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This is a very broad definition of ""measurement"", and does not require the intervention of a human observer. In classical physics, complete knowledge of the situation at a particular time contains sufficient information to determine the situation at any other time. When classical laws apply, and the state at some time is known from measurement, the state at all times can be calculated, at least in principle. For example, we can reasonably assume that Venus continues on its orbit while it is on the far side of the Sun and cannot be observed. Experience tells us that when Venus reappears it will be observed in precisely the position found by calculation from prior measurements. It is unreasonable to think that the same calculations do not hold while Venus is not observed. When classical laws apply, and the state has been measured at some time, then the state can be said to be //effectively measured// at any time, whether or not it is actually observed, and whether or not a calculation is actually performed.
Deletions:
This is a very broad definition of measurement, and does not require the intervention of a human observer. In classical physics, complete knowledge of the situation at a particular time contains sufficient information to determine the situation at any other time. When classical laws apply, and the state at some time is known from measurement, the state at all times can be calculated, at least in principle. For example, we can reasonably assume that Venus continues on its orbit while it is on the far side of the Sun and cannot be observed. Experience tells us that when Venus reappears it will be observed in precisely the position found by calculation from prior measurements. It is unreasonable to think that the same calculations do not hold while Venus is not observed. When classical laws apply, and the state has been measured at some time, then the state can be said to be //effectively measured// at any time, whether or not it is actually observed, and whether or not a calculation is actually performed.
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Hilbert space has been set up to describe measurement at particular time. So time is a parameter, not an operator. The ""time-energy uncertainty relation"". In the uncertainty relation for time-energy,
