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Debate 5.

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

Post 29
Dear EPR Debates, I came again across the debate and re-read some of the posts and related answers. Unfortunately I miss my posts about Goedel theorem and the ensuing discussions. These were in the page of www.galileoprincipia.org. As I see (or I think) all posts are transformed into this page except my posts and our discussion considering Goedel's theorem and the incompleteness Theorem for formal system. I think it was a nice discussion and is at the heart of the matter.

Post 30
Dear Post 29, please send us a copy of all posts that are missing and we shall upload them immediately. Please send them at our email admin(at)eprdebates(dot)org by specifying the title of the debate you refer to. Please accept our apologies for the occurrence. It was due to our webmaster of the time leaving abruptly because of issues related to the Corona virus. We did our best to reconstruct the debate in the galileoprincipia.org which is now disconnected. The EPR Editorial Team.

Post 31
Dear Prof. Santilli I have the following question. How do you see the relation between your hadroinc mechanics, or the completion of quantum into hadronic mechanics and the Goedel's incompleteness theorem? Such a question is hot debated elsewhere concerning QM, for example: I found the following argument form Tom McFarlane, B.S. Physics, Stanford University, see https://www.quora.com/Is-G%C3%B6del-s-incompleteness-theorem-in-mathematics-equivalent-to-Heisenbergs-uncertainty-principle-in-physics "Goedel's theorem is a clear-cut, either/or dichotomy: an axiomatic system of sufficient expressive power is either complete, or it is consistent. There is no partial completeness combined with partial consistency. Heisenberg's uncertainty principle, on the other hand, allows for a quantum system to have both position and momentum, provided their uncertainties are not both arbitrarily small. The more certain the position, the more uncertain the momentum, and vice versa. No such intermediate mixture exists with completeness and consistency of axiomatic systems. "

Post 32
Hello Post 31, thank you for your important question. it is true that the two Goedel's incompleteness theorems have been essentially ignored in the 20th century physics, but perhaps, having been formulated in 1931, they did not escape the attention by Albert Einstein because said theorems can be construed as precursors of the 1935 Einstein-Podolsky-Rosen argument that "quantum mechanics is not a complete theory" http://www.eprdebates.org/docs/epr-argument.pdf.

I appreciated the request for my view, but I am afraid not to be a true expert in the indicated field because the two Goedel's incompleteness theorems do not belong to the rigorous mathematical definition definition of a "theorem" since that would require every word and/or assumption to be defined via equations. To illustrate my uneasiness as an applied mathematician, I indicate that, when applied to quantum mechanics, the second Goedel's incompleteness theorem implies that quantum mechanics cannot demonstrate its own consistency, by therefore triggering endless epistemological discussions, outside my field of expertise as an applied mathematician, on what are the basic assumption, what is the meaning of "consistency," etc..

Regrettably, with all respect, I have the same uneasiness with the indicated view by Tom McFarlane because, when dealing with "physical" systems such as quantum mechanical particles, it is necessary to identify the basic assumptions, namely, the sole representation of said particles as being point-like while moving in vacuum under sole action-at-a-distance, potential interactions. These basic assumptions are mandated by: the potential V(r) in the Schroedinger equation which is solely defined at isolated points; the differential part of said equation which is also solely defined at isolated points; etc. Under said assumptions, Tom McFarlane view on Heisenberg's uncertainties, related Bell's inequality, etc., are indeed valid. However, point-like particles do not exist in nature. But then the admission of the actual, extended, thus deformable character of particles implies the admission of interactions (expected, e.g., in the mutual penetration of nucleons in a nuclear structure) that are non-linear (in the wavefunction), non-local (because existing in a volume that cannot be reduced to points) and definitely not derivable from a potential, thus being structurally beyond any hope of treatment via quantum mechanics, related uncertainty principle, Bell's inequality and all that.

In fact, the indicated extended representation of particles and their non-non-non interactions have allowed three different proofs of the EPR argument discussed in details at our recent international teleconference in the field, see the recording of all lectures in the website of the World Lecture Series http://www.world-lecture-series.org/level-xii-epr-teleconference-2020. This teleconference also presented an invited talk by Evans T. D. Boney available in Section IV) delivered precisely on Goedel's incompleteness theorems and heir unreassuring implications for the standard model that may be of interest to you. In case I can be of any additional help, please do not hesitate to contact me. R. M. Santilli.

Post 33
Dear Prof Santilli, again I am glad to get your response, thank you. I do think, we understand each other well. Now, I think with final theory here it is meant, also in the spirit of Stepfen Hawking, that we approach contentiously, with new theories and their generalization, a better and better description of the nature with models, which are capable to describe the nature, however, not or never completely. I.e . Model-dependent reality. So, again to me completeness means the ability of reaching the final theory, which is not possible. If you, dear colleague Prof. Santilli, are able to prove a corollary to the effect that the absence of a final theory does not prohibit its completion. Fine, then my answer will be a Bohrian one, namely what do you means then with completion!. In my view, we have to be more precise or careful, in our description and interpretation of the results of the physical theories. Clearly to avoid an overloading at least from language point of view. When the Hadronic Mechanics is a "completion" of QM to honor Einstein's memory, for me personally that is right. However, as a scientist I would say, it leads to a misunderstanding, and especially to a lot of controversies, and possibly to a confusing when such a physical theory becomes available for wide audience. Finally, Hadronics Mechanics is a great generalization of the QM really!, to my today's understanding, because I still do not have a deep involvement in it, and so I do not see that it is a completion of QM, and I would say it is possible to introduce a hidden variable in it too (according to GOEDEL theorem, and not only), and it is then again not a completion in the same sense of EPR conclusion. Any objection is welcome!.

Post 34
Dear Post 33. Thanks for the additional comments and the nice words for hadronic mechanics, but this time we are completely disconnected because you do not appear to have inspected the refereed literature on the verification of the EPR argument and you commented before having time to view the numerous lectures in the field we just uploaded. For the record, I use he work "completion" between quotes because that is the term used by Einstein with full identification in his above quoted 1935. Unti you acquire the indicated knowledge there is no point for me to continue this contact because I cannot reproduce in a log about 50K pages of research in the field in the past century. Regards R. M. Santilli

Post 35
Dear Prof. Santilli, I am very grateful for your answer. I have read some of your monographs and watched some of your lectures in the web, including Evans T. D. Boney lecture form the last series in 2020. I think I understand you very well. In my opinion what Popper said "A theory should be considered scientific if, and only if, it is falsifiable." has the same contain of the Geodel incompleteness ``theorem``. However, this concerns more or less the inability of reaching final theory. In this respect, I do not see any contradiction to my earlier posts, which are missing!. In the next post, I will send one of them that I found after some search my computer. I appreciate if you post it again.

