Journal of Modern Physics, 2013, 4, 1159-1164
http://dx.doi.org/10.4236/jmp.2013.49155 Published Online September 2013 (http://www.scirp.org/journal/jmp)

TORI Axioms and the Application in Physics
Dmitrii Kouznetsov
Institute for Laser Science, University of Electro-Communications, Chofu, Japan
Email: dima@ils.uec.ac.jp, DmitriiKouznetsov@gmail.com
Received June 12, 2013; revised July 15, 2013; accepted August 9, 2013
Copyright © 2013 Dmitrii Kouznetsov. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACTTORI refers to the Tools for Outstanding Research and Investigation; the site with this name has been available since
March 2011 to February 2013 at http://tori.ils.uec.ac.jp; the clone is available at http://mizugadro.mydns.jp/t. TORI isbased on 6 axioms; any scientific concept is postulated to have the following properties: applicability, verifiability, refutability, self-consistency, principle of correspondence and pluralism. The examples of application in physics are suggested.
Keywords: Laws of Conservation; Fundamental Principles

1. Introduction
This article describes methodology used to built-up the
special scientific site called TORI [1], which is abbreviation of Tools for Outstanding Research and Investigation.
Since 2011 March to 2013 February 27, the site was available at http://tori.ils.uec.ac.jp/TORI [2]. The aggressive
removal of that site from the free access indicates theimportance of the problems touched there. Then, the cloneof TORI is arranged at http://mizugadro.mydns.jp/t [3].
The main principles of TORI are presented in this article.
The article is organized in the following way. Section
2 lists the axioms that are postulated as criteria to distinguish Science from other knowledge (religion, art, customs). Section 3 indicates, that the TORI axioms are notso new as they may look. Section 4 declares the satisfaction of the personal curiosity of researchers as main goalof Science. The TORI axioms appear as justification ofthis goal. Section 5 provides basic examples of application of the TORI axioms in Optics. Section 6 suggests
more examples of application of the TORI axioms. Section 7 discusses the future improvement of the methodology. Section 8 suggests the future ways of practical useof the TORI axioms.

2. Axioms
TORI appears as scientific philosophy (and, perhaps,
even scientific religion), based on 6 dogmas, postulates,
listed below. These postulates, or axioms, make difference between Science and pseudoscience, between science and various religions. TORI deals with concepts,
satisfying the following axioms:
Copyright © 2013 SciRes.

1) Applicability: The concept has some limited rangeof validity, distinguishable from the empty set.
2) Verifiability: In the terms of the already accepted
concepts, some specific experiment with some specificresult, that confirms the concept, can be described.
3) Refutability: In the terms of the concept, somespecific experiment with some specific result, that negates the concept, can be described.
4) Self-consistency: No internal contradictions of theconcept are known.
5) Principle of correspondence: If the range of validity of a new concept intersects the range of validity of
another already accepted concept, then, the new concept
either reproduces the results of the old concept, or indicates the way to refute it. (For example, the estimate of
the range of validity of the old concept may be wrong).
6) Pluralism: Mutually-contradictive concepts may
coexist; if two concepts, satisfying axioms 1 - 5, havesome common range of validity, then, in this range, thesimplest of them has priority.
These axioms were suggested in the Russian journal“Uspekhi” [4] (in Russian) and in the First issue of the“Far East Journal of Mechanical Engineering and Physics” [5]. Then, the special site, TORI, had been designed
to collect and develop concepts, based on axioms 1-6
above. Since that, these axioms can be referred as “TORI
axioms”.

