Electrons!

I’ve taken this post from a memoir I hope to finish soon of a canoe trip my daughter Angela and I took on the first 340 miles of the Mississippi River. It provides a good introduction to the material I want to talk about in the post to follow:

So much water!  I try to get my head around the notion that all this water is made up of molecules, two little hydrogen atoms clinging to a large oxygen atom like a miniature cartoon mouse head, all tumbling over each other.  Of course the molecules are not really solid, nor are the atoms, nor are the parts of the atoms.  It’s all about forces and big ideas. 

The molecules are so tiny and there are so many of them.  I wondered how many there were in this bit of river.  According to the Avogadro constant, there are 6.02 × 10²³ molecules in a mole.  The atomic mass of oxygen is 16, I remember that from high school chemistry, and the mass of hydrogen is a shade over one, so the atomic mass of water is almost exactly 16 + 2 = 18.  A mole of water is that number of grams, eighteen.  Since a gram of water has a volume of one cubic centimeter, thanks to the French, who set these units that way on purpose, a mole of water takes up about eighteen cubic centimeters.  This little section in the river was about 30 meters wide by a hundred meters long, and I guessed two meters deep.  That made 6000 cubic meters of water right there.  Since there are 100 centimeters in a meter, a cubic meter is 100 × 100 × 100 = 1,000,000, a million cubic centimeters.  Every eighteen of these is a mole, so there are a million divided by 18 moles in a cubic meter—about.   Ten over 18 reduces to 5/9, and I know the decimals for ninths just repeat the top, so that makes 55555.5… moles in each cubic meter.  We’ll call it 60,000, rounded to the nearest ten thousand, because I just wanted to know how many zeroes my number has. 

I did not share my thoughts with Angela.  It would annoy her, but this is just arithmetic and high school science, and I was curious.  So many people would run from a calculation like that, but it’s interesting.  It gives me perspective about life and the world and the universe when I think about that, and to never ponder such things is to lead a life I would have to call impoverished.

Okay, 60,000 moles in a cubic meter and 6000 cubic meters in this bit of river gives me 60,000 × 6000 = 360,000,000 moles in this section of river, or so.  Close enough.  In scientific notation we have 3.6 × 10⁸, and that makes multiplying by the Avogadro constant easier.  But I needed pencil and paper for this. 

Later I figured 3.6 × 10⁸ moles times 6.02 × 10²³ molecules per mole makes about 2.16 × 10³² molecules of water just right there, give or take an enormous number.  In standard notation, that’s 216,000,000,000,000,000,000,000,000,000,000.  I wonder how many there would be in the whole river.  You’d probably only have to tack on 5 or 6 zeroes but I’m not going to do it.

Electrons are more general; every substance has a specific pattern of electrons, so I turn my attention to them. Each oxygen atom has eight electrons, each hydrogen atom one. So every water molecule sports ten electrons, and in this patch of river there were 2.16 × 10³³.

How did all those electrons come to be?  And each one indistinguishable from the next!  John Wheeler’s suggestion that maybe all electrons are just one electron showing up all over has an odd plausibility when you think about it.

But it is astounding to think, as many electrons as there are in a drop of water, as many electrons as there are in a world, in the sun and all the planets, that for light years and light years across empty space are other clusters of identical electrons, that the universe is full of all of these identical particles.  What an absolutely astounding thought!  If all of those electrons are identical in all of their properties, including their mass and their charge, and all the protons and neutrons as well, what are we to make of that?  Could they have been different?  How do we know they are not different here from some other galaxy far across the other side of the universe?  The thought that electrons and protons have no such physical properties at all, but are dependent on some kind of pure idea, some kind of logical necessity springing from mathematical/digital properties makes it possible to imagine that our universe is necessarily as it is, and does not vary from one region to another.

Or what if there is something implausible and arbitrary about the universe in which we live?  I can buy quantum theory and the arbitrary nature of subatomic matter, but I have a lot more trouble conceiving of a variegated universe.  A variegated universe is even more inconceivable to me than the notion that every one of its approximately 10⁸⁰ electrons is identical to the next.

We talk about particles but an atom is not like a tiny solar system.  It has layers of fog that hold different discrete levels of energy that are necessarily digitized in some way.  An electron, like a photon, can be viewed either as a wave or as a particle, but there is something necessary about the amount of energy in an electron or in a photon.  An atom, being comprised of layers of fog or energy which repel the layers of fog of other atoms, is categorized just by those spheres or spheres of influence or layers of fog energy, all the way out to the full periodic table of the elements, and it is those layers of fog, those necessary digital layers or spheres of energy that for mathematical reasons determine the properties of the elements, the way they look, the way they behave, the way they like to link to each other, and these are determined by something necessarily mathematical and not just because they “want” eight electrons in their outer orbit, as we were taught in high school chemistry. 

That’s all they are, atoms; just patches of energy-fog that we like to imagine as systems of particles because we know peas and marbles and sand particles, and because that energy fog will not allow itself to be divided or quantified differently without a huge protest.

I find myself contemplating very seriously the notion that all reality, each sub-atomic particle has existence only as idea.  Perhaps at some level religion and science will find common ground, but far deeper and far stranger than any of us has ever imagined.