Рубрика: Физика

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// Исследования в области естественных наук. 2013. № 1 [Электронный ресурс]. URL: http://science.snauka.ru/2013/01/3279 (дата обращения: 26.01.2017).

B.M. Levin, E-mail: bormikhlev@yandex.ru

St. Petersburg, Russia


The formulation of the proposition of the experimentum crucis for experimental verification of the E.B.Gliner's fundamental idea ("-vacuum", 1965-2002) – of his "microstructure*, "returns" the Boltzmann constant (according to the original logic and intuition of Max Planck, 1900/1906) to the rank of the fundamental constants – c, G, ħ, that have defined a "cube of physical theories" (G.Gamov, D.Ivanenko, L.Landau-1928, M.P.Bronstein-1934, A.Zelmanov-1967/1969), thus opening the perspective of a "four-dimensional" generalization of the "cube" ("Planck's Hypercube", J.M.Fröhlich-2001).

The "fourth dimension" means, on the one hand, – in the limit  (k = 0) – "freezing" (in the finite state of -decay of the nucleuses 22Na, 64Cu, 68Ga, etc.) of the kinetic energy
of an ensemble of particles from real gas for the period of its interaction with the nucleus of an atom of long-range action; on the other hand, when the real constant k and T300K("resonance conditions"
of the lifetime spectra of annihilation of positrons/orthopositronium from -decay of 22Na in gaseous neon close to
the normal temperature),
is a
necessary condition of life of HOMO SAPIENS in the observable Universe.


The specific character of the positron annihilation lifetime spectra from -decay of the
22Na in
gaseous neon (9% of 22Ne in the natural composition of isotopes) at comparative measurements in the row of inert gases, and significant disagreements with the theory(QED)
of the results of absolute precision measurements of lifetime of free orthopositronium (o-Ps) compose the unique information accumulated for more than half a century of observations 1; it has obtained a full phenomenological description [6] 2.

To following statement has been taken as the basis of the Standard Model (SM) extension – the positron beta-decay of atomic nuclei with transitions of the type (changing 
spin state by ±1 while conserving its parity) principally differs from -decay by that, that it is a topological quantum transition and generates in substance
-o-Ps, that is capable to probe a change of the structure of space-time in a limited (macroscopic) "volume": space-time as a continuum in the SM – on the discrete spacelike cubic "latticeVSM with the sign "+" of all physical "charges" in its "nodes" and a compensating
it lattice of the 'mirror-world'with the sign "–" of all charges – , including the masses of quasiparticles ("electrons"and "protons"). All this takes place on the "background" of space-time of the GR.

A phenomenology of the addition of Hamiltonian Dynamics SM has been formulated: an atom of long-range action, as conjugated Hamiltonian cycles (chains)
of its nucleus and shell centered at the "localization point" of-o-Ps
– an extended
Hamiltonian Dynamics of the quantum field theory

The unique dynamics of o-Ps, containing one (it is important!) virtual photon, permits to watch such an extension of dynamics of the QFT and "local" doubling of dimensionality of space-time (VSM + 'mirror-world').
Owing to this, -o-Ps is a unique object of the Nature, capable to probe the 'mirror-world'
by virtue of oscillations




(here the prime means belonging to the 'mirror-world'
where – from the viewpoint of an observer – energy/mass and action have negative signs [7], because the Planck's constant, and also the velocity of light in theadditional -physics admit a
fundamental plus-minus signħ and c [8]).

This defines the occurrence of an additional single quantum mode of annihilation




where  is a notoph.
"In interactions, a notoph – just as a photon – transfers spin 1"

The abovementioned means that the considered extension of the SM (Hamiltonian cycles
and -o-Ps as a physical observer on the other and this side – the 'mirror-world' and VSM) narrows down the principle of causality to the causality conditioned: the principle of causality conditioned by presence of a physical observer.

The phenomenology of the additional -physics is adequate, because the decisive experiment has been already executed
otherwise, how one can understand and overcome the paradox to have been observed:
the "Mossbauer effect" in gas (! – neon, ~ 9% 22Ne) and a factor of ~ 2 (1.850.1) of comparative presence of orthopositronium,
created by beta-decay positrons (22Na) in "resonance conditions", when – on the estimation of the Standard Model (QED) – this factor is vanishingly small (~)?

The only possibility is as follows: in the conditions of an experiment in a limited "volume" (radius of ~1.3 cm, during << 2·10-6 s) on the basis of a additional realization ofthe supersymmetric QED/SQED [11], has come out the fundamental old ideas – the complete relativity [12] and the discrete space-time
(supersymmetric "shift"
due to oscillations of -o-Ps, as a step of the Hamiltonian
chain [6]).

In gas, there is formed a substate – a double-valued () spacelike, crystal-like structure: a cubic lattice of vacuum-like state of matter with "charges" of all physical interactions in its "nodes" ("+"), including masses of quasiparticles – "proton" (mp) and "electron"(me), and a compensating lattice of the 'mirror-world' ("–").

The conditions and results of the experiments, executed for half a century, and an adequate treatment of the problem of tachyons [13] ('tachyon' as a macroscopic spacelike atom of long-range action) do not exclude this for the finite state of -decay of the type  (QFT).

An actual example is as follows:




Now the initial -decay, forming an additional mode of annihilation of -o-Ps, should be represented as




These demonstrations of the additional physics "on the outside" of the light cone should be interpreted as a
displacement current of the unified field.

