When one great civilization declines, it seems to be replaced by a new power in the northwest. Ancient Egypt is followed by Ancient Greece, which is conquered by Rome. The first non-Roman emperor is Charlemagne in Francia. Later, the Netherlands to the north and Great-Britain to the northwest become rich and powerful. The foremost power in the 20th century is the US, even further west, and it might be followed first by Japan and then China: west, west.
I'm interested in long term economic history so I wonder whether there is some kind of overarching theory for this movement to the northwest. Climate change? Or maybe more advanced societies need resources that are more abundant in northern regions.
Because you're ignoring Asia and were taught a very Eurocentric version of history?
I mean, this is a very conventional "Western Civilization IS Civilization" model of "development." Where is Han China? It's a contemporary of Rome not only in time, but also in power.
During most of the time you are probably presuming Greece as a "great power" it's actually Persia that eclipses all its neighbors in terms of power and wealth. The Franks? What about the Abasyyid and Umayyad Calaphates, which were much larger, much richer, and much more militarily successful during the European medieval period?
Oh, yeah, the Mongol Empire and successor Khanates? If you're interested in the development of the modern economy, then you need to start with them and not some backwater European feudal power.
This is discussed heavily in World Systems Theory in Anthropology. It used to be a bigger subject of focus, but has since fallen out of favor.
Your premise is entirely contextual to the American perspective. First, what constitutes a "civilization"? Second, what makes it " great"? Are these products of their total economic worth? How is that measured? If the Spanish Empire was dominant in the late 1400s. / early 1500s (which is highly questionable given the Portuguese, the Venetians, the Mongols, etc - to name just a few competitors going west to east) did the combined wealth of all of Spain mean anything to the Aztecs? If the wealth that Spain acquired from Mesoamerica was in the form of gold and other things with a set value in Europe, and the Spanish monarchy was vastly enriched beyond their previous worth, then doesn't that mean the Aztecs were the greater civilisation and the transition went from west to east?
If it is measured in other ways, what are they? Population size? Number of other territories conquered? Literature? Music? Best cooking? Perhaps you mean technology? But there again, Asia was far ahead in many ways and they were not conquered by Europe but perhaps could be seen to have stagnated in some ways. But if you look backward from the US to the historical "mythology" of the nation and its founding population, it comes from the east to the west. If you look forward it would appear to move further west to China, but China was a world dominating force before, and it is just as equally seen as being to the east. The domination of one group by another is just a function of being their neighbor and the direction of conquest is not inherently one way or the other. However, since travel is now much easier it becomes possible to move economic wealth around the globe much more quickly. Conquest is merely the movement of wealth (i.e. potential energy) from one place to another. To see a directional trend is the result of one's individual perspective; which is a product of their definitions, worldview, experience, etc.