Neutrosophic Logic, Wave Mechanics, and Other Stories (Selected Works 2005-2008)

2009·2.4 MB·English

by  F. Smarandache

FLORENTIN SMARANDACHE & V. CHRISTIANTO
NEUTROSOPHIC LOGIC,
WAVE MECHANICS, AND
OTHER STORIES
SELECTED WORKS 2005-2008
FLORENTIN SMARANDACHE & V. CHRISTIANTO

NEUTROSOPHIC LOGIC,
WAVE MECHANICS, AND
OTHER STORIES
SELECTED WORKS 2005-2008
KOGAÏON ÉDITIONS, 2009

1
1
The front cover image represents the first author at a conference in
Indonesia in 2006 showing the journals "Progress in Physics" and
"Infinite Energy".
KOGAÏON ÉDITIONS, 2009
Division of CASA GROUP OF COMPANIES SRL
62, (cid:2)coala Her(cid:3)str(cid:3)u street, code 014153,
Bucharest - Romania, Europe
Website: www.kogaion-editions.com
e-mail: [email protected]
Tél./fax: [phone]
Copyright 2009 by Kogaïon Éditions and the Authors.
Plenty of ebooks can be downloaded from the following
Science Digital Library:
http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm
Peer Reviewers:
(a) Dr. M. Khoshnevisan -- School of Accounting and Finance, Griffith University,
Gold Coast, Queensland 9726, Australia
(b) Mark Alford, AFRL/RIEA, 525 Brooks Road, Rome, NY 13441-4503, USA
(c) Alok Dhital, Math & Sciences Dept., University of New Mexico, Gallup, NM
87301, USA
(ISBN-13): 978-973-7609-31-1
(EAN): 9789737609311
Published in Romania
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FOREWORD

There is beginning for anything; we used to hear that phrase.
The same wisdom word applies to us too. What began in 2005 as
a short email on some ideas related to interpretation of the Wave
Mechanics results in a number of papers and books up to now.
Some of these papers can be found in Progress in Physics or
elsewhere.

It is often recognized that when a mathematician meets a
physics-inclined mind then the result is either a series of endless
debates or publication. In our story, we prefer to publish rather
than perish.

Therefore, our purpose with this book is to present a selection of
published papers in a compilation which enable the readers to
find some coherent ideas which appear in those articles. For this
reason, the ordering of the papers here is based on categories of
ideas.

While some of these articles have been published in book format
elsewhere, we hope that reading this book will give the readers
an impression of the progress of our thoughts. A few other
papers are not yet published elsewhere, or being planned to
publish in other journal.

We wish to extend our sincere gratitude to plenty of colleagues,
friends and relatives all around the world for sharing their ideas,
insightful discussions etc. Special thanks to D. Rabounski, S.
Crothers, L. Borissova for their great service in Progress in
Physics journal.

One of these authors (VC) would like to thank to Profs. A.
Yefremov and M. Fil’chenkov for all hospitality extended to him
in the Institute of Gravitation and Cosmology of PFUR, where
this book is prepared. Discussions with Prof. V.V. Kassandrov,
Prof. V. Ivashchuk, & Prof. Yu P. Rybakov are appreciated. Many
thanks also to Dr. S. Trihandaru and others from UKSW, Central
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Java,Indonesia. Sincere thanks to good friends in PFUR,
especially to D. Kermite, Y. Umniyati, Anastasia Golubtsova &
Serguey– all other friends are of course worth mentioning here,
but the margin of this book is quite limited to mention all of you.

And to all other scientist colleagues, allow us to say: Full speed
ahead!

FS & VC, March 2009

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NEUTROSOPHIC LOGIC, WAVE MECHANICS, AND OTHER
STORIES: SELECTED WORKS 2005-2008

CONTENT

Foreword 3
Content 5

A. Unmatter and the Elementary Particles

1. “A new form of Matter-Unmatter, composed of Particles and Anti-
Particles,” – F. Smarandache (PIP, Vol. 1, 2005) 8
2. “Verifying Unmatter by Experiments, More types of Unmatter, and
a Quantum Chromodynamics formula,” – F. Smarandache (PIP, Vol. 2,
2005) 11
3. “Unmatter Entities inside Nuclei, predicted by the Brightsen
Nucleon Cluster Model,” – F. Smarandache & D. Rabounski (PIP, Vol.
1, 2006) 15
4. “On Emergent Physics, Unparticles and Exotic Unmatter States,” –
E. Goldfain & F. Smarandache, (PIP Vol. 4, 2008) 20
5. “Thirty Unsolved problems in the physics of elementary particles,” -
V. Christianto & F. Smarandache (PIP Vol.4, 2007) 26

