special relativity beyond the speed of light

(See also, on this web, Neutrinos Faster than Light?)

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Physics.org October 8, 2012**

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Physicists extend special relativity beyond the speed of light**

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"This 3D graph shows the relationship between three different velocities: v, u and U, where v is the velocity of a second observer measured by a first observer, u is the velocity of a moving particle measured by the second observer, and U is the relative velocity of the particle to the first observer. Image credit: Hill and Cox. ©2012 The Royal Society

"Now two physicists – James Hill and Barry Cox from the University of Adelaide in Australia – have shown that Einstein's theory of special relativity can be logically extended to allow for faster-than-light motion. They're quick to point out that their finding in no way contradicts the original theory, but simply provides a new aspect of it.

"'As far as I'm aware, this is the first natural, logical extension of Einstein's own theories,' Hill said. 'We certainly haven't superseded Einstein. The two theories are entirely consistent.'

"There have been other suggestions of objects exceeding *c* –
tachyons, for example – but these superluminal motions require
complicated mathematics such as imaginary masses and complicated physics
to ensure real, meaningful outcomes. In contrast, Hill and Cox's
proposal arises from the same mathematical framework as Einstein's
theory.

"As the physicists explain in their paper, the Lorentz transformation is traditionally used in special relativity to reconcile different observations made by different observers in different inertial reference frames, and it applies to relative velocities less than the speed of light. Here the scientists have proposed two new transformations that complement the Lorentz transformation to explain different observations, and both new transformations apply to relative velocities greater than the speed of light. The physicists aren't sure which of the two new transformations is the correct one, and they don't ignore the possibility that both transformations may be equally plausible if for some reason Einstein's theory bifurcates at c into two variations.

"The two new transformations apply for relative velocities between *c* and
infinity (not including either). Like Einstein's special relativity with
the Lorentz transformation, the proposed extensions break down at
exactly c, resulting in a singularity. Passing through the speed of
light is not defined.

"As a result, the singularity forms a kind of boundary so that all inertial reference frames fall into one of two sets relative to some rest frame: those with a relative velocity less than c, and those with a relative velocity greater than c. The physicists explain that there is no objective way to identify whether a particular reference frame is in the subluminal or in the superluminal set of frames other than by reference to some arbitrary rest frame.

"Although the theories cannot answer what happens at c, the scientists suspect that an object crossing the 'light barrier' may have some very interesting consequences. They compare our current understanding of this boundary to that of an object crossing the sound barrier for the first time, an event that was highly disputed before it was achieved in 1947.

"'People wondered what would happen,' Hill said. 'Were we all going to disintegrate? Would the plane fall apart? It turns out passing through the speed of sound led to a big bang. I suspect going through the speed of light will be more interesting. I have a feeling the world will change in some dramatic way as we move through the speed of light. All sorts of things could happen. Time and space could interchange.'

"He thinks that an experimental test of such a feat is not out of reach.

"'I think it's only a matter of time,' he said. 'Human ingenuity being what it is, it's going to happen, but maybe it will involve a transportation mechanism entirely different from anything presently envisaged.'

"More information: James M. Hill and Barry J. Cox. 'Einstein's special relativity beyond the speed of light.' Proc. R. Soc. A. DOI: 10.1098/rspa.2012.0340

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"Abstract**
We propose here two new transformations between inertial frames that
apply for relative velocities greater than the speed of light, and that
are complementary to the Lorentz transformation, giving rise to the
Einstein special theory of relativity that applies to relative
velocities less than the speed of light. The new transformations arise
from the same mathematical framework as the Lorentz transformation,
displaying singular behaviour when the relative velocity approaches the
speed of light and generating the same addition law for velocities, but,
most importantly, do not involve the need to introduce imaginary masses
or complicated physics to provide well-defined expressions. Making use
of the dependence on relative velocity of the Lorentz transformation,
the paper provides an elementary derivation of the new transformations
between inertial frames for relative velocities v in excess of the speed
of light c, and further we suggest two possible criteria from which one
might infer one set of transformations as physically more likely than
the other. If the energy–momentum equations are to be invariant under
the new transformations, then the mass and energy are given,
respectively, by the formulae *m *= (*p∞*/c)[(*v/c*)^{2} - 1]^{-1/2} and
ε
= *mc*^{2} where *p∞ *denotes the limiting momentum for infinite relative velocity. If,
however, the requirement of invariance is removed, then we may propose
new mass and energy equations, and an example having finite non-zero
mass in the limit of infinite relative velocity is given. In this highly
controversial topic, our particular purpose is not to enter into the
merits of existing theories, but rather to present a succinct and
carefully reasoned account of a new aspect of Einstein's theory of
special relativity, which properly allows for faster than light motion."

