My first German professor (a native German) told the class that an umlaut could be written as a line when writing by hand. However, my current German (a non native) professor strongly says otherwise.
That is, can ü be written as ū (only if handwritten)?
I couldn’t find anything online about it, but I’ve become quite used to writing it with a line … Hence I would like to see a second opinion before attempting to break a habit.
Ü/ü should not be written as Ū/ū in handwritten documents.
The 'ū' used to be the distinction between 'n' and 'u' in handwriting because they look very similar. It was a part of the 'Sütterlinschrift' as you can see here.
Some people do this, but that doesn't mean it's correct. It is just sloppy writing and (maybe) a remnant from "Sütterlin" that distinguished the "n" from the "u" that way, and thus has no relationship to umlauts.
Old handwriting (other than "Sütterlin") also allowed to write double consonants "nn" and "mm" as a single one with an added vertical bar on top (that's called Geminationsstrich). This habit is no longer in use today and would also be considered "wrong"
Note what kids learn in school today as two dots used to be (officially taught) two upward strokes until some decades ago. The reason this was done was apparently that you couldn't create proper dots on a slate that was used to teach writing until maybe 80 years ago.
nn as n̅ and u looked like n̅, how did you see the difference between nn and u?
I'd say it can be written this way. Not that it is taught to be written so, or even encouraged, but everyone who reads it will understand what is meant. I do not believe this is a remnant from the Kurrent or Sütterlin, because there a bowed line denoted something completely different, as has already been pointed out.Two short vertical lines or even a wavy line denoted the Umlaut. Also these older scripts are not intelligeble to most younger persons, not even in German speaking areas. This question isn't really limited to the German language, and might even be off topic because of that, since exactly the same diacritic signs with the same function are found in many other languages. The line, (curved, wavy or straight) is a very common way of writing these signs in other languages using these. In Swedish we were taught to write the dots as a curved line in cursive. https://sv.wikipedia.org/wiki/Skrivstil#/media/File:Svssfb.jpg (Nowadays cursive handwiting isn't even taught anymore.) The same goes for Danish and Norwegian. I therefore think it might have more to do with a common trait than with a supposed link to older ways of writing. The fact that writing this way in German could cause a confusion, because of the old n/u distinction function, might make it less approprate though.
I suggest that the premise of this question is somewhat incorrect. The umlaut dots cannot be written as a single line, but a single line is well what might end up on paper when writing quickly.
The faster you write, the higher becomes the chance you might just not sufficiently lift up the pen from the paper while moving between two points that are supposed to be disconnected in theory. That is why in most types of "Schreibschrift", more or less all letters are joined and reshaped in such a way that large parts of words can be written without lifting the pen up from the paper.
In order to write an umlaut, the writer has to place two dots right next to each other in short succession. Some writers might not lift up the pen sufficiently to avoid leaving a line between the points, and some may have stopped bothering altogether and just move from the left dot to the right dot without even attempting to lift the pen. (Note that we are talking about movements that take less than 10ths of seconds.)
To respond to your question: The umlaut dots cannot be substituted with the macron diacritic, but as German does not use a macron (and the few words that use an acute accent can be recognized from context), there is no danger for dots that look like a straight line to be misread as anything else. Or, as the difference here is quite subtle: If you ask a person whose handwriting features umlaut dots that look like a horizontal line to write very slowly, those dots should morph back to separate dots.
By the way, the same applies for a squiggly line: In handwriting, the umlaut dots are often written like a double acute accent instead of dots (again, because getting those two little right is easier for some people than getting two dots right when writing fast). If the writer does not properly lift the pen between the two "acute accents", the result is obviously a squiggly line.
Handwriting is very much a personal thing. Depending on when (in which decade) you learnt it, how careful you are, how generally clean it is and what general style you follow, the same word can look very different in different handwritings.
The only way to typeset umlauts in printed antiqua texts is with the umlaut diacritic ¨. But handwriting is never as strict as printing.
Among the many ways handwriting signifies umlauts, there are two arguably most common ways: either two dots (as in printing) or a double vertical line (||). Abstraction from the double dot may lead to accidental joining of the dots which may lead to future purposefully joining the double dot into a horizontal line. This is in no way more or less correct than any other method, as long as it is unambiguous with respect to the person writing it.
That last sentence is needed. As others have mentioned, a horizontal line is used in Sütterlin handwriting (and probably other types of Kurrent, too) to signify a double m or n. It is distinct from the brevis, which is used to differentiate between u and n whose shapes would otherwise be identical. Hence, Sütterlin writers typically use a double vertical line to signify umlauts. When using today’s handwriting, the difference between n and u is typically clear enough that no further brevis is needed and thus anything above the line is regarded as an umlaut.
Care should be taken when mixing German and e.g. French or Spanish words in handwriting. In these languages which employ acute accents, a horizontal line above a letter is typically interpreted by a reading German as an acute accent which may lead to confusion.