Post 36
Dear Post 36, thanks sincerely for your comments and sorry for the disappearance of various posts. The problem originated from the fact that the webmaster of the early website "galileoprincipia.org" disappeared with the passwords because of apparent family problems and we had to reconstruct the website to our best. PLEASE do send us any missing post, or their reconstruction to your best, and I will make sure they are uploaded. Regard, RMS

Post 37
I have this earlier post (updated), and hope it is valuable for the discussion of Debate 5.:
Dear Prof Santilli, I am grateful that you find the time to respond (post 36). I am sorry not give you a reference for GOEDEL (in German "GDEL" a German Mathematiician). See for example the following
http://www.ams.org/notices/200604/fea-davis.pdf
or https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
see also in this respect (Popper words in post 35)
https://en.wikipedia.org/wiki/Karl_Popper#/media/File:Popper_gravesite.jpg
Second, I am a theoretical physicist, the conclusion about the GOEDEL "A theory either is complete or is logical (consistency)" is very simplified. However, in my opinion it is a mathematical theorem, fundamental and important for the discussion of the completeness of QM or any other theory. Now, if I understand your work, the ``completed" QM is rather a generalization of the QM (and all previous physical theories). In other word it is really not a completion or can not, because actually there exist no complete theory by considering GOEDEL theorem. In my understanding Hadronics mechanics is a new theoretical foundation, that encompasses all previous physical theories. We will never reach a complete theory. In Other words, or in your own words: "quantitative science will never admit final theory. No matter how beautiful any given theory may appear, its generalization is only a question of time." d encompasses all previous physical theories, including the recent one, the QM.

Post 38
Hello Post 37, thank you, for your post which I believe is important for the proof of the EPR argument. I fully agree with your view with the clarification that I am a formula man and, as such, I am not an expert in Goedel theorems. Allow me to confess that I have uneasiness with the terminology of the theorems perhaps also due to my lack of knowledge of German. In fact, when referring to an ultimate theory, I always used the word "final" and not "complete" as indicated in my quote you nicely reproduced in the post. Also, I stated various times that "Up to the early 1990s, hadronic mechanics was incomplete because of the lack of a compatible generalization of Newton-Leibnitz differential calculus." Then, in the early 2000 I stated that "The construction of hadronic mechanics was finally completed with the 1996 isotopies and genotopies of the differential calculus" but positively this does not mean that hadronic mechanics became a final theory. I remember searching the dictionary for synonyms, but could find none better than "incomplete" and "complete," while the ultimate limitations were expressed by the clear cut word "final' which does not appear to be used in the two Goedel's theorems. Incidentally. you may have noted that I restricted my research to Bell's inequality and never treated the two Goedel theorems precisely because I did not want to get involved on discussions on the meaning of the used word "complete." I am sorry but that' sall I can say in the field. Regards RMS>

Post 39
Dear Post 33 (and also Prof Santilli),We are mostly in agreement here. I agree that this generalization of Quantum Mechanics in Hadronic Mechanics is interesting primarily as a representation, alongside the Copenhagen, Many-World's and Heisenberg, each with it's own set of native insights. I would propose calling it the Heisenberg-Santilli or Heisenberg-Einstein-Santilli operator formalism of quantum mechanics, given the similarity of the T operator stuff to the Propagator in the Heisenberg formalism.

Similarly, I understand now the completion is a reference to the EPR completion, but perhaps referencing Einstein directly is a way to avoid the confusion? Because it does seem that calling things like the calculus additions necessary to maintain consistency "completions" is overwrought on its face. Because sure we've lost uncertainty and gained the vaunted completeness... but we LOST UNITARITY!?!!! And reversibility? These are nontrivial losses, and patching them up with constant renormalization is not success.

That's a problem for me. That we gain true zero uncertainty in the theory only in the limit where T is zero? Thats basically when nothing is left, or at the event horizon of a black hole. And I would add... that in those places, the old theory also has zero uncertainty! When there is nothing, we all agree it is nowhere.

Which brings me to the core concern: the focus on completion leads to an obfuscation of the core issue at hand, which is falsifiability and differentiation from the existing paradigm. If your hadronic mechanics is to cause a paradigm shift, it will need a crucial experiment, within the existing paradigm. For the isodual theory, your positrons in horizontal flight is just that. But for the hadronic mechanics, what is it? General discomfort with quark confinement? Some hand-waving about valence bonding that seems to ignore the last 40 or so years of treatments of valence bonding?

I think we can all agree that these proposed confirmations of hadronic mechanics are considerably less decisive than a positron falling up would be for isodual mechanics. Nothing I've seen shocks the conscience enough to cause a paradigm shift. And I think failure to recognize the Kuhnian nature of epistemology leads to the occasional indulgence of conspiracy talk, when really we just need to make a better case for ourselves.

Post 40
EDITORIAL NOTES: regrettably Prof. Santilli could not comment on Post 39 because the statements contained therein could not be turned into equations. Therefore, the content of the post is outside his expertise or interest. The Editors want to comment on the following statements of Post 39:

1) "....similarity of the T operator stuff to the Propagator in the Heisenberg formalism." This statement is wrong, technically and conceptually, because the isotopic operator T generalizes the structure of the basic enveloping algebra of the Copenhagen interpretation of quantum mechanics for the representation of non-Hamiltonian interactions, while Heisenberg's propagator does nothing of that. Opposing views will be posted if and only if proved with equations, namely, the proof that Heisenberg's propagators generalize the enveloping associative algebras of quantum mechanics which is a total nonsense..

2) "... but we LOST UNITARITY!?!!! And reversibility? These are nontrivial losses" This blogger implicitly claims that quantum mechanics makes no sense because unitarity makes no sense in classical mechanics ???!!! Canonical transformations are replaced by unitary transformations in the transition from classical to quantum mechanics. Exactly along the same lines, unitary transformations are replaced by the covering isounitary transformations in the transition from quantum to hadronic mechanics with full verification of causal laws, of course, in the appropriate representation spaces rather than in the spaces of other mechanics as done by this blogger for hadronic mechanics but not for quantum mechanics for some reason. The claimed "loss of reversibility" by quantum mechanics is shocking for these editors because it implies that the blogger denies the irreversibility of particle reactions. The gained Lie-admissible representation of irreversibility and related thermodynamical laws appears to be disturbing for this blogger.

