ICE CUBES AND HOT-WATER BOTTLES

Can the arrow of time we seem to perceive be explained by an overall i ncrease in entropy? Several models suggest that the one macroscopic ar row of time which is associated with an overall increase in entropy ma y be identical to the arrows of time which are subject to our empirica l knowledge. These models turn out to be difficult to maintain if one considers a freeze-frame picture (or one containing a minimal period o f time) of nested systems of decreasing and increasing entropy. An obs erver who determines an arrow of time by measuring an increase or decr ease in entropy must obviously be located somewhere. This observer pos ition is in no case arbitrary-the individual situation of the observer determines, in each case, the outcome of the measurement. A fractal m odel suggests that the direction-generating agent is not to be found i n a system's increase in entropy, but rather in the choice of the obse rver's position. A thought experiment involving infinitely nested ice cubes and hot water bottles leads to the conclusion that for such free ze-frames involving a minimal time span, the concepts of isolated and open systems (which otherwise are indispensable concepts for the discu ssion of entropy) are unsuitable. If one considers observers placed wi thin different nested levels of the ice cube and hot water bottle univ erse, it will be impossible for these observers to determine whether t he embedding systems add up to a total increase or decrease of entropy : we will never know whether the ''outermost embedding nest'' is an ic e cube or a hot water bottle. An identification of the arrows of time which are subject to our empirical knowledge with an overall increase in entropy would not be plausible since there is no conceivable observ er capable of monitoring the system as a whole. A fractal nested model suggests that there are nested arrows of time with differing directio ns. What direction we experience depends, in each case, entirely on th e observer position chosen, i.e., the system we participate in. The on ly way to find out which arrow of time we are experiencing at the mome nt, say, in an ice cube, is to make contact with an observer in a hot water bottle-either with an observer in the hot water bottle embedding my ice cube or with one in the hot water bottle nested in my ice cube . The question: ''Is there a way out?'' must be discussed elsewhere. T he arrow of time defined by an overall increase in entropy is not cong ruent with the arrows of time of our empirical knowledge.