How does an electrical charge behave in a Klein bottle?

[HiggsBoson]

If the Klein bottle was made of a conductive substance. How would an electrical charge behave on it? Remember that hollow conductors have charges build up on the outer surface.

[Xittenn]

Anyway you look at it the charge will flow through the object following the path of least resistance. I would just like to note here the insulating nature of the geometry of the line connectors on power transmission towers!

 

 

these things

Edited January 10, 2011 by Xittenn

[swansont]

Interesting question. Klein bottles are not physically possible in 3-D; I suspect the charge distribution you'd along the surface wouldn't be uniform. But one would have to come up with the 4-D equations to show that.

[imatfaal]

Interesting question. Klein bottles are not physically possible in 3-D; I suspect the charge distribution you'd along the surface wouldn't be uniform. But one would have to come up with the 4-D equations to show that.

 

 

 

Swanson - could you elaborate on this bit "Klein bottles are not physically possible in 3-D"? You can't be saying that we cannot have a Klein bottle in our lumpen reality - cos I have one, you can get them on the internet . Are we talking about different Klein Bottles, or are you not referring to the same "in 3-D" as me. I think of a Klein Bottle as a two dimensional surface that has no recognizable inside and outside and looks like a bottle with a handle and a dimple (until you notice that handle and dimple are linked.

 

 

[insane_alien]

they aren't true klein bottles. a true klein bottle does not intersect itself

[imatfaal]

they aren't true klein bottles. a true klein bottle does not intersect itself

 

I thought it must be something like that - thanks for setting me straight.

[swansont]

OTOH, thanks for reminding me of a place to spend some of my disposable income, next time I have some "found money."

[Xittenn]

There is in existence the Mobius Resistor .... With all the combinations of circuit configurations that I have coming into my head I think maybe one could involve closing the manifold so to speak on a Mobius Resistor to form a klein bottle! The resulting configuration would impact the inductive properties created by the flow of charge through 4Dimmensional space(whatever that would mean.) I'm not at all familiar with spacialization in higher dimensions. I ordered a book on topology as my christmas present from my pappy, maybe this will help me or maybe someone who knows what space charges and current flow look like in 4D could elaborate more?

Edited January 11, 2011 by Xittenn

[Xittenn]

Reading through AJBs blog post got me thinking on a few things which led me to search for a 'klein bottle matter-charge trap' which I didn't find. I did however find this wiki article which looks like fundamentals http://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory of space-time research and space-time in higher dimensionality. I haven't explicitly studied any material of this nature and so it had completely alluded me and I'm linking it here because I thought it was relevant.