3) " If your [sic] hadronic mechanics is to cause a paradigm shift, it will need a crucial experiment, within the existing paradigm." The editors believe that this blogger mimics for some reason a lack of knowledge of the numerous experimental verifications of hadronic mechanics squarely "within the existing paradigm" because none of them can be formulated with quantum mechanics (see http://www.santilli-foundation.org/docs/elements-hadronic-mechanics-iii.compressed.pdf). The Editors.

Post 41
correction to post 37: I am sorry it is and also was (post 32), not (post 36)

Post 42
The guy of post 39 is out of whack. The isotopic (= axiom-preserving) branch of hadronic mechanics verifies unitarity and reversibility in the appropriate space,

Post 43
It seem so me that post 39 confirms Prof. Santilli's quote The most ascientific process of contemporary societies is the scientific process "http://www.eprdebates.org/santilli-quotes.php,

Post 44
Post 39 dubs "band-waving" the first attraction between valence pairs in molecular bonds (Post 39 now has repulsion....!!!!) and its first exact representation of experimental data for H2 and H2O (Post 39 has only approximate values....!!!) and he calls all this "hand-waving" ??? !!!, No wonder Post 40 justly speaks of mimicking !!!.

Post 45
Post 39. I agree with the most of your comment. The fact that we gain true zero uncertainty in the theory only in the limit where T is zero, is an important point. I have the following example and hope it applies for this case (T->0) or I am not mistaken in my statement. By considering information extracted by the experimenter (observer)form a system (atom) by detecting light, the condition T->0 can only be satisfied when the observation apparatus and the atom become close that mutual penetration is large enough. However, at this condition the atom and the apparatus become one-system and the observer can not get any information form the apparatus. That is why I am skeptic to accept Santilli proof of the lose of UNCERTAINTY!.

Post 46
Post 45, Einstein was skeptic as to whether quantum uncertainties are complete=final, so you are not alone to have skepticisms, but then you need credible technical arguments. The separation between politics and serious science is set by the question: do you have a formulation better than Santilli's hadronic mechanics for the uncertainties of particles in deep entanglement? Of course not. Hence you beg for a claim on the political intent of your view. This seems to be confirmed by your statement "Santilli proof of the lose [loss] of UNCERTAINTY!." I do not claim to be an expert theoretician, but it seems very clear that hadronic mechanics is a covering of quantum mechanics which is recovered uniquely and unambiguously for mutual distances "r" of particles bigger than the hadronic horizon. In plain language, hadronic mechanics recovers conventional uncertainties in full for sufficiently large values of "r" for which T = 1 under which all the old stuff you like comes back. So where is the loss ??? The most unreassuring implications of your post is that you implicitly oppose any advance over quantum mechanics for particles in deep mutual entanglement, despite the shameful, century-old failure by quantum mechanics to represent nuclear data. Santilli hadronic mechanics has indeed achieved the first and I believe the only - to date - exact representation of nuclear spins, magnetic moments and other data in the true ground state of isolate nuclei. Your skepticism implies that we should keep the old uncertainties for nuclear structures and not seek better a representation of nuclear data. I hope for your own sake you are "not" aware of the implications of such a view for nuclear fusions etc.

Post 47
Can anybody indicate the representation via equations of at least one of Goedel's theorems? I could find none, as a result of which said theorems are epistemological at best. Hence, I understand and support Prof. Santilli's silence on them in his three proofs of the EPR argument to keep a distance from senseless and endless semantics on names.

Post 48
Prof. Santilli, could you please elaborate on the physical meaning of the isotopic element and its functional dependence?

Post 49
I believe that Post 39 and his friend 45 belong to the organized interests initiated by Bohr opposing any surpassing of QM for their pockets.

Post 50
Hello Post 48, thanks for the best question I received of lately. Recall that QM is a Hamiltonian theory which means that a system can be represented by QM if and only if the system is representable via the Hamiltonian H = p^2/2m + V(r). In my view, the biggest insufficiency of QM in nuclear physics at large and nuclear fusions in particular, is the impossible admission of an explicit and concrete representation of strong interactions due to their non-Hamiltonian character created, in nuclear physics, by the mutual penetration/entanglement of the charge distributions of protons and neutrons in a nuclear structure established by nuclear data. For this reason, I introduced the isotopy ATB of the associative product AB of QM so that electromagnetic (and part of the strong, such as the exchange) interactions are represented by the Hamiltonian H while the isotopic element T represents strong interactions in their most general possible non-linear, non-local and non-Hamiltonian form. In regard to the functional dependence of the isotopic element T, I assumed:

1) In its simplest possible form, T must have the exponential structure,

(1)           T = exp X(....)

because such a form is the best for a smooth recovering of QM via the limit

(2)           Lim T_{X -->0} = I.

2) In order for strong interactions to be attractive, the function X(...) has to be negative definite,

(3)           T = exp [ - F(....)], ~~ F > 0.

3) F(...) is non-Hamiltonian by basic conception. Its primary functional dependence (again, in this simplest possible case) has to be in the wavefunction \psi(r) as a condition to represent the non-linearity of strong interactions (which is necessary for deep mutual penetration/entanglement). The non-locality of the strong interactions (also necessary for wave-overlapping/entanglement), joint with condition (2), restrict the simplest possible dependence of the isotopic element to the form (careful, when projected in our Euclidean space and not in isospace)

(4)           T = exp{ - f(....) \int \psi^\dagger(r) \psi(r) d^3r}, ~~ f(...) > 0

which form assures that, when the wave overlapping/entanglement is insignificant, one recovers QM smoothly, identically and uniquely.

4) The verification of the last statement by Einstein, Podolsky and Rosen in their 1935 paper that "the wavefunction of quantum mechanics cannot represent the entire physical reality," requires that f(...) be also dependent on wavefunctions, by reaching in this way in the expression

(5)           T = K exp{ - f(\psi. \psi*, ....) \int \psi^\dagger(r) \psi(r) d^3r},    K > 0,     f(...) > 0

where: \psi is the QM wavefunction; \psi* is the "completed" wavefunction of HM; "..." refers to a number of additional functional dependences, when needed, on the density \mu, temperature \tau, frequency \vu, particle mutual distance d, local energy E, etc.; and the factor K may also have the most general possible dependence, provided that K = I when the particles are no longer appreciably entangled (e.g., non-spherical shapes become the perfect sphere with radius 1 for isolated particles in vacuum), see Eq. (4.7), page 170 of the monograph http://www.santilli-foundation.org/docs/Santilli-113.pdf (formulated for the isounit I* = 1/T) and related Chapter 4 where one can see the achievement of the first attractive force between identical electrons in valence bonds, with related industrial applications for clean combustion of fossil fuels, see, e.g., www.hadronictechnologies.com. The above conception of non-Hamiltonian interactions realized with Isotopic element (5) has additionally allowed the first exact representation of "all" characteristics of the deuteron (not in a combination of excited states as done in QM to represent the spin 1, but) for the true ground state, see Section 2.7 of http://eprdebates.org/docs/epr-review-iii.pdf that, in turn, allowed the conception of the conception of new nuclear fusions between natural, positively charged nuclei and negatively charged synthesized nuclei to avoid the enormous Coulomb barrier that has prevented the achievement to date of industrially viable clean nuclear energies. Regards, Ruggero.

