Answer
There is no absolute standard of time.
Work Step by Step
Making such an appointment would actually be OK as long as you both referred to the same clock, e.g., the one in the office.
What would be a bad idea is making an appointment based on a personally perceived time interval. If you said "see you in a week," and your dentist took a trip at a high relativistic speed such that $\gamma = 52$, she'd return one week older, while you would have aged 52 weeks and waited nearly a year for your dentist to show up..
