Axial force and Mirror Matter: Stellar Formation

There are two controversial theories I often write about here: The first, The Axial Force, a force possible between neutrinos which have opposite charges on left and right handed particles. Matter or anti-Matter doesn't seem to matter to the axial force. This follows from the CPT theorem. Combining the three operations, C (swapping matter and anti-matter), P (swapping left and right), T (reversing the direction of time, or equivalently the velocities of all particles), must result in no change to any picture of what has happened. Since most diagrams of an interactions are inverted by time reversal, either C or P but not both are also reversed. I've documented the Axial force in the paper linked from my blog, written here often about its consequences. As far as I know I'm the only current active researcher in the axial force, although the idea may date back to the 1970s. I happen to think the axial force will lead to a good theory of dark energy.

The second theory I often report on is Mirror Matter. Mirror Matter theory, posits a second of copy of mirror versions of all the known particles. Its was introduced because of the bizarre fact that weak nuclear force, between known particle, always acts in a left handed fashion. If there is a righted handed weak force its force carrier is very heavy, to heavy to have been observed. Mirror Matter solves restores the symmetry because its weak force is right handed. The theory also gives a good candidate of dark matter and fitting in with the recent observations from DAMA, COGENT. There are a number of researchers working on Mirror Matter, although only a minority, including Robert Foot and Paulo Cirarcelluti

So what happens between the two theories, are they compatible, indeed do they together lead to further explanations of the universe? Assuming both the axial force and mirror matter are real, we have eight copies of every particle, Matter versus Anti-Matter, Left-Handed versus, Right-Handed, and Mirror versus Ordinary Particles. The Known forces are also copied, with an electromagnetic force, and an mirror-electromagnetic force. Because the mirror-electromagnetic force is invisible to ordinary particles, dark matter stays dark. Is they're a also a mirror axial force. Quite possibly, if the standard model plus axial force, works, then so would a mirror copy. But what more interesting if you combine the axial and the mirror axial force, you can mixed them produce two copies, A+A' and A-A'. We may assume that A-A' breaks and gains an mass, while the total axial force remains massless. If in ordinary matter right handed neutrinos are heavy, then in the mirror world left handed neutrinos are heavy. If the heavy neutrinos and mirror neutrinos are bound by some interaction to a heavy composite particle, this is exactly the breaking we'll see. We'd also see a split in mass between to the ordinary light neutrinos and they mirror partners, these could also would mix, to form a very light set of neutrinos and a second set in the keV range, that would decay down to the lightest version.

A Consequences of add the axial force to the mirror matter model is then, we'd see only 3 light neutrinos at the time of nucleosynthesis, saving mirror matter theory from over counting the light of masses number of degrees of freedom, as reported below.

One problem with the mirror matter theory is that although mirror and ordinary matter may both make up a galaxy, when it comes to individual stars or planets we don't seem to see mixed objects containing varying amounts of each. What separates the two forms of matter> Gravity should attract both equally. I have thought of an effect, that would lead to the separation of ordinary and mirror matter. Imagine a collapsing cloud of gas, containing a mix of ordinary and mirror matter in some proportion. As it condenses it will be resisted by the Fermi pressure of the neutrinos needed to cancel out the axial force of the most populous gas (normal or mirror), at some stage the Fermi energy will rise above the mass of the a sneutrino or vectrino (a light supersymmetric boson carring the axial force), at this stage the gas will pair produce the vectrinos the with the opposite charge to the most populous gas which will rapidly condense, the vectrinos matching the less populus gas will stream out of the area carrying the less populous gas with it. This would lead to visible outflows of gas in interstellar clouds forming stars. These are indeed observed, even from area with no visable protostar, and called Herbig-Haro objects.

The shared axial force also helps explaining the different proportions of mirror and ordinary matter. Observation show that there is four to five times as much dark matter as ordinary matter.
We might expect equal proportion of mirror and ordinary matter. However with the A-A' axial force broken, we will have two species of heavy neutrinos, mirror plus ordinary, and mirror minus ordinary with some mass difference between the two. The heavy state would then decay to the lighter version, leaving an differing total of mirror and ordinary states, depending on the decay rates and branching ratios to matter and anti-matter.

It would seem that the axial force and mirror-matter theory, work well together aiding each other
to produce an nearly complete theory of the universe, together explaining both dark matter, dark energy, the breaking of parity, and predominance of matter over anti-matter.

Finally It is possible that mirror matter may be directly detected soon, in Higgs experiments. Robert Foot et al, have speculated that recent signs of a Higgs boson at the Tevetron but with half its expected cross section, may be due to Higgs mirror Higgs mixing, leaving a summed state around 140GeV, and a differenced state around 120GeV. Both states would have half the usual cross section and decay half the time in detectable particles, and half the time into mirror matter which would show up in the cross sections.

