroes) (Elsevier, (1989). North-Holland, 1990) p. 97-109; p. 232 in the book [1]. [58] Aharonov Y. and Bohm D. Significance of Electromag- [36] Bell J. S. On the Einstein-Podolsky-Rosen paradox. netic Potentials in the Quantum Theory. Phys. Rev. Physics 1, 195-200 (1964); p. 14 in the book [1]. 115, 485 -491 (1959). [37] A. Einstein, Autobiography. in Albert Einstein, Philoso- [59] Olariu S. and Popescu I. I. The quantum effects of elec- pher Scientist, Edited by P. A. Schilp, p. 85, Library of tromagnetic fluxes. Rev. Mod. Phys. 57, 339 - 436 (1985) Living Philosophers, Evanston, Illinois (1949). [60] Bleszynski-Jayich. A. C., et al.: Persistent Currents in [38] Bell J.S. On the impossible pilot wave. Found. Phys. 12, Normal Metal Ring Science 326, 272-275 (2009). 989-999 (1982); p. 159 in the book [1]. [61] Koshnick N.C., Bluhm H., Huber M. E., Moler [39] Gerlach W. and Stern O. Das magnetische Moment des K.A. Fluctuation Superconductivity in Mesoscopic Alu- Silberatoms. Zs. Phys. 9, 353355 (1922). minum Rings. Science 318, 1440-1443 (2007). [40] Bohr N. Discussion with Einstein on epistemologi- [62] Gurtovoi V. L., Dubonos S. V., Nikulov A. V., Osipov cal problems in atomic physics. in Albert Einstein: N. N. and Tulin V. A. Dependence of the magnitude and Philosopher-Scientist, P. A. Schilpp, ed., pp. 200-41, direction of the persistent current on the magnetic flux The Library of Living Philosophers, Evanston (1949). in superconducting rings. J. of Experimental and Theo- [41] Einstein A. and Ehrenfest P. Quantentheoretische Be- retical Physics 105, 1157-1173 (2007); arXiv: 0903.3539 merkungen zum Experiment von Stern und Gerlach. Zs. [63] Gurtovoi V. L., Nikulov A. V., and Tulin V. A. Phys. 11, 31-34 (1922). Aharonov-Bohm effects in nanostructures. in Proceed- [42] Bell J.S. On the problem of hidden variables in quantum ings of 17th International Symposium ”NANOSTRUC- 25

TURES: Physics and Technology”, Belarus, Minsk, In- conducting Cylinder. Phys. Rev. Lett. 9, 9-12 (1962) stitute of Physics NAS, p. 87 (2009); arXiv: 0910.5172 [83] Nikulov A.V. Quantum Force in Superconductor. [64] Nikulov A. V. Bohm’s quantum potential and quantum Phys.Rev. B 64, 012505 (2001). force in superconductor. AIP Conference Proceedings, [84] Meissner W. and Ochsenfeld R. Ein neuer effekt bei Vol. 1101 ”Foundations of Probability and Physics-5” eintritt der supraleitfahigkeit. Naturwissenschaften 21, pp. 134-143 (2009); arXiv: 0812.4118. 787-788 (1933). [65] Strambini E., et al. Coherent Detection of Electron De- [85] Hirsch, J. E.: Electromotive forces and the Meissner phasing. Phys. Rev. Lett. 104, 170403 (2010). effect puzzle. J. of Superconductivity and Novel Mag- [66] Tonomura A. and Nori, F. Disturbance without the netism 23, 309-317 (2010); arXiv: 0908.409 force. Nature 452, 298-300 (2008). [86] Hirsch J. E. The Lorentz force and superconduc- [67] Jammer M. The Philosophy of Quantum Mechanics, tivity. Phys.Lett. A 315, 474-477 (2003); arXiv: John Wiley (1974), p. 204, quoting A. Petersen, Bul- cond-mat/0305542 letin of the Atomic Scientist 19, 12 (1963). [87] Bardeen J., Cooper L. N., and Schrieffer J. R. Theory [68] Palacios-Laloy A., et al. Experimental violation of a of Superconductivity. Phys. Rev. 108, 1175-1205 (1957). Bell’s inequality in time with weak measurement. Na- [88] Nikulov A.V. The Meissner effect puzzle and the quan- ture Physics 6, 442-447, (2010) tum force in superconductor. Phys. Lett. A 376, 3392- [69] Clarke J. and Wilhelm F.K. Superconducting quantum 3397 (2012); arXiv:1211.0002 bits. Nature 453, 1031-1042 (2008). [89] Birge N. O. Sensing a Small But Persistent Current. [70] Leggett A.J. and Garg A. Quantum mechanics versus Science 326, 244 - 245 (2009). macroscopic realism: Is the flux there when nobody [90] Nikulov A.V. Fundamental Differences Between Appli- looks? Phys. Rev. Lett. 54, 857-860 (1985) cation of Basic Principles of Quantum Mechanics on [71] Chiorescu I., Nakamura Y., Harmans C.J.P.M., and Atomic and Higher Levels. AIP Conference Proceed- Mooij J.E., Coherent Quantum Dynamics of a Super- ings, Vol. 905, FRONTIERS OF FUNDAMENTAL conducting Flux Qubit. Science 299, 1869-1871 (2003) PHYSICS: Eighth International Symposium, pp. 117- [72] Nikulov A.V. Flux-qubit and the law of angular mo- 119 (2007); arXiv: 0707.0827. mentum conservation. Quantum Computers and Com- [91] Kulik I.O. Magnetic flux quantization in the normal puting. 