When you fill the time sheet at work, are you logging the brain time vs. body time?

Here's a somewhat controversial opinion. I think the practice of logging time-sheets is inefficient, deeply flawed, and doesn't accomplish anything, including the very thing it's trying to measure, employee productivity.

Is there any difference in hours spent doing meaningful work and hours of wasted time staring at the computer? What matters is not the amount of time you are present at the office, but the amount of time that you're working at full potential.

An hour in a state of deep flow is very different from an hour of distracted work where you are constantly getting interrupted every 100 minutes.

How can the time-sheet differentiate between these two hours? It can't.