Wednesday, December 23, 2009

Coulomb, Avogadro, Faraday, Newton, & Jesus

Charge is measured in a unit called "coulombs", so named for the French physicist who defined electrostatic attraction and repulsion (Coulomb's Law). There are 6.02214e23 electrons per mole of electrons (Avogadro's number); further, there are 1.602177e-19 coulombs of charge per electron, so that means there are 9.64853e4 coulombs of charge per mole of electrons (Faraday's constant). Back to Coulomb's Law, any two point charges (nice, tidy, mathematically simple massless "points in space" that are easier to deal with than electrons, or nuclei, or Buicks) placed one meter apart and each having a +1C charge will repel one another with a force of 9 billion Newtons. That's the same force that 900,000 metric tons of weight exerts on this planet due to gravity - about 100 Eiffel Towers, to bring things back full circle to France.

A 1 gallon jug of water is about 4000 grams of H20, which at 18 grams per mole means that the water in that jug has about 210 million coulombs of charge, and if you placed another similar jug one meter away each would be exerting 4.1e26 N of force on the other. The scale of that is so fucked that the only comparable explanation of weight I can offer is that if you weighed the Earth itself on another Earth-like planet, it would be exerting less force due to gravity than the nuclei in one of those jugs of water.

Fortunately, the electrons in one jug have an equally strong attraction to the nuclei in the other, which cancels the incredible force of repulsion. It is an important distinction that both the attraction and repulsion forces are still present and still just as tremendously strong as we've described, they're just balanced so perfectly that the effects of those forces are diminished to nothing.

So what happens when some irresponsible ass turns the water in one of those jugs into wine (Jesus's First Sign)? Kind of a dick move, really. Being only 85-90% water, the rest of that shit has a completely different molar mass. Hell, ethanol (the majority of the difference) works out to slightly more than 46 g/mol instead of the 18 g/mol of water. The anecdote is clear: the water turned to wine, so I can only assume that if one can pull off such feats of alchemy they can do so with enough precision that I don't have to fuck around with estimating the amount and composition of all of the adulterants, dirt, and other shit floating around in that jug. So the water is water, and then it is not, and in that change there is no point for the universe in which all of this takes place to catch up to that fact; the electromagnetic force, infinite in range and ludicrous in potency, is not granted a reprieve from duty or a do-over - it simply continues to apply itself the entire time.

But along a given timeline those forces must at some point be particulate; either there is a point in this occurrence where the water is, from the perspective of the universe, not water and not yet wine, or there is a point where the change interrupts the constant force. In either case, the delicate balance of attraction and repulsion is broken.

At least the guys at CERN put a little more thought into whether to fuck with reality than having a snit with their mom about whether or not they would help.