Relativistic centripetal force question

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Discussion Overview

The discussion revolves around the relativistic centripetal force acting on a mass moving in a circular path. Participants explore the differences in force calculations based on relativistic principles, particularly focusing on the role of the Lorentz factor (gamma) in these calculations. The scope includes theoretical considerations of force in special relativity and its application to high-energy physics scenarios, such as those encountered in particle accelerators.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the relativistic force on a mass moving in a circular path is calculated using centripetal acceleration multiplied by rest mass and gamma squared, while others argue it should be gamma times rest mass.
  • One participant notes that the spacelike part of the four-force differs from the force three-vector by a factor of gamma.
  • There is a question regarding the correct magnitude of the relativistic centripetal force, with some asserting it should be gamma to the first power, while others suggest gamma squared.
  • A participant provides a specific application of the formula in the context of the LHC, questioning whether their calculations are correct.
  • Another participant emphasizes that the magnitude of the four-force is a relativistic invariant (gamma squared), whereas the force three-vector is frame variant (gamma), highlighting the complexity of answers in relativity.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of relativistic centripetal force, with no consensus reached. The discussion reflects multiple competing interpretations of how relativistic effects influence force calculations.

Contextual Notes

Participants acknowledge that relativistic scenarios often do not yield a single answer without careful attention to details, indicating potential limitations in the assumptions or definitions used in their discussions.

teve
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The last post in the thread https://www.physicsforums.com/showthread.php?t=466305 seems to say that the relativistic force on a mass moving on a circular path is the centripetal acceleration, v*v/r, times rest mass times gamma squared.

But the articles http://en.wikipedia.org/wiki/Force#Special_relativity and http://en.wikipedia.org/wiki/Special_theory_of_relativity#Force seem to suggest the force is the centripetal acceleration time rest mass times just gamma.

What am I missing? Are the situations different? If so, how?
 
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So then what is the magnitude of the (relativistic) centripetal force on a particle with rest mass m traveling at velocity v in a circle of radius r as observed from a frame at rest with the center of the circle? Is it (mvv/r) times gamma, or gamma squared? It is still not clear to me. It seems this should be a simple question and should have one answer.
 
Gamma to the first power. The spacelike part of the force four-vector simply isn't the force.
 
OK. Then in the LHC with gamma=7500, r=4300m (C=27000m), 2808 bunches of 1.15e11 protons each (proton m=1.67e-27kg), the LHC dipole magnets exert (on the average) a radial inward force per meter of very nearly (7500*(1.67e-27kg*2808*1.15e11)(c^2)/4300m)/27000m=3.131 N/m. 6.262 N/m for the two beams. Is this a correct application of the formula?
 
teve said:
What am I missing? Are the situations different? If so, how?
The magnitude of the four-force (gamma squared) is the force felt by the accelerating particle, it is a relativistic invariant. The magnitude of the force three-vector (gamma) is the force measured in the "lab" frame, it is frame variant.

teve said:
It seems this should be a simple question and should have one answer.
Things rarely have a single answer in relativity unless you pay very careful attention to the details.
 
DaleSpam said:
The magnitude of the four-force (gamma squared) is the force felt by the accelerating particle, it is a relativistic invariant. The magnitude of the force three-vector (gamma) is the force measured in the "lab" frame, it is frame variant.

Things rarely have a single answer in relativity unless you pay very careful attention to the details.


Thanks for that simple explanation. Now I can check that off on my list of things to figure out.
 

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