Is it possible to build a clock that will be immune to relativistic effects on the passage of time? Can a clock exist that will always display the time of the place in which it was set? For instance, if we built the clock on Earth, then put it on a spaceship which accelerated away from the Earth at a significant fraction of the speed of light, the clock would continue to display the time on Earth. To observers on the ship the clock would appear to run faster and faster as the ship accelerated.
Additionally, strong gravitational fields can change the flow of time. If our ship entered orbit around a black hole our clock would still compensate and display the real time on far-away Earth.
The clock must be self-contained. It can't communicate with other clocks or otherwise observe the universe outside of it, but it can be as big and complex as necessary.
EDIT: To clarify the capabilities of this clock: A clock that meets my specifications that was sent on a journey should display the same time as a clock left on Earth when it is returned to Earth.
Further EDIT: This clock should match a clock left on Earth at all times and places. If the starship travelers want to celebrate Christmas on the same day as their families on Earth they should be able to using this clock.