Conservation of charge in the Universe

[Pushoam]

TL;DR Summary

Conservation of charge

The charge of an isolated system is conserved.
This implies the charge of the universe is constant.
This implies that charge can neither be created nor destroyed.
This implies that the net positive charge and the net negative charge of the universe are conserved. Is this right?

 

[anuttarasammyak]

TL;DR Summary: Conservation of charge

This implies that the net positive charge and the net negative charge of the universe are conserved. Is this right?

A closed universe is neutral, i.e., total positive charges and total negative charges cancel by Gauss theorem. For an open universe which has infinite volume and where Gauss theorem is not applicable, I don't think we can say whether infinite number of charge particles have finite net conserved sum with zero, positive or negative sign.

 

[jbriggs444]

I don't think we can say whether infinite number of charge particles have finite net conserved sum with zero, positive or negative sign.

Indeed, this would be very much like evaluating the sum of an infinite, conditionally convergent series. The answer you get depends on the order in which you do the summation.

[It's not really conditionally convergent because it is not convergent at all]

 

[Pushoam]

So, for a close universe, the total charge, total positive charge and total negative charge are constant. Is it so?

 

[topsquark]

A closed universe is neutral...

It makes sense, but how do we know this? For all we know, the Universe started with a net charge!

-Dan

 

[PeroK]

So, for a close universe, the total charge, total positive charge and total negative charge are constant. Is it so?

No. There's pair production, for example:

https://en.wikipedia.org/wiki/Pair_production

 

[anuttarasammyak]

anuttarasammyak said:
A closed universe is neutral.
It makes sense, but how do we know this? For all we know, the Universe started with a net charge!

In a closed universe let us take any closed surface. The universe is divided into two parts : inside the surface and outside the surface. Electric flux go through the surface. The flux correspond to all the charges inside the surface in one end and to all the charges outside the surface in other end. Thus we know that charges inside and outside cancel.
This is the explanation I find in section 111 of The Classical Theory of Fields by Landau and Lifshitz. How do you think of this discussion ?

 

[topsquark]

In a closed universe let us take any closed surface. The universe is divided into two parts : inside the surface and outside the surface. Electric flux go through the surface. The flux correspond to all the charges inside the surface in one end and to all the charges outside the surface in other end. Thus we know that charges inside and outside cancel.
This is the explanation I find in section 111 of The Classical Theory of Fields by Lev Landau and Lifshitz. How do you think of this discussion ?

Ah! I see the point now. Hmmm.... wouldn't that argument have to hold for gravity as well? I'll have to ponder that one.

-Dan

 

[PeroK]

In a closed universe let us take any closed surface. The universe is divided into two parts : inside the surface and outside the surface. Electric flux go through the surface. The flux correspond to all the charges inside the surface in one end and to all the charges outside the surface in other end. Thus we know that charges inside and outside cancel.
This is the explanation I find in section 111 of The Classical Theory of Fields by Landau and Lifshitz. How do you think of this discussion ?

I don't follow this argument at all.

 

[anuttarasammyak]

I interpreted : The surface integral of electric field is common for inside region and outside region but with opposite sign due to opposite direction of surface inside/outside. Applying Gauss theorem charges outside and charges inside are same amount but with different sign. Thus they cancel in sum.

 

[PeroK]

I interpreted : The surface integral of electric field is common for inside region and outside region but with opposite sign due to opposite direction of surface inside/outside. Applying Gauss theorem charges outside and charges inside are same amount but with different sign. Thus they cancel in sum.

So, a closed universe with only two electrons is impossible because ...

 

[anuttarasammyak]

So, a closed universe with only two electrons is impossible because ...

… it contradicts with Gauss theorem.

 

[Vanadium 50]

Landau is saying that if you have a source of field lines, you must necessarily have a sink.

I'm not going to argue with that, but I think this requires a static universe as well as a closed one. It probably requires a classical universe as well - no quantum effects like vacuum screening.

 

[PeroK]

Landau is saying that if you have a source of field lines, you must necessarily have a sink.

I'm not going to argue with that, but I think this requires a static universe as well as a closed one. It probably requires a classical universe as well - no quantum effects like vacuum screening.

Or, even, that in a closed universe with only two electons milling around, then Gauss's law doesn't hold.

 

[PeroK]

… it contradicts with Gauss theorem.

Let's see a proof of Gauss's Law for a closed universe.