Evidence for Inverse Square Law at Extremely Large Distance?

In summary: The evidence from static fields is that classical EM is a good description of what's going on across the universe. However, there is no evidence that classical EM extends to infinity. Furthermore, the electric and magnetic fields are too weak to detect beyond a certain distance.
  • #1
Opus_723
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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?
 
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  • #2
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.
 
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  • #3
Opus_723 said:
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?

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
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
Opus_723 said:
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?

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
Drakkith said:
Via static fields, not very much, if any.

I think the field can take more credit than that. There are something like 26 orders of magnitude between table-top experiments and the size of the visible universe. For 20 of them, we know that classical E&M is a good description of what's going on. I think that's pretty good.

Furthermore, the reason we can't go out farther using this technique is because in deep space the electric and magnetic fields are close to zero. (The magnetic fields are a trillion times smaller than the earth's) So we're in a situation where any reasonable alternative theory gives the same answer as the standard one.
 
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1. What is the inverse square law and how does it apply to extremely large distances?

The inverse square law is a principle in physics that states that the intensity of a physical quantity, such as light or gravity, decreases in proportion to the square of the distance from the source. This applies to extremely large distances because as distance increases, the effect of the physical quantity becomes less and less, resulting in a decrease in intensity according to the inverse square law.

2. How was the evidence for the inverse square law at extremely large distances first discovered?

The evidence for the inverse square law at extremely large distances was first discovered by the English astronomer Sir Isaac Newton in the late 17th century. He observed the movement of planets and stars and noticed that their gravitational pull on each other followed the inverse square law at extremely large distances.

3. Can you provide an example of the inverse square law at extremely large distances?

One example of the inverse square law at extremely large distances is the intensity of light from a distant star. As the light travels a greater distance, its intensity decreases according to the inverse square law. This is why stars appear dimmer the farther away they are from Earth.

4. How is the inverse square law at extremely large distances used in modern science?

The inverse square law at extremely large distances is used in many areas of modern science, including astronomy, physics, and engineering. It is used to calculate the intensity of light and other forms of radiation at different distances, as well as the force of gravity between objects. It also helps scientists understand the behavior of electromagnetic waves, such as radio waves and microwaves, as they travel through space.

5. Is the inverse square law at extremely large distances always accurate?

While the inverse square law is a fundamental principle in physics, it is not always accurate at extremely large distances. In some cases, other factors, such as the curvature of space or the effects of relativity, can modify the behavior of physical quantities. However, for most practical purposes, the inverse square law is a reliable tool for understanding and predicting the behavior of physical phenomena at extremely large distances.

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