IIUC, there are two different interpretations of GR - either as curvature of space time (as in Misner Thorne Wheeler) or as a (spin-2)field that influences all matter (as in the books by Weinberg or in the Feynman Lectures on Gravitation) and that leads to the underlying Minkowski metric being inobservable. In the field interpretation, I can understand that fields do affect the distances between objects ("rulers"). I am trying to find a good heuristic or intuitive explanation or example, how the running of clocks is affected in the field interpretation. (There is a calculation in http://arXiv.org/abs/astro-ph/0006423v1 for the example of a H-atom, but this is rather un-intuitive and I seem not to be able to see the physics behind it.) As a simple example, consider a particle in a constant magnetic field. This could be sued as a clock by measuring the cyclotron frequency [tex]f_0=qB/2 \pi m[/tex] In a gravitational field, the frequency should become smaller so the clock runs slower than the far-away clock. However, I think m inside the gravitational field should be reduced (because of a gain in potential energy) by a factor (1-gR/c²) - because the energy needed to transport a particle from R to infinity is mgR - , which results in an increase of the frequency. Probably, the magnetic field also has to be transformed (the paper cited above shows how the vacuum susceptibility is affected), but again the physics behind that is not too clear to me. So is there any simple way to explain the time dilation in the field interpretation for this (or another) example?