This page gives plain-language summaries of physics papers. We draw no link to Dost or to any other text; reading side by side is the reader's own work.
Experiment: measured. Theory: calculated or proved. Interpretation: its meaning is disputed. The labels are our own classification; a paper may have more than one nature.
Main question: Is collapse a real physical process?
In standard quantum mechanics the wave function is taken to “collapse” during measurement, but this rule does not come out of the Schrödinger equation and when a measurement takes place is unclear; this problem is called the measurement problem. Collapse models change the equation itself: they add “spontaneous” collapses that are negligibly rare in small systems and frequent and random in large ones. Collapse thus becomes a physical process and can be tested by experiment. The two papers on this subject contain the first of these models and a proposal tied to gravitation.
On this page58. Collapse Models · Ghirardi 1986 — Unified dynamics for mic · Penrose 1996 — On Gravity's role in Quan …
The model (the GRW model) that adds random “spontaneous localization” processes to the Schrödinger equation and describes microscopic and macroscopic systems with a single dynamics.
In quantum mechanics the Schrödinger equation is linear and preserves superpositions. As a result of a measurement, however, a single outcome is observed. The standard account puts an additional “collapse” rule onto the equation for this and leaves unclear when a measurement takes place. Ghirardi, Rimini and Weber proposed replacing the two separate rules with a single unified dynamics.
In the model each particle undergoes spontaneous localization at random times. With the proposed numbers, this event happens for one particle at an average frequency of 10⁻¹⁶ per second; that is, about once in a hundred million years for a single microscopic particle. In the localization the wave function is multiplied by a structure about 10⁻⁵ cm wide around a chosen position and renormalized.
For a single electron or atom this effect is too rare to be observed; thus phenomena such as interference remain consistent with the standard theory. A macroscopic body, on the other hand, consists of a very large number of components, and the localization of one component spreads to the whole body through the entangled state. For this reason a macroscopic superposition collapses to a single position in as short a time as about 10⁻⁷ seconds. In this way a definite position is obtained for the pointer or the cat.
The center of localization is chosen at random, and the probability of this choice is set up to agree with the measurement probabilities of the standard theory; thus the model reproduces measurement statistics. The place where the theory departs from the standard theory is that superpositions are not preserved forever in large systems; this predicts small deviations that can be tested by experiment.
Limit: the localization frequency and width are free parameters of the theory; the values above are the proposed choice and have since been tested by experiment.
Afterwards: The continuous version of the model (CSL) and its testing by experiments are surveyed in the entry “Collapse Theories” in the Stanford Encyclopedia of Philosophy: according to this entry, experiments today place an upper bound of around 10⁻¹³ s⁻¹ on the frequency for localization of width 10⁻⁷ m.
Gen. Relativ. Gravit. 28, 581-600 theoryinterpretation
The proposal that describes quantum state reduction (collapse) by tying it to the difference in the geometry given to space-time by two mass distributions.
Penrose’s starting point is the measurement problem: quantum theory can describe a system as a superposition of several states, but a measurement gives a single outcome. According to Penrose, this requires quantum theory and general relativity to be considered together. His reason is this: the superposition of a mass located in two separate positions means a superposition of two different space-time geometries.
The proposal is this: as the difference between these two geometries grows, the superposition becomes unstable and after a certain time collapses to one of the two states. The time depends on the gravitational self-energy difference between the two mass distributions, E_G: roughly τ ≈ ħ/E_G. In words: if the difference is small (small mass, small displacement) the time is very long and the superposition is effectively preserved; if the difference is large (large mass, large displacement) the time is very short.
In this way the time at which collapse takes place is tied to a scale of mass and displacement; these scales are defined not by the properties of the measuring apparatus or the environment but by the state’s own space-time structure.
Penrose maintains that this process is independent of the measuring apparatus and objective: collapse requires neither an observer nor entanglement with the environment (decoherence). In this respect the proposal differs from approaches that describe collapse by environmental decoherence. Penrose counts collapse as an event arising from the state’s own geometric difference; the details of the measurement set-up play no role in this calculation.
Limit: this is a theoretical proposal, not an experimental result; the exact form of the collapse-time calculation and the question of which states it will collapse to are among the problems the paper takes up. A similar gravity-linked localization proposal was also made by Diósi.
