By “relativity” you mean what? If relativistic mechanics of point particles in a given background, then it is computationally as complex as classical mechanics. If the background (i.e. gravitational and electromagnetic fields) is to be determined dynamically, then it is harder because you have infinitely many degrees of freedom. But that’s the case of many non-relativistic classical systems (fluid dynamics...) too.
it seems to me that you would have to set up a system where the outcomes of relativity are explicitly stated, while the classical outcomes are implicit
What does this mean? I can think of several interpretations, all of them false:
It is impossible to calculate the evolution of a relativistic system from the initial state only, you also need to know the final state too.
It is possible to do calculate the relativistic evolution from the initial state, but you have to do it symbolically, numerical methods won’t work.
It is impossible to calculate anything numerically in a relativistic system, solutions have to be guessed and later verified, they can’t be systematically constructed.
It is impossible to calculate anything numerically in a relativistic system, solutions have to be guessed and later verified, they can’t be systematically constructed.
From a practical point of view, in general relativity this is almost true.
Because there is large gauge freedom in choice of coordinates and random choice of gauge will likely produce a coordinate singularity somewhere and you will not see what’s beyond. So you don’t reconstruct whole spacetime history, but you can reconstruct at least something, and perhaps use different coordinates to move further. Of course there are problems with precision whenever the equations are enough non-linear, but that’s nothing specific to relativity.
Not just that, you are free to choose a gauge that only “kicks in” the future. In fact there is no unique well-defined future history, just a future defined up,to gauge even if you fix a choice of gauge for the present.
By “relativity” you mean what? If relativistic mechanics of point particles in a given background, then it is computationally as complex as classical mechanics. If the background (i.e. gravitational and electromagnetic fields) is to be determined dynamically, then it is harder because you have infinitely many degrees of freedom. But that’s the case of many non-relativistic classical systems (fluid dynamics...) too.
What does this mean? I can think of several interpretations, all of them false:
It is impossible to calculate the evolution of a relativistic system from the initial state only, you also need to know the final state too.
It is possible to do calculate the relativistic evolution from the initial state, but you have to do it symbolically, numerical methods won’t work.
It is impossible to calculate anything numerically in a relativistic system, solutions have to be guessed and later verified, they can’t be systematically constructed.
From a practical point of view, in general relativity this is almost true.
Because there is large gauge freedom in choice of coordinates and random choice of gauge will likely produce a coordinate singularity somewhere and you will not see what’s beyond. So you don’t reconstruct whole spacetime history, but you can reconstruct at least something, and perhaps use different coordinates to move further. Of course there are problems with precision whenever the equations are enough non-linear, but that’s nothing specific to relativity.
Not just that, you are free to choose a gauge that only “kicks in” the future. In fact there is no unique well-defined future history, just a future defined up,to gauge even if you fix a choice of gauge for the present.
Gauge fixing has to be done for all history, else there is fewer equations than dynamical variables, of course.
The point is that this is very hard to do for general relativity.