Rational expectations characterize a model of the economy in which the agents in the model know the model, including model parameters. Presumably agents learn the parameters of the underlying model from looking at past realizations of the time series generated by the model. A better estimate of model parameters might come from looking at many realizations at a single moment in time (say, one lag ago). But, since the world has only one history, the latter estimate is not available.
Which estimate is used does not matter for some stochastic processes. Estimates across realizations and from past values of a single realization converge, in some sense, as the number of realizations and the number of time lags increase, respectively, without bound. This property is known as ergodicity. So rational expectations only makes sense if economic time series are ergodic.
Non-stationarity is a sufficient, but not necessary, condition for non-ergodicity. Since some time series in economics (for example, output per person-hour) are non-stationary, rational expectations cannot abide in a general theory for economics.
I provide some random references examining different aspects of macroeconomics after Lucas. Sent's award-winning book documents how this macroeconomics draws on the mathematics invented by the likes of Claude Shannon and Norbert Wiener. The above application of ergodicity to critiquing rational expectations is due to Paul Davidson, who offers a formalization of Joan Robinson's contast of history with equilibrium.
References
- Davidson, Paul (1982-82). "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. 5, N. 2 (Winter): 182-198
- Hartley, James E. (2006). "Kydland and Prescott's Nobel Prize: the Methodology of Time Consistency and Real Business Cycle Models", Review of Political Economy, V. 18, N. 1 (Jan.): 1-28
- Hoover, Kevin D. (1988). The New Classical Macroeconomics: A Sceptical Inquiry, Basil Blackwell
- Sent, Esther-Mirjam (1998). The Evolving Rationality of Rational Expectations: An Assessment of Thomas Sargent's Achievements, Cambridge University Press