The displacement current, postulated by Maxwell, has agreed the dynamics of electromagnetic field and the conservation of electric charge. Here there takes place the conservation of charges of all of the types – electric, leptonic, baryon, and
(that is, of the masses of the particles participating in the process).

In all publications till now, the phenomenology
of additional
-physics rested upon
the fundamental constants of physics – (velocity of light), G (gravitational constant)
(Planck's constant) – and upon the two-valuedness of the constants и
 is of principal value, because "… the Planck's constant 
and velocity of light
c enter 'in an even manner' into all the world's constant, such as the Planck's length 
(GN – gravitational constant), the fine structure constant , the Fermi constant
, etc., the Planck's constant  and the speed of light c are introduced on 
'parity basis',
that is, the world
's constant are invariant with relation to a simultaneous change of sign of the last mentioned (ħ → – ħ, c → – c)" (see a reference in [14]
to the monograph [15]). From the viewpoint of a real observer, their negative signs belong
to the 'mirror-world'.
Gravitation is common,
the gravitational constant
is positivethat is, an atom of long-range
action (positive mass)
falls in the field of gravitation, and the structure compensating it
(the 'mirror-world',
the negative mass) – rises (see footnote2).

In the concept of the complementary

-physics, it means that PHYSICS and a "PHYSICAL OBSERVER" in the
are merged together with the observable PHYSICS (by the PHYSICAL OBSERVER). In demonstrations of -o-Ps, this is realized in terms of its oscillations (*), in the nature of the species of HOMO SAPIENS – in his superconsciousness/subconsciousness
3This means that there has been denoted a way to study of the "… three 'great problems' of modern physics" and directly the "…third is the question of the emergence of lifei.e., the feasibility of explaining the origin of life
and thought on the basis of physics alone" (V.L.Ginzburg, Nobel Lecture-2003, Rev. Mod. Phys., v.76/3/, p.981, 2004).


The evolutions of the fundamental physics, the connection and interconditionality of its different divisions can be visually represented in the form of a "cube of physical theories" in the "coordinates" 1/с, Għ (A.Zelmanov, 1967/1969).
The history of formation of these notions and their modern status are laid down in two papers:
in the headlines "PHYSICS OF OUR DAYS" [17] and the "MAJOR PROBLEMS OF FUNDAMENTAL PHYSICS" [18] after publications [19].

Here are some small quotations from the paper [17], explaining the importance of the question:

"The first detailed paper, devoted to the system сGħ, 'World constants and limiting transition' was published at the beginning of 1928 by G.Gamov, D.Ivanenko and L.Landau";

"In the early thirties, M.P.Bronstein gave a detailed classification of physical theories on the base of cGħ and used them at quantization of gravitation. He introduced the term Għ/c-physics";

"To present M.Bronstein's ideas in a visual form, A.Zelmanov – in the Sixties – drew a 'cube of physical theories', constructed on three orthogonal axes 1/с, G,
(Fig. 1)


The cube of physical theories, that is an integral part of the modern physical folklore, is depicted in Fig. 2. In the origin of coordinates, there is Newtonian mechanics(NM), or, rather, that part of it, which disregards gravitation. Over it, there is nonrelativistic (Newtonian) gravity (NG), on the right – quantum mechanics (QM), in front – special relativity (SR).
 synthesis of SR and QM gives quantum field theory (QFT). The synthesis of NG and SR gives General Relativity (GR).
synthesis of QM and NG gives nonrelativistic quantum gravity (NQG) – the theory according to which it is not clear, whether the objects described by it do really exist <…>. And finally, the synthesis of all the theories in the future can lead to a comprehensive theory of everything. An English acronym of this theory is TOE ('Theory of Everything')".


Of particular interest are attached to [18] ([19)]. They revisited the classical and quantum-relativistic history of the world constants – anew and consecutively. After paper [17], the lecture [20] – published in a decade – served as a stimulus for returning to the problem of unification of the theory. On the base of the Planck's law of radiation of absolutely black body and of the notions of the future of physics from the positions of ideas of the mathematical theory of deformation of algebraic structures, the lecture's author has presented the "Planck's Hypercube", which is a unification of the fundamental theory in the "coordinates" 1/с, Għ with addition of the Boltzmann constant k. The [18] ([19]) contains some reasons against such an extension of the "idea of cube", as "… the status of k in the modern physics radically differs from that of c,
ħor the Planck's mass". This is an important clarification – "… in the modern physics", that is, in the Standard Model, and in this connection, the first half of the lecture's name appears successful [20] – 'Ein Blick zurück...' / 'To look back …'
and its finishing part '… ein Blick nach vorn'… to look forward'
(the SM plus the additional Għc-physics).

Independent considering the "Planck's Hypercube" [20] should be attributed not only to "A Mathematician's View of the Development of Physics" [21], but also to the logic and intuition of Max Planck, who still before the creation of quantum mechanics and relativity theory introduced four world natural units (of lengthtimemass, andtemperature) on the base of the proposed by him formula of the spectral power density of radiation of absolutely black body (in modern writing)


where ħ and k are present on an equal basis; the fundamental status of G and c before creation of the theory of relativity was already been defined by the Newton's theory of gravitation and by the electrodynamics by Faraday-Maxwell.

