Why doesn’t everything mix into everything else?

An acquaintance on Facebook recently asked, "I'm still not sure why the conglomerate of particles that become me keep a recognizable shape and don't suddenly get mixed up with someone else's, since they're all the same as far as anyone can tell." This prompts two interesting questions. First, why don't we collapse, one atom into another, and for that matter merge with the ground under our feet? What separates our feet from our shoes from the ground? Two reasons spring to mind. Electrons. Try and meld one molecule or atom into another, and it's the repellent electrostatic force[1] between the electron shells surrounding an atom's nucleus or a molecule's atoms that keeps everything, including you, from merging into one amorphous blob of goo. The weird rules of quantum mechanics. Specifically, the Pauli exclusion principle says that any two identical fermions (particles governed by Fermi-Dirac statistics, including electrons) cannot occupy the same quantum state. (Bosons -- such as photons -- are governed by Bose-Einstein statistics, which does allow them to occupy the same quantum state. That's why lasers lase.) Pauli exclusion is why electrons arrange into shells around atomic nuclei. This means none of our constituent atoms can meld into one another. These two fundamental characteristics of our universe, in essence, are what makes chemistry chemistry . . . and why we exist as independent physical entities. Second: what holds everything together? Why don't all material objects disintegrate and fly apart due to electrostatic repulsion between the constituent atoms ... and become one gigantic homogeneous expanding cloud of gas? [TBD] hydrogen bonds. van der Waals forces. [color-box][1]What is an electrostatic force? Suppose we have two non-moving charged particles, with charges $q_1$ and $q_2$, and separated by a distance $r$. The static force between these two particles, known as Coulomb's law, is proportional to the charge values and inversely proportional to the square of the distance between them. In SI units, we write the size of this force in Newtons as $$F = k_e \dfrac{q_1 q_2}{r^2}$$ where $k_e = \dfrac{1}{4 \pi \varepsilon_0} = 8.987 551 787...\times 10^9\,\mathrm{N\,m^2\,C^{-2}}$ is the vacuum permittivity, $\varepsilon_0 = 8.854 187 817...\times 10^{-12}\,\mathrm{F/m}$ (Farads per meter), and $\mathrm{C}$ is the unit of charge, the Coulomb. This is of the same form as Newton's law of gravitational attraction between two masses. It differs in the proportionality constant ($k_e$ vs. $\mathrm{G}$) and in that it involves the product of two charges instead of the product of two masses. Since masses are always a nonnegative quantity but charges can be positive or negative, this means Coulomb's law differs in one other respect: the force can be either repulsive (two positive charges or two negative charges) or attractive (a positive charge and a negative charge). Thus the rule of thumb: like charges repel, unlike charges attract. [/color-box]

Aperiodic Wanderings

astronomicalish musings

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