Spinning
Einstein
Summary
Nobel prize winner Sheldon Glashow and
colleague Andrew Cohen, of
Neutrinos
are the most abundant particle in the universe; in fact the universe has been
described as a vast sea of neutrinos, punctuated by other particles. Recent
experiments have shown that neutrinos have mass, even though our current best
theory of matter, the Standard Model, says they should be massless.
While formulating their “Very Special Relativity,” they discovered that a neutrino’s
mass may be a clue to an irregularity in space time.
From
the results of the MM experiments Einstein concluded the speed of light is
constant for all observers, regardless of their motion. He also assumed the
laws of physics are the same for all observers moving at constant speed. From
these two postulates, He derived SR.
If
these two postulates are true, then time must have certain symmetries, which
form the Lorentz symmetry group, which concerns rotations and changes in
velocity. The lorentz symmetry group, with the symmetry of space time
translations, are revealed by SR. SR
implies that the velocity of light is constant for all observers (is this a
postulate?) time slows and distances contract at near light speeds, energy and
mass are interchangeable, and two events that appear simultaneous to one
observer do not to another observer.
Today
scientists are wondering if Lorentz symmetry might be broken at small distances
or high energies. They are motivated by a search for the TOE. String theory and
loop quantum gravity suggest that Lorentz symmetry might be broken at the Plank
scale, 10-35 meters, where both QM and gravity come into play. Non-commutative geometry explicitly calls for
Lorentz symmetry breaking at the Plank scale.
Dozens
of experiments have unsuccessfully tried to reveal evidence of a break in
Lorentz symmetry.
Glashow and Cohen found a way to modify SR to reduce
the amount of Lorentz symmetry. This modification they call Very Special
Relativity (VSR). In this new
version, Lorentz symmetry is
prominent enough to maintain the
traditional features of SR, such as constancy of speed of light, but full
rotational symmetry of space-time is lost. “Not all directions are the same in
VSR” says Glashow. … there
is a preferred direction in space.” On earth, the preferred direction is down.
That’s because the mass of the planet breaks the symmetry of space time and gravity
selects a unique direction. G and C suggest that even in the absence of a mass,
space-time itself treats some directions differently. But don’t the underlying
laws of physics see every direction as equal? (Lorentz
symmetry). The break in rotational symmetry should be very small, and so
unnoticeable at the mid scales of earth. No break in rotational symmetry has
yet been documented. Cohen says that if you give up rotational space time
symmetry, other possibilities look very nearly rotationally invariant.
At how
small a scale would we find VSR’s Lorentz symmetry
violation?
The
answer lies in the neutrinos. Neutrinos interact with matter only through
gravity and the weak force. They are the least understood of the particles in
the Standard Model.
New explanations
of the strange qualities of neutrinos may be paving the way for a deeper
comprehension of the universe than the standard model affords.
In 1998, the Super-Kamiokande,
a Neutrio observatory in
The
neutrino spin is also puzzling. Researchers have discovered that some particles
can spin either to the “left” or “right”, while others can spin only in one
direction. Only massless particles can have one
directional spin, and only massless particles can
travel at the speed of light. Every
neutrino ever observed has had left handed spin, so the neutrino should travel
at light speed and be massless. How can a neutrino
have left handed spin and have mass? VSR appears to provide an answer. VSR’s lorentz violation occurs at
the scale of the neutrino’s size, so it can have mass. If it has mass, it cannot travel at the speed
of light.
VSR
makes some predictions that may be testable some day. It should limit tritium’s
momentum as it decays, releasing an electron and an antineutrino. Another possibility is that it could effect electron dipole moment.
Neither
of these predictions is currently testable.
Many
scientists do not put much stock in VSR, because even very small changes in SR
translate into big problems for GR. So although VSR might solve some problems,
it might create even bigger ones.