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I'm not asking for an in-depth philosophical discussion, I just want to know what exactly is meant when "measurement" is said in quantum mechanics and what the parameters on this are.

I have read in another stack post that an observable is a hermitian operator with a complete base (top answer here: What can be measured in quantum mechanics and how?), and my understanding is that we can measure any observable. I have also read that a measurement requires some interaction with a system. However, I am very confused about this. So, does this mean the term measurement applies only when some physical thing is done to a system? Can a measurement purely be mathematical? What does it mean to measure an observable non-mathematically?

Again, I'm not looking for some deep philosophy, I just want to understand what is being said when these terms are being used in textbooks and coursework.

Qmechanic
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Relativisticcucumber
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1 Answers1

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In brief: "measuring" a quantum particle means interacting with it so the measurement tool registers a "hit". An inevitable consequence is that the state of the particle after the hit isn't the same as it was before the hit, so for example the act of measuring where it is changes how fast it is moving, and the act of measuring its speed knocks it out of position. An accurate measurement of its position renders its speed unknown, and an accurate measurement of its speed leaves its position unknown.

niels nielsen
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