B. Entanglement, Neutrosophic Logic, and applications

6. “There is no speed barrier for a wave phase nor for Entangled
Particles,” – F. Smarandache (PIP, Vol. 1, 2005) 29
7. “Entangled states and Quantum Causality Threshold in the General
Theory of Relativity,” – D. Rabounski, L. Borissova, & F. Smarandache
(PIP, Vol. 2, 2005) 31
8. “Quantum Quasi-Paradoxes and Quantum Sorites Paradox,” – F.
Smarandache (PIP, Vol. 1, 2005) 38
9. “The Neutrosophic Logic view to Schrödinger’s cat paradox,” – F.
Smarandache & V. Christianto (PIP, Vol. 2, 2006) 40
10. “The Neutrosophic Logic view to Schrödinger’s cat paradox,
Revisited,” – V. Christianto & F. Smarandache (PIP, Vol. 3, 2008) 45
11. “A note on Geometric and Information Fusion Interpretation of
Bell’s theorem and Quantum Measurement,”– F. Smarandache & V.
Christianto (PIP, Vol. 4, 2006) 50
5
12. “Extension of Inagaki General Weighted Operators and a new
fusion Rule Class,”– F. Smarandache (June 2008) 55
13. “n-ary Fuzzy Logic and Neutrosophic Logic Operators,”– F.
Smarandache & V. Christianto (Octogon, to appear 2009) 59

C. Wave Mechanics, Gravitation and Quantization in
Astrophysics

14. “Schrödinger equation and the Quantization of Celestial
systems,”– F. Smarandache & V. Christianto (PIP, Vol. 2, 2006) 74
15. “Plausible explanation of quantization of intrinsic redshift from
Hall effect and Weyl Quantization,”– F. Smarandache & V. Christianto
(PIP, Vol. 4, 2006) 79
16. “Numerical Solution of Time-dependent Gravitational Schrödinger
equation,”– V. Christianto & F. Smarandache (PIP, Vol. 2, 2007) 83
17. “Kaluza-Klein-Carmeli metric from Quaternion-Clifford-space,
Lorentz’s force and some observables,”– V. Christianto & F.
Smarandache (PIP, Vol. 2, 2008) 88
18. “A note of Extended Proca equations and Superconductivity,”– V.
Christianto & F. Smarandache (PIP, Vol. 1, 2009) 95

D. Other topics: Quaternion space and their applications

19. “Less mundane explanation of Pioneer anomaly from Q-
relativity,”– F. Smarandache & V. Christianto (PIP, Vol. 1, 2007) 99
20. “Notes on Pioneer anomaly acceleration by Satellite-Shift formula
of Quaternion Relativity,”– A.P. Yefremov (PIP, Vol. 2, 2007) 103
21. “Reply to Notes on Pioneer anomaly acceleration by Satellite-Shift
formula of Quaternion Relativity,”–V. Christianto & F. Smarandache
(PIP, Vol. 3, 2007) 107
22. “Yang-Mills field from Quaternion Space Geometry, and its Klein-
Gordon representation,” – A.P. Yefremov, F. Smarandache , V.
Christianto (PIP, Vol. 4, 2007) 110
23. “Numerical solution of biquaternion Klein-Gordon equation,”–V.
Christianto & F. Smarandache (PIP, Vol. 1, 2008) 119
24. “On PT-symmetric periodic potential, Quark Confinement,” –V.
Christianto & F. Smarandache (PIP, Vol. 1, 2009) 121

Pictures at an exhibition (2006) 124
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FLORENTIN SMARANDACHE & V. CHRISTIANTO

