general relativity - What's the deal with the gyroscope?

In this article ("The problem with physics", Tony Rothman, ABC science) the author says in the 5$^\textrm{th}$ paragraph:

For example, one needs only first-semester equations to describe reasonably well the behaviour of a gyroscope; engineers can then go off and build gyrocompasses that guide aircraft or missiles to their destinations. But if you merely ask: "At what, exactly, is the gyroscope pointed?" you are plunged headlong into one of physics' deepest questions, one that led Einstein to develop his general theory of relativity — and that, even today, has no definitive answer. I know of no undergraduate textbook that acknowledges the question."

What is the issue he is referring to?

Answer

I don't know Tony Rothman so I don't know exactly what I had in mind, but I expect he's referring to Mach's principle.

When he says:

I know of no undergraduate textbook that acknowledges the question

there is a very good reason for this. Physics is concerned with the construction of predictive mathematical models of the real world and Mach's principle plays no part on this. It may or may not be true that thinking about Mach's principle helped Einstein to formulate General Relativity, but GR is not a formulation of Mach's principle and the extent to which GR includes Mach's principle depends on who you ask and what exactly you mean by "Mach's principle" anyway. See Is Mach's Principle Wrong? for more on this.