Single positive electric charge in a closed universe

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Discussion Overview

The discussion centers on the implications of having a single positive electric charge in a closed universe, exploring theoretical frameworks and the behavior of electric and magnetic fields in such a scenario. It includes considerations of classical physics, vacuum polarization, and the nature of fields in curved space.

Discussion Character

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

Main Points Raised

  • One participant notes that in a closed universe with only one positive charge, electric field lines cannot terminate on a negative charge or extend to infinity, leading to confusion.
  • Another participant speculates that if the universe has a polarizable vacuum and a spherical topology, polarization might create an opposite charge at the antipodal point.
  • A different participant raises the question of how magnetic fields interact with electric fields in a static universe, suggesting that an observer might detect both fields due to the curvature of space.
  • One participant asserts that a magnetic field cannot create an electric field, stating that it can only act as a velocity-dependent potential for charged particles.
  • Another participant counters that a changing magnetic field can indeed create an electric field.
  • A participant reiterates the initial scenario of a single positive charge in a closed universe, expressing ongoing confusion and referencing a discussion in a specific text.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of electric and magnetic fields in the context of a closed universe, with no consensus reached on the implications of a single positive charge or the interactions between fields.

Contextual Notes

The discussion involves assumptions about the nature of charges, the topology of the universe, and the behavior of fields in curved space, which remain unresolved and may depend on specific definitions and frameworks.

Dmitry67
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Say, all objects in a closed Universe are neutral, and there is only 1 (unbalanced) positive charge.

Lines of an electric field started on a positive charge can end only on the negative charge or they go into infinity. But in a closed universe there are no negative charges nor they can go into infinity.

I am puzzled.
 
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That seems to exclude the possibility of such a cosmos in a classical framework.

But if the cosmos has a polarizable vacuum and the topology of a spherical surface, then (I would speculate) the polarization would create a charge of opposite sign at the antipodian point.
 
What about the magnetic field?

Even if such universe is static (matter is delicately balanced with the dark energy) space is curved. Intuitively, 2 points in different places of a curved space do not belong to the same inertial system. So an observer on some distance from a charge would observe not only electric but also magnetic field?

Can that magnetic field create an electric field which cancels the original one?
 
A magnetic field cannot create an electric field. All it can be is a velocity dependent potential for a charged particle. And since there is only the one there is no way to detect it in any case.
 
Changing magnetic field can create an electric field.
 
Dmitry67 said:
Say, all objects in a closed Universe are neutral, and there is only 1 (unbalanced) positive charge.

Lines of an electric field started on a positive charge can end only on the negative charge or they go into infinity. But in a closed universe there are no negative charges nor they can go into infinity.

I am puzzled.

There is a good discussion of this on p. 457 of MTW.
 

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