3. Axioms TORI Are Not New
Axioms 1 - 6 above are not so original. Similar ideas had
been declared by various researchers in century 20 and
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D. KOUZNETSOVeven before. Since the postulating of the 6 axioms aboveat [1,3,4,5] and presenting them at the Sugadaira summer
school [6], I got many questions and suggestions to reduce, simplify the set of axioms. The need of each ofthem is indicated below.
Statement of Axiom 1, that the range of validity of theconcept should be limited, had been suggested to withdraw from the First axiom. Practically, this refers to extension of the range of validity of some concept to theFull Set. Empirically it is known, that the considerationof elements of the Full Set leads to contradictions; forexample, the “Barber paradox”: The barber in the military corpus is ordered to shave everybody, who does notshave himself: Should he shave himself?. Generalizing
this paradox, the “barber” should be replaced to “set”,
and “shave” should be replaced to “include as element”.
In order to avoid such paradoxes, the limit of applicability is important. Especially dangerous is consideration of
any concept that includes itself into area of applicability.
For this reasons, while possible, I do not treat the TORI
axioms, by themselves, as a scientific concept. Let thisset of axioms be considered as some special kind of religion; then, the only applications of these axioms in the
research activity should be qualified as “Science” (butnever the elaboration of these axioms). Then, the barber,
mentioned above, will never have need even to think
about shaving himself.
Need of verifiability (Axiom 2) comes from many
philosophies; in particular, the idea to recognize the tree
by its fruits is specified in the Bible; if some tree is declared to be fruitful, let it bring at least one fruit. Verifiability seems to be the oldest principle of science.
Requirement of refutability (Axiom 3) had been suggested by Karl Popper [7-9]. Concept, that does not allow
its refutation, cannot predict any non-trivial phenomenon:
any result of any experiment, observation, calculus canbe interpreted in favor of the concept. Popper uses term
“falsifiability”, that may have different (and sometimes
opposite) meaning; in particular, at the transliteration toother languages. For this reason, term “Refutability” isused instead.
Importance of Axiom 4 (self-consistency) can be seenfrom the analysis of the official methodology that wascompulsory in the USSR. The dialectics had been postulated as the base of the “omnipotent” and the only true
Marx theory. Then, with this pretext, many branches of
Science were attacked (Theory of relativity, Quantum
mechanics, Genetics, Cybernetics, etc.). With Axiom 4,
no dialectics, no doublethink [10] is allowed in any scientific concept; two independent researchers applying theconcept to some case are supposed to come the same
predictions. In order to avoid phenomena, typical for the
USSR and described by Orwell, the self-consistency isdeclared in the special axiom.
Copyright © 2013 SciRes.

The correspondence principle (Axiom 5) had beensuggested by Niels Bohr [11], aiming the application to
Quantum Mechanics; however, the principle is much moregeneral and should be applied to other concepts too.
Axiom 6 (pluralism) is necessary to protect the new,alternative concepts, while they are not yet developed
sufficiently to get status of principal; the tolerance withrespect to the new concepts allows the scientific revolutions considered by Thomas Kuhn [12].

4. Goal of Science
In TORI, the human knowledge, based on axioms above,is qualified as Science. The main goal of science is declared to be satisfaction of the personal curiosity of theresearchers. Then, the TORI axioms provide the apology,
the excuse, the justification, why the money of the taxpayers should be spend for the researcher’s curiosity. The
researches that do not satisfy the TORI axioms, contrary,should not get foundation from the taxpayers.
Observations of development of pseudoscientific projects indicate, that the curiosity is the key point of any
scientific research; there is no other way to make science.
Some projects, initially created as scientific, have to continue, in order to provide the foundation for the colleagues
employed, even if the need to reconsider the main doctrine of the project becomes evident. For example, thebig projects of building of the nuclear fusion power planton the base of laser ignition of targets continued longafter the failure of these projects become evident. The
continuation of those projects had been justified by theneeds of the industry. Generally, the attempts to submit
Science to other, more practical purposes, causes its profanation; it converts to the business of milking the budget,and leads to the frauds; and the colleague, being told
about the new scientific problem, ask first the economical question: “What is my personal profit in this activity?” In some cases, the main goal of science above overlaps with economical interests of the business persons andadministrators; in these cases, the certain branch of science, certain scientific projects get huge financial support. Often, this support replaces the curiosity, becomesthe main goal, killing the initially scientific orientation of
the project.
The TORI axioms help to reveal the scientific frauds,
but also to catch the unwanted errors. In such a way, theTORI axioms push the research into development of new,“outstanding” concepts, that can be verified, revised, used,and easy refuted as soon as a new, more efficient concept
happens to be valid in the same range of applicability.
The TORI axioms appear as empirical guess; it is wain
to try to “prove” them. They cannot be proven; the only
their efficiency in the research can be compared to that ofanother systems of postulates. The efficiency of TORI
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axioms can be compared to that of the Marx-Lenin philosophy (that was compulsory in the USSR and had suggested many predictions that happened to be just wrong).
The efficiency of TORI can be compared to that of dogmas of Christians (which did not prevent them from crusades, nor from the inquisition, nor from participation ofchristians at both sides of the front line during the World
Wars). Results of application of TORI can be compared
to any system of dogmas of any other religion, methodology, philosophy.
According to declaration above (not to apply TORI tothemselves), the comparison of efficiency of TORI tothat of other systems of concepts falls out of competenceof TORI; therefore, this comparison is not consideredhere anymore.

