Muhammad had physical relation with immature Aisha

Aisha was immature girl when Muhammad had consummated the marriage (i.e. had sex) with her.

I'm going to prove this by refering to a Hadith from Sahih (authentic) Bukhari.

Sahih Bukari, book 48, hadith number 829 is a long hadith. This hadith describes the missing necklace incident which happened approximately 5 A.H. Same incident also described in hadith number 805 of the same book. I'm going to quote just the relevant part of it:

...'Ali bin Abu Talib said, 'O Allah's Apostle! Allah has no imposed restrictions on you, and there are many women other than she, yet you may ask the woman- servant who will tell you the truth.' On that Allah's Apostle called Buraira and said, 'O Burair. Did you ever see anything which roused your suspicions about her?' Buraira said, 'No, by Allah Who has sent you with the Truth, I have never seen in her anything faulty except that she is a girl of immature age, who sometimes sleeps and leaves the dough for the goats to eat.'

Burayra explicitly states that Aisha was a girl of immature age, and further notes that Aisha was neglectful, forgetful and naïve when it came to her chores, falling asleep and letting animals run amuck. She was still described well after her marriage as a young, neglectful, forgetful, naïve girl of immature age who was "too simple-minded to deceive her husband". Far from a psychosocially mature adult, Aisha is described post-consummation as a psychologically immature girl.

[note: Muhammad's migration to the city of Yathrib (from Mecca to Medina) is an event known as the Hijrah. After that, muhammad had a mosque built, after which he consummated his marriage with Aisha. According to biography Muhammad (.pdf) written by Martin Lings, the consummation occurred two months subsequent to the completion of the mosque, which means that any mention of the mosque in Islamic holy literature is de facto set (chronologically speaking) either immediately (up to two months) before the consummation occurred, or some time after it. Various islamic sources set the date of consummation withing two years after Hijrah.]

In this Hadith the original arabic words that are used for girl of immature age, as: ﺍﻟﺠَْﺎﺭﻳَِﺔِ ﺍﻟْﺤﺪَِﻳﺜﺔﺍﻟﺴﻦَِ ِِّّ
(jariyathil hadeethaathil sanna). In Arabic, the phrase “jariyathil hadeethaathil sanna” literally means “pre-pubertal girl of new/recent/young age”.

The word ﺟﺎﺭﻳﺔ (jariya) has several meanings. It means a pre- pubertal girl, a young woman, a singer, slave girl/woman, concubine, or maid and even an old woman. During that time Aisha was a wife of Muhammad so, only one can fit Aisha which is pre-pubertal immature girl.
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Explanation of ﺟﺎﺭﻳﺔ ‎: If the text is indeed historic the term would generally mean just "girl", she may or may not be a servant or a slave but that is not what the term indicates. In historic texts, such as in Hadeeths, it means a girl before the age of maturity. Slave was referred to as (Amma) ﺃﻣﺔ, and servant as ﻣﻮﻻﻩ (mawllah). If your text is religious and ancient, you'll have not to confuse between these terms, because some hadeeths are interpreted incorrectly because of that confusion such as the hadeeth of the insane girl that took the prophet (pbuh) by hand, she is referred to as "ﺟﺎﺭﻳﺔ ﺧﺮﻗﺎﺀ" which actually means a little girl and not a mature bondswoman, that's why the prophet (Pbuh) allowed her to hold his hand. (source).

The word Jariya always comes with the notion of some kind of restriction. In case of a female if she is immature (mentally and physically). In case of an adult female if she is a slave (therefore has limited rights) and in case of old female who can not do things or move around because of her old age. See also lane's lexicon.

Therefore, the word Jariya in Aisha's case means a girl who is immature i.e. a child.