Having noticed the outstanding scientific qualifications of "emperor alikar", I took sympathy on you and examined
in detail. I apologize for not having looked at it closer before.
I followed you in detail up to paragraph #13. At that point you make some fundamental mistakes which impact everything you do further on. I will try to explain your errors in paragraph #13 in detail.
13. For any point, G, on line segment EM, (except when G=E) the angle BGR is greater than 45 degrees. The speed of light is constant in each reference frame. BG forms the reference frame for galaxy G, so the path of the light from the distant source must form a 45 degree angle with BG. This is a contradiction which means that G cannot lie on line segment EM. It must lie somewhere below EM on our diagram.
At this point, what you should do to your diagram is add the trajectories of some assorted distant galaxies. Those trajectories would be straight lines from B terminating on the line segment EC. They would appear to be receding from the trajectory of the earth (line BE) at some velocity less than light. The second thing you should do (just to clarify the picture in your mind) is to add in the lines which would indicate the time as measured locally at those distant galaxies.
Those lines are not too difficult to estimate as the clocks in the distant galaxies run slow by exactly the factor sqrt(1-v*v) [since, in the units of measure in our diagram, c is unity]. If you divide the BE line segment up into equal time steps, the corresponding time steps along the trajectories of those distant galaxies are longer (the local clocks seem to take longer to mark off those equivalent time periods). The resultant curves are simple hyperbolas with the line BC as the limiting tangent at infinity. Note that the amount of time which appears to pass for an object moving very close to BC is very close to zero!
Now, in that diagram, it is very easy to see what the interpretation of what is seen via the incoming light along the line ME should be. There is a question as to exactly what you mean by the phrase "one that is now 2 billion light years from Earth". The issue is the meaning to be attached to the word "now". One could presume to know the future trajectory of that distant galaxy and interpret that point in your diagram to be on the line segment EC but this is not the common interpretation used by the astronomers I know. The common interpretation is to place the point (which is in fact your point G) on the line segment ME: i.e., where it is now is interpreted to be where we have to look for it now, the source point of the incoming light.
The time we are looking at is usually interpreted as the time as measured at the source of the light: i.e., the time is given by those hyperbolic curves we drew. Now this should resolve your problem with the fact that we cannot possibly see back to the beginning as the incoming light is coming from point M which is certainly far from the origin of the big bang; however, the events you are watching (in their own rest frame) are occurring very close to the time origin.
The last point I would like to make concerns your problem with the fact that the angle BGR is greater than 45 degrees. Your contention that the light must intercept the BG line at 45 degrees is correct; however, that measurement must be done in the reference frame of G. If you make corrections for the Lorentz contraction and the time distortion due to relativistic effects, you will find that the local angle BGR is indeed 45 degrees. The fact that it is greator than 45 degrees in your construct is simply a reflection of the fact that, in your system the relative velocity between light and the frame of G is not c as it cannot be.
I hope I have clarified the problem for you. By the way, I would not look to Yanniru as a source of explanation of my paper. Your comprehension of mathematics is an order of magnitude better than his. I am afraid there is no one on this forum except you who has any hope at all of following my math.
With regard to Mikes comments,
1) laws of physics can serve as a filter for nonsense. If a concept won't work with them, we know it won't work at all, except as a fiction.
2) our thoughts are all fiction; the real business is the physical processes which spawn and assess our thoughts to determine which will be sent to archives...which will further shape the material universe
3) Every internally consistent set of concepts which is true ACTUALLY INCORPORATES all the laws of physics as we know them, and this is a guide to the creating of excellent concepts for public policy and personal conduct.
These are essentially the questions I would like to pursue. From my perspective, having proved what I have proved, I can only say one thing for sure. If anyone gives me an explanation for anything which is inconsistent with fundamental physics, I know the circumstance must fall into one of two categories:
Either, they are completely full of bull and their ideas are not well thought out at all (in which case my best bet is to completely ignore their existence and what they have to say) or, their basic fundamental concepts and ideas do not map into my basic fundamental concepts and we simply are not communicating (in which case my best bet is to completely ignore their existence and what they have to say).
Now that sounds a lot like Mike's #1, but to really make it equivalent, one would have to add a phrase obtaining, "if a concept won't work with them, I know it won't work at all, except as a fiction within my mental picture of reality". The fact that I can only constrain that admonition to my mental picture is significant and I would very much enjoy discussing that fact.
His comment #2 I do not understand; but #3 seems to be a very intelligent observation but a little difficult to implement. I certainly agree with #4!
The issue in my head is communication. We must communicate through mechanisms provided by our subconscious. The problem is that we have no real conscious control of what our subconscious thinks is true (it is a real sucker for illusions) so we can never be confident that the mental model of reality it has constructed is internally self consistent. Certainly, if our intuition (our subconscious solution) violates fundamental physics on any subject our subconscious model of the universe is inconsistent. On the other hand, I think the subconscious is a trainable entity and it would be very valuable to confront it on a regular basis with situations which break it's ideas. Your subconscious is very bright and it will come up with a solution which will fulfill its needs which you cannot break. Now that is just a statement of opinion based on my interactions with my subconscious over many years.
Have fun -- Dick
PS Mike, I originally composed this to Paul but he also asked about your post. When I came to post it, I decided that I could save a lot of work by calling your attention to it. Thanks for being understanding.