Can Time Be Represented as an Operator in Quantum Mechanics?

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The discussion centers on the existence of a time operator in quantum mechanics, highlighting that there are negative responses to this question. It connects to the non-existence of position operators in relativistic quantum mechanics, where the framework involves a four-vector (t, x, 1, x2, x3). There are also concerns regarding velocity operators, which reportedly have eigenvalues restricted to +c and -c, suggesting a potential link to the time operator issue. Additionally, the energy-time uncertainty principle is mentioned, noting that while it is used to estimate particle decay rates, it does not invoke an operator for time. The conversation references a resource that outlines the time-energy uncertainty principle and discusses the reasons why a true time operator cannot exist in quantum mechanics.
arivero
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It has been asked if there exists an operator representing time. I remember some negative answers, but I do not remember the arguments.

In relativistic QM this relates to the non-existence of position operators; we are working with an (t,x,1,x2,x3) vector there. Also I believe to remember some provlem with velocity operators -its eigenvectors been only +c and -c, or so- but I am unsure about if both questions are related.

also, Energy-time indetermination is usedto estimate decay rates of particles. But there an operator is not invoked.
 
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