In some kinds of electron tunneling, such as in graphene, electrons behave as if they were massless - as described by the so-called "massless Dirac equation". However, the electrons move at a lower velocity than c in actuality (to an external observer). This is called Klein tunneling - Wiki has a lightweight piece on the phenomenon. http://en.wikipedia.org/wiki/Klein_paradox This is from the same Oscar Klein who is credited for the Kaluza-Klein theory of "enfolded" extra-dimensionality. Curiously, a different Klein (Felix) came up with a geometry for manifold "looping" which can be visualized in macro-reality as the 'Klein bottle' and it too is a dimensional thing. This geometry may also have special relevance at the nanoscale in describing the dynamical Casimir effect (DCE) and even more so, when combined with Klein tunneling. Dirac electrons are observed in nano-geometry and on 2D surfaces where they cross energy barriers which they should not be able to cross. The Klein bottle is a good visual metaphor for that phenomenon, in that electrons are fungible. This can offer insight about the tiny bit of excess energy which derives from the most common kind of fusion in the Universe, reversible proton fusion - but in a way that occurs in Casimir cavities, as a replacement for the gravity field. IOW - recirculating electrons in Casimir cavities, which act 'as if' relativistic, can catalyze P+P "reversible fusion", in which there is seldom any observable difference in the two protons, which temporarily fuse to 2He and immediately 'fission' back to two protons - with almost no other significant change other than shedding magnons during QCD color change (as 2He reverts to P+P). A tiny amount of gluon mass is lost. Jones
ADDENDUM (long "boilerplate") - Because of the complexity of how DCE and
reversible proton fusion would fit into the big picture of LENR, I have
modified the following general framework to incorporate it into a larger
context. Otherwise, It is too easy to be misunderstood - without
consideration of the entire realm of interlocking relationships.
An evolving theory of nanomagnetism which incorporates the dynamical Casimir
effect, magnons, and reversible fusion accepts that there can be several
different methods for nuclear and quasi-nuclear gain with hydrogen at the
nanoscale. Here are the gainful metal-hydride reactions for which there is
substantial experimental evidence (in roughly chronological order):
1) The original LENR of P&F which is seen with palladium and deuterium, and
involves fusion to helium or tritium.
2) The original f/H (fractional hydrogen) mechanism of Mills, now expanded
by Miley and others as Rydberg hydrogen or as the DDL (deep Dirac layer). No
radioactivity involved.
3) A Focardi/Rossi mechanism involving the transmutation of nickel into
copper or other metals. This can be described as a version of the W-L beta
decay mechanism, as can Brillouin's mechanism.
4) The Storms mechanism, which is similar to 1) and is true LENR in the
sense of fusion of protons to deuterium, but suggests a much higher
probability of beta decay of 2He, so that substantial deuterium can happen.
5) A nanomagnetism mechanism which is quasi-fusion (QCD
reversible-proton-fusion) and a strong force reaction - not involving the
weak force). The "ash" is magnon "radiation" from protons which interact
magnetically. This is QM based and consequently can leave trace
radioactivity and transmutation.
6) Any combination or permutation of the above - since none of them are
mutually exclusive.
This list is NOT what most theorist's want to accept: that there could be
several overlapping mechanisms for gain in hydrogen loaded nanocavities or
matrices. It is anti-Ockham, but in fact all of QM is anti-Ockham.
Essentially we must ask - why not many mechanisms? After all, most of the
universe is composed of hydrogen, and there is no logical reason that
quantum interactions of subatomic hydrogen should be simple - just because
the atom itself seems simple at first glance. When broken down to quarks,
gluons and color change etc, simplicity disappears.
The nanomagnetism theory is the only one (of the above) which can account
for non-chemical endotherm, which has been seen in some hydride systems -
and is perhaps more of a shocking anomaly than excess heat. Endotherm, in
this case means that when a large amount of outside heat is put into the
system, a substantial fraction of that heat seems to physically disappear,
as if there was a magic internal heat sink - far surpassing any chemical
explanation by orders of magnitude. Celani, Technova, Ahern and others have
seen this physical feature - but have not pursued it.
DCE, the dynamical Casimir effect was introduced by Julian Schwinger in 1992
in "Casimir Energy for Dielectrics." Although he was a proponent of cold
fusion, it is not clear to what extent Schwinger himself was fully promoting
DCE as an alternative explanation for gain (or else as a predecessor
condition for nuclear reactions). He simply did not have all the pieces to
the puzzle then, but was suggesting the idea that electron tunneling and QM
effects such as the Lamb shift can account for some excess energy. The Lamb
Shift, superparamagnetism, and the DCE are interleaved and together portend
both anomalous heating AND anomalous cooling. All you need is the correct
material in the correct geometry in the same way that the Casimir force
itself can be either attractive or repulsive. The explanation of internal
thermal loss is a huge surprise to many observers.
The Lamb shift is a small difference in energy between two energy levels of
the hydrogen atom in quantum electrodynamics (QED) so it can go either way
if asymmetric. It is basically a spin-flip. It was the harbinger of modern
QED as developed by Schwinger and others. The Lamb shift is tiny in each
instance, but lattice phonons move a terahertz frequencies and higher, so
the "transaction rate" for tiny incremental gain or loss in contained
hydrogen, due to the Lamb shift, is staggering... same with the dynamical
Casimir effect of photons, as the two fit like hand-in-glove. All one needs
to realize either anomaly over time is to impose asymmetry in a lasting way.
Magnets are good at that.
Superparamagnetism is a form of magnetism, and can appear in ferromagnetic,
ferrimagnetic, and/or multiferroic nanoparticles. Wiki has a decent articles
on all of these topics. In properly sized materials containing nickel at the
nanoscale, for instance, ferro-magnetization can flip rapidly under the
influence of temperature around a threshold level, and with asymmetric gain
or loss. The typical time between flips is called the Néel relaxation time
which is below a nanosecond.
In the absence of an imposed magnetic field, the flip time of the
nanoparticles (due to magnon interaction) is longer than the polarized Néel
relaxation time. This is why a magnetic field can assist with excess thermal
gain or loss (the Letts/Cravens effect). Everything is complicated in a
scenario when anomalous heat comes from the DCE, since this may involve
either the Lamb shift or relativistic effects or both. There are proved
relativistic effects in Casimir cavities, and that implies energy anomalies
which can be either exothermic, endothermic, or both. Eventually the source
of heat being "from DCE" is not descriptive of the physics, since it is a
"proximate cause," and not an ultimate cause.
The ultimate cause of excess heat is thought to be conversion of a tiny
percentage of proton mass into energy. Proton mass is an average around the
value of 938.27MeV, with potential to supply as much as several KeV without
being noticed from the high end of the distribution. The heavier fraction of
protons can supply energy via "magnons"... and yes - magnons are the final
piece of the puzzle, since under QCD these are the quantum of spin - and can
transfer mass into "spin waves" to cause spin flips with hydrogen, or simple
core heating in elements with magnetic susceptibility. Magnon transfer can
happen whenever quark color change happens in protons (which is often in
confined systems- where protons are captured in Casimir cavities).
Jones
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