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New York, N.Y., March 11, 2019


Figure 1. Albert Einstein

A Tribute To Albert Einstein:
R. M. Santilli's 1998 Confirmation of A. Einstein's 1935 Prediction that Quantum Mechanics is not a "Complete" Theory

A PubRelco Interview of Sir Ruggero Maria Santilli. with Scientific and Industrial implications.

Q 1. Prof. Santilli, we have been told that you spent four decades of your research life to honor and verify Einstein's 1935 historical prediction of the lack of completeness of quantum mechanics against continued worldwide opposition. Is this correct?

A. Yes, it is true that I dedicated four decades of studies to honor Albert Einstein not only for his colossal discoveries everybody knows but also because he was a true scientist since he expressed doubts on the final character of the theories of his time which is a sign of rare scientific greatness. Yes, it is true that, with due exceptions, the worldwide orthodox scientific community opposed Einstein's vision on the lack of final character of quantum mechanics. Therefore, my studies aiming at verification of the indicated Einstein's vision were opposed and obstructed in numerous ways, but this is part of the scientific process that has occurred and will continue to occur whenever dealing with fundamental advances.

Q 2. Prof. Santilli, can you please explain in a language accessible to the general audience Einstein's 1935 argument that quantum mechanics is not a final theory?

A. According to quantum mechanics, the position of particles cannot be identified with the same precision we can achieve in classical mechanics. Consequently, Einstein conjectured the possible existence of a generalization of quantum mechanics he called "completion," such to admit limiting values that would recover the classical determinism, namely, the capability to achieve exact measurements. He communicated this view to his post doctoral associates Boris Podolsky and Nathan Rosen at the Princeton Institute for Advanced Study, and all three together (indicated as "EPR" from the initials of their last names) published in the May 13th issue of the Physical Review of the American Physical Society a paper entitled Can Quantum Mechanical Description of Physical reality be Considered Complete? This historical paper became known as the EPR Argument.

Q 3. Was Einstein courageous to express such a revolutionary view?

A. Yes indeed. To fully understand his courage, let me recall that in 1935, Nazi Germany was considered the dominant political and military power since the U.S.A., at that time, were considered to be a mere agricultural country. Einstein had emigrated to the U.S.A. only two years earlier (in 1932), and his theories were still very controversial (we are far from the 1945 verification of Einstein's celebrated equation E - mc2 by the atomic bomb).

Q 4. Do you have other historical comments on that time?

A. In 1935, the perception of a Nazi dominance was not only related to political and military dominance but also included a scientific dominance following the Gestapo takeover of academia. Additionally, we have to remember that the primary originators of quantum mechanics, such as Planck, Schroedinger, and Heisenberg, were German scientists. These aspects are important to appraise Einstein's courage in expressing his view on the incompleteness of the German science dominating at that time. Einstein's courage and clear dedication to the pursuit of "new" scientific knowledge were a great motivation for me to prove that he was correct with his EPR argument.


Figure 2. Niels Bohr

Q 5. Can you please outline the academic rejections of the EPR argument?

A. The rejections of the EPR argument were initiated by the Danish physicist Niels Bohr with an article published in the October 15, 1935, issue of the Physical Review, Rejection of the EPR argument. This article was followed by a large number of articles and monographs easily identifiable in an internet search that, to my knowledge, generally agree with Bohr's 1935 rejection. Most notable are mathematical theorems within the context of the field called local realism, such as the theorems by J. S. Bell, J. von Neumann and others essentially claiming to confirm Bohr's rejection of Einstein's view.

Q 6. Can you express your view on all these rejections?

A. As far as I am concerned, I never accepted Bohr's paper for scholar for various reasons, such as: 1) Bohr's objections were published in a rush only five months following the appearance of the EPR argument, thus without sufficient time for in-depth criticisms; 2) There are credible rumors that Bohr's wrote the article following pressure from German scientists who originated quantum mechanics; 3) Bohr's article is essentially motivated by the widespread political/non-scientific view that quantum mechanics can represent the entirety of the universe, expectedly, until the end of time; 4) Bohr's paper cannot be considered scientifically impeccable because he does not identify the mathematical and physical conditions under which his own view was correct; 5) The last criticism applies to all subsequent works in the field and applies in particular to the mathematical theorems by Bell, von Neumann, and others.


Figure 3. An illustration of the main quantum mechanical criticism of the EPR argument, the impossibility of determining with absolute accuracy the distance "d" between two protons due to Heisenberg's uncertainty principle.

Q 7. What is your view on the main point of this historical controversy?

A. To my knowledge, Einstein never claimed that quantum mechanics is wrong, thus implicitly accepting its validity under given conditions. Einstein's main point was the lack of completion of quantum mechanics, namely, quantum mechanics is not the final theory of the universe due to the possible existence of a generalization "completion" (in Einstein's words) of quantum mechanics into a theory recovering classical determinism under limit conditions. I never accepted Bohr's argument or any of the large number of his followers because their denial of a possible generalization of quantum mechanics is political/non-scientific in my view.

Q 8. What is your view of Niels Bohr?

A. I believe that Bohr initiated a true scientific obscurantism which is still in full action today because the entirety of the universe, from its most minute structure to its biggest cosmological dimensions continue to be treated to this day via quantum mechanics without any consideration of its limitations, let alone the dismissal without counter-measurements of various experiments disproving its universal validity throughout the universe.

Q 9. Do you think that Niels Bohr was an antisemitic Nazi sympathizer?

A. Definitely not. Danish people are known to have opposed Nazism in any possible way and Bohr is on record to have helped various Jewish physicists to leave Germany and emigrate to the U.S.A. However, I believe that his scientific mind had been controlled by German scientists of the time because serious science is always expressed in cautious terms and every theory is known to have limitations.

Q 10. In your view, what are conditions under which criticisms of the EPR arguments are valid?

A. Bohr and all his followers tacitly assumed at the basis of their objections the most fundamental assumption of quantum mechanics namely, the approximation of particles as massive points according to Newton's original conception four centuries ago. In fact, such a silent assumption is inherent in the main equations of quantum mechanics that are notoriously based on Newton's differential calculus, namely, a calculus that can only be defined at isolated points. My inability to accept Bohr's views stems from the fact that, in the physical reality, particles are not points since they are extended, therefore deformable and hyperdense. Consequently, there are conditions (known as exterior dynamical conditions) under which particles can be approximated as massive points moving in vacuum resulting in the full validity of quantum mechanics (and Bohr's views), as it is the case for atomic structures, particles in accelerators, crystals and numerous other cases. However, there are conditions (known as interior dynamical problems) under which the approximation of particles as massive points is no longer effective, as it is the case for the structure of particles, nuclei, and stars. In fact, Enrico Fermi and numerous other distinguished scholars, expressed doubts (known to Niels Bohr) as to whether the geometry, let alone the physics of quantum mechanics is applicable to the structure of the microcosm.


