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**COMMENTS ON THE RECENT HYPOTHESIS OF NEGATIVE MASSES**

*The author of recent paper [1] submit the hypothesis that new dynamical effects in Bose-Einstein Condensation can be interpreted via negative masses. Despite a bibliography unusually vast for a Letter, PRL editors did not request the authors to quote the originator of negative masses, P. A. M. Dirac, because such a quotation would have brought to light the fact that negative masses violate causality in QM. In addition, PRL editors did not add comments on the interpretation of negative masses as characterizing antimatter; because such an interpretation would imply violation of the PCT theorem and other inconsistencies [2].Since Prof. Santilli (Email: research-at-thunder-energies-dot-com) is a leading expert in the field, we contacted him and he released the following comments:Newton's basic notion is that of "massive points," subsequently adopted by Galileo and Einstein, because necessary for compatibility with the local-differential character of the differential calculus. The representation of particles with their extended character has requested a necessary broadening of the differential calculus into the covering isodifferential calculus [3-6]. New dynamical effects not representable with Newton's laws are then evident to all.For a truly rudimentary outline,m the first step is the isotopic (axiom-preserving) lifting of the conventional product AB of all QM quantities into the isoproduct I first presented in monographs [3] I wrote when I was at Harvard under DOE support(1) A*B = ATB, T > 0.The simple realization of the isotopic element T(2) T = Diag (a, b, c, d), a, b, c, d > 0allows an immediate representation of the spheroidal share of particles with semi axes a, b, c, as well as a representation of their density d. The isotopic lifting of functional analysis, metric spaces, etc. then follows by lifting all associative products into form 91).The next step is the generalization of ordinary numbers n, m into isonumbers with generalized unit I*, called isounit, and related rules I wrote while visiting the JINR in Dubna, Russia in 1993 [4](3) I* = 1/T, n' = nI*, m' = mI*, n'*m' = (nm)I*, .The generalization of numeric fields turned out to be necessary to maintain causality because isotope formulations are noncanonical at the classical level and nonunitary at the operator level (as an example the problem of causality for Dirac's negative masses is resolved by assuming a "negative"-definite new unit [2]).The invariance of the formulation then requires the lifting of the Newton-Leibnitz differential or into the isodifferential that I first presented in the 1996 mathematical memoir [5](4) d' r' = T d[rI*(r, ...)] = dr + r T dI*(r, ...)Isomathematcs is the generalization of all branches of 20th century applied mathematics via the use of isoproduct (1) and related reformulation of functional analysis, metric spaces, geometries, Lie's theory, etc. formulated on over isofields and elaborated via the isodifferential calculus. The mathematical literature on isomathematics is nowadays quite vast. I merely quote here the six volumes by Prof. D Svetlin Georgiev [6] on the isodifferential calculus and the PhD. course going on at advanced mathematics departments http://www.i-b-r.o*

[3] R. M. Santilli, Foundation of Theoretical Mechanics,

Volume I (1978) and II (1982) Springer-Verlag, Heidelberg, Germany,

http://www.santilli-foundation

http://www.santilli-foundation

[4] R. M. Santilli, ``Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and "Hidden Numbers," of Dimension 3, 5, 6, 7,"

Algebras, Groups and Geometries Vol. 10, 273 (1993)

http://www.santilli-foundation.org/docs/Santilli-34.pdf

[5] R. M. Santilli, ``Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures,"

http://www.santilli-foundation

[5] R. M. Santilli, ``Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures,"

Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996),

http://www.santilli-foundation.org/docs/Santilli-37.pdf

[6] S. Georgiev, Foundations of the IsoDifferential Calculus,

Volumes, I, II, III, IV,V, and VI Nova Scientific Publisher (2015 on).

**HADRONIC MECHANICS**

[7] R. M. Santilli, "Relativistic hadronic mechanics: nonunitary, axiom-preserving completion of relativistic quantum mechanics,"

Found. Phys. Vol. 27, 625-729 (1997),

http://www.santilli-foundation.org/docs/Santilli-15.pdf

[8] R. M. Santilli, Elements of Hadronic Mechanics,

Vol. I and Vol. II (1995) [15b], Academy of Sciences, Kiev,

http://www.santilli-foundation.org/docs/Santilli-300.pdf

http://www.santilli-foundation.org/docs/Santilli-301.pdf

[9] I. Gandzha and J. Kadeisvili , New Sciences for a New Era:

Sankata Printing Press, Nepal (2011)

http://www.santilli-foundation.org/docs/RMS.pdf

[10] R. M. Santilli, "An Introduction to New Sciences for a New Era,"

Clifford Analysis, Clifford Algebras and their Applications, in press (2017)

http://www.santilli-foundation.org/docs/new-sciences-new-era.pdf

THE NEUTRON SYNTHESIS FROM THE HYDROGEN ATOM

[11] R. M. Santilli, ``Apparent consistency of Rutherford’s hypothesis on the neutron structure via the hadronic generalization of quantum mechanics - I: Nonrelativistic treatment”, ICTP communication IC/91/47 (1992)

http://www.santilli-foundation.org/docs/Santilli-150.pdf

[12] R. 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

[13] R. M. Santilli, ``Confirmation of Don Borghi’s experiment on the synthesis of neutrons," arXiv publication, August 15, 2006

http://arxiv.org/pdf/physics/0608229v1.pdf

[14] 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, 14 (2014) 405–41

www.thunder-energies.com/docs/neutron-synthesis-2014.pdf

[15] R. M. Santilli, ``12 minutes Film on the Laboratory Synthesis of Neutrons from a Hydrogen Gas"

www.world-lecture-series.org/newtron-synthesis-08-14

http://www.santilli-fo

[6] S. Georgiev, Foundations of the IsoDifferential Calculus,

Volumes, I, II, III, IV,V, and VI Nova Scientific Publisher (2015 on).

[7] R. M. Santilli, "Relativistic hadronic mechanics: nonunitary, axiom-preserving completion of relativistic quantum mechanics,"

Found. Phys. Vol. 27, 625-729 (1997),

http://www.santilli-foundation

[8] R. M. Santilli, Elements of Hadronic Mechanics,

Vol. I and Vol. II (1995) [15b], Academy of Sciences, Kiev,

http://www.santilli-foundation

http://www.santilli-foundation

[9] I. Gandzha and J. Kadeisvili , New Sciences for a New Era:

Sankata Printing Press, Nepal (2011)

http://www.santilli-foundation

[10] R. M. Santilli, "An Introduction to New Sciences for a New Era,"

Clifford Analysis, Clifford Algebras and their Applications, in press (2017)

http://www.santilli-foundation

THE NEUTRON SYNTHESIS FROM THE HYDROGEN ATOM

[11] R. M. Santilli, ``Apparent consistency of Rutherford’s hypothesis on the neutron structure via the hadronic generalization of quantum mechanics - I: Nonrelativistic treatment”, ICTP communication IC/91/47 (1992)

http://www.santilli-foundation

[12] R. 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

[13] R. M. Santilli, ``Confirmation of Don Borghi’s experiment on the synthesis of neutrons," arXiv publication, August 15, 2006

http://arxiv.org/pdf/physics/0

[14] 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, 14 (2014) 405–41

www.thunder-energies.com/docs/

[15] R. M. Santilli, ``12 minutes Film on the Laboratory Synthesis of Neutrons from a Hydrogen Gas"

www.world-lecture-series.org/n

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