: Perhaps so, but the "twin paradox" in Relativity states that the age of each twin is dependent on his path of travel. For a conservative field, all physical parameters are path independent.--[[User:Aschlafly|Andy Schlafly]] 23:07, 30 July 2010 (EDT)
:: Simeon, your mathematical work is rigorous and correct. However, the twin paradox example is interesting to study here. I am aware that the twin paradox is solved by the non-inertial turn-around of the ship when it is going back home. However, in this solution, it is still noted that there is an age difference between the twins. [http://mentock.home.mindspring.com/twins.htm Wikipedia affirms this] and so do [http://mentock.home.mindspring.com/twins.htm other sites]. Such an age difference in twins shows that there is some sort of path dependence. I understand that traveling at near-c speeds in space is not the same thing as moving from point A to B in a gravitational field, but the concept does seem to be a bit similar. Could you maybe explain this for us a bit? Thanks. [[User:PhyllisS|PhyllisS]] 00:52, 31 July 2010 (EDT)