Or to restate the question, does quantum mechanics or the quantum field theory state or imply that we can only observe the wave in a collapsed state?

And if they don't, do we have any promising research directions towards measurement methods that don't cause a wave collapse?

EDIT: It's probably worth clarifying that this really isn't a question about HOW wave collapse occurs. And it certainly isn't a philosophical question about different interpretations of quantum mechanics. What I would like to understand is the statement that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured. Is it because of the definition of what is a measurement? Or an observation based on empirical evidence? Or a result that can be mathematically derived from theory?

  • $\begingroup$ Following a measurement, the state of the system must be in an eigenstate of that measurement. So if the initial state is not an eigenstate, then it must be different after the measurement than before (which is presumably what you mean by a "collapse"). $\endgroup$ – WillO Mar 19 '19 at 0:49
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    $\begingroup$ You should look into the concept of "weak measurements," which make precise the relation between degree of collapse and amount of information extracted from the measurement. $\endgroup$ – Rococo Mar 19 '19 at 1:10
  • $\begingroup$ @WillO One of the bits that I struggle to understand is where does this necessity for the system to jump to an eigenstate after the measurement come from. The answer can of course be, well, this is how a measurement of a quantum system is mathematically defined (this reads a lot like a def.: en.wikipedia.org/wiki/Measurement_in_quantum_mechanics). But a. I would expect something as meaningful as an action and consequence within any system be derived from some basic axioms rather than defined and b. if it is defined, it doesn't really say anything about what is practically possible?! $\endgroup$ – means-to-meaning Mar 20 '19 at 0:29
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    $\begingroup$ @means-to-meaning traditionally, this is considered a postulate of quantum mechanics. Very recently, there is a claim that it can be derived from other postulates: quantamagazine.org/… (semi-popular article), arxiv.org/abs/1811.11060 (paper) $\endgroup$ – Rococo Mar 20 '19 at 2:30

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