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Warning: This is a highly hypothetical question.

I am bothered with Dirac's description of the system when making a measurement. Without quoting his statement (from The Principles of Quantum Mechanics, Dirac, 1930), he simply states that one of the axioms of quantum mechanics is that regardless of the current state of the system, once we make an observation, the system forcefully "jumps" to an eigenstate of the observable. It, particularly, jumps to the eigenstate associated with that specific eigenvalue that we measured.

Now, my question goes as follows, let us assume a hypothetical continuous observer; that is, an observer that observers (measures) the system continuously without a pause. Let us assume, furthermore, that we observed the system in one state, and hence ensured that it jumped to an eigenstate associated with the measurements (eigenvalue), according to Dirac. Let us assume, additionally, that we start applying external effects to the system (probably forces) so as to change the system's state, which is admissible by quantum mechanics. Let us assume, now, that we let the continuous observer observe the system while applying the external forces (agents or any physical effect). We have two possibilities at this point: It is either the case that the state will NOT change, or that it will ACTUALLY change.

If the state changes while continuously observing, then Dirac's axiom fails miserably and this postulate of quantum mechanics collapses.

On the other hand, if the state remains the same while observing, then by making the external applied forces arbitrary, we can generate any possible state of the system. But then, this means that regardless of the state of the system, the measurement will be always the same with this specific observer (measurer). However, since we know that the system can actually have different measurements when measured at different times and in different states (then by different observers), we can say that the measurement has nothing to do with the state of the system. Rather, it is associated with the observer. Hence, by studying the observer itself, we can get the measurement without bothering to measure the system.

To save you some time, my photonics professor said that there is nothing like a continuous observer. His answer did not really convince me for I am creating a hypothetical situation.

Norbert Schuch
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1 Answers1

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What happens after a measurement is controversial and different accounts of what is happening in reality will give different answers. My answer presupposes that quantum mechanical equations of motion such as the Schrödinger or Dirac equation are accurate descriptions of reality.

A measurement is an interaction between the measurement device $M$ and a system $S$ that produces a record: a piece of information about the system that can be copied, discussed, criticised etc. A measurement interaction takes place suppresses interference between the different values of the measured observable:

https://arxiv.org/abs/0707.2832

As a result the different values of the measured observable evolve autonomously and to reflect this you update the relative state of the system concerned:

https://arxiv.org/abs/2008.02328

There are other theories that provide different equations of motion and so different accounts of measurement such as spontaneous collapse or pilot wave theories:

https://arxiv.org/abs/2310.14969

https://arxiv.org/abs/2212.12175

alanf
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