5. Laser Science
Misinterpretations, discussions, conflicting concepts exist in any science, and the Laser Science is not exception.
In this section, few examples are mentioned, in which themethodology TORI (even while it had not yet been declared) had been used to defend the correct, self-consistent interpretation and/or to refute some results as “wrong”.
In order to avoid citing of a hundred of references, below,
the only my articles with the solutions are mentioned; thecriticized articles are cited there.
The idea of quantum consideration of the optical solitons had been considered in century 20. The photon wave
function, that can be interpreted as a classical soliton, hadbeen constructed. Two colleagues had calculated the time
evolution of the distribution of the intensity operator;
they found that this distribution spreads with time. On
the base of this observation, they made conclusion, thatthe quantum fluctuations annihilate the optical soliton. It
took serious efforts to show that such a concept is wrong.
The main difficulty was, that initially, the statement
about quantum annihilation had not been formulated as ascientific concept, namely, neither ways of verification
nor ways of the refutation had been indicated. Roughly,
the annihilation means that parts of the soliton (id est,
photons or clusters of photons) can be found, registeredat large mutual separation, say, big in comparison to thewidth of the initial soliton. Inability to detect such separated particles can be interpreted as sufficient evidence
for refutation of the concept of the quantum annihilation.
The detection of separated (un-coupled) photons corresponds to the four-order correlation for the photon wave
function. Then such a correllator had been calculated [13,14] (and happened to be stable); the concept of quantum
annihilation of the optical soliton had been refuted. Now
the concept of quantum stability of the idealized opticalsoliton is accepted by the scientific community.
In century 20, talking about Quantum Optics, it was
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convenient to consider the quantum oscillator. Such phenomena as squeezing and the fractal revival of the quantum wave packets had been discussed. The concept of the
optical filed as quantum oscillator was supposed to bevalid in all cases. The limits of description of the lightwith a single mode (that is in certain sense equivalent toa harmonic oscillator) were not even mentioned. The useof the First axiom of TORI would reveal this fault. The
estimates of the efficiency of the excitation of othermodes by the simple nonlinearity [15] had revealed thatthe single-mode approximation is quite limited, at least,
for the traveling waves and pulses. Some squeezing canbe achieved in such a configuration, but no fractal revival
is possible: the state of photons in the chosen mode becomes entangled with states of field in other modes. Thisentanglement dominates; at the consideration of a single
mode, it appears as thermal noise that is much stronger
than the effect expected. In such a way, no fractal revival
can be achieved in traveling wave. Indeed, during 15
years since that prediction, no fractal revival of thequasi-classical wave packets in the traveling wave had
been reported. The range of applicability of the description of light as quantum oscillator happens to be very
narrow.
The idea of combining of light guided in optical fibers,
at the appropriate splicing and splitting, revives again andagain in various countries. The increase of the brightness
had been expected for the multimode optical pump at thelinear combining of fiber delivering the pump (Arizona,2003). The real-time discussion had prevented the publishing of such a concept. Indeed, the concept does notsatisfy the Axiom 5 (principle of correspondence): therange, where one still can use the Liouville Theorem, thatprohibits the increases of brightness in linear optical systems, had not been indicated. The careful measurement
confirmed, that the combining of guided light enhances
the numerical aperture, occupied by the beam; this sets
the natural limit of the combing.
Another application of the correspondence principle refers to the wonderful properties of the Yb-doped Gadolinium-based ceramics. Many curves of the efficient
cross-sections of the the laser transition had indicated thestrong violation of the McCumber relation. No indication
to narrowing of limits of applicability of the McCumber
relation had been supplied in the articles that promoted
the new laser material. On the base of the correspondence principle (axiom 5), the curves published in various journals were qualified as errors [16]. In that specificcase, the mistake had been attributed to the re-absorption;
the samples were not optically thin, as the treatment of
the primary data implied.
Recently, the formalism of superfunctions [17-25] had
beed suggested, that allows to deal with the opticallythick samples and still recover the local properties of the
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laser materials [24]; the improvement of precision ofcharacterization of optical materials is expected with thisformalism.
The lack of pluralism (Axiom 6) made difficulties in
discussion and promotion of the interpretation of the quantum reflection from the ridged mirrors in terms of the
Zeno effect. The only simplicity of the formula suggested
and the tremendous agreement with the fresh data forquantum reflection of He atoms saved the new concept,
and allowed the publication of the corresponding theory[27,28].
Perhaps, any researcher had observed the wrong publications, statements, presentations, where the mistake could
be revealed with axioms TORI, without to drill throughthe deduction, nor dig deep into the experimental set-up.
Usually, there is no need to declare the publication as“wrong”, it is sufficient to indicate, which basic principle
should be revised on the base of the new result. I suggest
only one example: “Medium with such a wonderful properties is very interesting. It should allow to make not only
new efficient laser, but also the perpetual motion machine of Second kind.” Usually, the authors are not readyto negate the fundamental principles, and consider such a
diplomatic construction as kind of accusation, and sometimes found mistakes in their deductions or experiments.
After to get some new result, the researcher is supposed to formulate it as refutable concept, and try to refute it by himself. At the Bisson-effect (Switching ofemissivity and photoconductivity in Yb-doped ceramics),
the pump light is converted to the emission of white light,
if the pump power exceeds some threshold value [29].
The initial estimate of size of the pumped spot and thetotal amount of power converted to the white visible light
leaded to estimate of the effective temperature. This effective temperature happened to be well above the temperature of melting of the sample. That estimate leaded
to the conjecture, that the new quantum phenomenon
takes place, the multi-photon excitation of electrons into
the conduction band, weakly coupled to the vibrational
degrees of freedom.
The attempts to verify such a conjecture were done:
Electrons in the conduction band are supposed to convert
the dielectric to, as minimum, some kind of semiconductor. Indeed, the raise of conductivity for many orders ofmagnitude had been detected at the avalanche of thebroadband light emission. In this sense, the verification(TORI axiom 2) had been successful.
Also, we tried to refute (Axiom 3) the concept. If theelectrons in the conduction band are uncoupled from thevibrational degrees of freedom, then the effect should bestronger at low temperatures, while no phonons affect the
up-conversion of light by electrons. Merging of the sample into a liquid happened to be sufficient to eliminate theeffect. In such a way, the concept about the new beautiful
Copyright © 2013 SciRes.

