Philip Verdieck
Supporting Actor
Well said. I forgot that TNG introduced (or showed use of) a starship synchronizing with a Federation Time Beacon (Cause and Effect).My understanding, such as it is, has been that the warp drive creates a field inside which a bubble of subspace is preserved in which normal matter/gravity/time/etc. continue to exist. Outside the bubble, space distorts/warps as it interacts with the field, with the space ahead contracting and the space behind expanding so that the bubble is perceived to be traveling many multitudes of the speed of light.
By contrast, impulse drives are basically fusion-powered rockets and provide actual propulsion rather than apparent propulsion. I think I read somewhere that full impulse power is roughly a quarter of the speed of light, or around 46,500 miles per second. At that speed, roughly 1.03 seconds would be perceived to have gone by for every 1 second aboard the starship -- roughly two extra seconds every minute. If a starship was traveling at full impulse for a full 24 hours, that would still only result in a roughly 48 minute discrepancy between the starship's time and the observed time. Starships on Trek shows tend to be traveling at full impulse for far less time than 24 hours, so the relativistic effects are so small as to be negligible. Presumably every time a starship comes out of warp in Federation space, it can contact a data source and recalibrate its internal clock with the objective accounting of time.
I think Spock just did calculations against start charts or something in TOS (The Naked Time).