Why do interest rates keep falling?

One of the most important macroeconomic developments over the past few decades has been the continual decline in interest rates.  In the early 1980s, the federal funds rate peaked around 20% and then after the financial crisis interest rates remained stuck near zero for about 7 years.  A variety of explanations have been given as the cause of this development, but my own personal theory is that we have simply started running out of useful investment opportunities.

The basic argument goes something like this.  Back at the beginning of the industrial revolution the amount of physical capital existing in society was quite low.  Over the subsequent century that means there was a wealth of useful investment opportunities that saw the amount of capital gradually increase decade after decade.  My theory is that there is basically a limit to the amount of useful capital accumulation.  If you look at human capital, there is a limit to how much education is really useful, where even if we might eventually get everyone to 25 years of schooling, giving everyone say 50 or 60 years of schooling just doesn't make sense.  Similarly, back in 1900 nobody owned a car and over the course of the 20th century we made it the point where most everyone has 2 cars, but at some point we aren't going to need 5 or 6 cars per family.  

The practical way this develops in an economy is that at first, with a limited amount of capital to invest, the most valuable investment projects are done first.  If interest rates start at say 7%, then you invest in all the projects with a rate of return above 7%, and then once those are done interest rates fall to 6% and you do all the projects with a rate of return above 6%.  This process keeps happening until interest rates keep falling and eventually you reach the point where we have enough capital to offset all the depreciation, plus invest in all the new technologies that are developed, and don't need to do any additional capital accumulation. When this happens, interest rates fall to zero and you still have excess savings to invest with nowhere to go.

If this were the reason for the low interest rates, then this is likely going to be a permanent problem.  At this point, interest rates in the US have fallen to the point that they hit zero in the trough of the business cycle, but still go above zero in the peak.  In the latest business cycle in Japan and Europe, interest rates have remained near zero throughout the entire cycle, and its perfectly possible this might be true for the US in the current business cycle and every business cycle after that.  In that case, we might be facing the real possibility that interest rates are going to remain at zero in perpetuity, and should restructure our institutions (perhaps by giving the Fed some control over fiscal policy) so that we can deal with such a development.  Most economists still expect to have interest rates rise above zero in the US, but just in case they're wrong, we do need to start planning for world of interest rates that stay near zero forever.