Figure 4. A view in the leftof the conception of a nucleus according to quantum mechanics essentially consisting of a sphere with points in its interior, and a view at the right of the conception of the same nucleus according to Einstein's completion of quantum mechanics consisting of protons and neutrons in conditions of partial mutual penetration as established by nuclear experimental data.

Q 11. Do you have an example understandable by the general audience?

A. When two protons, as in Figure 3, are the two nuclei of the hydrogen molecule, they are in vacuum at large mutual distance, in which case said protons can indeed be effectively approximated as point particles resulting in the exact validity of quantum mechanics as well as of Bohr's view. In particular, we will never be able to achieve a measurement of their mutual distance with the precision achievable in classical mechanics. However, when the same two protons are members of a nucleus, their approximation as massive points are no longer effective as established by the fact that quantum mechanics has been unable to achieve an exact representation of nuclear data in about one century of efforts. Finally, the claim of the exact validity of quantum mechanics becomes blatantly political/non-scientific when the same two protons are in the core of a star due to the dramatic differences between the exterior conditions of the original conception and experimental verification of quantum mechanics, essentially those for massive points in vacuum, and the interior conditions here considered for two extended and hyperdense protons under extreme pressures. According to Einstein vision, it is possible that, at a limit of extreme pressures, the mutual distance between the indicated two protons in the core of a star can be identified with the same precision achievable in classical mechanics.


Figure 5. A view of Harvard's University Science Center where Prof. Santilli initiated his studies of the EPR argument.

Ruggero Maria Santilli
Ruggero Maria Santilli

Q 12. How did you get involved in studies verifying the EPR argument?

A. In 1978, I was at Harvard University under support from the Department of Energy and was asked to search for basically new energies and fuels. Therefore, I decided to study the fundamental synthesis in nature, that of the neutron from the hydrogen atom occurring in the core of stars. I immediately discovered that quantum mechanics is completely inapplicable (and not violated) for such a problem because quantum mechanics has been conceived and tested for the fusion of two particles or nuclei into a third with a mass defect which is converted to energy, according to Einstein's equation E = mc2. By contrast, the mass of the neutron is bigger than the sum of the masses of the electron and the proton, thus causing the inapplicability for the neutron synthesis of the basic axioms of quantum mechanics. Independently from these technical aspects, quantum mechanics was completely inapplicable because you cannot fuse two points, the point electron, and the point proton, into a third point, the point neutron. Only a theory representing the dimension and density of the particles had some chances of success. Such a theory did not exist and had to be constructed. This scenario was sufficient to identify rather clearly in 1978 the need for a "completion" of quantum mechanics into a broader theory representing the actual size and density of particle and such a completion could only be along the EPR argument.

    
Figure 6. Stars (left view) initiate their life as an aggregate of hydrogen. When their dimension and internal pressures reaches certain values, the proton and the electron of the hydrogen are "compressed" into a new particle conceived in 1910 by Ernest Rutherford and called the neutron. The&nbsview in the right illustrates Rutherford's compression which has been solely described by a completion of quantum mechanics according to the EPR argument.

Q 13. Can you please outline subsequent developments?

A. It took decades for the construction, first, of the new mathematics due to the need for the completion of Newton's differential calculus from its definition at points to a definition in volumes. This was achieved in the 1996 paper  Isotopies of 20th century mathematics resulting in a new mathematics known as hadronic mathematics (Amidst a large bibliography, I should mention the six volumes of Foundations of the IsoDifferential Calculus, by the mathematician S. Georgiev published by Nova Scientific Publisher). Then it took additional time for the construction of the consequential completion of quantum mechanics into a covering theory today known as hadronic mechanics and the completion of quantum chemistry into a discipline known as hadronic chemistry. Then it took a decade for the verification of the new mathematical and physical theories in various fields (see the 2016 Review of Hadronic Mechanics). Only following all that was I in a position to verify that EPR completion of quantum mechanics permitted the quantitative representation of the totality of the characteristics of the neutron in its synthesis from the hydrogen atom at the non-relativistic as well as relativistic levels (see the recent review of the neutron synthesis).

Q 14. Does your synthesis of the neutron confirm the EPR argument?.

A. The representation of the synthesis of the neutron confirms the existence of a completion of quantum mechanics we call hadronic mechanics. However, the full proof of the EPR argument requires the additional confirmation of the existence of limiting conditions under which particles recover the classical determinism. I achieved the latter proof in the 1998 paper
R. M. Santilli, "Isorepresentation of the Lie-isotopic SU(2) Algebra with Application to Nuclear Physics and Local Realism," Acta Applicandae Mathematicae Vol. 50, 177 (1998),
http://www.santilli-foundation.org/docs/Santilli-27.pdf

The first part of the proof deals with the verification that the theorems by Bell, von Neumann, and others are indeed valid under the undisclosed assumptions of dimensionless particles treated via Newton's differential calculus. The second part of the proof deals with the clarification that the indicated theorems, by no means, disprove Einstein's vision since particles are in fact extended in the physical reality. The third part of the proof deals with direct verification of the EPR argument, namely, the existence of limiting conditions under which extended particles treated via hadronic mathematics and the completion of Newton's differential calculus have identical classical counterparts.

Q 15. Did you advertise such a historical discovery?

A. No. I am a scientist, and as such, I do not advertise my work. I merely published papers available to all colleagues with the word "completion" in the title, such as the paper published by Found. Phys. Vol. 27, pages 625-729 (1997) entitled Relativistic hadronic mechanics: nonunitary, axiom-preserving completion of relativistic quantum mechanics.


Figure 7. As recalled in Figure 6, the first synthesis in nature is that of the neutron in the core of stars from one electron and one proton. Such a synthesis predicted the existence, subsequently verified, of the compression of two electron within the proton, resulting in a negatively charged particle depicted in this figure which is known as pseudoproton.

Q 16. Can you provide an example illustrating the recovering of classical determinism?

A. Recall that we can identify the center of mass of a star or of a black hole with classical accuracy. When the two protons of Figure 3 are in their interior, their mutual distance, as well as their distance from said center of mass, is predicted to be identifiable with classical accuracy. Another example is given by the recently confirmed, negatively charged pseudoproton given by the compression of two electrons inside the neutron (Figure 7). In this case the two electrons are constrained to rotate with opposite spins within the hyperdense neutron, thus having a fixed mutual distance with classical determinism and the same holds for the distance of the electron pair from the neutron center due to very strong constraints that simply do not exist for point particles in vacuum.


