[wallace_f]

I've never been able to feel comfortable understanding reference frames. Even considering simpler examples: So what if a probe is launched to catch our solar system's recent cigar-shaped visitor. Assume we catch it and want to bring back a sample of equal mass to the probe. So what determines the kinetic energy required to return this sample to earth? Is the delta relative to that of the probe, to the solar system, or to its origin? What if it is was accelerated to 0.1c relative to its launch site in another galaxy, but is only travelling at 0.001c relative to us?

Common sense dictates that the probe and the sample would require equal fuel to return to earth; but to an observer riding this cigar-rock, why would the universe cut our probe some slack if we changed its kinetic energy rather than the observer?

[IntronExon]

It’s from the frame of reference of the probe you make fuel calculations. The various observers don’t necessarily need to agree on the ordering of events (Relativity of Simultaneity), but they will always agree on the laws of physics, which are the same everywhere. If it takes a given amount of fuel to accelerate a mass to a given degree, everyone will agree on that point. It might take som calculation to make that clear to all of the observers, but they will agree regardless if some are in accelerating reference frames, and others inertial.