Interaction between neutrino flavor oscillation and Dark Energy as a super-luminal propagation

by Marco Lelli

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As it is well known a recent series of experiments, conducted in collaboration between CERN laboratories in Geneva and the Gran Sasso National Laboratory for Particle Physics, could have decreed the discovery of the transmission of a beam of super-luminal particles.
Experimental data indicate that the distance between two laboratories (approximately 730 km) was covered by a beam of neutrinos with an advance of  approx 60 nanoseconds with respect to a signal travelling at the relativistic limit speed c (which takes a time interval of the order of 2,4.10-3 s to perform the way).
Neutrino beam starts from CERN and after travelling 730 km through the Earth’s crust, affects lead atoms of  the OPERA detector at Gran Sasso laboratories. Production of neutrino beam is due by the acceleration and collision of protons and heavy nuclei. This event produces pions and kaons, which then decay into muons and νμ.
The initial energy of  neutrino beam is 17 GeV and its composition is almost entirely due to νμ.
Publication of  the OPERA experimental data immediately got a deep world mass-media echoes: the possible confirmation of the results of the experiment seems to imply an explanation leading to change our current thoughts about theory of relativity and, therefore, the intimate space-time nature. In this assumption c may not be considered a speed limit on the quantum scale investigation.
In this paper we try to show how the uncertainty principle and the oscillation in flavor eingenstates of neutrino beam may provide a possible explanation for OPERA’s data.
Our research assumes two basic hypotheses.

First approximation: approximation in number of  flavor eigenstates  (and then in mass eigenstates) within is supposed to play neutrino oscillation.
We consider this oscillation between two flavor eigenstates. Then we assume that each component of  the neutrino beam can be described by a linear combination of two eigenstates of flavor. These two eigenstates are: μ flavor (the flavor of neutrino beam generation) and τ flavor.
Oscillations in this two flavor was already observed in first half of 2010 within the same OPERA experimental series.
Although, as it is known, the neutrino oscillation cover three mass eigenstates for its complete description, we assume here an approximation for dominant mass of neutrino τ, which reduces the description of neutrino propagation in a linear combination of only two mass eigenstates.
In this approximation we can now describe the propagation of each neutrino produced at CERN as a combination of two mass eigenstates as follows:

Flavor and mass eigenstates are related by a unitary transformation which implies a mixing angle in vacuum similar to Cabibbo mixing angle for flavor of quarks:


Second approximation: we suppose that propagation of neutrino beam is in vacuum. The propagation in vacuum is determined by the temporal evolution of the mass eigenstates

We can consider valid this assumption, at least in first approximation, because matter interacts in particular with νe and less with νμ and ντ.νe weakly interacts with matter by W± and Z° bosons while νμ and ντ only by Z° bosons. So the principal possible effect consists in a massive transformation of νe in the |νμ› eigenstate.
Considering the small number of νe in starting beam we can neglect this effect.
Assuming that in the initial state  only νμ are present in the beam, through a series of elementary steps, we can get

then we can obtain the probability

In the approximation mμ « Eμ we can write

and finally the transition probabilities between eigenstates of flavor

νμ beam produced at CERN propagates as a linear superposition of mass eingestates given by the following relation

This superposition generates an uncertainty in propagating mass  neutrino that grows over time and is equal to

This uncertainty in the mass eigenstates of the neutrino implies an uncertainty in the energy of propagation.
Given the relativistic equation

taking the momentum of propagation p=cost, the uncertainty linked to neutrino mass eigenstate is linearly reflected in an  uncertainty in the propagation energy:

Therefore we have

Following  the uncertainty principle we have

so the uncertainty (12), about the value of νμ energy of  propagation, causes a corresponding uncertainty in its time of flight between the point of production and the point of arrival.
This uncertainty is expressed as follows:

In OPERA case available experimental data are:

Assuming sen²2θ12=1, in analogy with the value attributed to Cabibbo quark mixing angles, and a value for Δm12 ≈ 10-²eV ≈ 1,6.10-²¹ J  we have


(14) shows that the advance    on the propagation of neutrino beam, detected in the execution OPERA experiment, is between the range determined by the uncertainty principle.
The advance Δt is then interpreted by the uncertainty principle and the neutrino flavor oscillation during propagation. This oscillation implies an uncertainty in the neutrino propagation energy, due to the linear superposition of its mass eigenstates, which affects the uncertainty of its flight time.
According to this interpretation, therefore, the results of OPERA experiment, if confirmed, would represent not a refusal of the condition of c as a relativistic speed limit, but rather a stunning example of neutrino flavor oscillation according to physics’s laws known today (uncertainty principle  and speed limit c).
The range indicated in (14) depends on the competition of two factors. On one hand, the intrinsic nature of inequality of the uncertainty principle, on the other our fuzzy knowledge of Δm12 between mass eigenstates of neutrinos with different flavors.
One of the most convincing experimental proofs of flavor neutrino oscillation is the lack of solar electron neutrinos measured experimentally respect to the theoretically expected flow.
OPERA, as well as other tests, was designed to observe possible flavor oscillation in a neutrino beam running along the earth’s subsurface. Any oscillation can be found by observing a change of flavor in a fraction of neutrinos in the arrive.
However, if this happens, neutrino mass eigenstate is described by a linear superposition of mass eigenstates of pure muon neutrino and tau neutrino.
This condition generates an uncertainty on the propagation energy, which translates into an uncertainty on the flight time.
This is directly proportional to the total flight time and the square of the difference between the mass values of the different flavors of neutrinos, while it is inversely proportional to the total energy of the beam.
In this interpretation, therefore, the advance of the flight time of the neutrino beam with respect to the velocity c, far from being a refutation of the relativistic speed limit, is a good demonstration of neutrino flavor oscillation.
So we could use the advantage Δt in an attempt to determine, more accurately, the value of Δm12.
On the other hand, examples of physical effects equivalent to a super-luminal propagation of particles are considered in other fields of contemporary theoretical physics. Hawking effect about the emission temperature of a Black Hole is, under this respect, a very significant example.
Cosmic neutrinos flavor oscillations. We can now consider what could be the value of the advantage Δt respect to the time of flight of c in the case of neutrinos coming, for example, from a SuperNova explosion.
In this case the average energy of neutrinos νe is of the order of 10^7 eV and the time of flight, for example in the case of  SuperNova 1987a, of the order of 10¹² s.
Under these conditions we have

