Why Eigenvalues in Quantum Measurements
Most recent answer: 07/31/2014
- Ashutosh (age 20)
Mumbai,India
That's a very deep question I an give a partial answer.
What is the apparatus that measures the quantity X? By definition, it's something that acquires different macroscopic (large-scale) states depending on the value of X. Now let's say you saw an output of the measurement operation that was not in an eigenvalue of X. Then, by definition of the measurement apparatus, it would also not be in an eigenstate of the macroscopic properties. You would be seeing, for example, some superposition of a detector needle in visibly different positions.
Now here's where my answer gets fuzzy. There's a rule of nature that our experience has only definite values of macro phenomena. Cats are not found in states consisting of very healthy and very dead versions. How that rule arises is at the core of the "measurement" problem. Is it that the full quantum state, with all its parts, emerges, but our conscious experience branches into separate macro-coherent streams? Do all the streams except one somehow collapse away? Was there some sort of (non-local) hidden fact-of-the matter beforehand, so that only one of the streams is fully real?
You can find more on this by searching this site and others for "quantum measurement", Bell Inequalities", "Many Worlds", "Copenhagen", etc.
Mike W.
(published on 07/31/2014)