Figure 8. A view of the "Directional Neutron Source" being produced and sold by the U. S. publicly traded company Thunder Energies Corporation to scan suitcases for possible concealed nuclear materials.

Q 17. Does Einstein's vision have any new industrial applications?

A. Yes, indeed. The surpassing of quantum mechanics according to the EPR argument permits the conception, treatment and industrial development of a virtually unlimited number of new technologies. As an illustration, among several possibilities, I initiated experimental verification of the laboratory synthesis of the neutron from the hydrogen gas in early 2000. These experiments were then confirmed by numerous additional verifications, such as that of the experimental collaboration that are, de facto, experimental confirmations of Einstein's vision on the lack of final character of quantum mechanics. Recall that the neutron is one of the most important particles in nature. Hence, the capability of synthesizing a flux of neutron on demand has clear industrial relevance. Consequently thanks to the collaboration by my wife Carla Gandiglio Santilli, we did set up in early 2014 the publicly traded company Thunder Energies Corporation which is in production and sale of an equipment synthesizing neutrons on demand from a hydrogen gas called " Directional Neutron Source with a number of applications, such as the detection of nuclear material that may be concealed in baggages, the detection of precious metals in mining operations, and other uses.

    

Figure 9. An illustration in the tkeftof the primary reason that has prevented the achievement of the controlled fusion. namely, the Coulomb repulsion between two nuclei which reaches astronomical values at the needed mutual distance. 
A view in the right of the new conception of nuclear fusion under study at Thunder Energies Corporation which is based on the synthesis of negatively charged nuclei which, as such, turns Coulomb repulsions into Coulomb attractions.

Q 18. Are you studying other new technologies dependent on the EPR argument?

A. Yes. A primary reason we have been unable to achieve a controlled nuclear fusion in seventy-five years of efforts and billions of dollars of taxpayer money is that nuclei are positively charged. Consequently, nuclei experience the Coulomb repulsion which, at the distance needed for the fusion reaches astronomical values because it is proportional to the inverse square of the distance (Figure 9). At Thunder Energies Corporation we have learned how to synthesize the neutron and the negatively charged pseudoproton. We are now studying the synthesis of negatively charged nuclei that would turn the above repulsion into a very strong Coulomb attraction between nuclei, thus implying a basically new conception of controlled nuclear fusion that cannot be formulated via quantum mechanics, let alone industrially developed, while being fully treatable via the EPR completion of quantum mechanics. (see also the preceding PubRelCo Interview Jan. 2, 2019 (.

Q 19. What are your concluding remarks?

A. I believe that Einstein's vision on the lack of final character of quantum mechanics is, by far, the most important legacy by Albert Einstein because it implies a true scientific renaissance encompassing all quantitative sciences, with advances simply beyond our imagination at this writing (see the monograph New Sciences for a New Era). Therefore, I hope that colleagues will join our team in honoring Einstein's legacy of such historical proportion.

Q 20. Can you please quote other scientists who participated in the 'completion' of quantum mechanics according to the EPR argument?

A. The literature in the EPR argument is truly vast and, in my view, it should be divided into the following two classes:

Epistemological Studies. The best references I can provide in this class are the following monographs, among many others, each with a vast literature:
Sir Karl R. Popper, Quantum Theory and the Schism in Physics, Routledge, London (1982);
Prof. Jeremy Dunning Davies, Exploding a Myth, Horwood, England (2007);
Prof. Lee Smolin, Einstein's Unfinished Revolution, the Search for What Lies Beyond the Quantum, Penguin Press New York (2019),

Technical Treatments. I hope to have indicated in this interview that quantitative studies on the confirmation of the EPR argument require the necessary 'completion' of the mathematics used by Bohr, Bell, von Neumann and others, with particular reference to a 'completion' of Lie's algebras at large and that of the SU(2)-spin. The studies in these 'completions' that eventually permitted my 1998 proof of the EPR argument (see Q14) are truly numerous. AI provided a general, bibliography up to 2008 in page 121 to page 162 of Volume I of my series of five volumes Hadronic Mathematics, Mechanics and Chemistry. I provided a bibliographic update in my 2016 memoir An introduction to the new sciences for a new era. I apologize to authors of additional studies in support of the EPR argument because too numerous to be quoted in this interview.

Q21. The famous British philosopher of science Sir Karl Popper states in page 14 of the monograph you quote: ...... in his approach Santilli distinguishes the region of the "arena of incontrovertible applicability" of quantum mechanics (he calls it "atomic mechanics") from nuclear mechanics and hadronics, and his most fascinating argiument in support of the view that quantum mechanics should not, without new tests, be regarded as valid in nuclear and hadronic mechanics, seems to me to augur a return to sanity: to that realism and objectivism for which Einstein stood and which had been abandoned by those two very great physicists, Heisenberg and Bohr. Do you have any comment?

A. I remember that Sir Karl Popper contacted me in 1981 when I was at Harvard University and had initiated my studies on the verification of the EPR argument. The central point which he greatly supported was the need to verify experimentally the validity or invalidity of quantum mechanics within the hyperdense media inside hadrons, such as the validity of Pauli's exclusion principle under external strong interactions which I indicated beginning with the title of my 1978 Harvard paper. Such an experimental verification is the evident serious basis for the validity or invalidity or the EPR argument. It is unfortunate for America and mankind that, some thirty eight years later, the conduction of the much needed basic experiments in the interior of hadrons has been systematically opposed by academia and the available experimental evidence on the inapplicability of quantum mechanics inside hadrons continues to be dismissed and discredited with serious environmental consequences I hope to indicate in a future interview.

Q22. Could you please provide a reference on the experimental evidence of the inapplicability of quantum mechanics inside hadrons which is so crucial for the validity of the EPR argument?

A. A summary with original literature is available in my 2016 memoir An introduction to the new sciences for a new era



     

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COMMENTS

Post 1
Dear editors, could you please contact Prof. Santilli and ask him what is the strongest evidence supporting Einstein's vision that quantum mechanics is 'incomplete'? Thanks. Cwe6io

Post 2
Dear Cwe6io, thanks for your interest and important question. I never accepted the completeness of quantum mechanics since the time of my graduate studies in physics in the 1960s at the University of Torino, Italy. In the course of time,, I have provided three proofs of increasing complexities of Einstein's vision on the lack of completeness of quantum mechanics. Here is a non-technical outline with technical references.

