- #36
bluecap
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PeterDonis said:And this is precisely what you cannot "assume". If we were talking about classical objects, you could; but we aren't, we're talking about quantum objects. And with quantum objects you cannot assume classical trajectories; you have to devise an experimental setup that actually measures a definite trajectory. And if you do that, you will find that the interference goes away.
The eigenstates I have been talking about are states that the measured quantum object could be in. They are not states of the detector. In the usual simple analysis of an experiment like the double slit, the detector is not assigned a state at all; it's just a label for "whatever it is that produces the measurement result". Immediately after a measurement, the measured quantum object is in an eigenstate of the measured observable whose eigenvalue is the measurement result.
It's not a matter of what is sent/received. It's what happens in between. In the double slit experiment, if there is no apparatus set up to measure which slit the particle goes through, then you cannot assume it has a definite trajectory during the experiment. At the end of the experiment, the particle will be detected at some position on the detector, so it has a definite position then. (Actually, even then it's not in a position eigenstate, since as vanhees71 pointed out there is no such thing; instead it's in a state with a very narrow spread of the wave function in the position basis. But that's getting beyond a "B" level discussion.) But you cannot assume that the particle took a particular trajectory through space to get to that ending position.
If we modify the double slit experiment to detect which slit the particle went through, then we can say it has a definite position as it passes through the slit, since we are measuring it. (Again, it's actually a state with a narrow spread in the position basis.) Since this is also sufficient to eliminate the interference pattern at the final detector, it is usually assumed that the particle takes a definite trajectory throughout the experiment in this case. But strictly speaking, we can't assume that, because we only measure the position at the slit; we don't measure it in between the source and the slit or in between the slit and the detector. It's just that whether or not we assume a definite trajectory during these unmeasured portions of the experiment makes no difference to our analysis of the results.
I know what happens in between where there is no position when it's not eigenstate of position, but for totally new laymen, the best way to convince them is if the emission starts with position and detection ends up with no position. Can you think of any present or proposed experiments where this can be demonstrated or done? Best is if the double slit detector can be put in state to measure the spin or energy of the particle instead of position as the double slit is the best example we have now. I want an example because I'll write an article about it for laymen in my school. Thanks.
I can't speak for him, but I would interpret what he said as follows: position is always a well-defined observable, whether or not a particular particle is in an eigenstate of it. The same would be true for any other observable. It's just emphasizing the distinction between observables and states of the system. Observables are associated with measuring devices--detectors; which observable a given detector measures depends on how it is constructed. Position is a well-defined observable because we know how to construct detectors that measure it (and how to model those detectors mathematically).
It's also important to realize that ordinary language is a very poor tool to use when trying to understand this subject. The proper tool is math. Which also means it's very difficult to properly treat this subject at a "B" level. It really helps to take the time to get a solid background in the underlying math.