An experimental result coming from Neutrino research gives for all particles the ratio ( s i / m i ) defined by Quantum Inertial theory in conjunction with the Micro-quanta paradigm

Rejecting some old misconceptions (such as the “pulling” gravitation that ravaged classical physics) the InertialGravitational theory supported by the Micro-quanta paradigm incorporates both the relativistic concepts of Mass Momentum Energy and the quantic Inertial Model of the particle mass. The flux of micro-quanta supports primarily the physical interaction that generates the Inertial forces defined by Newton. Scholars believing that Inertial forces originate from the properties of the empty space, do not pertain to the community of physicists believing on Newton’s Inertial Law. This great ancient physicist admitted he was unable to explicit the physical nature of his Law of Inertia (“Hypotheses non fingo”). However, marking the difference between “empty” and “absolute” space, he remained in his conviction that some unknown physical reality originates (in the absolute space) the inertial forces upon accelerated masses. At present, Micro-quanta paradigm describes the quantic objects that generate through collisions the physical inertial forces on particles. Since the flux of micro-quanta fills all space, there is no need to refer these collisions to some external System of reference. The relative velocity between quanta and particles comes out from the momentum that micro-quanta confer to particles. By this reason the Microquanta paradigm defines on pure dynamical bases the relativistic formalism that Special relativity derived from kinematics, so creating flaws that produced the well known paradoxes. To reveal the micro-quanta it's not necessary to devise particular experiments. The technique of the accelerometers has given many evidences of the physical reality guessed by Newton to explain inertial forces exerted on masses. Since the action of micro-quanta is always manifested in statistical terms, classical and relativistic physics allowed to describe Inertia and Gravitation without knowing the quantic nature of these phenomena. The micro-quanta Paradigm shows in particular the proportionality between cross section and mass (ratio Au) of all particles colliding with micro-quanta. To the aim of calculating the transmission across matter of micro-quanta and neutrinos (which show the same nature) the only unknown quantity is the numerical value of the ratio Au. Recalling that micro-quanta flux fills all space, it appears also interesting to search about neutrino collisions with micro-quanta flux as possible cause of the oscillations phenomena that occur during neutrino travels across the (so called) astronomic “empty” space. A quantitative indication on the ratio Ao is found in this paper from an experimental measurement of the solar neutrino flux interacting with the Earth mass in the course of the Borexino research carried out at Gran Sasso National Laboratory.


Introduction
Quantum Inertia-Gravitation theory is derived, according to the strict Equivalence principle, from the Microquanta paradigm proposed in 2007 to describe both inertial and gravitational forces originating from the collisions on particles of the Micro-quanta isotropic flux.Derivation of Mass and Momentum of particles moving in space filled by Micro-quanta flux can be done through Compton's collision law.This procedure shows the same formal description of Mass -Momentum -Energy given by Special Relativity, but their significance is greater because now the relativistic quantities are generated from dynamical bases, whereas S.R. was developed within an empty space through kinematical bases that are responsible for some well known troubling paradoxes.This means that the new theory is more adherent to the physical nature of dynamical phenomena since it gives indications about the (very small) cross sections characterising particles respect to the incident micro-quanta, which show the same very low interaction with matter that characterises neutrinos.The numerical constants of Micro-quanta (energy, wavelength, flux) may be derived from the Quantum Pushing Gravity force originated by the shielding-effect of micro-quanta flux between two particles.This requires dropping the Newton's pulling gravitation and cancelling the misconception of the "gravitational" mass" that was debated by classical physics.The Inertial mass becomes the only mass that can be measured.On the other hand, the recent measurements of the gravitational constant G examined by the Committee of NIST Institute (CODATA 2014) showed discrepancies among them with standard relative uncertainty equal to 4.7x10 -5 .This value has to be compared with the uncertainty of other fundamental constants of physics.For instance : Quantum magnetic flux = 6.1x10 -9 , Fine structure constant = 2.3x10 -10 , Electron mass = 1.2 , Atomic mass constant = 1.2x10 -8 , etc. Leaving to CODATA his proper evaluations, I'm convinced that the high discrepancies on the measured G are the symptom of the statistic nature of the so called "universal" gravitational constant proposed by the old pulling gravity.The reason may be guessed recalling that the gravitational pushing force (due to the mutual shielding between particles immersed in the micro-quanta flux) is pulsating due to the relative positions occupied (for very small times) by adjacent particles that are pushed each other by the incident micro-quanta.In fact, contrary to the absence of any "macroscopic shield" postulated