Postulate of determinacy The Brownian motion

A visible state Sa at time %a completely determines the visible state for any subsequent time tB. 

This statement is clearly not a direct expression of an experimental fact. Apart from a very small group of aerodynamical processes, we always deal with turbulent motions of the gas, where it is impossible to follow the visible state with our measuring instruments. Furthermore, even the best insulation against thermal conduction and radiation is completely unsatisfactory unless we deal with very short periods of observation. 

The above statement is therefore a postulate, which goes considerably beyond the possibility of an experimental check. Our observations cannot tell us anything about what the sequence of state of an actual isolated gas quantum would be over a very long period of time and whether it would satisfy the principle of determinacy. 

As soon as we include a microscope among the instruments of observation of the visible state, we discover the Brownian motion. For such a more precise visible state the principle of determinacy does not seem to hold any more. On the other hand, it has been shown that this phenomenon is surprisingly well suited to a statistical interpretation.147 

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