Hello DrRocket! Fancy meeting you here!
This thread has been very interesting but, as you know, my ability to appreciate the nuances of the arguments presented here is limited - to say the least.
To simplify things (for me), let me take a question posted elsewhere in another thread and pose it here in the hope that the answer might help me differentiate the various definitions you good folks have been debating.
If I take a 1 kg mass, pick it up off the floor and place it on a shelf 2 m high, what - if anything - changes.
From what I've read here I'm guessing that the rest mass and the invariant mass remain the same. Of course I could be wrong about that.
That reduces the question to: Does the relativistic mass or equivalent energy content (whichever term you prefer) increase, decrease, or remain the same relative to the Earth?
It's my understanding that these last two terms are always relative to something else.
Best Regards
Chris
Edited to correct spelling error