# I Evidence for Inverse Square Law at Extremely Large Distance?

1. Mar 26, 2016

### Opus_723

This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some incredible distance, but maybe has an as-yet-undetected correction that causes the force to actually hit zero at some finite distance.

It seems likely that if this distance were large enough, we wouldn't be able to detect any deviation, but have we managed to put any empirical lower bounds on the distance over which the inverse square law holds? I imagine that changing the inverse square law would affect the propagation of light, so does the light from distant galaxies rule this out on the scale of the observable universe?

2. Mar 26, 2016

Staff Emeritus
The best evidence we have is from galactic magnetic fields, which don't show a deviation from predictions. That says that ordinary E&M, which includes Coulomb's Law, is good to at least 10 kpc.

3. Mar 27, 2016

### Staff: Mentor

Well, the following link puts an upper limit on any violation of Coulomb's law as (2.7 ±3.1)x 10-16: http://staff.ustc.edu.cn/~bjye/em/TEST-KL.pdf
Note that this is an upper limit, as anything larger than this should be detectable by modern experiments. No lower limit would really exist. This also assumes that any violation of Coulomb's law is a smooth, continuous modification to the inverse square law. I suppose it's always possible that a violation could manifest as an abrupt change or discontinuity at larger distances, but if so, we'd have a very strange law indeed.

4. Mar 27, 2016

### Opus_723

I was mostly interested in how confidently we can say that the force is finite (nonzero) at arbitrarily large distances. I understand that we have quite strong upper limits on any deviation from the inverse square law over laboratory distance scales. By a "lower bound", I meant an empirical lower bound on the spatial extent of a charge's influence. Vanadium's point about galactic magnetic fields is exactly the sort of thing I'm looking for.

It might be better to rephrase the question. What evidence do we have that particles can actually interact across the entire universe like the inverse square law suggests?

5. Mar 27, 2016

### Staff: Mentor

Via static fields, not very much, if any. Via dynamic fields we have extremely good evidence, as the fact that we can see EM radiation emitted more than 13 billion years ago suggests.

6. Mar 27, 2016