Relativity Paradox w/ Charged Spheres

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Discussion Overview

The discussion revolves around a thought experiment involving two positively charged spheres and their behavior under acceleration, drawing parallels to the Bell's spaceship paradox. Participants explore the implications of electromagnetic forces and relativistic effects in different reference frames, focusing on the complexities of interactions between accelerated charged objects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a scenario where two charged spheres are balanced by a string and accelerated, questioning the effects of electromagnetic forces and potential breaking of the string.
  • Another participant challenges the initial premise, stating that the forces between accelerated charged objects are more complex than simply adding a magnetic term, highlighting the importance of their positions along the acceleration axis.
  • Further discussion includes the consideration of delayed charge distances and electromagnetic wave momentum as factors influencing the interaction between the charges.
  • One participant suggests that the argument could be made without acceleration, proposing a scenario with charged bodies at rest in one frame and moving in another, raising questions about the presence of magnetic fields and electric field magnitudes.
  • Another participant clarifies that there is no length contraction in the direction orthogonal to motion, and discusses how the repulsion between charges may be affected by magnetic fields and the weakening of the spring in the setup.
  • A later reply notes that the thought experiment is distinct from the Bell's spaceship paradox, emphasizing that it pertains to the behavior of charged objects under proper acceleration.

Areas of Agreement / Disagreement

Participants express differing views on the implications of electromagnetic forces in the context of acceleration and reference frames. There is no consensus on the validity of the initial thought experiment or its relation to the Bell's spaceship paradox.

Contextual Notes

Participants highlight limitations regarding the assumptions made about the setup, the dependence on the positions of the charges, and the complexities of electromagnetic interactions that may not be fully resolved in the discussion.

Xynon
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There is a similar thought experiment I imagined to help me begin to understand the Bell's spaceship paradox:

Consider two positively charged spheres, placed side-by-side inside a frame S' with a string stretched to the point where it balances the repulsive electrostatic force between them. For sake of simplicity, assume that the frame S' and the spheres are perfectly rigid and frictionless. One sphere is directly mounted to the frame S' and the other sphere is tied to the frame S' with a very thin thread same as in the Bell's paradox.
8VFlAkv1F.jpg

The frame S' starts accelerating relative to the frame S.

According to the frame S', everything is stational and the rope would stay intact. But according to frame S, there would be an attractive magnetic force between the spheres which would break the rope.
 
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The image doesn't work.

The force between two accelerated charged objects is a bit more complex than just adding a magnetic term. And the "nice" magnetic term is only present if the objects are at the same coordinate along the acceleration axis - but in that dimension you don't have any length contraction.
 
mfb said:
The image doesn't work.

The force between two accelerated charged objects is a bit more complex than just adding a magnetic term. And the "nice" magnetic term is only present if the objects are at the same coordinate along the acceleration axis - but in that dimension you don't have any length contraction.

What else comes into play between two accelrated charges? Delayed charge distances/potentials? or EM wave momentum?
f3aA8F

I will try to fix the image. In the image, the two charges are at the same coordinate of the acceleration axis (with a distance between them on the perpendicular axis). So wouldn't the magnetic force break the thread? And why no contraction there? We find many examples of charges moving together to have magnetic forces between them. No contraction no magnetic force right?
 
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Xynon said:
View attachment 204004
Do you really need to have acceleration? Seems to me you can make your argument by proposing that S' is moving at constant velocity with respect to S.

Propose 2 charged bodies at rest and no magnetic fields with respect to S'.
Then, with respect to S, the charged bodies are moving so there are magnetic fields but there is no apparent change to the magnitude of the electric field to balance the forces.
 
Xynon said:
And why no contraction there?
There is no length contraction orthogonal to the direction of motion.

In the frame of an external observer, the repulsion between the charges reduces based on the magnetic field, but the spring gets weaker as well (for the same reason!).

There is no Bell-like paradox here because everything stays simultaneous in all frames as the setup is orthogonal to the line of motion and acceleration.
 
Xynon said:
There is a similar thought experiment I imagined to help me begin to understand the Bell's spaceship paradox
This thought experiment is about the behavior of electrically charged objects undergoing proper acceleration, so is pretty much unrelated to Bell's spaceship paradox (which is a cleverly disguised exercise in relativity of simultaneity). I have taken the liberty of changing the title accordingly.
 
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