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SN1987A in Support of Tachyon Neutrinos



This was posted on another list where this topic in under discussion. I felt
it might be appropriate to post this on the PHYS_L list. I apologize for it's
tutorial nature. I hope list members find this interesting.

In Einstein's theory of Special Relativity, there are three possible
kinematic states for particles.   These three classifications of particles are
commonly called, Tardyons, Luxons and Tachyons.
           1) Tardyons are particles whose rest mass squared is positive.
Their velocities are required to always be less than c, the velocity of light in
a vacuum.
           2) Luxons are particles whose rest mass squared is zero. These
particles must always travel at the speed of light.
            3) Tachyons, whose rest mass squared is negative. They are
required by Special Relativity to always travel at velocities greater than c.
   In the standard model Quarks and electrically charged leptons, as well as
the heavy bosons (the W and Z bosons) are known to be tardyons. The other
force carrying particles, the photon, the color charged gluons, and the
hypothetical graviton are Luxons. Until very recently the neutrinos, the non
electrically charged leptons were thought to be Luxons also. However recent observations
of neutrino flavor oscillations have indicated that at least two of the three
neutrino flavors are not Luxons. Even more surprising, experiments to measure
directly the mass of these particles, using the endpoint energy spectrums
observed in weak force decays has provided persistent evidence that these
particles have negative mass squared values.
    For most Physicist these results are greeted with skepticism.   These
measurements are difficult and are open to systematic errors which are the plague
of all difficult experiments. However these experiments are not the only
evidence which supports the idea that neutrinos are tachyons. A fall off in the
detection of high energy protons in the cosmic ray spectrum may well be another
signal that Neutrinos are tachyons.
     Free Protons are believed immune from weak force decays. This is because
the sum of the energies of the end products of any decay process must be less
than the energy of the decaying particle. However if neutrinos are tachyons,
then for protons boosted to the Pev energy level, the neutrino decay product
will have negative energy in the inertial frame of the decaying proton.
Therefore the sum of daughter products energies will be less than the decaying
proton's energy, making weak force proton decay possible. This is described by the
following equation.

             E'=gamma*(E-u*p)   when u>E/p  or u>c^2/v

Where u is the relative velocity in the direction of the tachyon's motion and
v is the relative velocity of a second observer. From this we can a sign
change in the energy observed for the neutrino if the proton is boosted to the
phase velocity of the decay product neutrino. This situation can only occur for
tachyons since the phase velocity of tardyons are superluminal.   However the
cosmic ray proton spectrum may not be the only astronomical evidence for
tachyon neutrinos.
         SN1987A is the name of a supernova event detected in 1987. This
event is believed to have occurred approximately 170000 light years from earth. At
several neutrino observatories detectors were able to measure neutrino
interactions believed to be a result of neutrinos emitted by this supernova.

        IMB found 8 events within 5.58 seconds with energy levels between
19mev and 39mev.

         K2 found 11 events within 12.439 seconds between 6.3 mev and
35.4mev.

        Bakun found 5 events between 12mev and 23.3 mev.

    All these events are believed to have occurred within 15 seconds, thought
synchronization uncertainties may extend this time to about one minute.

  Supernova models predict that the emission of visible light follows the
neutrino burst after a few hours. By reconstructing when the visible light was
observed it can be determined that the neutrino events were observed between 2
and 3 hours before the supernova was detected by observation of the visible
effects. This accords well with supernova models.
   However this is not the whole story. Five neutrino events were observed at
the LSD neutrino observatory at Mount Blanc within 7 seconds at energy levels
between 5.8 and 7.8 Mev. These events were observed 4 hours and 43 minutes
BEFORE the events recorded at IMB, K2 and Bakun. In addition one event was
recorded at K2 4 hours and 43 minutes before the events recorded earlier at IMB and
Bakun.  Also it should be noted that the LSD observatory detected two events
at the IMB and K2 times between 7 and 9 mev within an interval of 13 seconds.
How can these very early events be explained? A closer look at the physics of
neutrinos is required.
  The electron, muon and tau neutrinos are eigenstates of the weak
interaction. These weak eigenstates are linear combinations of mass eigenstates.

