petrushka.googol Posted February 13, 2015 Posted February 13, 2015 Why is the inverse square law exponentiated to the power 2 ? Why not 3, 4, 5 etc ? And why is it universal ? Please explain.
Strange Posted February 13, 2015 Posted February 13, 2015 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. 3
Robittybob1 Posted February 13, 2015 Posted February 13, 2015 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"?
petrushka.googol Posted February 14, 2015 Author Posted February 14, 2015 What did you mean by "universal I mean the paradigm is all 0 inclusive to include all transverse waves (of all wavelengths).
ajb Posted February 14, 2015 Posted February 14, 2015 It is only 'universal' in 3+1 dimensions. You see this from Strange's explanation.
John Cuthber Posted February 14, 2015 Posted February 14, 2015 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). 1
Strange Posted February 14, 2015 Posted February 14, 2015 I think it is also only true for massless force carriers. (I don't really know why; I assume because they follow null geodesics.)
John Cuthber Posted February 14, 2015 Posted February 14, 2015 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.
swansont Posted February 14, 2015 Posted February 14, 2015 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. 3
michel123456 Posted February 15, 2015 Posted February 15, 2015 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?
Strange Posted February 15, 2015 Posted February 15, 2015 Like Hubble's law? Which part of that is like Hubble's law?
MigL Posted February 15, 2015 Posted February 15, 2015 (edited) 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, 2015 by MigL
michel123456 Posted February 15, 2015 Posted February 15, 2015 (edited) 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, 2015 by michel123456
swansont Posted February 15, 2015 Posted February 15, 2015 Hubble's law is directly proportional. Yes. IOW, not an inverse square, or an inverse, or a constant, which were the three examples given.
petrushka.googol Posted February 18, 2015 Author Posted February 18, 2015 (edited) 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, 2015 by petrushka.googol
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