Quantum Soccer — Greg Egan

2024-03-12 12:44:21

Quantum Soccer

Within the recreation of Quantum Soccer, the purpose is to form the wave operate of a quantum-mechanical “ball” in order that the likelihood of it being inside one of many targets rises above a set threshold. That is achieved through the use of the movement of the gamers to change the vitality spectrum of the wave operate: when a participant strikes throughout the sphere, the vitality that this motion gives (or absorbs) permits transitions between sure modes of the wave operate. The pairs of modes concerned rely upon the participant’s velocity; the precise guidelines are spelt out within the mathematical details, nevertheless it’s simple to experiment utilizing trial and error.

Applet controls
The velocity management units the x– and y-velocities of a participant in metres per second. Click on or drag the mouse on this management to set the velocities, then choose a participant. If a participant has already been chosen, the brand new velocity will probably be utilized instantly.	v_x = chosen x-velocity	The aim management selects the likelihood threshold for the ball being inside one of many targets with a purpose to rating.	The decision management units the dimensions of the grid on which the wave operate is computed.
	v_y = chosen y-velocity	If the Auto-reverse choice is checked, gamers reverse routinely after they encounter an impediment. In any other case, they halt.	The RESTART button begins the sport once more from scratch.
	If the OK sounds choice is checked, sounds play when targets are scored.	The demo buttons play scripted demonstrations, by which the 2 groups cooperate to point out how targets could be achieved. (Actual play, in fact, would come with very totally different techniques.)

Gamers are chosen by clicking on them; click on on an empty spot to de-select the participant.

The inexperienced panel represents the taking part in subject (which is 100 metres by 50 metres). The “ball” is a wave operate confined to lie inside the borders of the sphere (it may well’t tunnel out, because the vitality barrier is assumed to be infinitely excessive). The wave operate is drawn as contours of the sq. of its magnitude, with section indicated by the color of the contour strains.

The likelihood of the ball mendacity inside the targets is proven above each. If the worth crosses the edge, the aim flashes white and the gamers and wave operate are reset to the beginning configuration.
(In case you have checked the OK sounds field, then sounds are performed when targets are scored.)

If you happen to select probabilistic scoring reasonably than a proportion threshold within the aim management, then at any time when the time is a a number of of fifty seconds,
a measurement is carried out on the ball to find out whether or not it’s contained in the left-hand aim, contained in the right-hand aim, or neither – however which doesn’t localise it
any additional than that. The wave operate determines the possibilities for these three outcomes, nevertheless it can not assure any specific consequence.
If the ball is measured to be inside a aim, the rating is counted, however the gamers aren’t reset to their beginning configuration.
The wave operate is projected right into a subspace that is dependent upon the results of the measurement, such that the ball (in the mean time of measurement) undoubtedly lies
within the area it was discovered to be in, to the extent that’s potential given the finite variety of eigenfunctions obtainable with which to localise the wave.

The blue panel shows the spectrum of the wave operate: the amplitude of every of the potential modes, with the section indicated by a dial, and the frequency of the mode (in milliHertz, i.e. cycles per 1000 seconds) proven beneath it. Hyperlinks are drawn in gray between pairs of states for which transitions are enabled by the present movement of the gamers; additionally, in case you click-and-hold (or click-and-drag) on the speed management, the hyperlinks for the speed you specify will seem briefly in purple on the spectrum panel.

You’ll be able to preview a single mode by clicking on it: this shows it on the sphere, with out affecting the wave operate of the ball or registering any targets. You may also show the very best goal-scoring spectrum, by holding down the shift key and clicking wherever on the blue panel. This wave operate produces peaks of over 50% likelihood in alternate targets at any time when the time is a a number of of fifty seconds. (If extra modes had been included, these peaks can be even greater.)

Keyboard operation

The next features could be carried out with the keyboard, after clicking someplace on the applet first, so it receives the keystrokes reasonably than your browser.

Setting velocities with the keyboard
Keys that alter the x-velocity (when typed alone), or the y-velocity (when mixed with the SHIFT key):	preceded by the MINUS (-) key for a detrimental velocity	the digit keys, 0-9, SELECT a velocity.
	the UP arrow key INCREASES the speed.
	the DOWN arrow key DECREASES the speed.
	R REVERSES the speed.
Keys that alter BOTH x– and y-velocities:	B reverses BOTH x and y velocities.
	Z units each x and y velocities to ZERO.
	H HALTS all gamers.
Choosing gamers with the keyboard
RIGHT ARROW	selects the NEXT participant, in crew order
LEFT ARROW	selects the PREVIOUS participant
SHIFT RIGHT ARROW	selects the subsequent MOVING participant
SHIFT LEFT ARROW	selects the PREVIOUS MOVING participant