This comment from Chris is interesting:
I would speculate that the the massive productivity gains were due to a massive resorting of American society along cognitive lines; from 1940 to 1970 a large number of high ability people who were previously locked into agriculture and industry were able to sort themselves into more innovative positions. This would lead to a massive burst of innovation, which led to increases in productivity, as previously unlocked talent was put to use. From 1970 to 1990 this resorting was mostly winding down and productivity in the economy was heavily constrained by the population due to people still being necessary for most tasks and most of the potential innovation overhang being used up from 1940 to 1970. Although computers were increasingly able to challenge people on some tasks during the 1970's, their effect was small (although increasingly noticeable in how long it took employment to rebound after recessions from 1980 on). From 1995 on productivity gains began to accelerate due to computers hitting a tipping point and their increasing ability to replace or augment people in areas across the economy. Wages remain stagnant post-2000, because a growing number of people are being displaced at the lower levels of economic activity and competing for jobs that are ultimately constrained by the population, services (this would have happened earlier, but was masked by the initial burst of innovation following the cost of information falling to zero). Most of those displaced do not have the cognitive ability to perform economically useful innovation due to the sorting during the 1940-70 period and are unable to take advantage of the jobs on the high end of the income scale. An income gap forms and begins to accelerate.
There's a huge literature on this topic, so don't take the speculation here as the last word, but food for thought. In Farewell to Alms Greg Clark asserts that the main beneficiaries of the regime of perpetual economic growth since 1800 have been the unskilled workers, who closed the wage gap with skilled workers up until 1970. At that point, the wage gap between the skilled and unskilled started to open up again. Also remember that though it is conventional wisdom to bemoan the increase in inequality in the modern capitalist economies, every civilized society before 1800 was far less egalitarian in the distribution of wealth and power than modern economies (in contrast to "savages," who had egalitarianism because of the lack of a very wealthy class; everyone was poor more or less).