10, 42-61 (2010); arXiv:1005.3776. state. Zh. Exsp. Teor. Fiz. 58, 2171-2175 (1970) (Sov. [73] Leggett A.J. Superconducting Qubits - a Major Road- Phys. JETP 31, 1172-1176 (1970)) block Dissolved? Science 296, 861-862 (2002) [92] Kulik I.O. Flux quantization in normal metal. Pis’ma [74] Nikulov A.V., Zhilyaev I.N. The Little-Parks Effect Zh. Eksp. Teor. Fiz. 11, 407 (1970) (JETP Lett. 11, 275 in an Inhomogeneous Superconducting Ring. J. Low (1970)). Temp.Phys. 112, 227-236 (1998). [93] Nikulov A. V. Quantum limits to the second law and [75] Koshnick N.C., Bluhm H., Huber M. E., and Moler breach of symmetry. arXiv: cond-mat/0505508. K.A. Fluctuation Superconductivity in Mesoscopic Alu- [94] Nikulov A.V. About Essence of the Wave Function on minum Rings. Science 318, 1440-1443 (2007). Atomic Level and in Superconductors. AIP Conference [76] Tinkham M. Introduction to Superconductivity. Proceedings, Vol. 962, QUANTUM THEORY: Recon- McGraw-Hill Book Company, New-York, 1975. sideration of Foundations - 4, pp. 297-301 (2007); arXiv: [77] Burlakov A.A., Gurtovoi V. L., Ilin A. I., Nikulov A. 0803.1840. V., and Tulin V. A. A possibility of persistent voltage [95] Nikulov A.V. Observations of Persistent Current at observation in a system of asymmetric superconduct- Non-Zero Resistance: Challenge to the Second Law ing rings. Phys. Lett. A 376, 2325-2329 (2012); arXiv: of Thermodynamics. AIP Conference Proceedings, Vol. 1207.0791 1411, Second Law of Thermodynamics: Status and [78] Gurtovoi V.L., Ilin A.I., Nikulov A.V., and Tulin V.A. Challenges, pp. 122-144 (2011) Weak dissipation does not result in disappearance of [96] Tanaka H., Sekine Y., Saito S., and Takayanagi H. persistent current. Fizika Nizkikh Temperatur, 36, 1209- DC-SQUID readout for qubit. Physica C 368, 300-304 1218 (2010); arXiv: 1004.3914 (2002). [79] Burlakov A. A., Gurtovoi V.L., Dubonos S.V., Nikulov [97] Tanaka H., Saito S., Nakano H., Semba K., Ueda M., A.V., and Tulin V.A. Little-Parks Effect in a System of and Takayanagi H. Single-Shot Readout of Macroscopic Asymmetric Superconducting Rings. JETP Letters 86, Quantum Superposition State in a Superconducting 517-521 (2007); arXiv: 0805.1223. Flux Qubit. arXiv: cond-mat/0407299. [80] Dubonos S.V., Kuznetsov V.I., and Nikulov A.V. Seg- [98] Aristov V. V. and Nikulov A. V. Quantum computa- ment of an Inhomogeneous Mesoscopic Loop as a DC tion and hidden variables. Proceedings SPIE Vol. 7023, Power Source. in Proceedings of 10th International Sym- Quantum Informatics 2007 (2008). posium ”NANOSTRUCTURES: Physics and Technol- [99] Gurtovoi V.L., Dubonos S.V., Karpi S.V., Nikulov ogy” St Petersburg: Ioffe Institute, p. 350-352 (2002); A.V., and Tulin V.A. Contradiction between the Re- arXiv: physics/0105059 sults of Observations of Resistance and Critical Current [81] Dubonos S. V., Kuznetsov V. I., Zhilyaev I. N., Nikulov Quantum Oscillations in Asymmetric Superconducting A. V., and Firsov A. A.: Observation of the External-ac- Rings. J. of Experimental and Theoretical Physics, 105, Current-Induced dc Voltage Proportional to the Steady 257-262 (2007); arXiv: 1011.6149. Current in Superconducting Loops. Pis’ma Zh. Eksp. [100] Burlakov A. A., Gurtovoi V.L., Dubonos S.V., Nikulov Teor. Fiz. 77, 439-444 (2003) (JETP Letters, 77, 371- A.V., and Tulin V.A. Could two degenerate energy 375 (2003)); arXiv: cond-mat/0303538. states be observed for a superconducting ring at Φ0/2? [82] Little W. A. and Parks R. D. Observation of Quantum arXiv: cond-mat/0603005 Periodicity in the Transition Temperature of a Super- [101] Burlakov A.V., Gurtovoi V.L., Ilin A.I., Nikulov A.V., 26 and Tulin V.A. Experimental investigations of the Institute p. 128-129 (2011); arXiv: 1103.3115 change with magnetic flux of quantum number in super- [102] Jaynes E.T. Quantum beats. in Foundations of Ra- conducting ring. Proceedings of 19th International Sym- diation Theory and Quantum Electrodynamics, A.O. posium ”NANOSTRUCTURES: Physics and Technol- Barut (ed.), New York: Plenum Press, 1980. ogy”, Russia, St. Petersburg, Ioffe Physical-Technical