quantum effect had been refuted. The broadband emission can be attributed to the heating of the sample, thatenhances the absorption of the pump, converting it to thethermal radiation. In such a way, the promising concept
had been refuted at very beginning. Even if the non-termal component of the Bisson-effect exists, it is difficult
to extract it at the background of the banal heating of thesample and the corresponding thermal emission. In thesimilar way, the jump of the electric conductivity of dielectrics can be attributed to the raise of the temperatureand corresponding re-structuring of the surface of thesample.
The cases above show the examples of application of
the TORI axioms to the Laser Science. However, the general principles of TORI (Except, the idea of refutability
by Karl Popper) were not declared that time. Contrary,
the TORI axioms were formulated as generalization ofthat experience. In this sense, the TORI axioms appear as
empiric observation, as simplification of the practical activity of treating and analyzing scientific (and not so scientific) results.

6. Not Only Laser Science
Initially, the TORI axioms were supposed to describe
concepts that deal with the Laser Science. However, theirapplication is not limited to the Laser science. The two
examples of application of the TORI axioms in otherareas refer to the Mathematics of Computation and Complex Analysis, namely, evaluation of tetration [17-21] andother superfunctions [22-26] and to observation of processes that happen with science in Russia and, in particular, at Skolkovo [31,32].
Application of the TORI axioms to computational
mathematics happened to be successful in many senses.
The general formalism of superfunctions is constructed;
the effective algorithms of the evaluation are implemented;
many non-trivial superfunctions [25] are described [17,19,20,22,23,26]; the beautiful figures are plotted; eventhe use in the Laser Science is suggested [24,26].
The second attempt, about observation of decay ofscience in Russia, happens to be less successful. Many
links and evidences in support of article [32] were collected at TORI; but 2013.02.27, within a week since thereviewers of “Physics Today” got the manuscript [32] forthe evaluation, the site http://www.ils.uec.ac.jp/TORI
had been attacked, the free reading access had been disabled [2], and it takes serious efforts to recover it.
Some colleagues suggest to set some kind of taboo on
the scientific research of certain topics. However, thisshould be explicitly declared, for example: “Our goal isfuture degradation of culture, technology and science inRussia. Therefore, the scientific analysis of things that
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sia, should not be published”. While such a declaration is
not written, not accepted as Law, not published, Sciencein Russia should be considered as appropriate topic forthe scientific research. Then, the attack 2013.02.27 onsite TORI should be qualified just as barbarian vandalism.
An alternative solution could be just following theverbal orders of pseudo-scientists and avoiding discussion of any fraud in science, as A. Kaminskii suggests[30]. As a development of this idea, the prohibition tosubmit “Errata” and negative review reports could beconsidered. From my point of view, such an attitude would
kill any science in a country within few generations ofresearchers.