As you can see, the fundamental Planck's formula works and through the looking glass ('mirror-world': negative sings of fundamental constants: 


Proposition of experimentum crucis of the additional Għ/c
-physics which defines physical nature of "resonance conditions"
of lifetime spectra of annihilation of positrons (orthopositronium) from -decay 22Na in gaseous neon (see footnote *), is based on occurrence – to power balance of double resonance – of a term proportional to kT. The matter is that -decay is proton decay (in the nucleus!) by borrowing energy from the nuclear medium


As it follows from phenomenology of the additional Għ/c-physics, a spacelike structure (atom of long-range action with a quasiparticle – "proton" in its every "node" appears as a reaction of the unified field at -decay of 22Na (generalized displacement current) (**). Nucleuses of 22Ne atoms are selectively connected (at the expense of the exchange p-"p"-interactions of a nucleus) with "nodes" of the nucleus of an atom of long-range action for a period of 
– in power competition with other isotopes of gas-neon (20Ne21Ne). There occur "resonance conditions" ("Mossbauer's effect"), defined by the equality


where is a difference of masses of neutron (n) and of proton (p);  is the energy of a nuclear -quantum, marking the instant of -decay ("start" at lifetime spectrum recording); 
effective topological mass of neutrino (), participating (along with -o-Ps) in the "vertical" oscillations "VSM
 'mirror-world";  is the number of "nodes" of the nucleus of atom of long-range action.

It can be seen, that fine tuning of the double resonance (closeness of  and  ) is possible by changing the temperature of gas neon. At the exact resonance (close to ), the half of -o-Ps, formed in neon (Iis an observed intensity of lifetime spectrum of the orthopositronium component) annihilates to the 'mirror-world' by the mechanism


giving a contribution to the peak of "instantaneous" coincidences of the lifetime spectrum (see, in [11] Refs. [8] and [16], accordingly). The gas-neon temperature increase – in relation to the resonance temperature – should raise an observable output of orthopositronium. The fall of temperature of gas-neon is in this respect less definite, as there increases the role of van der Waals molecules in slowing-down
positrons, forming positronium, and interpretation of projected observations becomes more complicated.

Since in all measurements, executed earlier, the temperature of gas samples was not controlled, and in laboratory conditions, it could not differ more than by ,
then implementation of experimentum crucis is obvious: it is necessary to compare lifetime spectra of annihilation of positrons from 22Na in gaseous neon of high cleanliness in the range of temperatures  at temperature control the measuring chamber to an accuracy of .

It is supposed to watch the temperature resonance: increasing the intensity of the orthopositronium component of lifetime spectra (I2) on either side of the temperature range. With distance from the peak of temperature resonance, one supposes a growth I2 (up to 2 times) and accordingly – after subtraction of the contribution of the orthopositronium component – more and more distinct visualization of the shoulder, that is, the normalization by this criterion of position of neon in the row of inert gases in the experiments of 1965–1975 (USA, Russia, England, Canada).

Thus, the fundamental idea of "Planck's Hypercube" strengthens the confidence in expected results of the experimentum crucis, and is an important stimulus.

Do not be in the publications [18,19] of the critical analysis "Planks Hypercube" idea, the lecture [20] would most likely not be noticed, as it was published in a non-reviewed magazine (which is absent in the Science Citation Index).

Here we have an example of how substantial criticism becomes constructive.





B.M.Levin, V.I.Sokolov. About physical nature "resonance conditionsin the lifetime annihilation spectra of the positrons
(orthopositroniumfrom -decay 22Na in gaseous neon. Preprint-1795 A.F.Ioffe Physical Technical Institute Russian Academy of Sciences, St. Petersburg, 2008 (seeAPPENDIX); B.M.Levin. Additional Physics "outsideLight Cone. III. http://science.snauka.ru/2012/10/1545


1 With due consideration of refusal of the Michigan group in the latest work [1] from results of the previous precision measurements [2-5].

2    The significance of work [1] as a whole is still positive, as its result has made it possible to understand – on the base of phenomenology of the additional
-physics – that the electric field inputted to measuring cell, has closed an earlier observed effect of exceedance of the rate of self-annihilation of -o-Ps by (0.20.023)% [5] in comparison with the calculated value () because of counteraction to gravity on the atom of long-range action (vacuum-like state of matter/VSM, positive mass) and on the compensating structure of the 'mirror-world' (negative mass) [6].

3    B.M.Levin. PHYSICS AND CONSCIOUSNESS /NEW ASPECT/, "LISS", St. Petersburg, 2002. It is assumed that the atom of long-range action is plugged-in – by "nodes" of the nucleus of the atom of long-range action () in volume of the diameter
~ 1 cm) – to the neural network of a human being, like an additional processor of huge information
capacity (N(3) ~ 1019 "nodes"/cells) and by virtue of a very fast response (the switching-over time of the order of the Planck's time ~ 1043 s). So additional Għ/c-physics develops an information model of the nature of consciousness, based on the theory of cellular automata [16].




