Define the term power law, in terms of mathematics and physics. Then give at least three examples of power laws that exist in physics. Additionally, define the terms scale invariance and universality. Give at least two examples of universality in physics.
Define the term power law, in terms of mathematics and physics. Then give at least three examples of power laws that exist in physics. Additionally, define the terms scale invariance and universality. Give at least two examples of universality in physics.
Power law - The power law states that a relative change in one quantity results in a proportional relative change in another quantity, independent of the initial size of those quantities: one quantity varies as a power of another. The simplest example of the power law is a square; if you double the length of a side (say, from 2 to 4 meter) then the area will quadruple (from 4 to 16 meter squared).
Power law can be represented mathematically as:
where: X and Y are variables,
c is a constant,
is an exponent.
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