Source-linked AI summary
Is a system's wave function in one-to-one correspondence with its elements of reality?
Roger Colbeck, Renato Renner
TL;DR
The paper examines two assumptions underlying its result and formalizes relevant variables in spacetime. It relates one assumption to existing experimental tests, while noting that the other has received limited experimental attention.
Problem
The work depends on two assumptions, discussed separately and described as essentially those used in earlier work.
Method
The paper introduces spacetime variables and assigns coordinates to measurement settings, outcomes, and pre-existing information according to their causal locations.
Results
The first assumption has been experimentally investigated with results compatible with quantum theory within experimental tolerance.
Takeaways & Limitations
Experimental data can bound how closely the Markov chain condition holds, but no experiment can establish it precisely.
Takeaways & Limitations
The freedom of choice assumption is difficult to probe because it concerns information in a hypothetical higher theory.
Abstract
from arXiv · showhide
Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function---the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e. an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [Pusey et al. arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.
I. ADDITIONAL DISCUSSION OF THE ASSUMPTIONS
The paper formalizes its assumptions using spacetime variables, which represent values accessible at specified spacetime points. Measurement settings and outcomes receive coordinates that constrain their causal ordering relative to pre-existing information.
- I. ADDITIONAL DISCUSSION OF THE ASSUMPTIONS: Spacetime variables are random variables paired with coordinates in four-dimensional spacetime.They may represent values accessible at the spacetime point specified by those coordinates.
- I. ADDITIONAL DISCUSSION OF THE ASSUMPTIONS: The measurement setting A is assigned the spacetime point where the measurement is chosen, while X is placed where its outcome becomes available.The coordinates of X can be any point in the region where the outcome is available.
- I. ADDITIONAL DISCUSSION OF THE ASSUMPTIONS: The outcome X lies in A’s future lightcone, whereas pre-measurement information Γ must not lie in A’s future lightcone.This assignment encodes the intended causal relation between choosing a setting, obtaining an outcome, and accessing prior information.
A. Correctness of quantum theory
The correctness assumption requires standard quantum theory to describe measurement statistics, both for individual outcomes and for specified joint measurements involving an enlarged system and environment.
- A. Correctness of quantum theory: The correctness assumption concerns statistical predictions made within standard quantum theory, without referring to additional parameters in a higher theory.It is divided into two parts for the paper’s argument.
- A. Correctness of quantum theory: QMa requires the Born-rule probability for outcome X = x under setting A = a to be determined by Ψ and the corresponding projectors.The measurement setting is represented by a family of projectors parameterized by possible outcomes.
- A. Correctness of quantum theory: QMb extends the requirement to joint statistics involving an initial measurement and arbitrary additional measurements on an enlarged system.The enlarged system includes the original system together with measurement-apparatus and environmental degrees of freedom.
- A. Correctness of quantum theory: The measurement process in QMb is modeled as an isometry from the system Hilbert space to a larger system–environment Hilbert space.Restricting the resulting state to the original system recovers the initial measurement description.
- A. Correctness of quantum theory: The assumptions apply the Born rule to both single-system outcomes and joint distributions involving outcomes of additional measurements.This distinction separates QMa from the stronger joint-statistics requirement QMb.
B. Freedom of choice
Freedom of choice means that measurement settings are independent of pre-existing information outside their future lightcones. The paper relates this formulation to weaker assumptions used in Bell-type analyses.
- B. Freedom of choice: Freedom of choice is often implicit in discussions of quantum foundations, including much of Bell’s work.Bell later stated the assumption explicitly.
- B. Freedom of choice: A spacetime variable A is free with respect to Ω when it is independent of the variables in Ω outside A’s future lightcone.This excludes dependence on pre-existing values relative to any reference frame.
- B. Freedom of choice: The definition interprets causal influence through future lightcones: variables correlated with A must be capable of having been caused by A.This is the spacetime-based motivation for the mathematical definition.
- B. Freedom of choice: For the main-text information Γ, freedom of A reduces to PAΓ = PA × PΓ because Γ lies outside A’s future lightcone.Thus the setting is statistically independent of Γ.
- B. Freedom of choice: In the bipartite scenario, free settings satisfy PA|BYΓ = PA and PB|AXΓ = PB.The appendix notes that de Broglie–Bohm theory does not obey these conditions when Γ includes the wave function and hidden trajectories.
- B. Freedom of choice: Bell’s weaker independence condition can follow from full freedom of choice and is sufficient for the result when combined with local causality.The literature sometimes treats this weaker implication as the definition of free choice.
II. CONNECTION TO EXPERIMENT
The appendix connects the assumptions to experimental tests. Single-system statistical predictions agree with observations within experimental tolerance, while other assumptions remain harder to test directly.
- II. CONNECTION TO EXPERIMENT: The main argument assumes that measurement outcomes obey quantum-theory statistics, whose experimental status can be examined.The corresponding assumption is divided into two parts as in the earlier result on which the argument builds.
- II. CONNECTION TO EXPERIMENT: Experiments have investigated the first part and found results compatible with quantum theory within experimental tolerance.Observed data can bound the distance from the relevant Markov-chain condition, although they cannot establish it exactly.
- II. CONNECTION TO EXPERIMENT: The second part has received little experimental attention to date.A microscopic measurement procedure demonstrably inconsistent with unitary dynamics would falsify that assumption and indicate new physics.
- II. CONNECTION TO EXPERIMENT: Freedom of choice is harder to probe because it concerns Γ, information belonging to a hypothetical higher theory.A device that predicts measurement settings before they are chosen could falsify the assumption in a specific case.