Abstract

A spring term is added into Newton’s law of gravitation. The universe accelerates to luminal or superluminal speed at the outer rim of the Hubble sphere where no matters can be observed. Such a big bang is explained three dimensionally from which we obtain the Hubble constant 10-17.5 /s which is the square root of the cosmological constant   10-35 /s2  .  The missing mass of galaxies in the rotation curves can be clarified via the virial theorm in which galaxies mass 1041    kg and their spring constant 10-31 /s2 match with other authors. Under certain conditions in Sect.5, the Schroedinger equation can be reduced to 1^st order for long range interaction and 2^nd order(both time and spatial part) for micro interaction; whereas the latter has the same form as the Klein-Gordan equation. Upon a simple modification of the classical field theory, we derive the equation V(r) = a ln(1 + b/r) + C which is compatible with the well known Cornell potential in quark confinement. Such a modified field theory can furtherly apply to planetary motions by adding a spring term in the Binet equation to estimate different spring constants of the sun for the inner planets;they are  1��-14  /s2Mercury, 10-15/s2 Venus amd 10-16 /s2    (Earth). Since spring is a fluid which cannot break except its value k decreases at farther distance. A comparison with the Fischbach’s fifth force is also dicussed in the conclusion.

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