> The second is defined as being equal to the time duration of 9,19,26,31,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom.
https://en.wikipedia.org/wiki/Second
Unless the laws of physics aren't constant over very long time periods for some reason, we could (if we were around to do it) measure time 10^18 years from now just the same as we do today.
We can measure the elements left behind and we have determined that the fine structure constant was the same then as it is now.
If the laws of physics have remained constant for that long then most scientists think they will remain constant in the future.
https://en.wikipedia.org/wiki/Natural_nuclear_fission_reacto...
That said, although I agree the laws of physics are likely to remain constant, 1.7 billion years is only just about 12% of the age of the Universe. And, that time period only reflects the most recent 1.7 billion years. So, there's still some theoretical wiggle room there for the fine structure constant to vary over time. After all, heat death is not expected to occur for much more 100 trillion years (if that is our ultimate fate)! [0]
Edit: Come to think of it, if the laws of physics aren't constant, how would it be possible to pose a coherent definition of a unit of time at all?
---
[0]: https://en.wikipedia.org/wiki/Future_of_an_expanding_univers...