guthriedm15's blog

The definition of an integral is given below:

An integral is basically the summation of values for a certain function within a certain range. In fact, integrations use Riemann summations. Riemann sums are used to approximate the total are under a curve.

Energy is often spoken of in continuous terms when relatively large systems are being considered. A good example of energy being treated as continuous is when problems are being solved with the ideal gas law. Consider a system that is constant in pressure, and the temperature increases. The volume must also increase to compensate for this change. Typically, we think of this compensation and the increase in temperature as continuous processes. We rarely think of the increase in temperature as a quantized process in our daily lives.

We think of energies (and measures of energies) in our lives as continuous because it gives us useful and easy to understand approximations. In macroscopic systems, these approximations are typically close enough for the purposes of daily life.

While these approximations are true, they are technically incorrect. Because all systems are made up of atoms, things on the quantum scale, they must all follow the rules that are established in the quantum scale of things. Energy is quantized at all levels; energy in a continuum is just an abstract and useful idea that can be applied to larger systems.

Because the laws of physics apply everywhere in the universe, all energy is quantized. Since all energy is quantized, that means that everything should be quantized because everything is interrelated. Momentum, for example, must be quantized because it can be related to the energy of a system.

Source:

http://archives.math.utk.edu/visual.calculus/4/definite.1/

http://en.wikipedia.org/wiki/Riemann_sum

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