1) 1967 PROOF OF THE EPR ARGUMENT
FOR IRREVERSIBLE SYSTEMS OF EXTENDED PARTICLES

Inspired by Einstein, I cannot accept quantum mechanics as a final theory because said mechanics was conceived and verified for isolated systems of point p[articles in vacuum, such as the atomic structure, thus being strictly reversible over time,. This is also established by the invariance under anti-Hermiticity (time reversal) of the brackets of the time evolution, the Lie product [A, B] = AB - BA = - [A, B] between two Hermitean operators A, B. Consequently, quantum mechanics is completely unable to provide a consistent representation of the irreversibility over time of high energy scattering processes, nuclear fusions and all energy releasing processes in dramatic disagreement with thermodynamics. Therefore, during my graduate studies I initiated the search for a completion of quantum mechanics into a form incorporating irreversibility. After learning that the ultimate structure of quantum mechanics is given by Lie algebras I spent the entire 1965 year at various European mathematical libraries to locate a covering of Lie algebras and finally did locate Albert's notion of Lie-admissible algebras (i. e., , algebras with product (A, B) such that the attached anti-symmetric product (A, B) - (B, A) = [A, B]* is Lie). I published in 1967 my Ph. D. Thesis on the embedding/completion of Le algebras into their Lie-admissible covering with product (A, B) = pAB - qBA;. In subsequent works of 1967-1968, I introduced the time evolution

idA/dt = (A, H) = pABH- qHA,       (1)

(where p and q are non-null scalars) which is irreversible whenever p ≠ q due to the breaking of the anti-Hermiticity of the product (A, B) ≠ -(A, B). When I joined Harvard University in the late 1970s under DOE support, I proposed the construction of a completion of quantum mechanics into hadronic mechanics with basic Lie-admissible algebras (A, B)* = ARB - BSA where R(t, ...) and S(-t, ...) are non-singular Hermitean operators representing the extended character of hadrons in forward and backward motion, respectively, and proposed the completion of quantum mechanics into hadronic mechanics for irreversible systems with basic dynamical equations given by the Lie-admissible generalization of Heisenberg's equations

idA/dt = (A, H)*= ARH - HSA,       (2)

which are clearly irreversible for R ≠ S. Eqs. (2) were introduced for the first time in my 1978 Harvard's paper, see Eqs. (4.15.34b), page 746, and then treated in details in the monographs with Springer-Verlag, see Volume II, 1981, Foundations of Theoretical Mechanics, page 163. The latest presentation at Nuovo Cimento irreversible Lie-admissible dynamics includes the proof of the universality of law (2) for all possible irreversible processes and the proof that the classical image of Eqs.. (2) is given by the Historical Lagrange's and Hamilton's equations, not the truncated form used for quantum mechanics, but the original forms with external terms representing irreversibility. Experimental verifications and industrial applications of Lie-admissible law (2) for nuclear fusions and other energy releasing processes are available in Section 3 of f the 2016 general reviews.

The point important for Cwe6io's question is that Bell's inequality, von Neumann theorem and related works cannot be consistently defined under irreversibility due to the loss of 'all' Lie algebras, let alone that of the quantum time evolution and off the SU(2) spin algebra, thus establishing the validity of Einstein's vision on the lack of completeness of quantum mechanics beyond credible doubts.

2) 1998 PROOF OF THE EPR ARGUMENT
FOR REVERSIBLE SYSTEMS OF EXTENDED PARTICLES

I never accepted the quantum mechanical description of nuclear structures as ideal spheres containing point-like nucleons because of excessive - at time embarrassing - differences between the predictions of the theory and nuclear experimental data beginning with the simplest nucleus, the deuteron. Therefore, in the same originating paper of 1978, I proposed the particular case of Lie-admissible algebras known as Lie-isotopic (or Lie-Santilli)algebras occurring for R = S = T = T > 0 representing volumes and densities of hadrons, and Lie-isotopic brackets [A, B]* = ATB - BTA (see the latest paper on Lie-Santilli isotheory and references quoted therein). I then proposed the simpler branch of hadronic mechanics with Lie-isotopic generalization of Heisenberg dynamical equations

idA/dt = [A, H]* = ATH - HTA ,       (3)

which verify the ten conventional total conservation laws. Eqs. (3) were first introduced in my 1978 Harvard's paper, see Eqs. (4.15.49), page 752, and treated in details in the two monographs, see Volume II, 1981, Foundations of Theoretical Mechanics, page 153. The first known exact representation of nuclear magnetic moments and spins, additional experimental verifications and industrial applications of hadronic mechanics with dynamical equations (3) - when applicable - are available in Section 2 of f the 2016 general reviews. My 1998 proof of the EPR argument came out as a natural consequence of the Lie-isotopic generalization of Lie's theory in general, and of Pauli's matrices in particular, for extended, deformable and hyperdense nucleons in conditions of partial mutual penetration with consequential under linear and non-linear, local and non-local and potential as well as non-potential interactions fully treatable by hadronic mechanics but beyound any dream of treatment via quantum mechanics .

3) 1998 PROOF OF THE EPR ARGUMENT
VIA HIDDEN VARIABLES

Another aspect of 20th century sciences I could not accept is the widespread belief that "quantum mechanics does not admit hidden variables λ," because such a belief tacitly assumes or implies our achievement of terminal mathematical knowledge. In reality, mathematics is still at its infancy and so many new mathematics remain to be discovered. In fact, the central idea of all my studies is the generalization of the conventional associative product AB into the axiom-preserving isoproduct

A*B = ATB,         (4)

which implies a generalization of all mathematics I learned at the graduate school since it must be applied to all possible products, including the product of numbers, functions, matrices, operators, etc. .Then, in my view, the ensuing new mathematics provides an explicit and concrete realization of hidden variables via the simple realization

T = Diag. (λ, 1/λ),   Det T = 1.     (5)

My 1998 proof of the EPR argument via hidden variables then follows from realization (5), of course, under a technical knowledge of the Lie-Santilli-isotheory in general and the isotopies of Pauli's matrices in particular.

