Can Gauss's Law Explain the Field of an Electron in a Closed Finite Universe?

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Discussion Overview

The discussion revolves around the application of Gauss's Law in the context of a closed finite universe, specifically considering the electric field generated by a single electron within a hypothetical 4-sphere. Participants explore the implications of this scenario on the consistency of Gauss's Law and the nature of electric fields in finite space.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how Gauss's Law applies in a closed finite universe, noting an inconsistency when considering the flux through a sphere surrounding an electron.
  • Another participant suggests that stipulating a total charge of zero in the universe might resolve some issues, but raises a question about the implications for gravity.
  • A later reply challenges the notion of inconsistency, explaining that Gauss's Law indicates the presence of sources within the volume and clarifies the relationship between electric field flux and the actual electric field magnitude.
  • One participant expresses uncertainty about how to respond to the clarification provided by another participant.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the interpretation of Gauss's Law in this context, with some asserting inconsistencies while others provide counterarguments. The discussion remains unresolved as differing viewpoints are presented without consensus.

Contextual Notes

Limitations include assumptions about the nature of electric fields in finite space and the implications of charge distribution on gravitational fields, which are not fully explored.

Khashishi
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How does Gauss's divergence law work in a closed finite universe? Let's say the universe were a 4-sphere, with a single electron. How can I work out the field of the electron? If I draw a 3-sphere around the electron, then I split space into two regions. One region contains an electron, so Gauss's law tells me that the flux through the sphere is -e*4pi. But the other region doesn't contain any electron, so Gauss's law tells me that the flux through the sphere going the other way is 0. That's inconsistent.

It seems if I think about it a little more, it makes no sense to have an infinite range force in finite space. An electron's field lines would "wrap around" and overlap itself onto infinity.
 
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It seems that problems could be avoided by stipulating that the total charge in the universe is 0. But what about gravity then?
 
Khashishi said:
It seems that problems could be avoided by stipulating that the total charge in the universe is 0. But what about gravity then?

Well Gauss' law for gravity is Newtonian gravity, which we know is incorrect.
 
Why is it inconsistent? Gauss' Law essentially tells you whether or not you have any sources within the volume enclosed by your surface.

For the region without the electron, the flux of electric field through the surface is indeed zero, since any flux entering the volume from outside (where the source is located) is exactly countered by the flux leaving the volume.

For the region with the electron, the only electric fields in the universe (as you defined it) are from the electron, and can only pass outwards through the surface i.e. there is no field coming inwards to counter it, and thus the flux is non-zero.

Are you mixing up flux of the electric field with the actual magnitude of the electric field?

That's not meant to be an insulting question; it's just that I did precisely that when I learned about Gauss' Law. :redface:
 
Actually, I think I see where you're coming from now. I'm not sure how to answer that.
 

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