Dear Basudeba,
My congratulations to you and your colleagues, by both way of your review of my essay, and to your own out of the box sense of intuitive logic, couple with your science to push the envelope of knowledge.
Your reply is both a personal edification and a challenge for me to explain, myself with the due respect you and your colleagues most certainly deserve.
First: I am not a physicist, nor am I a mathematician of any significance, but my suppositions are based on an A = A logic, that I have spent nearly 60 years wrestling with. Albeit, the Cosmos as I have written about is anything but A=A. It is an anomaly, as I believe it is required to be. Otherwise, I believe we would be deceiving ourselves to define an unbounded open system as one that is closed.
Actually, at times I have to get up and run to break the intuitive insights, that in a sense trap me (Claustrophobic in nature) in this absolute conundrum, we call existence, and have been and will be infinitely bound too. The philosophical question often becomes: "What's the Point?" And in fact we are Trapped, by a system of the infinitely impossible. Forever and Forever. It bears a haunting mental impression upon me from time to time.
So I am very serious about my understandings, albeit not of the stellar work you have done working out a proof you believe in. Even as I question its assumptions in the following paragraphs. In fact, if I am accurately getting my head around it, it actually proves my point: "That infinity is beyond the scope of mathematics, as you appear to have used "Time" along with measurement to validate it through an ongoing basis, which is a dynamic description, not a static definition. As a quantity you appear to make it grow or it is born anew upon extended discovery. Very respectfully that is an assumption, not a proof.
Additionally, you seem to use relativistic mathematics to assume a "Scalar" absolute for all objects. If "Entaglement" is true, then scalar mathematics is not appropriate, as the pragmatic fact of "Locality" breeches a "spectrum" if you will of length. I too believe all things are based on a spectrum or scalar foundation, but I have no concrete answer to Superposition's or Entanglements, save that they may defy our known levels of scalar measurement's. They may be 10 billions smaller than a plancks constant, but appear as relative objects. Who Knows?
NOTE: The type 's of mathematics we use Euclidian or Quantum Geometry, or new mathematic's of the future may change everything. But infinity is not one of them. For me, it is as immutable as Time and Space. And just as unexplainable, other than by defining it - as an ongoing process. But that to me confines it, and infinity has no boundaries. If it did what would be on the other side of it? This is an infinite loop built into a question. And it may have the brilliance of your minds to attempt to make it fit into a round hole, but it will not, and cannot. Not in the bigger scope of things we are infinitely bound by.
I would love to understand in better terms, what I may be missing in your wonderful reply, but I am stuck in my own Lambda = confusion. I guess? I do believe you have explained infinity and possibly it's counter-part of the Quantum continuum in a process of what I would call "ongoing discovery". That is worthy of superior note. I have no question about it. By the way, your comment about "A surprised Eddington: You even further solidify my argument, by suggesting a "scale" is moving with light, its length would shrink to zero. Hence it will require and infinite number of scales to measure the wave-length of light. NOTE: Anytime we inject an infinite number mathematics and explanation comes to a halt, save for the meta expressions...
By the way, your response is beyond my total comprehension, but I believe I understand the core of your comments... At least I hope so.
Again I very much applaud your research, your willingness to step away from the knowledge of the past, and stand on your own shoulders, albeit with the help of history as well. But your independent out-of -the-box thinking is much appreciated, and where we need to move - as science finds its way to improve both our human knowledge and humanity itself.
Now regarding your comments about Energy. I am a little confused as I really stepped out-of-the-box to describe the use of Energy (Liner) combined with Energy (Non-Liner) to equal increased Energy, which will as normal energy does, atrophy with time. But the outcome of using natural energies, such as Electrostatics, Magnetism, and Gravity, hold a game changer for the planet. For improving communication among peoples of the world and to a better world [Period.] I have several ways I have designed this in my head over the years, and hope to find the right physicists to work with someday to pursue it.
This is not using typical "Action = Reaction" or "Like for Like" energy and matter, but changes the formula: E = E(*). Note Gravity in a non-linear mode multiples itself.
This is doable, and surprising we have not achieved it as of yet. Of course given my concepts are correct. And that is a small issue to me, but I know a heresy to a very though crowd of physicists by and large.
Again, Basudeba and your colleagues... Many Thanks. Your response was a true edification for myself.
If I can clarify anything: Ask away... Thanks very much again, Russ