$E=m{c}^2$ versus Symmetry for Lorentz Covariant Physics

Abstract

The famous equation $E=m{c}^2$ is a version of particle mass being essentially the magnitude of the (energy-)momentum four-vector in the setting of `relativistic' dynamics, which can be seen as dictated by the Poincaré symmetry adopted as the relativity symmetry. However, as Einstein himself suggested, the naive notion of momentum as mass times velocity may not be right. The Hamiltonian formulation perspective gives exactly such a setting which in the case of motion of a charged particle under an electromagnetic field actually has the right, canonical, momentum four-vector with an evolving magnitude. The important simple result seems to have missed proper appreciation. In relation to that, we present clear arguments against taking the Poincaré symmetry as the fundamental symmetry behind `relativistic' quantum dynamics, and discuss the proper symmetry theoretical formulation and the necessary picture of the covariant Hamiltonian dynamics with an evolution parameter that is, in general, not a particle proper time. In fact, it is obvious that the action of any position operator of a quantum state violates the on-shell mass condition. The phenomenologically quite successful quantum field theories are `second quantized' versions of `relativistic' quantum mechanics. We present a way for some reconciliation of that with our symmetry picture and discuss implications.

arXiv comment22 pages Revtex, no figure, published version

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Cited by in corpus (4)

• Lorentz-covariance of Position Operator and its Eigenstates for a massive spin $1/2$ field
• Quantum Mechanics in Curved Space(time) with a Noncommutative Geometric Perspective
• Equivalence Principle for Quantum Mechanics in the Heisenberg Picture
• On Locality of Quantum Information in the Heisenberg Picture for Arbitrary States