Hi Israel,
It's nice to see you here as well! Thanks for reading my essay and commenting. I see much to clarify based on your comments, so I'm glad you've given me a chance to do that. I'll address things point-by-point.
"...based on the mathematical formulation of special relativity (SR) one can conclude that the world doesn't evolve."
Yes, I'm arguing that one can, and often does--but really doesn't have to--conclude this.
"So, to solve this problem you're suggesting to add an additional absolute time dimension, is this correct? As I understood, the idea that you expose in your essay is that the four dimensional space-time of relativity should be embedded in an absolute time dimension?"
No, that's the point of confusion. I'm saying that very often people *do* think of space-time as existing, and that's a five-dimensional concept that's not acknowledged. I quoted Weyl and Ehlers in the essay; above, I've quoted a few paragraphs from Brian Greene's Life of the Cosmos, which really illustrates this. See the big long post that's two above here, on Jun. 29, 2013 @ 23:30 GMT.
To understand what I mean by this, think of a block of wood that's just sitting somewhere. That's a four-dimensional concept. It occupies a three-dimensional place as time passes. The space-time concept that's often been derived erroneously from relativity is a similar five-dimensional concept, extending throughout all of space-time as some extraneous time passes. There are two important differences, though: there is some flow of thought through the timelike dimension of space-time, like a river where the map stays the same but there's a constant flux through it; and, due to general relativity, space-time usually isn't thought to be just a frozen block, but something that changes. Think about it: space-time has to be thought to exist, in an extra dimension of time, in order to be able to change.
Consider the following from Einstein's autobiography: "It is a wide-spread error that the theory of relativity is supposed to have, to a certain extent, first discovered, or at any rate, newly introduced, the four-dimensionality of the physical continuum. This, of course, is not the case. Classical mechanics, too, is based on the four-dimensional continuum of space and time. But in the four-dimensional continuum of classical physics the subspaces with constant time value have an absolute reality, independent of the choice of the reference system. Because of this the four-dimensional continuum falls naturally into a three-dimensional and a one-dimensional (time), so that the four-dimensional point of view does not force itself upon one as *necessary*."
In a completely analogous way, I'm arguing that because of relativity and a really sloppy way of thinking of things which has a lot to do with the complete inconsistency of our languages with the whole block universe concept, people do very commonly think of space-time five-dimensionally, which is a very wrong way of thinking. They think of space-time existing, as a four-dimensional view of things, in much the same way that people used to incorrectly think of classical mechanics as describing a three-dimensional view of things.
Does that make sense? I'm just arguing that the whole concept is completely muddled and wrong. That's what I meant in my abstract when I said the concept of time in physics is a mess. I then offered just the existence of the three-dimensional Universe, as a way out of the mess that's motivated by cosmology.
You then asked how I would define time. I'd define time in terms of existence, and I'd say that the three-dimensional Universe exists; it evolves from one time to the next, continuously. All that exists is the three-dimensions of reality--and that is a four-dimensional concept, described by four-dimensional physics with time as one dimension. Do you see what I mean?
"You discuss the issue of simultaneity and the twin paradox"
I don't think I wrote anything at all about the twins paradox. I searched the PDF to be certain, and the word "twin" isn't there. Perhaps you're referring to the discussion of time dilation and the relativity of simultaneity. That was meant to illustrate that Einstein's interpretation of the relativity of simultaneity is wrong.
"...I just wonder if you are aware of this."
I'm well aware of the literature on the relativity of simultaneity and its implications.
With regard to the rest, I prefer to keep a chin up. Reason based on sound logic and empirical evidence will prevail. And in that regard, thank you for recommending my essay to Daniel and others. I appreciate that.
And I very much look forward to reading your essay. Thanks very much for commenting, and if you would like further clarification on any points in my essay, please don't hesitate to ask.
Best wishes,
Daryl