Post 51
Thank you Prof. Santilli. To my understanding the isotopic element T can only have values between 1 (recovering of QM and zero (recovering of Einstein's full determinism)?

Post 52
Yes.<.p>

Post 53
Dear Sir post 47. I think you misunderstand me! First, if you read my post 33, you will see that I am fully agree with you about Santilli Hadronic Mechanics, which Prof Santilli has recognized, see post 38. 2nd, thank you for the correction lose->loss. 3rd, We discuss science and nothing else, open mid is my home. 4th, now my point in post 45 is that: we do not know exactly whether the nature for itself deterministic or not, this needs a final theory!, we try to describe the nature by models in the spirit of Stepfen Hawking, see post 33. I presented my example about atom-apparatus to discuss the conditions for the validity (my view) of the claim of Santilli the loss the UNCERTAINTY. We mankind when we measure the nature we test the validity of our models. The extraction of information express the fact that we transform the nature behavior to our consciousness. We have to extract the information by apparatus and T->0 is achieved by the condition that apparatus and the atom become close that mutual penetration is large enough. Under this condition the atom and the apparatus become (closed) one-system, and we can not gain any information from (now becomes) is a closed-one-apparatus-atom system. This sets some limitation on the claim of Santilli of the loss of UNCERTAINTY, in my view. It is a simple Gedanken-Experiment.

Post 54
Post 53, please accept my apologies for misinterpreting your comments. Your comments regarding "limitations" on Santilli's proofs of the EPR argument are definitely valid and worth discussing. However, allow me to suggest that we should first discuss what is "Einstein isodeterminism" per Santilli's definition in his papers, and then pass to their limitations. This is recommendable because said proofs are mathematical. As stated by Santilli himself, their physical interpretation is essentially unknown at this writing. Also, their experimental verification requires "direct measurements under strong interactions", namely, a technology that does not exist in my knowledge at this moment. Sorry again for my misinterpretation.

Post 55
I feel I should disagree with Post 53 in his view that Santilli's isodeterminism is purely mathematical. In the event that is the whole story, Heisenberg's uncertainties are purely mathematical because the former is constructed via an isotopy/axiom-preserving map of the latter. In reality:

Heisenberg's uncertainties were formulated for particles under electromagnetic interactions (because derivable from a potential), while,

Santilli's isodeterminism was formulated for strong interactions (because of contact non-Hamiltonain character). Hence there is a lot of underlying physics including industrial equipment based on it

The main issue is how to test Santilli's isodeterminism? I agree here with Post 54 because the tests require measurements under strong interactions, and that's not a cut of tea. However, it should be recalled that the first test here needed was proposed beginning with the title of Santilli's first paper introducing the words "hadronic mechanics",

R. M. Santilli, "Need of subjecting to an experimental verification the validity within a hadron of Pauli exclusion principle," Hadronic J. Vol. 1, 574-901 (1978), http://www.santilli-foundation.org/docs/santilli-73.pdf

Since that paper is 327 page long, I would appreciate whether Prof. santilli can tell us the main gist. We can then look for alternatives.

Post 56
Dear Post 55, thank you, it's okay no problem. The limitation here means that the loss of UNCERTAINTY is limited to very extreme conditions. And one may ask under such conditions what about all physical laws. I must admit that I am not familiar with strong interaction, I should learn about it first.

Post 57
Post 56, I assume you know well QM. But then allow me to suggest that you study HM and its experimental verifications before entering into epistemological aspects related to "limitations." You will see that quantum equations and related laws (not just names) are replaced by covering hadronic equations and related laws.

Post 58
ELEMENTARY REVIEW OF RECENT STUDIES ON EINSTEIN'S DETERMINISM
Dear Post 55, thank you your request for me to provide an introduction to the experimental evidence supporting recent studies on Einstein's determinism. I confess that I hesitated to answer due to the limitations of the html format for equations, as well as for the technical character of the topic which requires a knowledge of at least the references of the announcement of our recent teleconference in the field [1], which references are reproduced below for convenience and are assumed to be known. The understanding of my elementary review also requires a knowledge of the lectures delivered at said teleconference [2].

1. Uncertainties for point-like particles.
We assume a knowledge that quantum mechanics can only represent point-like particles in vacuum (exterior dynamical problems) due to the sole possible definition of potentials, Laplacians, etc at isolated points. Assume: a conventional Hilbert space H over the field of complex numbers C with states |ψ(t, r)> (where r is the Euclidean coordinate); normalization

(1)           <ψ| | ψ> = 1;

and quantum mechanical realization of the linear momentum

(3)           p |ψ > = - i ℏ ∂r |ψ >.

The familiar Heisenberg's representation then follows

(3)           i dA/dt = [A, H] = AH - HA,

(4)           [r, p ] = i ℏ ,   [r, r] = [p, p] = 0.

A well known procedure then yields Heisenberg's uncertainties for point-particles

(5)           Δ r Δ p ≥ (1/2) | <ψ | [r, p] |ψ> | = ℏ /2

2. Experimental verifications of uncertainties for point-particles.
I personally believe in uncertainties (5) for point particles because of the clear experimental, verifications of Heisenberg's basic equations (4) and (5) for the hydrogen atoms and other exterior dynamical systems. These verifications are at times called indirect experimental verifications of quantum uncertainties (5). In fact, it is easy to prove that, in the event Eqs. (3) (4) are not verified experimentally, uncertainties (5) are invalid. Needless to say, in one century of repeated studies, there are also a number of direct experimental verification of quantum uncertainties (5), namely, verification with direct measurements of uncertainties (5) for exterior dynamical problems, such as the excellent experiments by Prof. Gerald Eigen (view his lecture in list [2]), and experiments quoted therein.

