On 5/5/2025 5:36 AM, John Clark wrote:
Time is not an operator because it is not an observable in the way that position, momentum and energy are, instead it's a parameter, the stage against which things happen. We can say that a particle has a position, a momentum and an energy but a particle doesn't have a time. Mathematically that means that in quantum mechanics position, momentum and energy are all Hermitian operators but time is not. However it remains true that Δt × ΔE ≥ ℏ/2, and of course Δx × Δp ≥ ℏ/2
It remains true if you correctly interpret Δt as the time for the expected value of the energy of the variable E to change by a standard deviation. In other words by using whatever energy E refers to as a clock. That's why it remains true even though there is no t operator in the sense of measuring a universal time.
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