While this seems to be true given the expansion of the universe, is it strictly necessary? What if some value R does repeat, throwing the universe into an endless loop? At some point, the chains of r’s leading up to R0 and R1 would differ; wouldn’t we need another variable to encode that?
...throwing the universe into an endless loop? At some point, the chains of r’s leading up to R0 and R1 would differ...
The point of an endless loop is that it is endless and R never will differ outside of that loop, how could it? Everything happens exactly the same way it did last time, and for exactly the same reasons. A universe also can’t enter such a loop starting outside (given reversible physics), and there wouldn’t be any seem where it is all stiched together.
I’m not sure how this would go together with many-worlds. But if one considers two branches, where one branch eventually gets into exactly the same configuration at some point of the other (extremely unlikely, obviously, but consider all possible branches...), we could compress our model of reality without loosing information by treating them as one. This is quite similar to the endless loop above.
Well sure, if you parametrize with a time factor the result will be a periodic function. But you can still de-parametrize and simply have a closed loop described relationally. A parametrization of a circle usually consists of periodic functions, but that doesn’t mean the circle itself is periodic. It’s just there.
Also remember that “exactly the same configuration” means exactly the same configuration, of everything, including for instance your calendar, your watch, and your brain and its stored memories. So pretty much by definition there would be no record of such a thing happening. We wouldn’t need another variable to encode it because we wouldn’t need to encode it in the first place.
“We don’t need the t.
It’s redundant.
The r never repeats itself.”
While this seems to be true given the expansion of the universe, is it strictly necessary? What if some value R does repeat, throwing the universe into an endless loop? At some point, the chains of r’s leading up to R0 and R1 would differ; wouldn’t we need another variable to encode that?
The point of an endless loop is that it is endless and R never will differ outside of that loop, how could it? Everything happens exactly the same way it did last time, and for exactly the same reasons. A universe also can’t enter such a loop starting outside (given reversible physics), and there wouldn’t be any seem where it is all stiched together.
I’m not sure how this would go together with many-worlds. But if one considers two branches, where one branch eventually gets into exactly the same configuration at some point of the other (extremely unlikely, obviously, but consider all possible branches...), we could compress our model of reality without loosing information by treating them as one. This is quite similar to the endless loop above.
(I am not a phycisist!)
Then, it would render the configuration a Periodic function, yet Periodic functions are still parameterized by a time-factor.
Well sure, if you parametrize with a time factor the result will be a periodic function. But you can still de-parametrize and simply have a closed loop described relationally. A parametrization of a circle usually consists of periodic functions, but that doesn’t mean the circle itself is periodic. It’s just there.
Also remember that “exactly the same configuration” means exactly the same configuration, of everything, including for instance your calendar, your watch, and your brain and its stored memories. So pretty much by definition there would be no record of such a thing happening. We wouldn’t need another variable to encode it because we wouldn’t need to encode it in the first place.