This is a very useful check, I went through the protocol, and it shows that the correct general Lorentz transforms of the potential vector and charge density is:
J’ = J — gamma rho v + (gamma – 1) (J dot v^)v^
A’ = A – gamma phi v / c squared + (gamma – 1) (A dot v^)v^
These useful results can now be applied to gravitomagnetism and to the generalization of dynamics. Many thanks indeed to co author Horst Eckardt for this checking work using the computer augmented by hand calculations. My preliminary calculations today show that orbital precession can be described by the general Lorentz transformation of force, the factor x of x theory can be defined in terms of the spin connection vector.
To: EMyrone@aol.com
Sent: 29/07/2015 12:36:18 GMT Daylight Time
Subj: Re: Discussion of Note 323(4)Attached is the calculation with 4-vectors. They are called J4 and A4. On the first/second page the Transform in Z direction is performed:
J4 –> L * J4
A4 –> L * A4The results are 4-vectors, column form, each line is a component. There is a commen factor gamma (I had to use capital gamma for internal reasons of Maxima).
On the second/third page the general transformation matrix Lambda and the expressionsJ4 –> Lamba * J4
A4 –> Lambda * A4are shown, again in 4-vector notation. Each line is an algebraic expression for the respective component. Components 1-3 contain the vectors J and A without a gamma factor.
(beta has been repaced by b for internal reasons).
There seems to be a principal difference between vector and tensor transformations. Please check this protocol in detail.Horst
Am 29.07.2015 um 09:53 schrieb EMyrone:
I have been thinking about this myself. I recommend multiplying the general matrix (50) of note 323(3) with each column vector, A sup mu and J sup mu, using computer algebra, then translating the results into vector notation to see whether the gamma disappears or not. It is of course ultra important to sort out the fundamentals. It has been established that there is agreement between the Wikipedia site and Jackson for the general Lorentz transformation of fields, which becomes the general Lorentz transform of accelerations in the new theory I have in mind – creating a theory of general relativity out of the well known work of Coriolis in general dynamics. You have already checked by computer algebra that the matrix (50 of note 323(3) leads to the right expressions for the Lorentz transform of fields. So your computer coding is as usual, rigorously correct.
To: EMyrone
Sent: 28/07/2015 16:11:08 GMT Daylight Time
Subj: Re: Note 323(4): Double Check on the Lorentz TarnsformsThis is for a Lorentz boost in Z direction. For an arbitrariy direction of velocity the problem from nore 323(3) remains. Either the general Lorentz matrix is erroneous, or the effect is that gamma disappears for J and A. For the F tensor the gamma in front of E and B is there. There seems to be a difference if a vector or a tensor is transformed, because of the similarity transformation for the tensor.
Horst
Am 28.07.2015 um 15:18 schrieb EMyrone:
This note gives the general Lorentz transform of charge current density and the potential four vector. The two basic errors in the Wikipedia article “Classical Electromagnetism and Special Relativity” are pointed out. The Lorentz covariance of the field equations is given in Eqs. (15) and (16). Note that ECE2 is a theory of general relativity which produces equations with the same structure as the Maxwell Heaviside field equations but in a space with both non zero torsion and non zero curvature. The concepts of torsion and curvature do not exist in MH. So I refer to the transformation of ECE2 as a pseudo Lorentz transform. It is a generally covariant transform that looks like a Lorentz transform. The gravitomagnetic field equations transform in the same way. By using these concepts the well known theory of G. G. Coriolis (1835) can be written as a theory of general relativity. Developments such as this will be the subject of the next notes for UFT323.