Steven Pinker in "The Language Instinct" claims that there is strong psychological evidence for the existence of a sharp age cutoff for the ability to acquire a flawless foreign accent (I may dig up the exact reference, if needed). In other words, there is a fairly narrow age threshold (around 20-odd years) below which exposure to a foreign accent is more or less sufficient to acquire it and above which it's physiologically impossible. Has this phenomenon been confirmed or refuted by any systematic study?
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One of the reasons the feral children data are difficult to assess is that the brains of these children are often underdeveloped or have developed differently because they weren't stimulated with language at a young age. (For a more scientific explanation of the how of this, see Curtiss et al 544-545+.) As I mentioned in my comment to Askalon, while that data supports the idea that there is a critical period for acquiring a faculty for language, it doesn't say much about what factors influence how successful you will be in acquiring native-like competence in a second language. Although age is often speculated to be a factor in acquiring native competence, estimates on the cutoff have ranged from as low as 3-4 to as high as puberty.
Infant Studies of Phoneme Perception
Even very young children show decreased sensitivity to contrasts not present in their native language. For example, Hindi has many contrasts that English doesn't, for example differentiating aspirated and unaspirated stops like [pʰal] and [pal]. Werker and Tees (1984) trained infants to expect a reward (a little puppet show) when they heard aspirated syllables (this is called a conditioned head turn technique). Then, they tested them, playing aspirated and unaspirated stops and measuring how often the infants turned at the appropriate times. If they failed to turn after hearing an aspirated stop, this was counted as a miss, and if they turned after hearing an unaspirated sound, this was counted as a false alarm. At 6-8 months, infants scored well -- they had fewer than 2/10 misses or false alarms -- while those in the 10-12 month group did remarkably poorly -- approximately only 2/10 correct hits. I cannot find the citation, but I have heard vocalic categories are cemented even earlier. And keep in mind that this is before these infants are even babbling!
Immigrant and Foreign Language Learner Studies
Native "accent acquisition" means successful acquisition of the language's phonology (i.e. the system of sounds in a language). The cutoff you're referring to is the critical period hypothesis, which claims that there's a critical period (from birth up to around 7-ish or puberty, give or take) during which a person is capable of acquiring a language and achieving native-like competence, but after this critical period it becomes very difficult or impossible to achieve fully native-like competence. It's thought that there isn't one single cutoff point though, but rather that it varies depending on what part of language you're talking about: phonology is thought to have the earliest cutoff age, while syntax is thought to have the latest (it's much more common to see non-native speakers with excellent syntax but errors in their phonology than vice versa). The phonology is therefore most often the place where unsuccessful native-like acquisition most often manifests itself, in the form of a non-native accent.
So to get to your question about evidence for this. There is some evidence, but it's limited, and some of the proposed evidence has been criticized as not valid. There are some cases of feral or deaf children/adults who grew up without a language (surpassing at least part of the critical period before they were discovered). These people are often used as evidence that the difficulty with successfully acquiring a language (including phonology) is biologically linked to age. It's rather clear that normal adults have trouble acquiring a new language and gaining native-like competence as well, but one could claim that that's perhaps because of interference caused by the language they already know. With feral or non-lingual deaf people though, they don't know any language (so there's clearly no interference from a native language), so some linguists claim that their lack of or limited success in acquiring a language must be linked to their age.
A frequently mentioned case is that of Genie, a girl that was brought up in isolation by abusive parents and never learned a language as a child. She was found at age 13, after which a linguist worked with her and she started to learn English. She was never able to learn English beyond a rudimentary level. Studies with deaf children who started learning a sign language later in their childhood (and having never learned the spoken language of their parents) have also shown a correlation with age and the level of their success in their acquisition of the language.
Some of this evidence has been criticized. For example, feral children such as Genie have also obviously suffered traumatic experiences that have affected them psychologically, which could be a factor in their unsuccessful language acquisition. Cases of late learners of sign language provide better evidence because they were generally well cared for, despite lacking a language.
I believe that the existance of a cut off period is imposible to measure due to the large number of factors affecting language accuisition. As an English language teacher and a person who has very near native competence in a foreign language, I believe that older people are less likely to achieve native competence in pronunciation because to mimick a native accent perfectly, in the majority of cases, would necessitate presenting oneself as having a different identity to that you have been raised with.
Children are less concerned about changing their identity than adults are and will more willingly mimick a native accent.
That is why they aquire native pronunciation much more efficiently - and the same is true for adults who are not shy or ashamed to assume a different identity - they also master foreign accents.
Purely anecdotally: We live in Taiwan and my son learned Chinese from age 4. Today, he is often told that if he speaks over the phone, it cannot be determined that he is not Chinese. Even the very best of adult-learner speakers of Chinese I know, even when 100% fluent, cannot shake the accent/inflection that marks them as "non-native".
The origin of accent
When a child begins to speak, he/she sets its articulatory base on that of the people surrounding him/her. Different languages have different normal movements of the parts of articulatory base in the time of talking. For that reason the speech effect in the vocal tract is different. When the tissues there are still young and yield to speech actions, permanent changes take place on the pharynx wall. A mechanical speech apparatus is formed in the vocal tract, which is serviceable until the death of the owner. After a certain critical period all new acquired languages are spoken with that instrument. As the native language has a limited number of sounds and their characteristics are only for that language, all the others are pronounced incorrectly.
A person can have more than one talking instrument in his/her vocal tract - for instance, when a child is born in a bilingual family.
For comparison: a person has a melody in his/her head and he/she can make it audible with the help of musical instruments, whereas each of them has its own "accent". But the melody can be right with all instruments.
Why phoneticians do not want to admit that they have no idea about the origin of accent?