The Disappearing Theory of Oscillating Neutrinos

John Williams

2007-04-25 jmw:

Topic: The Disappearing Theory of Oscillating Neutrinos

The problem gradually has been recognized over the past
several decades: Experiments and observations, notably the
K2K experiment, have found that the creation flux of neutrinos
of a given flavor (flavors are named electron, muon, or
tauon) exceeds their destruction flux. Neutrinos seem to
disappear in flight.

A theory of quantum oscillation has been proposed to explain
these disappearances. This theory can curve-fit the data,
but it is based on a weakly constrained matrix (below),
so the fit itself does not confirm the theory well.

Only one experiment ever seemed to show an appearance of
a new flavor while a different flavor was disappearing:
The LSND experiment. Recently, a replication of LSND,
MiniBOONE, yielded enough data to allow one to conclude
that the LSND result was a fluke of chance and was wrong:
There was no such appearance.

This leaves physicists with no evidence of any oscillation,
only of disappearance.

The oscillation theory is based on a mixing matrix which
transforms a flavor vector to a vector of mass.
The matrix is invertible and generally is assumed to relate
three mass eigenstates to three flavor eigenstates. To ease
the calculations, often just two (dominant) flavors are
assumed, making the matrix 2x2. A transformation yielding
a mass vector with two components zero would yield a mass
eigenstate; a transformation yielding a flavor vector with
two components zero would yield a flavor eigenstate.

The usual theory assumes that a neutrino creation or destruction
interaction must be defined by a flavor eigenstate; therefore,
because the mixing matrix is assumed nondiagonal, the neutrino's
mass must be "indefinite" -- the interaction does not involve
a mass eigenstate. This assumption allows the theory
to calculate neutrino propagation quantum mechanically, the
mass eigenstate wavefunction phases being treated
separately, so that the creation and destruction points
imply a mass-vector phase shift during propagation.

Because the mass phase has changed during propagation,
given a flavor eigenstate at creation, the
probability of a different flavor at destruction may be
different from zero. Thus, neutrino flavor oscillates
as a function of propagation distance. A detector
designed to detect a certain relative frequency of
electron or muon neutrinos at one distance should detect
a different frequency at a different distance.

The fact that no appearance of a fraction of a new flavor
ever has been detected has been explained as a flaw in
the experiments or the flavor calculations, which are
based on computer simulations and are very complicated.

However, there is a fundamental problem: Misuse of the
phrase "the mass is indefinite". Quantum mechanics ONLY
deals with interaction probabilities; it does not deal
with velocities or distances.

The neutrino propagation distance is not an interaction,
and the mass can not be "indefinite" during propagation.
A specific neutrino particle must have a specific mass
during propagation. Otherwise, neither momentum
conservation nor energy conservation can be asserted,
both depending on the mass of a massive particle.

Noone has claimed that the propagation of a neutrino is
in a virtual interval in which energy might "briefly" (in
this relativistic-interval context) be nonconserved.
If they did, they would imply a mass eigenstate outside
the propagation interval, and, in particular, during the
interactions.

Instead, theorists have argued interminably whether their
calculations (formally) should assume energy or mass
conservation and derive the other conservation. The
results differ quantitatively and are a constant source
of dispute in the field. I can supply references if
a reader is interested.

The problem is that the theory itself, as currently
formulated, is inconsistent with the rest of physics.
It is mostly consistent, but not entirely so. The
inconsistency arises because of misuse of "the mass
is indefinite". Yes, quantum-mechanically, a quantity
such as location or energy often can not be predicted.
The "mass is indefinite"? Maybe, but, in all the
rest of quantum mechanics, the mass COULD be known
precisely AFTER the interaction in question has occurred.

Nope. Not according to the current theory: The mass is
forever "indefinite" -- if it weren't so, the theory would
not work and the flavor would fall into a noneigen state.

We need nore thought on this problem. The last experiment
showing a oscillation INTO a flavor, LSND, has been
rejected, and all there is anymore, is disappearance.

Who has a better theory of neutrino disappearance?
Is it possible that neutrinos might decay? What
about their interaction cross-section? Is it possible
the cross-section might decrease as a function of
proper time in propagation? Any other ideas?

Help!