Quantum Measurement under Heisenberg Picture?

[LarryS]

TL;DR

What happens during a quantum measurement under Heisenberg picture?

When a quantum measurement occurs under the Schrödinger picture, the wave function collapses to one of the eigenvectors of the operator-observable and the value measured is the corresponding eigenvalue of that eigenvector. What happens during a quantum measurement under the Heisenberg picture where the operator assumes the full time-dependence?

Thanks in advance.

 

[PeterDonis]

When a quantum measurement occurs under the Schrödinger picture, the wave function collapses

This is interpretation dependent. Not all interpretations have collapse.

What happens during a quantum measurement under the Heisenberg picture where the operator assumes the full time-dependence?

As far as the minimal version of QM that is within scope for discussion here (discussions of interpretations belong in the QM foundations and interpretations forum), there is no difference between the Heisenberg and Schrödinger pictures as far as predictions of measurement results are concerned.

 

[LarryS]

This is interpretation dependent. Not all interpretations have collapse.
As far as the minimal version of QM that is within scope for discussion here (discussions of interpretations belong in the QM foundations and interpretations forum), there is no difference between the Heisenberg and Schrödinger pictures as far as predictions of measurement results are concerned.

Are the values measured also eigenvalues of the dynamical Heisenberg operator?

 

[PeterDonis]

Are the values measured also eigenvalues of the dynamical Heisenberg operator?

They are eigenvalues of the particular operator which is the value of the dynamical Heisenberg operator at the time $t$ at which the measurement is made.

 

[andresB]

Do note that the Heisenberg picture is build from the Schrödinger picture in a way so that they agree in stuff like expectation values.

 

[vanhees71]

All pictures of time evolution are equivalent (with some care concerning technical issues like Haag's famous theorem). Thus also any interpretation of the theory with regard to physics are independent of the choice of the picture of time evolution. If an interpretation depends on the choice of the picture, it's worthless and does not provide a sound and solid basis for the interpretation of the mathematical formalism in the sense of physics. The only thing an interpretation must provide is a consistent formulation of how the mathematical formalism is related to observations in nature.

[Moderator's note: Off topic content deleted.]

 

[Demystifier]

Summary:: What happens during a quantum measurement under Heisenberg picture?

When a quantum measurement occurs under the Schrödinger picture, the wave function collapses to one of the eigenvectors of the operator-observable and the value measured is the corresponding eigenvalue of that eigenvector. What happens during a quantum measurement under the Heisenberg picture where the operator assumes the full time-dependence?

Thanks in advance.

The Heisenberg picture moves the Hamiltonian evolution from the state to the observable. But the collapse is a non-Hamiltonian evolution, so it is not affected by the transition from the Schrödinger to the Heisenberg picture. In other words, if there is a state collapse in the Schrödinger picture, then there is also a state collapse in the Heisenberg picture.

 

[PeterDonis]

But certainly there is an update of information represented by a projection of the state.

See Rule 7 here:

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

As has been communicated in previous discussions, that Insights article describes the "minimal" version of QM that is the basis for all discussion in this forum. Any discussion of interpretations over and above that belongs in the QM foundations and interpretations forum.

 

[PeterDonis]

Moderator's note: A number of off topic posts about "collapse" have been deleted. Please note my reminder about the forum rules in my previous post.