by classical Gravitation, the Pushing gravity cannot exclude that some fraction of nucleons constituting the test mass may not participate (for a fraction of time) to the macroscopic pushing force.Besides, the uncertain nature of the mass has been enlightened during the half-century research on the Higgs problem, that recently produced the large boson observed at CERN accelerator.Such result appeared disappointing.In his article "My life as a boson" P. Higgs observed that it was far from the original concept suggested in his paper (1964) which described an "invisible field strewn across space, so to give mass every object in the universe".The parallelism between this original picture and the flux of micro-quanta (that generates the mass of particles by collective collisions on charges) appears evident (see Inertial model of particles, paragr.3).In addition to these scientific activities, the experimental evidence of the physical reality guessed by Newton is today given by some widely used commercial devises.Not many physicists have considered that the accelerometers are able to measure the absolute acceleration (no recourse to some external reference system) by calculating (Newton) the ratio between the measured inertial force and the test mass.Accelerometers are widely used not only in aerospatial applications, but also in the field automobile incidents, mechanical analysis, smartphones, etc.
The structure of Quantum Inertia-Gravitation theory allows discovering new effects unknown to current physics.For instance, the mysterious "oscillations" that neutrinos undergo travelling across the so called "empty" cosmic space, receive new theoretical interest thinking that all space is filled by physical micro-quanta.

Theoretical and Empirical Bases of Micro-Quanta
Defining and calculating Quantum Gravitational force is possible only by defining the structure of both Inertial and Gravitational Interactions, that classical and relativistic physics showed to be tightly linked.The strict Equivalence principle assumed that both inertial and gravitational forces originate from the same physical reality.In the present paper the flux of Micro-quanta paradigm is analysed in order to verify this requirement.Some historical misconceptions gave rise to unphysical concepts, such as the "unlimited" gravitational collapse depending entirely on the characteristics of the old pulling gravitation.In nature there are many examples of gravitational collapses, among which the spectacular collapses of Supernovae, enlighting for months a whole galaxy.But this collapse isn't unlimited because in the places with remnants of supernovae it has been observed the presence of Neutron stars whose mass is of the order of some Sun masses.After the theoretical study about the finite volume of the gravitational collapsing bodies (Loinger, 2010), some papers showed (Michelini, Jan. 2010, Nov. 2010) that Micro-quanta paradigm, which does not shows the gravitational unlimited collapse, is able to explain some observed-phenomena, such as the mysterious cause that ended Glacial Eras.This cause is still waiting a physical explanation that did not come from the great effort developed by two international missions in Antarctica: VOSTOK (Petit et al., 1999) and EPICA (Augustin et al., 2004) which extended the drilled Ice cores up to one million years ago.Besides, some experimental observations (such as the excess infrared emissions from planets, the planetary physics, the Earth high seismicity) are still waiting a rational explanation.For instance, the strong seismic events on Earth and other planets (with the satellite Io) appear to be linked to planets which show solid crust.In fact these events may be attributed to the same cause found analysing the Dansgaard-Oeschger events.Firstly observed by drilling two Ice cores in Greenland (Stuiver & Grootes, 2000) these phenomena revealed large and rapid warmings on both hemispheres at regular interval around 1470 years.At a first time, this regularity was attributed to some astronomical events, but the analysis carried out by S.Ramstorf on the D-O events between 11,500 and 45,000 years B.P. (Ramstorf, 2003) showed that actually the standard deviation from the most probable period was about 120 years.This result ruled out any possible astronomical influence.Taking in mind that the release of energy from micro-quanta collisions on the Earth mass amounts to a thermal power around 2.6 x10 15 watt, I put forward the hypothesis (Michelini, 2011) that the quasi-regular D-O rapid warming events may be triggered by a low increase of the internal temperature producing a thermal expansion of the mass able to produce an increase of the planet radius (some metres) sufficient to induce tensile stresses on the solid crust surpassing the elastic limit of the rocks.This produces fractures through which the fluid magma penetrates across the crust, giving rise to orogenesis, to large earthquakes and to the continuos volcano activities.In the D-O events the fracturing process regarded two hemispheres (Raisbeck, 2007).When the snow cup and the clouds mantle became so thick to prevent the solar energy might reach the surface, the global temperature was so low that no external phenomenon couldn't warm the planet.What gave the thermal energy that put Glacial Eras to an end?Probably it was the periodic heating of the surface produced by the magma escaping through fractures open on the stressed crust by thermal expansion of internal mass due to power generated by micro-quanta collisions.
