Relational quantum mechanics

Rovelli, Carlo

doi:10.1007/bf02302261

Cited by 816 publications

(624 citation statements)

References 28 publications

Supporting

Mentioning

554

Contrasting

Unclassified

Order By: Relevance

“…Again, the observer himself, who is exterior to the system, is not described in the framework of quantum mechanics. In Rovelli's relational interpretation [86] a quantum mechanical description of some object is regarded as a codification of its properties which is "observer-dependent", that is, relative to a particular apparatus. Then, while a first "observer" A who gathers information about S regards reduction as real, a second observer testing S + A can consider that reduction has not taken place.…”

Section: Mikhail Gorbachevmentioning

confidence: 99%

“…An interaction H SA is then switched on between S and a second apparatus A , analogous to A but coupled to the componentŝ v of s in some v-direction. It is the new diagonal marginal stater(τ dec ), equal to the diagonal part ofr(0), which is then 84 Being quick is hardly ever good 85 You should not put too much hay on your fork 86 He who embraces too much fails to catch tested by A . In this measurement ofŝ v the probability of reading m = +m F on A and findingŝ in the v-direction is r ↑↑ (0) cos 2 1 2 θ + r ↓↓ (0) sin 2 1 2 θ, where θ and φ are the Euler angles of v. The measurement ofŝ v alone would have provided the additional contribution r ↑↓ (0) sin θe iφ .…”

Section: Dutch and French Proverbsmentioning

confidence: 99%

See 1 more Smart Citation

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

View full text Add to dashboard Cite

The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

show abstract

Section: Mikhail Gorbachevmentioning

confidence: 99%

Section: Dutch and French Proverbsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

View full text Add to dashboard Cite

show abstract

“…1), it is a conditioned state. The PaW mechanism was criticized in [6,12] and a proposal that overcomes these criticisms [21,22] used Rovelli's evolving constants of motion [3,23] parametrized by an arbitrary parameter that is then averaged over to yield the correct propagators. Although the end result matches the quantum predictions [24], the averaging used there amounts to a statistical averaging which is typically reserved to unknown physical degrees of freedom rather than to parameters with no physical significance.…”

mentioning

confidence: 99%

“…Many such proposals have appeared in the literature (e.g. [1][2][3][4][5][6][7][8][9][10][11]), but none seem entirely satisfactory [6,[12][13][14][15][16]. One of these is the Page and Wootters (PaW) mechanism [5] (see also [2,[17][18][19][20]), which considers "time" as a quantum degree of freedom by assigning to it a Hilbert space H T .…”

mentioning

confidence: 99%

Quantum time

2015

View full text Add to dashboard Cite

We give a consistent quantum description of time, based on Page and Wootters's conditional probabilities mechanism, which overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows one to reproduce the correct statistics of sequential measurements performed on a system at different times. DOI: 10.1103/PhysRevD.92.045033 PACS numbers: 03.65.Ta, 06.30.Ft, 03.65.Ud, 03.67.-a Time in quantum mechanics appears as a classical parameter in the Schrödinger equation. Physically it represents the time shown by a "classical" clock in the laboratory. Even though this is acceptable for all practical purposes, it is important to be able to give a fully quantum description of time. Many such proposals have appeared in the literature (e.g. [1][2][3][4][5][6][7][8][9][10][11]), but none seem entirely satisfactory [6,[12][13][14][15][16]. One of these is the Page and Wootters (PaW) mechanism [5] (see also [2,[17][18][19][20]), which considers "time" as a quantum degree of freedom by assigning to it a Hilbert space H T . The "flow" of time then consists simply in the correlation (entanglement) between this quantum degree of freedom and the rest of the system, a correlation present in a global, time-independent state jΨii. An internal observer will see such a state as describing normal time evolution: the familiar system state jψðtÞi at time t arises by conditioning (via projection) the state jΨii to a time t (Fig. 1), it is a conditioned state. The PaW mechanism was criticized in [6,12] and a proposal that overcomes these criticisms [21,22] used Rovelli's evolving constants of motion [3,23] parametrized by an arbitrary parameter that is then averaged over to yield the correct propagators. Although the end result matches the quantum predictions [24], the averaging used there amounts to a statistical averaging which is typically reserved to unknown physical degrees of freedom rather than to parameters with no physical significance. (A different way of averaging over time was also presented in [25] to account for some fundamental decoherence mechanism.)Here we use a different strategy: we show that the same criticisms can be overcome by carefully formalizing measurements through the von Neumann prescription [26] (which we extend to generalized observables, positive operator valued measures [POVMs]). We show how this implies that all quantum predictions can be obtained by conditioning the global, timeless state jΨii: this procedure gives the correct quantum propagators and the correct quantum statistic for measurements performed at different times, features that were absent in the original PaW mechanism [6,16]. We also show how the PaW mechanism can be extended to give the time-independent Schrödinger equation and give a physical interpretation of the mechanism.What is the physical significance of the quantized time in the PaW representation? One is free to consider the time quantum degree of freedom either as an abstract purification space without any physical signific...

show abstract

“…In this sense, the probability of |P i is affected by the probability distribution of |R j . The state |P i of the to-be-studied system has no individual absolute meaning, it makes sense only relative to the state |R j of the measuring device as a reference [11,12], namely, the state is relational [13,14]. The entangled state is purely a quantum state, having no classical correspondence.…”

Section: A Relational Interpretationmentioning

confidence: 99%

The Cosmological Constant Problem and Quantum Spacetime Reference Frame

Luo¹

2017

Preprint

View full text Add to dashboard Cite

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model. We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρc0 (ρc0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term in the effective action; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. We also generalize the equivalence principle to be valid for all quantum phenomenon.

show abstract

Relational quantum mechanics

Cited by 816 publications

References 28 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Quantum time

The Cosmological Constant Problem and Quantum Spacetime Reference Frame

Contact Info

Product

Resources

About