measurement in quantum mechanics or the black hole information paradox) and there might even be experimental implications.

Although we have discussed several of these issues in previous papers [@cqg; @njp; @piombino], the latter were written with an audience of relativists and quantum gravity experts in mind, and involving a particular approach to quantum gravity we have been pioneering [@prldiscrete; @ashtekar]. Since many of the results are really robust and independent of details of quantum gravity, we are giving a presentation in this paper with minimal references to issues that may be unfamiliar to physicists from outside the research area of gravitational physics.

The plan of this paper is as follows: in the next section we will derive the form of the evolution equation of quantum mechanics when the time variable, used to describe it, is measured by a real clock. In section III we will consider a fundamental bound on how accurate can a real clock be and the implications it has for quantum mechanics in terms of real clocks and its consequences. Section IV discusses the implications of the formalism.

Quantum mechanics with real clocks
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Given a physical situation described by a (multi-dimensional) phase space $q,p$, we start 