Veracity of axial scarnhorst effect as the cause of superluminal neutrinos

Because I have studied the effect of an possible axial force on neutrinos for nearly five years, and spent nearly 17 years digesting as much of the ArXiv physics preprints as possible, I've been very quick to find an explanation of the the faster than light neutrinos measured at OPERA. Indeed with that many papers in mind, its always going to be quick to find some appropriate prior art to solve almost anything. Since my readership is too small to expect much criticism, it falls to me to take a step backwards and check the solution against all the other possibilities.

For the Axial Force Scarnhorst effect to be the cause of OPERAs neutrino velocity, we require:

1. The Velocity Measurement to be correct.

We will leave this experimentalists to eventually prove or disprove, currently the evidence is officially 6 sigma, or has a 99.99966% probability of being correct, plus previous evidence from MINOS. However the possibility of systematic errors or mistakes can easily remove such claim precision

2. The existence of an axial force between neutrinos

This is what I've been discussing regularly through this blog, but as yet, have yet to get
any other qualified researchers to look at in depth. It is a however a simple copying of QED to
the neutrino, and explains, the chirality of the neutrino, how the neutrino and lepton number stay conserved once over taken by a accelerating particle, and how the weak force may have different strengths (symmetry breaking), for left and right handed particles.

3. The Correctness of the Scarnhorst effect

The Scarnhorst effect, is the modification of the speed of light, in the vacuum of QED, due to the energy of background electromagnetic fields. Normal Fields and any scattering will slow done light. However negative energy density such as in the Casimir effect will result in photon that travel faster than the speed of light in a vacuum.

4. Given 2. and 3. The Axi-photon and high speed neutrino may be superluminal

The Scarnhorst effect also will carry over axial force. An minor correction to our article below, is that the strength of speed up depends, on mass of the lightest left handed neutrino squared times its right handed partner (these masses will in general be different).
$$ v = 1 - {44/135} α^2 {ρ/{m_l^2m_r^2}} $$

5. The existence of axially charge background fluid in matter

We have already show that one of the baryons needs to have a axial charge in the neutrino does, and the charge is conversed. Further this has to be the proton, as neutron scattering shows no long range forces. Fermi pressure means that in terrestrially density matter (rock, water), this fluid must mainly be bosons carrying the axial charge which are so far undetected. This is a generic prediction of our axial force, but this background fluid will be bound to matter, and lead to a negative energy density in matter only, which leads to the Scarnhorst superluminal neutrinos recorded at CERN. Below we predict at binding energy of 1 keV per litre of water, which in fact isn't bound at all at terrestrial temperatures. However we neglected to use the right handed neutrino mass. For a 1 keV right hand neutrino the binding energy is more like $10^{18}$ eV per litre or about a tenth of a Joule, in the right range not to have be measured, but to resist thermal effects. Using the Bohr formule as an approximation for the binding energy, this gives a axially charged bosons with a mass around 500eV. In general, we have approximately.
$$ M_{bos} = 1/2 M_{right}* (M_{right}/1000) (eV) $$

6. Relativity and Causality

We require in general, that the speeds of all massless particles, be the same in the vacuum, so that Einstein relativity which has been measured very accurately still applies. In fact Anber and Donoghue, seem to have demonstrated this will in deed occur, when multiple fields theories interact with some common particles. The presence of matter provides a preferred frame, so that relativity is not effected by the result. However sending signals between the CERN OPERA type experiment, and a second neutrino experiment that happened be to aboard a star ship traveling extremely near the speed of light, could send signals backwards in time. This violation of causality does not seem to be a problem for Quantum Mechanics though. D. Deutsch. Phys. Rev. D, 44:3197–3217, has show that, at least in the many worlds interpretation, that closed time like loops are admissible.

7. Other Solutions for superluminal neutrinos

Purely tachyonic neutrinos would travel faster than light in the vacuum, and would be faster at low energy, which would be contrary to supernova observation particularly SN1987A. Mixing between badyonic and tachyonic (faster and slower than light) neutrinos, might be possible. But is a field theory with a 120 * sqrt(-1) MeV right handed neutrino viable or not? Matter scattering effects should in general slow any particle, not accelerate it. Any tachyon solution would also lead to the neutrino radiating its energy alway, which also does not seem to happen.

The Scarnhorst effect on neutrino would be general to any field theory of interacting neutrinos, in which normal matter contains a negative or binding energy in that field. What other classes of fifth force, felt by the neutrino are possible? Broken symmetries would lead to massive force carriers, which would in general slow neutrinos. Thus we require a hidden or chameleonic force, not detected to date but which interacs with neutrinos. Baryon minus Lepton numbers theories are common, but would show up in modified hydrogen atoms and neutron scattering. Intergenerational forces between neutrinos would seem to lead to flavour changing neutral currents which have not be observed at particle accelerates. Our axial force seems to be only solution for superluminal neutrinos at present, but a absence of other ideas, does not mean an absence of other solution.

