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

TL;DR

This paper demonstrates that local projective measurements in a relativistic quantum field theory are consistent across different reference frames, ensuring the same final state up to coordinate transformations due to locality and covariance.

Contribution

It shows that wavefunctional collapse from local measurements is consistent across frames in relativistic quantum systems, based on locality and covariance principles.

Findings

Wavefunctionals collapse on different time-slices but lead to the same final state.

Consistency of post-measurement states is guaranteed by locality and covariance.

Final states are related by coordinate transformations, ensuring physical equivalence.

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.