During the Tang dynasty, China expanded further west then at any other point in ancient Chinese history. How much further could it have expanded? Let's say it's westward expansion wasn't checked by the Abbasid Caliphate at the Battle of Talas, how much further west could the Chinese have expanded? What would the cultural and politic effects of a larger Tang China be?
China essentially managed to reach its limits IOTL under the Tang due to its system of efficiently incorporating generals from territories that it had captured while maintaining a balance of power with regional states. For example, the Tang army at the Battle of Talas was led by Gao Xianzhi (Go Seonji), who was of Goguryeo descent, and he managed to conquer extensive tracks of territory within Central Asia that are still considered to be some of the most inhospitable places in the world. Managing to trek through these regions would have been difficult enough, but he also succeeded in sieging and taking over a significant amount of fortresses in the process, which was no small feat. As a result, Talas generally reflected the Abbasid Caliphate and the Tang Dynasty's furthest expansions, so a different outcome probably wouldn't have made a significant difference in the long run.
However, this system also backfired due to the fact that numerous regional generals were assigned to control large amounts of territory with significant armies, which greatly increased the potential of political instability over time. An Lushan, who is the most well-known, was a Sogdian/Tujue general who already had command of well over 100,000 troops within Central Asia about a decade before the rebellion, and was highly regarded by the Tang emperor at the time, but decided to revolt and planned to conquer Chang'an due to complicated political tensions involving the court. He was far from the only autonomous general at the time, though. For another example, Li Zhengji (Yi Jeonggi), was another general of Goguryeo descent who eventually controlled more than 100,000 troops, many of whom were also ethnically Korean, within Shandong by 765, when the soldiers revolted, despite the fact that the An Lushan Rebellion had only been laboriously suppressed two years earlier. His descendants also continued to control Shandong until 819 despite the fact that there was a possibility that any remaining autonomous regions still had the potential to instigate internal turmoil in a similar manner as the An Shi Rebellion.
If Tang China still undergoes the An Lushan rebellion four years later, Central Asia will still be completely lost. And An Lushan is not the only independence-minded general there is either, so another rebellion by another man is always possible. Note that a win at Talas won't eliminate other threats to the Tang in Central Asia, namely the Tibetan and Uyghur Empires, so there's always the possibility that Arab domination over the region is replaced with the influence of another non-Chinese state.
I'm of the opinion that avoiding the An Lushan rebellion won't necessarily allow Tang China to control Central Asia, but it's the first question to be asked in a scenario like this.
Agreed here, given the fact that the Battle of Talas and the An Shi Rebellion were only two of numerous chaotic conflicts during the mid-8th century.
There were other Tang generals apart from An Lushan who also controlled significant portions of Central Asia, so they also present alternate possibilities.
Given that Central Asia was a bad neighborhood at the time, as the last poster implied, the T'ang were probably at their limits and unsustainable limits at that. The earlier Han were just as well positioned and bogged down after reaching similar limits. The T'ang western armies were using large amounts of Turkic mercenaries that proved to be unreliable, biting them in the butt at Talas.
This too.
If the T'ang had been so inclined, the T'ang could likely have used the Sung-hwa (Sungari, Heilongkiang (Amur ) and Wu Su Li (Ussuri) Rivers as supply lines for conquering Manchuria, Nu-er Khan (Russian Far East) and then west up the Heilongkiang (Amur River) to conquer and sinicize the GoTurk.
Hardly. Regardless of the fact that this doesn't address the OP, which specifically asked for a
western expansion after the Battle of Talas, this scenario would be virtually impossible given the conditions at the time. Goguryeo, which had continued to hold out for 70 years prior (and was a major factor in the Sui's collapse), was finally conquered in 668, but the complex system of alliances among the Yemaek (which had been the ethnic majority within Goguryeo), Mohe/Malgal (of which some were probably Yemaek tribes, given their locations), Xianbei/Khitan, and Tujue, continued to be maintained. As a result, they revolted in 696 by taking advantage of disturbances among the Khitan due to their constant suppression, and established the Jin (changed to Balhae in 718) after defeating the Tang at the Battle of Cheonmun-ryeong (Tianmenling) in 698. Within a few decades, Balhae rapidly expanded to cover most of Goguryeo's former possessions, meaning that by 751, Manchuria had no longer been under Tang's control for about 30-40 years or so.
An alliance with Silla in order to attack Balhae would also be out of the question by the mid-8th century, given that Silla deliberately severed all diplomatic ties with the Tang for about 50 years after the Silla-Tang War (670-6), and although it eventually reestablished ties with its former enemy around 730 in response to Balhae's growing influence, a combined campaign into Manchuria in 732 ended in failure due to inclement weather. In addition, Silla eventually established stable diplomatic relations with Balhae by the mid-8th century mostly due to a shared cultural bond, along with facilitating trading relations in order to extend trade routes, some of which extended into Central Asia and Japan.