What is the meaning of the uncertainty relation ΔE Δt ≥ ħ during the energy measurement of a particle?
My understanding is that Δt should be the time-window of the detector. But I am not sure. What happens if the detector is open for a shorter interval of time than ħ/ΔE ? Is the recorded energy distribution distorted (widened) in comparison with the true one?
Hi Sofia, yes, the detector time window is as important as the source. If the detection time window is too small you'll introduce an uncertainty in the energy of the detected particle as per ΔE Δt ≥ ħ
On the face of it, I would say that, since delta t is easier to control tan delta E, the numerical value of the latter can only be ascertained once the experiment---with a given delta t---is performed.
No, Raul, it doesn't go like that. Please pay attention that Δt is the time-window of the detector, not of the source. At the source, if the relation ΔE Δt ≥ ħ is not satisfied because the source aperture is open for a too short time, the distribution of energy is going to be falsified.
The question is what happens at the detector, whether the detector window also should be left open enough time, or else the energy distribution would be falsified.
Hi Sofia, yes, the detector time window is as important as the source. If the detection time window is too small you'll introduce an uncertainty in the energy of the detected particle as per ΔE Δt ≥ ħ
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