There is an old [intriguing result](http://math.ucr.edu/home/baez/uncertainty.html) in non-relativistic QM, stating (roughly) that there is an Heisenberg Time-Energy Uncertainty Relation. 


Unfortunately, in QM time is not an operator like space, and an old result shows that if there was one, it would imply negative values of the Energy operator. 


However, if I remember well, in the Dirac equation negative energy does pop up, in the infamous Dirac's sea. Moreover, time and space are indeed unified by relativistic constraints.


Thus I wonder: is there some setup of relativistic QM where the above T-E relation pops up in some form or another, as a genuine analogue of the other one X-P between space and momentum?


PS I am well aware that the standard path to relativistic QM is to demote space to the same rank of time, ie as parameters, not to promote time to an operator. But I know that in principle something like this could also be done, thought it would lead to a more complicated picture. 


ADDENDUM The mathematical rationale behind my question is basically this: I would like to think of the E-T pair as some kind of rotation of the X-P operators pair



Time-Energy Uncertainty Relation in relativistic Quantum Mechanics
You don't really need quantum mechanics to address this issue, in classical mechanics you would ask whether time and energy can be thought of as canonically conjugate variables (because quantization would then produce an uncertainty relation between these operators). You would then want to treat energy $E$ as a dynamical variable, like position $x$, which means that the Hamiltonian $H(x,E;p,t)=H\_0(x,p;t)-E$ must depend explicitly on time $t$, like it does on momentum $p$. The Hamilton equations of motion,
$$\dot{q}=\partial H/\partial p,\;\;\dot{p}=-\partial H/\partial q,$$
$$\dot{E}=\partial H/\partial t,\;\dot{t}=-\partial H/\partial E,$$
tell you that, indeed, $E$ and $t$ are canonically conjugate like $q$ and $p$.


There is a fun discussion along these lines at [Physics SE](http://physics.stackexchange.com/questions/16812/energy-is-actually-the-momentum-in-the-direction-of-time), in response to the question "Is energy actually momentum in the direction of time?"