NEUTROSOPHIC LOGIC,
WAVE MECHANICS, AND
OTHER STORIES
SELECTED WORKS 2005-2008

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April,2005 PROGRESSINPHYSICS Volume1
A New Form of Matter—Unmatter, Composed of Particles and Anti-Particles
FlorentinSmarandache
Dept.ofMathematics,UniversityofNewMexico,200CollegeRoad,Gallup,NM87301,USA
E-mail:[email protected];[email protected]
Besidesmatterandantimattertheremustexistunmatter(asanewformofmatter)in
accordancewiththeneutrosophytheorythatbetweenanentity<A>anditsopposite
<AntiA> there exist intermediate entities <NeutA>. Unmatter is neither matter nor
antimatter, but something in between. An atom of unmatter is formed either by (1):
electrons,protons,andantineutrons,orby(2): antielectrons,antiprotons,andneutrons.
At CERN it will be possible to test the production of unmatter. The existence of
unmatterintheuniversehasasimilarchancetothatoftheantimatter,anditsproduction
alsodifficultforpresenttechnologies.
1 Introduction Etymologically“un-matter”comesfrom[ME<OE,akin
toGr. an-,a-,Latin in-,andtothenegativeelementsin no,
Thisarticleisanimprovedversionofanoldmanuscript[1]. not, nor] and [ME matie`re < OFr < Latin material] matter
Thisisatheoreticalassumptionaboutthepossibleexistence (see[3]),signifyingno/without/offthematter.
of a new form of matter. Up to day the unmatter was not There are two types of unmatter atoms, that we call
checkedinthelab. unatoms:
According to the neutrosophy theory in philosophy [2],
u1. The first type is derived from matter; and a such
betweenanentity<A>anditsopposite<AntiA>thereexist
unmatter atom is formed by electrons, protons, and
intermediate entities <NeutA> which are neither <A> nor
antineutrons;
<AntiA>.
u2. Thesecondtypeisderivedfromantimatter,andasuch
Thus,between“matter”and“antimatter”theremustexist
unmatteratomisformedbyantielectrons,antiprotons,
somethingwhichisneithermatternorantimatter,let’scallit
andneutrons.
UNMATTER.
In neutrosophy, <NonA> is what is not <A>, i.e. One unmatter type is oppositely charged with respect to
<NonA> = <AntiA>∪<NeutA>. Then, in physics, NON- theother,sowhentheymeettheyannihilate.
MATTER is what is not matter, i.e. nonmatter means anti- Theunmatternucleus,calledunnucleus,isformedeither
mattertogetherwithunmatter. byprotonsandantineutronsinthefirsttype,orbyantiprotons
andneutronsinthesecondtype.
The charge of unmatter should be neutral, as that of
2 Classification
matterorantimatter.
The charge of un-isotopes will also be neutral, as that
A. Matterismadeoutofelectrons,protons,andneutrons.
of isotopes and anti-isotopes. But, if we are interested in a
Each matter atom has electrons, protons, and neutrons, negative or positive charge of un-matter, we can consider
excepttheatomofordinaryhydrogenwhichhasnoneutron. an un-ion. For example an anion is negative, then its cor-
The number of electrons is equal to the number of pro- responding unmatter of type 1 will also be negative. While
tons,andthusthematteratomisneutral. takingacation,whichispositive,itscorrespondingunmatter
oftype1willalsobepositive.
B. Oppositely,theantimatterismadeoutofantielectrons, Sure, it might be the question of how much stable the
antiprotons,andantineutrons. unmatteris,asJ.Murphypointedoutinaprivatee-mail.But
Diracalsotheoreticallysupposedtheexistenceofantimatter
Each antimatter atom has antielectrons (positrons), anti-
in1928whichresultedfromDirac’smathematicalequation,
protons, and antineutrons, except the antiatom of ordinary
and finally the antimatter was discovered/produced in large
hydrogenwhichhasnoantineutron.
accelerators in 1996 when it was created the first atom of
The number of antielectrons is equal to the number of
antihydrogenwhichlastedfor37nanosecondsonly.
antiprotons,andthustheantimatteratomisneutral.
Theredoesnotexistanunmatteratomofordinaryhydro-
C. Unmatter means neither matter nor antimatter, but in gen, neither an unnucleus of ordinary hydrogen since the
between,anentitywhichhascommonpartsfromboth ordinary hydrogen has no neutron. Yet, two isotopes of
ofthem. the hydrogen, deuterium (2H) which has one neutron, and
F.Smarandache.ANewFormofMatter—Unmatter,ComposedofParticlesandAnti-Particles 9
8
Volume1 PROGRESSINPHYSICS April,2005
artificially made tritium (3H) which has two neutrons have We can collide unmatter 1 with unmatter 2, or unmatter
corresponding unmatter atoms of both types, un-deuterium 1withantimatter,orunmatter2withmatter.
