The New Scientist article, "Dimension-hop may allow neutrinos to
cheat light speed", here:
http://www.newscientist.com/article/dn20957-dimensionhop-may-allow-
neutrinos-to-cheat-light-speed.html
suggest dimension hops as the means for neutrinos traveling faster
than light, as measured in the CERN OPERA experiment, described by
Adam et al., "Measurement of the neutrino velocity with the OPERA
detector in the CNGS beam" here:
http://arxiv.org/abs/1109.4897
The arrival time of the neutrinos across a 730 km distance was 60.7
ns early, representing 2.48x10^-5 relative difference vs light travel
time.
This measurement conflicts with early arrival time data for neutrinos
from supernova. The New Scientist article quotes Marc Sher of the
College of William and Mary in Williamsburg, Virginia, "It's not
reasonable." ... "If neutrinos were that much faster than light, they
would have arrived [from the supernova] five years sooner, which is
crazy," says Sher. "They didn't."
This implies a difference in travel speed in matter vs vacuum for the
neutrinos.
A possible hypothesis to explain this difference is that dense matter
presents numerous tunneling barriers to the neutrinos in their flight
through such matter. The neutrinos spend 2.48x10^-5 of their travel
time tunneling through barriers when traveling through matter with
the density of the crust material. More accurately, about 2.48x10^-5
of the distance travelled in crustal matter is made up of tunneling
barriers for the neutrinos. This neutrino tunneling occurs
infinitely fast, because the quantum wavefunction of the neutrino is
already "there", on the other side of the barrier with some
probability. That probability is large because the size of a neutrino
wavefunction is large for a particle, due to its 2 eV or less rest
mass. When tunneling occurs the wavefunction collapses, because the
center of mass of the particle is suddenly changed. Its momentum and
velocity remain in tact though, and its quantum wavefunction rebuilds
with the new center of mass. The neutrino is thus teleported through
small tunneling barriers, and its effective speed is increased.
Such a large proportion of tunneling distance implies an extrememly
dense set of tunneling barriers in matter. It implies the tunneling
barriers are composed almost entirely of virtual particles within
atoms, because the nuclear barrier lengths and cross sections are too
small to account for the speed-up. The electron clouds must create
vast numbers of virtual particles that present tunneling barriers to
the neutrinos. An alternate explanation could be that these virtual
particles actually present access ports to alternate dimensional
paths through them. Taking such teleporting pathways could still be
considered a form of, called, tunneling.
The conflict between the observation of a difference of speed of
travel of neutrinos in dense matter vs vacuum is explained bythis
hypothesis. This hypothesis might be verified by sending a neutrino
beam through the earth's core, which is far more dense, and thus
should provide a much more dense virtual particle environment, a more
frequent tunneling environment for the neutrinos.
This hypothesis creates some mysteries, however.
The total tunneling distance Dt encountered by the OPERA experiment
neutrinos would be:
Dt = 730 km * (2.48x10^-5) = 18.1 meters
Using a mean atomic mass of 40 the mean nuclear radius Rn is:
Dn = (1.25x10^-15 m)*40^(1/3) = 4.3x10^-15 m
and the mean nucleus diameter is 8.6x10^-15 m.
If the mean tunneling distance is 8.6x10^-15 m, then (18.1 m)/
(8.6x10^-15 m) = 2.105x10^15 tunneling events would have to occur in
the 720 km travel distance. The mean free path is (720 km)/
(2.105x10^15) = 3.42x10^-10 m, or about 3.42 angstroms, roughly the
distance between atoms. Conversely, if there is one tunneling event
per atom, the tunneling distance is roughly the distance across the
mean sized nucleus. Unfortunately, the nuclear cross section is
insufficient for nuclear tunneling to be an explanation.
The mean nuclear cross section sigma would be Pi*(4.3x10^-15 m)^2 =
5.81x10^-29 m^2. The nuclear density rho to explain a mean free path
L would be given by:
rho = 1/(sigma L) = 1/((5.81x10^-29 m^2)*(3.42x10^-10 m)) =
5x10^37/m^3
rho = 8.4x10^13 mol/m^3 or 8.4x10^7 mol/cm^3
For average atomic weight 40 that is:
rho = 3.36x10^9 gm/cm^3 = 3.36x10^22 kg/m^3
This exceeds the density of the nucleus itself: 3×10^17 kg/m3, and
the densities of neutron stars. It seems reasonable then that the
interaction must be with virtual particles, which have no
gravitational mass, and which can have extreme densities.
Suppose the mean tunneling distance is the Planck length Lp =
1.616x10^-35 m. The mean free path L then is:
L = (1.616x10^-35 m)/(2.48x10^-5) = 6.513x10^-31 m
Suppose the particle cross section sigma is:
sigma = Lp^2 = (1.616x10^-35 m)^2
We then have an average virtual particle numerical density rho:
rho = 1/(sigma L) = 1/((1.616x10^-35 m)^2 * (6.513x10^-31 m))
rho = 5.89x10^99/m^3
These numbers only set a limit on virtual particle density. It could
be much less if the diameters are many Planck lengths wide.
This high virtual particle density would have to be due to the effect
of the electron-nucleus field. This implies the atom is a very busy
place, even outside the nucleus.
The fact early arrival time is not dependent on energy indicates the
fast tunneling is more likely provided extra-dimensionally than
simply due to ordinary wavefunction collapse. If the teleporting were
due to wavefunction collapse then delay should be a function of the
de Broglie wavelength, which is a function of momentum. Under the
hypothesis, collision of a neutrino with a virtual particle then
results in the taking of an instant, or much faster than c, path to
the other side of the position occupied by the virtual particle.
Another variation of the hypothesis exists if sound can travel on
strings at superluminal speeds. The interaction then involves a
neutrino-virtual-photon string merging on the arrival side and
similar string separation on the departure side. If the string
vibration propagation speed is not instant, but significantly larger
than c, the same result occurs - an early arrival of the neutrino.
In the case of the OPERA experiment this merely means the 18.1 meter
cumulative tunneling distance calculated above would be replaced by a
longer cumulative distance during which neutrinos effectively travel
at the speed of sound in the strings. The neutrinos then are
momentarily converted from a separate string into a vibration, a
pulse, traveling on a momentarily merged string.
The hypothesis is tenuous. However, it indicates a possible
experimental direction, looking at the effect of a through earth's
core pathway.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
