Part IV
The kinematics of events is evidence of the persistence of time. The dynamics of events is evidence of the direction of time. In stating the tendency to equilibrium of a closed system, the second law describes the total energy of the system follows a direction of transfer of kinetic and inertial energy between bodies in collision that defines the direction of time.
Even though the statistical probability of two bodies colliding on a line through the center of their masses is far less than any other angle of collision, the question of increasing entropy forward in time is not in the probability of occurrence but that even with such precise angles of collision, the energy transfer has a direction from one mass to the other that is contrary to the laws of motion when this order is reversed.
The direction of transfer of kinetic energy to inertial energy and vise a verse is determined by the mass and velocity of each body in collision as discussed above.
When the direction of transfer of energy is defined as the direction of time, the laws of motion must be reformulated to incorporate time as an intrinsic aspect of dynamics such that time is a physical dynamic, the direction of which determines the laws of motion. With such a reformulation of the laws of motion, the dynamics of time-reversal does contradict the laws, the laws would in-fact predict such dynamics through a reversal of time as the reversal of time is a reversal of the dynamics.
This line of reasoning presents the following conjecture:
1. The laws of physics are expressed as equations of time-reverse symmetry.
2. Only the time-forward dynamics of these equations are observed in nature, a fact stated by the second law.
3. The time-reverse symmetry of the kinematics of certain events present dynamics that contradict the laws of physics and -
4. the time-reverse symmetry of the dynamics of the same events present kinematics that contradict the second law
5. time is therefore an intrinsic aspect of physical dynamics.
6. Time is physical change, physical change is dynamical and dynamics follow the second law.
7. Time is therefore the physical dynamics of change, the mechanics of which define its direction as stated by the second law.
This definition of time expresses an as yet unknown, universal physical dynamic governing all physical change. A dynamic that has a temporal bias that accounts for both the relativistic quantitative and qualitative transformation of dimension between frames in motion and proximity to mass.
There exists such a dynamic in the one definitive, “qualitative” transformation of dimension expressed in mass-energy equivalence revealed by special relativity. The ontological meaning of mass-energy equivalence has remained a fundamental question in relativistic physics. Francisco Flores distinguishes the two prominent notions of equivalence as:
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The Same-Property Interpretation of E=mc^2.
Most physicists and philosophers regard the terms "mass" and "energy" as designating properties of physical systems. Thinkers such as Eddington (1929), and more recently Torretti (1983), argue that since mass and energy are numerically equivalent according to Einstein's famous equation, the properties mass and energy are the same. For example, Eddington states that "it seems very probable that mass and energy are two ways of measuring what is essentially the same thing, in the same sense that the parallax and distance of a star are two ways of expressing the same property of location" (1929, p. 146). According to Eddington, the distinction between mass and energy is artificial. We treat mass and energy as different properties of physical systems because we routinely measure them using different units. However, one can measure mass and energy using the same units by choosing units in which c = 1, i.e., units in which distances are measured in units of time (e.g., light-years)[1]. Once we do this, Eddington claims, the distinction between mass and energy disappears.[3]
The One-Stuff Interpretation of E=mc^2.
Interpretations in the second group establish a connection between the terms "mass" and "energy," which are again treated as terms designating properties, and the two basic constituents in the ontology of physics: matter and fields. The equivalence of mass and energy is then taken to show that we can no longer distinguish between matter and fields. Einstein and Infeld (1938) offer a clear articulation of this interpretation. According to Einstein and Infeld, in pre-relativistic physics one can distinguish matter from fields by their properties. Specifically, matter has energy and mass, whereas fields only have energy.
Since mass and energy are distinct in pre-relativistic physics, there are physical criteria that allow us to distinguish matter from fields qualitatively. So it is reasonable to adopt an ontology that contains both matter and fields. However, in relativistic physics, the qualitative distinction between matter and fields is lost because of the equivalence of mass and energy. Consequently, Einstein and Infeld argue, the distinction between matter and fields is no longer a qualitative one in relativistic physics. Instead, it is merely a quantitative difference, since "matter is where the concentration of energy is great, field where the concentration of energy is small"(1938, p. 242). Thus, Einstein and Infeld conclude, mass-energy equivalence entails that we should adopt an ontology consisting only of fields.[3]
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These two interpretations differ only in their use of time, which leads each to understand equivalence as an expression of spatial-temporal translation. Both interpretations are equivalent to each other but present different ontological arguments through their applications of time. The first removes time by setting c=1, this translates the energy of mass to a purely spatial quantity, a quantity that must increase significantly from local time as one second becomes one light-second or 3x105 km.
The second includes time by inverting the translation of the first, concentrating spatial dimension per unit time thus all motion is a relative measure of time. This translates the energy of mass to a spatial function of time - when time is considered constant mass is a concentration of space, when space is considered constant mass is a concentration of time - both are the same condition we label matter the energy of which we label mass.
These translations have no physically real meaning because they are, as is all of physics, based on a strictly kinematical definition of time. Expressing the equivalence of mass and energy by removing time can only have meaning when time is the dynamic that changes energy to mass in the first place. Likewise, expressing matter as the region of a field of space-time where the strength is greater can only have meaning if time is the dynamic that changes the strength of the field.
Eddington and Torretti’s interpretation implies we can define the mass of a particle as the energy required to condense the vast region of space equal to its mass when c is set to unity, down to the physically real or temporally constant, spatial dimension that we measure as the particle when c is 3x10^5km/s.
Einstein’s and Enfeld’s interpretation implies matter is a physically real condition of a field identifiable as the point of transition of strength, one side of which is the increased strength we call mass, the other side the decreased strength we call gravitation.
Taken together, these two interpretations present the following conceptual model of mass.
The fundamental dimensions space(Length) and time are the kinematical constituents of a continuum of the field we call motion(space/time). The energy of a field of motion is measured as a ratio of the space-time of the field with respect to the space-time of the observer. The energy of a field of space-time extends from and increases toward its origin. The origin is a finite region labeled matter referring to the position of increased strength we label mass. When two or more fields interact, we label the redistribution of energy, observed as the motion of their origins - gravitation. Imparting a change of position on the origin of a field with respect to the position of an observer, requires changing the ratio of space-time in the subject field, the quantity of this change of energy is labeled inertial mass. The change in the ratio of space-time imparted by one field on another with respect to the space-time of the observer, is the quantity of energy we call gravitational mass.
The classical definition of constant, linear motion is the traversal of a constant quantity of space per unit time, which presumes the constancy of time. But since time is a measure of motion of a system we define as a clock, we have no means of establishing the constancy of time or the constancy of space. We can only measure each with respect to the other relative to the space -time of the observer. The model described above is then of little use for it digresses to the same circular logic of present ontological models that require any quantitative measure of space and time be defined by the constancy of c, the constancy of which is determined by our measure of space and time.
Escaping this circular logic requires changing our notion of time, a change that sustains our relativistic measure of dimension while affording a definitive distinction between mass and energy.
As shown in the previous thought experiments, when time is the kinematics of a system, its reversal presents dynamics in conflict with the laws of physics. When time is the dynamics of a system, its reversal is in conflict with the second law. As the second law does not define the dynamics responsible for the temporal bias of mechanics, but is an observational law that states the mechanics display a temporal bias in their dynamics, then a successful definition of time must define a temporal symmetry of dynamics that uphold the laws of physics while explaining the observational evidence of temporal bias expressed by the second law. Such a symmetry suggests the dynamical bias expressed by the second law is a fundamental process of time, the reverse of which has not or cannot be observed. This does not mean the symmetry does not exist, it simply means the principle of symmetry must define the framework from which the laws arise.
In the mechanism used by Eddington and Torretti to achieve equivalence, we find the removal of time from the mechanics of a system expressed by E=mc^2, expands the dimension space by changing the dimension time to the dimension space. The result, while numerically equivalent is also nonsensical for a system is not a system without time. But the mathematical principle they invoke is quite sound and when reversed, this mechanism reveals something quite real. It reveals a process of physical dynamics that is invisible when time is considered the kinematical evidence of its own existence. If removing time by setting c=1, expands space resulting in a temporally static spatial condition, then it is undeniably true that replacing time reverses this process by condensing space. Removing and replacing time in E=mc^2 is obviously a conceptual mechanism not a protracted, physically real event. But this concept reveals the expansion and condensation of space is in principle, as defined by the principle of relativity as a measure of time, a very real process. With this conceptual change of ontological entities where the process of space condensing is the dynamic we call time - time becomes the universal dynamic of a background independent field. It does not take time for space to condense, the condensation of space is time. The condensation of space is not observed in classical mechanics, instead what is observed is the passage of time. If we choose to observe the condensation of space we can, as did Eddington and Torretti , set c=1. Or, as did Einstein and Enfeld, measure differing quantities of space by setting time to a universal constant. In both cases, we find the dynamic we call time creates a region of increased strength in a field of space-time, a condition we call matter, the strength of which we call mass. We now have a definition of time that is, as we will see, a dynamic that not only upholds the laws of physics through the symmetry of its reversal, but explains the temporal bias of the second law as a necessary and natural dynamical bias. We also have a numerical value for this process that is a specific and relative rate of condensation that defines the spatial-temporal dimension we call mass, a definition that gives physically real value to Einstein and Enfeld’s delineation of matter and energy. The numerical value is exactly the value removed by Eddington and Torretti, the same value we replaced to see the model, it is of course c, the constancy of which is now not only an observational translation of kinematical measure, but a dynamical translation of dimension. The constancy of c is the axis of symmetry between energy and mass, a numerically falsifiable and relative measure of motion that determines our qualitative delineation of the transformation of space-time to mass.
[3] Francisco Flores - The Equivalence of Mass and Energy - 2004, Stanford Encyclopedia of Philosophy.