At 09:42 AM 4/23/02 -0700, Tim May wrote: > >And even if the world were Newtonian, in a classical billiard ball >sense, with Planck's constant precisely equal to zero, predictability is >a chimera. Consider a game of billiards, with perfectly spherical >billiard balls, a perfectly flat table, etc. Trajectories depend on >angles to a precision that keeps going deeper and deeper into the >decimals. For example, predicting the table state after, say, 3 seconds, >might require knowing positions, speeds, and angles (in other words, the >vectors) to a precision of one part in a thousand. Doable, one might say.
Predictability gets much worse if one of the walls of a pool-table is curved, then the uncertainty in a perfectly-round ball's momentum is magnified after reflection, compared to a pool-table of 3 or more flat walls. You may have meant to imply this --if spherical balls hit other balls the uncertainty is similarly magnified-- but its worth noting the difference in predictability between flat and curved-wall abstract billiards. There is a fascinating demo-photograph that shows reflections off 4 stacked steel balls is a classical fractal. >But after 30 seconds, any "errors" that are greater than one part in a >billion would lead to "substantially different" table states. Fail to >know the mass or position or elasticity or whatever of just one of the >billiard balls to one part in a billion and the outcome is no longer >"predictable." Exactly. This is why some of us severe quantum skeptics still accept atomic-level generated uncertainty (resistor, junction, radioactive) and the entropy harvested therefrom. --- Lorentz' weather-sim was deterministic, but screwing up a small decimal fraction as he retyped something totally hosed his expected results ---that's the concept.
