Newtons 2nd Law corrected for Relativity

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Discussion Overview

The discussion revolves around the application of Newton's second law in the context of relativity, specifically focusing on how to modify the equations for a damped harmonic oscillator. Participants explore the implications of relativistic effects on mass, force, and the relationship between electric and magnetic forces in moving charge systems.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents the equation F = d(mv)/dt and asks how to correct it for relativity in a damped harmonic oscillator context.
  • Another participant suggests modifying the equation to d(mvγ)/dt = -kx - cv, introducing the Lorentz factor γ.
  • A participant questions whether corrections for length contraction and time dilation are necessary, suggesting that only mass needs to be adjusted as a function of velocity.
  • There is an agreement that the x and t coordinates are based on the observer's frame of reference, implying no need for further corrections in those variables.
  • Another participant introduces the concept that magnetism arises from relativity and discusses the force between moving charges, questioning if additional considerations are needed due to their relative motion.
  • A later reply indicates that the interaction between moving charges requires special relativity and retarded fields for accelerating charges, referencing advanced electromagnetism texts.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of correcting spatial and temporal coordinates in addition to mass. While some agree on the sufficiency of adjusting mass, others highlight the complexities introduced by the relative motion of charges, indicating that the discussion remains unresolved.

Contextual Notes

Participants have not fully explored the implications of relativistic effects on spatial and temporal coordinates, nor have they reached a consensus on the necessary corrections for the forces between moving charges.

SSGD
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F = d(mv)/dt Newtons 2nd Law
F = -kx Spring Force
F = -cv Damping Force

d(mv)/dt = -kx + -cv

How would you correct the equation for a damped harmonic oscillator for relativity. If it is possible. I just want a one dimensional solution unless you have to go to a two dimensional or three dimensional model to because of relativity.
 
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[itex]d(mv\gamma)/dt = -kx + -cv[/itex], with [itex]\gamma=1/\sqrt{1-v^2/c^2}.[/itex]
 
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That is it? You wouldn't have to correct x for length contraction or t for time dilation. Just correct the m as a function of velocity.
 
SSGD said:
That is it? You wouldn't have to correct x for length contraction or t for time dilation. Just correct the m as a function of velocity.

That's right. They're your x and t coordinates, and you aren't moving relative to yourself.
 
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Oh... I understand. You have been a lot of help.
 
From some of the reading I have done, magnetism is product of relativity and electric fields.

Columbic Force between a positive charge and a negative charge is

F = kpe/r2 so because I am using my own position and time then check me if I have it.

d(mvγ)=kpe/r2 or is there more to it because the two particle are moving relative to each other as well.
 
There is much more to it. The equation for the force between two moving charges needs special relativity if they have constant velocity, and 'retarded fields' if they are accelerating. This is covered in advanced EM texts.
 

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