Origin of Quantum Mechanical Results and Life: A Clue from Quantum Biology

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1 igin of Quantum Mechanical Results and Life: Clue from Quantum iology iswaranjan Dikshit STRCT lthough quantum mechanics can accurately redict the robability distribution of outcomes in an ensemble of identical systems, it cannot redict the result of an individual system. ll the local and global hidden variable theories attemting to exlain individual behavior have been roved invalid by exeriments (violation of ell s inequality) and theory. s an alternative, Schrodinger and others have hyothesized existence of free will in every article which causes randomness in individual results. However, these free will theories have failed to quantitatively exlain the quantum mechanical results. In this aer, we take the clue from quantum biology to get the exlanation of quantum mechanical distribution. Recently it was reorted that mutations (which are quantum rocesses) in DN of E. coli bacteria instead of being random were biased in a direction such that the chance of survival of the bacteria is increased. Extraolating it, we assume that all the articles including inanimate fundamental articles have a will and that is biased to satisfy the collective goals of the ensemble. Using this ostulate, we mathematically derive the correct sin robability distribution without using quantum mechanical formalism (oerators and orn s rule) and exactly reroduce the quantum mechanical sin correlation in entangled airs. Using our concet, we also mathematically derive the form of quantum mechanical wave function of free article which is conventionally a ostulate of quantum mechanics. Thus, we rove that the origin of quantum mechanical results lies in the will (or consciousness) of the objects biased by the collective goal of ensemble or universe. This biasing by the grou on individuals can be called as coherence which directly reresents the extent of life resent in the ensemble. So, we can say that life originates out of establishment of coherence in a grou of inanimate articles. 6 Key Words: Quantum iology, iased Will, Consciousness, Non-locality, Quantum Entanglement DOI Number: /nq NeuroQuantology 018; 16(4):6-33 Introduction Classical or Newtonian mechanics is deterministic and if it were erfectly correct, we could redict all the future events of the universe by feeding in the data of all articles of universe to a huge machine (so called Lalace demon ) which has infinitely large calculating ower. ut unfortunately, it has been exerimentally roved that classical mechanics is only an aroximate theory which fails at the microscoic level whereas quantum mechanics wins both at the micro and macroscoic level. Since the discovery of Schrodinger s equation in 196, quantum mechanics has established itself as a robust theory of nature exlaining nearly all the henomena observed in the universe. ut intrinsically, it is able to rovide only a robabilistic rediction of exerimental results. The accuracy of its rediction can be confirmed only if an infinitely large number of exeriments are carried out in identical systems. In a single exeriment on an individual system, the resentday quantum mechanics cannot redict the result with robability one (i.e. with 100% accuracy). That s why in their famous aer, (Einstein et al., 1935) exressed the view that resent day. Corresonding author: iswaranjan Dikshit ddress: Laser and Plasma Technology Division, habha tomic Research Centre, Mumbai , India bdikshit73@yahoo.co.in Relevant conflicts of interest/financial disclosures: The authors declare that the research was conducted in the absence of any ommercial or financial relationshis that could be construed as a otential conflict of interest. Received: 11 February 018; cceted: 5 March 018

2 quantum mechanics is incomlete and hoed that it may be comleted in future by including some local hidden realistic (oe-existing) variables in the system being measured. y assuming these local hidden variables to be the cause of outcomes, (ell, 1964) derived an inequality exression for the sin correlation among entangled airs of articles which contradicted the quantum mechanical sin correlation Consequently, Initially sect (sect et al., 198; 198b; 1999) and then a large number of otheesearchers (Tittel et al., 1998; Ou et al., 1988; Shih et al., 1988; Weihs et al., 1998; Colbeck et al., 011; Merali et al., 011) carried out exeriments which decisively violated the ell s inequality and thus ruled out the future ossibility of local hidden variables to comlete the quantum theory. Recently, non-local (global) hidden variable theories like deterministic ohmian mechanics (ohm et al., 195; Genovese, 005) have also been roved to be incomatible with quantum mechanics and relativity, theoretically by (Leggets, 003) and (Gisin, 011) and exerimentally by Groblacher and Paterek (Groblacher et al., 007; Paterek et al., 007). While reorting the exerimental