3. Isodeterminism for extended particles.
We assume a knowledge of isomathematics (Tutoring Lecture I of Ref. [2]) and its characterization of the isotopic branch of hadronic mechanics for the representation of extended particles in continuous mutual penetration/entanglement (Interior dynamical problems) [12] [13]. Assume the axiom-preserving/isotopic lifting/"completion" of "all" quantum mechanical products AB between arbitrary quantities A, B into the isoproduct

(6)           A*B = ATB,   T > 0,

where the isotopic element T represents extended particles in interior dynamical conditions and their ensuing non-linear, non-local and non-potential interactions (please look at Post 50 for the positive-definiteness of T > 0). Then, the isounit of the theory is given by

(7)           I' = I'(r, p, ψ, ...) = 1/T > 0,     I' * A = A * I' = A

Assume the iso-Hilbert isospace H' over the isofield C' of isocomplex isonumbers n' = n I' with isostates |ψ'(t, r')> (where t' = t for simplicity and r' = r I' ∈ C' represents, this time, a volume); isonormalization

(8)           <ψ | * | ψ> = <ψ | T | ψ> = T ,

where one should note the necessity of the above isorenormalization (instead of <ψ | * | ψ> = <ψ | T | ψ> = I' ) since T can be a constant as a particular case; and the realization of the isolinear isomomentum of hadronic mechanics via the isodifferential calculus

(9)           p'* | ψ'(t, r') > = - i ∂'r' |ψ' (t, r')> = - i I' ∂r' |ψ'(t, r') >,

where the upper dash represents quantities in H.

The repetition of the derivation of Eqs. (3, 4) under isotopy then yields the iso-Heisenberg isorepresentation[13]

(10)           i d'A/d't = [A, H]' = ATH - HTA,

(11)           [r, p ]' = i I';,   [r, r]' = [p, p]' = 0.

Note that hadronic mechanics recovers quantum mechanics uniquely, unambiguously and entirely at the limit T = 1 (Post 50).

As it is well known, N. Bohr [4] strongly opposed to his death Einstein's desire for a return to classical determinism. For the case of two point-like particles with spin 1/2 in vacuum represented by quantum mechanics (qm), Bohr's view was supported by J. S. Bell [5] who computed an inequality of the type

(12)           Dqm ≤ 2,

whose value prevented the existence of classical counterparts, thus preventing a realization of Einstein's determinism (see the vast literature in Ref. [6]).

First verification of the EPR argument [3]. The following two-dimensional realization of the isotopic element T for particles with spin 1/2 , first introduced in Ref. [7],

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

provides an explicit and concrete realization of Bohm's hidden variables. [5]. The repetition of of the derivation of Bell's inequality [5] via hadronic mechanics (hm) for the representation of two expended particles with spin 1/2 in continuous overlapping/entanglement and hidden variables λ and μ, respectively, yields the expression [7]

(13)           Dhm = (1/2)(λ μ-1 + μ λ-1) Dqm

whose large factor implies that the explicit and concrete realization of hidden variables permitted by hadronic mechanics establishes the existence of classical counterparts for systems of extended particles with spin 1/2 in interior dynamical conditions, by therefore identifying conditions under which Einstein's determinism is possible (see Ref. [7] for the identification if specific classical images).

Second verification of the EPR argument [3]. The step by step isotopy of the derivation of uncertainties (5) yields the isodeterminism for extended particles [8]

(14)           Δ' r Δ' p = (1/2) | <ψ' | * [r, p] * |ψ'> | = T/2

which isodeterminism progressively and smoothly connects Heisenberg's uncertainties (5) occurring for T = 1 to Einstein's full determinism occurring for T = 0 at the extreme densities of Schwartzchild's horizon [8]

(15)         T = 1 / (1 - 2M/r) --> r -->0 = 0,

with intermediate conditions depending on the density of the deep entanglement of particles.

Third verification of the EPR argument [3]. The proof of the last statement of Ref. [3], that "quantum mechanical wavefunctions cannot represent the entire physical [and chemical] reality," was done in monograph [15] and Ref. [11], Section 2.8, with the first known identification of an attractive force between the two identical electrons in valence bonds with ensuing exact representation of molecular data. This proof is not reviewed here for brevity. We merely note that hadronic laws (13) (14) are solely possible under the "completion" of quantum mechanical wavefunctions for non-linear, non -local and non-potential interactions. The achievement of an attractive force between identical valence electrons is then consequential.

4. Indirect Experimental verifications of isodeterminism.
In my view, as it is the case for uncertainties (5), the most important verifications of isodeterminism (13) are given by the experimental verifications of the basic laws of hadronic mechanics, the iso-Heisenberg isorepresentation and its isounitarily isoequivalent iso-Schr\"oringer isorepresentation [13], since the latter uniquely and unambiguously imply the former.

4.1. Verification via the synthesis of the neutron from the hydrogen. The neutron is 0.782 MeV heavier then the sum of the masses of the proton and the electron, under which conditions no representation via quantum mechanics is possible for various technical reasons. Following decades of research, the iso-Schr\"odinger isorepresentation has permitted the representation of the totality of the characteristics of the neutron in its synthesis from the hydrogen at the non-relativistic and relativistic levels, as well as the industrial construction and sale of an equipment producing neutrons on demand from the hydrogen in the desired direction, energy and flux (see Ref. [15], Vol. IV, the first lecture by Prof. S. Beghella-Bartoli in Ref. [2] and independent review [18]).

4.2. Verification with the characteristics of the deuteron. The basic dynamical laws of hadronic mechanics have additionally permitted the first known exact representation of all characteristics of the deuteron thanks to the first known representation of strong interactions via the isotopic element T (see Section 2.7 of Ref. [11]).

4.3. Verification via nuclear magnetic moments. Recall that, in one century of efforts, quantum mechanics has been unable to achieve an exact representation of the magnetic moment of the smallest nucleus, the deuteron, with embarrassing deviations of the predictions of the theory from experimental data for heavier nuclei. The first proof [7] of the EPR argument [3] was applied in the same paper [7] for the first known numerically exact representation of nuclear magnetic moments because the extended character of particles implies their deformability under strong interactions, thus providing the missing anomalous contribution for exact representations (see also Section 2.7 of Ref. [11]).

