Abstract
There is a fundamental difference concerning the concept of particle in Newtonian and in relativistic Physics. In Newtonian Physics a particle is a ‘thing’ which has been created once and since then exists as an absolute unit for ever. Concerning the physical quantities associated with a particle they are divided in two classes. The ones which are inherent in the structure of the particle such as mass, charge etc. and characterize the identity of the Newtonian particle and those which depend on the motion of the particle in a reference system such as velocity, linear momentum etc. Newtonian particles are assumed to interact by collisions creating larger systems. This interaction of particles happens in a way that the overall inherent quantities of the particles are conserved (i.e. mass, charge) while some of the motion dependent physical quantities such as energy, mass and linear momentum etc. are also conserved. Finally the systems consisting of many particles have additional physical quantities such as temperature, pressure etc.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Why we do not have to consider the case that one subset of four-vectors is null and the subset of the remaining four-vectors is timelike? Is this case covered?
- 2.
The unit in the direction of B a is B a∕B hence the B in the denominator.
- 3.
It is possible to compute the extremals of the quantity (17.34 ) without any calculations if we note that the quantity under the square root is non-negative. Therefore the maximum value occurs for the minimum value of the denominator which is \({\mathbf {B}}_{(A)}^{2}=0\) and the minimum when the denominator is maximum, that is, when \({\mathbf {B}}_{(A)}^{2}\) is infinite.
- 4.
The “=” does not mean that we can equate the corresponding components of the four-vectors because the decompositions/componets refer to different coordinate frames. It simply indicates that they refer to the decomposition of the same four-vector in different LCF. The components of each vector are related to the other via the Lorentz transformation which relates the corresponding LCF frames.
- 5.
For the standard treatment see Example 10.7.3.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Tsamparlis, M. (2019). Geometric Description of Relativistic Interactions. In: Special Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-27347-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-27347-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27346-0
Online ISBN: 978-3-030-27347-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)