  1. Vallery R.S., Zitzewitz P.W., and Gidley D.W. Resolution of the Orthopositronium-Lifetime Puzzle. Phys. Rev. Lett, v.90(20), p.203402, 2003.
  2. Gidley D.W., Rich A., Sweetman E., and West D. New Precision Measurements of Decay Rates of Singlet and Triplet Positronium. Phys. Rev. Lett., v.49(8), p. 525, 1982.
  3. Westbrook C.I., Gidley D.W., Conti R.S., and Rich A. New Precision Measurements of the Orthopositronium Decay RateA Discrepancy with Theory. Phys. Rev. Lett., v.58(13), p.1328, 1987.
  4. Westbrook C.I., Gidley D.W., Conti R.S., and Rich A. Precision measurement of the orthopositronium vacuum rate using the gas technique. Phys. Rev., v.A40(10), p.5489, 1989.
  5. Nico J.S., Gidley D.W., and Rich A., Zitzewitz P.W. Precision Measurements of the Orthopositronium Decay Rate Using the Vacuum Technique. Phys. Rev. Lett., v.65(11), p.1344, 1990.
  6. B.A.Kotov, B.M.Levin, V.I.Sokolov. Orthopositronium: "On the possible relation of gravity to
    electricity". Preprint-1784 A.F.Ioffe Physical Technical Institute Russian Academy of Sciences, St. Petersburg, 2005;http://arXiv.org/abs/quant-ph/0604171
  7. Linde A.D. The multiplication of the Universe and problem of cosmological constant. Phys. Lett., v.B200(3), p.272, 1988;http://arXiv.org/abs/hep-th/0211048
  8. Kotelnikov G.A. Inversion of a sign on speed of light – new transformation of discrete symmetry in electrodynamics. Izvestiya VUZov, №12, p.69, 1992 (in Russian).
  9. Ogievetskii V.I., Polubarinov I.V. Notoph and its possible interactions. Sov. J. Nucl. Res., v.4, p.156, 1968.
  10. Levin B.M., Kochenda L.M., Markov A.A., Shantarovich V.P. Time spectra of annihilation of positrons (22Na) in gaseous neon of various isotopic compositions. Sov. J. Nucl. Phys., v.45(6), p.1119, 1987.
  11. B.M.Levin. A Proposed Experimentum Crucis for the Orthopositronium Lifetime Anomalies. Progress in Physics, v.2, p.53, 2007 / http://www.ptep-online.com (PiP); B.M.Levin, V.I.Sokolov. On an additional realization of supersymmetry in orthopositronium lifetime anomalies.http://arXiv.org/abs/quant-ph/0702063
  12. Andreev A.F. Spontaneously broken complete relativity. JETP Lett., v.36(3), p.100, 1982.
  13. Andreev A.Yu., Kirzhnits D.A. Tachyons and the instability of physical systems. Phys-Usp., v.39(10), p.1071, 1996.
  14. Prokhorov L.V. On Physics on the planck scaleStrings and symmetries. Phys. of Particles and Nuclei, v.43(1), p.1, 2012.
  15. Levin B.M. Nachalo Vselennoi, zvyozdnoe nebo i fizicheskii nablyudatel' (The beginning of the Universe, starry skies and physical observer – in Russian), St. Petersburg: Nestor-Hystory, 2009.
  16. Berkovich S.Y. Mutual Synchronization in Network of Digital Clocks as the Key Cellular Automaton Mechanism of Nature. Computational Model of Fundamental Physics. Institute for Information Science and Technology. George Washington University. Report GWU LIST 86-28. 1986; Berkovich S.Y. Cellular automaton as a model of relativity: search for new representations of physical and informational processes. /Chapter 6. The brain and its ability to process information. The new paradigm/. Moscow, Moscow University Publisher (Russian), 1993.
  17. Okun L.B. The fundamental constants of physics. Sov. Phys. Usp., v.34(9), p.818, 1991.
  18. Okun L.B. On the Article of G.GamovD.Ivanenkoand L.Landau "World Constants and Limiting Transition". Phys. At. Nucl., v.65(7), p.1370, 2002.
  19. Okun L.B. Cube or hypercube of natural unitshttp://arXiv.org/abs/hep-ph/0112339v1 27 Dec 2001; In: Michael Marinov memorial volumeMULTIPLE FACETS OF QUANTIZATION AND SUPERSYMMETRY, Ed. by M.Olshanetsky, A.Vainshtein. World Scientific Publishing Co., 2002, pp. 670-675.
  20. Fröhlich J. Ein Blick zurückein Blick nach vorn. Phys. Blätter, B.57(7/8), S.53, 2001.
  21. Faddeev L.D. Matematicheskii vzglyad na evolyutsiyu fiziki. Priroda (Nature – in Russian), №5, с.11, 1989; Ludvig D. Faddeev. A Mathematician's
    View of the Development of Physics. Proc. of the 25th Anniversary Conf. – Frontiers in Physics, High Technology & Mathematics 31 October-3 November 1989, eds. H.A.Cerdeira & S.O.Lundqvist (1990), p.238-246; in MISCELLANEA MATHEMATICA, Berlin Heidelberg, Springer-Verlag (1991), p. 119-127; Institut des hautes études scientifiques (1998), p. 73-79.




B.M. Levin, V.I. Sokolov












The proximity of a difference of the neutron and proton
mass mnp and energy of the nuclear gamma-quantum in transition  whereby the moment of appearance of the positron in substance is marked at registration
of the lifetime spectra positrons (orthopositronium) annihilation, allows to present the physical nature of the "resonance conditions" in gaseous neon at room temperature (1990), established experimentally (1987), as a twofold resonance. Registration
of the resonance as a result of measurement of temperature dependence
of the
lifetime parameters quasi-free positrons ("shoulder") and orthopositronium
(I2) in a range of temperatures  is supposed.


