I am reading the book How Is Quantum Field Theory Possible? by Sunny Auyang, and he raises an interesting point in chapter 4 (p. 23):
L. E. Ballentine argued that the projection postulate leads to wrong results. Even when the quantum system somehow triggers its environment to produce a measurable eigenvalue, its state does not collapse. Consider the track left by a charged particle in a cloud chamber. The incoming particle is usually represented by a momentum amplitude. It encounters the first cloud-chamber atom and ionizes it, leaving the tiny droplet that we observe. This process is sometimes construed as a position measurement that collapses the particle's amplitude into a position eigenstate. The interpretation is untenable. A position eigenstate is a spherical wave that spreads out in all directions. Hence it would be impossible for the particle to ionize subsequent atoms to form a track that indicates the direction of the original momentum, which is allegedly destroyed in the first ionization.
In other words, the projection postulate of QM is inconsistent with bubble chamber tracks. Is there an accepted resolution to this?
I can think of a few ideas:
- The projection postulate is wrong.
- Droplets in bubble chambers do not count as position measurements.
- The droplets are position measurements, but only localize the position to a finite region of space, and this allows some of the "momentum" part of of the wavefunction to remain intact upon collapse.
But all of these seem to have issues and conflict with other principles of QM. Curious if there is a standard resolution, or if this necessarily gets into the contentious realm of quantum interpretations.
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