Quantum Measurement under Heisenberg Picture?

Assuming that we can "just ignore" the "collapse" issue is simply not acceptable. If you cannot post without mentioning "collapse", then please do not post.In summary, when a quantum measurement occurs under the Schrodinger 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. In the Heisenberg picture, the Hamiltonian evolution is moved from the state to the observable, but the collapse is a non-Hamiltonian evolution and is not affected by this transition. The update of information represented by a projection of the state still occurs in both pictures, and any discussions of interpretations beyond this "minimal" version of QM
  • #1
LarryS
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What happens during a quantum measurement under Heisenberg picture?
When a quantum measurement occurs under the Schrodinger 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.
 
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  • #2
referframe said:
When a quantum measurement occurs under the Schrodinger picture, the wave function collapses

This is interpretation dependent. Not all interpretations have collapse.

referframe said:
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 Schrodinger pictures as far as predictions of measurement results are concerned.
 
  • #3
PeterDonis said:
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 Schrodinger pictures as far as predictions of measurement results are concerned.
Are the values measured also eigenvalues of the dynamical Heisenberg operator?
 
  • #4
referframe said:
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.
 
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  • #5
Do note that the Heisenberg picture is build from the Schrodinger picture in a way so that they agree in stuff like expectation values.
 
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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.]
 
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  • #7
referframe said:
Summary:: What happens during a quantum measurement under Heisenberg picture?

When a quantum measurement occurs under the Schrodinger 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 Schrodinger to the Heisenberg picture. In other words, if there is a state collapse in the Schrodinger picture, then there is also a state collapse in the Heisenberg picture.
 
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  • #8
Demystifier said:
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.
 
  • #9
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.
 

Related to Quantum Measurement under Heisenberg Picture?

1. What is the Heisenberg picture in quantum mechanics?

The Heisenberg picture is one of the two commonly used formulations of quantum mechanics, along with the Schrödinger picture. In the Heisenberg picture, the operators representing physical observables, such as position and momentum, evolve in time while the state of the system remains fixed. This is in contrast to the Schrödinger picture, where the operators remain fixed and the state of the system evolves in time.

2. How does quantum measurement work in the Heisenberg picture?

In the Heisenberg picture, the measurement of a physical observable is represented by the evolution of the corresponding operator. This means that the measurement process itself is not explicitly included in the formalism, but is instead described by the change in the operator representing the observable being measured. This is in contrast to the Schrödinger picture, where the measurement process is explicitly included in the evolution of the state vector.

3. What is the uncertainty principle in the Heisenberg picture?

The uncertainty principle in the Heisenberg picture is a fundamental principle of quantum mechanics that states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is represented by the commutation relation between the position and momentum operators, which states that the product of their uncertainties must be greater than or equal to a certain value. This principle is a consequence of the wave-particle duality of quantum systems.

4. How does the Heisenberg picture differ from the Schrödinger picture?

The main difference between the Heisenberg picture and the Schrödinger picture is in the way time evolution is represented. In the Heisenberg picture, operators evolve in time while the state of the system remains fixed, while in the Schrödinger picture, the state of the system evolves in time while the operators remain fixed. This leads to different mathematical formulations of quantum mechanics, but both pictures are equivalent and can be used to describe the same physical phenomena.

5. What are the advantages of using the Heisenberg picture in quantum mechanics?

One advantage of using the Heisenberg picture is that it allows for a more intuitive understanding of the measurement process. In this picture, the measurement of an observable is represented by the evolution of the corresponding operator, which can be thought of as the physical quantity being measured. Additionally, the Heisenberg picture is often used in calculations involving time-dependent systems, as it simplifies the mathematical expressions and can lead to more efficient calculations.

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