The "resonance conditions" of the positrons (orthopositronium) annihilation lifetime spectra in gaseous neon are formulated by the description of physical conditions of experiment [1,2]. Here on the basis of the fact which is earlier not examined in this context, the model of this phenomenon – the twofold delayed resonance − is considered.

In the work [3] experimental diagrams
of non-exponential features
("shoulder") of the annihilation of the positrons from 22Na for all inert gases at room temperature have been received. The neon stands out in a number of inert gases visually, i.e. obvious absence of a shoulder (or its
"blurring") on diagrams. This phenomenon has soon been confirmed in a wide range of pressure [4] and in the subsequent is reliably established on set of measurements of four experimentalist's groups

In second half of 70th the attention to association "22Na as the positrons source-gaseous neon" has been attracted and statement of a question about paradoxical experimentally
realization of the nuclear gamma-resonance (NGR in gas!) of the nuclear -quantum [8] with a collective of the atomic nuclei ²²Ne (~9 % in neon of natural isotopic composition) in macroscopic volume of a measuring vessel has been formulated


Direct experiment has confirmed this hypothesis: the "isotopic anomaly" of the orthopositronium (o-PsTPs), i.e. increase of intensity (I2) orthopositronium lifetime component (factor ) when the content of an isotope 22Ne was decreased to 4.91% in comparison with the natural neon (8.86 %) and, accordingly, visualization of a shoulder [1] was observed. It was possible to explain this effect through consideration of the mirror universe additional version (B. Holdom, 1986-S.L. Glashow, 1986
3). Taking into consideration the oscillations  admit decrease in observable value
 up to 2 times [9] (the primed symbols indicate a belonging to the "mirror Universe").

In succeeding years on the same basis the quantitative description of the independent supervision Michigan groups has been also obtained: excess () of the o-Ps self-annihilation rate () from absolute measurements of its lifetime in non-resonant conditions in measurements with buffer gases [10] and in vacuum [11] ("-anomaly") [12]. This effect was agreed quantitatively on the basis of calculations of theo-Ps annihilation probability on one ァ-quantum and neutral supersymmetric spin 1 boson U (P.Fayet, M.Mezard, 1981

where x = mU/me, and on
the intensification factor owing to the o-Ps oscillation
on  "units" of the space-like formed in a final state of the -decay nuclei [9,12]:


It is success of the model because significant efforts of experimenters and theorists within two decades (1983-2003) did not give a substantiation of the "-anomaly" neither within the framework of Standard Model (SM), nor behind it
4. The basis of the model is the representation for -decay of the nuclei  and  () as about topological quantum transition [9].

It is necessary to emphasize that the basic work [1], in which the "isotopic anomaly" of the annihilation lifetime spectra of the positrons (orthopositronium) in neon was observed, generally has not of the involved attention.

The Michigan group of experimenters (in its present personnel) in the new work with the changed technique of experiment [13] even has refused from former own results of the measurements [10,11] relating to the "-anomaly" [12].

The alternative to this ambiguous decision is submitted in the preprint [14].

The fundamental bases
of the new physics ("additional -physics") and the received results can be presented as (see [9,12,14]):

  1. In the final state of the
    -decay () a "defect" of limited macroscopic "volume" of space-time arises,
    which is considered as a matrix for formation of the response in transient (topological quantum transition) with participation of the all physical interactions (a generalized displacement
  2. In modern SM excessively widely a null energy condition (NEC; otherwise, − the weak energy condition of the General Relativity/GR) is treated, as absolute ban of the negative sign energy (mass). However the negative density of energy (or mass)
    of the compensating field does not lead to any basic difficulties (A.D. Linde, 1988
    1. Energy of the o-Ps ground state
      exceeds energy of the parapositronium (р-PsSPs) on the size eV (the superfine splitting, W≃6.8 eV is the Ps binding energy). The part of the shift eV it is caused by that during time  the triplet quantum system exists in the form of one (it is significant!) virtual photon, i.e. in the "state" without electric charges ("new annihilation force", onR.P.Feynman, 1961

    This fact in the "additional physics" is interpreted as impossibility to locate the center of the mass [9] within a volume, smaller than , where  is the dynamical fundamental length ("shift") [12,14]

    cm.    (1) 6

  3. Weak energy condition GR is replaced with "boundary condition" on the "surface" of the space-time "defect" (see pnt.1): supersymmetric degeneracy
    for para- and ortho-superpositronium (W0, P. Di Vecchia & V.Schuchhardt, 1985
    3) is realized in a nth Ps state at enough big n = N

,        (2)

where WN is the binding energy of the Ps Nth state.

