Daily Inspiration — Whoa, man, that’s like some heavy-duty physics!

One(1)Two(2)Three(3)

means that the 1st electron is in the first place, the 2nd is in the second place and the 3rd is in the third place. There are 5 other possibilities. For example, Electron 1 can be in place two and electron 2 can be in place one. Electrons 1 and 2 have swapped places. Every time that happens, there's a minus sign. If there are an even number of swaps, then there's a plus sign; odd number of swaps contributes a minus sign. The wave function has a structure like this.

One(1)Two(2)Three(3) + One(2)Two(3)Three(1) + One(3)Two(1)Three(2)
- One(3)Two(2)Three(1) - One(2)Two(1)Three(3) - One(1)Two(3)Three(2)

Yes, physicists really do work with combinations like this, and they have a name: they're called Slater determinants. With just four electrons, there are 12 positive terms and 12 negative terms. The number of plus and minus terms in the Slater determinant increases very rapidly - I want to say increases exponentially with the number of electrons, but that would be an understatement. The number of combinations is much bigger than that. There are 10⁸⁰ electrons in the universe and their wave function is a Slater determinant with 10⁸⁰! terms. That's "10⁸⁰ factorial" which is the biggest number you're ever likely to come across in a discussion of one universe.

Quiz for the truly nerdy: How big a number is 10⁸⁰ factorial? If you tried to write it down, how many digits would you have to write? Is it bigger or smaller than a googol? Is it bigger or smaller than a googolplex?

We talk about a particular electron being in a particular place, or following a particular orbit. But this is a shorthand, a fiction. The truth is that every electron in the universe participates equally in this behavior, whatever it is, and all the electrons are continually checking in with each other and coordinating their behaviors, such that if you shine a light on this place and look, exactly one electron will appear under your flashlight, and the one you catch has an equal probability of being any of the 10⁸⁰.

Next Page  1  |  2

(Note: You can view every article as one long page if you sign up as an Advocate Member, or higher).