SCENARIO WHERE MUSLIMS ARE DEFEATED.
It is clear that the western Conquests of Justinian did not bring prosperity and overal good for the Empire. The only thing Justinian and Belisarius achieved was the exchaustion of the East and the a slaughter in the West.
BUT, if Justinian instead of following the Roman dream West, went to full scale war with Sassanid Persia and subsequently conquered it, then his empire would have becomed unchecked and his borders as safe as they were during early Roman Expansion.
If Byzantium conquered Persia during the Justinian age then the Muslims would have no chance against the full might of the imperial armies. It would be a hard fight, but at the end it would have concluded to the extinction of the Muslim Arabs.
Persia plauged Byzantium for centuries after Justinian, lowered population and economical growth, it was a true sickness for the empire.
The only reason why the Arabs managed to spread so fast and conquer so many territories so fast was because of the weakness of both Persian and Roman empires after the Romano-Persian war of Heraclius.
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SOME THINGS ABOUT THE EASTERN ROMAN EMPIRE.
It is clear that Eastern Roman ways of dealing with a threat was very diferent than the ways than the Western Roman ways.
A typical classical Roman goverment during the classical ages, if it became threatened by another nation, it mobilized huge armies and crushed it to the ground without any economical considerations. The Eastern Roman Empire though because of all its wealth, became accustomed into bribing its enemies most of the time in order to delay devastation. What the Eastern Roman Empire did though wasnt protecting its people, but delaying the inevitable and strengthening the enemy's resolve and power. If the Eastern Roman Empire has Western way of dealing with threats then Persia would have been conquered in a second, along with most of Eastern Europe, instead of bribing and playing it defencive.