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@aol.com
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.