and it is conceivable that it may start a continuous sequence of oscillations in mass eigenstates.
The logical consequence of this situation is a superposition of two equally probable mass eigenstates.

We lose the information of to the initial state of the emitted neutrino along the way.
So the  uncertainty in mass eigenstates  exists with respect to the state of arrival of the neutrino and a mixing of  mass eigenstates with the same probability equal to ½.
In this hypothesis we have

therefore an advantage Δt of approx six orders of magnitude lower than in the OPERA case.
Interpretation of the principle of uncertainty used above.  The uncertainty principle is commonly intended as an aid to explanation for the impossibility of determining, by observation, contemporarily the position and momentum of a physical system, with absolute precision, because the one excludes the other.
Assuming this interpretation the uncertainty principle could explain , in the case of OPERA, a set of measures centered on an advance Δt=0 with a spread on the obtained measurement results  in the order of (14).
In contrast, the  experimental measurements provided by OPERA appears to be centered on a value of Δt ≈ 60 ns in advance respect to the time of flight of c!
Which explanation is therefore possible to give to the application of the uncertainty principle to justify the consistency of the data provided by OPERA with the fundamental laws of physics known today?
The most coherent interpretation seems to be as follows: the temporal evolution of the neutrino mass eigenstate introduces a temporal evolution in the state of total energy that interacts with space-time producing a reduction of the time of flight. This interaction has to be coherent with the uncertainty principle.
Energy gained or released by neutrino, during oscillation, must be released or gained by space-time, according to the principle of conservation of energy.
A more accurate explanation will require the introduction of some new hypotheses.
We suppose below that space-time possesses a quantized structure. We define a fundamental 1D string element that has the dimension of a length or a time. This fundamental element is a 1D vector in the 2D string wolrdsheet: we call this element the quantum of space-time.
To each 1D of space-time is associated a 1D energy-momentum vector (the total energy associated to a quantum of space-time) that is related to the module of the 1D quantum of space-time with a relation of constraint that we define below.
To introduce the basic unit of space-time we introduce the Polyakov 2D string action  and we proceed to its quantization finding the 1D elementary quantum of space-time

Now we want to consider (17) in the limit n -> 1. The infinitesimal parameters dσ and dτ take the meaning of physically limit movement along, respectively, the spatial direction and  temporal direction of the 2D string worldsheet.
We can call these limit movement as follows

Ω^x e Ω^0 take the meaning of quantum of space-time in space direction and time direction  in the 2D string worldsheet.
Therefore, in this case, to each spatial direction of the elementary string element corresponds a temporal direction that, in a Minkowski’s manifold, is orthogonal to the space direction. The relation (18) binds the module of the element of string along the spatial direction with respect to temporal direction, in the case of a Minkowski’s manifold, and have the values lp and lp/c.
Double differentiation

appearing in (17) must now be rewritten taking into account that in a Minkowski’s manifold, for relations (18), we can write


Since it is possible to show that 2D string worldsheet action of Polyakov coincides with Nanbu-Goto action

given the relation

and because we have

we can rewrite (18) as follows
In (20) with Tμν we have indicated relation Tμν = μν. So we indicate string tension in 2 dimensions as a tensor of rank 2.
In a Minkowski’s manifold we have:
So the string tension in a Minkowski’s manifold can be written as a tensor of rank 2 whose product with the module of the fundamental string elements (the quantum of space-time) in spatial and temporal direction is constant and equal to Planck’s quantum of action. Contracting one of the two indices of tension with one of the two vectors Ω^μ or Ω^ν we get the 2D energy-momentum vector for the string element along the direction μ and ν respectively,
it is now possible to define the following relation

Relation (23) was obtained in a Minkowski’s manifold: it is therefore valid in a region of space-time in which the action of gravitational energy is negligible. Under these conditions (23) defines a relation of constraint: the product of the 1D length of the fundamental string element (the length of the module of the quantum of space-time) and the 2D energy-momentum vector of 2D string worldsheet associated with this element is constant and equal to Planck’s constant.
2D energy- momentum vector Eν thus defines the  expectation value of energy of empty space that corresponds to the amount of energy needed to increase string length of an element of length lp along ν direction.
Similarly we can define Eν as the 2D energy-momentum vector associated with the increase of a quantum of space-time along ν direction. For these reasons, in a Minkowski’s manifold, (23) takes the form:

valids in each quantum of space-time.
Calculation of the anticipation Δt in the time of flight. (24) can be written taking into account variations in the 2D string worldsheet fundamental element:

multiplying the two members is obtained the variational relation of least action for the elementary 2D string worldsheet:

