Classical Mechanics without Absolute Space.pdf

a s t r o - p h / 9 5 0 9 1 5 8 1 O c t 1 9 9 5 CLASSICAL MECHANICS WITHOUT ABSOLUTE SPACED. Lynden-Bell and J. KatzInstitute of Astronomy, The Observatories, Cambridge, U.K.Racah Institute of Physics, Hebrew University, Jerusalem, IsraelAbstract A relative mechanics with no absolute space is shown to be equivalentto Newtonian mechanics applied in a universe of zero net angular momentum.Closed spaces in General Relativity have no angularmomentum and shrivel toone point as the mass-energy contained tends to zero, so obeying Machs principleon the origin of inertia.IntroductionNewton [1] claimed that rotation was absolute and invented the concept ofAbsolute Space independent of the motion of the bodies therein. Mach [2] pointedout that Newtons experiments in no way excluded the idea that dynamical ro-tation was relative to distant masses in the Universe. Here we outline a classicaltheory in which only relative motions are meaningful, (no absolute space, no ab-solute rotation) which agrees precisely with Newtonian mechanics when the latteris applied in a world in which the whole Universe has no net angular momen-tum. Our mechanics is independent of frame rotation. The Universe breaks thatsymmetry.In General Relativity there is a corresponding result that applies to closeduniverses with hyperspherical topology. In those the vanishing of the angularmomentum is an inevitable consequence of closure.Background ObservationsBarrow et al. [3] have rened the strict limit on the rotation of the Uni-verse rst derived by Hawking [4] and collaborators [4,5] from the isotropy of themicrowave background radiation. They deduce that the Universe has turned byless than 1012 of one rotation in the time since the Big Bang. This amazinglystringent limit rests on the assumption that the microwave background radiationwas last scattered at a redshift around z = 1000. The directly observed localinertial frame dened from the celestial mechanics of the solar system (essentiallyusing i