Inverse square law and infinite intensity

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Discussion Overview

The discussion revolves around the implications of the inverse square law in the context of sound and electromagnetic radiation, particularly focusing on the concept of intensity as distance approaches zero. Participants explore the limitations of applying classical physics to these scenarios and the resulting paradoxes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the implications of the inverse square law for sound intensity, noting that as distance approaches zero, intensity seems to approach infinity, which contradicts real-world observations.
  • Another participant suggests that the concept of a point source generating sound is flawed, as real sound sources have finite sizes that limit how close one can approach.
  • A participant proposes a similar scenario with electromagnetic radiation, questioning why intensity also appears to approach infinity as the radius tends to zero, expecting a limiting value instead.
  • One participant introduces the example of electron-positron annihilation to illustrate the complexities involved when applying inverse square laws at very small distances.
  • Another participant discusses the limitations of classical physics in this context, suggesting that quantum effects alter the behavior of forces at short ranges, preventing infinities from occurring.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of classical physics to these scenarios, with some suggesting that classical models break down at small distances due to quantum effects, while others focus on the limitations of point sources in generating sound or radiation.

Contextual Notes

Participants acknowledge that classical physics may not adequately address the phenomena being discussed, particularly at very small scales where quantum mechanics may play a significant role. There is also a recognition of the limitations of the inverse square law in these contexts.

Who May Find This Useful

This discussion may be of interest to those exploring the intersections of classical and quantum physics, particularly in relation to the behavior of forces and intensities at small distances.

fluidistic
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This is weird, I have no clue on how to solve the following question that I "invented" while walking in the street due to car sounds.
I know that the intensity of sound -let's say the source of sound is a dot/point- decreases as 1/r² do. If I'm at a distance 1 m, I can hear 4 times "stronger" than if I'm at 2 m from the source. Now if I approach the point source I'll be getting an extremely loud sound and if I eventually reach the point-like source, I'd get an infinitely loud sound. I know this doesn't happen in reality so I went wrong somewhere.
Where did I go wrong?! I really can't see!
Edit: I know I should reach a finite value, say I_0. But as r tends to 0, I(r) seems to tend to \infty.
 
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The issue is that a point source doesn't generate sound, only an object of finite size, and the size of the object and how much it's moving limits how close you can get to the object.
 
rcgldr said:
The issue is that a point source doesn't generate sound, only an object of finite size, and the size of the object and how much it's moving limits how close you can get to the object.

Thanks for the reply.
What about if we replace the word sound by EM radiation?
If we look at http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html, we make the sphere radius tend to 0, we get huge values for I. Even if r is a very little larger than 0, we still get a HUGE value for I. I'd have thought we'd reach a limiting value, say I_0.
 
The closest real world example of this would be an electron and positron approaching each other and annihilating (converted into energy). I don't know how close they get to each other before the transition from matter to energy takes place.
 
This is actually a profound question. To avoid the complexities of sound being a pressure wave, let's instead look at the electrostatic fields of a point charge (Coulumb's law). The force of one electron on another electron depends on the inverse of the square of the distance between them. So if we were strong enough to push two electrons right on top of each other, there would be an infinite force. But infinities cannot exist in real life, so where did we go wrong?

It turns out that the inverse square law itself is not exactly right. When you get close enough to something, weird quantum effects take over which cause the force to actually not reach infinity, but taper off. In this case, the electrostatic force at very short range gets screened by the vacuum polarization, which is caused by constant electron-positron pair production/annihilation in vacuum allowed by the uncertainty principle. In summary:

Short answer: Weird quantum effects take over for very small distances so that inverse square laws no longer apply exactly.

Long answer: Read up on http://en.wikipedia.org/wiki/Vacuum_polarization"
 
Last edited by a moderator:
Thanks for the information.
So basically we can't deal with this question with classical physics? :/
I'm going to bed now, will think about this question...
 

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