In my previous post, I discuss the Fermi Energy needed to allow enough neutrinos to
live inside ordinary substances, in order to balance out the effects of an axial force. Its clear, the values are just to high to be practically possible. This doesn't yet rule out the axial force, provided a scalar or vector particle with mass in the region 10meV to 1eV, exists, such a particle, would not be subject to Fermi repulsion, and could be present in whatever quantities needed to balance out the axial charges on nucleons. Scalar or Vector neutrino (normally scalar, but I find theories with fundamental scalars unattractive), are present in super-symmetric theories with unknown masses. So a super-symmetric theory might allow an axial force.
Such a particle would also help with another problem the axial force faces, Radiation
from the Sun and Stars. The hot gases in star is in thermodynamic equilibrium and as such we expect all degrees of freedom to have equal energy. Thus we would expect the Sun to radiate an equal amount of photons and axi-photons. The axi-photons would be absorbed in the Earth atmosphere, and we'd observe a Sun burning half as brightly as expected. Astronomers current calculations describe the brightness of the Sun up to a few percent either way, so a Sun radiating equal amounts of axi-photons is not credible.
Let us investigate a super-symmetric vector (spin-1) analog of a neutrino, also with +1 or -1 axial charge, with a mass in the 1 eV region ( 1eV ~13000 Kelvin). We'll call it a Vectrino. Vectrinos are more interesting to us, than sneutrinos because, an
axi-photon can easierly pair produce Vectrinos, spin 1 -> spin 1 + spin 1. Remember this is in three dimension of spin, the extra spin on the RHS of the equation, can occur if the Vectrino, anti-Vectrino pair is emitted near 45 degrees to the incoming axi-photon. The Vectrinos can further scatter producing more axi-photons. The result is that Vectrinos lead to a region, absorbing all the axi-photon and other axial energy converting it in to a region as dense in Vectrinos as pressure will allow. It will act as an opaque thermal conduction barrier, allow only standard light through.
This wouldn't happen with scalar neutrinos, where the spin 1 -> spin 0 + spin 0, is impossible, and pair production is strongly suppressed.
Our Vectrino dense region would occur in the suns chromosphere, absorbing up coming energy in a region containing little hydrogen. At the top of the chromosphere high temperature protons, attracted by the axially negative region, would supply the pressure necessary to keep the Vectrinos compressed and in place. Light would cross the region normally and find a lot few protons in the corona to be shared between. Thus we have a new explanation of solar coronal heating, which has needed one of a while, see this paper.
Our original paper, used right handed neutrinos with a mass of a around 30eV, to preform the same trick of stabilising matter against Fermi pressure, and heating the
solar corona. However I do not now believe such massive particles could exists without there decay energy, showing up, in for instance the boiling of water. Scalar or Vector particles on the other hand, would cap the Fermi energy at just below there mass. The balance of Fermi-energy, axial binding energy, and scalar mass energy, would be hidden in lab experiments.
We have saved the axial force, at the expense of adding a usually new particle. The particle belong to super-symmetry, but an unusually form of super-symmetry, and the axial force was already unknown to physics. Scientifically, our belief in the axial force must reduce accordingly. It would help if one experiment or observation definitively needed an axial force, but without that the axial force is reduced to the realm of possible but not likely or needed.
Thursday, 19 May 2011
Wednesday, 18 May 2011
The Axial Force and the neutrino sea.
Regularly readers will know that my blog is many about the possibility of a fifth force, which acts primary between neutrinos. The strength of the force is unknown, but
can be comparatively large and still not noticeable by traditionally experimental because it doesn't interact with electrons at all. The simplest case a long force is a fully conversed charges with a massless force carrier, the axi-photon. I have not yet
investigate the case of massive force carrier, but the massive case would show up to easierly in accelerator experiments for masses ranges 137 MeV (more massive than a Pion) to 100 GeV.
If neutrinos carry this conversed charge so much protons and or neutrons, specifically the charge on the Neutron must equal the charge on a proton plus the charge on a neutrino, so that beta decay can occur. Further since both protons and neutrons can flip the spins easierly. The axial charge on a spin up nucleon is the same as that on a spin down nucleon. This is the opposite to neutrinos where by definition a right handed neutrino or anti-neutrino has the opposite axial charge to the left handed neutrino.
In any material with a axial net charge its nuclei, the axial force will collect a sea of neutrinos in order to the cancel out it the net axial charge. Since neutrinos are light this will effective screen out the axial force, and make it very difficult to observe, hence why the axial force has not yet been observed. However neutrinos are fermions can as such there is a limit to how many can be placed in a given volume of material. I make a terrible error, in my first paper. I used the wrong formule of the Fermi Energy of the neutrino sea, I used the non-relativistic, when formule when most of the neutrinos are clearly travelling near the speed of light.
