Why is the inverse square law exponentiated to the power 2 ?

 

Why not 3, 4, 5 etc ?

 

And why is it universal ?

 

Please explain.

An intuitive explanation is: Imagine light spreading out from a point. It illuminates a sphere. If you double the radius then the area increases by a factor of 4 (area = 4 pi r²) so the brightness is 1/4. In other words, the amount of light at any distance is proprtional to 1/r².

 

Actually, it isn't universal. The weak force, for example, falls off much more rapidly.

Why is the inverse square law exponentiated to the power 2 ?

 

Why not 3, 4, 5 etc ?

 

And why is it universal ?

 

Please explain.

What did you mean by "universal"?

What did you mean by "universal

 

I mean the paradigm is all 0 inclusive to include all transverse waves (of all wavelengths).

It is only 'universal' in 3+1 dimensions. You see this from Strange's explanation.

It is also only true for a point source.

An infinitely long glowing wire gives an inverse first power law and an infinitely large flat luminous sheet gives an inverse zeroth power (it's just as bright if you are near it as if you are far away).

I think it is also only true for massless force carriers. (I don't really know why; I assume because they follow null geodesics.)

That sounds reasonable. Sound follows an inverse square law and phonons have zero mass.

Also I think that a finite mass implies a finite range so the particles would,in some way, "die out" at large ranges.

The inverse square law makes sense for particles that just carry on, getting more and more spread out as the sphere they are reaching gets bigger.

 

However the force between two dipoles- say two small magnets, doesn't follow the 1/r^2 law,even though the force carriers are photons.

Why is the inverse square law exponentiated to the power 2 ?

 

That's what a square is: the power of 2. If it was to the power 3, it would be an inverse cube law.

It is also only true for a point source.

An infinitely long glowing wire gives an inverse first power law and an infinitely large flat luminous sheet gives an inverse zeroth power (it's just as bright if you are near it as if you are far away).

Like Hubble's law?

Like Hubble's law?

 

Which part of that is like Hubble's law?

Somewhat off topic, but it was asked...

 

The range of forces propagated by bosons of a particular mass is dictated by Quantum Field Theory.

It is a consequence of the Uncertainty Principle and Special Relativity.

The HUP tells us that you need particles of a certain momentum to influence physical processes at a specific distance, and SR relates that momentum to a specific mass.

 

Massive bosons >> short range

Lighter bosons >> longer range

Massless bosons >> infinite range

Edited February 15, 201510 yr by MigL

Which part of that is like Hubble's law?

Hubble's law is directly proportional.

 

 

 

An infinitely long glowing wire gives an inverse first power law (...).

Edited February 15, 201510 yr by michel123456

Hubble's law is directly proportional.

 

 

Yes. IOW, not an inverse square, or an inverse, or a constant, which were the three examples given.

Would string theory have any corrections to the basic inverse square relationship ? String theory projects 11 dimensional space ( 4 basic + 7 curled up dimensions ). Would there imply some delta-correction to the conventionally accepted norm ? I wonder ?

Edited February 18, 201510 yr by petrushka.googol