Let us introduce a force that has opposite charges on left and right handed particles, due to quantum anomalies electrons cannot feel such a force. But neutrinos on the other hand seem to need such a force. The equations of motion of particles allow for forces that act either equally between opposite spins, Vector forces, and ones that act oppositely between opposite spins, Axial forces. So we may introduce a axial force between neutrinos. Noticing that beta decay produces both an electron and an anti-neutrino, we may see, that a W particle would hold both charges of

both the vector electric force and neutrino axial forces. The W particles (V-A) vector-axial nature first noted by Enrico Fermi, is then derived from the combination of forces on electron and neutrinos. That the Weak force has a (V-A) nature was completely unexpected and was discovered after experimenters noticed that electrons emitted by decaying cobalt-60 held in an magnetic field only spun in the left handed direction. The weak force was from then on described as left handed (V-A) force, but no clear mechanism for arrived at for explaining why the weak force left handed.

In fact under the symmetry of special relativity, left handedness doesn't remain left handed, you may over take a particle spinning in a left handed manner compared with its direction of motion, looking backwards you would see a right handed spinning particle. Thus relativity needs a right handed force as well a left handed force, and right handed as well as left handed neutrinos. In addition, it has been proved by L.M. Slad, that a axial force is need in addition to a left and right handed weak force, in order to give a definite handedness to the fields, that survives relativistic transformations. Having an axial force allows a neutrino to reverse its direction without reversing its handedness, it merely emitted a spin-1 axi-photon after the reversal. It is this axi-photon that carries the fifth force. The symmetry of the axial force allows left and right handed neutrino andleft and right handed W particles the carriers of the weak force to have different masses. This is possible because an axial force is created by gauge invariance (Adams1, Section 2), whenever a particle has its mass described by as a Majorana mass, with different masses for left and right handed particles. The asymmetry noticed at low energy, that neutrinos are light and left handed and that the weak force has a mass and is left handed, then required another symmetry that of the axial force. We thus have 3 reasons for believing in an axial force.

1. That gauge invariance is possible for neutrinos with Majorana mass. Implies an axial force.

2. That the weak force handedness is compatible with relativity. Implies an axial force.

3. That the weak force is V-A, may be retrodicted from an axial force between neutrinos.

I have been investigated the axial force for some five years now, and have blogged about it frequently at my previous blog site and written several papers for it. I managed to use the axial force to defend causality if neutrinos happened to travel faster than light. This I now regret as the OPERA experiment that saw faster than light neutrinos, turned out to be incorrect. The Axial force works whatever the speed of neutrinos are, both normal masses or tachyonic masses is fine to the axial force.

I have found that the axial force could be quite strong maybe as strong as a sixtieth of the strength of the electromagnetic force and still not be noticed. The reason is that neutrinos so very light, that the slightest forces on them causes them to move very quickly, as large measurement distances, bigger than 5 nanometers in air, and much less in solids the axial force is completely screened by the motions of background neutrinos. This makes the axial force a chameleon force, hidden from normal experiments, and explains why it has not be detected by other experiments. For my next article I will write of a experiment that might detect an axial force, and hope I can get experimentalists to try performing it.

## Comments

It appears that you (and, I suppose, L. M. Slad) have a few significant misunderstandings of the "handedness" of the Weak Nuclear Force, as well as that of the Fermions.

While you are correct that, classically, "you may over take a particle spinning in a left handed manner compared with its direction of motion, looking backwards you would see a right handed spinning particle." However, the spin of Fermions is not classical "rotation of a body", but a Quantum Mechanical angular momentum like quantum phenomenon.

Perhaps you should look up how "handedness" or "helicity" relates to "chirality" in Fermions. It's actually chirality that the Weak Nuclear Force "deals with", not handedness or helicity.

Now that that issue is "out of the way", we can take a closer look at why the Weak Nuclear Force "deals with" only left hand chirality, and not right hand chirality.

The usual derivation/formulation of the Dirac Equation* (for Fermions) always has equal mixtures of left and right chirality. However, for massless particles (as we once thought neutrinos were), the left and right chiral portions are completely separable. In fact, it becomes "impossible" to distinguish between a right handed (in chirality) particle from the anti-particle of the left handed particle.

This seemed rather abhorrent to many physicists.

However, once it was found that the left-right chiral symmetry (parity) was not respected by particle interaction involving the Weak Nuclear Force (what you alluded to when you said "experimenters noticed that electrons emitted by decaying cobalt-60 held in an magnetic field only spun in the left handed direction"), physicist had an even stronger reason to get rid of the left-right symmetry of the neutrinos.

Now, once one no longer has right handed (chiral) neutrinos, the left-right symmetry of the Weak Nuclear Force (or Electro-Weak Force) is broken! One then has a choice of either having it simply *be* broken (which causes significant issues in Quantum Field Theories), or one can have this interaction simply be between the left-hand representation of the Poincaré group (so left-handed [chiral] particles interact with it, but right-handed particles do not).

