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- Thread starter ahmad2l
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Simon Bridge

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i.e. "collapse" refers to the way the wavefunction changes once a measurement has been made.

Looking up the definitions of the terms should give you a good idea. What did you find?

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naima

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I never found a corresponding description in Heisenberg picture.

operators jump? with given amplitudes?

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i.e. "collapse" refers to the way the wavefunction changes once a measurement has been made.

Looking up the definitions of the terms should give you a good idea. What did you find?

I think so.words of "collapse" and "reduction" are used in Dirac and Born interpretation of QM

and "decoherence" is used in von Neumann's measurement theory that is based on density matrix. in Dirac interpretation there is a border between quantum and classical worlds and interaction between these two worlds causes "reduction" but in von Neumann there isn't any border between quantum and classical worlds and consciousness observer causes off-diagonal components of density matrix vanish.

I think for these details, different words used for different theories.

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Simon Bridge

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So you already knew the answer - well done!

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Decoherence is for example the evolution from a pure state of the type [itex]c_{1}|\Psi>_{1}+c_{2}|\Psi>_{2}[/itex] (maybe with more vectors the sum) to a density matrix [itex] |c_1|^{2}| |\Psi>_{1}<\Psi_{1}|+|c_2|^{2}| |\Psi>_{2}<\Psi_{1}| [/itex]

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kith

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In the Schrödinger picture, a time dependent state ket gets projected onto a time independent eigenket of the observable. In the Heisenberg picture, this time (in)dependency is reversed.According to Schrodinger the state vector evolves with time and collapse is a jump to another temporal curve. I never found a corresponding description in Heisenberg picture.

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naima

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At time t = 0 suppose i find that an obervable O1 has a given value. time goes from 0 to t, O1 (0) evolves to O1 (t) and i make another mesurement. Can i avoid to return to Schrodinger point of view to find the probabilities for each eigenvalues of O2?

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Simon Bridge said:So you already knew the answer - well done!

No, it didn´t know the answer, it is a typical situation people asking on a forum not know the answers to them. And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

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DrChinese

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No, it didn´t know the answer, it is a typical situation people asking on a forum not know the answers to them. And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

Not sure what this is about, StarsRuler. Simon did answer. Maybe you didn't notice he is a very prolific responder.

-DrC

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Simon Bridge

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On the contrary, it is very common that people pose questions when they do know the answer - they may not realize they knew all along or lack confidence in their knowledge and just need help making the connection.No, it didn't know the answer, it is a typical situation people asking on a forum not know the answers to them.

The question posed by ahmad2l in post #1 was answered in post #4

...please read post #2 (above) and check the author credit. Thank you.And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

I find it is important to read the

Aside: in many cultures it is considered rude to refer to a person as an "it".

Since gender is largely irrelevant, you may prefer to avoid "he" and "she" etc in favor of just writing the poster's handle or, maybe, a gender-neutral abbreviation like "OP".

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Thank you gentlemen, I almost knew the answer, but I was a bit confused when I read :

http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics

and

http://books.google.com/books/about/Foundations_of_Quantum_Mechanics_an_Empi.html?id=KjFKZTodbEIC

In this book again for "decoherence" and "reduction", new words selected:weak projection and strong projection

I think the interpretation of Bohr and Dirac and ...was incomplete and was completed by von Neumann because they did not distinguish between pure and mixed state

Von Neumann said the measurement is the reduction of the pure state to mixture ,that means quantum prababilites reduced to classical.this is called weak projection

strong projection means :reduction of classical probabilites to an eigenvector

therefore:

(transition from pure state to mixed state) according to von Neumann = (decoherence) according to von Neumann = weak projection

{(transition from pure state to mixed state) +(transition from mixed state to eigenvector)} according to von Neumann=strong projection according to von Neumann= collapse or reduction of state vector according to Bohr and others

http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics

and

http://books.google.com/books/about/Foundations_of_Quantum_Mechanics_an_Empi.html?id=KjFKZTodbEIC

In this book again for "decoherence" and "reduction", new words selected:weak projection and strong projection

I think the interpretation of Bohr and Dirac and ...was incomplete and was completed by von Neumann because they did not distinguish between pure and mixed state

Von Neumann said the measurement is the reduction of the pure state to mixture ,that means quantum prababilites reduced to classical.this is called weak projection

strong projection means :reduction of classical probabilites to an eigenvector

therefore:

(transition from pure state to mixed state) according to von Neumann = (decoherence) according to von Neumann = weak projection

{(transition from pure state to mixed state) +(transition from mixed state to eigenvector)} according to von Neumann=strong projection according to von Neumann= collapse or reduction of state vector according to Bohr and others

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kith

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Yes, simply use the time-dependent eigenstates (of O2) I talked about in my previous post.At time t = 0 suppose i find that an obervable O1 has a given value. time goes from 0 to t, O1 (0) evolves to O1 (t) and i make another mesurement. Can i avoid to return to Schrodinger point of view to find the probabilities for each eigenvalues of O2?

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