During this research I was encouraged by the rising of new problems put on the table of scientific community by the Neutrino research, whose detectors require specific locations, such as old mines of coal and other natural or artificial shields against the radioactive cosmic rays.Such rough materials, disregarded by the classical physics, became the key for detecting the advanced physics of neutrinos,, The widely use by theorists of the classical astronomic observations, to proof their theories, inaugurated by Einstein at beginning of XX century, was definitely set.

Characteristics of Micro-quanta paradigm versus Special Relativity
Since Quanta of energy are defined (E = hν) independently of their size, then micro-quanta interact with particles in the same way as photons (Compton's equation).The micro-quanta , filling the space, act as interaction waves of the Inertia of particles.The momentum of particles was defined by classical physics q i = m o v in the empty space.Now this quantity comes out in a proper form when the space is filled by micro-quanta with energy E o = h o ν o which transmit power to the particles through the Doppler frequencies (ν f ,ν b ) whose definition can be derived from Micxro-quanta paradigm.These values are linked to the relative velocity of the micro-quanta incident forward (c+v) or behind (c ˗ v) the particle.The old bargain required by S.R. for summing or detracting high velocities can be now dropped since in the case of collisions between micro-quanta and particles these ones are described with proper kinematical characteristics.The mathematical proof (M.Michelini, Nov.2010) shows simply that each particle receives the momentum where N i = σι φ o το is the number of incident micro-quanta during the time το of each collective collision.Substituting and performing the calculation one obtains

This equation reproduces the relativistic formalism of momentum
with a new term that transfors the particle cross section in the rest-mass where p o = E o φ o /c is the energy density of micro-quanta in space.The term in brackets is constant for all particles because it depends on micro-quanta constants, so that the ratio represents a fundamental result that gives the cross section encountered by micro-quanta incident on a particle with mass m i .In other words the present approach, based on dynamical quantities, shows that the particle mass originates from interaction of micro-quanta on the charges.This fulfils in principle the mechanism originally suggested by P. Higgs in 1964.On the contrary, Special Relativity obtained the "relativistic" formalism assuming an empty space and using kinematical equations that produced erroneous predictions, such as the well known paradoxes, the "transverse" mass and the Fitzgerald's contraction.Micro-quanta do collective collisions on the cross section σι οφ particles during the time τ o .. Since the average density of micro-quanta in space equals n o = φο /c, the average distance between two micro-quanta is x o = (1/n o ) 1/3 .We assume that the duration of collision τ o = x o /c equals the time necessary to cover the average distance x o between two adjacent microquanta travelling on the same beam, so hitting the particle at any average interval τ o .Now we use (to continue the present reasoning) the numerical values given in par.5 after the calculations of the micro-quanta constants performed by implementing the preceding paragraphs.So, using the value x o = 4.526x10 -32 resulting from eq(5a) we obtain the duration of the collective collision το = 1,508x10 -40 sec. (2) To verify this result we recall that the energy ΔΕ released by each quantum colliding on the particle is fixed by the Conpton's equation .Let's recall that each incident micro-quantum release also to the particle a momentum that is statistically balanced by the action of its diametrically opposite momentum, preserving the total momentum of any free particle.In the case of micro-quanta ΔΕ satisfies the ratio which, adopting the value E o = 1.289x10 -32 resulting from eq(5b), gives us the ratio (E o /m i c 2 ) for any particle.For instance, nucleons (that constitute 99,95% of the neutral masses) take the value The total energy N i ΔΕ released by a collective collision with generic duration τ, corresponds to which is the number of colliding micro-quanta in the Compton's equation The energy ΔΕ released by each micro-quantum is a small fraction of the energy E o .We observe that in the preceding equation both sides result equal to E o when the number N i = (σι φο τ) equals This gives a correlation between the number of micro-quanta of a collective collision (duration τ ) and the massenergy m i c 2 of any particle.To this aim we rearrange eq(2c) in the form which confirms eq(1a) implying that τ = το as expected.Some trouble arises from the relative increase of mass of particles at any collective collision Y = Δm i / m i = ΔΕ / m i c 2 = (E o / m i c 2 ) 2 .In the case of nucleons the velocity of increment is which is troubling.However we don' forget that the Inertial Model of particle have to g ive answers to the still hidden process of rapid collapses shown by instable particles., which may grow or disappear.Let's now show what happens to the duration of collision τ derived from eq(2d) when we assume the value A o ≈ 1.43x10 -14 coming from an experimental result of the Neutrino research described in parag.4. Substituting the numerical values of φο and E o found in parag.5 in conjunction with the assumed value of A o , we calculated τ = 1.506x10 -40 sec.Comparison with τ o = 1.508x10 -40 sec given by eq(2) shows a little difference that may depend on the assumed A o .Considering that τ o has been calculated through a radically different procedure (based on the average distance x o between two adjacent micro-quanta travelling on the same beam) τ o might be in principle very different from τ .This did not happen, supporting our theory.. Another point to be enlightened is the existence of a value of A o derived directly from theoretical way.

The Inertial Model of particles
The fundamental time interval τ o scans the rhythm of collisions of micro-quanta upon matter in the universe.Notice that their average distance x o is much smaller than the "size" of elementary particles.For instance the "radius" of a nucleon r n is about 10 -20 .The energy of the particle is given multiplying the energy E o by the number N i of micro-quanta in a collective collision Recalling the electromagnetic energy m i c 2 of particles, the balance of these quantities gives which expresses the Inertial Model of stable particles.Resuming , this model presents shell-particles with cross section σ i and thickness xο much less than radius,.In fact eq(3) can be interpreted as the product of the particle volume ( σ i xο ) of thin shells multiplied by the energy density p o = φ o E o /c of micro-quanta in space.In other words, the colliding micro-quanta are scattered by the repulsive forces between the uniformly charged microparticles that constitute the charge and the mass confined within a sphere whose surface represents the cross section of particles.In other words, the flux of recoiling micro-quanta act the confinement of the repulsive micro-charges constituting the elementary charge.In practice the repulsive electric force is balanced by the newtonian force of inertia F in = -m*(Δv/Δt) due to each scattered micro-quantum (mass m*= E o /c 2 ) that undergoes the re-direction (Δv/Δt) of the velocity c.The statistical distribution of the collisions generates the "compression" p o upon the micro-charges Δe that repel each other.Taking in mind the reasoning given in parag.6 (substantially affirming that Δt = το ) we may affirm that the Inertial model of particles is based on Newton's concept that mass of particles is generated by the momentum re-direction of an isotropic flux of incident micro-quanta.Rearranging eq(3) gives us the ratio which confirms eq(1a) stating the uniformity of this ratio : a fundamental result of the Micro-quanta paradigm.This fact is not present in Special Relativity because it assumed the concept of "empty" space, widely accepted at beginning of XX century, that ignored other physical realities possibly present in space.

An experimental result coming from Neutrino research
Let's analyse the structure of eq(3a): we don't know all micro-quanta constants, so we have to find the value of A o from the experience.To this aim we recall that between single Micro-quantum and Neutrino (Michelini, 2012) there is a relationship: both show a particular attitude of ignoring matter.The Micro-quanta flux is also involved in generating the mass of particles, as shown by the Inertial model.Low energy solar neutrinos show a little interaction with particles, differently from high energies neutrinos around 30-50 Gev.Then I made the hypothesis that Neutrinos are directional waves constituted of very high number of Micro-quanta packaged without forming elementary charges in their interior.So they differ from the high energy γ-rays containing a rotating pair electron-positron.
