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

  • Andrea Rossi

    Thank you for your insight,
    Warm Regards,

  • Physicists can reconcile this discrepancy by adding a fourth neutrino with a specific mass, although such a move would require modifying the Standard Model, the theory of subatomic particles that has taken decades to build. Despite being 70 percent of the universe, dark energy was only discovered in 1998 by two.. Mobilis in mobili! Theoretical Physics Division, IHEP, Chinese Academy of Sciences. The Data That. Interaction between neutrino flavor oscillation and Dark Energy as a super- luminal propagation. Dark Energy. We illustrate this possibility in two different models of space–time foam based on D-particle fluctuations in either flat Minkowski space or a stack of intersecting D-branes. In several experiments, researchers have detected each of the neutrino flavors and even. Therefore we will impose that neutrinos are superluminal in the . Division, IHEP, Chinese Academy of Sciences. A simple formula for the relationship between particle spin and mass is also . EM field propagation. In several experiments, researchers have detected each of the neutrino flavors and even watched them oscillate back and forth between flavors. Has OPERA found superluminal particles? Theoretical physicists, particularly theoretical particle physicists, are nearly infinitely flexible. They measured the distance between CERN and Gran Sasso, and divide. Marco Lelli. These are models in which neutrinos interact not with the usual. Gravitational waves are superluminal in water surface analogy of . Home · Journals · About. Cherenkov radiation of superluminal neutrinos does not . ISRN High Energy Physics. Nevertheless, theory predicts oscillation between the three ordinary. It leads to a Lorentz violation in the neutrino sector. Direct Download. Please see Scince Magazine. As it is well . About. It could be that really high-energy neutrinos travel at a different. In a new study, a team of physicists thinks it s time to put the question of the fourth neutrino s existence to the test. Italian National Institute for Nuclear Physics, in Gran Sasso National. Even if dark energy is simply caused by a cosmological constant, the. Following the usual effective field theory logic, this coupling is expected to arise in neutrino dark energy models. The results are freely available to the nuclear physicists’ community so that. Physicists working at the Daya Bay Reactor Neutrino Experiment in China have. TextSharp™ 5. The Chinese experiment detects electron antineutrinos produced via nuclear beta.

  • Andrea Rossi

    Robert Sini:
    I have just finished to study ” Quantum Theory of Tunnelling” of Prof. Mohsen Razavy. Now: if you study this book and the book of Prof. Norman Cook “Models of the Atomic nucleus”, there is already the theory that can explain the Rossi Effect. As Prof. Focardi said: ” To understand LENR it is not necessary try to write exotic things, it is already all there, in the Physic texts: we have just to study better what has been written.”. Reading what I was writing, I understood that I was just copying the work of these great Professors, plus the unpublished work of Prof. Suffritti of the University of Sassari ( Italy). Therefore, I just scrapped my papers.
    About the clownerie of the “electron capture”: it is totally groundless: anybody serious knows that electron capture can happen only in atoms with strong excess of protons and this situation does not exist in LENR. It is just an easy pseudo-theory to resolve difficult problems without a serious and very difficult study.
    Warm Regards,
    p.s. Forgot to say: another important pillar is “Nuclear Models” of Greiner-Maruhn. In these 3 books you have all the theoretical work done. The rest is experimentalism and industrialization.

  • Robert Sini

    Dr Andrea Rossi:
    After the publication of your patent, which is the status of the theory behind the so called Rossi Effect?
    What do you think of the electron capture as an explication of the LENR?
    Thank you,

  • Andrea Rossi

    Sven Johansson:
    Right now ( 08.45 p.m., May 23rd) I am in the factory of the Customer testing the Hot Cat in the container of the computers, beside the 1 MW E-Cat. This is the core of what will be the domestic heater. We are working also on this, do not worry. It is difficult to foresee the scheduling, but we are going on. My teeth are so tight that to talk I had to become ventriloquous ( he, he, he…)
    Warm Regards,

  • Andrea:
    When will we be able to heat up the long and expensive Swedish winters with your E-Cat?
    Keep the good work and your teeth tight.

