Energy-momentum of non-free classical particle

Click For Summary
SUMMARY

The discussion centers on the application of the energy-momentum relation E² = p² + m² in classical physics, specifically regarding free and non-free particles and fields. It is established that this relation holds true only for free particles, while the energy-momentum tensor must be employed in scenarios involving forces or sources. Participants emphasize the necessity of the energy-momentum tensor for accurately describing mass and energy interactions within force fields.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with the energy-momentum relation E² = p² + m²
  • Knowledge of the energy-momentum tensor in field theory
  • Basic concepts of force fields and their effects on particles
NEXT STEPS
  • Study the derivation and applications of the energy-momentum tensor
  • Explore classical field theory and its implications for particle physics
  • Investigate the role of forces in modifying energy-momentum relations
  • Learn about the implications of non-free particles in relativistic contexts
USEFUL FOR

Physicists, students of classical mechanics, and anyone interested in the foundational principles of energy and momentum in the context of force fields and particle interactions.

atyy
Science Advisor
Messages
15,170
Reaction score
3,378
Let's discuss only classical fields and particles.

For fields, E2=p2+m2 applies only if the field is free. In the presence of sources, we have to use the energy-momentum tensor.

For particles, does E2=p2+m2 apply only when they are free, or does it work even if they are acted on by a force?
 
Physics news on Phys.org
The energy-momentum tensor has to be used for all forms of mass/energy that are in a force field.
 
Thanks!
 

Similar threads

Undergrad E=mc^2 and acceleration
  • · Replies 26 ·
Replies
26
Views
2K
Graduate The Lagrangian of a free particle ##L=-m \, ds/dt##
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Meaning of the invariants built from the angular momentum tensor
  • · Replies 1 ·
Replies
1
Views
1K
High School Robert Wald's General Relativity: Energy-Momentum Relation
  • · Replies 8 ·
Replies
8
Views
2K
Graduate How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Dirac's derivation of the action/Lagrangian for a free particle
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad I have a question about gravity -- If the value of the energy momentum tensor (Tμν) becomes zero, can it become gravitational-free?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Energy Density in E Field: Does it Contribute to Inertial Mass?
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad The Energy - Momentum Equation vs the Energy - Mass Equation
  • · Replies 131 ·
5
Replies
131
Views
12K
Graduate Dirac on localization of energy in the gravitational field
  • · Replies 16 ·
Replies
16
Views
2K