results demonstrating the inconsistencies of nonlocal hidden variable theories, Groblacher (Groblacher et al., 007) wrote, Ouesult suggests that giving u the concet of locality is not sufficient to be consistent with quantum exeriments, unless certain intuitive features of realism are abandoned. To escae from this nogo situation, originally Schrodinger and then Conway and Kochen roosed that every elementary article in the universe has some amount of free will which causes the uncertainty oandomness in the exerimental result (Schrodinger, 1936; Conway et al., 006, 009). This is a kind of exression of creativity by the article. However, this free will theory could neither quantitatively rove the quantum mechanical results noovide any basis for ostulates of quantum mechanics. The free will theory based on stochastic model develoed by Conway and Kochen has also been refuted later on by (Goldstein et al., 010). In this aer, instead of taking the will of nature as comletely free, we take it to be biased to maximally satisfy the laws of universe and collective goals of the ensemble. ecause there is a will (or consciousness) in each article, there will be some amount of randomness in the outcomes of individual exeriments. However, the biasing of the will by nature generates a secific attern or distribution in the outcomes of reeated exeriments carried out on identical systems. We get this clue from surrising exerimental results in quantum biology in which it was recently reorted that adative mutation haens in DN of bacteria (Merali, 014; McFadden et al., 1999). In resonse to a changing environment, mutations in E. coli bacteria (which are quantum rocesses) instead of being random were found to be biased in a direction such that the chance of survival of the bacteria is increased. Using our biased will aroach, we will form a foundation on which the ostulates of quantum mechanics can stand and for some cases we will directly derive the established quantum mechanical results without using quantum mechanical formalism. In section-, we will first see how by considering the biased will of the system and without using quantum mechanical formalism (such as oerators and orn s rule), we can correctly redict the robability distribution of sin along any arbitrary direction that agrees with the quantum mechanical redictions. In section-3, using the biased will aroach, we will derive the exression for exectation value of sin correlation between two entangled articles that again exactly matches with the conventional quantum mechanical relation. We will also discuss how oosite sin may be understood in a single air of entangled articles searated by huge (sacelike) distances without need of suerluminal information transfer. In section-4, we theoretically justify the form of generalized quantum mechanical wave function of a free article using biased will so that interference of matter waves and exressions for quantum mechanical oerators can be exlained. Thus, by means of three different cases, we rove that the origin of quantum mechanical results is the will (or consciousness) of the objects biased by the collection or universe. Finally in conclusion, we try to find out the basic structural distinction between non-living and living bodies (or life and death) based on the concet outlined in this aer. We infer that in non-living bodies, the constituent arts have minimal quantum coherence striving to satisfy only the basic laws of the universe such as conservation of angular momentum, energy, maintaining symmetry of sace etc. ut, living bodies have greater extent of quantum coherence among its constituent arts so that more comlex goal oriented behaviors are exhibited (for self-reservation, ain avoidance etc). 7

3 Derivation of sin robability distribution from biased will Consider a fundamental article such as an electron whose sin angular momentum s is quantized that can be of either + h or h along the direction of measurement (reason for quantization will be exlained in end of section 4). Let the electron initially asses through a Stern-Gerlach magnet so that its sin is aligned along Z-axis and let it be + h. Of course, in this case sin along other two erendicular directions are undefined. Now we want to find out the robability that its sin is found to be + h when measured along any arbitrary direction making an angle θ with Z-axis as shown in Fig.1. Figure 1. Direction of sin measurement (Initially article sin is aligned along OZ and then sin is measured along OM) ecause of resence of will of the article, there will be a uncertainty in result in the individual exeriment which can be ± h. ut whatever be the result, angular momentum of the article is not conserved (it is initially + h along Z-axis and finally ± h along OM as shown in Fig.1). This haens because of sueriority of law of quantization of sin over the law of conservation of angular momentum. However, if we carry out the exeriment on a large number of