  • Andrea Rossi

    You are not stupid and I am not allowed to give data regarding the 1 MW E-Cat before the end of the test.
    Warm Regards,

  • Edmund

    Dr Rossi:
    I do not know if you can answer to this question, but I want to try.
    You said that you are finding the 250 kW Ecats more efficient than the smaller ones. But we all know you are working only in the 1 MW Ecat several months since. As a consequence of this I desume you have 250 kW Ecats mixed with normal Ecats inside the 1 MW plant.
    Am I stupid?

  • Andrea Rossi

    Michael Kors:
    Yes, I did.
    Warm Regards

  • Dr Rossi:
    Did you find in the books of Norman Cook and of Greiner – Maruhn bases for your theoretical explication of the Rossi Effect?

  • Andrea Rossi

    The Customer is utilizing the 1 MW plant and to the necessary extent we are providing technical assistance. This is all the information I am able to provide, until I’m given further permission from the Customer.
    Warm Regards,

  • Is the Customer of IH utilizing the 1 MW plant delivered to him?

  • […] Vows Fight to Defend Intellectual Property February 29, 2012 Andrea Rossi responded to an inquiry about the recent test of his E-Cat mentioned by Roland Pettersson with a stern […]

  • Andrea Rossi

    Dear Eng. Mario Del Pozzo:
    Thank you very much for your important comment, and it is a shame that it is not also in English, so most of our readers will not read it. Anyway, I answer to you in English, to make it up.
    First of all, thank you very much for your kindness and your suggestion about ignoring the pre-paid puppets. I agree.
    The pre-order for the 4 E-Cats is accepted, when we will contact you we will see particular conditions for the Institutions you mentioned.
    Now the answers:
    1- yes
    2- It is not a constant, it is an average
    3- 1 kWh/h is the average consume, but you can have higher peacks and self sustained mode. At th end of the day, you will find that for each kWhe you get 6 kWht
    4- same as above
    5- there is not a limit, you can go also with zero wh at the input , but at the end of the day you will still have respected the ratio 1:6
    6- no (see above)
    7- you do not need to do any variation, the control system makes the job.
    8- also 1 hour, but it depends on the specific conditions, but remember that the average will be reached, sooner or later
    9- yes
    10- If you are talking of domestic E-Cats, you will never go over 80 C. But the answer is complex, and you must put a distinction between the industrial plants that want to make electric power, the domestic E-Cats from which the owners want to get electricity and the Customers who do not need electricity.
    In the first case, we are working with Siemens to find the right cycle, for the domestic we are making a research, and if we will be able to resolve the problem we will retrofit the E-Cats of the Customers owners of thermic E-Cats. The last cathegory, of course, has not the problem.
    Again thank you and
    Warm Regards,
    Andrea Rossi

  • Andrea Rossi

    Dear Rob:
    Not bad.
    Warm Regards,

  • Andrea Rossi

    Dear Francesco Toro:
    I have not time to deal with sites which offend my person: this fact is the evidence of their weakness against my technology, and what counts is not my person, what counts is my technology. As I always said, E-Cats answer with facts to the chatters of pre-paid puppets. Honestly I really have not time to see their links that you propose, I just ignore all this meaningless noise. My time, in this moment, is very important and I cannot waste it.
    Warm Regards,