4.4. Verifications via nuclear spins.. Recall that, also in one century of research, quantum mechanics has been unable to represent the spin J = 1 of the the deuteron in its ground state since that would require, for stability, a singlet coupling of protons and neutron in which case the spin would be null, J = 0. This occurrence has forced orthodox physicists to represent the spin J =1 via a combination of excited orbital states against the incontrovertible experimental evidence that an isolated deuteron is in its ground state with J = 1. The iso-Heisenberg isorepresentation and the related regular isotopies of the SU(2) spin symmetry [10] have permitted the achievement of an exact representation of the spin of nuclei in their actual ground state [14].

4.5. Representation via the anomalous behavior of the mean life of unstable hadrons with speed. The admission that particles have an extended wavepacket implies that hadrons are hyperdense media caused by the total mutual penetration/entanglement of their constituents. The resulting internal, non-linear, non-local and non-Hamiltonian interactions can manifest themselves in the outside via the experimentally measured deviation from quantum predictions of the mean life of unstable hadrons with energy from 0 to 100 GeV. By contrast, these deviations are exactly represented by relativistic hadronic mechanics (see Volume IV of Refs. [15]).

4.6. Verifications via the Bose-Einstein correlation. It is generally believed at orthodox institutions that relativistic quantum mechanics is exactly verified by the Bose Einstein correlation. However, the fit of experimental data requires four arbitrary parameters (called "caoticity parameters"?), whose introduction from basic axioms is impossible since the quantum mechanical expectation value of the Hamiltonian <ψ | H |ψ> for the two-point correlation functions is only two-dimensional. By contrast, the use of relativistic hadronic mechanics has permitted the exact representation of the experimental data from first unadulterated principles for the two-point correlation function thanks to the isoexpectation values <ψ | * H * |ψ> = <ψ | T H T |ψ> which provide experimental values of the shape, dimension and density of the proton-antiproton fireball (see Vol. IV of Ref. [15]).

4.7. Experimental verifications via molecular data. As well known, quantum mechanics is exactly valid for the structure of one hydrogen atom, while failing to achieve an exact representation of two hydrogen atoms bonded into the molecule H-H, since the quantum representation misses the rather large amount of 941 kcal/mole in the representation of the H2 binding energy. By acknowledging the historical value of the quantum chemical valence, I achieved its "completion " with an attractive force between the identical valence electrons, that permitted the representation of binding energy of the hydrogen and water molecules numerically exact to the desired decimal value (see Refs. [11], [15] Vol. V, and [16]).

A number of additional experimental verifications exist via the use if the irregular isosymmetries for extended particles in interior conditions (see Ref. [10], [13], and Vol. III of Ref. [15]), but they cannot be reviewed in this rudimentary presentation for brevity. However, to prevent major misrepresentations, it is necessary to recall that, by no means, "particles in interior conditions" (electron, proton, neutron, etc.) are the same as the corresponding "particles in exterior condition," because the latter particles are unitary irreducible representations of the Lorentz-Poincare' symmetry, while the former particles are isounitary isoirreducible isorepresentation of the covering Lorentz-Poincare'-Santilli isosymmetry called isoparticles. The main difference is due to the fact that non-Hamiltonian interactions represented with the isotopic element T cause renormalizations of intrinsic characteristics (mass, charge, magnetic moment, etc., first identified in Eq. (5.1.36), page 841. Ref. [17] of 1978), without which none of experimental verifications 4.1 to 4.7 would be possible.

5. Direct experimental verifications of isodeterminism.
Post 55 has identified what appears to be the expected, most important, yet most, difficult, direct verification of isodeterminism, that via the confirmation or disproof of Pauli's exclusion principle under strong interactions. In essence, alongside the isodeterminism, the mutations of intrinsic characteristics of particles increase with the increase of the density of the hadronic media. In particular, the spin 1/2 of electrons and protons does not need to be mutated for the structure of the neutron and of light stable nuclei. However, hadronic mechanics predicts that, at the extremely high energies of ongoing particle collisions at CERN, FERMILAB, DESY and other laboratories, the intrinsic angular momentum of particles cannot remain the same as when in vacuum due to surrounding resistive forces, thus implying the prediction (made in 1978 [17]) that Pauli's exclusion principle cannot be verified in the extremely high density scattering regions. Thanks for the interest and best wishes. R. M. Santilli

REFERENCES

[1] 2020 International Teleconference on Einstein's Determinism

[2] Lectures delivered at the 2020 teleconference

[3] A. Einstein, B. Podolsky , and N. Rosen, ``Can quantum-mechanical description of physical reality be considered complete?,'' Phys. Rev., vol.~47 , p. 777 (1935),
http://www.eprdebates.org/docs/epr-argument.pdf

[4] N. Bohr, ``Can quantum mechanical description of physical reality be considered complete?" Phys. Rev. Vol. 48, p. 696 (1935),
http://www.informationphilosopher.com/solutions/scientists/bohr\-/EPRBohr.pdf

[5] J. S. Bell: ``On the Einstein Podolsky Rosen paradox" Physics Vol. 1, 195 (1964),
https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

[6] Stanford Encyclopedia of Philosophy, ``Bell's Theorem" (2019),
https://plato.stanford.edu/entries/bell-theorem

[7] 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.eprdebates.org/docs/epr-paper-i.pdf

[8] R. M. Santilli, ``Studies on the classical determinism predicted by A. Einstein, B. Podolsky and N. Rosen," Ratio Mathematica Volume 37, pages 5-23 (2019),
http://www.eprdebates.org/docs/epr-paper-ii.pdf

[9] R.M. Santilli, ``Studies on A. Einstein, B. Podolsky, and N. Rosen prediction that quantum mechanics is not a complete theory, I: Basic methods," Ratio Mathematica Volume 38, pp. 5-69, 2020,
http://eprdebates.org/docs/epr-review-i.pdf

[10] R.M. Santilli, ``Studies on A. Einstein, B. Podolsky, and N. Rosen prediction that quantum mechanics is not a complete theory, II: Apparent proof of the EPR argument," Ratio Mathematica Volume 38, pp. 71-138, 2020,
http://eprdebates.org/docs/epr-review-ii.pdf

[11] R.M. Santilli, ``Studies on A. Einstein, B. Podolsky, and N. Rosen prediction that quantum mechanics is not a complete theory, III: Illustrative examples and applications," Ratio Mathematica Volume 38, pp. 139-222, 2020,
http://eprdebates.org/docs/epr-review-iii.pdf

[12] R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume I (1995), Mathematical Foundations,
http://www.santilli-foundation.org/docs/Santilli-300.pdf

[13] R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume II (1994), Theoretical Foundations,
http://www.santilli-foundation.org/docs/Santilli-301.pdf

