Sorry, but you can't attach yourself to a photon, not if you have non-zero mass. By a "free-falling observer" I mean a free-falling massive observer, not quite the same thing as (free-falling) photon. A photon does not define a local inertial reference frame.Yes, that is what Bergmann says in my posted quote....it makes sense, actually, because attached to a photon, you'd be freely falling (no acceleration) and all would be "normal" from your frame of reference...
In my rocket example, the apple has zero kinetic energy and zero potential energy in the apple's own inertial frame. In the rocket's accelerating frame, the apple initially has increasing kinetic energy, offset by decreasing potential energy. So, potential energy is dependent on reference frame.Potential energy IS independent of frame of reference,