- #1
gpran
- 20
- 1
Point Particle in Relativity and Electrodynamics:
“The Classical Theory of Fields” – by Landau and Lifshitz, in its discussion about classical size of a particle, concludes that:- Thus we come to the conclusion that in classical (non-quantum) ‘relativistic mechanics’, we cannot ascribe finite dimensions to particles which we regard as elementary. In other words, within the framework of classical theory elementary particles must be treated as ‘points’.
In a paper – “Classical radiation theory and point charges”- by F H J Cornish, Journal-Proceedings of the Physical Society, the ‘abstract’ says that:- The usual theory for a continuous system may not be applied without some alteration to a system of point charges because the orthodox electromagnetic energy-momentum tensor for the field leads to infinite self energies. In this paper, a class of modified energy-momentum tensors are constructed in such a way that the field singularities do not lead to difficulty and the corresponding equations of motion are derived. (Couldn’t read the complete paper as it is not freely available).
In “Classical Electrodynamics (third edition)” by J. D. Jackson, the Poynting’s theorem analysis starts with:- If there exists a ‘continuous distribution’ of charge and current, the total rate of doing work by the fields in a finite volume is given by volume integral of (J.E). For a point charge described by a delta function, this derivation faces difficulties as discussed in- “A relook at radiation by a point charge. I”, Canadian Journal of Physics (available on T- space). However, this Larmor formula based on Poynting’s theorem seems to have been proved ‘experimentally’ for an accelerating charge. Maybe, F H J Cornish in above mentioned paper is suggesting a remedy.
Even in quantum mechanics, the particle is assumed as a point particle which may follow a probabilistic distribution pattern under potential field. My question is: How to reconcile the issue of size of a fundamental particle, under these circumstances of contradictory requirements by these important theories? Also, if a particle has finite size, then how to define volume (Vol= L1. L2 X L3 ) of a particle in a four dimensional space ?
“The Classical Theory of Fields” – by Landau and Lifshitz, in its discussion about classical size of a particle, concludes that:- Thus we come to the conclusion that in classical (non-quantum) ‘relativistic mechanics’, we cannot ascribe finite dimensions to particles which we regard as elementary. In other words, within the framework of classical theory elementary particles must be treated as ‘points’.
In a paper – “Classical radiation theory and point charges”- by F H J Cornish, Journal-Proceedings of the Physical Society, the ‘abstract’ says that:- The usual theory for a continuous system may not be applied without some alteration to a system of point charges because the orthodox electromagnetic energy-momentum tensor for the field leads to infinite self energies. In this paper, a class of modified energy-momentum tensors are constructed in such a way that the field singularities do not lead to difficulty and the corresponding equations of motion are derived. (Couldn’t read the complete paper as it is not freely available).
In “Classical Electrodynamics (third edition)” by J. D. Jackson, the Poynting’s theorem analysis starts with:- If there exists a ‘continuous distribution’ of charge and current, the total rate of doing work by the fields in a finite volume is given by volume integral of (J.E). For a point charge described by a delta function, this derivation faces difficulties as discussed in- “A relook at radiation by a point charge. I”, Canadian Journal of Physics (available on T- space). However, this Larmor formula based on Poynting’s theorem seems to have been proved ‘experimentally’ for an accelerating charge. Maybe, F H J Cornish in above mentioned paper is suggesting a remedy.
Even in quantum mechanics, the particle is assumed as a point particle which may follow a probabilistic distribution pattern under potential field. My question is: How to reconcile the issue of size of a fundamental particle, under these circumstances of contradictory requirements by these important theories? Also, if a particle has finite size, then how to define volume (Vol= L1. L2 X L3 ) of a particle in a four dimensional space ?