[14] R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume III (2016), Experimental verifications,
http://www.santilli-foundation.org/docs/elements-hadronic-mechanics-iii.compressed.pdf

[15] R. M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Volumes I to V, International Academic Press, (2008),
http://www.i-b-r.org/Hadronic-Mechanics.htm

[16] R. M. Santilli, Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels, Kluwer Academic Publishers (2001),
http://www.santilli-foundation.org/docs/Santilli-113.pdf
Russian translation by A. K. Aringazin,
http://i-b-r.org/docs/Santilli-Hadronic-Chemistry.pdf

[17] R. M. Santilli, "Need of subjecting to an experimental verification the validity within a hadron of Pauli exclusion principle," Hadronic J. Vol. 1, 574-901 (1978),
http://www.santilli-foundation.org/docs/santilli-73.pdf

[18] I. Gandzha and J. Kadeisvili, New Sciences for a New Era, Sankata Printing Press, Nepal (2011),
http://www.santilli-foundation.org/docs/RMS.pdf

Post 59
Prof. Santilli! following your magnificent Post 58, in addition to the great honor reviewed in Post 19, I feel obliged to reproduce the words expressed by the famous British historian Sir Karl Popper in his inspiring book Schism in Physics, Cambridge University Press (1982) on Sir R. M. Santilli (http://santilli-foundation.org/santilli-nobel-nominations.html):

"I have mentioned Santilli, and I should like to say that he-one who belongs to a new generation - seems to me to move on a different path. Far be it from me to belittle the giants who founded quantum mechanics under the leadership of Planck, Einstein, Bohr, Born, Heisenberg, de Broglie, Schrodinger, and Dirac. Santilli too makes it very clear how greatly he appreciates the work of these men. But in his approach he 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 arguments in support of the view that quantum mechanics should not, without new tests, be regarded as valid in nuclear and hadronic physics, seem 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."

Post 60
Prof. Santilli, I have initiated the best study I can of your works and would appreciate your help in understanding steps that for you are perhaps trivial. The first one is the inapplicability of Scrhoedinger equation for the bound state of a proton and an electron at 10^{-13} cm. I can get nothing that makes physical sense despite their mutual "astronomical Coulomb attraction" you have mentioned. Thanks.

Post 61
Hi Post 60. I think you got it the way you put it: by using QM you get nothing that makes physical sense for the fusion of a proton and an electron into the neutron in the core of stars despite their huge attraction. I did study Prof. Santilli's long journey and I believe you should do the same. FIRSTLY, you should understand how hadronic mechanics makes full sense for the synthesis of particles with excess mass by studying the derivation of all (note, all) features of the π0 in its synthesis from the positronium despite about 132 MeV excess mass (!). This is best done in Table 5.2, page 849 of Prof. Santilli's originating paper http://www.santilli-foundation.org/docs/santilli-73.pdf. None of the various subsequent reviews come even close to that presentation. SECONDLY, you should understand how hadronic mechanics achieved a representation of all (note, all) features of the neutron in its synthesis from the proton and the electron at the non-relativistic level. Again, this is best done in Prof. Santilli's originating paper with no better second http://www.santilli-foundation.org/docs/Santilli-21.pdf. THIRDLY, to understand the relativistic treatment you got to study first Santilli's isosymmetries, particularly the Lorentz-Poincare'-Santilli isosymmetry, see the review http://eprdebates.org/docs/epr-review-ii.pdf. After you got such a knowledge, then you should study, again, Prof. Santilli's original relativistic representation of all (note, all) features of the neutron in its synthesis in the core of stars with no better presentation on record in my view http://www.santilli-foundation.org/docs/Santilli-18.pdf. But then you may ask why bother? To see the answer look around in academia. There is nothing besides rotten postures in opposing new discoveries to protect their turf. The sole scientific novelty around is that by Prof. Santilli. Therefore, sooner or later our Feds will finally understand that and test Santilli's hyperfusion between synthesized negatively charged deuterons and natural deuterons into helium, D(-1, 2, 1_up) + D(1, 2, 1_\down) = He(2, 4, 0) + 2e http://eprdebates.org/docs/epr-review-iii.pdf.At that point you will be the expert because orthodox physicists will only blab by comparison.

Post 62
Prof. Santilli, attending your lectures at EPR-2020 conference on the completion of QM as suggested by Einstien, Rosen and Podolsky was a great experience. Your arguments are foolproof and deserve to be acknowledged by the scientific community. You have opened new vistas for theoretical and experimental Physics as well as in the fields of Mathematics and Chemistry. Your work is epoch making and deserves to be awarded by the Nobel prize. Your dedication and devotion to the subject is unparalleled. In fact, your work is going to affect classical thinking giving way to a new way of thinking which is most modern.

Post 63
Dear Post 62, I believe I have provided ample proof that, when I was at BU, MIT, Harvard University, ICTP, JINR and other institutions I never looked for an academic career and solely searched for new scientific knowledge, at times against the view of my distinguished colleagues, because I knew then and know now the pressing need of new knowledge for the otherwise unsolvable, increasingly alarming environmental problems such as recycling nuclear waste, clean nuclear energies, clean combustion of fossil fuels et al. Thank you, Post 62, your nice words provide a sense to all these efforts for so many years. Best wishes, Ruggero Santilli

Post 64
Prof. Santilli, your recent release on Einstein's isodeterminism is brilliant. I am developing a deeply complimentary theory, and have a the following Question: Would the singlet coupling of a negative energy pseudophoton (with its implied reversal of properties within this system) and a positive energy photon add to spin two, or spin zero? Thanks!

Post 65
Dear Post 64, thanks for the intriguing and important question. To our knowledge, the pseudoproton is made up of ordinary matter, thus existing in our spacetime, because synthesized by our Directional Neutron Source via the compression of an electron inside a neutron. As such, the sole new features of the pseudoproton with respect to the proton are the reversal of the sign of the charge and of the direction of the magnetic moment. Under these conditions, a singlet state of a pseudoproton and a proton has spin zero. BUT, this view is based on the central feature of the synthesis of the neutron (which persists in the synthesis of the pseudoproton), namely, the compression of a particle with spin 1/2, the electron, inside an hyperdense particle with spin 1/2, the proton (the neutron), yields the total angular momentum 1/2 of the neutron (pseudoproton) because of the constrained angular momentum of the electron within a hyperdense hadron with spin 1/2. This feature is fully represented by the irregular SU(2) spin symmetry (for its treatment, see Section 3 of the paper http://eprdebates.org/docs/epr-review-iii.pdf, and for its application to neutron and pseudoproton, see Section 2.6 of http://eprdebates.org/docs/epr-review-ii.pdf). The corresponding important question of the total spin of a bound state of a true antiproton (existing in its isodual spacetime over isodual numeric fields) and a proton (existing in our spacetime over ordinary numeric fields) was raised by Evans Boney during the discussions of our recent International Teleconference on Einstein's Determinism, but we do not know the answer at this writing due to basic aspects currently under investigation. Ruggero

Post 66
Prof. Santilli, please indicate the reason for which the total spin of coupled antiproton-proton pair is unsettled. Thanks.

