The discussion centers around the nature of time in physics, particularly in the context of quantum mechanics. Participants explore whether time can be considered an observable quantity, how it is represented mathematically, and the implications of these representations for measurements and physical understanding.
Participants do not reach a consensus on whether time can be considered an observable in the same sense as position. Multiple competing views remain regarding the representation of time in quantum mechanics and its implications for measurement.
There are unresolved questions regarding the definitions and assumptions underlying the discussion of time as an observable, particularly in relation to quantum mechanics and measurement techniques.
It is an experimental question. Those the expectation values of fields best describe the measured "classical" fields in the LCD screen.A. Neumaier said:Ok, so you take the subset of coherent states whose electric field is zero at all but one pixel ##x##. But for each ##x## this still leaves an infinity of coherent states with different intensity; which ones do you pick for ##|x\rangle##?
Ok, so you pick one coherent state per pixel with the experimental intensity. Now coherent states corresponding to neighboring pixels will substantially overlap. Thus the eigenstates of your position operator will have significant support in a number of pixels close to the intended one. This means that measuring ##X## will produce a superposition of pixels with probabilities that are maximal at the intended pixel but significantly less than 1. This means that you always get blurred measurements of the pixels, not true position measurements. This is sufficient for recognizing whether the digit 3 or 4 appeared, but not for a reduction of the digital time measurement process to one with true position measurements.Demystifier said:It is an experimental question. Those the expectation values of fields best describe the measured "classical" fields in the LCD screen.
My intuition is that the overlap will be small, but I guess we are both guilty of not quantifying our intuitions.A. Neumaier said:Now coherent states corresponding to neighboring pixels will substantially overlap. Thus the eigenstates of your position operator will have significant support in a number of pixels close to the intended one.
Yes, and the electric field changes with time. Thus time is not an observable but a parameter that tells which value ##E(t)## of the electric field applies in a particular instant. Similar for position. To talk about position you need to say at which time you mean it.Demystifier said:a relevant observable is the electric field in the screen. I believe you would agree with that.