Faster than light neutrinos, A possible solution

I've been a few weeks late to comment on CERN's OPERA experiment's paradigm breaking result, that neutrinos travel faster than light (nature), (orignal paper). Initial skeptism has not lead to any resolution of the result via mis-measurement. The excess is in speed measured is small, three thousandth of a percent, the muon neutrinos, crossing the 732 kilometers from the CERN lab where there created to the OPERA neutrino detector in Italy, some 60 nanoseconds earlier than the light would have done. OPERA quote a 6 sigma statistical significance and the results do match with earlier measurement at the MINOS experement at Fermilab. The quoted speed at OPERA is (v − c)/c = [+2.48 ± 0.28(stat) ± 0.3(syst)] × 10−5.

Standard Special Relativity does allow for particles that travel faster than light, know as tachyons, they obey the standard equations of relativity except they have negative squared mass, another words imaginary mass in the sense of complex numbers. Allowing Tachyons however cause quantum field theory to be unstable, describing a vacuum that would decay. More over the OPERA results do not fit standard tachyons, the tachyon mass of the neutrino would be i*120MeV in gross contrast to the measured neutrino mass, and also tachyons travel slower with increasing energy, nearer the speed of light from above at infinite energy, and traveling infinity fast when the have zero energy. OPERA in fact notice a constant speed for neutrinos across a doubling of energy from 17 to 35 Gev. While vacuum stability might be saved by the handedness (chirality) of neutrinos, empty space emitting a back to back pair of an neutrino and an anti-neutrino would violate spin conservation by one unit, due to the neutrino being left handed while the anti-neutrino is right handed. Thus a field theory of tachyonic chiral neutrino might be stable while it would be unstable for normal particles. However such a theory still would not fit the OPERA results.

Moreover neutrinos in empty space do not apear to be superluminal. When the supernova SN1987A exploded in the large Magellanic could the neutrinos where detect to arrive some 3 hours before the light. This might seem superluminally however the light is delayed by traveling though the stars core. If the neutrinos traveled at the OPERA speed, they would have arrived some 4.5 years earlier.

In order to achieve a resolution of the OPERA result compatible with both quantum field theory and the light speed measurement of the supernova neutrinos. It is necessary to find a theory where the speed of propagation of neutrinos is faster than light only in the presence of a matter field. In fact quantum field theory can vary the speed of light depending on the energy density of the QED vacuum, a result found in 1994 by Latorre, Pascual and Tarrach. Given a vacuum energy density of ρ. The speed of light is modified to.

$$ v = 1 - {44/135} α^2 {ρ/m_e^4} $$

In unit where c=hbar =1.

In keeping with our axial force, the same formula should carry over to the speed of axi-photons and the maximum speed of neutrinos (approached as the neutrino speed became very much greater than there rest mass time c squared). The electron mass in the formula would replaced with the mass of the lightest neutrino, and alpha with the axial coupling constant, which we predicted was some 60 times smaller the than alpha in QED.

$$ α_ν =~ {1/137} * {1/60} =~ 0.121*10^{-4}$$

The mass of the lightness neutrino is unknown, but we estimated to be 0.14 milli-electron volts in order to produced dark energy. This would lead to a negative energy density of

$$ ρ = -2*10^{-12} (eV)^4 = -2 (meV)^4 $$

Interestingly this is in the same region as the observed figure of dark energy density in cosmology about 3 (meV)^4, however dark energy is still a positive energy density, only the pressure need be negative, representing a self attracting fluid. The standard speed of supernova neutrinos further would imply that the these is no dark energy in the local region of our galaxy, stellar radiation must blow the region clear of any dark energy. Since no expansion of trapped galactic cluster is observed this is very compatible with cosmology.

In ordinary situations the QED and QAD vacuum energy would be both zero for empty space, and for matter depend quite separately upon the electron density and columb potential and the neutrino density and axial potential. We have already shown that ordinary matter would contain a background sea of neutrinos necessary to cancel the axial charges of the nuclei of atoms, and this background sea would be bound to nuclei with some energy density. From the above we have
around 1 nano eV per cubic nanometer. A binding energy this small, requires a light bosonic particle carrying the axial force, with an rest mass not much larger than the neutrino.

In our paper we have shown that, Neutrino scattering on the the background sea, is strongly suppressed at high energies, falling as $(m_v/E)^2$. The neutrino speed would approach approach the modified speed as $1-(m_v/E)^2$, Thus in the earth between CERN and OPERA, the measured speed would be the modified speed of axi-photons, given the axial binding energy density. An experiment demonstrating the axial force nature of the superluminal speed of neutrino could be produced, by vary the composition of material the neutrinos travel through. The excess speed would vary as bind energy density, which would vary as the atomic number density of the matter passed.