The heart of the measurement puzzle, namely the problem of definite outcomes, remains unresolved. This paper shows that Josef Jauch's 1968 reduced density operator approach is the solution, even though many question it: The entangled "Measurement State" implies local mixtures of definite but indeterminate eigenvalues even though the MS continues evolving unitarily. A second, independent, argument based on the quantum's nonlocal entanglement with its measuring apparatus shows that the outcomes must be definite eigenvalues because of relativity's ban on instant signaling. Experiments with entangled photon pairs show the MS to be a non-paradoxical superposition of correlations between states rather than a "Schrodinger's cat" superposition of states. Nature's measurement strategy is to shift the superposition--the coherence--from the detected quantum to the correlations between the quantum and its detector, allowing both subsystems to collapse locally to mixtures of definite eigenvalues. This solution implies an innocuous revision of the standard eigenvalue-eigenstate link. Three frequent objections to this solution are rebutted.
The heart of the measurement puzzle, namely the problem of definite outcomes, remains unresolved. This paper shows that Josef Jauch's 1968 reduced density operator approach is the solution, even though many question it: The entangled "Measurement State" implies local mixtures of definite but indeterminate eigenvalues even though the MS continues evolving unitarily. A second, independent, argument based on the quantum's nonlocal entanglement with its measuring apparatus shows that the outcomes must be definite eigenvalues because of relativity's ban on instant signaling. Experiments with entangled photon pairs show the MS to be a non-paradoxical superposition of correlations between states rather than a "Schrodinger's cat" superposition of states. Nature's measurement strategy is to shift the superposition--the coherence--from the detected quantum to the correlations between the quantum and its detector, allowing both subsystems to collapse locally to mixtures of definite eigenvalues. This solution implies an innocuous revision of the standard eigenvalue-eigenstate link. Three frequent objections to this solution are rebutted.
The fully entangled Schrodinger cat state obtained immediately upon measurement of a superposed two state quantum system by a detector is often said to paradoxically predict macroscopically different outcomes simultaneously. However, nonlocal interferometry experiments and their accompanying quantum theoretical analyses, testing momentum entangled photon pairs over the full range of phases, demonstrate that the cat state does not fit this description. This state instead represents two nonlocally coherent correlations between its subsystems. Even if the detector is a cat, this state is not paradoxical. Furthermore, standard quantum theory correctly predicts the experimentally observed nonparadoxical outcomes. Thus both quantum theory and quantum experiments show there is no Schrodinger cat paradox associated with measurement. This resolves the problem of definite outcomes and, with it, the measurement problem. Upon entanglement with a detector, superpositions collapse nonlocally and unitarily to one definite macroscopic outcome. No special collapse postulate is needed.
This paper resolves the problem of definite outcomes, also known as "Schrodinger's cat" and the "problem of wavefunction collapse." It's the problem of understanding how nature goes from a coherent superposition of possible outcomes to a single definite outcome. This "measurement problem" has not to my knowledge been solved. The analysis stems from an insight into entanglement demonstrated in two nonlocality experiments involving pairs of momentum-entangled photons. These show that an entangled state of two subsystems is not a superposition of products of paired states, but instead a superposition of correlations between paired states. The "premeasurement state" is just such a superposition with the proviso that one subsystem is the detector of the other subsystem. This state is not a paradoxical superposition of macroscopic detector states; it is instead a superposition of correlations between detector states and microscopic quantum states. Thus, Schrodinger's cat isn't "smeared" between dead and alive but instead represents a nonlocal superposition of correlations between states of the cat and states of the nucleus: This is what we want. We also critique one previously claimed resolution of the measurement problem and seven previously claimed proofs that the measurement problem is unsolvable.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
The entangled “measurement state” (MS), predicted by von Neumann to arise during quantum measurement, seems to display paradoxical properties such as multiple macroscopic outcomes. But analysis of interferometry experiments using entangled photon pairs shows that entangled states differ surprisingly from simple superposition states. Based on standard quantum theory, this paper shows that the MS (i) does not represent multiple detector readings but instead represents nonparadoxical multiple statistical correlations between system states and detector readings, (ii) implies that exactly one outcome actually occurs, and (iii) implies that when one outcome occurs, the other possible outcomes simultaneously collapse nonlocally. Point (iii) resolves an issue first raised in 1927 by Einstein who demonstrated that quantum theory requires instantaneous state collapse. This conundrum’s resolution requires nonlocal correlations, which from today’s perspective suggests the MS should be an entangled state. Thus, contrary to previous presumed proofs of the measurement problem’s insolubility, we find the MS to be the collapsed state and just what we expect upon measurement.
Nonlocal interferometry, in which two photons are entangled in the (MS) of quantum measurement theory, illuminates the measurement problem. Experiments done in 1990 by Rarity and Tapster and by Mandel's group, in which each photon measures the other, probe the effect of a variable phase factor inserted between the two superposed terms of the MS. The results show that, when a bipartite (two-part) system is in the MS, its subsystems are not in superpositions but are instead in collapsed, or mixed, states with each subsystem exhibiting a definite, but unpredictable, outcome. Standard quantum theory (without the collapse postulate) predicts this MS and thus correctly predicts these observations. The experiment confirms that, when a quantum system and a measuring apparatus are entangled in the MS, the state actually detected by an observer of either subsystem is the local or reduced state of the subsystem. The global superposition state, which continues evolving unitarily, merely records the nonlocal correlations and does not contradict the definite, non-superposed, outcomes. Thus Schrodinger's cat, example, is in a non-paradoxical mixture of being alive on trials when the nucleus didn't decay, and dead on trials when the nucleus decayed. This resolves the problem of definite outcomes, with no assistance from human minds, other worlds, hidden variables, the environment, a collapse postulate, collapse mechanisms, or for all practical purposes arguments.