Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
468894 | Computers & Mathematics with Applications | 2011 | 19 Pages |
Special relativity considered in [Albert Einstein, Zur Elektrodynamik der bewegte Körper, Ann. Phys. 17 (1905) 891–921], and gravitation, studied in a series of papers, notably in [Albert Einstein, Zum gegenwärtigen Stände des Gravitationsproblemen, Phys. Z. 14 (1913) 1249–1262], are further analyzed regarding the principle of relativity, gravitation, and the notion of mass. The energy relation derived by Einstein from the relativistic Maxwell equations is applied to potential energy W(x)W(x) of the gravitational field along the right line for which Einstein’s transformations are valid. This defines the intensity G(x)=dW/dx of the relativistic force of gravity along a right line of observation in the gravitational field. The force is proportional to the observed acceleration according to the formula εG(x)=μξττ=μxttβ3 where μμ is the inert mass in the second Newton’s law of motion and εε is the charge (mass) in the relativistic electromagnetic (gravitational) field. In everyday life, we see that all bodies visually fall under gravity (i.e. in a common gravitational field) with the same observed acceleration ξττξττ as if having equal inert and gravitational masses: μ/ε=1μ/ε=1, with respect to the synchronized time ττ. However, if the principle of relativity extended by Einstein to the case of the uniformly accelerated rectilinear motion is valid, then this relation should also be true with respect to xttxtt, that is, (μ/ε)β3=1(μ/ε)β3=1, in proper time tt of a still observer and of the carrying system (falling body), thus, depending on velocity vv at which the acceleration ξττξττ is measured. This means that the inert mass μμ and the gravitational mass εε can be considered equal only at v=0v=0, and otherwise are related by the equation ε=μβ3≥με=μβ3≥μ, where Einstein’s calibration factor β=[1−(v/V)2]−0.5≥1,|v|