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Old 06-16-2013, 07:43 AM
 
Location: Frankfurt, Germany
745 posts, read 876,424 times
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Why does taking a number and multiplying it by itself so significant, and leads to deep insights into the fundamental nature of reality and existence?

Gravity and electromagnetism, for example, operates on an inverse square law. You will never fully understand "e=mc2" without understanding the concept that kinetic energy increases proportional to the speed squared of a given object.

The dispersion relation of particles is also a "squared" relationship.

So what is so special about multiplying a number by itself that it manifests in basic physical laws? Why is it that if something is moving 4 times as fast, that it has 16 times the energy? Does it have something to do with spacetime being geometric?
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Old 06-17-2013, 10:29 AM
 
Location: SoCal
5,922 posts, read 9,071,768 times
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Because physical phenomena happen in 3D, not in 2D. So spreading effects occur over an area, not a point or a line.

If you haven't already read it, I suggest the book "Flatland".
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