I looked at Tach's document. The guy seems to go off on a math frolic at a moment's notice, but without at any time engaging his brain. What an unnecessarily complicated mess that document is! And wrong besides. This is usual for Tach. Overcomplication. Introduction of irrelevancies. An over-reliance on math untempered by any physical intuition. Top it with a hefty does of blindness to his own errors and you get the mess that is Tach's attempts at physics.