  • mario del pozzo

    Chi scrive è un vecchio ingegnere che prova a sviluppare progetti per usare l’ecat in impianti esistenti. In sistesi mi pare che l’ecat sia una macchina (cm33x33x6/10kg)che trasforma 1 kWh elettrico in 6 kWh termici. Ora a me, come ingegnere, non interessa come ciò avvenga, non interessa quello che succede dentro la macchina. Interessa però sapere quello che succede fuori, come si comporta la macchina verso l’esterno, altrimenti fornire ad un cliente un progetto affidabile diventa impossibile.
    Mi pare, se ho capito, che un modulo ecat sia in grado a regime di fornire max 10 kWh termici/ora assorbendo 1.67 kWh elettrici. Mi chiedo:
    1. posso mantenere il regime pieno carico, ad esempio, per 100 giorni ?
    2. il consumo elettrico resta costante (a pieno carico) a 1.67kWh/ora ?
    3. se riduco la potenza elettrica entrante a 1 kW (1 kWh/h) ho in uscita
    6 kWh termici/ora ?
    4. e se riduco la potenza entrante a 100 W ho in uscita 0.6 kWhtermici/h?
    5. c’è un limite alla potenza entrante sotto il quale la reazione cessa ?
    6. la potenza entrante dev’essere sempre mantenuta ?
    7. Per variare l’energia entrante serve un variatore di tensione (se la
    resistenza riscaldante è fissa) oppure posso per alcuni minuti non
    alimentare la macchina ?
    8. in tal caso per quanto tempo posso non alimentare l’ecat prima che la
    reazione cessi ?
    Penso di usare l’ecat in impianti a circuito chiuso per riscaldare acqua in serbatoi di accumulo esistenti. E’ ovvio che la richiesta di calore da parte dell’utente, il volume del serbatoio, la caldaia esistente e le caratteristiche dell’ecat vanno relazionate tra loro, cercando di rendere
    massimo il rendimento dell’impianto. Supponiamo che l’ecat sia alimentato con 1 kWh/ora. Ho in uscita 6 kWh termici/ora. Con buona approssimazione facendo circolare nell’ecat 8 litri d’acqua al minuto ho un DeltaT=10°C:
    9. se faccio circolare 4 l/minuto ho DeltaT=20°C ? E se 16 ho DeltaT=5°C ?
    10. c’è una portata minima al di sotto della quale non posso andare ?
    11. il DeltaT è sempre lo stesso quale che sia la T dell’acqua entrante ?
    Cioè se entrano 8 litri d’acqua al minuto a 20°C escono a 30°C. Se
    invece entrano a 80°C escono a 90°C ?
    Avrei altre domande ma mi fermo qui. Prenoto, se posso, 4 ecat. Uno per conto dell’Istituto Salesiano PIO XI, uno per l’Istituto Gerini, uno per il Borgo Ragazzi Don Bosco, tutti a Roma. Uno infine per me.
    Consiglio:ignori i pupazzi.Li consideri:cresceranno.Li ignori:svaniranno. Mio nonno, uomo dell’800, diceva “quando un cane abbaia offendersi è da sciocchi”. Preciso che ho massimo rispetto per i cani quadrupedi.
    Buon lavoro.
    ing. mario del pozzo

  • Rob

    Dear Mr.Rossi,
    To me it seems that the very small amount of gamma radiation is due to the fact that metal powder is an essential component in the process. Electromagnitic radiations can be absorbed due to eddy currents that occur. Eddy currents will produce heat due to the electrical resistance within the metal.
    Compare this with induction cooking on nana scale.
    In short, much gamma radiation is generated, but most of it is absorbed within the metal powder.
    The rest is absorbed by the lead shielding.

  • Andrea Rossi

    Dear Carl Friedrich Gauss:
    No, the peak remains the same, but it will take less time to start the process.
    Warm Regards,

  • carl friedrich gauss

    Dear Ing.Rossi,

    is possible to exploit the existing boiler to send the water temperature in such a way as to depress the peak for the ignition of the E-Cat ..?

    in practice, I turn on the boiler, the water heats up and then turn on the E-Cat, perhaps reducing the peak inrush.


