Return to Question

Everybody has observed that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than an half hour. What is the fundamental reason for this?

And there are many other natural systems that change extremely rapidly. Even in rock climbing, for example, if you have placed the feet on a hold, they may slip off in a fraction of a second in case of improper foot placement. Wahat are the reasons for ultra-rapid changes in time, i.e. that for a (field) quantity $X(t)$, the value

$$S_X(t) := \lim_{\epsilon \rightarrow 0} (X(t+\epsilon)-X(t))$$

does not tend to zero?

Everybody has observed that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than half hour. What is the fundamental reason for this?

And there are many other natural systems that change extremely rapidly. Even in rock climbing, for example, if you have placed the feet on a hold, they may slip off in a fraction of a second in case of improper foot placement. What are the reasons for ultra-rapid changes in time, i.e. that for a (field) quantity $X(t)$, the value

$$S_X(t) := \lim_{\epsilon \rightarrow 0} (X(t+\epsilon)-X(t))$$

does not tend to zero?

Everybody has observed, that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than an half hour. What is the fundamental reason for this?

And there are many other natural systems that change extremely rapidly. Even in rock climbing if you have placed the feet on a hold, they may slip off in a fraction of a section in case of improper foot placement. Wahat are the reasons for ultra-rapid changes in time, i.e. that for a (field) quantity $X(t)$, the value

$S_X(t) := \lim_{\epsilon \rightarrow 0} (X(t+\epsilon)-X(t))$

does not tend to zero?

Everybody has observed that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than an half hour. What is the fundamental reason for this?

And there are many other natural systems that change extremely rapidly. Even in rock climbing, for example, if you have placed the feet on a hold, they may slip off in a fraction of a second in case of improper foot placement. Wahat are the reasons for ultra-rapid changes in time, i.e. that for a (field) quantity $X(t)$, the value

$$S_X(t) := \lim_{\epsilon \rightarrow 0} (X(t+\epsilon)-X(t))$$

does not tend to zero?