Some time ago, someone in this forum asked how you measure momentum. One of the answers said that if it's a charged particle, you can let it pass through a bubble chamber and a magnetic field, and measure the curvature of the bubble trail. But this isn't really a direct measurement of the momentum. The bubbles appear at locations where the particle has interacted with the liquid, and each interaction that produces a bubble is an approximate position measurement. So what we actually do here is to make a series of approximate position measurements, and(adsbygoogle = window.adsbygoogle || []).push({}); inferan approximate value of the momentum.

Consider a Stern-Gerlach apparatus. A beam of silver atoms is sent through an inhomogeneous magnetic field and is split in two. How do we measure the spin? We put detectors at the locations of the outgoing beams so that we can tell if a particle has been detected there or not. Then weinferthe value of the spin from the fact that we have prepared the system so that the spin eigenstates are entangled with states that almost have a well-defined position.

In a recent thread, someone talked about measuring wavelengths by sending a photon into some sort of cavity, which will absorb the photon if it has the "wrong" wavelength. If we're able to detect the photon there, then weinferthat it had the "right" wavelength. (I don't know the details of this experiment, so I could be wrong about some of it).

In all of these situations, the measurement device really just says "yeah, it's here", and we use our theoretical knowledge of the state preparation procedure to infer the value of the quantity we're really interested in. My question is, areallquantum physics experiments like that? Is there any way to measure an observable directly? Are there any measurements that have an actualnumberas a result, or are all the numbers we think of as measurement results inferred from "yes" and "no" answers about a particle's position from our measuring devices?

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# What operators can we measure directly?

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