### Lack of Time

Posted:

**Thu Dec 07, 2017 10:11 pm**In quantum mechanics, there is no time operator. Time, they say, is a parameter, not an observable. There is, therefore, no time operator.

This means that in the quantum theory of measurement, where every observable is associated with an operator, time cannot be measured.

This also produces problems in the interpretation of the time-energy uncertainty relation. The position-momentum interpretation is straightforward: since the position and momentum operators don't commute, there is some residual uncertainty in their simultaneous measurement - if you measure both at the same time, which comes first? But if time is not an operator, what does this mean?

The energy is of course associated with an operator: the Hamiltonian. It is also the time component of the 4-momentum. So, it makes sense that there should be an energy-time uncertainty relation.

But, for some reason its conjugate, the time, isn't an operator, can't be measured quatum mechanically. So what does that mean for the uncertainty relation?

Does that make sense? Are all time measurements classical? (if so, what does that mean for universal interpretations of the wavefunction, e.g. Everett's?)

Why doesn't the symmetry hold up?

This means that in the quantum theory of measurement, where every observable is associated with an operator, time cannot be measured.

This also produces problems in the interpretation of the time-energy uncertainty relation. The position-momentum interpretation is straightforward: since the position and momentum operators don't commute, there is some residual uncertainty in their simultaneous measurement - if you measure both at the same time, which comes first? But if time is not an operator, what does this mean?

The energy is of course associated with an operator: the Hamiltonian. It is also the time component of the 4-momentum. So, it makes sense that there should be an energy-time uncertainty relation.

But, for some reason its conjugate, the time, isn't an operator, can't be measured quatum mechanically. So what does that mean for the uncertainty relation?

Does that make sense? Are all time measurements classical? (if so, what does that mean for universal interpretations of the wavefunction, e.g. Everett's?)

Why doesn't the symmetry hold up?