The Number That
Haunts Physics

The invoice

Every floor I ever laid in Vermont is still sending me invoices, and my knee pays them. Scroll down and this oak board gets walked on: one cycle, one scratch. The finish dulls where the traffic goes, the grain opens, a nail starts to lift. Floors wear, hinges wear, knees wear. E ti pareva.

Brand new. Still smells of varnish.

Scrolling does the walking, or use the slider. Keep this board in mind. The next plate has something that doesn't wear out.

The loop that doesn't wear out

Two carts, two tracks. The first, in Fig. 1, runs a spiral: every lap lands a little off the last one, the wheels scuff, the rails shed grit, and sooner or later the whole business piles up in the middle. Everything we build does this. My knee does this.

The second, in Fig. 2, runs a closed loop and comes back to exactly the same mark, every lap. Nothing drifts, so nothing grinds. The blue line is the path it has travelled: however many laps it runs, the line never gets any thicker. In Flux, this is the electron.

Both carts are running at walking pace.

Now push the tempo all the way up. The electron doesn't run at walking pace: it laps its loop about 10²⁰ times a second. At that tempo the cart is everywhere on its track at once, and the loop looks perfectly still. It ticks, all the same. Ma dai.

Two turns

A brass medallion on a leather strap, the other end clamped to a post. Turn the medallion once, a full 360°, and it looks exactly as it started. The strap disagrees: it keeps a twist that no amount of fiddling will remove. Turn it a second time and something absurd happens. Now the whole mess can be undone without ever turning the medallion back: keep it facing the same way and carry it once round the post. Ma dai.

Drag the medallion sideways, or use the slider.

The electron behaves like the medallion. A single full turn does not bring it home; it needs two, 720°. Physicists call this spin ½. In the essay I call it the loop counting its own laps. The strap trick itself is old, honest geometry: any object tethered to its surroundings has this property. Try it with a belt and a book, or with a glass of water on your open palm, which you can turn twice round without spilling a drop; your arm is the strap.

Open the clock

For about a century we have read 137 off the face of nature the way you read the time off a clock: from the outside. You see the hand move. You don't see why. Scroll, and the front comes off. Behind the hand there is a wheel, behind that wheel another, all the way back to a crank. The hand isn't doing anything; it is being done to. Take the crank and drive it yourself. Stop the wheels, and the hand stops with them.

From the outside you see the hand move. That is all you see.

The number didn't move. The mechanism closed underneath it, like opening the back of a clock and finding the gears give you twelve.

One machine, three consequences

One stream, three wheels. The big one throws lightning. The little one drops apples. The heavy one keeps cannonballs going the way they were already going, and complains if you try to change that. Physics files these under three separate mysteries: electromagnetism, gravity and inertia. In Flux they may be three consequences of one structure, the way three wheels on one millrace are three consequences of one stream. Close the sluice and watch which wheels stop.

The sluice is open. One stream, all three wheels turning.

Press Honest scale and the apple's wheel shrinks to its true size next to the lightning's: about forty orders of magnitude smaller. It hasn't gone anywhere; it is simply too small to draw on this or any page. The cannonball's wheel stays as drawn, because this comparison is only between lightning and apple.

The balance

Now run the machine backwards. On the right pan, under glass, the electron, weighed the ordinary way: measured. On the left pan go two things only, Newton's constant and Planck's constant, and the same machinery is left to work out what the electron ought to weigh. Nobody tells it the answer.

The left pan is empty, so the electron's side hangs low.

The stage that acts

Physics usually treats the vacuum as a stage: empty scenery the actors move across. Look at a wave in a tank. Nothing travels down the tank. Watch the specks of dye: each turns in a small circle and ends up exactly where it started. The wave is the water itself, doing the moving. In Flux the vacuum isn't scenery. It is the water.

Now shove it. Tap the water, or use the buttons. Shove gently or shove hard, and the ripple leaves at the same speed either way. Push on the vacuum and it pushes back, and that push-back is inertia; its ripples travel at exactly the speed of light.

Watch the specks behind the front glass: each turns in a small circle, deeper ones in smaller circles, and comes back to where it started. The wave passes; the water stays. (Circles drawn at 5× true size.)

Maybe the knobs are gears

The Standard Model reads like a control panel: a row of knobs, each set by hand to whatever the measurements say, none connected to any other. Try it here. Grab a knob and turn it. Four of them turn together, as if something behind the panel had an opinion. Then lift the panel.

Drag a knob sideways to turn it. Keys 1 to 5 pick a knob, arrows turn it.