identical articles, the robability will be so biased by nature that total angular momentum of the collection is maximally conserved along OM in which direction the articles have freedom to have any one of the two ossible sin values. If is the robability of getting sin + h along OM, then (1- ) is robability of getting sin h. For N number of identical articles on which exeriment is carried out, to satisfy the law of conservation of angular momentum along OM in addition to the existing law of quantization, Initial total angular momentum along OM Final total angular momentum along OM h h h N cosθ N + + (1 ) N 1 + cosθ cos ( ) θ (1) Thus, Eq. (1) exactly reroduces the conventional quantum mechanical robability distribution to get sin + h along any arbitrary direction. We have derived it by use of the concet of biased will of nature without alying quantum mechanical oerators and orn s rule. Derivation of sin correlation in quantum entangled articles using theory of biased will Sin correlation in a air of entangled articles and is given by the roduct of their measured sins along re-decided directions (sins are taken to be +1 or -1 excluding the constant art h or h ). If we select to measure the sin of article along unit vector a r and sin of article along b r, quantum mechanics redicts that exectation (or average) value of sin correlation is given by, P( a, b a b cos θ () Where θ is the angle between unit vectors a r and b r. bove quantum mechanical sin correlation has been exerimentally validated by numerous authors. Now we will derive the same average sin correlation given by Eq. () using the concet of biased will of nature without using quantum mechanical formalism. Let us consider N number of entangled airs (or twins) of articles 1 1,, 3 3,.. N N emerging from a common source of sin 8

4 zero. Particles in each air i i move in oosite directions before being exosed to exerimental setus for measurement of sin along certain directions a r and br as shown in Figure. their sin correlation. Let us call this grou of members which are identical before exeriment on i as Grou-I. Similarly, ( 1 ) N numbers of airs constitute identical members of Grou-II all of which have sin oositely aligned to direction of a r as shown in Fig.. Now for Grou-I, if is the robability of getting sin along the direction of b r, as er our axiom of biased will of nature, will be such that total angular momentum in grou-i along the measurement direction b r is conserved (s in this direction only i has freedom to have any sin). Since, initial angular momentum of all twins before birth is zero, final angular momentum along the direction of b r in Grou-I which has N members is also zero. So mathematically from Fig., we get, N cos + ( N )( + 1) + (1 )( N )( 1) 0 θ 1 cos θ (3) Figure. Two different grous of members in ensemble of entangled airs (For Grou-I airs, first measurement result is sin-u and for Grou-II it is sin-down) lthough sin is a roerty of individual article, the correlation (ooduc of sins in a twin is only a roerty of twin which can be +1 (if i and i both are aligned along or oosite to a r and b esectively) or -1 (if either of i and i is aligned along and other is oosite to redecided direction). So, for the measurement of correlation, each twin or air i i reresents a single member (or coherent air) in statistical ensemble of N number of twins. However, measurement of sin is a two-ste rocess in which at first we have to measure the sin of (say) i and then go for i. Only after knowing the sin state of i, we get to know the sin correlation. Just after the sin measurement of i (and before measuring i), all the members in the ensemble cannot be considered identical since some of i s have sin along unit vector a r and others have sin oosite to it. If is the robability of getting sin of i along direction a r, N members are exactly identical in the sense that all of them have i along a r before exressing Now, all of N members in grou-i have one artner sin along a r and N members have other artner sin along the direction b r. So, correlation ooduct of sin for each of N members is +1. Hence, ( 1 ) N members have correlation equal to -1. Exectation (or average) value of sin correlation in Grou-I is then given by, sum of correlatio ns of all members P( a, b I Number of members P( a, b I + 1) + (1 N P( a, b 1 I ) 1) Putting the value of from Eq. (3) in above, P ( a, b cos θ I (4) Similarly, we can roceed to calculate the average correlation for Grou-II which has ( 1 ) N number of identical members all of which have sin oositely aligned to direction of a r as shown 9

