Comment They exist. (Score 1) 47
Chip-scale atomic clocks are a thing. The problem is that they aren't exactly low enough power to be wrist mounted as they need 115 mW constantly. You absolute can make it into a wristwatch (and people have) but it will need regular charging... unless you are using betavoltaic nuclear batteries. However to reach the power output needed with what is on the market, you would need about 120K of them.
The natural reaction to this is "what's the purpose of building up that kind of arm strength if the batteries are just going to die in 50 years?" and the answer is the diamond battery! This is a newer betavoltaic battery which is in the same power output range but lasts for thousands of years because it's based on Carbon-14.
Start doing those reps today because the watch of your dreams is 2400Kg.