Question about length contraction.

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Discussion Overview

The discussion revolves around the concept of length contraction in the context of two charged spheres connected by a spring. Participants explore how relativistic effects influence the interaction between the spheres, the spring's behavior, and the implications of electromagnetic fields in a moving frame.

Discussion Character

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

Main Points Raised

  • One participant questions why the Coulomb repulsion between the charged spheres does not push the spring back apart when viewed from a moving frame, considering length contraction.
  • Another participant suggests that the charged field also experiences length contraction, which adjusts the distance between the spheres according to the charge they experience.
  • There is a discussion about the equilibrium state of the spring when length contracted, with one participant asserting that it is in equilibrium at its contracted length.
  • Participants debate the nature of the spring's equilibrium and whether it is influenced by the rest length of the spring in the moving frame.
  • One participant introduces the idea of treating the charged spheres as point particles, questioning if this changes the analysis.
  • Another participant emphasizes that all physical processes, including atomic bonds, are affected by length contraction, leading to a change in the shape of fields at relativistic speeds.

Areas of Agreement / Disagreement

Participants express differing views on the implications of length contraction for the behavior of the spring and the charged spheres. There is no consensus on how these factors interact or the nature of equilibrium in this scenario.

Contextual Notes

Participants highlight the complexity of the situation, noting that assumptions about the shape of fields and the behavior of materials under relativistic conditions may influence the discussion. The relationship between the electromagnetic fields and the mechanical properties of the spring remains unresolved.

Who May Find This Useful

This discussion may be of interest to those studying relativistic physics, electromagnetism, and the interplay between mechanical systems and electromagnetic fields.

cragar
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Lets say I have 2 charged spheres that are connected by a spring and they are a distance d apart. The spring is made of a material that will not allow the charge to evenly distribute. And each sphere has the same charge q on it. Now I move with respect to this object and I should see the spring length contracted. Now the charged spheres are closer together but why wouldn't the now stronger coulomb repulsion want to push the spring back out in my frame. And I guess there in now a B field because the charges are moving. Does the B field affect it though? There is probably something I don't understand about length contraction and where would the energy come from to push it back apart. Any help will be much appreciated.
 
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You are assuming the charged field itself somehow remains spherical. It too is length contracted, putting the spheres at the correct distance for the amount of charge they experience.

Make it simpler; remove the spheres and charges and just examine the spring. It's a foot long, but length contracted, its only half that. Why does it not bounce back? Because, at a half foot in length, it is in equilibrium.
 
OK thanks for your answer. Why can we say the spring is in equilibrium at a half of foot? Is it just because in our frame that is the springs rest length. Not that this would make a difference but if instead of charged spheres we had electrons at each end, that we could treat as point particles.
 
cragar said:
Why can we say the spring is in equilibrium at a half of foot?
The atoms and their bonds are length-contracted. A spherical field of any sort, when seen at relativistic speeds, is going to be lozenge-shaped - shorter along the direction of motion. All physical processes (such as solid material matrices) will be likewise squished.
 

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