Ok, here goes. With this initial post, I'm introducing an alternative system of physical theory; that is, an alternative to Newton's system of physical theory. To many of you, the idea of using a system of physical theory is undoubtedly unfamiliar, since the system we ordinarily use to construct physical theory is taken for granted, and seldom explicity recognized.
However, when it is understood that Newton's great accomplishment was the inauguration of a program of research that made the systematic investigation of physical phenomena possible in an unprecedented manner, it's easy to see that underlying that program was a system of mechanics to investigate and classify the properties of all physical objects. Consequently, in the words of David Hestenes of Arizona State University, "Newtonian mechanics is, therefore, more than a particular scientific theory; it is a well defined program of research into the structure of the physical world." 
Similarly, Dewey B. Larson, in publishing his three volume treatise, The Structure of the Physical Universe,  has done much more than introduce a particular scientific theory, he has inaugurated a well defined program of research into the structure of the physical world. While this claim may seem startling and therefore incredulous at first, it becomes a very compelling pronouncement upon further investigation. Here's why: Larson redefines the fundamental concepts of space and time.
Since the fundamental concepts of space and time are the foundation of Newtonian mechanics, as well as general relativity and quantum mechanics, their redefinition necessarily redefines the science which is built upon them. Under Newton's program, our grand goal is to "describe and explain all properties of all physical objects."  Hestenes explains that the approach of this program is determined by two very important, general, assumptions: "first, that every physical object can be represented as a composite of particles, and second, that the behavior of a particle is governed by interactions with other particles." This means that we should be able to describe nature in terms of a few kinds of fundamental particles which interact in a few fundamental ways.
The great power of this approach, according to Hestenes, is that the properties of the particles and the relationships between them via interactions can be precisely formulated mathematically. The expression of the existence of a particle over time in the function x(t), "when specified for all times in an interval...describes a motion of the particle." From this it is clear that the central hypothesis of Newton's program of research is that "variations in the motion of a particle are completly determined by its interactions with other particles," leading to Newton's second law of motion. Thus, this hypothesis defines the entire program from Newton's day to this. As Hestene's puts it:
Hestenes adds, "The classification is not complete today, but it has been carried a long way." Indeed, it has. The long road has been both an exciting and frustrating adventure for several centuries, and has brought unimaginable changes to civilization, since its inception in the days of Newton. The really big news today, however, is that we are "stuck" in the words of Steven Weinberg. While we have the standard model, that, though "ugly and ad hoc" in the words of Hawking, is considered by many as the greatest intellectual achievement of the 20th Century, it is still missing a most fundamental interaction of physical objects, the very one that perplexed Newton himself: gravity. While this glaring failure has given rise to decades of effort leading to string theory, loop quantum gravity, and other lesser known approaches to find a solution, the inevitable conclusion, reached by more and more investigators, is that we can't get there from here, that something else is needed.Newton's [second] law becomes a definite differential equation determining the motion of a particle only when the force f is expressed as a specific function of x(t) and its derivatives. With this much understood, the thrust of Newton's program can be summarized by the dictum: focus on the forces. This should be interpreted as an admonition to study the motions of physical objects and find forces of interaction sufficient to determine those motions. The aim is to classify the kinds of forces and so develop a classification of particles according to the kinds of interactions in which they participate.
The trouble is, of course, that most suggestions all have one thing in common: they are constructed under the same system of physical theory; that is, they are constructed under Newton's program of research that focuses on the forces of interaction between particles contained in space and time. It might be argued that modern theoretical physics has long since abandoned the concept of particles for the field concept, and the concept of force interaction for the concept of particle exchange, but just as replacing Newton's concept of absolute space and time, with Einstein's space-time, doesn't alter the definition of motion, even so modifying the concepts of particles and interactions doesn't alter the definition of motion, and it's the definition of motion, the function x(t), upon which Newton's program of research is founded.
What Larson did was to redefine motion, thus making it possible to initiate a new program of research founded on the new definition. To understand Larson's new definition, it's important to recognize that motion in Newton's program is always the one-dimensional motion of objects, or fields, defined in terms of a stationary reference, or background, of space and time. This leads immediately to a conflict between general relativity (GR), which must be used to describe gravity, and quantum field theory (QFT), which is used to describe the rest of physical phenomena in the standard model. Since, in GR, gravity is space-time, but in QFT, fields must propagate in a fixed background of space and time, the perplexing question is, how can a wave function of gravity evolve over itself?
This predicament has lead to the dire need of a non-pertubative string theory, or a background-free string theory, in which a quantum theory of gravity can be formulated, which is currently, and has been for many years, the holy grail of modern theoretical physics. Whether or not this can be done remains to be seen and depends on such esoteric subjects as the evidence for SUSY, etc. However, the point here is that this predicament is fundamentally based in the definition of motion, which in QFT requires a fixed background of space and time, but which GR has eliminated. Thus, we have a choice; we can give up GR as a description of gravity, and by so doing free up the background of space and time, or we can keep our pet theory of gravity and give up our ability to describe fundamental particles in terms of fundamental interactions.
Of course, no one has the clout to do either, so we are "stuck." Unless, that is, we can find a way to define motion without having to incorporate a non-dynamic background of space and time to describe the time evolution of fields in the Schroedinger equations, and without having to incorporate a dynamic background of spacetime to describe gravity in the Einstein equations.
If such a prospect interests you, stay tuned.
1) David Hestenes, "New Foundations for Classical Mechanics, Second Edition," Kluwer Academic Publishers, 1986.
2) Dewey B. Larson, "The Structure of the Physical Universe, Revised and Enlarged Edition, in Three Volumes," 1979.