The point here important is that hidden variables are indeed prohibited by the Copenhagen realization of the basic axioms of quantum mechanics, that with the simple associative product Ab. By contrast, hidden variables are fully admitted by the basic axioms of quantum mechanics under the more general realization of the product A*B = ATB, thus explaining their true 'hidden'' character, to such an extent that quantum and hadronic mechanics coincide at the abstract, realization-free level by conception and construction.. Ruggero Maria Santilli (email: research@thunder-energies.com)

Post 3
I would like study Prof. Santilli's Lie-isotopic formulations prior to studying the more complex Lie-admissible covering. Can anybody explain to a non-expert the main assumptions used by Prof. Santilli in his 1998 proof of the EPR argument http://www.santilli-foundation.org/docs/Santilli-27.pdf? Thank you. Csd37ty

Post 4
Csd37ty//Post 3, here are Santilli's basic assumptions you requested, mostly in his own words,:
    4.1. . Hadrons must be represented as they are in nature, that is, extended, deformable and hyperdense.
    4.2. Extended hadrons are in conditions of mutual penetration as occurring, for instance, in nuclei. This second condition is necessary because extended and isolated hadrons in vacuum can one well approximated as being point-like, thus verifying quantum mechanics and related uncertainties..
    4..3. Under conditions 4.1. and 242, we have the non-linear, non-local and non-potential interactions playing a crucial role in Santilli's proof of the RPR argument, as you can verify. It should be recalled from Santilli's analysis that the latter non-Hamiltonian interactions cannot exist without the mutual penetration of hyperdense charge distributions.
    The rest of the http://www.santilli-foundation.org/docs/Santilli-27.pdf can be derived from the above three basic assumptions via compatibility arguments. For instance, the conditions of non-hamiltonian character combined with the condition of time reversal invariance, restrict all possibilities to Santilli's Lie-isotopic formulations with dynamical equations (3), and the same holds for other aspects. Xwe40io

Post 5
Can anybody indicate how Prof. Santilli represented assumptions 4.1, 4.2, and 4.3 in a form as elementary as possible? Csd37ty

Post 6
Csd37ty/Post 5 if you believe that structurally new assumptions 4.1, 4.2 and 4.3 Can be represented with 20th century mathematics, I suggest you should jump in a lake to cool down. The mathematics represents said assumptions did not exist and Santilli had to build his new isomathematics to achieve the needed representation. If you want to be a "researcher," you got to sit down and study it. Xwe40io

Post 7.
Xwe40io/Post 6, I understand and agree but could you please indicate the foundations of Santilli's new isomathematics used in the proof of the EPR argument? Csd37ty

Post 8.
Hi Csd37ty/Post 7,, that's it to my knowledge. After joining the Department of Mathematics of Harvard University under DOE support, Santilli had a true stroke of genius because in one single mathematical assumption, he represented all conditions 4.1, 4.2,, and 4.3 . In fact, Santilli introduced the generalization of the product AB between "all" possible quantities A, B (numbers, functions, matrices, operators, etc.) into form (4) (see page 160, Vol. II of Santilli's Foundations of Theoretical Mechanics) and preceding literature) where the quantity T , called the isotopic element, is solely restricted to be positive definite, but otherwise having an arbitrary dependence on the characteristics of the hyperdense medium considered, such as time t, coordinates r, momenta p, wavefunctions ψ, pressure τ, temperature ξ, etc.). The axiomatically important aspect s that the new product A*B (I am here copying Santilli's words) is "isotopic" in the Greek sense of remaining associative A*(B*C) = (A*B)*C.

To see the huge implications, you have to understand that extremely simple assumption (4) implies the generalization of the totality of the 20th century applied mathematics and of related physical and chemical formulations, all generalizations indicated in the above monograph being Einstein's 'completions.'.

Santilli then introduced the following realization of the isotopic element

T = Σk-=1,..,,m Diag. (1/n12, 1/n22, 1/n32, 1/n42,) e   (6a)

n = n (t, r, p, ψ, τ, ξ, ...) > 0,   Γ = Γ(t, r, p, ψ, τ, ξ, ...) > 0, (6b)

where n12, n22, n32 are the semiaxes of the hadron assumed as ellipsoids and n42 represents the density of the hadron considered, all n's being normalized to the value n = 1 in vacuum. As everybody can see, realization (6) represents indeed all conditions 4.1,4.2, and 4.3, the later conditions (non-Hamiltonian interactions) being represented by the exponential function. Realization (6) also represents for the first time nuclei as a collection org extended and hyperdense nucleons in conditions of partial mutual penetration (see the r.h.s. of Figure 4).

In 1993, Santilli recognized that, for consistency, isomathematics had to be formulated over new numbers, today known as santilli isonumbers n' = nU with isoproduct (4) and arbitrary unit U, called Santilli isounit,

U(t, r, p, ψ, τ, ξ, ...) = 1/T > 0 ,     (7)

first introduced in the paper isonumbers. The isouni verifies indeed the axiom of a multiplicative unit, U*n' = n'*U = n'. Once isomathematics is formulated over isofields, then all scalar quantities must have the structure of an isonumber, e.g., the isocoordinates must have for consistency the form r; = rU. Among a number of independent studies and applications of Santilli isonumbers, one may consult the monograph by the Chinese mathematician Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory,.

In 1996, santilli realized that a representation of extended, deformable and hyperdense hadrons via realization of type (5) elaborated via Newton's differential calculus is grossly inconsistent because the former is solely defined on volumes, while the latter is solely defined on points. Therefore, he had the courage of generalizing Newton's differential calculus into a form called Santilli isodifferential calculus with basic isodifferential< and isoderivative/p>

d'r' = T d (rU) = dr + rTdU,      (8a)

∂' f'(r')/∂'r' = U∂ f'(r')/∂ r'      (8b)

first introduced in the mathematical memoir isodifferential calculus, that has extended, for the first time in history, Newton's differential calculus defined for isolated points into a new differential calculus defined on volumes represented by the isotopic element T or the isounit . Among a number of independent studies on Santilli isodifferential calculus, one may consult the six volumes written by the French mathematician S. Georgiev, Foundations of the IsoDifferential Calculus, Volumes, I, II, III, IV,V, and VI Nova Scientific Publisher (2015 on).

In his 1081 Volume II of Foundations of Theoretical Mechanics Santilli introduced a step by step isotopic 'completion' of the various branches of Lie's theory, today known as the Lie-Santilli isotheory, with basic isocommutator rules

[XI , xj]* = Xi T Xj - XJ T Xi = Cijk Xk       (9)

Santilli then conduscted systematic studies on the development and application of the above theory, see the 1995 monographs Elements of Hadronic Mechanics. Among a large number of independent studies, one may consult the monograph by the 1993 Greek mathematicians D. S. Sourlas and G. T. Tsagas Mathematical Foundation of the Lie-Santilli Theory.

The latter theory was then used by Santilli in 1998 for the lifting of the SU(2) spin (which is necessary to define the spin of an extended, deformable and hyperdense particle under non-Hamiltonian interactions) and consequently proved the EPR argument.

Isomathematics is today refereed to a mathematics based on isoproduct (4), defined on an isofield with isounit (6) and elaborated with the isodifferential calculus, thus including a compatible isotopic generalization of functions, metric spaces, geometries, topologies, etc. (see the quoted paper for vast contribution by mathematicians I cannot possibly quote here).

