Alexandra de Markoff

The Fundamentals
A Tiny Summary These points are covered in The Fundamental Existent in a style available to those who have studied in this field for some time. For those who prefer a style suitable to the layman may want to begin with Relative Expansion and follow the links at the bottom of the page. Then return to the Fundamental Existent to see the "big picture" of unification in physics.
Other Links: Are there Aether Atoms? Just For Fun:
A Texture Generator Antica Farmacista
(I've got to support my research somehow and this ^ is how I do it.) 
"…there is really only one viable route from sense to symbols: from the ground up." Harnad, S. (1990) The Symbol Grounding Problem. Physica D 42: 335346. 

In the past, relativity, in spite of the insights it has taught us about length, has treated rulers as objects external to its model. Quantum mechanics, however, has focused on the role of the measuring process in the context of its model and as a result, has been highly successful. In both models, though, it is assumed that measurements are possible without consideration of how this is so.  
I have developed a theory that builds a unification of ideas into what I call a "deeply unified field theory", in that rather than trying to unify the four fundamental forces, it unifies the physical units of measurement for space, time and mass. Central to this development is how pure geometry may be used to represent reality.  
This unity is achieved, in some sense, through a conservation of the identity of an abstract and real line. That is, the idea of a line is conserved with respect to real and abstract space. I think of this conservation as a semantic alignment, or as a bridge, between the real and the abstract.  
I have made two assumptions. The first is that "existents are". The second assumption is that each existent may be represented geometrically as an unbounded, unpreferred and real frame. I call each existent a "fundamental existent" or "SubSpace particle", since it is a part of the space we’ve known throughout history (and because I like Star Trek) and "particle" because of its "discrete" nature. These two assumptions are the two fundamental halves of this model. That is, what is represented and how it is represented. The goal I have set for myself is to use these two assumptions to construct the laws of physics.  
I use the notion I develop of a line to define a "relativity axiom". This axiom defines a relative number as a representation for a measurement of length, from which you can represent the measuring process as an integral part of the abstractions of a physical model.  
MeasuredLength = (TARGET)/(RULER)  
This statement expresses the number of
equivalent reference objects "contained" in the target in an abstract and very
profound way. TARGET represents a physical length to be measured, and RULER represents a
reference length (abstract units!). No material properties about either of these
two lengths are assumed! You can use this expression to build other concepts  static and
dynamic for example. Say that a series of measurements always yielded the same single
value. You can use this pattern to define the prototype of a static pattern with respect
to the RULER. If a series of measurements of one TARGET yielded different values then you
have a dynamic pattern. You can use these two patterns to classify other measurement
patterns into static or dynamic categories. This seems simple enough, but when you
consider the dynamic case, you can ask which element is really changing, the RULER or the
TARGET!? Because of the relative and "unprefered" nature of TARGET to RULER, we
could easily switch the roles of the two. So, with respect to one ruler a measured length
might be increasing, and with respect to another ruler it would be shrinking! (I have
applied this idea to estimate Hubble’s constant and it is surprisingly close!) (also see "Is Matter Shrinking?") 

Kant has taught us that we can’t really "know" what reality is. The best we can do is represent it. In my model I present a ruler as a model of a "real" geometric axis of a frame or SubSpace. From this representation I relate one axis to another through its scale. That is:  
Scale = (RULER1)/(RULER2)  
It turns out that this scale behaves almost exactly like mass. The difference between scale and mass is that the scale of a frame accounts for the inertia of "massless" photons (How can a massless object posses inertia?) as well as massive atoms. But, more importantly, the SubSpace model emphsizes that the scale of a frame or mass can be directly related, in a very general way, to coordinates, frames, force and the geometric curvature of a frame.  
The relativity axiom introduces a new way of constructing a coordinate system that is explicitly related to a measurement. I call this kind of coordinate system a "reference dependent coordinate system". Einstein constructed the basis function for his spacetime continuum as a differential function to avoid where in the universe the origin of this continuum might be. As cleaver as this was, it avoided how a pair of existents defines the endpoints of a "real" line and thus a "real" unit length – the foundation piece of a "real" coordinate system. That is it lacks a definition of a measurement and how this definition is related to coordinates. Consequently general relativity missed a profound relationship found in quantum mechanics – the uncertainty principle. The SubSpace model derives the fundamental piece of this principle: (Planck’s constant)(frequency)=(mass)(c^2). (Although Einstein discovered this piece of the puzzle he did so as an assertion.) It further shows that a SubSpace particle manifests a solitonic form whose behavior matches that of a photon. One of the most exciting features of this model is that there may be a loophole in Heisenberg’s principle! (The Fundamental Existent for details)  
This SubSpace coordinate system can be
Euclidean with respect to one frame and nonEuclidean with respect to another. The
SubSpace model shows how, with clear and simple math, this nonEuclidean feature gives
rise to a potential difference. But, there is something of a mystery here, in that the
potential difference I have found, from this pure geometric approach, resembles, in
magnitude, the strong force rather than a gravitational force (what I expected). And
this is my next hurdle. It seems that to understand how conventional mass is related to
the gravitational constant, I will have to construct a completely new nuclear and atomic
model :( .

A comment from Laurent Nottale:

Relative Expansion Applet Lab The Fundamental Existent Links
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