so we have

and then

From (28) we obtain (13) and the result (14). In (28) the term   is an appropriate constant of integration that take in to account vacuum fluctuations of energy of magnitude   for the system under investigation.
Conclusions. Conducing our analysis in 2D we quantize the 2D Polyakov string worldsheet action, obtaining a constraint relation that relates 2D energy -momentum vector and the module of 2D elementary  string element (the quantum of space-time).
We have therefore assumed that the neutrino flavor oscillation interacts with the energy associated with each element of the 2D worldsheet string (or the space-time) exchanging energy. This exchange is obeying the law of conservation of energy.
This kind of interaction does not require any hypothesis of fifth force, and may, on the contrary, be assumed of gravitational type, in the sense that the energy due to the neutrino mass eigenstates interacts with the energy of the elementary string element with an easy phase overlapping, just as it is with a gravitational mass.
We can therefore assume that neutrino, through the temporal evolution of its mass eigenstates, exchanges energy with space-time. This exchange causes a change, a contraction in the length of the 2D fundamental  string element. Integration of this contractions along the path of neutrino flight produces as a result the observed advantage    in the time of the flight.
The energy associated with each elementary quantum of 2D string worldsheet in a Minkowski’s manifold corresponds to the energy of empty space-time, ie the vacuum energy of the gravitational field in absence of gravitational source. The target of a forthcoming work will be to show how this vacuum energy is able to produce effects phenomenological equivalent to hypothesis of dark energy and dark matter under certain conditions.
Basing on the assumptions here introduced the same uncertainty principle, from first and irreducible principle of physics, assumes the rank of derived condition through (25) – (28) by a more fundamental principle that is (23).


[1] B. M. Pontecorvo, Sov. Phys. Usp., 26 (1983) 1087.
[2] L. Wolfenstein, Phys. Rev. D, 17 (1978) 2369.
[3] S. P. Mikheev e A. Yu. Smirnov, Il Nuovo Cimento C, 9 (1986) 17.
[4] S. Braibant, G.Giacomelli, M. Spurio, Particelle ed interazioni fondamentali, Springer, 2010.
[5] J. N. Bahcall, “Neutrino astrophysics” (Cambridge, 1989);
[7] H. A. Bethe e J. R. Wilson, Astrophys. J., 295 (1985) 14.
[8] G. Pagliaroli, F. Vissani, M. L. Costantini e A. Ianni, Astropart. Phys., 31 (2009) 163.
[9] V. S. Imshennik e O. G. Ryazhskaya, Astron. Lett., 30 (2004) 14.
[10] W. Baade e F. Zwicky, Proc. Natl. Acad. Sci. U.S.A., 20 (1934) 259.
[11] A.M.Polyakov, Gauge Fields and Strings, Harwood academic publishers, 1987.
[12] Measurement of the neutrino velocity with the OPERA detector in the CNGS beam,  arXiv:1109.4897.
[13] F. L. Villante e F. Vissani, Phys. Rev. D, 76 (2007) 125019.
[14] F. L. Villante e F. Vissani, Phys. Rev. D, 78 (2008) 103007.
[15] M. A. Markov, “The Neutrino” (Dubna) 1963.

by Marco Lelli

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444 comments to Interaction between neutrino flavor oscillation and Dark Energy as a super-luminal propagation

  • Andrea Rossi

    Dear Franco:
    Thanks to you,
    Warm Regards,

  • Franco

    Caro Dott.Rossi e prof Focardi da qualche anno seguo le vostre sfide alla fisica convenzionale.TRamite la Sua Fusione Fredda
    spero che sia la svolta per le nuove generazioni a lei la speranza facendo un salto metaFisico vedo i miei figli esperti e tanti nuovi uomini che producono, riparano, assistono questo umile oggetto. quindi viva la realtà con serenità Non si Faccia turbare da niente. Io Aspettero con ansia l’uscita ufficiale e parteciperò con impegno ed onore ad ogni esperimento cercando magari di sostenerla . Grazie Franco T.

  • Joe

    Wladimir Guglinski,

    Your theory is interesting. I congratulate you for devising it.

    Still, I must complain that SR is not a theory of matter, but of observation. All matter, even “exotic”, falls under its rubric. SR claims that, although observations made in various frames of reference can vary, the laws of Nature that they yield must be identical within each frame. Otherwise, Nature would not be Nature. That is the reason for which we consider the laws of physics to be universal.

    In the case of the neutrino, seeing it FTL from Earth, and STL (slower-than-light) from its own frame, means that we have established 2 contradictory laws of Nature, which is, of course, absurd. The only way to resolve this issue is to consider SR to be false – in particular, its reciprocity postulate. Rescinding that postulate would have the neutrino be either FTL, or STL, and not both. (This would likewise resolve the infamous Twins Paradox.) Therefore, again, the conclusion is that SR, in its present form, can not be used to invalidate the neutrino’s either FTL, or STL, status.

  • Wladimir Guglinski


    Joe wrote in January 29th, 2012 at 8:49 PM :

    “Conclusion: SR can not explain the FTL travel of a neutrino”

    Dear Joe,

    when Einstein developed his Theory of Relativity, he did not have knowledge on the existence of anti-matter.
    His theory was developed by considering the ordinary matter.
    Therefore, the postulate of relativity (according to which no body can travel faster than light) is concerning to ordinary matter.

    According to my Quantum Ring Theory, the neutrino is composed by [positron-electron].

    In QRT there are two sort of spins:
    1- intrinsic spin- it’s the rotation of the particle about its axis (similar to the Earth dayly rotation)
    2- quantum spin- it’s the rotation of the particle about the center of the helical trajectory traveled by the particle. This is the spin measured in the experiments.

    In the spin-fusion phenomenon proposed in my QRT (when a particle moves about another one) the particle loses its helical trajectory, and so it loses its quantum spin. So, thanks to the spin-fusion, a fermion becomes a boson.

