don’t we already know that the entire state of the universe is used to calculate the behavior of particles? for example, doesn’t every body produce a gravitational field which acts, with some magntitude of force, at any distance, such that in order to calculate the trajectory of a particle to the nth decimal place, you would need to know about every other body in the universe?
The second version is much worse than the first. If you need to know the universe out a certain distance to calculate to the Nth place and a further distance to calculate to N+1-st place, that’s not too bad. But if you need everything to calculate anything, that’s terrible. I believe that the my version is true for GR (and some versions of quantum gravity), but the bad version is true for all other theories. People get around it by assumptions like constant density far away.
But the real way that they get away from it is by not thinking in terms of action at a distance from all the masses far away, but rather thinking in terms of gravitational potential field that exists and can be measured locally, but summarizes all information about far away objects.
The second version is much worse than the first. If you need to know the universe out a certain distance to calculate to the Nth place and a further distance to calculate to N+1-st place, that’s not too bad. But if you need everything to calculate anything, that’s terrible. I believe that the my version is true for GR (and some versions of quantum gravity), but the bad version is true for all other theories. People get around it by assumptions like constant density far away.
But the real way that they get away from it is by not thinking in terms of action at a distance from all the masses far away, but rather thinking in terms of gravitational potential field that exists and can be measured locally, but summarizes all information about far away objects.
why?
Because we can’t actually get infinite information, but we still want to calculate things.
And in practice, we can in fact calculate things to some level of precision, using a less-than-infinite amount of information.