5 in Fig.. If ' is the robability of getting sin along the direction of b r in grou-ii, as er our theory of biased will of nature, it will be such that total angular momentum in grou-ii along the measurement direction b r is conserved. Since, initial angular momentum of all twins before birth is zero, final angular momentum along the direction of b r is also zero. From Fig., mathematically we get, ( 1 ) Ncosθ + ' (1 ) + 1) + (1 ' )( 1 ) 1) cosθ ' (5) Product of sin for each of ' (1 ) N members is -1. Hence, ( 1 ' )(1 ) N members have correlation equal to +1. verage value of sin correlation in Grou-II is then given by, ' (1 ) 1) + (1 ' )( 1 ) + 1) P( a, b II (1 ) N P ( a, b ' + 1 II Putting the value of ' from Eq. (5) in above, P( a, b cos θ (6) II Thus from Eq. (4) and (6), we find that irresective of whether the twin is in Grou-I or II, the average value of correlation is ( cosθ ). So, we can generalize the result and write the exectation value of correlation as, P( a, b cos θ (7) Thus, we could derive the exectation value of sin correlation in entangled airs of articles which exactly matches with the relation derived by conventional quantum mechanical formalism. We can rove that Eq. (7) is relativistically invariant i.e. it holds indeendent of state of motion of observer. The roof is as follows. If measurements of sin of i and i are carried out in sace like searated regions, certainly for some observers, event at i will haen before i. In that case, those observers will classify the members to Grou-I and Grou-II as er the sin result at i and aly the law of conservation of angular momentum along direction a r since they can know about the correlation only after sin measurement of i. Thus, adoting a similaocedure as before, they will also derive the same sin correlation given by Eq. (7). It is interesting to analyze the case of a single air of entangled articles when sin is measured along same direction for both of them ( θ 0). It has been a surrise to everyone how one article in the air gets knowledge about the sin of other artner so that it can be aligned in oosite direction relative to other esecially if both are searated by sace-like region and suerluminal seed of information is not allowed. We can understand this from Eq. (7) which dictates that for θ 0, average sin correlation is erfect i.e. P( a, a) 1. So, if there are millions of airs of articles with which exeriments are carried out, each of them must contribute a sin correlation of -1 (none +1) to the sum of correlations so that average remains - 1 otherwise it will shift towards +1. This means, each of the millions of airs must have oosite sin which we can state in terms of robability that robability for getting oosite sin must be one. So, even if we carry out the exeriment on a single entangled air, it must show oosite sins in its artners. Thus we conclude that oosite sin observed in a single air of entangled articles is not due to suerluminal information transfer from one to other, rather it is due to the fact that sin correlation is a roerty of air as a whole (which can be called quantum coherence) and it becomes exactly -1 due to Eq. (7). voiding the suerluminal information transfer is imortant as when seed of information exceeds that of light, causality rincile is violated since ordering of two events occurring in sace-like searated regions can be changed by state of motion of observer. Quantum mechanical wave function of a free article from biased will of nature: It is well known that interference of matter waves can be exlained only if generalized quantum mechanical wave function of a free article of momentum and energy E is taken as, i ( Et ) h ψ ( r, e (8) Where r is sace coordinate, t is time, is a constant and h is reduced lank s constant. Fundamental justification for the above form of 30

6 wave function is also very imortant as it is the only basic equation from which the two conventional quantum mechanical oerators in formalism (momentum and energy oerators) are derived. In this section, by using our biased will aroach, we will theoretically derive the generalized form of wave function given by Eq. (8). Let us suose that the comlex function related to the extent of resence of a single free article at any oint of sace-time is given by, ( r, f ( r, e ig ( r, t ) ψ (9) Where, magnitude f ( r, and hase g ( r, are two arbitrary real functions of sace-time. If we consider the extent of resence of article at each oint of sace r as an indeendent variable, then each of these values of ψ ( r, t ) can be reresented as an orthogonal vector ψ ( r, r (where r is unit eigen vector) in a multidimensional mathematical sace (called Hilbert sace) and the total ψ is reresented as a vector sum of these comonents. ut due to quantization of the resence of the article, it can only be detected at a single oint in sace at any time. So, each oint of sace will have a robability for aearance of the article. To have a robabilistic interretation of ψ ( r,, total resence must be equal to one (i.e. ψ must be a unit vector) and it must be written as a sum of its scalar comonents. In any multidimensional vector sace, the resultant can be written as a scalar sum of rojections of its vector comonents along itself (i.e. ψ ) as all of them are collinear. Using definition of rojection oerator, ψ, Similarly, rojection of ψ on r