Ice Cubes and Hot Water Bottles

Abstract

Can the arrow of time we seem to perceive be explained by an overall increase in entropy? Several models suggest that the one macroscopic arrow of time which is associated with an overall increase in entropy may be identical to the arrows of time which are subject to our empirical knowledge. These models turn out to be difficult to maintain if one considers a freeze-frame picture (or one containing a minimal period of time) of nested systems of decreasing and increasing entropy. An observer who determines an arrow of time by measuring an increase or decrease in entropy must obviously be located somewhere. This observer position is in no case arbitrary — the individual situation of the observer determines, in each case, the outcome of the measurement. A fractal model suggests that the direction-generating agent is not to be found in a system's increase in entropy, but rather in the choice of the observer's position. A thought experiment involving infinitely nested ice cubes and hot water bottles leads to the conclusion that for such freeze-frames involving a minimal time span, the concepts of isolated and open systems (which otherwise are indispensable concepts for the discussion of entropy) are unsuitable. If one considers observers placed within different nested levels of the ice cube and hot water bottle universe, it will be impossible for these observers to determine whether the embedding systems add up to a total increase or decrease of entropy: we will never know whether the "outermost embedding nest" is an ice 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 observer capable of monitoring the system as a whole. A fractal nested model suggests that there are nested arrows of time with differing directions. What direction we experience depends, in each case, entirely on the observer position chosen, i.e., the system we participate in. The only way to find out which arrow of time we are experiencing at the moment, 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. The arrow of time defined by an overall increase in entropy is not congruent with the arrows of time of our empirical knowledge.