Volume 20: Pages 42-45, 2007

Nuanced Relativity: The General Equation

Allen D. Allen ¹

¹CytoDyn, Inc., 1511 Third Street, Santa Fe, New Mexico 87505 U.S.A.

Nuanced relativity points to hν(c/ν)²as a general expression for the total energy of any wave‐particle. When ν = c, the total energy E is “naked”: hν. When ν < c, the total energy E is “dressed” by rest mass and is greater than hν by a factor of (c/ν)². When E is “well dressed,” ν                           c, hν   E, the dynamic Newtonian symmetry dT = ∫pdν = (1/2)mν², where the indefinite integral ∫ denotes the antiderivative of its argument, accompanies the kinematic symmetry dx = ∫ν_xdt = (1/2)a_xt². Rest energy is recognized as a form of potential energy V = m₀c². The Hamiltonian then gives the total energy as H = V + T = m₀c² + m₀c²(γ − 1) = hν(c/ν)².

Keywords: relativistic energy, rest mass, wave‐particle duality, dynamic and kinematic symmetry

Received: February 2, 2005; Published Online: January 8, 2009