Dear Juan Ramón and Pentcho
Thank you for your stimulating messages. I am glad that Juan , with his sophisticated mathematical background, seems to have found many agreements with my statements, even though they are based on the mostly qualitative Beautiful Universe Theory model and earlier studies refred to therein. I have read Juan's "General relativity as geometrical approximation to a field theory of gravity"(viXra:1203.0042) and see that like a skilled matador he has tackled the General Relativity bull with skill and panache. I wish I understood the mathematical details, but from my own analysis, GR became vastly complicated because it was formulated using the language of Special Relativity SR. The simple and elegant equivalence principle (gravity = acceleration) had to carry the excessive baggage of SR with its unphysical and unrealistic postulate that c is constant. That twisted the whole universe into a complicated and unphysical geometrical pattern. In my theory gravitational potential is due to local energy gradient in the nodes making up the universal medium (the quantized ether).
To answer Pentcho's concerns, I must explain the difference between the presuppositions and hence mathematical language of SR and GR on the one hand, and my BU on the other. In SR and GR time, velocity, distance are all continuous functions, but they obey a strange and abstract rule: c is constant. These starting points lead to the Lorentz transformations and the sort of calculations Pentcho derived above.
In BU the starting points are that there is a discrete absolute background space, like points on the corners of a fixed graph. Absolute also refers to time - there is complete simultanity in this world. The maximum speed momentum can travel between nodes is c, but when the nodes are denser, they momentum travels at a slower rate. From the above starting points I have concluded through much thought-experimentation that all the experimental results of SR (clocks slowing down as length contracts, and GR ( clocks slowing down and light bending near massive objects etc.) can be derived from this BU model.
I know that such a verbal and arguments (plus visual illustrations) is not enough. When I finalized the BU model in 2005 I was hoping, and am still hoping, that some more skilful mathematician will describe this world in a rigorous mathematical description.
Take the matter of velocity addition. In a continuous medium 4+5 =9. But imagine a world where the maximum allowed number is 9 where 7+5= 9 ! What kind of math do I need for this? Perhaps an easier way to understand this 'maximum velocity' rule is to imagine a long line of soccer fans making a 'cheering' wave one person lifts his or her hands when the one before does so. Imagine the healthiest people can transmit the wave at c, but some older, less healthy people take time to transmit the wave at less than c...
And thanks Juan - no more zombie cats (and no more point photons please - read Eric Reiter's essay!) in the brave new world of physics!
Vladimir