    In the structure of the neutrino, the electron gyrates very close about the positron, and they interact via the spin-fusion mechanism. So, the electron loses its quantum spin, and the neutrino has spin 1/2.
    While the electron gyrates about the positron, the positron gyrates about the center of the helical trajectory.

    As the electron gyrates very close to the positron, we have:

    a) the two electromagnetic fields of electron and positron vanish one each other. However, as there is not a perfect overlap of their two fields, then the electromagnetic field of the neutrino is not totaly null. But it is very weak.
    This is the reason why the interaction of the neutrino with the matter is almost null.

    b) in QRT the particles have two gravitational fields: one composed by attractive gravitons, and another by repulsive gravitons.
    If repulsive and attractive gravity should have the same value of interaction, the resultant gravitational field of the neutrino should be zero, and its gravitational mass should be null.
    But repulsive gravity is a litle weaker than the attractive gravity, and the resultant iis a very weak attractive gravitational fiedl. So, the neutrino has a very weak gravitational field, responsible for its very weak gravitational mass.

    This structure of the neutrino explains why its mass is very small, in spite of it is formed by positron-electron.
    The sum of the masses electron+positrion is 0,5MeV/c²+0,5MeV/c² , but the mass of the neutrino is about 0,04eV/c² only, because the neutrino has its electro-magnetic-gravitational field very near to zero.

    In the anti-neutrino, the positron gyrates about the electron, and the electron gyrates about the center of the helical trajectory.

    According to current theories, there are three sort of neutrinos (or flavors):

    1- electron neutrinos
    2- muon neutrinos
    3- tau neutrinos

    According to Quantum Ring Theory, there are four sort of neutrinos:

    1- electron neutrinos – the intrinsic spin iSp of positron and the intrinsic spin iSe of electron has the same direction of the neutrino motion. So, iSp and iSe have the same direction.

    2- muon neutrinos- iSp of the positron has the same direction of the neutrino motion, while iSe of the electron has contrary direction of the motion. So, iSe and iSp have contrary direction.

    3- tau neutrino- iSp and iSe they both have contrary direction of the neutrino motion. So, iSp and iSe have the same direction.

    4- noum neutrino- iSp has contrary direction of the neutrino motion, while iSe has the same direction of the motion. So, iSp and iSe have contrary direction.

    Obviously the muon and the noum neutrinos have the same properties, and therefore the noum neutrino behaves as it should a muon neutrino. From the viewpoint of their interaction with matter, there is NO difference between them.

    These differences in the structure of the three neutrinos are responsible for their different interaction with matter.
    -> in the electron and tau neutrinos, iSp and iSe are alligned, and so they interact strongly with matter than the muon neutrino, where iSp and iSe have contrary directions.

    In the botton of the page 205 of the book Quantum Ring Theory it is writting the following:
    In the right side of [4.11] the term [e-]^e-p into the electronic neutrino means that the electron has its intrinsic spin aligned with the positron’s spin, while [e]^e/p in the muonic neutrino means that the electron and the positron have their intrinsic spins in contrary directions”

    Einstein’s Theory of Relativity is applied to the electron (matter). His theory is also applied to the positron (anti-matter).
    However, the neutrino is not matter. But the neutrino is not anti-matter too.
    Let’s call ordinary matter the electron and the positron.

    The neutrino is not ordinary matter. It is actually an exotic combination of matter/anti-matter, and such combination does not follow the laws of ordinary matter.

    Therefore, the fundamental postulate of Einstein’s relativity (according to which ordinary matter cannot travel faster than light) cannot be applied to the neutrino, because it is not ordinary matter.

    So, faster than light neutrinos do not violate Einstein’s relativity, because his theory was developed for ordinary matter, and the neutrino is a sort of exotic combination of matter/anti-matter, which does not follow the laws of ordinary matter.

    In short: neutrinos can move faster than light without violating Einstein’s relativity.

    Today the experiments in CERN are made with half of the capacity of the LHC, and the neutrinos move 60 nanoseconds faster than light.
    I think that in the upcoming years, when the LHC will run with its full capacity, the researchers will get neutrinos that move with about 80 nanoseconds faster that light.

    If this prediction of mine be confirmed by LHC experiments in the future, then only my Quantum Ring Theory can save Einstein’s theory.


  • Marco Lelli

    Dear Vladimir,

    Probably I not have been sufficiently clear in the writing of my papers, and this may lead the reader to misinterpret part of what is written there. I take my responsibility. I try to explain better here.

    In the proposed work is supposed that the space-time is quantized. The relation of space-time quantization is derived from the expression of the 2D world-sheet string Polyakov action (or, which is the same thing, the Nambu-Goto action).

    From 2D world-sheet string action we get a simple relation of constraint that links the modulus of the momentum-energy vector and the modulus of the length (in spatial or temporal terms, respectively) of the quantum of space-time.

    This momentum-energy vector is interpreted as the energy associated with each point of space-time ( distance behind two distinct points is equal to one quantum of space-time).

    It is assumed therefore that the oscillation in flavor eigenstate (and therefore in mass eigenstate) of the neutrino beam interacts gravitationally with the energy of empty space-time.

    This interaction leads to a decrease in the modulus length of the quanta of space-time involved in the path of the beam due to the increase in the mass eigenstate of the neutrino.

    This contraction is determined by the relation (23) which indicates that energy and length of the quantum of space-time are inversely proportional.

    To this space-time shrinking corresponds an advantage in the flight time of the neutrino beam which is consistent with that observed in OPERA. We can conclude, on the other hand, a superluminal speed of the neutrino beam.

