special relativity beyond the speed of light
(See also, on this web, Neutrinos Faster than Light?)
Physics.org October 8, 2012
Physicists extend special relativity beyond the speed of light
"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 'We certainly haven't superseded Einstein.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
"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 = mc2 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 accelerate 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 ms/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
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.