Physical immortality is probably impossible since organisms process energy and there is PROBABLY only a finite amount of energy in the universe, unless an organism can somehow recycle used up energy, physical immortality is doomed.
Even if one could stop the aging process one has the problem that eventually the sun will burn out. The only option then is to go to another star system that can support life but then that star will burn out and eventually all the stars in the universe will burn our. One would then have to develop a way to extract energy from dark matter. Even if one could go this far I am sure the problems of physical immortality is a doomed idea for reasons beyond these I have already mentioned