Difference between real rates of interest and nominal rates of interest?

I am currently answering this question but would like to get a broader view of answers. Discuss the difference between real rate of interest and nominal rate of interest and examine whether there are any grounds for the belief that changes in the nominal rate of interest only have an impact on a firms investment decision if they are accompanied by a change in the real interest rate.

1. Nominal Interest Rates vs. Real Interest Rates
Suppose we buy a 1 year bond for face value that pays 6% at the end of the year. We pay $100 at the beginning of the year and get $106 at the end of the year. Thus the bond pays an interest rate of 6%. This 6% is the nominal interest rate, as we have not accounted for inflation.

Whenever people speak of the interest rate they're talking about the nominal interest rate, unless they state otherwise.
Now suppose the inflation rate is 3% for that year. We can buy a basket of goods today and it will cost $100, or we can buy that basket next year and it will cost $103. If we buy the bond with a 6% nominal interest rate for $100, sell it after a year and get $106, buy a basket of goods for $103, we will have $3 left over. So after factoring in inflation, our $100 bond will earn us $3 in income; a real interest rate of 3%. The relationship between the nominal interest rate, inflation, and the real interest rate is described by the Fisher Equation:

Real Interest Rate = Nominal Interest Rate - Inflation
If inflation is positive, which it generally is, then the real interest rate is lower than the nominal interest rate. If we have deflation and the inflation rate is negative, then the real interest rate will be larger.