"Reciprocal principle" (M. Born, 1938
3) allows to formulate a boundary condition for complete degeneracy Fermi-gas with boundary energy
 (Fermi's level) in discrete х-space as

         = WN    (3)


as N(3) is the number of cells in the р-space, displayed in the х-space in volume V of fundamental space-like structure (object). The condition (3) unifies the standard quantization of an atomic states and the quantization of the х-space postulated here (its limited volume in the space-time "defect"). This postulate, going from linear sequence of the main quantum number in atom (n = 1,2,3, …, N) to number of cells ("units") of 3-dimensional space-like structure ("atom of long-range action") N3 – is designated in formulas by index N(3). From (2) and (3) we receive values:

  • number of cells of the 3-dimensional fundamental spacelike structure (object)

N(3) =     (4);

  • linear size,
    of the fundamental space-like structure during time
    /c, where

    is the Bohr's radius of the positronium Nth state

rN = 
.        (5)

If to "occupy"
each cell by quasi-particles of the natural structural unit of the stable substance
'electron-proton for 
> 0 and
'electron-hole-proton-hole' for 
< 0, we shall receive the fundamental two-sign () mass

g.    (6)

Comparison of received value
M with Planck mass obviously (accuracy ~ 0.1 %)


  1. Experimental bounds accumulated in the two decades of intense studies of the orthopositronium problem lead one to the conclusion that theadditional single-quantum mode of the orthopositronium annihilation involves not a photon but a notoph ( is a zero-mass, zero-helicity particle which a complementary in properties to the photon, V.I. Ogievetsky, I.V. Polubarinov, 1966 3) and two mirror photons 
    with a negative total energy of eV [12]:


These points to augmenting of the framework in which the nature of the o-Ps anomalies could be analyzed (from QED to supersymmetric QED/SQED) and phenomenology of the mechanism of energy and momentum deficit compensation in a single-quantum mode were first formulated [12]. Treated from the SM standpoint, however, detection of quantum of energy 1.022 MeV in the "stop" channel of the fast-slow coincidences is forbidden. Detection of a single-notoph o-Ps mode should also be
accompanied by observation of an energy deficit (supersymmetry) in the "stop" channel of the lifetime spectrometer: indeed, single-notoph annihilation is identified in the scintillator by the Compton-scattered electron , which is bound in the long-range atom "shell" in a "pair"  with the "electronic hole"  (negative mass) in the "C-field"/"mirror" structure. Half of the notoph energy, MeV, is transferred to -hole and, thus, "disappears" ("anti-Compton scattering"; see J.L. Synge, 1974, cited in Ref. [16]). As result, the additional single-notoph mode is detected by lifetime spectrometer in the peak "instantaneous" coincidences [1,15,16] – an effect which is traced on experimental data [4]. In result of the "isotopic anomaly" and "-anomaly" substantiation the alternative to the Michigan's conclusions with the offer of the experimentum crucis was considered [14].

Let's to pass directly to a substantiation of the "resonance conditions" connection "-gaseous neon" in dynamics of the "additional
-physics" [8,9,12,14].

In the elementary representation of the proton decay in a neutron-deficit nucleus (-decay) it is possible by loan of energy from the nuclear environment

energy .

Restriction on the upper number of the nucleus (atoms) 22Ne  [9,14], participating in a macroscopic collective nuclear state '22*Ne(in a source )-22Ne(in gas)' is earlier received.

The proximity of the nuclear -quantum energy and a difference between the neutron and proton masses mnp
8, seeming accidental in SM, in "additional -physics" supposes statement of a question on the physical nature of the "resonance conditions" [2]. However use now an approximate values  not enough. On the tabulated data (W.-M.Yao et al., J. Phys. G, 2006, v.33, p.1)


MeV (Nuclear Data Sheets, 2005, v.106, №1, p.12),

i.e. the essential difference keV takes place.

The question now arises about width of the prospective twofold resonance. Occurrence of a  (quasi-particle) in each units of the space lattice VSM and the binding by them of the nuclei ²²Ne of the atoms from the gas environment's
9 the response onto -decay () on the background of the "mirror" as a displacement current in the electrodynamics [14]
10 (see a footnote 4). At binding due to exchange -proton interaction on units of space lattice VSM of number  of nucleus 22Ne atoms of neon from gas at room temperature for the period of the o-Ps lifetime, the

2 keV is "frozen" (temperature of gas 300 K).    (7)

On creation of the generalized displacement current the energy is "spent" (). There is a prospect to connect a difference  with a resonance of energy of the response, as neutrino in a final state of transition


as well as  in o-Ps, also participates in the oscillations  during the o-Ps lifetime
[9,15]. Such oscillation of the electronic neutrino differ from oscillation between
neutrino aromas (for solar and atmospheric neutrino), found out in last decade. In the neutrino oscillations on a background of the "mirror" its aroma is conserve, but neutrino assumed additional effective (topological) mass as it is inherent in transformations the "left-right particles" at oscillations in topological quantum transitions [17]. Then excess of a difference of masses  above  can be presented as

 keV.    (8)

From (7) and (8) we find  keV.

It is interesting, that the effective topological mass of the neutrino is close to value of mass heavy 17-keV neutrino as possible result of mixing of various own mass of the neutrino states (keV/c2; the brief review of the problem 17-keV neutrino see in [19]). The experimental studying of this question in the beginning rather encouraging (1985-91), has been interrupted after lines of works with alternative techniques and negative result (1991-93). The drama history of experimental studying of the 17-keV neutrino [19] is similar to a history of the orthopositronium problem [12,14].

Possible also another interpretation of surplus of energy


due to the shift of a level 22*Ne(2+), caused by connection with VSM lattice (see a footnote 9) is possible also.