    A similar interaction (gravity type), between mass eigenstates of a particle and energy of the vacuum of space-time, can only occur when a particle that travels at the speed c changes its state of mass along its path. This happens for neutrinos.

    Following the same assumptions we also try to shows how the advantage time of beams of cosmic neutrinos reaching the Earth from SuperNova showing many orders of magnitude lower.

    Finally we show how, assuming the relation of constraint (23), the same Heisenberg uncertainty relation loses its status as a “principle” to become instead a relation derived from a more fundamental constraint relation.

    How do you see there is no reference to the reference system of the neutrino!

    As regards the reference to the vector bosons of the weak force in my paper, this is wrote in a very large physics literature and widely accepted by the scientific community.

    This, of course, does not necessarily make it true. I suppose, however, represents a haliby, at least in part, that will lead you to forgive the author of the paper.

    About your Quantum Ring Theory, well publicized in your post, I confess all my IGNORANTIA MAXIMA.

    However I declare myself maximally available to study it if you’ll be so gentle to send me some documentation to the following address:

    With sincere esteem

    Marco Lelli

  • Andrea Rossi

    Dear Giuliano Bettini:
    The time to go where the E-Cat work, take a picture, put in in this blog. This week I have no time, next week probably.
    Warm Regards,

  • Andrea Rossi

    Dear Erik:
    Thank you, I’ll see.
    Warm Regards,

  • Erik

    Dear Mr. Rossi,

    Somebody probably brought this up already, but doesn’t this engine ( sound like a perfect match for the e-cat? It almost looks like a plug-n-play solution (at least for powering boats).

    Regards Erik

  • Giuliano Bettini

    Dear Andrea Rossi,
    (from Guido Chiostri):
    “is it possible to see pictures of the rooms where E-cats are tested 24 hours per day ?”
    You said: “Yes.”
    But please, how, where and when?
    Best Regards
    Giuliano Bettini

  • Joe

    Wladimir Guglinski,

    In SR, a preferred frame of reference is not allowed. Therefore, objective reality can only be deduced logically. And there exists 4 possible scenarios:

    1. Earth sees neutrino traveling faster-than-light (FTL). This contradicts neutrino’s seeing Earth as traveling FTL, so it can not be true.

    2. Neutrino sees Earth traveling FTL. Likewise, this contradicts Earth’s seeing neutrino as traveling FTL, so it also can not be true.

    3. Earth and neutrino do not travel FTL, rendering the FTL speeds outside their own frames of reference as illusory. But, in SR, illusions are not allowed; subjective experience is identical to objective reality. Therefore, this scenario can not be true.

    4. Earth and neutrino do travel FTL, rendering the slower-than-light speeds inside their own frames of reference as illusory. But, again, in SR, illusions are not allowed; subjective experience is identical to objective reality. Therefore, this scenario, too, can not be true.

    Conclusion: SR can not explain the FTL travel of a neutrino.

  • Albert Ellul

    Dear Ing. Rossi.

    Has there been any progress in your patent applications worldwide? I just hope that you manage to get the patents in your name. You definitely deserve it. Besides, this will surely help in the commercialisation of the e-Cat for everyone’s benefit.

  • Wladimir Guglinski

    Marco Lelli wrote in his paper:

    “We can consider valid this assumption, at least in first approximation, because matter interacts in particular with νe and less with νμ and ντ.νe weakly interacts with matter by W± and Z° bosons while νμ and ντ only by Z° bosons”

    Dear Marco,
    W± and Z° bosons do not exist in the structure of the matter.

    They are produced only in the collisions of particles, and they have a very short time-life.
    So, as they do not exist within the structure of matter, the neutrinos cannot interact with matter via W± and Z° bosons.

    The quantum theorists believe that W boson works in the decay of the neutron, because they believe that neutron has a quark structure (d,u,d).

    However the quark structure (d,u,d) of neutron is wrong, because it is impossible from such model to explain the Don Borghi experiment and the Conte-Pieralice experiment.
    Only from a model of neutron formed by proton-electron it is possible to explain those two experiments.

    The concept according to which the exchanging of W and Z bosons mediate the weak intereaction comes from the Yukawa’s theory of neutron.
    In his theory, a meson jumps between two protons within the structure of the neutron.
    Such Yukawa’s idea of interaction via the exchanging of a particle is wrong, because today we know that Yukawa model of neutron is wrong.
    But such concept of interaction via exchanging of particles was addopted in Particle Physics, in spite of it is wrong.

    Into the neutron formed by proton-electron, the electron moves about the proton, and the electron loses its helical trajectory (so within the neutron’s structure the electron moves with a rectilinear Newtonian trajectory). As the electron loses its helical trajectory, it loses its quantum spin, and it becomes a boson. That’s why the neutron has a spin 1/2.

    Such phenomenon according to which a fermion loses its spin is named “spin-fusion” in my Quantum Ring Theory.

    The Standard Model has many unsolved puzzles, because the spin-fusion is not considered in Quantum Mechanics.

    For instance, consider the paradox of mesons Rho.
    The mesons pi and the mesons Rho (have the same structure, according to the Standard Model (Rho are excited mesons):

    • The meson pi(+) has structure ud’ , its rest mass is 140MeV , and its time decay is 2,6×10^-8s

    • The meson Rho(+) has structure ud’, its rest mass is 770MeV , and its time decay is 0,4×10^-23s

    • The meson pi(o) has structure (uu’+dd’)/2^1/2 , its rest mass is 135MeV, and its time decay is 0,8×10^-16s

    • The meson Rho(o) has structure (uu’+dd’)/2^1/2 , its rest mass is 770MeV, and its time decay is 0,4×10^-23s.