  • Andrea Rossi

    Dear Enzo Amato,
    I can only confirm a COP 6 (energy COP).
    Warm Regards,

  • Andrea Rossi

    Dear Christian Bistriceanu:
    That is a storm in a glass of wine. We are working very hard, while they chatter, and we are warriors: never mind the paper tigers.
    They tried to destroy us with a very malicious move, but shoot tennis balls against a tank: the manufacturing of our production plants is going on regularly, our plans are developing regularly and our E-Cats will go to the People respecting our scheduled march, in the scheduled locations.
    We have reached already a tremendous number of pre-orders and our first year of production is covered: this is the ocean in which our warship is navigating: let alone the storms in wine glasses, made by self referencial imbeciles or pre-paid puppets.
    Warm Regards,

  • Enzo Amato

    Dear Andrea Rossi,

    sorry for a new boring post about the “cost COP” of the home eCat, but I see another problem. If I need about 15 KWh/day for a eCat (about 30 for two), this could be a serious problem for the whole production of electric energy. Actually I need 15 KWh/day for my house. With the eCats I would have a consumption of 2x-3x this value. If every household had one (or two) eCats, this could be a very big problem for the production of electrical energy in the whole land. The electrical power could be not enough for sooooo many eCats. With for example 10.000.000 eCats, this would be a power of 150 GWh (these are a lot of, for example, nuclear plants)!! For this reason too I thing that the self sustaining mode would be very important.


    Enzo Amato

  • Christian Bistriceanu

    Dear Andrea,

    I trust you will carry on with your work and deliver the E-CAT to the market. It is clear to me now that the infernal machinery to destroy you and the E-CAT has been started. I wish you could find the time in the near future to contradict with hard evidence the skepticism.

    God speed and I am a firm believer in your technology until I will see irrefutable evidence to the contrary!!

    Best regards,

  • Andrea Rossi

    Dear CWatters:
    We are manufacturing in the USA all what necessary to make the production, which also will be made in the USA, of the E-Cats, in our factory in Florida.
    All the other information is confidential and there is no reason at all for us to give more public information, presently, regarding our production present and future, mainly for safety and security reasons. We give only due information to the due Authority and our right to confidentiality and privacy must be respected. I received many other comments similar to yours, so this answer is valid for them as well.
    Warm Regards,

  • Andrea Rossi

    Dear Keith W:
    Yes, the E-Cat will be programmed to avoid to sum the peaks.
    Warm Regards,

  • Keith W

    Dear Mr Rossi

    I have a couple more questions if I may.
    In your replay to Bernie Koppenhoffer ( it is not clear in your reply if you mean that the e-cat is designed to be installed along side (in parallel) with the existing heat generator or whether it is meant to replace the existing heat generator. If it only supplements the existing system then the savings may not be so great and would make installation and control more complex.

    For installations where you need to ‘stack’ two or more home e-cats for higher heat outputs, this would cause a high current draw if they all ‘powered up’ at the same time. Most houses would not be wired for such a load on a single spur. Is the e-cat controller intelligent and ‘aware’ of other e-cats to prevent them starting up at the same time?

  • CWatters

    The BRC Incident Report says..

    “Currently all production, distribution and use of these devices is overseas”.

    Is theis correct? There no working ECAT in the USA?

  • tj

    To — Daniel De Caluwé

    The 51.5 million capital cost figure is based on borrowing 30 million @ 4%, and then paying it back over 30 years in 360 equal payments, just like a 30 year mortgage. A.R. said the e-cat is expected to have at least a 30 year life span.

    When A.R. estimated a 30 million price tag for a self sustaining 45 MW electricity producing e-cat, it seemed implicit that the price included the turbine and generator.

    Personally I think super critical CO2 turbine systems would offer important advantages of 40–50% efficiency, mechanical simplicity, and compact size.

    Ideally the turbine coolant temperature would be engineered to be hot enough for use in a combined heating, hot water, and adsorption AC system. Large buildings are perfect candidates for combined systems.