and un-tritium respectively. The isotopes of an element X Whentwo,three,orfourofthem(unmatter1,unmatter2,
differ in the number of neutrons, thus their nuclear mass is matter, antimatter) collide together, they annihilate and turn
different,buttheirnuclearchargesarethesame. into energy which can materialize at high energy into new
For all other matter atom X, there is corresponding an particlesandantiparticles.
antimatteratomandtwounmatteratoms
Theunmatteratomsarealsoneutralforthesamereason
4 Existenceofunmatter
that either the number of electrons is equal to the number
ofprotonsinthefirsttype,orthenumberofantielectronsis
Theexistenceofunmatterintheuniversehasasimilarchance
equaltothenumberofantiprotonsinthesecondtype.
tothatoftheantimatter,anditsproductionalsodifficultfor
Ifantimatterexiststhenahigherprobabilitywouldbefor
presenttechnologies.AtCERNitwillbepossibletotestthe
theunmattertoexist,andreciprocally.
productionofunmatter.
Unmatter atoms of the same type stick together form
Ifantimatterexiststhenahigherprobabilitywouldbefor
an unmatter molecule (we call it unmolecule), and so on.
theunmattertoexist,andreciprocally.
Similarlyonehastwotypesofunmattermolecules.
The1998AlphaMagneticSpectrometer(AMS)flownon
The isotopes of an atom or element X have the same
the International Space Station orbiting the Earth would be
atomic number (same number of protons in the nucleus)
abletodetect,besidescosmicantimatter,unmatterifany.
butdifferentatomicmassesbecausethedifferentnumberof
neutrons.
Therefore,similarlythe un-isotopesoftype1 ofXwill 5 Experiments
beformedbyelectrons,protons,andantineutrons,whilethe
Besidescollidingelectrons,orprotons,wouldbeinteresting
un-isotopesoftype2 ofXwillbeformedbyantielectrons,
incollidingneutrons.Also,collidinganeutronwithananti-
antiprotons,andneutrons.
neutroninaccelerators.
An ion is an atom (or group of atoms) X which has
Wethinkitmightbeeasiertoproduceinanexperiment
last one or more electrons (and as a consequence carries a
anunmatteratomofdeuterium(wecancallitun-deuterium
negative charge, called anion, or has gained one or more
oftype1).Thedeuterium,whichisanisotopeoftheordinary
electrons (and as a consequence carries a positive charge,
hydrogen, has an electron, a proton, and a neutron. The
calledcation).
ideawouldbetoconvert/transforminadeuteriumatomthe
Similarly to isotopes, the un-ion of type 1 (also called
neutronintoanantineutron,thenstudythepropertiesofthe
un-anion 1 or un-cation 1 if resulted from a negatively
resultingun-deuterium1.
or respectively positive charge ion) of X will be formed
Or,similarlyforun-deuterium2,toconvert/transformin
by electrons, protons, and antineutrons, while the un-ion of
a deuterium atom the electron into an antielectron, and the
type2ofX(alsocalledun-anion2orun-cation2ifresulted
proton into an antiproton (we can call it un-deuterium of
fromanegativelyorrespectivelypositivechargeion)willbe
type2).
formedbyantielectrons,antiprotons,andneutrons.
Or maybe choose another chemical element for which
Theionandtheun-ionoftype1havethesamecharges,
any of the previous conversions/transformations might be
whiletheionandun-ionoftype2haveoppositecharges.
possible.
D. Nonmatter means what is not matter, therefore non-
matter actually comprises antimatter and unmatter.
6 Neutronsandantineutrons
Similarlyonedefinesanonnucleus.
Hadrons consist of baryons and mesons and interact via
3 Unmatterpropulsion strongforce.
Protons,neutrons,andmanyotherhadronsarecomposed
Wethink(asapredictionorsupposition)itcouldbepossible from quarks, which are a class of fermions that possess
at using unmatter as fuel for space rockets or for weapons a fractional electric charge. For each type of quark there
platforms because, in a similar way as antimatter is presup- exists a corresponding antiquark. Quarks are characterized
posed to do [4, 5], its mass converted into energy will be by properties such as flavor (up, down, charm, strange, top,
fuelforpropulsion. orbottom)andcolor(red,blue,orgreen).
It seems to be a little easier to build unmatter than Aneutronismadeupofquarks,whileanantineutronis
antimatterbecauseweneedsayantielectronsandantiprotons madeupofantiquarks.
only (no need for antineutrons), but the resulting energy A neutron (see [9]) has one Up quark (with the charge
2 19
mightbelessthaninmatter-antimattercollision. of +3×1.606×10 C) and two Down quarks (each with the
10 F.Smarandache.ANewFormofMatter—Unmatter,ComposedofParticlesandAnti-Particles
9