Edited to replace the word "measure" with a better concept.
間
refers to the time space between two points; speaker feels he has the ability to determine a start and end point at the moment of making the statement. (間 has explicit time boundary)
内
however refers to "time space within"; for when it is difficult for the speaker to determine a start and end point. It refers to the general time during which an event/state is occuring. (No explicit time boundary for 内)
That is why it seems strange to say (though not totally unacceptable)[1]:
雨が降らない間にテニスをする。
But is okay to say:
雨が降らない内にテニスをする。
Because one cannot assess the start and end point of the duration within "not rain"
In your example 先生が見てない(間に/内に)逃げよう
, the time during "teacher is not looking" isn't a predictable or planned event (No explicit time boundary). Therefore 内に
would be more appropriate for your example sentence.
Edited: To try to explain the apparent contradiction with Tsuyoshi's example using 晴れている
:
晴れている[○間に][○うちに]作業を終わらせよう。
Versus,
雨が降らない[×間に][○うちに]作業を終わらせよう。
It should have something to do with the speaker's expectation of future circumstances:
The speaker takes the default standpoint of "clear weather" as a default weather.
We normally do not worry "when the duration of [clear weather]
ends". But rather we would think in the manner of "when does [other weather]
begin?". It becomes unimportant to assess a start and end point for a default standpoint. Since it's a default standpoint, both 間 and 内 can be used and will not sound unnatural or not smooth.
For [other weather]
there is a start and end point, but the speaker expects [other weather]
(e.g. rainy) to behave in a way that he cannot determine a start and end point for it.
Now for the case of "teacher is not looking"
, the speaker takes the default standpoint of "teacher is always paying attention"
because that is how he would expect the teacher to behave. The alternative: duration of "teacher is not looking"
becomes hard for the speaker to determine a start and end point.
References:
- [1] Makino, S., & Tsutsui, M. (2010). A dictionary of basic Japanese grammar. pg. 512-515 entry for uchi ni