    But note the following:

    1- The masses of pions pi(o) and pi(+) have a difference of 5MeV.
    But Rho(o) and Rho(+) have the same mass 770MeV
    Why ????

    2- The pions pi(+) and pi(o) have different time decays: 2,6×10^-8s and 0,8×10^-16s.
    But the mesons Rho have the same time decay: 0,4×10^-23s
    Why ????

    There is no way to explain it from the current Standard Model of Modern Physics, because:

    A) If we use an argument so that to explain the difference of mass 5MeV between pi(o) and pi(+), however the same argument would have to be applied to the masses of Rho(o) and Rho(+), and they would have to exhibit a difference of mass too. But Rho(o) and Rho(+) have the same mass !!!

    B) If we use an argument so that to explain the difference of time decay between pi(o) and pi(+), however the same argument would have to be applied to the time decay of Rho(o) and Rho(+) , and they would have to exhibit a difference of time decay. But Rho(o) and Rho(+) have the same time decay !!!

    This paradox is eliminated by considering a structure of mesons working via spin-fusion mechanism, as is shown in my new book entitled THE MISSED U-TURN, the duel Heisenberg vs Schrodinger – from Newton to Rossi’s eCat , to be published in the upcoming months by an important publishing house in London.

    Many other paradoxes not explained by the Standard Model are explained by considering the spin-fusion mechanism.

    The data collected in the LHC is enough to confirm the Supersymmetry theory. However the experiments shows that Susy is a wrong theory.
    Other experimental finding are also suggesting that Standard Model is incomplete.

    So, there is need to consider New Foundations for Physics. And “spin-fusion” mechanism is one among other new foundations which deserve to be considered seriously by the physicits.


  • Wladimir Guglinski

    Joe wrote in January 29th, 2012 at 12:40 AM :

    “Earth sees neutrino as neutrino sees Earth. While it might be true that s’< s from Earth's point of view, the inverse is true as well: the neutrino senses the Earth as the one that is suffering all the effects of very fast flight.

    Dear Joe,
    the data obtained in the experiments were not collected by the neutrino.

    The data were measured by the physicits who work in the CERN, and they work in the surphace of the Earth. The apparatus they use in the experiment do not move together with the neutrino, when they get their data.

    If the neutrinos should make the measurements, perhaps they could get the result suggested by Marco Lelli.
    But they did not make it.

  • Andrea Rossi

    Dear Robert:
    We are ready to fight.
    Warm Regards,

  • Joe

    Wladimir Guglinski,

    I believe that Marco Lelli is wrong in his explanation for the ostensibly greater-than-‘c’ neutrino. I do not believe that Nature works through uncertainty. All phenomena occur with regularity, which implies certainty at all levels. This cause-and-effect paradigm is the thing that allows us the luxury of science. If Nature were uncertain, Nature would not be Nature.

    Although, I do not understand your use of Special Relativity in this case. In SR, each of 2 frames of reference that are in relative motion with each other will witness all phenomena occurring in the other in a reciprocal manner. Earth sees neutrino as neutrino sees Earth. While it might be true that s'< s from Earth's point of view, the inverse is true as well: the neutrino senses the Earth as the one that is suffering all the effects of very fast flight. So we really get nowhere with this line of reasoning since both situations "balance out".

  • Robert

    Dear Dr. Rossi,

    I hope your dream of bringing your invention to the world at large will become a reality. It really does have the potential to change the world in a profoundly positive way – a true revolution. But my fear is that there are many powerful companies, organizations and even countries that will not just stand by and let your invention take away their market share and profits from traditional energy sources. They will see what you are doing as a threat to their wealth and not care about the wonderful benefit to humanity. Their greed is something to be worried about.

    Anyone who finds a cure for cancer, or a solution to the energy crisis, needs to be very, very careful about their own personal safety. I wish anyone who would attempt to hinder your progress to be exposed and to fail. And I wish for you good health, and continued successes to make your life’s dream a reality.

  • Andrea Rossi

    Dear Roberto:
    I will,
    Thank you,
    Warm Regards,

  • Wladimir Guglinski

    Marco Lelli wrote in his article:

    “Which explanation is therefore possible to give to the application of the uncertainty principle to justify the consistency of the data provided by OPERA with the fundamental laws of physics known today?
    The most coherent interpretation seems to be as follows: the temporal evolution of the neutrino mass eigenstate introduces a temporal evolution in the state of total energy that interacts with space-time producing a reduction of the time of flight. This interaction has to be coherent with the uncertainty principle.”

    Dear Marco,
    your argument makes no sense.

    You cannot consider the time in the referential of the neutrino.

    Suppose that a man leaves the Earth in a spaceship with a constant relativistic speed V, so that the time evolution here in our planet is 5 times faster than within the spaceship.

    t = time in the Earth
    t’ = time within the spaceship
    So, t’= t/5

    What is the distance traveled by the space during a time t?
    If we consider the time t in the Earth, we have s=V.t
    But if we consider the time t’, we have s’=V.t’, and s’=s/5 (a distance 5 times shorter).

    Of course the correct distance traveled by the spaceship is s=V.t (we have to use the time t measured by a clock situated in the Earth, and not a clock within the spaceship).

    In your article, you did not consider the time evolution in the Earth. Instead of, you have considered the time evolution of a clock moving close to the neutrino.
    So, while the distance traveled by the neutrino is s (measured here in the Earth), in your article the distance traveled by the neutrino is s’ (which is not correct), because s'< s (s is the distance measuered in the experiment).