**The Implications in a Nutshell**

**The Infinitely Flat Structure of the Universe**

**Traveling faster than
light : absolute one-sidedness of the absolute dead center cube
:: virtual left-handedness of neutrinos : virtual
left-handedness of real trinary logic :: c not the limit
of all velocity : infinitely flat structure of the universe.**

** **

For the ‘absolute
one-sidedness of the absolute dead center cube’ and the
‘infinitely flat structure of the universe’, cf. Leahy, *
Foundation*, Sections III.3 and IV.2, et passim.^{1}
For a succinct summary, cf., in particular, p. 544: “The absolute transcendence of ‘foreignness and
intimacy’ in the form of the conception now actually existing of
the ‘infinite number of infinitely transparent absolute
actualities’/of the ‘absolutely flat sphere the surface of
which is an absolutely transparent depth’/of the
‘absolute’/perceived/thought ‘coincidence of the “circumference”
and the “infinite straight line”’ this absolute opening/absolute
exteriority of the outside which is the ‘very beginning
of the absolutely unconditioned differentiation of time itself’,
this outside *identically* inside/inside *absolutely*
outwardized manifests itself, finally & absolutely, as
that completely fundamental structure now occurring for the
first time in history, at once the completely transparent
essential transcendentality of thought, the very
structure & identity of very existence.”

“The relative orientations of spin and linear momentum for neutrinos and antineutrinos is apparently fixed and intrinsic to the particles.

“For neutrinos the spin is always opposite the linear momentum and this is referred to as ‘left-handed’, whereas the antineutrinos are always ‘right-handed’. . . . This ‘left-handed’ vs. ‘right-handed’ characterization is not meaningful for other particles, like electrons. An electron could have spin to the right and be traveling right and therefore be classified as right-handed. But from the reference frame of someone traveling faster than the electron, its velocity would be to the left, while its spin would be unchanged. This would mean that the electron is a left-handed particle with respect to that reference frame.

“For neutrinos, however, which are
traveling at the speed of light or very close to it, you cannot
accel**e**rate to a greater speed and thereby change their
‘handedness’. We say that the neutrinos have ‘intrinsic parity’,
all of them being left-handed. This causes the weak interactions
which emit neutrinos or antineutrinos to violate
conservation of parity. The property which has been
called left-handed and right-handed here is sometimes called
‘helicity’. The helicity of a particle is defined as the ratio m_{s}/s,
or the z-component of spin divided by the magnitude of the spin.
By this definition in this case, the helicity is +1 for a
right-handed antineutrino and -1 for a left-handed neutrino.”

Note that on the “Index of
the Ethic of Simplicity” (Leahy, *Beyond Sovereignty*, p.
88) the physics analogue of real trinary logic 0 (≠ zero) |
Readiness | Quantum-quality is the weak force.

In the event that neutrinos
were in
fact to travel faster than light then we would have to say for the
first time that neutrinos are *virtually* left-handed, that is,
‘intrinsically’ left-handed only in the event that the ultimate
frame of reference were *c*. But where the ultimate frame of
reference is thought itself for the first time in history (cf.,
above, citations from *Beyond Sovereignty*, *Novitas Mundi*,
and *Foundation*) relativity itself is absolutely relative
and neutrinos are *virtually* left-handed as is real trinary
logic (see, on this web,
Quantum Gravitational vs.
Quantum Logic: Virtually Left-handed Real Trinary Logic).^{2}

**Note**

^{
1}
D.G. Leahy, *Foundation:
Matter the Body Itself* (Albany, 1996).
Note in this connection that the body diagonal of the absolute dead
center triple-cube (= 337.7099347; cf., on this web,
Logically Outfitted Cube(s)
and
Sorted Diagonals)

divided by the inhomogeneities/smooth inflationary surface ratio (=
1e-4;
at 10^{−37} seconds after the beginning of the universe
when it
first became transparent to light,
inhomogeneities that
become the seeds of the large scale structure of the
universe; cf., on this web,
The Light, the Logic, & the
Inhomogeneities) raised to the fourth power effectively
equals the metric value of the radius of the observable universe:

(337.7099347/1e-4)^{4} = 1.3e26.

^{
2}
See also, on this web,
The Pythagorean Komma, 82944, Neutrino Oscillation & Real Trinary
Logic and
Speaking of Faster
than Light . . . Macroscopically! Or, Wither Distance?
Or, What of Time?.