Measurement units are defined in relation to some amount of physical quantity or physical phenomena. I have a doubt if certain amounts of a certain physical concept can never be measured by a given physical quantity.
For instance, suppose I have a rational amount of time written in the form:
Then measuring that through periodic physical process is simple, I run the cycle $p$ times and I see how much is the $q$th part of it..., but how would I see the amount of seconds for an irrational amount of time? By the very definition it can't be written as "a part of some number of cycles" anymore.
So, is it impossible to ever be able to 'detect' or 'measure' an irrational amount of stuff?
Edit: my question is only loosely related to the dupe because mine is about dectability/measurability rather than existence.