> Even if a continually slowing observer (CSO) could exist, it's
> relationship to a normal computer would not be the same as that of a
> normal observer to a RAC. To a normal observer, there is some finite
> subjective time in the future when the RAC will have gone through an
> infinite number of clock cycles, but to the CSO there is no finite
> subjective for when a normal computer will have gone through an infinite
> number of clock cycles. This is obvious when you consider that any finite
> subjective time for the CSO is also a finite objective time.
Doesn't this assume that objective time is discrete? With continuous
objective time there is no objective fact of the matter about whether a
given interval is finite or infinite. There are algebraic transformations
like t' = 1/t which turn finite times into infinite, and vice versa.
In the example above with the RAC, you have a time t measured by an
ordinary observer and a time t' measured by the RAC. Then in the CSO
case you have the time t measured by the CSO and time t' measured by an
ordinary computer. The relationship between t and t' seems to be the
same in each case. The only difference is in terms of "objective time",
but it's not clear that is uniquely defined (or even meaningful at all).