The uncertainty principle for time and energy is $$\Delta t \Delta H >\frac{|[H,t]|}{2}.$$ What are the eigenstates of the time operator? How can anything be in a superposition of time states? What does the commutation relation mean?
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1$\begingroup$ Time in quantum mechanics means exactly the same thing that it means in classical physics: time is that which the clocks show. There can be no such thing as a meaningful time operator because we can't make a meaningful ensemble of clocks. Clocks have to show exactly the same time to be meaningful. They can't have a probability distribution/wave function. Neither can clocks be considered isolated systems. Clocks are, by definition, the most open and dissipative systems possible. They are, if you will, 100% measurement and they have no unitary evolution. $\endgroup$– FlatterMannCommented Aug 2 at 11:45
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1$\begingroup$ arxiv.org/abs/2108.13974 $\endgroup$– alanfCommented Aug 2 at 22:13
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There is no well-defined time operator, and the expression itself is controversial. It is quite well explained on Wikipedia.
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1$\begingroup$ this does make an attempt at explaining what I want to know, but it is still very ambiguous to me. $\endgroup$ Commented Aug 2 at 11:44