is rojection of ψ ψ ψ ψ ψ ( r,. ψ along ψ is From above we conclude that each rojection of the total system along osition eigen vectors contributes a collinear comonent to constitute the total system. So, all these magnitudes can be added to get, 1 3 ψ ( r, + ψ ( r, + ψ ( r, (10) Now since the above Eq. (10) is a scalar equation, we can have robabilistic interretation and conclude that ψ ( r, is the robability density of hysically finding the article at r at time t (Here, we have actually roved orn s rule). Since for a free article, sace must be hysically symmetric and article must continue to exist with time (these are the biasing by the universe), robability density * ψ ( r, ψ ( r, ψ ( r, must be indeendent of r and t. This indicates, using Eq. (9), ψ * ( r, ψ( r, ( f ( r, t ) ) must be indeendent of sace-time i.e. f ( r, t ), where is a constant. Thus Eq. (9) reduces to, ( r, e ig ( r, t ) ψ (11) To know the mathematical form of function g ( r, t ) i.e. whether it is a linear or nonlinear function of sace-time, for simlicity, let us consider only one coordinate, say x. So, ψ ( x ) ig e ( x) Generally, the hase is given with resect to a reference angle which can be arbitrarily chosen by different observers. ut, difference of hase between any two oints in sace must be same for all observers stationary with resect to each other irresective of their location (required for symmetry of sace). If g ( x 1 ) and g ( x ) are hases at oints x 1 and x as recorded by a stationary observer located at O and g ( x 1 ' ) and g ( x ' ) are hases recorded at same oints by another stationary observer having a shifted origin O, then, g ( x 1 x1 and ) g ( x ) g ( x ' ) g ( ' ) (1) x 1 ' x1 Dividing Eq. (1) by (13), g( x ) g( x1 ) g( x ') g( x1 ') x x x ' x ' 1 x x ' (13) 1 31

7 In differential form, dg ( x) dg ( x' ) dx dx' Since both sides of above equation are functions of different variables, the ratio must be a dg( x) constant, say k. So, k dx Integrating above differential equation and taking g ( x) 0 at x0, g ( x ) x dg ( x) kdx g ( x) kx 0 0 Thus we see that hase must be a linear function of x. Since, all four coordinates of sace time must be considered at ar, hase g ( r, t ) must also be linear function of sace-time. Taking into account the oosite sign of time with resect to sace in relativistic sace-time metric (+---), g ( r, kr ωt The constant k before r haens to be same as / h and constant ω before t haens to be same as E / h where is momentum, E is total energy and h is universal constant equal to reduced Plank constant. So we get, 1 g( r, ( Et ) h Putting the above in Eq. (11), we get, i ( E h ψ ( r, e (14) bove equation is same as the desired Eq. (8) for free article wave function with fixed momentum and energy. Using this equation, as mentioned in conventional text books (eiser, 1987), we can now rove the quantum mechanical momentum oerator to be ( i h ) and energy oerator to be ( ih ). Using Eq. (14), we can also generate t interference attern and form wave ackets for localized articles. If Eq. (14) is used in Einstein s relativistic energy exression, we will recover the Dirac equation which will lead to quantization of sin. Thus, we have found that the generalized form of free article wave function on which the whole of quantum mechanics stands can be derived from our theory of biased will of nature. Conclusion and Scientific Imlications In this aer, by assuming that the inanimate articles have a will (or consciousness) and that is biased to maximally satisfy the laws of universe such as conservation laws and symmetry of sace, we have derived the correct sin robability distribution with angle without using quantum mechanical formalism such as oerators and orn s rule. Similarly, by using the biased will, we have exactly reroduced the quantum mechanical sin correlation in entangled airs of articles. We have also exlained the oosite sin in a single entangled air when it is measured along same axis without requiring the suerluminal information transfer so that relativistic causality is not violated. Finally, we have develoed a theoretical justification for the form of generalized quantum mechanical wave of a free article using biased will of nature so that interference and quantum mechanical oerators can be derived on which the whole of quantum mechanics stands. Thus, we have roved that origin of quantum mechanical results lies in the will of the objects biased by the whole. Scientific imlications of the above analysis are significant since we could extraolate our observations in living organisms to inanimate matter to infer that motivations of the universe both in form of conservation laws and collective goals of systems can affect the quantum mechanical results. This biasing by the grou on its individual member can be called as coherence of will which directly reresents the extent of life resent in the ensemble. Thus, life originates out of establishment of coherence in a grou of inanimate