Is momentum conserved in all inertial frames?

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Discussion Overview

The discussion centers around the conservation of momentum in different inertial frames, particularly in the context of special relativity. Participants explore the implications of momentum conservation for both particles and systems of particles, as well as its relationship to the first postulate of special relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that momentum is conserved in any inertial frame according to the principles of special relativity.
  • Others clarify that while momentum is conserved, it is not the same across all inertial frames, as it depends on the velocity of the particle, which varies with the choice of frame.
  • A participant notes that when particles interact through fields, momentum can be transferred into those fields, leading to the conservation of the total momentum of particles plus fields.
  • One participant emphasizes the importance of momentum conservation in validating the first postulate of special relativity, arguing that if momentum were not conserved, it would undermine the assertion that physics is the same in all inertial frames.

Areas of Agreement / Disagreement

Participants generally agree that momentum is conserved in inertial frames, but there is a lack of consensus on the implications of this conservation and its relationship to the first postulate of special relativity. Some points remain contested, particularly regarding the role of fields in momentum transfer.

Contextual Notes

Participants express uncertainty about the necessity of momentum conservation for validating the first postulate, indicating a potential gap in understanding the relationship between these concepts in special relativity.

MichaelW24
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and is the momentum of a particle the same in all inertial frames?

Thanks for any help
 
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In the context of special relativity, the momentum of a particle or a system of particles is conserved in any inertial frame. (Frames that include gravity sources would not be inertial by definition).

The momentum of a particle however is not the same in all inertial frames, the momentum is obviously dependent on the velocity of the particle, and the velocity of the particle depends on the choice of the frame.
 
pervect said:
In the context of special relativity, the momentum of a particle or a system of particles is conserved in any inertial frame. (Frames that include gravity sources would not be inertial by definition).

The momentum of a particle however is not the same in all inertial frames, the momentum is obviously dependent on the velocity of the particle, and the velocity of the particle depends on the choice of the frame.
If the particles interact through fields then there is momentum transferred into the fields. In that case its the the total momentum of particles + field that is conserved.

Pete
 
pmb_phy said:
If the particles interact through fields then there is momentum transferred into the fields. In that case its the the total momentum of particles + field that is conserved.
Pete

Yep, good point.
 
pmb_phy said:
If the particles interact through fields then there is momentum transferred into the fields. In that case its the the total momentum of particles + field that is conserved.
Pete

In fact, (in classical field theory) we normally say a system is "sufficiently isolated" when the Lagrangian of a system is transationally invariant, and so gives rise to a conserved canonical energy-momentum tensor (i.e. implying total momentum and energy is conserved).
 
sorry, I am specifically talking anout special relativity; my lecture notes say that momentum must be conserved but I don't understand why this is nessecary to validate the first postulate, can somebody explainm why if momentum isn't conserved them the first postulate is invaudatted?

Thank you very much again for your help!
Micahel.
 
MichaelW24 said:
sorry, I am specifically talking anout special relativity; my lecture notes say that momentum must be conserved but I don't understand why this is nessecary to validate the first postulate, can somebody explainm why if momentum isn't conserved them the first postulate is invaudatted?
Thank you very much again for your help!
Micahel.


Postulate I says physics is the same in all inertial frames.

My rest frame is an inertial frame.

That moomentum conservation is true is part of the physics in my rest frame.

Therefore momentum conservation is true in all inertial frames.
 

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