As a German I can assure you that both "a" in Ratte and Rathaus sound the same. The "a" in Rathaus is just spoken a bit longer and the following "t" is hardly pronounced, whereas the "a" in Ratte is spoken very short and the "t" is pronounced strongly. I hope that helps.
I.e., they have the same quality but different quantity, and German does distinguish vowels by length, so they are different sounds in the sense that two words that otherwise sound the same can be distinguished by vowel length. "Ratten" and "raten", for a relavent example, are not homophones and nor are "Massen" and "Maßen" (German learners might be frustrated to learn that in fact these two are opposites in some contexts).
A few remarks on methodology in linguistics (the science).
A phone is a class of sounds (as opposed to their instances which are all unique) that can be reliably described by articulatory or acoustic features (phonetics) or by patterns found in EEG (I'm thinking of MIT's voiceless mic).
A phoneme is another type of "sound" class used in linguistics and it is arguably the more important: phonemes, as studied in the context of a particular language, is the finite set of sounds (a few dozens at most) from which you build different words in that language. Phonemes always come in pairs, since they are defined as the minimal distinctive linguistic unit that can yield a difference in meaning.
Substitute /p/ with /f/ in/fear/ and you get /pear/, i.e. another word, a difference in meaning --> thus /p/ and /f/ are phonemes.
But substitute /r/ with /rrrrr/ in /Braveheart/ and you get the same word but with a scottish accent. These do not form a phonemic pair but allophonic variations of the same phoneme (here according to different geographic areas but they can also vary according to age, social status, gender, etc ...)
The two vowel lengths sound too different to me (native speaker) for this to really work. The difference is the difference between aː vs a in IPA. I'm struggling to find a similar vowel length example in English and Wikipedia only has examples with an Australian accent. :)
Yeah, it doesn't really exist in English. I'd even argue that the Australian pronunciation doesn't change the vowel length as much as it adds a chain shift [1] (similar to the Canadian/Algonquin "ou" pronunciation).
It's one of the most difficult things to pick up when learning Japanese as well. There are lots of words that are basically homophones except for vowel length and tone. To an English speaker they tend to sound identical, but to a Japanese speaker if you get it wrong the result is unintelligible. For example "地図" (in romaji: chizu and pronounce cheezu with a short "ee") is "map" and "チーズ" (in romaji: chiizu and pronounced cheezu with a long "ee") is "cheese" (though they have the same tones... I'm struggling to think of an example with different tones as well as vowel length).
The thing that helped me the most for this was singing songs. Once you understand that there is a necessary rhythm to the words, it makes it much easier to use that rhythm in speaking. Or at least it did for me -- YMMV.
Even if it's not really a vowel length change in Australian English, I'm pretty confident it is in South African English (as spoken by me and many others). Ferry/fairy are distinguished by vowel length only.