articles. We are now in a osition to state the basic structural distinction between non-living and living bodies based on the concet outlined in this aer. In a non-living entity, the constituent arts have minimal quantum coherence among themselves and they try to satisfy only the basic laws of the universe such as conservation of angular momentum, maintaining symmetry of sace etc. ut in living bodies, the constituent arts have greater extent of quantum coherence in the will (or consciousness) so that more comlex goal oriented behaviors are exhibited for selfreservation, leasure enhancement, ain avoidance etc. Death of an organism indicates the destruction of this coherence and tendency of living organism to reserve itself is truly tendency to reserve its coherence. It has been 3

8 recently reorted by (Hameroff, 004) that the origin of cancer in cells can also be traced to the imairment of quantum coherence during mitosis. To make a dead cell alive or to find a cure for cancer, we have to search for ways to reestablish the coherence or macroscoic entanglement in its constituents. Of course, much more research is required in interdiscilinary subjects like quantum entanglement in macroscoic systems (Vedral, 008) and quantum biology (Lambert et al., 013; Josehson et al., 1991; Stra, 198; Hameroff et al., 014) to mathematically model and modify the rocesses and behaviors exhibited by living organisms. References sect, Grangier P, Roger G. Exerimental realization of Einstein-Podolsky-Rosen-ohm Gedankenexeriment: a new violation of ell's inequalities. Physical Review Letters 198; 49(): sect, Dalibard J, Roger G. Exerimental test of ell's inequalities using time-varying analyzers. Physical Review Letters. 198; 49(5): sect. ell's inequality test: more ideal than ever. Nature 1999;398(674): eiser. Persectives of modern Physics, Singaore: McGraw-Hill ook Comany, 1987 ell JS. On the Einstein Podolsky Rosen Paradox. Physics, 1964; 1(3): ohm D. suggested interretation of the quantum theory in terms of" hidden" variables. I. Physical Review 195; 85(): Colbeck R, Renner R. No extension of quantum theory can have imroved redictive ower. Nature communications 011; (411): 1-5. Conway J, Kochen S. The free will theorem. Foundations of Physics 006; 36(10): Conway J, Kochen S. The strong free will theorem. Notices of the MS 009; 56():6-3. Einstein, Podolsky, Rosen N. Can quantum-mechanical descrition of hysical reality be considered comlete?. Physical Review 1935;47(10): Gisin N. Imossibility of covariant deterministic nonlocal hidden-variable extensions of quantum theory. Physical Review 011; 83():0010. Goldstein S, Tausk DV, Tumulka R, Zanghì N. What does the free will theorem actually rove. Notices of the MS 010; 57(11): Gröblacher S, Paterek T, Kaltenbaek R, rukner Č, Żukowski M, selmeyer M, Zeilinger. n exerimental test of non-local realism. Nature 007; 446(7138): Hameroff SR. new theory of the origin of cancer: quantum coherent entanglement, centrioles, mitosis, and differentiation. iosystems 004;77(1-3): Hameroff S, Penrose R. Consciousness in the universe: review of the ch OR theory. Physics of Life Reviews 014; 11(1): Josehson D, Pallikari-Viras F. iological utilization of quantum nonlocality. Foundations of Physics 1991; 1(): Lambert N, Chen YN, Cheng YC, Li CM, Chen GY, Nori F. Quantum biology. Nature Physics 013; 9(1): Leggett J. Nonlocal hidden-variable theories and quantum mechanics: n incomatibility theorem. Foundations of Physics 003; 33(10): Genovese M. Research on hidden variable theories: review of recent rogresses. Physics Reorts 005; 413(6): McFadden J, l-khalili J. quantum mechanical model of adative mutation. iosystems 1999; 50(3): Merali Z. Quantum mechanics braces for the ultimate test. Science 011; 331: Merali Z. Solving iology's Mysteries Using Quantum Mechanics. Discover 014; December 9, ( htt://discovermagazine.com/014/dec/17-thisquantum-life ) Ou ZY, Mandel L. Violation of ell's inequality and classical robability in a two-hoton correlation exeriment. Physical Review Letters 1988; 61(1): Paterek T, Fedrizzi, Gröblacher S, Jennewein T, Żukowski M, selmeyer M, Zeilinger. Exerimental test of nonlocal realistic theories without the rotational symmetry assumtion. Physical Review Letters 007; 99(1): Schrödinger E. Indeterminism and free will. Nature 1936; 138: Shih YH, lley CO. New tye of Einstein-Podolsky-Rosen- ohm exeriment using airs of light quanta roduced by otical arametric down conversion. Physical Review Letters 1988; 61(6):91-4. Sta HP. Mind, matter, and quantum mechanics. Foundations of Physics 198; 1(4): Tittel W, rendel J, Zbinden H, Gisin N. Violation of ell inequalities by hotons more than 10 km aart. Physical Review Letters 1998; 81(17): Vedral V. Quantifying entanglement in macroscoic systems. Natur. 008; 453(7198): Weihs G, Jennewein T, Simon C, Weinfurter H, Zeilinger. Violation of ell's inequality under strict Einstein locality conditions. Physical Review Letters 1998; 81(3):