Post 67
Prof. Santilli, The bound state of the particle and its antiparticle is indeed crucial to consider, and I would like to consider it a bit further. First let's note that there are bound states for positronium and muonium that are more accessible than the proposed antiprotonium (?)... and I would suggest Prof. Kaplan's work developing MAGE as very interesting and relevant (https://arxiv.org/abs/1802.01438 ). But on to the math. As Prof. Santilli notes, there is indeed the question of 0 or 2 total spin (responding to Post 64), but let's examine further ramifications of this concern. For instance, gravitational mass. The isodual particle has mass -M, and the particle has mass M, when projected into the spacetime we live in. The usual two-body treatment would suggest breaking this into a center of mass and reduced mass, each of which has the sort of concern Prof. Santilli mentions.

Post 68
Dear Posts 66 and 67, your questions are deeply related and quite important indeed. Unfortunately, html commands are limited and, therefore. my comments will be at best rudimentary. The only way I know is to start from the foundations to check them out in order not to be sorry later. Also, I can express below my personal view and be grateful to anybody who has strong counterarguments. "THE" starting point is the lack of "completeness", in my view, of charge conjugation

(1)           ψC(t, r) = - ψ(t, r)

because it maps antiparticles in the spacetime and Hilbert space of particles, thus preventing the representation ofc matter-antimatter annihilation (since two positive masses cannot annihilate into light). For this reason, I "completed" charge conjugation into the isodual map, denoted with the upper index "d", which is also an anti-Hermitean map like charge conjugation [1],

(2)           ψd(t, r) = - ψ(- t, - r)

the main difference is that the isodual map must be applied to the totality of quantum mechanical quantities and all their operations You miss one isodual map and get an Italian minestrone. Despite its elementary character, the isodual map (2) has far reaching implications such as: the positive energy of particles is mapped into negative energy for antiparticles (Dirac 1929), thus allowing a quantitative representation of matter-antimatter annihilation; the Minkowskian spacetime is mapped into a new spacetime coexisting with our own; charge conjugation solely applies in a Hilbert space, while the isodual pam applies beginning at the classical level, with its application to a Hilbert space being a small particular case, thus rendering inevitable the study of the possible existence of antimatter galaxies; etc.To start addressing the issues raised by Posts 66 and 67, let us recall from Ref. [1] the maps of the quantum mechanical eigenvalue equation for spin and energy into their isodual images which have not raised controversies to date (below we assume E>0)

(3)           J3 × ψ(t, r) = +/- ½ ψ(t, r) - - > J3d ×d ψd(td, rd) = (-/+ ½) (- ×) [- ψ(-t, - r)]

(4)           H(r, p) × ψ(t, r) = E × ψ(t, r)    -->

           --> Hd(rd, pd) ×d ψd(td, rd) = (- H) (-×) [- ψ(-t, -r)] = - H(r, p) × ψ(- t, - r) =

            = Ed ×d ψd(td, rd) = - E × ψ(-t, -r)

Consequently, the spin and energy reverse their sign when represented in their isodual space as I believe we all agree. The open issues raised by Posts 66 and 67 occur in the projection of the isodual values into our spacetime. The projection adopted in Ref. [1] for reasons indicated below is given by

(5)           J3d×d ψ(t, r) = +/- ½ ψ(t, r)

(6)           Hd ×d ψ(t, r)] = E × ψ(t, r)

namely, the eigenvalues of the isodual quantities have to be computed on conventional Hilbert states because they represent our world.

It then follows that the projection in our Hilbert space of isodual spin an d energy coincide with conventional values. In this case, a particle-antiparticle state in singlet coupling has spin zero in our space as well as in the isodual space, while the energy of the positronium is positive in our space and negative in its isodual (for more details please inspect Section 2.3.14 'Isoselfdual bound states, page 131, Ref. [1]]).

Question: so where is the controversy? Answer: in Ref. [1], solely for isoselfdual states (see below) I assume projections of the type

(7)           Hd ×d ψ = (-H) (-×) &psi = H × ψ

while others assume the different projection

(8)           Hd × ψ = (-H) × &psi = - H × ψ

namely, they do not subject the product × to the isodual map, thus ending up with opposite results.

The reasons underlying my assumption are several. To begin, the isodual theory must be formulated on isodual numeric fields, namely, numbers with a negative unit which means that negative values are measured with negative unit. But then, the projection in our space of a negative isodual quantitive measured with negative unit has to be positive for consistency. This is a crucial assumption for the consistency of any theory on antimatter because NEGATIVE ENERGIES IN OUR SPACETIME VIOLATE CAUSALITY (DIRAC 1928), The only way I know to solve this basic flaw is via isodual numbers because a negative energy referred to negative units is as causal as a positive energy referred to positive units, and the same goes for time, etc.

extended particles and antiparticle systems that cannot be reviewed here (see Ref. [1]). In a nutshell, when isolated in vacuum, particles and antiparticle have everything opposite to each other. Annihilation then follows prior to any projection in one space or another. When in a state the deep entanglement needed for a bound state, the notions of "electron" and "positrons" as commonly understood are gone in favor of isoparticles much similar to two identical electrons turning their huge Coulomb repulsion into a huge attraction in their valence bond. To my understanding, the positive energy of the positronium is a result of the mutation of the structure of both particles and antiparticles. This is essentially what I know. Again, I gratefully invite criticisms of technical character, by keeping in mind that I am not an expert of epistemological studies. Cheers Ruggero Santilli

[1] R. M. Santilli, Isodual Theory of Antimatter with Applications to Antigravity, Grand Unifications and Cosmology, Springer (2006).
www.santilli-foundation.org/docs/santilli-79.pdf

Post 69
Prof. Santilli, thank you for your detailed review on your isodual theory of antimatter. I agree with your equations (5) and (6) because the product × is the base product of the theory beginning with the isodual numbers and, consequentially it must be subjected to isoduality. The implications are big and exciting. Congrats!

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