A New Blog: The Inertia Question

[MSimon]

*

http://inertiaquestion.blogspot.com/201 ... stion.html

*

I'm looking for pdf links for the sidebar.

[Aero]

Can the Tajmar effect be explained using a modication of inertia?
http://arxiv.org/PS_cache/arxiv/pdf/091 ... 1108v1.pdf

[Giorgio]

Is it only for pubblished works or there will also be a section to non mainstream ideas?

Shoul the latter be, you might want to consider also the Heim hypothesis and proposed experimental verifications:
http://www.hpcc-space.de/publications/d ... Hauser.pdf

The above PDF summarize pretty well everything. More material here if interested:
http://www.hpcc-space.de/publications/index.html

[DeltaV]

Can the Tajmar effect be explained using a modication of inertia?
http://arxiv.org/PS_cache/arxiv/pdf/091 ... 1108v1.pdf

More by McCulloch:
http://arxiv.org/find/astro-ph/1/au:+Mc ... /0/all/0/1

The latest one proposes a cyclotron experiment to see if inertia is due to Unruh radiation.
http://arxiv.org/abs/1004.3303

[DeltaV]

http://arxiv.org/abs/physics/0305024
Concept of Quaternion Mass for Wave-Particle Duality : A Novel Approach

The author incorrectly describes a quaternion as a combination of scalar and vector. It is actually a combination of scalar and pseudovector*. A common oversight.
Still an interesting paper touching on inertia, though.

* Vectors ("polar" vectors) involve "translation" (velocity, force, E field, ...).
Pseudovectors ("axial" vectors) involve "rotation" (angular velocity, torque, B field, ...).

Cross products obey the following rules:
axial x axial --> axial
polar x polar-->axial
axial x polar --> polar
polar x axial --> polar

The Cartesian unit vectors i, j, k must therefore all be axial vectors since i x j = k, j x k = i, k x i = j, and it wouldn't make sense to have a mixed basis. In quaternion language, units i, j, k are actually half-turn (pi rad, 180 deg) rotations about their respective axes.

Any two quaternions obey the product rule [[a, A]] [[b, B]] = [[ab - A.B, aB + bA + AxB]], generally noncommutative. For normalized quaternions, which have sqrt(a^2 + A^2) = 1 where A = |A|, the scalar part a = cos (theta/2) and the pseudovector magnitude A = sin(theta/2), where theta is the rotation angle and A is the rotation axis.

So the "translational", Cartesian frame in which traditional Gibbs-Heaviside vector operations are performed actually has a rotational basis when viewed using quaternions. An axial vector can always mimic a polar vector, but the converse is not true. The failure to clearly and consistently distinguish between axial and polar vectors dates from the birth of various hypernumber concepts in the mid-to-late 19th century and is IMHO a contributor to the current confusion in physics. A bloody literature war was fought over this in the late 1800s. Quaternions were suppressed by the early 1900s. 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.

A recent (1960s-present) approach, Hestenes' Geometric Algebra, clearly distinguishes axial from polar (pseudo from non-pseudo), yet he still starts his derivation with a translational bias (point to line to rhombus to parallelepiped to ...). It works well, but might it be missing something?

[MSimon]

Thanks!

[DeltaV]

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.

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]].

Altmann (1986, 1989) uses outline-font brackets instead of double brackets and outline-font letters (which I don't have here) as shorthand for bracketed objects (quaternions), along with bold font for pseudovectors and plain font for scalars. So A_outline_font = [[a, A]], i_outline_font = [[0, i]], etc. It works well for tracking what sort of objects you are dealing with.

Substituting [[0, i]], [[0, j]] and [[0, k]] into the equations Hamilton scribed onto Broom Bridge in 1843, i^2 = j^2 = k^2 = ijk = -1 and also into ij=k, jk=i, ki=j, then verifying these using the product rule [[a, A]] [[b, B]] = [[ab - A.B, aB + bA + AxB]] is a good exercise. BTW the right quaternion (= rotation) on the left side, [[b, B]], is assumed to occur first (operator convention).

[DeltaV]

A partial list of inertia related papers on arxiv.org --

http://arxiv.org/ftp/arxiv/papers/0912/0912.3049.pdf
http://arxiv.org/PS_cache/arxiv/pdf/081 ... 3936v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/080 ... 3318v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/080 ... 3146v6.pdf
http://arxiv.org/ftp/arxiv/papers/0803/0803.4465.pdf
http://arxiv.org/PS_cache/arxiv/pdf/080 ... 1599v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/080 ... 0284v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/071 ... 3415v6.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703141v1.pdf
http://arxiv.org/PS_cache/hep-th/pdf/0611/0611341v3.pdf
http://arxiv.org/ftp/physics/papers/0611/0611167.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 9144v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 9026v4.pdf
http://arxiv.org/ftp/physics/papers/0607/0607136.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 4131v5.pdf
http://arxiv.org/ftp/math-ph/papers/0604/0604051.pdf
http://arxiv.org/ftp/astro-ph/papers/0601/0601478.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/ ... 0117v1.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/ ... 8182v2.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0409/0409026v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 9010v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 2096v4.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/ ... 0013v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 5086v3.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0202/0202005v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 7008v1.pdf
http://arxiv.org/ftp/gr-qc/papers/0106/0106003.pdf
http://arxiv.org/ftp/physics/papers/0105/0105095.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/ ... 3110v1.pdf
http://arxiv.org/ftp/physics/papers/0103/0103044.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 3008v2.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/ ... 1082v1.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/ ... 1081v1.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0012/0012102v1.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 2025v3.pdf
http://arxiv.org/ftp/physics/papers/0010/0010018.pdf
http://arxiv.org/PS_cache/physics/pdf/0 ... 6021v1.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0002/0002046v1.pdf
http://arxiv.org/PS_cache/physics/pdf/9 ... 6059v4.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/9903/9903065v1.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/ ... 1194v1.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/ ... 9158v1.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/9412/9412012v4.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/9706/9706056v1.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/ ... 3012v1.pdf

** WARNING: At least one of these is wrong. **

Is it any wonder we don't have flying cars yet?

[IntLibber]

Oh geeze, I positively HATE quats.... now I gotta learn them to navigate spacetime with mah warp drive?

[DeltaV]

Oh geeze, I positively HATE quats.... now I gotta learn them to navigate spacetime with mah warp drive?

viewtopic.php?p=46056&highlight=#46056

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.

So you want to continue the cover up?

http://mendelsachs.com/wp-content/uploa ... verse3.pdf

Page 8
Generalization of Einstein’s Field Equations

Einstein’s field equations
...
are 10 independent, nonlinear differential equations. But they are too few in number,
...
The number of essential parameters of the Lie group,
...
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.
...
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.
...
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