7. Discussion
Often, the researchers believe that they present some kindof the “objective knowledge”, or even some kind of the“absolute true”. This can be expressed with sentences“Our results are true, and there cannot exist any experiment, contradicting our results” or “Why should I help
competitors to refute our result?”. The attempt to describe a gedanken experiment, that could refute the concept, or any alternative concept, is often interpreted as apersonal offense, that justifies any reciprocal response(canceling of the opponent’s presentation, the attack on
the website of the opponent, etc.). Such an attitude should
be qualified as pseudo-scientific and condemned. The
axiom 3 (refutability) could mitigate this antagonism,
converting science to the academic activity and promoting civilized ways of scientific discussions.
Purification of science from pseudoscience is notstraightforward, because the scientific revolutions [12]should be allowed. The TORI axiom 6 defends the pluralism, allowing consideration of new, “crasy idea”, analternative concepts (under condition, that it satisfies
axioms 1 - 5). The new idea may look pretty creasy. The
Galvani effect (with frog’s legs) looked nonsense. Violation of the fundamental concept of conservation of number of atoms of each kind in any closed system (at thediscovery of radioactivity) did not look better. The negation of the universal time (in the special theory of relativity) and the absence of classical trajectories (in Quantum
Mechanics) also give good examples of breaking rules,
that seemed to be “absolute true”. Even concept about
failure of axioms of arithmetics (existence of some “Mizugadro number” as biggest integer, for which the axioms of arithmetic begin to fail), in principle, could betreated as scientific, as soon as one suggests any way torefute such a concept. The TORI axioms are ready forvery strong scientific revolutions, still allowing to identify and reveal the pseudo-science, frauds and mistakes.
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sander Kaminskii thinks, that it is vain to fight against
the pseudo-science, and it is better to allow the pseudo-scientists to get grants and to spend them to some fake researches, than to reveal the wrong publications [30]. However, the scientific consideration should at least honestly
declare, what is happening to the Science. The TORI
axioms give the formal criteria to distinguish science frommagia, ufology, astrology, scientology, politics, religions,and other kinds of knowledge, that may look similar toscience.
For the beginning of century 21, the TORI axioms
seem to be most formal criteria to separate Science among
other kinds of the Human knowledge and Human activity.
However, as soon, as some new, more efficient criteria
will be suggested, the TORI axioms will have to be replaced with a more modern and efficient philosophy.

8. Conclusions
The 6 axioms TORI are formulated. These axioms appear
not only as a tool for the efficient research, but also as
justification of the main goal of science as satisfaction of
curiosity of researchers. I think the TORI axioms should
be declared as primary and main requirements for all
manuscripts submitted for the publication in a scien- tificjournal.
Axiom 3 (Refutability) seems to be the most important
for the beginning of 21st century. Each article should indicate, in which case (new deduction, simulation, observation, experiment, measurement) the authors should
confess: “Sorry, our concept is wrong”. Only if someways of the refutation exist, the non-trivial predictions
can be done on the base of the results presented.

9. Acknowledgements
Most of content of this article had been available at [1].
This article is inspired by Shigeaki Nishio, Hitoki Yoneda,
Akira Shirakawa, Mitsuru Musha, Takashi Mukaiyama,
Hajime Nishioka, Ken-ichi Nakagawa, Nobuyuki Nakamura, and Makoto Morinaga, who had disabled the access to tori.ils.uec.ac.jp/TORI, where the TORI axioms
are described.

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