Is it true that in America people pronounce the double t as d?
- Bottle as [bodl]?
- Hotter as [hoder] with a short er?
- Better as [beder] with a short er?
This is known as flapping (or tapping), and it is done in some words that have double t, but not all of them. It's also done in some words that only have a single t (like water and beautiful), and between some words, (like "what a").
The rule, according to Wiktionary, is:
American English has a sound change known as intervocalic alveolar flapping, in which /t d/ are both pronounced as an alveolar flap [ɾ] between vowels or liquids and when not at the beginning of a stressed syllable
Wikipedia clarifies that last point:
It does not occur, in most dialects, if the /t/ or /d/ immediately precedes a stressed vowel, as in attack [əˈtʰæk]
In IPA, /d/ or /ɾ/ may be used, depending on the word:
Does this make some words (with d vs. t) sound the same? Yes, but not always. For me (a native AmE speaker), latter and ladder sound exactly the same, while there seems to be a big difference between the words writer and rider (which have identical IPA: /ˈraɪdər/). The i in rider is slightly longer, as this blog says:
As it happens, in many North American dialects (including mine), the vowel before original (underlying) /d/ is slightly longer phonetically than original /t/. Thus the vowel of “toy Y[o:D]a” is slightly, but perceptibly longer than “Toy[oD]a” in many dialects of American English.
A Linguist in the Wild - Flap Minimal Pairs
(There's an interesting story behind the Toyota vs. toy Yoda example, BTW.)
This may be a difference between articulation and perception (that is, you know you're saying it differently, but nobody hears a difference). Research indicates that while the one vowel is "slightly longer", it may not be enough for anyone to distinguish between the two forms:
The researchers used 4 pairs of words, where a pair consisted of two identical surface representations, with one underlying /t/ and one underlying /d/ phoneme. The word pairs in question are: leader–liter, wedding–wetting, tida–title and madder–matter.
Their results have shown that native speakers are unable to identify acoustically for certain whether a sound in a given word is a flapped /t/ or a flapped /d/ — the pattern they have found is that the participants relied heavily on a d-bias (test subjects identified more /d/’s correctly than /t/’s and therefore, when in doubt, listeners were more likely to choose /d/).
Flapping in American English: A Theoretical Approach
It's really easy to find resources once you know what it's called. Here are some I found: