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Energy in Special Relativity - ebook/pdf
Energy in Special Relativity - ebook/pdf
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Presented in this paper the new relativistic formulas for kinetic, rest and total energies differ from the commonly applied analogous expressions. The new relativistic kinetic energy and its relation with the spatial part of the four-momentum are given by the expressions similar to its classical equivalents. In particular, I justified that the rest energy is half of the amount determined by the traditional relation. The most popular formula of physics (mass-energy equivalence principle) is not correct.

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Zbigniew Osiak ENERGY IN SPECIAL RELATIVITY Zbigniew Osiak EҭERGY Iҭ SPECIAL RELATIVITY Energy in Special Relativity By Zbigniew Osiak Self Publishing © Copyright 2011, 214 by Zbigniew Osiak All rights reserved ISBN: 978-83-272-3448-3 Portrait of the author by Rafał Pudło e-mail: zbigniew.osiak@gmail.com Energy in Special Relativity Zbigniew Osiak The Wroclaw College of Humanities, Wroclaw, Poland The University of the Third Age in the Wroclaw University, Wroclaw, Poland E-mail: zbigniew.osiak@gmail.com Abstract I give new relativistic formulas for kinetic, rest and total energies. The change in kinetic energy of a particle will be determined as the work done by the spatial part of the Minkowski four-force. I present a new relation between the relativistic kinetic energy and the spa- tial part of the four-momentum also interpretation of the temporal component of the Minkowski four-force. Contents Abstract 1 Introduction 2 The Lorentz covariant four-dimensional Minkowski equations of motion 3 The spatial part of the Minkowski four-force 4 The new formulas for energies in relativistic mechanics 5 The square modulus of the four-velocity 6 The new relation between kinetic energy and momentum 7 The temporal component of the Minkowski four-force 8 A more general form of the Mikowski equations of motion 1 1 2 2 3 3 4 4 5 6 Zbigniew Osiak 2 Energy in Special Relativity 9 Conclusions and discussion References 1 Introduction 6 7 The traditional form of the mass-energy equivalence principle proposed by Einstein [1] E0 = mc2 is sometimes derived [2] using the Planck equations of motion [3] F = d(mγv)/dt. Usage of these equations in special relativity leads to errors because they are not covariant under Lorentz transformations. The Lorentz covariance of the physical equations and the Lorentz invariance of the speed of light in a vacuum are the two basic postulates of special relativity. In my view, the Planck equations of motion are an interesting example of a heuristic hypothesis and have only historical significance. For calculation of the relativistic kinetic energy and its relationship with the rest and the total energies it is necessary to use the Lorentz covariant four-dimensional Minkowski equations of motion [4]. 2 The Lorentz covariant four-dimensional Minkowski equations of motion The Lorentz covariant four-dimensional Minkowski equations of motion are given by: ˜Fα = mγ d˜vα dt = m˜aα (1) where ˜Fα – components of the Minkowski four-force; α = 1, 2, 3, 4; m – invariant mass of a particle; γ ≡ (1 − v2c−2) 2 – Lorentz factor; c – speed of light in vacuum; ˜vα ≡ γ (dxα/dt) – components of the four-velocity; x1 ≡ x, x2 ≡ y, x3 ≡ z, x4 ≡ ict; i – imaginary unit; v ≡ dr/dt – three-dimensional velocity; r ≡ (x, y, z) = (x1, x2, x3) – three-dimensional position vector; v2 ≡ (dx1/dt)2 + (dx2/dt)2 + (dx3/dt)2 – square modulus of the three-dimensional velocity; ˜aα ≡ γ (d˜vα/dt) – components of the four-acceleration. − 1 Self Publishing (28.12.2011) www.virtualo.pl
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