TY - JOUR

T1 - E=mc2 versus symmetry for Lorentz covariant physics

AU - Kong, Otto C.W.

AU - Ting, Hock King

N1 - Publisher Copyright:
© 2023 The Physical Society of the Republic of China (Taiwan)

PY - 2023/6

Y1 - 2023/6

N2 - The famous equation E=mc2 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.

AB - The famous equation E=mc2 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.

KW - (Quantum) relativity symmetry

KW - Casimir invariants

KW - Lorentz covariant quantum mechanics

KW - On-shell mass condition

KW - Quantum field theory

KW - Relativistic dynamics

UR - http://www.scopus.com/inward/record.url?scp=85159148390&partnerID=8YFLogxK

U2 - 10.1016/j.cjph.2023.04.008

DO - 10.1016/j.cjph.2023.04.008

M3 - 期刊論文

AN - SCOPUS:85159148390

SN - 0577-9073

VL - 83

SP - 480

EP - 488

JO - Chinese Journal of Physics

JF - Chinese Journal of Physics

ER -