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Border Guards
Quantum Soccer
* Quantum Soccer applet | Mathematical details
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Quantum Soccer
In the game of Quantum Soccer, the aim is to shape the wave function
of a quantum-mechanical "ball" so that the probability of it being
inside one of the goals rises above a set threshold. This is achieved
by using the motion of the players to alter the energy spectrum of
the wave function: when a player moves across the field, the energy
that this action provides (or absorbs) enables transitions between
certain modes of the wave function. The pairs of modes involved
depend on the player's velocity; the exact rules are spelt out in the
mathematical details, but it's easy to experiment using trial and
error.
Applet controls
The goal control The
selects the resolution
v[x] = probability control sets
chosen threshold for the the size of
x-velocity ball being inside the grid on
one of the goals which the
in order to wave function
The velocity control sets score. is computed.
the x- and y-velocities If the
of a player in metres per Auto-reverse
second. Click or drag the option is
mouse on this control to checked, players The RESTART
set the velocities, then v[y] = reverse button starts
select a player. If a chosen automatically the game
player has already been y-velocity when they again from
selected, the new encounter an scratch.
velocity will be applied obstacle.
immediately. Otherwise, they
halt.
If the OK The demo buttons play scripted
sounds demonstrations, in which the
option is two teams cooperate to show how
checked, goals can be achieved. (Real
sounds play play, of course, would include
when goals very different tactics.)
are scored.
v[x] = [] []
This page requires JavaScript to be v[y] = [ ] [RESTART]
enabled. Auto-reverse
[ ]OK [Demo 1] [Demo 2]
sounds
This page requires JavaScript to be enabled.
This page requires JavaScript to be enabled.
Players are selected by clicking on them; click on an empty spot to
de-select the player.
The green panel represents the playing field (which is 100 metres by
50 metres). The "ball" is a wave function confined to lie within the
borders of the field (it can't tunnel out, since the energy barrier
is assumed to be infinitely high). The wave function is drawn as
contours of the square of its magnitude, with phase indicated by the
colour of the contour lines.
The probability of the ball lying within the goals is shown above
each one. If the value crosses the threshold, the goal flashes white
and the players and wave function are reset to the starting
configuration. (If you have checked the OK sounds box, then sounds
are played when goals are scored.)
If you choose probabilistic scoring rather than a percentage
threshold in the goal control, then whenever the time is a multiple
of 50 seconds, a measurement is performed on the ball to determine
whether it is inside the left-hand goal, inside the right-hand goal,
or neither - but which does not localise it any further than that.
The wave function determines the probabilities for these three
outcomes, but it cannot guarantee any particular result. If the ball
is measured to be inside a goal, the score is counted, but the
players are not reset to their starting configuration. The wave
function is projected into a subspace that depends on the result of
the measurement, such that the ball (at the moment of measurement)
definitely lies in the region it was found to be in, to the extent
that is possible given the finite number of eigenfunctions available
with which to localise the wave.
The blue panel displays the spectrum of the wave function: the
amplitude of each of the possible modes, with the phase indicated by
a dial, and the frequency of the mode (in milliHertz, i.e. cycles per
1000 seconds) shown beneath it. Links are drawn in grey between pairs
of states for which transitions are enabled by the current motion of
the players; also, if you click-and-hold (or click-and-drag) on the
velocity control, the links for the velocity you specify will appear
temporarily in red on the spectrum panel.
You can preview a single mode by clicking on it: this displays it on
the field, without affecting the wave function of the ball or
registering any goals. You can also display the best possible
goal-scoring spectrum, by holding down the shift key and clicking
anywhere on the blue panel. This wave function produces peaks of over
50% probability in alternate goals whenever the time is a multiple of
50 seconds. (If more modes were included, these peaks would be even
higher.)
Keyboard operation
The following functions can be performed with the keyboard, after
clicking somewhere on the applet first, so it receives the keystrokes
rather than your browser.
Setting velocities with the keyboard
preceded by the the digit
MINUS (-) key for a keys, 0-9,
Keys that alter the x-velocity negative velocity SELECT a
(when typed alone), or the y velocity.
-velocity (when combined with the the UP arrow key INCREASES the
SHIFT key): velocity.
the DOWN arrow key DECREASES the
velocity.
R REVERSES the velocity.
B reverses BOTH x and y
Keys that alter BOTH x- and y velocities.
-velocities: Z sets both x and y velocities to
ZERO.
H HALTS all players.
Selecting players with the keyboard
RIGHT ARROW selects the NEXT player, in team
order
LEFT ARROW selects the PREVIOUS player
SHIFT RIGHT ARROW selects the next MOVING player
SHIFT LEFT ARROW selects the PREVIOUS MOVING player
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* Quantum Soccer applet | Mathematical details
* Complete Text | Quantum Soccer
* "Border Guards" contents
* Back to home page | Site Map | Side-bar Site Map
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Border Guards / Quantum Soccer / created Monday, 26 April 1999 /
revised Sunday, 8 November 2009
Copyright (c) Greg Egan, 1999-2009. All rights reserved.