In any case, the affinity of sizes  and
mnpсhas led to the new offer of experiment, which need to confirm (or to deny) the prospective physical nature of the "resonance conditions" astwofold delayed resonance. The point is that in energy of the response (8) there is component varying with temperature of gas. Hence, uncertainty of temperature of the measuring chamber of the order, quite probable in laboratory conditions, can testify to a different degree nearness of temperature of the measuring chamber in works [3-7] around of a source of positrons in radius


to the temperature peak of the twofold resonance.

It can cause uncertainty of visualization of a shoulder (its blurring [8]) and extremely wide scatter of its quantitative characteristic  (see a footnote1). Thus, prospective width of the twofold resonance is eV.

The statement of search experiment is obvious: it is necessary to compare
the positrons
annihilation lifetime spectra from 22Na in gaseous neon
of high purity in enough wide intervals of temperatures with accuracy .

The observation by the method - delayed coincidence high intensity of the lifetime spectra of the orthopositronium component (I2) and (after its subtraction) more and more precise visualization of a shoulder at removal from "peak" temperature on tails of a temperature range is expected, i.e. normalization by this criterion of the neon position in the set of the inert gases (see Ref. [3]). As the peak of a temperature resonance is approached, decrease I2 is supposed (up to 2 times; see [1]) and, accordingly, blurring of a shoulder, as takes place according to the works [3-7], in which the temperature of the chamber was not fixed. This effect is most pronounced on a positive branch of a temperature resonance, as with decrease the temperature the role of the van der Waals molecules (Ne⋅⋅⋅Ne) grows, and the mechanism of a shoulder formation varies, because non-elastic scattering of the  increased [8]. It first of all concerns to the measurements carried out earlier at cryogenic temperatures down to 30K [5], which cannot be discussed in a considered context.

Thus, receives substantiation the term entered earlier the "atom of long-range action" ( units) [14] for a designation of limited macroscopical "volume" of space-time (VSM) as
the delayed twofold resonance determines the "nucleus of long-range action atom" (units) [9, 12,14].

Methodologically the offer of experiment is unique insofar at positive outcome its realization will restore interest at once to two constructive directions of expansion of the modern

The expected result would mean existence of an additional mode of the annihilation o-Ps, formed by -decay positrons

where the "atom of long-range action" together with compensating structure of the "mirror" () could apply for a role of the ninth massless pseudo-Goldstone boson spin 1 with all consequences of restoration following from it chirality in limited "volume" of space-time of a final state of -decay of the type ()



*The authorized text of the preprint-1795/2008 A.F.Ioffe Physical Technical Institute Russian Academy of Science.

As against helium and argon the extremely wide scattering of the experimental values of the parameter describing of the duration of the shoulder in a neon was observed:
p = 500-900 ns atm [4] (see also comment in the work [5]: tis duration of the shoulder, p is pressure of gas; parameter
p in neon was not measured in work [5] as the shoulder was not observed), ns atm [6], ns atm [7]. On diagrams of the work [3] shoulder in neon is absent, though in the table value tp = 488 ns atm is resulted. In all these works the high-purity neon was used.

In the method
of the delayed -
coincidences the -quantum marks "start". "Stop" is marked on one of the annihilation
quanta. Energy
the -quantum in the descriptions of an experimental method is approximately MeV.

See References.

Augmenting of the SM are justified because the all physical interactions participate in -decay: electroweak, strong and gravitational (in terrestrial laboratory).

Postulated by J.C. Maxwell
the displacement
current has agreed dynamics of the electromagnetic field and the electric charge conservation. Here takes place the conservation of all types of charges – electric, lepton, baryon and "gravitational charge" (the masses of the particles participating in process).

It is necessary to emphasize, that the term the "mirror Universe" in a context of the "additional -physics" [9,12,14] assumes "local" realization
of the global version of the mirror universe (Holdom-Glashow, 1986). The concept of discrete scalar
"С-field" with negative density of mass (F. Hoyle & J. Narlikar, 1964 3), added by the concept antipodal symmetry of action and energy in mirror universe (A.D. Linde, 19883), are used in [9,12,14] for a substantiation of indemnification of energy and "charges" of all physical interactions of the space-time GR "defect" in the final state of -decay (). Representation about of the space-time "defect" develops the concept vacuumlike states of matter (E.B. Gliner, 19653: VSM, "-vacuum"). In order to prevent misunderstanding in the subsequent the term the "mirror universe" is replaced with the term "mirror".

The consecutive decision assume four-dimensional generalization (space-time) of the "three-dimensional" boundary energy of Fermi
 (a degeneracy electronic gas). The correctness of this assumption is justified by recent outstanding achievement – the proof of the Poincaré hypothesis (G.Perelman, 2002-2003).

Usually also is point out an approximate value
mnpс2 = mnс2 – mpс2 = 1.28 MeV (compare with a footnote 2).

Thus it is formed quasi-nucleus in which the level 22*Ne (2+) is kept, but during lifetime of the o-Ps [9,15] its energy owing to interaction with quasi-proton () lattices VSM can change. Comparison of defects of masses of nuclei 23Na (– 9.5296 MeV), 22Na (–5.1840 MeV), 21Na (–2.1858 MeV) shows, that VSM most likely includes only quasi-nucleus  [14]. Besides sodium has a unique stable isotope 23Na (100 %).