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: This proposal is also known as the Diósi–Penrose model; according to the Stanford Encyclopedia of Philosophy, the simple form of the model was refuted in 2021 by an experiment carried out in an underground laboratory (Donadi et al.).
59. Relational Quantum Mechanics and QBism
Main question: Is the state defined relative to an observer, is it a subjective probability?
What does the quantum state (the wave function) describe: the world, an observer’s knowledge, an agent’s expectation? Relational quantum mechanics holds the state to depend on the relation between two systems; each system may carry a separate state for other systems. QBism, for its part, takes the probabilities of the Born rule to be the subjective, personal probabilities of the agent making the measurement. Both give up the idea that the state is independent of the observer, but they place the observer’s role differently.
A proposal of relational quantum mechanics, which argues that the quantum state is not independent of the observer and that a system is described relative to another system.
Rovelli likens the discomfort known as the measurement problem to the discomfort created by the Lorentz transformations before Einstein. That discomfort came from the observer-independent notion of time. Rovelli puts forward that the discomfort in quantum mechanics too comes from a wrong concept, the concept of an observer-independent state of a system (or of observer-independent values of physical quantities).
For this reason he poses the question of “the interpretation of quantum mechanics” in a different form: the aim is to derive the formalism of the theory from a few simple physical postulates. For this he takes up reformulating quantum mechanics in terms of information theory.
In the proposed framework all systems are equivalent. There is no distinction between observer and observed; any physical system can be an “observer” for another system. The theory describes only the information systems have about one another, that is, their states relative to one another. Even so, the paper maintains that the theory is complete.
The paper also maintains that this information-theoretic formulation can describe the collapse of the wave function without counting it as an additional physical process: measurement is the measuring system’s acquiring information about the measured system, and this information is relative to that measuring system. The same two systems can be described as an entangled superposition for a third observer who does not take part in the measurement. These two descriptions are not a contradiction; they belong to two separate points of view. The author therefore stresses that the phrase ‘the state of the system’ is always said relative to another system.
Limit: this is a proposal of interpretation; it does not change the theory’s experimental predictions. Also, two observers’ attributing different states to the same event is not counted as a contradiction in this framework; this point has been the subject of later discussions.
Afterwards: A detailed account of the approach is in the entry “Relational Quantum Mechanics” in the Stanford Encyclopedia of Philosophy. Wigner’s-friend-type thought experiments have been the main ground on which this interpretation is tested.
The paper that introduces the QBist interpretation, which ties the quantum state to the agent’s subjective probabilities, and shows how quantum “nonlocality” disappears in this interpretation.
The paper is an introduction to the QBist interpretation of quantum mechanics. The authors put forward that this interpretation removes the paradoxes, puzzles and pseudo-problems that have occupied the foundations of quantum theory over the last ninety years. As an example, they show in detail how the problem of quantum “nonlocality” disappears in this interpretation.
QBism’s starting point is this: the probabilities given by the Born rule are the subjective (Bayesian) probability values of the agent making the measurement; the quantum state too is treated not as an observer-independent description of the world but as a summary of the agent’s own expectations. Measurement is an action the agent takes on the world, and the outcome is the agent’s experience. The change of the state after measurement is the agent’s updating of their knowledge.
In the discussion of nonlocality the paper maintains this: in Bell tests, the measurement outcome on one side updating the expectation of the agent on the other side does not mean that something far away is instantly affected; for what is updated is not a physical state but the agent’s personal probabilities.
The authors present QBism as an interpretation; they do not propose any change in the mathematical formalism of quantum mechanics. What changes is the answer to the question of what the formalism describes. For this reason experimental results such as violations of Bell inequalities apply just the same for QBism, and the interpretation retells them in its own language. The paper’s aim is to provide an introduction for a reader; in place of detailed mathematical derivations it presents the basic moves of the interpretation and the example of nonlocality.
Limit: QBism is an interpretation; the predictions of the theory remain the same as those of standard quantum mechanics, and it cannot be told apart from other interpretations by experiment. The main criticisms directed at the approach concern what conception of physical reality the subjectivity of the quantum state could be reconciled with; this is disputed.
Afterwards: A survey of the approach together with other pragmatist interpretations is in the entry “Quantum-Bayesian and Pragmatist Views of Quantum Theory” in the Stanford Encyclopedia of Philosophy.