Finally, sd37ty/Post 7 allow me to warn you against the posture assumed by some that "Santilli mathematics is too complicated." This is a non-scientific and self-disqualifying posture because the (regular branch of) isomathematics can be constructed via non-unitary transforms

W(AB)W = A' T B',       (10a)

WW ≠ I,   A' = WAW,   B' = WBW,   T =(W W)-1   (10b)

and the same holds for numbers, functions, Lie theory, etc. Xwe40io

Post 9
Dear Xwe40io/Post 8, could you please indicate how Prof. Santilli escaped the uncertainty principle as a necessary condition to prove the EPR argument? Thanks. Csd37ty

Post 10
Dear Csd37ty/Post 9, to answer your question you have to accept the idea of extended and hyperdense protons and neutrons in conditions of partial mutual penetration as occurring in a nuclear structure, (Figure 4 of Prof. Santilli's interview) you have to understand the emergence of nonHamiltonian forces, you have to understand the mathematics for their representation and, above all, admit that the assumption of the exact validity of Heisenberg's uncertainty in the interior of a nucleus is non-scientific The serious physics states: We do not know. After you see all the above, you have to study hadronic mechanics. Here is the gist to my knowledge. From Santilli isodifferential calculus, Eqs. (8), the hadronic isomomentum is uniquely defined by

p' * ψ'(t', r') = - i ∂' ψ'(t', r') = - i U ∂ ψ'(t', r')      (11)

It is then easy to see that isolinear momenta isocommute on isospace over isofields by therefore confirming the principle of isotopies

[p'i, p'j]' = p'i * p'j - p'j * p'i = 0       (12)

This occurs because the isotopic element T of the isoproduct "*" , Eq. (1) cancels out with its inverse, the isounit U =1/T. However, isomomenta no longer commute in our spacetime,

[p'i, p'j] = p'i p'j - p'j p'i ≠ 0       (13)

because, in the absence of the isotopic product, the derivative does act non-trivially on the isounit U due to its general dependence on local coordinates, and his eliminates Heisenberg's uncertainty principle for the study of interior problems and actually replace it with a much more general principle. Cheers PS. People who thinks that this violates experimental evidence state so out of ignorance, Prof. santilli has proved that the above generalization solely holds locally in the interior of nuclei, while recovering the conventional uncertainty for their center of mass.. In fact, when isolated, nuclei represented with isotopic element (5) verify all ten total conservation laws 9see the Lorentz-Poincare'-Santilli isosymmetry in the references of Post 2).

The above expressions illustrate the crucial importance of Santilli's isodifferential calculus (8) because, in its absence, there was no possibility of achieving a consistent definition of linear momentum in hadronic mechanics. In fact, as stated various times by Prof. Santilli: Prior to the discovery of the isodifferential calculus in 1996, we had no means of confronting hadronic mechanics with experimental data because we did not know how to define its angular momentum, its basic commutation rules, etc.Xwe40io

Post 11
Dear Xwe40io/post 10 , thanks for your great help. Hoping not to abuse your time, I have one final point to understand before studying Prof. Santilli';s 1998 proof of the EPR argument. My question is related to the general belief that quantum mechanics does not admit "hidden variables" which belief was then used as an alternative objection against the EPR argument. What is Prof. Santilli's proof that "hidden variables" do exist? Thanks again, Csd37ty

Post 12
Dear Csd37ty/Post 11, thanks for another important question deserving attention. The answer is so simple to appear trivial. Prof. Santilli proved that all basic axions of quantum mechanics admit "hidden variables" in the very notion of product. Hence, his first , and most fundamental assumption of the isoproduct Eq. (1) is an explicit and concrete realization of "hidden variables" realized via the isotopic element T in the isoproduct (4). To see it, recall that T = 1 for the conventional realization of quantum mechanics, that used by Bohr. Hence, in his 1998 paper Prof. santilli assumes Det T = 1 with concrete and explicit realization (5) of hidden variables . The third d proof of the EPR argument, that based on "hidden variables," then becomes elementary, see the 1998 paper http://www.santilli-foundation.org/docs/Santilli-27.pdf Good luck . Xwe40io

Post 13
I Nominated Prof. Ruggero M. Santilli for the 2019 Nobel Prize in Physics for his 1998 historical paper on the proof of the EPR argument: R. M. Santilli, "Isorepresentation of the Lie-isotopic SU(2) Algebra with Application to Nuclear Physics and Local Realism," Acta Applicandae Mathematicae Vol. 50, 177 (1998), http://www.santilli-foundation.org/docs/Santilli-27.pdf. Department of Physics, University of ......., Tdf55yy

Post 14
In the e: Russian Physics Journal, Vol. 61, No. 3, July, 2018 (Russian Original No. 3, March, 2018) Quantum field approach in classical physics and geometrodynamics, V. Lasukov has shown the following: A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multi-particle process of creation of a pair of scalar particles by a non-stationary potential barrier is contained in the solutions of Newton's one-particle equation. The corresponding solution does not depend on Planck's constant. It is shown that for any spatial quantum problem there exists a temporal classical analog. The obtained results can be used in quantum geometrodynamics. Qet450uo

Post 15,
My electron theory from 1983 up to 2000 deals with Einstein's GR theory completed by the principle of Thermodynamics. The surprising result and not expected at all is:
    1. the mass is not a point particle
      2. masse and charge both depend on the fine structure Constant
    3. The FSC is derived by this theory
    4. The second law reveals the nature of Quantum Gravity based on GR And explains dark matter as entropy increaser.
In one word: The hypothesis: the electron is a point particle is wrong. Pfdg38ty

Post 16
It seems to me that Santilli is one of few scientists who has attempted not to to build on Quantum Mechanics, but to accept Einstein's views, and to develop his own theories. Also, as a Dane I want to point out that I agree with Santilli that Niels Bohr was absolutely not a sympathizer of the Nazis although he worked with German physicists in the early thirties. Supposedly his mother was Jewish, and the story of his sudden and dramatic escape from Nazi-occupied Denmark to England in a small plane is not unknown. He was lying on the floor of the plane barely able to stretch out. I think of science as many building blocks that never end. Vsd33iup

Post 17
My dear Bdf58hj, you want to enter into the opaque politics at Harvard University? The records at the DOE indicate that the research contracts were administered by Harvard's MathematicsDepartment with the mathematician Prof. Shlomo Sternberg as Principal Investigator and Prof. RT. M. Santilli as co-investigator who had his office at the Department of Mathematics, Figure 5 of the PubRelCo Interview. This is the evidence. The additional evidence is that Prof. Santilli's mathematical discoveries at Harvard have been superior to those of his colleagues there since the latter worked on extremely advanced yet small mathematical details, while Prof. Santilli generalized all of mathematics, as you can see from Post 8. The rest is Harvard's opaque politics I prefer to be silent. Bdf58hj

