Charge distribution in the universe

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1. Aug 5, 2015

1. The problem statement, all variables and given/known data
Can we consider the universe to have a uniformly charged distribution?
If so, shouldn't the field at any point in space be zero? Since the universe is infinite, will it be symmetrical about any point, field should be zero right? Why is this not true?

2. The attempt at a solution
Can we argue that the infinite universe may be considered to be a sphere?
Thus if at any two points the field is zero, can we obtain a contradiction saying that, field is zero only at the centre of a uniformly charged sphere, and there cannot be two centres, so its absurd to say field at any 2 points is zero?

Thanks!

2. Aug 5, 2015

HallsofIvy

Staff Emeritus
Your argument that the infinite universe "may be considered to be a sphere" so has a specific center is wrong. An infinite universe does not have a "center".

3. Aug 5, 2015

I agree, that was the part I was not convinced about, anyway.
But then how do we explain the fact?
Is there any other argument that we may put forward to explain it?

4. Aug 5, 2015

jbriggs444

Are you aware of infinite series which are conditionally convergent? Such a series has terms which get smaller and smaller. If you add them all up in order, the sequence of partial sums converges to a particular number. For instance, 1 - 1/2 + 1/3 - 1/4 + 1/5 + ... But if you rearrange the series in a different order you can make the sum come out differently. It turns out that for a conditionally convergent series, it is possible to attain any sum you like with some suitable rearrangement of terms.

So how does that apply to an infinite universe? If the universe were infinite, homogeneous and flat (it's not) then you could partition it into a bunch of pieces. Say, for instance that you parcelled it out as a set of cubes each 1 light year on a side. Each of those cubes, by hypothesis, has the same charge as every other one. Each one exerts some net force on a test charge placed at the center of any chosen coordinate system. What result could you get if you added up the electrostatic forces exerted by all of those parcelled-out cubes?

5. Aug 5, 2015

Wait, are you implying that the sum of the electrostatic forces may be converged to any real number?
It still seems to me that, by symmetry, that it would sum up to be zero, always :/
Still not too clear..

6. Aug 5, 2015

jbriggs444

Yes, that is what I am saying. Since any number can be determined, the mathematical result is not defined.

Indeed, if a result were uniquely determinable, that result would have to be zero. But first you have to show that the result is uniquely determinable. There's the rub.

7. Aug 5, 2015

phinds

Whoever told you that the universe is infinite misled you. It MAY be infinite, and in fact it evidence continues to pile up that it probably is, but there is not yet any such conclusion, so such questions can only be correctly phrased as "IF the universe is infinite ... "

8. Aug 6, 2015

andrevdh

Last edited: Aug 6, 2015
9. Aug 6, 2015

jbriggs444

That is a limit to the size of the observable universe -- we can only see light that is 13.82 billion years old, so we can only see 13.82 billion light-years out. In the context of the question at hand this does indeed put a finite limit on the influence of a uniformly charged expanding universe.

Whatever it is, it can't affect a test charge here. So it is irrelevant in this thread.