Is the concept of energy increasing as it approaches the speed of light based on the fact that this is only true relative to the observer?
Lets say, there's a scenario where a person in a rocket ship is going past the Earth approaching the speed of light relative to somebody standing on the Earth. From the perspective of the man on the Earth, the energy of the person in the rocket ship & the rocket ship itself have an increased energy compared to their energy at rest, but from the perspective of the person on board the ship, he and the rocket ship have the energy at rest and the Earth has an increased energy compared to it being at rest.
To add on to this, lets say the man on Earth got on his own second spaceship and eventually caught up close to the first spaceship and is approaching the same speed as the first spaceship. Relative to the second spaceship, would the increased energy of the first spaceship gradually lower down to it's energy at rest up until they become the exact speed?
Is this all true?
(I want everyone to understand that I am focusing on the increase of energy due to an object/particle at speeds approaching the speed of light, I already understand how energy increases in Newtonian physics due to the equation of KE.)