Role of the collapse in the instrumentalist interpretation

[atyy]

The person using QM to make predictions constitutes an observer in the sense described above, but is the idea of an observer limited to this sense? Observer can refer more generally to a classical apparatus, correlated with the quantum system, that renders a measurement outcome. With the double slit experiment, most people would consider the interference-destroying measurement to be made by the detector at the slits, rather than the scientist reviewing the detector data at a later time.

What I'm challenging is the insistence that an observer in this sense must be excluded from the quantum state, since the classical properties necessary to establish a measurement outcome can be identified in a quantum framework.

The point is that ultimately, one needs an observer that is excluded from the quantum state. Whether the measurement apparatus is considered part of the observer is subjective. If the physicist considers its "self" to be real, it must still define "self". For example, does a physicist's "self" include its fingernails, or clothes? If that is subjective, then whether the measurement apparatus is part of the "self" is also subjective.

 

[Morbert]

The point is that ultimately, one needs an observer that is excluded from the quantum state. Whether the measurement apparatus is considered part of the observer is subjective. If the physicist considers its "self" to be real, it must still define "self". For example, does a physicist's "self" include its fingernails, or clothes? If that is subjective, then whether the measurement apparatus is part of the "self" is also subjective.

Then I wouldn't object to this convention, provided we acknowledge that the emergence of classicality necessary for a measurement scenario is not similarly subjective. Whether we use $\rho_s$ or $\rho_s\otimes\rho_m$, the data $\epsilon_i$ can be included in a classical (boolean) logic long before the scientist or their fingernails need to be considered.

Also, it seems this notion of an observer as "the entity using the theory to make predictions about an experiment they choose to conduct" would also be excluded from the state even if we use a classical theory.

 

[kith]

The person using QM to make predictions constitutes an observer in the sense described above, but is the idea of an observer limited to this sense? Observer can refer more generally to a classical apparatus, correlated with the quantum system, that renders a measurement outcome. With the double slit experiment, most people would consider the interference-destroying measurement to be made by the detector at the slits, rather than the scientist reviewing the detector data at a later time.

Things are simple, if we use the word "observer" to refer to the actual person who performs the measurement in union with her means of investigation. Statements like "the measurement is made by the detector" make things unnecessarily complicated. They replace the clear meaning of the term "measurement" as an intentional process of an entity to gather data for building models with something unclear.

If we want to talk about the physical processes happening at the detector, we have a precise technical language at our disposal (the language of decoherence) which we should use.

 

[kith]

Also, it seems this notion of an observer as "the entity using the theory to make predictions about an experiment they choose to conduct" would also be excluded from the state even if we use a classical theory.

Yes and we could give up the realism of classical mechanics and instead use a similar ontology as in instrumental QM to reflect this. But we can't go the other route: in QM we can't simply take the state of the observer as determined but unknown without getting into problems. In classical mechanics, we can, so we usually do.

 

[Morbert]

Things are simple, if we use the word "observer" to refer to the actual person who performs the measurement in union with her means of investigation. Statements like "the measurement is made by the detector" make things unnecessarily complicated. They replace the clear meaning of the term "measurement" as an intentional process of an entity to gather data for building models with something unclear.

The convention you describe above seems reasonable, but perhaps we can obtain further specificity. Von Neumann, in his theory of measurement[1], makes a distinction between measurement as a physical process and observation as perception. He uses an example of a thermometer measuring the temperature of a system, and an observer observing the length of the mercury in the thermometer. I.e. Perhaps it is useful to make a distinction between the generation of data by an apparatus (measurement), and the subjective experience of/inference from this data by the user (observation).

Using this language, an observer is excluded from the system modeled by quantum mechanics, but a measurement process can be included.

If we want to talk about the physical processes happening at the detector, we have a precise technical language at our disposal (the language of decoherence) which we should use.

Just a point of clarification: Decoherence is important in this process I was calling measurement, but it isn't sufficient. Decoherence establishes a logic for classical properties in the apparatus so that it has the ability to express data, but it is the establishment of a logical equivalence between classical properties of the apparatus and quantum properties of the measured system that is key to a measurement process.

[1] https://press.princeton.edu/books/h...mathematical-foundations-of-quantum-mechanics

 

[kith]

Von Neumann, in his theory of measurement[1], makes a distinction between measurement as a physical process and observation as perception.

I don't agree with this reading of von Neumann.

In his presentation, $I$ is the system of interest, $II$ are the means the observer uses to perform the measurement and $III$ is the "actual" observer (which does not necessarily include her whole body). What he does is to prove that the boundary between what is considered to be the quantum system and what is considered to belong to the observer can be shifted, i.e. the divisions $I \,\, | \,\, II\!+\!III$ and $I\!+\!II \,\, | \,\, III$ give the same predictions.

He doesn't say that the physical process involving $I + II$ generates data which are simply perceived by the observer, which is false (see below).

I.e. Perhaps it is useful to make a distinction between the generation of data by an apparatus (measurement), and the subjective experience of/inference from this data by the user (observation).

The quantum interaction between the system and the apparatus doesn't generate data, it generates possible data. The observer is not just there to take note of previously generated data, he is necessary to objectify one of the possibilities. I disagree with your notion of "measurement" because it doesn't reflect this.

 

[Morbert]

In his presentation, $I$ is the system of interest, $II$ are the means the observer uses to perform the measurement and $III$ is the "actual" observer (which does not necessarily include her whole body). What he does is to prove that the boundary between what is considered to be the quantum system and what is considered to belong to the observer can be shifted, i.e. the divisions $I \,\, | \,\, II\!+\!III$ and $I\!+\!II \,\, | \,\, III$ give the same predictions.

