I apologize for being snippy and rude, because I certainly was (especially in the initial version of my post), but you triggered one of my pet peeves. And I'm not wrong.
There are some words where the long/short contrast is neutralized, and
arigatô is in fact one of them. One often hears it pronounced with a short (or even "clipped") o; for those desiring more accurate phonetic descriptions (as I always do) the latter is a short vowel followed by a glottal stop. Another word of this type is
sayônara (hiragana
sa-yo-u-na-ra), which can be pronounced and written as
sayonara (hiragana
sa-yo-na-ra);
Kenkyusha's New Japanese-English Dictionary (the "Green Goddess") lists both. If every o in Japanese is long, as you claim, why does this dictionary differentiate between short o and long o?
Here's an example of long o vs. short o that is NOT negligible. The surname Ono (hiragana
o-no) has a short o and means "small field", whereas the surname Ôno (hiragana
o-o-no) has a long o and means "LARGE field". The latter is often romanized as "Ohno" to make this distinction clear.
To quote the Wikipedia article on
Japanese phonology: "Vowels have a phonemic length contrast (i.e. short vs. long). Compare contrasting pairs of words like
ojisan /ozisaN/ 'uncle' vs.
ojiisan /oziisaN/ 'grandfather', or
tsuki /tuki/ 'moon' vs.
tsûki /tuuki/ 'airflow'." (In the interest of full disclosure, I changed the macron on the long "u" to a circumflex in this quote, so that this forum could process it.)
I welcome you to PROVE me wrong. Duration of residency in Japan is not sufficient. I've heard of more than a few Anglophone expats in Japan who never bothered to learn the language. To give an example known to me personally, my uncle was stationed at Yokosuka for two years when he was in the Navy, and his wife and kids never left the base. I wouldn't trust anything they said about the Japanese language without outside corroboration.