How does it couple universally?

The Kohn-Luttinger proved the effect named after them only in the limit of weak repulsive interactions (since the proof is perturbative).

What is the guarantee that if the short-distance repulsive attractions are very strong (compared to the kinetic energy of the fermions), the effective long-distance force would be attractive?? That is quite relevant to physics of High-Tc materials too.

And btw, in the case at hand (neutrinos) what is the ratio of potential to kinetic energies (so called r_s in condensed matter books)?

I’m an undergrad, and at one point I took an astronomy survey course — it filled credits and I’ve always had an interest in subatomic and galactic physics (but chose not to pursue an acadamian’s lifestyle). Having covered all the traditional and accepted theories and concepts, on the last day of the course the professor went over a number of “alternative” and less-accepted theories.

One of these was the statement that magnetism and plasma physics has been somewhat ignored over the years, and that there are some plasma physicist theories that try very hard to explain galaxy spin rates through magnetic forces, and also redefine many concepts, such as pulsars and solar radiation.

I’m well aware that dark matter and neutrinos have emerged from the same process — as mathematical placeholders, and that the discovery of neutrinos has emboldened many to pursue evidence of dark matter. Why aren’t the plasma physics concepts ever considered much? Do they have an inconsistent or unrealistic view of the universe? Are they just too unplausible? Is it merely an unpopular area of science that hasn’t garnered enough support to be taken seriously?

It seems that if we were able to assume magnetic effects supported galactic rotation, then neutrinos may present a plausible gravity interactor. What, then, would this do for evidence of dark energy?

In the limit of zero-cross section or non-interacting particles, I think one would get a BEC, a degenerate bose gas which won’t have a Goldstone mode. But any infinitesimal interaction would turn it into a quantum liquid (superfluid) with the velocity of Goldstone modes proportional to sqrt(interaction strength).

Yes, I missed the point completely. I was (wrongly) thinking about bosons to start with and having a zero-cross section of scattering among themselves. If the fermions (neutrinos) are non-interacting then yes, of course one just gets degenerate Fermi gas. Any infinitesimal four-fermion term would turn it into a superfluid.

Excuse me for my lack of understanding, but if gravitons are Goldstone bosons, why won’t they be lost (along with superfluidity) once temperature rises just above a very small fraction of Fermi temperature (weak coupling calculation would give extremely low T_c.)

“If that were true, ordinary metals would be superconducting at room temperature.”

No, the T_c for such a superfluid would be very low so I am not talking of room temperature superfluidity (infact that is what I was wondering at the end of my last comment in the context of McElrath’s paper.).
To reiterate, I think that at zero-temperature a Fermi liquid with infinitesimal repulsive interactions would turn into a superfluid (not taking into account any lattice, phonons or disorder). As you raise temperature, the cooper pairs would break at a very low T_c (K-L estimate was about 10^-17 in units of Fermi temperature) above which one would just have a Fermi liquid.

…K-L estimate was about 10^-17 in units of Fermi temperature

And how does 10^{-17} T_F compare with the temperature today?

I’ll try to answer a couple questions here:

1) The 10^{-17}K number in the Kohn-Luttinger paper comes from the usual
assumption that Delta x = 1/p (the de Broglie wavelength), which I
argue in the second section is not correct for cosmological relics.
Instead one must use Eq.5 or Eq.6, for which (inserting the neutrino
self-interaction cross section) one derives T < M_W as the transition
temperature (if you insist on stating it as a temperature). Note that
the K-L 10^{-17} transition temperature is correct for electrons,
because electrons have a Coulomb pole, and remain localized to their de
Broglie wavelength due to the strong scattering implied by this Coulomb
pole. In other words in terms of the QM barrier penetration
coefficients, T=0 and R=1 for electrons while T=1 and R=0 for
cosmological relics (T=transmission, R=reflection). Cosmological relics
are undergoing index of refraction physics, while electron scattering is
dominated by elastic scattering, which causes localization. As such, I
doubt that my results imply anything useful for high T_c
superconductors or any observable phenomena in condensed matter physics.

2) On universal couplings: I agree it is far from obvious that this will
happen. I do have an idea for how they will arise that will appear
soon. I believe this system MUST have universal couplings, otherwise
one could easily show that the Standard Model (due to background
neutrinos) is incompatible with gravitational equivalence principle
tests, even if gravity is a separate force. All particles (including
photons and gluons) do couple to the neutrino-graviton: the couplings
are 4-point operators which may arise at 1- or 2-loop.

3) On Weinberg-Witten: Sean, sure one can choose to work in a
diffeomorphism invariant formalism, but then one must add breaking terms
which correspond to the fact that particles can move faster than the
speed of light in the medium, and that G_N is varying. I cannot perform
a coordinate transformation to get to a region of space with a different
G_N: I would find my covariant stress tensor is not conserved, which is
one of the assumptions of Weinberg-Witten, and therefore their theorem
is not applicable here.

Jacques, I’m unsure what you’re getting at.

The Fermi temperature for this system is just T_F=E_F/k = sqrt(m^2+p_F^2)/k which is ~10^{-3} eV today. The critical temperature for this phase transition is ~ M_W, which is not the same as the Fermi temperature. It is this critical temperature that Kohn-Luttinger calculate as 10^{-17} K, which is relevant for an atomic or electronic gas with Coulomb interactions.

I did not quote a critical temperature and left it as a cross section in my paper because this requires knowing the cross section as well as n(T), which are model-dependent. e.g. the cross section depends on particle content and n(T) (may) depend on Hubble expansion, depending on your assumptions.

Dear Bob, thanks for your explanation but I am still not totally convinced. Basically my confusion is related to what Jacques wrote just above. But just for clarity let’s back up a little bit.

If I understand correctly, the ‘n’ in the equation 3 is just density of fermions. Thus the temperature quoted there is just the degeneracy temperature for fermions (T_F) and may not have anything to do with the superfluid instability temperature of this Fermi liquid (which one would expect to be much lower atleast for electrons). Till this stage we haven’t mentioned anything about them being cosmological relics (which is taken into account in eqn. 5 and 6), this discussion should hold for usual (uncharged) electrons/He-3 too. I hope by ‘quantum liquid’ you meant a BCS like state of interacting fermions and not just (perhaps strongly interacting) fermi liquid.

Even after taking into account the effect of refraction physics you mentioned, the discussion in section 2 seems to be about at what energies do particles (which are fermions) overlap with each other, Why should the temperature/energy at which this happens would be of the same order as the one at which they would further undergo a BCS like instability (which could very well happen at a much lower temperature like for electrons)?

Jacques, Tarun, I am proposing a new mechanism for the quantum liquid transition in Sec.2. In the RG approach, Delta x of the state does not enter the problem at all, and the only scale is the momentum p (and de Broglie wavelength), so the RG treatment only predicts the transition temperature if Delta x ~ 1/p for all time, which is definitely not satisfied for cosmological relics.

Fundamentally what is required for a superfluid is wave function overlap. This is satisfied by the time-expansion of wave packets, and is not described at all by the RG.

For the record, when I use the phrase “quantum liquid”, I mean Delta x > n^{-1/3}, and that’s all. By “Super-fluid” I mean the existence of a lower energy ground state than the free particle state. (with or without the classic consideration of viscosity)

Thanks Nemo

My confusion over this paper centers around lorentz violation. I thought that when it came to neutrinos, lorentz violation was invoked as an alternative to massive neutrinos to explain neutrino oscillations.

http://arxiv.org/pdf/hep-ph/0703263v1
http://www-boone.fnal.gov/slides-talks/conf-talk/tayloe/RT_CPT07.pdf

Yet this paper is dealing with massive neutrinos

My understanding was that one of the most “intuitive” arguments against lorentz violation was the potential for second law violations around a black hole

http://arxiv.org/pdf/hep-th/0603158v2

I’m probably not sophisticated enough to understand all the nuances of these arguments, but I would certainly love to hear more.

p.s.

Just in case people missed it, the MiniBoone Collaboration released its latest paper on the observed neutrino excess

http://arXiv.org/pdf/0812.2243v2

As I understand it, this intriguing model comprises a sea of neutrinos, each a wave packet a la QM, and the superfluid properties stem from the waves of these packets overlapping on average.

I also gather that these wave packets have stretched out over time. But if their expansion rate is not that of the expanding background space, wouldn’t this imply that their overlap, again on average and roughly speaking, changes in phase over time as a kind of beat.

Perhaps that accounts for the observed acceleration in the Universe’s expansion rate, this being simply one upward trend of a longer-term (and lengthening) cycle.

Presumably this cycle, if it exists, was much shorter during the Big Bang and the resulting slight relative changes in the strength of gravity and dark energy played a role in condensing out particles and reheating and so on. Also, if at an early stage the waves didn’t overlap at all then gravity (in this model) would be absent and dark energy unckecked. Inflation anyone? 😉