Von Neumann discusses two divides: The "observer/observed" divide and the "actually observed/measuring instrument/actual observer" divide. The bit I've put in bold implies you consider the quantum/classical divide to be the same as the observer/observed divide.

The division $I\!+\!II \,\, | \,\, III$ means the interaction between the measuring instrument and the actually observed system is explicitly modeled, and $II$ (whether it is a thermometer, or the light + observer eye, or the retina + brain) must have classical properties if they are to be perceived by the actual observer. So this would be an example of the classical/quantum divide differing from the observer/observed divide, since the classical properties needed to express the measurement result are on the "observed" side of the observer/observed divide. A useful distinction can therefore be made between the classical apparatus serving as the measuring instrument and the actually observed system, independent from what we implicitly or explicitly model.

You might object to a description of these measuring instrument properties as classical under the division $I\!+\!II \,\, | \,\, III$ because they are handled within a quantum framework. But we can identify classical properties in a quantum theoretic framework[1] and it is useful to do so when understanding the measuring process.

He doesn't say that the physical process involving $I + II$ generates data which are simply perceived by the observer, which is false (see below).

The quantum interaction between the system and the apparatus doesn't generate data, it generates possible data. The observer is not just there to take note of previously generated data, he is necessary to objectify one of the possibilities. I disagree with your notion of "measurement" because it doesn't reflect this.

Instrumentalism frames QM as a theory that makes statistical claims. It returns relative frequencies and expectation values that the user can compare against the data produced by the experiment. If this is what you mean by generates possible data, I agree, but this doesn't contradict the common sense understanding of a measuring instrument interacting with $I$ and producing data, to be studied by the actual observer. We just have to not expect QM to describe the actualisation of the data. It instead describes the statistics the actualised data will follow.

[1] https://aip.scitation.org/doi/10.1063/1.531886

 

[kith]

Instrumentalism frames QM as a theory that makes statistical claims. It returns relative frequencies and expectation values that the user can compare against the data produced by the experiment.

Textbook instrumentalism goes beyond probabilities and expectation values and talks about the state of the individual system after a single measurement. I didn't realize that you might have an ensemble view of instrumentalism in mind. When you talk about "data" are you always referring to many runs?

If this is what you mean by generates possible data, I agree [...]

Sorry, I should have been clearer here. By "possible data" I meant that if we include $II$ in the quantum description, the final state of the combined system is an entangled state which corresponds to a multitude of possible measurement outcomes and not a state which corresponds to a single, actualized measurement outcome.

[...]but this doesn't contradict the common sense understanding of a measuring instrument interacting with $I$ and producing data, to be studied by the actual observer.

If we take $II$ to be the thermometer we don't get a definite temperature after a single measurement but a superposition which corresponds to different temperatures. When the actual observer determines the temperature by looking at the thermometer, she doesn't simply perceive an external fact but is herself integral to its establishment. We shouldn't call the interaction between $I$ and $II$ a "measurement" because it isn't sufficient to establish the fact.

 

[Morbert]

Textbook instrumentalism goes beyond probabilities and expectation values and talks about the state of the individual system after a single measurement. I didn't realize that you might have an ensemble view of instrumentalism in mind. When you talk about "data" are you always referring to many runs?

I had a frequentist unserstanding of probabilities in mind, but a Bayesian understanding would be compatible as well. But more to your point: I was understanding the initial quantum state as an input, and only probabilities (however they are interpreted) as output. As opposed to both the final quantum state and probabilities as output. The physicist can of course incorporate her knowledge of a measurement result from a previous experiment in her preparation of a subsequent experiment. E.g. If she learns of a measurement result $a_i$, she can write down the quantum state for the next experiment $$\rho'_s = \Pi_{a_i,t_0}\rho_s\Pi_{a_i,t_0}$$
that is if we use the convention $I \,\, | \,\, II\!+\!III$. If we instead use $I\!+\!II \,\, | \,\, III$ then she constructs $$\rho'_{s,m}\otimes\rho_{m'} = (\Pi_{\epsilon_i,t_0}\rho_s\otimes\rho_m\Pi_{\epsilon_i,t_0})\otimes\rho_{m'}$$ where $m'$ is the 2nd measuring instrument

Sorry, I should have been clearer here. By "possible data" I meant that if we include $II$ in the quantum description, the final state of the combined system is an entangled state which corresponds to a multitude of possible measurement outcomes and not a state which corresponds to a single, actualized measurement outcome.

If we take $II$ to be the thermometer we don't get a definite temperature after a single measurement but a superposition which corresponds to different temperatures. When the actual observer determines the temperature by looking at the thermometer, she doesn't simply perceive an external fact but is herself integral to its establishment. We shouldn't call the interaction between $I$ and $II$ a "measurement" because it isn't sufficient to establish the fact.

We both agree that in the real world, a thermometer reports a definite temperature. We both agree that we can use QM to construct a final state that is a superposition*. Where we seem to disagree is you say "this final state is what QM reports as the result of $I$ and $II$ interacting, but instead a definite temperature is recorded , so this interaction is not a measurement in any meaningful sense". I say "QM does not report the final state as the result of $I$ and $II$ interacting. Instead QM reports a probability for each possible result of $I$ and $II$ interacting, and the final state is merely an ingredient in the computation of these probabilities". I don't know how substantive this disagreement is, and it might just come down to language convention.

*Ignoring for the time being things like information loss irreversibly and mixed states, which are admittedly important factors if we want to explore what it means to establish a fact.

 

[timmdeeg]

Thanks for answering my question, very much appreciated.