10 As  it is determined in [9] by the oscillations  and by the contribution of the spin-spin magnetic splitting in superfine structure of the Ps eV the response is delayed for the period of the Ps formation in gas. It is necessary to emphasize, that participation in the response of spacelike sector ("tachyon") does not create causal anomalies as VSM cannot be system of reference (E.B.Gliner, 1965 3). The common analysis shows, that "… tachyon in non-stable system does not transfer the information by the super light velocity but only such carry and forms the basis for prohibition of movements with a greater than light velocityTherefore participation of a tachyon in real physical process of reorganization of system does not contradict any common principles. <…> Irrespective ofwhether a tachyon will be sometime found out in the nature as independent particlesthey already today make the major element of the systems which are finding out instability in relation to phase transition in a stable condition" [18].

11 "If group of symmetry was group there should be the ninth pseudo-Goldstone boson. Its absence – the direct experimental proof of the chirality nonconservation (absence of invariance is relative  in quantum chromodynamics" [20]. As for a long time has noticed R.Fejnman ("… following of the Gell-Mann's offer"), "… Young-Mills theory obviously is not engaged a massless field which should leave a nucleus and to be appreciable. Therefore theorists did not investigate attentively a massless case" [21].

Certainly, such specification QCD does not break the "color" confinement, however keeps the fundamental status of strong nuclear interaction when its carrier is quasi-particle  in "units" of the .


  1. B.M. Levin, L.M. Kochenda, A.A. Markov, and V.P. Shantarovich. Time spectra of annihilation of positrons (²²Na) in gaseous neon of various isotopic compositions. Sov. J. Nucl. Phys., 1987, v.45(6), p.1119.
  2. B.M. Levin. Orthopositronium: a program for critical experiments. Sov. J. Nucl. Phys., 1990, v.52(2), p.342.
  3. P.E. Osmon. Positron lifetime spectra in noble gases. Phys. Rev., 1965, v.B138, p.216.
  4. Goldanskii & Levin. Institute of Chemical Physics, Moscow (1967): in Atomic Energy Review. Table of positron annihilation data, ed. by B.G. Hogg and C.M. Laidlaw and V.I. Goldanskii and V.P. Shantarovich, v.6, 1968, p.p. 154, 171, 183, IAEA, Vienna.
  5. K.F. Canter, and L.O. Roellig. Positron annihilation in low-temperature rare gases. II. Argon and neon. Phys. Rev.A, 1975, v.12(2), p.386-395.
  6. P.G. Coleman, T.C. Griffith, G.R. Heyland, and T.L. Killen. Positron lifetime spectra for noble-gases. J. Phys.B, 1975, v.8 (10), p.1734.
  7. A.C. Mao, and D.A.L. Paul. Positron scattering and annihilation in neon gas. Canad. J. Phys., 1975, v.53(11), p.2406.
  8. B.M. Levin. Time spectra of positron annihilation in neon. Sov. J. Nucl. Phys., 1981, v.34(6), p.917.
  9. B.M. Levin. On the Kinematics of One-Photon Annihilation of Orthopositronium. Phys. At. Nucl., 1995, v.58(2), p.332.
  10. C.I. Westbrook, D.W. Gidley, R.S. Conti, and A. Rich. Precision measurements of the orthopositronium vacuum decay rate using the gas technique. Phys. Rev.A, 1989, v.40(10), p.5489.
  11. J.S. Nico, D.W. Gidley, and A. Rich, P.W. Zitzewitz. Precision Measurements of the Orthopositronium Decay Rate Using the Vacuum Technique. Phys. Rev. Lett., 1990, v.65(11), p.1344.
  12. B.M. Levin. Orthopositronium: `Annihilation of positron in gaseous neon'http://arXiv.org/abs/quant-ph/0303166
  13. R.S. Vallery, P.W. Zitzewitz, and D.W. Gidley. Resolution of the Orthopositronium Lifetime Puzzle. Phys. Rev. Lett., 2003, v.90(20), p.203402.
  14. B.A. Kotov, B.M. Levin, and V.I. Sokolov. Orthopositronium: "on the possible relation of gravity to electricity", Preprint 1784, A.F.Ioffe Physical Technical Institute Russian Academy of Sciences, Saint-Petersburg, 2005; http://arXiv.org/abs/quant-ph/0604171
  15. B.M. Levin, and V.P. Shantarovich. Anomalies in the time spectra of positron annihilation in gaseous neon. Sov. J. Nucl. Phys., 1984, v.39(6), p.855.
  16. B.M. Levin, and V.I. Sokolov. On an additional realization of supersymmetry in orthopositronium lifetime anomalies.
  17. Ya.B. Zeldovich. Gravitation, Charges, Cosmology and Coherency. Usp. Fiz. Nauk (in Russian), 1977, v.123(11), p.502-503.
  18. A.Yu. Andreev, D.A. Kirzhnits. Tachyon and the instability of physical systems. Phys. Usp., 1996, v.39, p.1071
  19. H.V. Klapdor-Kleingrothhaus, A. Staudt. Teilchenphysik ohne Beschleunger. B.G.Teubner, Stuttgart, 1995.
  20. V.A. Rubakov. The classical gauge fields. Theories with the fermions (in Russian), Moscow, "URSS", 2005, p.89-90.
  21. R. Feynman. Quantum theory of gravitation. Acta Phys. Pol., v.24(2), p.697.

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