The correct formula is.
$$E_F = {\h c}/{2} ({3 ρ}/{π} )^{1/3} $$
Thats the Energy of the most energetic neutrino assuming a neutrino number density of ρ The total Energy is just
$$E_T = {3/4}N E_F = {3/4} {ρ}V E_F $$
We don't need to know the strength of the axial force to calculate the Fermi Energy due to neutrinos (we assume 3 kinds as so far known). If the force isn't strong enough to bind neutrinos of the maximum (fermi) energy to the substance, then the substance will be left with an overall charge. This might lead to a detectable long range forces between substances, which might well have been observed already.
In fact the Fermi energy for most substance is rather large, assuming the axial charge is -1/2 on a proton and +1/2 on a neutron. We have.
The total energies are thus just to high to be practicle, some 2.7 Mega Joules in one cubic centimeter of tap water.
In order to save the axial force we need to add either several sterlie neutrinos in the 1eV to 1KeV ranges, or more add scalar sneutrinos in the mass range 0.1 eV to 100eV. Scalar neutrinos would not generate any Fermi Energy at all, and would allow any density of matter. Similar arguments apply for any long ranges force that need to cancelled inside matter. For instance a chameleonic B-L (baryon number minus Lepton number) force,
again needs a light charged scalar particle in order to solve the problem of Fermi-Energy.
can be comparatively large and still not noticeable by traditionally experimental because it doesn't interact with electrons at all. The simplest case a long force is a fully conversed charges with a massless force carrier, the axi-photon. I have not yet
investigate the case of massive force carrier, but the massive case would show up to easierly in accelerator experiments for masses ranges 137 MeV (more massive than a Pion) to 100 GeV.
If neutrinos carry this conversed charge so much protons and or neutrons, specifically the charge on the Neutron must equal the charge on a proton plus the charge on a neutrino, so that beta decay can occur. Further since both protons and neutrons can flip the spins easierly. The axial charge on a spin up nucleon is the same as that on a spin down nucleon. This is the opposite to neutrinos where by definition a right handed neutrino or anti-neutrino has the opposite axial charge to the left handed neutrino.
In any material with a axial net charge its nuclei, the axial force will collect a sea of neutrinos in order to the cancel out it the net axial charge. Since neutrinos are light this will effective screen out the axial force, and make it very difficult to observe, hence why the axial force has not yet been observed. However neutrinos are fermions can as such there is a limit to how many can be placed in a given volume of material. I make a terrible error, in my first paper. I used the wrong formule of the Fermi Energy of the neutrino sea, I used the non-relativistic, when formule when most of the neutrinos are clearly travelling near the speed of light.
The correct formula is.
$$E_F = {\h c}/{2} ({3 ρ}/{π} )^{1/3} $$
Thats the Energy of the most energetic neutrino assuming a neutrino number density of ρ The total Energy is just
$$E_T = {3/4}N E_F = {3/4} {ρ}V E_F $$
We don't need to know the strength of the axial force to calculate the Fermi Energy due to neutrinos (we assume 3 kinds as so far known). If the force isn't strong enough to bind neutrinos of the maximum (fermi) energy to the substance, then the substance will be left with an overall charge. This might lead to a detectable long range forces between substances, which might well have been observed already.
In fact the Fermi energy for most substance is rather large, assuming the axial charge is -1/2 on a proton and +1/2 on a neutron. We have.
| Material | Neutrino Density $cm^{-3}$ | Fermi Energy |
|---|---|---|
| Day Air | $1 * 10^{13} $ | 1.9 eV |
| Water | $3.34 * 10^{22} $ | 1.3 KeV |
| Uranium-238 | $3.5 * 10^{24}$ | 4.68 KeV |
| Bismith | $1.78 * 10^{24} $ | 3.5 KeV |
| NaCl (Salt) | $2.7 * 10^{22} $ | 1.27 KeV |
| Pyrex Glass | $ 1.16 *10^{21} $ | 0.4 KeV |
| Palladium | $4.89* 10^{23} $ | 3.3 KeV |
| Copper | $ 2.34* 10^{23} $ | 2.6 KeV |
| Zinc | $ 1.76 * 10^{23} $ | 2.4 KeV |
| Barium Chloride | $ 2.9*10^{23} $ | 2.24 KeV |
The total energies are thus just to high to be practicle, some 2.7 Mega Joules in one cubic centimeter of tap water.
In order to save the axial force we need to add either several sterlie neutrinos in the 1eV to 1KeV ranges, or more add scalar sneutrinos in the mass range 0.1 eV to 100eV. Scalar neutrinos would not generate any Fermi Energy at all, and would allow any density of matter. Similar arguments apply for any long ranges force that need to cancelled inside matter. For instance a chameleonic B-L (baryon number minus Lepton number) force,
again needs a light charged scalar particle in order to solve the problem of Fermi-Energy.
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