  • Andrea Rossi


  • Andrea Rossi

    Dear Reader:
    There is another imbecile that has written in some blog that I sold in New Zealand a 1 MW plant and that it is not working well: well, it is not working at all, for the simple reason that I never sold, nor installed, nor put in operation any plant at all in New Zealand!!! This is another example of the maliciousness of the snakes, but also is the demonstration how afraid are their puppeteers of us: but do not worry, I never am impressed by paper tigers, and our production line for the E-Cats is growing up day by day: we will surely not be stopped by some puppet-lie.
    Warm Regards,
    p.s. I love New Zealand, and I have been there as a tourist, a trip I will never forget. But I never worked there, so far.

  • Andrea Rossi

    Dear Claud:
    There is not “my version” , there is only one version of the Florida Bureau inspection at Leonardo Corporation, as a matter of fact it is the version derived from the actual facts: We have been very glad to receive their visit and we have explained to them all we had to. We agreed with them that we will keep them informed of all our developments and also explained to them that we do not use radioactive materials and do not produce radioactive materials. The persons we talked with are very prepared and expert, they have been right and correct, and I have been honoured to deal with them. What we said beyond this is confidential and I have nothing to add at all. I give no information at all regarding our factory, as I always said, until our production will be officially announced. I can say, and I am delighted to say this, that the Officers of the Florida State I have been contacted from are glad that we are making jobs in Florida with a company that respects the Law. Of course they will have free access to us in our Florida site, also to verify that we do not use radioactive material and we do not produce radioactive material and, also , we agreed that we will not sell in the USA the domestic E-Cats before the due certification, that will certify that no radiations are emitted from the E-Cats outside the body of the E-Cats while they are working.
    Warm Regards,

  • Claud

    Dear Andrea can you please give us your version of the Florida Bureau inspection referred on some site ?
    Thank you and good afternoon.

  • Andrea Rossi

    Dear Tim:
    We will give the exact data as soon as we will have a well defined project. We are still working on it.
    Warm Regards,

  • Tim

    Just a comment about waste heat from the 30% efficient steam turbine. To get that efficiency they need to reject heat at a low temperature. says the heat can be rejected at 30C, so the rejected heat may not be worth much. District heating systems require higher temperatures, which would lower the efficiency of the turbine.

    If it isn’t proprietary, it would be interesting to know the output pressure/temperature of the turbine.

  • Joseph Fine


    Since 30% of 45 MW is 13.5 MW (not 15 MW), only 6 MW is available for sale, not 7.5 MW.

    Also, as you said, there are 31.5 MW (not 27.5 MW) of waste heat available. (I stand corrected.)

    So the corrected (if not correct) formula is:
    $ Energy Charges Annual Total = Electric + Heat
    ( $ECAT ) = 6000*8760*X + 31500*8760*X/3 = 52,560,000 X + 91,980,000X = 144,540,000 X.

    For X @ $0.06/kWh-e, $ECAT = $8,672,400/yr.
    (if you sell heat for 2 cents/kWh-th).

    Six cents/kwh-e is still better than 19 cents/kwh-e delivered (Northern NJ – NY area).
    But to sell heat, it is better to take advantage of an existing heat distribution infrastructure.

    And the revised ratios for combined electric and heat vs electric only is:
    (6000 + 10,500)/6000 = 2.75

    If Heat Cost is X/2 cents/kwh instead of X/3, the ratio (E + H)/E increases to:
    (6000 + 15750)/6000 = 3.625

    So heat is more important than electricity for efficiencies < 33%)

    Have to do other things,


  • Daniel De Caluwé


    i) You wrote: ‘The $30 million cost of a 45MW Rossi plant financed @ 4% for the 30 year life of the plant would equal $51,560,850 in capital costs.’

    My answer:

    I wonder how you get the amount of $51.56 million?