In January 2012 at LNGS laboratories, the Borexino Experiment measured a very low day-night asymmetry in neutrino flux, that is a low interaction with matter of solar neutrinos observed at midnight, i.e. after travelling across the diameter of the Earth mass.(Borexino collaboration, 2912).The scattered neutrinos resulted a fraction around 0.001 of the total flux, showing a neutrino mean free path of the order l ≈ 10 3 (2R) = 1.27x10 10 .This result may be introduced in the formula of Micro-quanta paradigm where δ m is the average density of the tested mass.This equation is valid when the cross section of the exploring Quanta is negligible compared to the cross section σ n of nucleons (as it happens for solar neutrinos).Solving for the unknown A o one obtains A o = (σ n /m n ) ≈ 1.43x10 -14 for particles constituting the Earth mass, in practice nucleons.This ratio obtained by solar 7 Be neutrino measurements may be assumed also for micro-quanta.
Substituting in eq(3a) it appears that a second equation is necessary to obtains the distance xο and the microquanta energy E o .This require to write the equation of Quantum Pushing of gravitation.

Origin of the Gravitational Pushing force
Micro-quanta show very small energy E o and wavelength λ o of the order of the Planck's length l p = 4.05x10 -35 , so they pertain to the class of physical objects introduced by micro-quanta and characterised by the second Planck's constant h o = E o λ o /c.The energy E o can be calculated assuning the experimental Gravitational force numerically equal to Newton's gravity G m n 2 / r 2 adopting the measured G.This force is the Quantum Pushing gravity expressed in terms of Micro-quanta collisions on nucleons representing 99.95% of the masses where (2E o /c) is the momentum released by each recoiling micro-quantum.The mutual shielding between particles reduces the quantum flux incident on the shaded side of each particle.For theoretical reasons the central tubular beam (cross section equal to Δσ), placed along the line joining the centres of two particles, shows zero quanta (missing beam).The beam (φο Δσ)(Δσ/2πr 2 ) is the real beam diametrically opposite to the missing beam, so the gravitational Pushing force drives any pair of facing particles.For the sake of simplicity, the total flux reduction on the shaded face may be concentrated on a central beam with a small area Δσ.So we have to calculate Δσ in order to respect the equivalence with the actual shielding effect on the shaded side.Recalling eq(2a), the value referred to the fundamental time interval το = x o /c = 1.508x10 -40 sec.This shows that the physical origin of Newton's inertial force, acting upon an accelerating particle, depends on receiving more collisions on forward side than on behind side.Since the momentum released by each incident micro-quantum is the same on each side, the force unbalance depends on the different number of collision upon the two sides.This is confirmed by the Principle of Inertia stating that the uniform strait motion of a free particle continues indefinitely.In the language of microquanta this means that the flux upon particles at uniform motion is absolutely isotropic, that is the collision rate upon forward side equals that upon behind side.Concluding, Newton's inertial force depends on the collision anisotropy originated by the change Δv of particle velocity.
Speaking of acceleration respect to some external inertial system of reference (as stated by classical physics) is misleading because what matters is the local generation of the inertial force upon particles in accelerated motion directly "observed" by the micro-quanta.
Let's consider the new technology of Accelerometers, whose detector is contained within a strong black box, which transmits the accelerations due to accidents.bythrough the ratio between the measured inertial force and the test mass.Many types of detectors are used in terrestrial and spatial vehicles for recording shocks happened at any place of universe.No recourse to an inertial frame of reference is needed.Newton guessed the quantum character of the Law of inertia notwithstanding that Quantum concept were ignored at his time.On the contrary Newton failed in defining the Law of pulling gravitation because nature is capricious and hides the Quantum pushing gravity under the classical pulling gravity.Of course Newton didn't have at his disposal the concept of Quantum, which was attaint after more than two centuries, when Planck defined the quantum of light and Einstein gave the quantum explanation of the photovoltaic effect.It is worth noticing that the first introduction in 1748 of the pushing gravity concept (based on very small ultra-mundane corpuscules, due to George Louis Lesage) failed for the absence of Quantum concept.