TY - JOUR
T1 - Conservation of the Energy-Momentum
T2 - A Simple Demonstration of the No-Interaction Theorem in Classical Physics
AU - Ares de Parga, G.
AU - González-Narvaez, R. E.
AU - Mares, R.
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - In Relativity the sum of 4−vectors in different points does not generally represent a 4−vector. By using this result, it is shown by simple methods that the total energy-momentum of a system of point particles represents a well-defined 4−vector if the particles do not interact. It is proved that this is equivalent to the no-interaction theorem in Classical Physics. This theorem difficulties the study of a system of interacting particles since it is not even possible to define the total energy-momentum nor the reference frame where the system is at rest. This impediment is avoided by adding to the energy-momentum tensor the stress tensor describing the interaction. As an example, this is applied to a system of charged particles. In the process, the equation of motion for a charged particle including the self-force is formally obtained. However, when a thermodynamic system is analyzed from two different reference frames with a relativistic relative velocity, the interaction between the particles and the walls of the volume cannot be described by means of a covariant stress tensor and consequently the proposed technique is not feasible. Despite the above mentioned drawbacks, a covariant theory of the relativistic transformation laws of the thermodynamic quantities is developed.
AB - In Relativity the sum of 4−vectors in different points does not generally represent a 4−vector. By using this result, it is shown by simple methods that the total energy-momentum of a system of point particles represents a well-defined 4−vector if the particles do not interact. It is proved that this is equivalent to the no-interaction theorem in Classical Physics. This theorem difficulties the study of a system of interacting particles since it is not even possible to define the total energy-momentum nor the reference frame where the system is at rest. This impediment is avoided by adding to the energy-momentum tensor the stress tensor describing the interaction. As an example, this is applied to a system of charged particles. In the process, the equation of motion for a charged particle including the self-force is formally obtained. However, when a thermodynamic system is analyzed from two different reference frames with a relativistic relative velocity, the interaction between the particles and the walls of the volume cannot be described by means of a covariant stress tensor and consequently the proposed technique is not feasible. Despite the above mentioned drawbacks, a covariant theory of the relativistic transformation laws of the thermodynamic quantities is developed.
KW - Energy-momentum tensor
KW - No-interaction theorem
KW - Point particles
UR - http://www.scopus.com/inward/record.url?scp=85026499313&partnerID=8YFLogxK
U2 - 10.1007/s10773-017-3489-1
DO - 10.1007/s10773-017-3489-1
M3 - Artículo
SN - 0020-7748
VL - 56
SP - 3213
EP - 3231
JO - International Journal of Theoretical Physics
JF - International Journal of Theoretical Physics
IS - 10
ER -