    – Because if you only use the simple (intrest-)formula (4% /yr) * 30 years = 1.2; and then $30 million becomes $36 million and not $51.56 million

    – But if you use the more complex intrest-formula, the $30 million becomes much more than $51.56:

    Because (1.04)**30 = 3.24; and than $30 million becomes $97.3 million, which is much more than $51.56 million

    So could you explain what formula you use and how you get these $51.56 million?

    ii) Anyhow, if we work with $97.3 million, we still get $3.24 million capital costs each year for the 45 MW heat & power plant; or $0.05 (= 5 cents) per kWhe of electricity, which still is very good! 😉

    iii) Joseph Fine calculates with $30 million (E-cat only) + $15 million (for the Siemens turbine), and then we have $45 million as total investment cost, so in that case the numbers become higher.

    Kind Regards,

  • Andrea Rossi

    Dear Ron Stringer:
    It happens many times that I am attacked by some idiot on the
    , but our IT Guy is very good and fixes. When you get these problems, just be patient, try again after some hour.
    Warm Regards,

  • K. D.

    It should be in my previous calculations

    Still, there will be 70% of heat energy (31.5 MW)left for sell or use by customer.

    In North New Jersey presently the price of electricity is $0.122/kW plus delivery $0.065/kW, so supplying own electric energy from Mega E-Cat give lot of saving on delivery only for plants or apartments complexes.

    The other positive thing is independents in case of some catastrophic events.
    The snow falling in North-Eastern part of USA on the last day of October 2011, was the reason that hundreds of thousands of households lost electric power for many days or weeks.

  • Joseph Fine

    K.D., A.R.,

    For the formula I mentioned earlier: X = cost per KWh-electric in cents.

    $ Energy Charges Annual Total = Electric + Heat
    ( $ECAT ) = 7500*8760*X + 30000*8760*X/3 = 65,700,000 X + 87,600,000X = 153,300,000 X.

    The total billing ratio for combined electric and heat vs electric only is:
    (7500 + 10,000)/7500 = 2.333

    If the Heat Costs are X/2 cents/kwh instead of X/3, the ratio (E + H)/E increases to:
    (7500 + 15000)/7500 = 3.0

    So heat is an important component.

    For an efficiency of 30%, exhaust heat may be only 100-101 degrees C. And 30% efficiency is not 33% efficiency, so 45 MW in results not with 30 MW of waste heat but 70% of 45 MW = 27.5 MW. (Still useful.)


  • Ron Stringer

    I’m having trouble getting you at the address, Dr. Rossi. Is there a problem? – Ron

  • Joseph Fine

    K.D., A.R.,

    If 45 MW-thermal are provided to the turbine, then 15 MW-electrical (MWe) are generated and 30 MW-thermal are available for sale or internal use. As before, 7.5 MWe (of the 15) sustain the reactor, and 7.5 Mwe are for sale.

    Combined Heat and Power (CHP) or District Heat (central heating for a town or industry) costs about 10-12 cents per Kwh-thermal or roughly half the cost of electricity. It is more common in Europe where electrical heating is prohibitively expensive.

    For the sake of argument, assume electricity is sold for 6 cents per Kwh and the waste Heat can be sold for 2 cents per Kwh. You can use other prices and ratios to reflect local conditions.

    There are 8760 Hrs/year (except Leap years). 7.5 MW-electric is 7500 KW-e and 30 MW-thermal is 30,000 KW-th. I used X for the cost per Kwh-e and X/3 as the cost of heat. You can develop your own formula.

    ($ Energy Charges Annual Total) = Electric + Heat
    ( $ECAT ) = 7500*8760*X + 30000*8760*X/3 = 65,700,000 X + 87,600,000X = 153,300,000 X.

    So at 6 cents per electric and 2 cents per thermal Kilowatt-Hr, (X = 6), the
    $ECAT (Energy Charge Annual Total) is $9,198,000 and, if X = 10 cents per electric and 3.3 cents per thermal kilowatt, the result would be $15,330,000. The total, even at 1/3 the cost of electricity, is about 2.5 times what you get for electricity alone. I’m sure there are aspects that have to be considered, such as Heat sales are easier to make in countries where the infrastructure, piping, plumbing etc. already exists. Anyway, that’s my formula.
    Your results may be different.


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