                                  v_f=SUM[U_fm*v_i]

Each mass eigenstate has its own momentum. These leads to different speeds
for the mass eigenstates and hence to their eventual separation after long
distances and time of flight. This puts these mass eigenstates into a region of non
oscillation. Now if Neutrinos are truly tachyons then their velocities behave
inversely from tardyons as a function of energy and rest mass.

               v_tach=c*sqrt(1+(E_0/E)^2)

Therefore low energy tachyons and heavy tachyons travel at a higher velocity
than light or high energy tachyons. Looking at the neutrino detection data we
can make the following assumptions.

           1) All the SN1987A neutrinos were emitted in a few seconds.

           2) The faster Superluminal mass eigenstates of all neutrinos
reached the earth about 4 hours and 43 minutes before the slower superluminal mass
eigenstates.

          3) LSD and K2 (one event) detected the faster superluminal mass
eigenstates.

   The mass eigenstates m_1 is thought to be associated with the electron
neutrino flavor while M_2 is thought to be associated with the muon neutrino
flavor. Finally M_3 is believed associated with the Tau neutrino flavor. If one
uses the experimentally determined mass values measures in tritium decays
-27(ev^2) and using the energy levels observed at the later neutrino events at IMB.
K2, and Bakun than the travel times are in close agreement with the observed
neutrino events. If the assumption is made that the earlier neutrino events
were the detection of the M_2 or m_3 mass eigenstates then calculations give a
value averaged at -541(ev^2). This value is not excluded for the muon neutrino
mass values measured in muon decay experiments. No information is available
concerning the tau neutrino mass values.
    Therefore it seems reasonable to conclude that the neutrino detection
events observed from SN1987A are supportive of the idea that neutrinos are
tachyons.
   Objections have been raised that the whole notion of tachyons is
inconsistent and would lead to causality violations. However as has been demonstrated
in an earlier post it is possible to modify the Dirac equation to produce a
consistent Quantum field theory for tachyons and using the re interpretation
principle avoid causality violations. ( However differences as to which events are
causes and which events are results do exist as a function of the inertial
frame of the observer though remain completely consistent in any  one given
inertial frame.)
  The mathematical structure revealed by special relativity provides for the
existence of three kinds of particles, the Tardyons, Luxons and Tachyons.
Since we know for sure that two of these three possibilities exist should we
really be surprised if the third possibility exist as well. From a philosophic
point of view the existence of tachyons is a sensible notion.
  Nevertheless Science is not philosophy. For an idea to be accepted it must
be testable and subject to falsification. I have already cited the current
experimental evidence. Is there some future possible observation which falsify
the notion of tachyon neutrinos? The answer is yes. Since the tachyon must
travel at superluminal velocities it may never undergo helicity flip. These means
that evidence for sterile neutrinos would highly disfavor the existence of
tachyon neutrinos. In addition, if neutrinos are tachyons, they must be Dirac
particles. This means a confirmed observation of double beta decay would falsify
the theory that neutrinos are tachyons. So far no confirmed double beta decay
has been observed. In addition, the Large Mixing angle MSW solar neutrino
oscillation (which is highly favored by current data) predicts delta mass squared
values which are consistent with Dirac Neutrinos, not majorana neutrinos.

<A HREF="http://arxiv.org/PS_cache/hep-ph/pdf/0210/0210417.pdf";>http://arxiv.org/PS_cache/hep-ph/pdf/0210/0210417.pdf</A>

    At the very least we can safely say that this a scientific question which
is amenable to observation and experiment. As disturbing as it may be for
some, there is considerable evidence that nature didn't neglect the third part of
the kinematic triad of Tardyons, Luxons and Tachyons. However, we must await
further supernova events as well as further refinements of end point energy
spectrums results in weak force decays to be reasonable certain that Neutrinos
are Tachyons. Below is a useful link with numerous papers on this topic.

http://www.to.infn.it/~giunti/NU/Supernova_Neutrinos/

Bob Zannelli