Reality or Locality? Proposed Test to Decide How Nature Breaks Bell's Inequality

Figure 7

If “hidden variables” are governed and determined by nondissipative (Hamiltonian) equations no attractor will result, yet a structure differing from pure randomness will emerge. Such a result would imply the same conclusion regarding the world as noted in the text accompanying Figure 5. The example shows the modern reconstructed phase space of the “restricted circular three-body problem” in astronomy [22], where Poincaré first glimpsed what today is known as deterministic chaos, nondissipative in this case. This (the corrected and printed version [23]) was his winning contribution (price money: 2,500 Swedish Kronor) to a contest announced in 1885 to celebrate the 60th birthday of the Swedish King Oscar II in 1889. What Poincaré found was that small changes in the initial conditions (such as positions and initial velocities of planets) produced huge and unpredictable outcomes-deterministic chaos in today's parlance.