Wow, talk about putting your foot in it further!The jacobian must satisfy the following requirements:
1. Its elements must be well defined, $$g_{22}=g_{22}(x,x')$$ isn't by virtue of being dependent on both x and x'
2. $$JJ^T=I$$ . This is clearly not happening
3. det(J)=1 . This is happening but it is immaterial given that 1 and 2 are not.
Chew on this.
$$JJ^T=I$$ would imply J is an element of O(N) for the appropriate N, which isn't required. Jacobians don't need to satisfy that, that's just a nice case. The Lorentz transforms don't satisfy that, as they are defined by a metric $$\eta$$ invariance. If you were working in complex coordinates than J wouldn't be automatically real but the transformation could still be valid.
Tach you just keep digging yourself deeper and deeper. Why don't you quit while you're.... well you're not 'ahead' but before you make even more of a fool of yourself, though that'll be hard to manage.
Who are you trying to convince here? Unlike yourself Guest and przyk clearly paid attention in their courses on vector calculus. You obviously didn't.Sour grapes for being proven wrong, eh?
So when you assert something we can see to be utterly false we should let it slide? If you can't accept correction then you move even further into the crank territory Eugene lives in. Guest was right, you're projecting your own faults onto other people. No one here thinks Eugene has a physically viable model but that doesn't mean all your criticisms of him are accurate. We can correct you and still not agree with Eugene, despite you clearly thinking otherwise.There is no "relativity in curved spacetime" in his paper. Try to stay on topic.