WI: Alexander the Great killed at the Battle of the Granicus?

In OTL, Clitus the Black saved Alexander the Great from a certain death at the hands of Spithridates. What if he had failed? With Macedonia without a sucessor, the empire he had built probably would have fallen. With a longer-lived Achaemenid dynasty, how would the conversion of India to Buddhism have impacted a Zoroastrian Persia? Frex, Menander the Hellenistic King according to Wiki was one of Buddhism's greatest benefactors. Would a Zoroastrian king have been so tolerant? How does the abscence of Greco-Buddhism impact Buddhist art and the emerging Mahayana sects? How, also, would history differ in India and Palestine and Egypt? Would Judaism have developed in a different way without (presumably) the Hasmoneans and a Roman conquest? Would the Roman Empire and Christianity (and therefore Islam, as well) be completely butterflied away? Or, would an increasingly powerful Roman Republic have warred upon a future descendant of the Achaemenid dynasty and thereby sparked an early version of the Byzantine-Persian wars? Would European culture itself be radically, or only moderately different without such a unifying figure? After all, Alexander the Great is arguably to the West what Shi Huangdi was to the East. How would a longer-lived Achaemenid Empire have reacted to the Chinese, if it survived that long? Also, one more thing....

When the Achaemenid empire finally falls, what replaces it?

Discuss.
 
If there is a Christianity, (or equivalent) then it is certainly going to be of a far different flavour than OTL. Without Greek as a lingua franca and the strength of Greek philosophy, Christianity is going to be quite intensely effected.

Of course, that's just a selection. Really, this would have such a massive change on political/religious events, you can come up with practically anything really.
 
I can't really see the Achaemenid Empire survive all that much longer even if you remove Alexander. It's still weak internally. The Parthians
will come knocking sooner or later.
 
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