- #1
Morbert
Gold Member
- 676
- 550
- TL;DR Summary
- Terms like "minimal interpretation" and "ensemble interpretation" and "instrumentalist interpretation" are sometimes used interchangeably. This thread makes notes of some distinctions made in literature.
I've recently had a look back at the review by Home and Whitaker as well as Asher Peres's book "Quantum Theory: Concepts and Methods". Both "minimal interpretation" and "ensemble interpretation" refer to categories of interpretations rather than interpretations themselves. Specifically, you can have an ensemble interpretation that is not minimal, and a minimal interpretation that is not an ensemble interpretation. Below is a table considering a minimal instrumentalist interpretation, a pre-assigned-values (PIV) ensemble interpretation, and the minimal ensemble interpretations. The table does not fully describe each interpretation. It only highlights some points of distinction between them.
Some remarks:
Both instrumental and ensemble interpretations could be considered anti-realist insofar as the the state of a system does not represent an actually-existing thing. Ensembles are infinite, as "finite ensembles, in fact, constitute individual systems, and quantum mechanics is not supposed to make predictions about individual systems. So an ensemble must be an infinite affair." (Sudbery). Even ensembles where members are pre-assigned values is still fictitious due to this infinite character. Similarly, the instrumentalist Peres describes the quantum system as a useful abstraction that does not exist in nature, characterized by the probabilities of outcomes of every conceivable test on a system.
Home + Whitaker consider a state ##|\psi\rangle = \sum_r \langle r|\psi\rangle|r\rangle## and say that, according to a PIV ensemble interpretation, this represents an infinite ensemble of systems, each with a value ##r##. And according to the minimal ensemble interpretation, it represents an ensemble of systems each in linear combination of ##|r\rangle## states. The latter seems recursive and inconsistent to me. I have argued against it in previous threads but perhaps it is accepted.
There is disagreement in literature to the significance of the collapse postulate. As such the last column in the table is the least definitive.
Some remarks:
Both instrumental and ensemble interpretations could be considered anti-realist insofar as the the state of a system does not represent an actually-existing thing. Ensembles are infinite, as "finite ensembles, in fact, constitute individual systems, and quantum mechanics is not supposed to make predictions about individual systems. So an ensemble must be an infinite affair." (Sudbery). Even ensembles where members are pre-assigned values is still fictitious due to this infinite character. Similarly, the instrumentalist Peres describes the quantum system as a useful abstraction that does not exist in nature, characterized by the probabilities of outcomes of every conceivable test on a system.
Home + Whitaker consider a state ##|\psi\rangle = \sum_r \langle r|\psi\rangle|r\rangle## and say that, according to a PIV ensemble interpretation, this represents an infinite ensemble of systems, each with a value ##r##. And according to the minimal ensemble interpretation, it represents an ensemble of systems each in linear combination of ##|r\rangle## states. The latter seems recursive and inconsistent to me. I have argued against it in previous threads but perhaps it is accepted.
There is disagreement in literature to the significance of the collapse postulate. As such the last column in the table is the least definitive.
Interpretation | Quantum states refer to | Probabilities are | Is probability ascribed to single events? | Do ensembles have structure? | The collapse postulate |
Minimal instrumentalist interpretation | Macroscopic preparation procedures | The likelihood of outcomes of macroscopic tests | Yes | N/A | No significance is attributed to the interpolation of the wavefunction across repeated measurements. |
Pre-assigned-value ensemble interpretation | Infinite ensembles of identically prepared systems | Portions of the ensemble with the corresponding property | No | Yes | The postulate describes the division of the ensemble into subensembles, each represented by possible states after collapse |
Minimal ensemble interpretation | Infinite ensembles identically prepared systems | Relative frequencies for macroscopic tests over the ensemble | No | No | The postulate describes the creation of subensembles, each represented by possible states after collapse |
Last edited: