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From Local to Global Relativity

Tuomo Suntola
Year: 2008 Pages: 39
Keywords: newton, relativity
Newtonian physics is local by its nature. No local frame is in a special position in space. There are no overall limits to space or to physical quantities. Newtonian space is Euclidean until infinity, and velocities in space grow linearly as long as there is constant force acting on an object. Finiteness of physical quantities was observed for about 100 years ago ? first as finiteness of velocities.

The theory of relativity introduces a mathematical structure for the description of the finiteness of velocities by modifying the coordinate quantities, time and distance for making the velocity of light appear as the maximum velocity in space and an invariant for the observer. Like in Newtonian physics, no local frame, or inertial observer, is in a special position in space. Friedman-Lema?tre-Robertson-Walker (FLRW) metrics derived from the general theory of relativity predicts finiteness of space if a critical mass density in space is reached or exceeded.

In the Dynamic Universe approach space is described as the three-dimensional surface of a four-dimensional sphere. Finiteness of physical quantities in DU space comes from the finiteness of total energy in space ? finiteness of velocities is a consequence of the zero-energy balance, which does not allow velocities higher than the velocity of space in the fourth dimension. The velocity of space in the fourth dimension is determined by the zero-energy balance of motion and gravitation of whole space and it serves as the reference for all velocities in space. Relativity in DU space means relativity of local to the whole ? relativity is a measure of locally available share of the primary rest energy, the rest energy of the object in hypothetical homogeneous space. Atomic clocks in fast motion or in high gravitational field do not lose time because of slower flow of time but because part of their energy is bound into interactions in space. There is no space-time linkage in the Dynamic Universe; time is universal and the fourth dimension is metric by its nature. Local state of rest in DU space is the zero-momentum state in a local energy frame which is linked to hypothetical homogeneous space via a chain of nested energy frames.

Predictions for local phenomena in DU space are essentially the same as the corresponding predictions given by special and general theories of relativity. At extremes, at cosmological distances and in the vicinity of local singularities differences in the predictions become meaningful. Reasons for the differences can be traced back to the differences in the basic assumptions and in the structures of the two approaches.