Sure, there are lot's of things that don't change in different reference frames. We call them "invariants". Einstein got so fed up with hearing people talk nonsense about relativity that he tried to rename it "Invariants theory" but by them the name had stuck.
Sticking to Special Relativity (because I don't know GR well enough to discuss it properly) here's some invariants:
, where d is distance and t is time interval ((1) is just a special case of this.).
None of those seem intuitively like they should be invariant. (2) sort of replaces t, which seems like it should be invariant but isn't. (3) sort of replaces the inertial mass m, which seems like it should be invariant but isn't.
As for why inertial mass (defined as what you have to multiply v
by to get p
) increases as |v
| increases, there's a very simple argument based on symmetry and conservation of p
. However, it's just a little long for these Q&A.
(published on 05/12/11)