As we have seen, according to Hestenes, the grand goal of Newton's program of research is to "describe and explain all properties of all physical objects." Hestenes identifies two fundamental assumptions that are necessary to accomplish this ambitious goal. First, it is assumed that all physical objects are composites of particles, and, second, it is assumed that the behavior of a particle is governed by its interactions with other particles. Thus, the program seeks "to explain the diverse properties of objects in terms of a few kinds of interactions among a few kinds of particles." [1]

Hestenes explains that the power of this approach lies in the fact that particles, and their interactions, can be precisely defined in terms of the motion of the particle; that is, the description of its existence at a given location, at a given moment of time, consists of a mathematical function, x(t). Using this function and the principles of calculus, physicists can define the velocity and momentum of any particle at a given location, x, and at a given instant of time, t, and quantify interactions between them in terms of the acceleration and force aspects of these motions, because the derivatives and integrals of the calculus enable them to precisely model both the existence of the particles and the interactions between them, and consequently predict their behavior.

However, there is an additional assumption in this program that Hestenes fails to clearly elucidate. It is that the description and explanation of the behavior of the particles, in terms of their interactions, assumes a knowledge of the inertial, magnetic, and electrical properties of the particles. In other words, the Newtonian program that seeks to describe nature in terms of the existence of particles and their interactions from moment to moment, must assume first that particles exist with a given value of mass, magnetic moment, and charge; that is, these values must be put into the system, before the power of the system, to investigate the properties of particles of matter and to classify them and their interactions accordingly, can be applied!

Thus, given two particles, particle A and B, the properties of one of which, particle A, are unknown, we can calculate its properties, if we know its interaction with B, the properties of which are known. Or, alternately, if we know the properties of particle A, we can predict its interaction with B. However, because the foundation of the system is based on the function x(t), a function of space and time, and the dimensions of inertia, magnetic, and electrical properties are not known in terms of space and time, the function x(t), used to describe the behavior of particles and their interactions is an observed relationship; that is, f, the force, or quantity of acceleration, is simply a unit of acceleration, expressed in terms of space and time, multiplied by mass, a measured quantity with an unknown relationship to space and time.

In other words, we don't know why the total quantity of acceleration is determined by the number of mass units of a particle. We just know that it is, and we use this knowledge in our system. Without the knowledge of the mass (or magnetic moment, or charge, if applicable) of a particle, we must know the total acceleration, the force acting on it. Without a knowledge of the force, we must know the mass. For instance, given the mass, we can find the momentum of a particle, located at point x, at time t, because it is a function of x(t). Conversely, given the momentum, we can find the mass of a particle located at point x, at time t, for the same reason.

What this means is that Hestenes' characterization of the grand goal of Newton's program, as an effort to "describe and explain all properties of all physical objects ... in terms of a few kinds of interactions among a few kinds of particles," is entirely limited to the description and explanation of how the given properties of particles are related to one another.

Moreover, because the function x(t), which is the fundamental relationship in the system, upon which everything is based, is a relation of space and time, the definition of space and time is crucial to its operation. Therefore, the definition of space and time that the system employs, Newton's definition initially, is crucial to the operation of the system. Consequently, whenever the system has failed to produce the correct results, it is the definition, or interpretation of the definition, of the nature of space and time, that has been the target that physicists naturally zero in on.

Fundamentally, this problem is seen as a challenge of coping with the frame of reference that the definition of space, as a set of points that satisfies the postulates of geometry, creates. Early on, they had to contend with relatively moving frames of reference of space and time, wherein corrections were needed to ensure that comparisons were made in proper inertial frames to preserve the integrity of the function x(t). Thus, we see the Galilean transformations, the Lorentzian transformations, and, then, the gauge transformations devised to cope with increasingly sophisticated issues of space and time.

However, we don't need to know the details of these issues and their resolutions to know that they are issues stemming from the definition of space and time, used in the Newtonian system of physical theory. This is clear to all, as we've seen in the discussion of David Gross's interview on PBS, in the previous post. Hence, the question, how can we define space and time in such a way as to avoid these problems, is clearly coming more and more into focus. As we saw in the beginning of this series, the major recalcitrant problems that face modern physicists are once again being attributed to the background reference of space and time, required by the function x(t). Indeed, it introduces into the latest and most modern of research projects in Newton's program, namely GR, QFT, and string theory, irreconcilable contradictions. So, this time they don't just seek to change it, as was done in the past, but they seek to eliminate it altogether.

Nevertheless, it's vital to point out, that, if the problems and challenges that persist in the Newtonian program, are so obviously connected with the nature of space and time, then maybe that's a clue that our efforts to describe and explain how the properties of the constituents of radiation, matter and energy, namely their inertial, magnetic, and electrical properties, are related to one another, are in trouble, because we don't know the true nature of the properties themselves. Maybe, the most important lesson we have learned in the course of pursuing the Newtonian research program, is that the nature of these properties is intimately related to space and time. The fact that needed corrections to the frame of reference used are constantly arising, indicates that the properties themselves, not just the relations between them, have something to do with space and time intrinsically.

Therefore, perhaps the time has come to change the program. To change it from a program that seeks to describe and explain how, given the properties of particles, they relate to one another in a reference frame of space and time that describes their motion, to a program that seeks to describe and explain their intrinsic properties, in terms of the only known relation of space and time, motion.