Are deterministic descriptions and indeterministic descriptions observationally equivalent?
Abstract
The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measuretheoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measuretheoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measuretheoretic deterministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measuretheoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measuretheoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measuretheoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticize the claims of some previous philosophy papers on observational equivalence.
 Publication:

Studies in the History and Philosophy of Modern Physics
 Pub Date:
 2009
 DOI:
 10.1016/j.shpsb.2009.06.004
 Bibcode:
 2009SHPMP..40..232W
 Keywords:

 Indeterminism;
 Determinism;
 Chaos;
 Observational equivalence;
 Prediction;
 Stochastic processes;
 Ergodic theory