Switch the histories of East and West Rome. Have the Western Empire rule onward for centuries while the East descends into chaos and war before stabilizing far down the line.
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I'd suggest an early incredible victory for the Sassanids that collapses during an intermediate period. Perhaps replace Bahram IV with an effective and aggressive ruler.
Forgive me for the diner-napkin approach to this.
Early Shananshah takes Egypt and Anatolia from the East, killing Arcadius after capturing him in a battle. This shock victory shocks the Empire, leading to huge numbers of Romans fleeing or actively relocating to Greece, Italia and Africa from Anatolia and the newly Persia territories.
That's pretty awesome for something you call a "diner-napkin approach".
The only question that nags at me in this context is what you write about Egypt. If huge amounts of coin continue to flow out of the Empire, that will still cause major economic troubles down the line. I know insights on this vary, but I find the idea that this strutural outflow of gold was one of the causes of Rome's economic troubles to be very plausible.
Of course, you mention Rome expanding northwards as they develop the required farming equipment. Presumably you mean the heavy plough. If that's the case, eventually northern European regions within imperial control can replace foreign Egypt as the major source for food production. I'm just not sure it can do that before the Romans run into major trouble that might cause a western collape after all. (Not merely because of the outflow of gold, but because historically, Roman responses to the problems made things worse. If you tend to react to the deficit by decreasing the gold amount per coin and also raising taxes... things will only get worse. That's what the Romans did, and barring a sudden development of ATL economic theory, I don't see that going otherwise here.)
Of course... if in addition to your scenario, one also indtroduces some kind of "Greek revolt" whereby Greece goes independent as well, that actually helps. The east (including Greece) was far more densely populated than the west. If you presume that many imperial loyalists from the east migrate west to take on the strengthening role you describe, but Greece itself (later) goes independent, then Rome will ultimately have far fewer mouths to feed. Therefore, less need for food imports from Egypt, and less drain of gold. That way, Rome might just avoid the major economic problems until it can get its own heavy plough-facilitated agriculture going in Gaul etc. -- which would then forestall the orginial cause of the economic problems altogether.
Also, dropping Greece brings the scenario closer to the OP's idea of "the west" staying Imperial, while "the east" falls apart. If you add some major wars between various eastern states (not inconceivable), I'd say we're there.
What about the Huns? Wouldn't they still have attacked the area around the end of the fourth century, and been a problem for the Persians?
This is really interesting, I would love to see a more fleshed out version of this timeline.I'd suggest an early incredible victory for the Sassanids that collapses during an intermediate period. Perhaps replace Bahram IV with an effective and aggressive ruler.
Forgive me for the diner-napkin approach to this.
Early Shananshah takes Egypt and Anatolia from the East, killing Arcadius after capturing him in a battle. This shock victory shocks the Empire, leading to huge numbers of Romans fleeing or actively relocating to Greece, Italia and Africa from Anatolia and the newly Persia territories.
This leads to the establishment of new settlements and cities to prevent overcrowding and riots in the Empire. The Roman Empire reverts to the Dominate System under Honorius - who suddenly has the remaining forces of the East (based in Greece) directly reporting to him, rather than Stilcho. Constantinople is the Bulwark of the East rather than "City of the Worlds Desire" ITTL.
Greece, Africa and the various refugees from the East help build up an arm of the military that is loyal to the Empire, which operates in the East out of Constantinople, Illyricum, and Treverorum in Gaul, purely imperial forces to help wrestle the West into line.
These forces allow the beginning of a slow process of de-Germanification of the Army, and a Romanisation of the Foederati peoples.
Meanwhile, Constantinople, backed by Roman and Foederati troops is the bulwark that protects Europa from Asia. In the early years the various Anatolian territories do break away from Persia (as does Egypt and the Levant), with the overstretched Sassanids losing control over their empire piece by piece until they only rule Mesopotamia, forced to build alliances to protect their rich territory from invasion by the Persians of the Iranian Plateau, and later tribes that invade via that route. (i.e. White Huns, etc). Repeated invasions as per OTL cause chaos in the region, alongside smaller invasions by Arabs - who don't NEED to unite to expand because of the fragmented nature of the East. Why doesn't the West re-invade? Because the reforms needed in the Roman Empire take forever, and their resources are tied up in the navy, defence, and trying to free up resources in Gaul, Germania and Pannonia.
An optimistic scenario is that a combination of Anatolian-Greek,Egyptian,Arab and Iranian alliances/kingdoms reign over parts of the Middle east, with the occasional inclusion of invaders from central asia mixing things up. The Roman Empire pushes north as they develop the required farming equipment. Egypt is a prominent power that dominates trade and sells huge quantities of food to the Empire (Essentially taking huge amounts of coin from the Empire like India did IOTL).