### Abstract

Suppose the postulate of measurement in quantum mechanics can be extended to quantum field theory; then a local projective measurement at some moment on an object locally coupled with a relativistic quantum field will result in a projection or collapse of the wavefunctional of the combined system defined on the whole time-slice associated with the very moment of the measurement, if the relevant degrees of freedom have nonzero correlations. This implies that the wavefunctionals in the same Hamiltonian system but defined in different reference frames would collapse on different time-slices passing through the same local event where the measurement was done. Are these post-measurement states consistent with each other? We illustrate that the quantum states of the Raine-Sciama-Grove detector-field system started with the same initial Gaussian state defined on the same initial time-slice, then collapsed by the measurements on the pointlike detectors on different time-slices in different frames, will evolve to the same state of the combined system up to a coordinate transformation when compared on the same final time-slice. Such consistency is guaranteed by the spatial locality of interactions and the general covariance in a relativistic system, together with the spatial locality of measurements and the linearity of quantum dynamics in its quantum theory.

Original language | English |
---|---|

Pages (from-to) | 3102-3115 |

Number of pages | 14 |

Journal | Annals of Physics |

Volume | 327 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2012 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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*Annals of Physics*, vol. 327, no. 12, pp. 3102-3115. https://doi.org/10.1016/j.aop.2012.08.004

**Instantaneous spatially local projective measurements are consistent in a relativistic quantum field.** / Lin, Shih Yuin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Instantaneous spatially local projective measurements are consistent in a relativistic quantum field

AU - Lin, Shih Yuin

PY - 2012/12/1

Y1 - 2012/12/1

N2 - Suppose the postulate of measurement in quantum mechanics can be extended to quantum field theory; then a local projective measurement at some moment on an object locally coupled with a relativistic quantum field will result in a projection or collapse of the wavefunctional of the combined system defined on the whole time-slice associated with the very moment of the measurement, if the relevant degrees of freedom have nonzero correlations. This implies that the wavefunctionals in the same Hamiltonian system but defined in different reference frames would collapse on different time-slices passing through the same local event where the measurement was done. Are these post-measurement states consistent with each other? We illustrate that the quantum states of the Raine-Sciama-Grove detector-field system started with the same initial Gaussian state defined on the same initial time-slice, then collapsed by the measurements on the pointlike detectors on different time-slices in different frames, will evolve to the same state of the combined system up to a coordinate transformation when compared on the same final time-slice. Such consistency is guaranteed by the spatial locality of interactions and the general covariance in a relativistic system, together with the spatial locality of measurements and the linearity of quantum dynamics in its quantum theory.

AB - Suppose the postulate of measurement in quantum mechanics can be extended to quantum field theory; then a local projective measurement at some moment on an object locally coupled with a relativistic quantum field will result in a projection or collapse of the wavefunctional of the combined system defined on the whole time-slice associated with the very moment of the measurement, if the relevant degrees of freedom have nonzero correlations. This implies that the wavefunctionals in the same Hamiltonian system but defined in different reference frames would collapse on different time-slices passing through the same local event where the measurement was done. Are these post-measurement states consistent with each other? We illustrate that the quantum states of the Raine-Sciama-Grove detector-field system started with the same initial Gaussian state defined on the same initial time-slice, then collapsed by the measurements on the pointlike detectors on different time-slices in different frames, will evolve to the same state of the combined system up to a coordinate transformation when compared on the same final time-slice. Such consistency is guaranteed by the spatial locality of interactions and the general covariance in a relativistic system, together with the spatial locality of measurements and the linearity of quantum dynamics in its quantum theory.

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UR - http://www.scopus.com/inward/citedby.url?scp=84868508231&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2012.08.004

DO - 10.1016/j.aop.2012.08.004

M3 - Article

AN - SCOPUS:84868508231

VL - 327

SP - 3102

EP - 3115

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 12

ER -