Post 18
Einstein was right when he did not agree with the EPR experiment conclusions and had said, "spooky action at a distance"? cannot occur and that, "God does not play dice"?. See page 11: Linear Polarization http://vixra.org/pdf/1303.0174v5.pdf. Lwe11op

Post 19
Lwe11op/Post 18, Thank you, thank you for those refreshing memories that, unfortunately are maliciously forgotten by the establishment! cdf47uo

Post 19
I now understand from Santilli's Post 2 the reason that tsuggered the Estonia Academy of Sciences to list Santilli among the most illustrious applied mathematicians of all times with the quotation precisely of his Ph. D. Thesis on Lie-admissible formulations. all this occurring in 1990 under USSR domination and without any previous contact with Santilli (see Figure 10 below). The listing is self-qualifying for so many who have opposed for decades Santilli's research to honor Einstein. Bsd34o




Figure 10. Santilli 's 1990 Nomination by the Estonia Academy of Sciences among the most illustrious app>lied mathematicians of all times

Post 20
It is so important that your synthesis of the neutron confirms the EPR argument. Congratulations and good luck. I would like you to take into account that the main stream now is accepting the quantum non locality based mainly on the Alain Aspect experiment. Msd2yu

Post 21
The question raised by Msd2yu/Post 20, is important. Can anybody outline the main steps of the representation and experimental verification of the synthesis of the neutrons from the the hydrogen? Tnbaks. Bdf37si

Post 22
Hi Bdf37si/Post 21, here is what I could gather from referee3d papers. Following the construction of hadronic mechanics, and only following that, see the mionograohs
R. M. Santilli, Elements of Hadronic Mechanics, (1995), Academy of Sciences, Kiev,
Volume I: Mathematical Foundations. anf
Volume II: Theoretical Foundations,.,
the following refereed publications are on record:

1. The non-relativistic representation of the neutron synthesis was first achieved in the paper
. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron as a compressed hydrogen atom, Hadronic J.{\bf 13}, 513 (1990).
http://www.santilli-foundation.org/docs/Santilli-21.pdf.

2. The relativistic representation of the neutron synthesis was first achieved in the paper
. M. Santilli, "Recent theoretical and experimental evidence on the synthesis of the neutron," Communication of the JINR, Dubna, Russia, No. E4-93-252 (1993), published in the Chinese J. System Eng. and Electr. Vol. 6, 177 (1995)
http://www.santilli-foundation.org/docs/Santilli-18.pdf.

3. Following attempts initiated in the 1950 that failed because of lack of technical knowledge on the mechanism of the synthesis, the first experimental synthesis of the neutron in laboratory from a hydrogen gas was achieved in the paper
R. M. Santilli, "Apparent confirmation of Don Borghi's experiment on the laboratory synthesis of neutrons from protons and electrons, Hadronic J. {\bf 30}, 29 (2007)
http://www.i-b-r.org/NeutronSynthesis.pdf.

4. The above laboratory synthesis was confirmed by systematic tests done at Thunder Energies Corporation..such as the test
R. M. Santilli and A. Nas, "Confirmation of the Laboratory Synthesis of Neutrons from a Hydrogen Gas," Journal of Computational Methods in Sciences and Eng, in press (2014)
www.thunder-energies.com/docs/neutron-synthesis-2014.pdf

5. The most recent experimental confirmation has been given by the international collaboration
Richard Norman, Anil A. Bhalekar, Simone Beghella Bartoli, Brian Buckley, Jeremy Dunning-Davies, Jan Rak, Ruggero M. Santilli "Experimental Confirmation of the Synthesis of Neutrons and Neutroids from a Hydrogen Gas, American Journal of Modern Physics, Vol. 6(4-1), page 85-104 (2017)
http://www.santilli-foundation.org/docs/confirmation-neutron-synthesis-2017.pdf.

6. The above tests were generally done with five different neutron detectors identified in the quoted papers. In addition, recall that when irradiated with a neutron flux, Natural silver (Ag) is transmuted into Cadmium (Cd) and Gold (Au) is transmuted into Mercury (Hg). Santilli has provided in 2018 experimental evidence on the presence of Cd in irradiated Ag and the presence of Hg in irradiated Au, thus confirming that the Thunder Energies Directional Neutron Source does indeed synthesize neutrons, see the paper
R. M. Santilli, "Apparent Experimental Confirmation of Pseudoprotons and their Application to New Clean Nuclear Energies," International Journal of Applied Physics and Mathematics Volume 9, Number 2, April 2019
http://www.santilli-foundation.org/docs/pseudoproton-verification-2018.pdf.

7. An independent review up to 2011 is available in the monograph
Gandzha and J. Kadeisvili, New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli, Sankata Printing Press,\\ Nepal (2011),
http://www.santilli-foundation.org/docs/RMS.pdf.

I hope this info is sufficient. Cheers. Ker27fi

Post 23
I agree with you that science nowadays is done via organized gangs slandering any advance over their beliefs. The slandering of Santilli's synthesis of the neutron from the hydrogen is quite easy because physicists (with due exceptions) are unaware of the complexity of the rapid DC discharge necessary to "compress" an electron inside a proton, whose achievement required three years of tests by Santilli and about half a million dollars in cost. Qualified criticism expressed in respectful language and published in refereed journals are much welcome for the advancement of our new technologies. But crackpots moving criticisms without technical content are the enemy of science. Dwer328hj

Post 24
I believe that Santilli address the real historical issue. Einstein, Podolski and Rosen conclude their historical paper EPR Argument with the statement: While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible Prof. Santilli has done exact that, shown that, under a proper new dynamics for interior systems, the wave function is modified in such a way to approach classical determinism as it is the case for the two electrons of the pseudoproton, the two electron in covalence bonds, and other cases. Lfg38ty.

