Originally the Schwartzschild Metric was a relativistic interpretation of Newton's inverse-square-law of gravity. This interpretation is masked by modern mathematical notation, which obscures the means of unifying the laws of physics if possible interpretations of the mathematics are ignored with regard internal intricacies.
A Newtonian connection to relativity is with regard to the principle of equivalence. Einstein founded general relativity on this principle and it is also conditional to Newtonian Mechanics. The point of emphasis is the origin of mass. According to general relativity, space-time curvature is determined by the presence of mass, but mass is essentially defined according to Newtonian Mechanics, as with regard to its inertia maintaining relative motion in the absence of restraint. This definition is only modified by special relativity theory according to relative space-time instead of as formulated by Newton according to absolute space and absolute time.
Without relativistic modification, Newtonian Mechanics remains extremely accurate for predicting results. At the limit of zero relative motion, relativity theory and Newtonian Mechanics converge. This convergence also applies to Newton's inverse square law of gravity. We calculate Earth's mass, for instance, according to the law and then compare all other mass according to space-time curvature.
The significance of this point is with regard to analogies of special and general relativity for the unification of relativity and quantum physics. The rationale for this unification is given in my book A Mystic History In Light Of Physics. After showing special and general relativity are mathematically analogous by way of defining space and time in the gravitational field as relative instead of light speed as variable, I asked why unification was not possible since special relativity is essentially a unification of electrodynamics and mechanics.
An anomalous physicist claimed the unification was not allowed because of the principle of renormalization of Quantum Mechanics. He claimed this principle was at fault, as to avoid infinities whereas general relativity maintains them with the concept of a singularity. However, I claim renormalization is only the quantum version of "relative", and that the singularity is a limiting condition similar to how light speed is a limiting condition to which matter can neither reach nor exceed. As Stephen Hawking redefined the black hole as able to emit Hawking radiation, the singularity can likewise be redefined. Consequently, our finite universe is merely an observable part of a multiverse of infinite extent.
The connection is with regard to a relativistic decrease in mass according to space-time curvature and a relative increase in mass according to the probability condition of Quantum Mechanics. The probabilities are exact predictions. If the probability is 3 observations out of 4 attempts, then 3 observations occur, as predicted, although they occur in any order of the 4. Respectively, if the spatial dimensions of the observable universe remain the same, then the probability of observing the same amount of its mass remains the same. A relativistic decrease in mass is thus balanced by a probable increase in other mass.
The relativistic decrease in mass primarily occurs because of energy emitted to gravitate mass to a greater density. This decrease is further evident with an analogous interpretation of the Schwarzschild Metric. It obtains the same form of invariance of the interval of special relativity by varying space and mass instead of light speed in a gravitational field. Instead of slower light speed, the gravitating mass with regard to the inverse square law is relatively less whereas the size of the local gravitational field becomes relatively greater. These conditions are further explained as analogous to special relativity. Analogous to a relativistic contraction of length in relative motion, for instance, is a spatial contraction of the gravitational field.
Conservation of mass-energy is also conditional to the invariance of the multiverse. In Newtonian Mechanics, kinetic energy is not conserved by inelastic collision. It is conserved according to special relativity. However, mass-energy apart from the change had not been shown to be conserved. For a change in relative motion of a particular system, there is both an increase and decrease of mass-energy with respect to how it is viewed from a new state of relative motion. It need not be conserved unless compensated for with regard to an observable invariance of a universe within the multiverse.
There is also an additional condition apart from relative motion of special relativity. It is according to space-time curvature and the inhomogeneous nature of the gravitational field. Mass determines space-time curvature. Conversely, space-time curvature determines observable mass. Two or more opposing masses tend to cancel space-time curvature between them. Moreover, indications are that if all portions of mass were evenly distributed throughout the universe, there would be no gravity and observable mass; such that, a version of the Mach principle, as with regard to the relative distribution of mass at large, applies.
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