  • Roberto

    Caro Andrea Rossi Grazie per la sua risposta, se deciderà di provare questa idea non dimentichi di utilizzare all’interno del circuito un liquido che non evapori e che non tema il gelo. Mi faccia sapere come è andata e buon lavoro. Cordiali saluti.

  • Andrea Rossi

    Dear Roberto:
    Now I have understood, sorry to be late. The idea is good, I will test it, thanks to you and to Italo A. Albanese: you have outsmarted me.
    Adesso ho capito, chiedo scusa per non avere capito prima. Si’, l’ idea proposta da Lei e da Italo A.Albanese vale la prova. Ci provo, OK?
    E grazie ad entrambi, siete stati piu’ svegli di me.
    Warm Regards,

  • Roberto

    Caro signor Andrea Rossi Provo a spiegare come si potrebbe fare ad arrivare al suo reattore con i raggi solari. Con uno specchio parabolico delle dimensioni di una normale antenna satellitare, i raggi solari vengono concentrati su un unico punto, dove si mette un ricevitore che ha al suo interno una serpentina di tubo di rame,all’interno del tubo circola (aiutato da una piccola pompa) un liquido che resiste ad alte temperature e quindi non evapora.un’estremità della serpentina verrà collegata ad un tubo di rame che attraverserà il suo reattore al posto delle resistenze e naturalmente andrà collegato all’altra estremità della serpentina. Poi con un termostato andremo a comandare la pompa che facendo circolare il liquido andrà a portare a temperatura il reattore che una volta avviato sempre tramite il termostato fermerà la pompa.Cosa ne pensa?Io ho già provato. in questo modo scaldo un bollitore da 80 litri.La temperatura della serpentina raggiunge in breve(10-15 minuti) 110 gradi centigradi e oltre. Grazie per l’attenzione che vorrà rivolgermi. Cordiali Saluti.

  • Andrea Rossi

    Dear Italo A. Albanese:
    About your last comment: can you explain better what you mean about solar energy application? What I understood was connected with the oiperation of the reactor.
    Warm Regards,

  • Andrea Rossi

    Dear Italo A.Albanese,
    I cannot give info about the reactor.
    Warm Regards,

  • Italo A. Albanese

    @Andrea Rossi (January 26th, 2012 at 3:58 PM)
    Simply heat the lead! The hot lead will warm up the core. If you need an higher temperature, just enclose the (liquid!) lead in a steel case.

    Best regards, Italo A.

  • Andrea Rossi

    Dear Roberto:
    I am not an expert of solar power, so maybe I miss something, but: how can I heat a reactor inside a heater, sorrounded by lead shielding, with solar power if not powering the resistance with the electricity made by the photovoltaic panels?
    Warm Regards,

  • Andrea Rossi

    Dear Neil Taylor:
    Thank you, I will click through.
    Warm Regards,

  • Hello Mr. Rossi,

    Here is another novel invention, apparently ready for the market, that may be an excellent fit for the E-Cats – both the home and industrial units – for the generation of electricity.

    Take a look at their website for further information:


    Here is short excerpt from their announcement:

    “The news is all Marnoch needs is a 20º C (38º F) or higher temperature spread and there’s potential to generate electricity. The system becomes more economical the wider the gap. It’s quite an idea for mechanical energy from low temperature heat spreads.”

    Kindest regards from a true believer and fan…NJT

  • Roberto

    caro andrea rossi, mi scusi ma forse non mi sono spiegato bene. Io intendevo, con un concetratore di raggi solari riscaldare direttamente il reattore e non con il fotovoltaico fare l’energia elettrica che serve per le resistenza e che adesso servono per portare a regime il suo reattore.Cordiali saluti.

  • Bhagirath Joshi

    Joe Explained:
    I consider the property ‘c’ to be the characteristic speed of the medium of aether. Whether or not it coincides with the speed “in vacuo” of a specific particle (photon, neutrino) is unimportant.

    My explanation:
    That is what I am saying too.. In Einstein’s famous equation , ‘C’ is assumed to be the speed of light. What I said that, that is not correct and value of ‘C’ may be much higher than the assumed speed of Light.

    Bhagirath Joshi

  • Joe

    Bhagirath Joshi,

    I consider the property ‘c’ to be the characteristic speed of the medium of aether. Whether or not it coincides with the speed “in vacuo” of a specific particle (photon, neutrino) is unimportant. The thing that is important is that every phenomenon in the Universe responds to its immediate environment; there are no islands of reality. So when we notice speed limits everywhere in Nature, we hypothesize the presence of specific media at those places. And we can also hypothesize an ULTIMATE medium which subsumes all others: aether. This, of course, is denied by Special Relativists who still cannot explain the presence of ‘c’ in their theory. (If there exists no aether, just vacuum, there should also exist no ultimate speed limit. This, of course, is contradicted by observed reality in particle accelerators.)

  • Andrea Rossi

    Dear Roberto,
    Yes, it is possible, of course, use solar power to make the electricity necessary for the resistance of the E-Cat.
    Warm Regards,

  • Andrea Rossi

    Dear Davide C.:
    ATTENTION: WE are not collecting money from the e-cat pre-orders, therefore if somebody offers you an e-cat and asks for money, is a bogus!!!
    Warm Regards,

  • Davide C.

    salve dott. Rossi,
    in un forum di finanza che frequento c’è un tale che sostiene di aver acquistato l’e-cat pagando un acconto.
    Alla mia rimostranza che Lei non ha ancora fissato il prezzo e che non accetta acconti, il tale ha risposto che invece li accetta e ha detto che mi può fornire anche il CRO del bonifico effettuato.
    Grazie per le eventuali informazioni che mi può dare, nei limiti della sua disponibilità.