Post 25
Prof. Santilli, please express your view on the "EPR Paradox" as outlined, for instance, in the website https://www.thoughtco.com/epr-paradox-in-physics-2699186. Thank you. Ysr39ui


Figure 11. A conceptual view of the entanglement of particles caused by the overlapping of their wavepackets with ensuing continuous and instantaneous communication without superluminal speeds violating special relativity

Post 24
Dear Ysr39ui / Post 24, thank you for raising such a pertinent question. In my view, the main issue of the debate on the 'EPR paradox' is that none of the participants, including Einstein, Bohr, Bohm, Bell, and others, identified the basic assumptions of quantum mechanics underlying their claims which are essentially the following:

1) The strictly point-like characterization of particles, which is inherent in the basic calculus underlying the treatment of the paradox, Newton's differential calculus, which can be solely formulated at isolated points. The paradox of superliuminal speed in particle 'entanglements' is then a mere consequence. In my view, the EPR paradox disappears when particles and their wavepackets are admitted to be extended and actually filling up the entire universe, of course, in a way rapidly decreasing with the distance. Hence, particles are continuously and permanently 'entangled' with their wavepackets, as illustrated in the figure, thus having continuous, thus instantaneous communications without any violation of special relativity.

2) The sole admission of interactions derivable from a potential, that is, of Lagrangian/Hamiltonian type. It appears that the 'entanglement' of wavepackets causes a 'contact interaction,' that is one without potential energy which has, nevertheless, physical implications as it is the case for a balloon moving in our atmosphere. Following decades of search, I illustrated the interactions between entangled wavepackets in the chemical notion of valence. According to quantum mechanics and chemistry, identical electrons in singlet valence coupling must repel, rather than attract each other due to their equal charge and magnetic moments. After initial studies I initiated in the late 1970s when I was at Harvard University, (see the chemistry debate). I finally achieved in the late 1990s the 'attractive' force between identical valence electrons in one way and one way only, via the entanglement of their wavepackets, called 'deep mutual penetration' in the related literature (see the 2001 monograph Foundations of Hadronic Chemistry). Besides the achievement of the first known exact representation if experimental data for the hydrogen and water molecules, the identification of an attractive force between valence electrons has permitted a deeper understanding of molecules, with the ensuing new HyperCombustion for the complete combustion of fossil fuels, which is under development by the U. S. publicly traded company Thunder Energies Corporation

3) Insufficiency of 20th century mathematics for a consistent treatment of entangled particles. As indicated earlier, entanglements effects are strictly non-potential. Additionally, entanglement effects are strictly non-local because defined over large volumes. The treatment of entanglements via the mathematics of quantum mechanics is grossly insufficient because said mathematics is solely definable at isolated points while the entanglement volumes cannot be reduced to a finite number of isolated points. Finally, entanglement effects are non-linear, that is, depending on power and derivatives of the wavefunctions. The biggest problem of the EPR paradox is the lack of admission that 20th century mathematics simply cannot treat non-linear, non-local and non-potential effects. For this reason, I initiated at Harvard University in the 1970s the construction of a 'completion' of 20thy century applied mathematics into a form, today known as isomathematics. which has been conceived and constructed for the representation invariant over time of non-linear, non-local and non-potential effects. The main idea is truly elementary and consists in the \generalization of all conventional product AB of arbitrary quantities A, B into the axiom-preserving, thus isotopic form ATB where T is a positive definite quantity providing the invariant representation of the extended character of wavepackets and their non-Hamiltonian interactions (see the 1978 monographs Foundations of Theoretical Mechanics, Volume I and Volume II). This initial formulation turned out to be 'incomplete' because not leaving invariant the unit '1' of the numeric field , thus requiring its formulation on numbers n* = n1* with arbitrary unit 1* = 1/T known as isonumbers All the above efforts continued to remain 'incomplete' because, by far, the most dominant limitation of quantum mechanics is its formulation via Newton's differential calculus, with consequential approximation of particles as isolated points. Following decades of trial and errors, I finally achieved in 1996 the 'completion' of Newton's differential calculus into a form today known as the isodifferential calculus. in which Newton's differential 'dr' is generalized into the broader form d*r* = Td(r 1*) = dr + rTd1*, with related derivatives, allowing the transition from the differential 'dr' at the isolated point 'r' to the isodifferential 'd*r* = Td(r1*)' which is defined over the volume T. The identification of a truly attractive force between entangled valence electrons was solely possible thanks to the use of isomathematics, and the same goes for numerous applications and experimental verifications (see the recent review general review.

4) The general belief of the lack of existence of hidden variables. An important branch of isomathematics is the 'completion' of Lie's algebras with historical brackets [A, B] = AB - BA at the bass of the Copenhagen interpretation of quantum mechanics into the iso-Lie algebras (see the recent review and original contributions quoted therein) with generalized brackets [A, B]* = ATB - BTA. Bohr 'hidden variables' can then be introduced very easily with the realization T = Diag. (λ, 1/λ). In the 1998 paper proof of the EPR argument, I presented the consequential inapplicability (and not the violation) of Bell's inequality for entangled wavepackets and the confirmation of the EPR Argument. The point to be stressed here is that the above concrete and explicit realization of hidden variables is achieved under the full validity of quantum axioms, solely subjected to a broader realization since the abstract axioms of mathematics and isomathematics, as well as Lie theory and iso-Lie theory, are the same. What we have in reality is an interpretation of quantum mechanics broaden than the Copenhagen form, today known as hadronic mechanics (see the 1995 monographs Elements of Hadronic Mechanics, Volume I: Mathematical Foundations. and Volume II: Theoretical Foundations).

5) Insufficient interest for experimental verifications and industrial applications of the EPR argument. All studies here considered originated from the inability of quantum mechanics to achieve any quantitative representation of Rutherford's synthesis of the neutron from a proton and an electron inside a star. The representation of the neutron synthesis was solely possible via the EPR completion of quantum into hadronic mechanics. Industrial equipment synthesizing neutrons on demand from a hydrogen gas are now in production and sale by Thunder Energies Corporation. The company is seeking nuclear physics laboratories interested in additional experimental tests and industrial applications of the ultimate process at the origin of stars, the synthesis of the neutron. Ruggero Maria Santilli, email: research(at)thunder-energies(dot)com

Post 26
May I comment that I feel the whole question of completeness relevant to several areas of theoretical physics, not just quantum mechanics although that area is certainly a definite case in point. Rather than write at length here, may I point anyone interested in the direction of the note, Completeness in Physics, by Rich Norman and myself which may be accessed quite easily on the viXra site. I think this note raises some serious questions which require answers as well as specifically mentioning the EPR Paradox. Jeremy Dunning-Davies.

Post 27
EDITORIAL NOTE: Prof. Dunning-Davies, please provide the link for your work that we cam gladly upload. in your post Thank you.

Post 28
Dear Prof. Dunning-Davies, I agree with you fully. In fact,, as I indicated in my writings and provided examples, the confirmation of the EPR Argument and the consequential elimination of the EPR paradox (see Post 25) have direct implications in the various branches of: mathematics, physics, chemistry, biology, astrophysics, etc. Best wishes. Ruggero M. santilli

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