a discussion forum for Polywell fusion
https://www.talk-polywell.org/bb/
Can the Tajmar effect be explained using a modication of inertia?
http://arxiv.org/PS_cache/arxiv/pdf/091 ... 1108v1.pdf
More by McCulloch:Aero wrote:Can the Tajmar effect be explained using a modication of inertia?
http://arxiv.org/PS_cache/arxiv/pdf/091 ... 1108v1.pdf
I also increased confusion by being lazy in typing. Unit quaternions are not the same thing as unit axial vectors, so they should be written as [[0, i]], [[0, j]], [[0, k]].DeltaV wrote:Hamilton made one mistake which increased the confusion... he thought that the quaternion units i, j, k were associated with 90 deg rotations, as i = sqrt(-1) is for complex numbers z = x + iy, instead of the correct pi rad or 180 deg.
viewtopic.php?p=46056&highlight=#46056IntLibber wrote:Oh geeze, I positively HATE quats.... now I gotta learn them to navigate spacetime with mah warp drive?
So you want to continue the cover up?IntLibber wrote:However, being an air force veteran who has entered area 51, I can say with certainty that the OSI intentionally promoted UFO reports around Area 51 as a means of discrediting anybody who saw any classified aircraft being tested there.
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Generalization of Einstein’s Field Equations
Einstein’s field equations
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are 10 independent, nonlinear differential equations. But they are too few in number,
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The number of essential parameters of the Lie group,
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is 16 in number. It implies that the most general form of the field equations, subject to the principle of relativity, must be 16, rather than 10.
Why are Einstein’s equations 10 in number rather than 16? It is because the form of these equations is more symmetric than they need be, in accordance with the (16- parameter) Einstein group. They are covariant (form-invariant) with respect to the continuous transformations, as they must be. But they are also covariant with respect to the discrete reflections in space and time, which is not required. By lifting the space and time reflection transformations, Einstein’s equations thereby factorize to 16 independent equations.
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The answer to this question comes from the fact that the irreducible representations of the Einstein group of general relativity obey the algebra of quaternions ...
We see here that any law of nature, whether in particle physics or in cosmology – the physics of the universe - that is compatible with the symmetry required by relativity theory, in special or general relativity, must be in terms of spinor and quaternion variables. This is a requirement of the algebraic logic – the group structure - of the theory of relativity. It is the reason that Dirac’s special relativistic theory of wave mechanics led to spinor degrees of freedom in the description of the electron (and a quaternion operator to determine these solutions). That is, the spin degrees of freedom in Dirac’s electron equation are not a consequence of quantum mechanics, per se, as many have claimed! It is a consequence of the symmetry imposed by the theory of relativity.
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The quaternion form yields 16 field relations that replace the 10 relations of Einstein’s symmetric tensor form of his field equations in general relativity. In addition to explaining gravity, as will be described below, the quaternion form predicts new physical effects in the cosmological problem of the universe as a whole. One important new feature is the torsion of spacetime. It predicts, as examples, the rotation of the galaxies and the Faraday Effect regarding the propagation of cosmic electromagnetic radiation, i.e. the rotation of the plane of polarization of this radiation as it propagates throughout the universe. Both of these are observed astrophysical effects, not predicted by then standard Einstein tensor formulation. A further prediction is an anisotropic expansion and contraction of the universe, in a spiral fashion(GRM). Another important difference is that the geodesic equation, that prescribes a natural motion along a curve of an unobstructed body, has a quaternion form. That is, to prescribe the motion of a body along a trajectory, parameterized by the time measure, one must have four parameters, rather than one, to prescribe the time change, as a body moves from one spatial location along its trajectory to another. This is a generalization of the time parameter in physics that was theorized by William Hamilton, in his discovery of the quaternion algebra in the 19th century.
It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.
A. Einstein