  • Roberto

    Buongiorno, seguo la vicenda del suo catalizzatore da gennaio 2011 e volevo solo esternare un’idea e passo al dunque. Non si potrebbe portare l’e-cat a temperatura utilizzando l’energia solare? In tal modo non si avrebbe nemmeno il costo dell’energia elettrica per portarlo a regime.Non essendo ne un ingegnere ne altro ma solo un appassionato,mi scuso sin d’ora se ho detto una fesseria. Complimenti e in bocca al lupo per il suo lavoro. Cordiali saluti.

  • Andrea Rossi

    Dear Alfonso Troisi:
    It is not easy: other energy sources need space, while with an electric resistance the E-Cat will be very small…we are studying, it is not easy.
    Warm Regards,

  • Alfonso Troisi

    Hello Mr. Rossi,
    I would like to know at what point are you with a different system to start the e-cat.

    The first generation e-cat will start only with electricity or will you be able to make it start in other ways (chemical reaction-gas-others).

    Best regards,

    Alfonso Troisi

  • Andrea Rossi

    Dear Alfonso Troisi:
    I can guarantee: I do not care of TAD (Tongue-Displaced-Air). We have to manufacture the E-Cat for everybody. This is the issue.
    Warm Regards,

  • Alfonso Troisi

    Hello Mr. Rossi and all,
    Just some considerations.
    I find it very sad that spreading the word about Mr. Rossi’s great tecnology all most people have to say is “I’m sure they’ll stop it”, or “I’m sure at the end the cost will be similar to other heaters” or whatever else can keep them from believing that this world ca be a better place and that there are outstanding man working for our future. An important achievement of the e-cat can be to give hope and optimism to this people.
    I’ve read your story, Mr. Rossi. Very impressive what you’ve been through. I’m glad you had the strength and the will to look forward. Please let our greatfullness and our hopes be fuel to you.
    Warm regards,

    Alfonso Troisi

  • JYD13

    Dear Dr ROSSI

    400° C in less than 5 seconds could be interesting.
    Could you see this ?

    I’am very impatient to see your wonderful work on the construction of the robotized factory !

    With great respect

  • Enrico Billi

    Indeed it is fascinating how neutrino physics could be used to get information about the structure of space-time beyond the classic general relativity.
    By now high energy gamma rays from deep space have been used to find signs of quantization of space-time, but they didn’t give any positive results, that i know.
    This paper is really interesting, well done Marco!
    Of course the theory need further experimental proof, but is a good start… so, lavolale lavolale!

  • Andrea Rossi

    Dear P.G. Sharrow:
    Within a couple of weeks we will have precise schedulings regarding the construction of the robotized factory, and the timing, so that I will be able to communicate the time terms within which we will able to start the deliveries, as soon as possible. We will work very hard on this.
    Warm Regards,

  • Scott Hansen

    Dear Mr. Rossi

    In order to start the reaction with much less energy and maybe just a battery, is it possible to form a long cone shape with the kernel and Heat just the tip. When the tip reaches temperature the reaction might cause a cascading reaction with the rest of the nickel. With a little insulation on the tip it probably wouldn’t take much energy heat. One concern would be that the tip way over heat.

  • Bhagirath Joshi

    I think the confusion is coming from the definition of ‘C’ being a constant it could take up any value. The peed of light is not a constant in first place since the speed of light is dependent on the medium it travels. Assuming E = mC2 being correct, the energy output in fission and fusion can be reevaluated. The best way to do is to analyze the yield data on detonation of nuclear weapons. Than one can calculate ‘C’ from the experimental data. I was told that the Hydrogen bomb produced far greater energy for annihilated mass. which indicates that the constant ‘C’ is not the speed of the light but some other value.

    Since these yield data is still classified, may be the scientist who can access these data will have to take up this task.

    Bhagirath Joshi

  • Mark Szlazak

    Starbucks Coffee uses Rossi powered espresso machines. The coffee giant is supports the green revolution with cold fusion machines in all their stores. Peets Coffee will not be far behind. Not as big a market but it does have PR value. “E-cat Inside” instead of “Intel Inside” on Starbucks cups, etc.

  • Joe

    The distance between CERN and Gran Sasso: fixed.
    The travel time for a neutrino along this route: fixed.
    v(of a neutrino) = distance/travel time
    > c.

    And yet, some theoreticians are trying to convince us that a neutrino is STILL slower than a photon.

  • The E-cat energy amplifier is just one part of an energy production system. It can not solve all energy needs in one “black box”, It just makes heat. I was willing to pay $4 to $5000 for that “black box” heater as a part of my farm energy system. Now Andrea says he can do it for $500.WOW! I’ll take two and a box of fuel cartridges. And my neighbors, when they see this work, will take a dozen more. Hot water for a winery, heating for greenhouses. How can I help to make this work faster!? pg

  • Andrea Rossi

    Dear Fabio,
    This is a very good question, we are thinking of this, also because the electric energy is very expensive. The pro of the electric resistance is its compactness: chemical energy (combustion) needs space for venting, burning etc. But you are right.
    Warm Regards,

  • fabio

    Dear Dr Rossi
    Why not use a chemical reaction (which can be very powerful in a short time) to create the right temperature to achieve self sustenance of ‘cat and that could be triggered by a cartridge inserted into the system and be ejected at the end of the task by the system itself.
    regards Fabio

  • Andrea Rossi


  • @Marco Lelli; I did a quick read and will have to do a real study next. To me a neutrino has very little spin and wobble, therefor little interaction and the least slowing of any particle in it’s travel. Perhaps the fastest particle is a neutrino and not a photon. pg

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