This latter choice required "projection" operators for the two subgroups of the Poincaré group. However, the Dirac "matrices"/operators provide just such an operator! *Et voilà*!

Of course, now that we "know" that neutrinos "must" have mass, we still have the issue of the lack of parity (chirality) symmetry, even though we no longer (in at least some sense) have the issue of indistinguishability of left- vs. right-handed (chirality) uncharged particles. Instead, we now have the issue of how can we have this lack of parity (chirality) symmetry, and the apparent lack of right-handed neutrinos, while "letting" them have mass. For instance, what "form" of mass are such particles "allowed" to have (Dirac vs. Majorana, or something else)?

May right-handed neutrinos actually exist, but ones that still don't interact with any of the three non-gravitational forces? (Such could be termed "sterile" neutrinos.)

These are the interesting questions, not some imagined "fifth force" to "make" the left-handed Weak Nuclear Force "work".

David

* There are formulations that have strictly left-handed or right-handed chirality. Within my Doctoral Dissertation I presented a derivation that encompasses all other formulations, and quite naturally (in 4D Minkowski spacetime) provides representations with unequally mixed left- and right-handed chirality: No need for "projection" operators to be imposed post-hoc.

You really must reread what I wrote. You are perpetuating the same fundamental error.

Like I said (emphasis added):

Perhaps you should look up how "handedness" or "helicity" relates to "chirality" in Fermions.It's actually chirality that the Weak Nuclear Force "deals with", not handedness or helicity.

Additionally, you indicate another fundamental error in (relativistic) logic with your statement:

... Both the possibilities leave the weak force changed in the new reference frame. The axial force adds the possibility that the neutrino will remain left handed by exchanging a spin-1 boson, so only with the axial force, can the weak force remain always left handed. So without the axial force, the weak force could not be a left handed only force.

There is simply *no way* that having an observer "boost" "to another reference frame where that neutrino is right handed (because the direction of motion has changed)" will be accompanied by a (massive) neutrino "exchanging a spin-1 boson" so "that the neutrino will remain left handed".

The neutrino simply doesn't care what reference frame the observer is in. That's fundamental to relativity!

Additionally, while "handedness", or (more precisely) helicity *does* depend upon the reference frame of the observer (for massive particles), chirality is reference frame *independent*! (For massless particles "handedness"/helicity is identical to chirality.)

David

We would hope the neutrino doesn't care what reference frame the observer is in, but eigenvalue of the chirality operator does depend on the reference frame. We may the point of emission or absorption to set the axis for the dirac matrices, but if the absorption point is boosted from the emission point the neutrino may become a mix of left and right handed states. We might now define the right handed part not to interact, but really we need a axial transformation to restore a whole neutrino at the absorption site.

At least you are now addressing chirality, rather than "handedness" or helicity.

However, you have a misunderstanding of the "chirality operator" that is, indeed, related to the "gamma_5" (γ_{5}) operator. γ_{5}, in 4D Minkowski spacetime, is (essentially) a pseudo-scalar operator and is invariant to changes in reference frame.* In fact, we can define the gamma operator in such a way that they even work properly in the curved spacetime of General Relativity, in which case, again for 4D Minkowskian/Lorentzian spacetime, γ_{5} is invariant to general coordinate transformations.**

So, no, the "eigenvalue of the chirality operator does *[not]* depend on the reference frame." Even coordinate transformations that change the "orientation' of the coordinates in spacetime only changes what chirality the eigenvalues indicate.

So, no boosts will case a pure chirality state to change to "a mix of left and right handed states."

David

* There are those that impose a direct relationship between transformations in 4D Minkowski spacetime (such as boosts) and those in the "Dirac spinnor" "space". This can lead to an *unnecessary* (truly inessential) transformation of the ("spinor") matrix representation of the γ_{5} operator.

One must learn not to be fooled by such unnecessary/inessential transformations.

** There is, of course, a sign change if we change to a coordinate system with the opposite "orientation" (chirality, in a higher dimensional sense).

For my Doctoral Dissertation I generalized the derivation of Dirac's equation with curved spacetime (not just within curved spacetime, because I didn't hold the spacetime curvature to be fixed, but allowed for it to depend upon the other fields as well [I even derived the contributions to the Energy-Momentum-Stress tensor]).

I found that the nature of chirality does not change with parallel transport, or any general coordinate transformations. In fact, I found that the chiral nature of a theory (using such a Dirac equation) is dependent upon the representation of the Dirac gamma operators one uses in formulating such, but the irreducible representations are not "mixed up" by any changes or choices in coordinate systems.

The fact is, the vary nature of the (strong) equivalence principle precludes parallel transport (or general coordinate transformations) from changing things like chirality: If a change in inertial reference frame, within Special Relativity can have no effect, then neither can parallel transport within General Relativity. It's as simple as that.

