cheers,

-cvj

Not sure we are agreeing here, my point was that even if you give up on Lorentz invariance (or on spin-statistics, as in low dimensional systems) fermions cannot condense. Basically, in Bose-Einstein condensation most of the particles occupy the same state, the lowest energy one, and fermions cannot do that by their statistics, no matter what their spin happens to be.

Of course, violating Lorentz invariance is possible, and even interesting!

http://www.molbio.wisc.edu/facstaff/Carroll.html

In QCD there are many condensates. Chiral symmetry is broken by a quark condensate, <q qbar>. This breaks electroweak symmetry! The W and Z get a tiny mass in this way.

The observed W and Z masses are much bigger than the QCD scale, though. Hence technicolor, where a techniquark condensate might break electroweak symmetry.

-cvj

A fermion getting a vev on it’s own would also violate Lorentz symmetry. You can have a *pair* of fermions form a Lorentz scalar and aquire a vev. In fact, this is known to happen in the theory of strong interations. Pairs of quarks and anti-quarks condense to get vevs of the form and which break the so-called chiral symmtery.

The problem with what you suggest is that the only Standard Model fermion with the right quantum numbers to break electroweak symmetry is the neutrino (well, all three of them). However, it takes a strong interaction to cause the fermion pairs to condense and we know very, very well that neutrinos don’t interact strongly with each other.

You could imagine that instead of introducing a new scalar, you put in some new fermions and a new interaction to make them condense. People have studied this possibility, which is called “Technicolor” for many years. It’s very difficult to get everything to come out right, but it is one of the theories on our list of know possibilities for what we might see at the LHC.

It was not to hard to find that life cycles of “energy and matter” could have found itself portrayed in our cosmos. So some questions come to mind here.

Was there some overall “geometrical expression” lying at the heart of this expose’?

Was there some quantum similarity that could “arise from” such expressions, might have found themselves in unification with those cosmological views?

While there was positive scenario revealled on our sense of GR of Riemann, there was negative results that formed in our views as a geoemtical expression as well. How would you portray these dynamcis if not within a cosmological palette, would suffice to create a dynamcial bulk teming with entities as expression oand continuace of this GR expression?

So while I am showing the ideas in a conceptual way, this might have a basis from which I am strugging to define further.

While math exists quite readily in all these minds here, I see a lot of pictures and general concepts that have formed from your math. I am struggling on these as well.

But for me one question remains: Why introduce a new (scalar) field that gets a vacuum expectation value? There are already plenty of fields around. I understand that a vector field can’t get a vacuum value, because that would violate Lorentz symmetrie. But what about the fermion fields?

http://www.mazepath.com/uncleal/lajos.htm Table 1

have not excluded chiral anisotropy of space (photons have zero rest mass and no Higgs diddling re plane of polarization rotation over cosmic distances,). Nobody has observed vacuum free fall of opposite parity test masses to detect a diastereotopic interaction with chiral space,

http://www.mazepath.com/uncleal/lajos.htm Table II

Consider single crystal solid spheres of crystallographic opposite parity space group P3121 and P3221 quartz. If there were a chiral anisotropy of space, each chirality would vacuum free fall along a minimum action trajectory, but the two trajectories would not be parallel. An Eotvos experiment with opposite parity quartz test masses would be telling – and require three months of continuous observation. (Each crystal parity against fused silica are the controls.)

Given a diastereotopic interaction between chiral space and identical chemical composition opposite parity single crystal test masses, their conversions to an identical achiral state must have different enthalpies. A right shoe does not fit on a left foot with the same energetics as a left shoe (or a sock) on a left foot. Benzil, C6H5(C=O)(C=O)C6H5 is an achiral molecule that crystallizes in parity space groups P3121 or P3221 as does quartz. Nominally flat benzil molecules are helically distorted in the solid state and homochirally so throughout a single crystal. The melt is strictly achiral (not merely racemic).

http://www.mazepath.com/uncleal/benzil.gif Stereogram of crystalline benzil, helix repeat unit

Racemic benzil powder enthalpy of fusion is a secondary standard for calorimeter calibration. Thermodynamic melting occurs from 94.55 – 94.86 C. with 112.0 J/g enthalpy of fusion (or 110.6 J/g. Both values are referenced. Sublimation must be controlled).

Signal amplitude will be modulated by the phase angle (local time of day) between Earth’s inertial (spin) and gravitational (solar orbit) accelerations, plus the samples’ relative geographic orientation (north-south or east-west). The experiment should be run with paired calorimeters. The best geographic latitude is 45 degrees N or S, and best in the winter,

http://www.mazepath.com/uncleal/lajos.htm Table III and Table IV

State of the art Eotvos balances are sensitive to 10-13 difference/average. By E=mc2, 10-13 g/g is 9 joules. That is an 8% divergence from racemic benzil enthalpy of fusion. A most extraordinary observation in physics – expensive apparatus, expensive test masses, three months to run – is a rapid inexpensive chemistry experiment.

Spontaneous symmetry breaking is selective for weak interactions, and gravitation is the weakest interaction of all. Mega-dollar Eotvos balance or undergrad p-chem lab, somebody should look!