Is human immortality possible ?
Before to try to answer this question we need to define what is life.
If we think to us as biological entity this become a biologic question , if we think to us as physical matter this become a physic question.
I think the human being is inside the mind and the mind is not a physic object .
Anyway I think everything is ultimately a program so I try to give an answer by defining a person as a program.
I am not saying that we can define a human as the program implemented by the brain because we know the brain change ; the brain change its matter and ( most important ) change its connections , change its program so if we want do define a person to be the same after some hours when his brain change we can not bound the program by the brain but by the program that change the brain .
The main question is : what happen if we run a program for an unlimited amount of time? There are 2 possibilities
1) enter in a loop (infinite loop) where it go to reuse previous state ( class 1 programs )
2) use always new states so eats every information resource
So in the first case the program die because make always the same things. He remember the same things he can not remember about different loop . It is not like in a movie where the protagonist everyday remember that the previous day is equal to the new day . It is not possible to remember that , to recognize that because it need more memory, it need more states but the program has not more new states so it is really a death.
In the second case the program become U because the difference between the program and U ( where U is the computational implementation of the unification of the physical law , the universe ) become infinitely less significant .
In this scenario I suppose the universe is discrete and the conclusion is that immortality ( as its extreme definition of an infinite life ) of programs is not possible .