David

P.S. In addition to finding a generalization of the derivation of Dirac's equation (which no longer requires "projection" operators like γ_{5}), I also found that the spacial integral used in Quantum Mechanics (such as for inner products, and other "projections" within Hilbert spaces, and for "wave function 'collapse' ") does not need to be along a flat spacetime slice, such as being perpendicular to the time coordinate of the observer's reference frame.

It also becomes quite clear that the Christoffel symbols of General Relativity are highly related to the (4-)vector "potentials" of Yang-Mills theory (which is a generalization of electromagnetism and forms the basis of the Electroweak and Quantum Chromodynamics theories, as a part of the Standard Model). Similarly, the Riemann Curvature Tensor is highly related to the Fields of Yang-Mills theory (as in the electromagnetic fields, which involve derivatives of the electromagnetic [4-]vector potentials).

As an additional bonus, it provides some potential "clues" for dynamics of the mass and gamma operators. (In the case of the mass operator, the dynamics are non-linear and, at least superficially, similar to the Standard Model Higgs field.) Unfortunately, the hard part is knowing which terms to keep and which terms to drop, since keeping all term should not differ from the dynamics of the Klein-Gordon equation (though possibly not, when one goes to second quantization, but that's pure speculation).

On another nit-picking issue...

In the beginning of your article you assert:

The weak force is the ... only force thatisn't long range, thanks to the Higgs mechanism, the weak forces carriers gain a mass [and, so,] can only travel a very short distance before there borrowed energy runs out.

While the massive force carrier effect (associated with the work of Hideki Yukawa, as in Yukawa potential) you allude to is certainly a significant part of the short range character of the weak force, it is also, most certainly, not the only way to have a short range force.

In fact, your assertion that "the weak force is the ... only force thatisn't long range" is violated by the simple fact that the strong nuclear force is also short range.

In the early days of nuclear physics, what was then considered to be the strong nuclear force was considered to be short range for precisely the reason you use for the weak nuclear force: The force carriers were expected to be massive. In fact, we found bosons with very much the expected mass: The pi mesons!

However, after a tortuous history, involving both experiments and theories, we have come to the point of recognizing that the actual strong nuclear force is mediated by massless bosons (gluons), and that the force actually has a far shorter range than we thought.

How can this be? How can a force be mediated by massless particles and yet not be long range like the electromagnetic force?

The answer is that the strong nuclear force, involving the SU(3) local symmetry, is a non-linear, self-interacting force! (The pi meson mediated "strong nuclear force" is but a residual force, much as the van der Waals force is a residual of the electromagnetic force.)

So there is another mechanism for obtaining a short range force, besides massive force carriers: Having a force with a strong self-interaction. (The weak nuclear force, with its SU(2) local symmetry, is also a self-interacting force. However, in this case, the self-interaction is not nearly as strong as it is for the strong nuclear force.)

David

the strong force isn't long range, its that it so strong at long range that it prevent quarks being free to produce a long range range.

Actually, the "if a free quarks did exist" scenario can be rather misleading. (Additionally, "asymptotic freedom" actually works in the opposite direction [though you probably understand that].)

Due to the self interactions of any non-abelian (Yang-Mills) field theory, the effective field can be quite short rage simply due to the "shielding" of virtual "force carrier" particles. (Of course, when the Fermions with which the "force carriers" interact are not extraordinarily massive [like Plank scale massive], the binding of their virtual particles adds further to the "shielding".)

A huge part of the problem, with the Strong Nuclear Force is that its interaction is so strong that one truly cannot do perturbative calculations, except at the tightly bound level where "asymptotic freedom" is a good approximation. So one cannot truly ask the question of whether the Strong Nuclear Force is long range or not.

However, if one plays with a highly weakened form of Quantum ChromoDynamics (QCD), one can then do perturbative calculations that start to look more like electromagnetism as the interaction goes to zero. However, this is due to the (effective) weakening of the self interaction, so the non-linear theory starts to look increasingly linear, and just like electromagnetism (except that it has more "components").

But, yes, these are all just "quibbling" on details. ;)

David

"agree.the so called "memristor" is a planar device,one could build an infinite slab...inside the magnetic field is null,just like in an infinite planar vacuum diode...the symmetry is broken by THE OUTSIDE CIRCUIT which the electric current takes...you might say that THE REST,the whole universe,behaves like a true memristor...."

same "chicken or the egg" question......a chicken INSIDE THE EGG?! the real question is the egg shell itself,the boundary,the division,the frontier......it look so much like the "holographic screen" that has been proposed....DUALITY hidden in plain sight.

i do not intend to make a habit of rebelling against bad upraised characters on others peoples blog but i do have a strong feeling about censure ship....if sascha or any other is entitled to post(allowed to post) it is because he will not exercise his bad manners,foul censure at his immediate and unpunishable,unblamable will.i sign my post only because if someone finds them to be of no value the that person could ignore them BY THEMSELVES.