How is the Born rule deduced from decoherence?

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    Born rule Decoherence
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SUMMARY

The discussion centers on the relationship between the Born rule and decoherence as presented in Steven Weinberg's "Lectures on Quantum Mechanics." Participants debate whether decoherence adequately addresses the measurement problem and the derivation of the Born rule. Key references include Weinberg's text, which spans pages 90-92, and works by M. Schlosshauer, specifically "Decoherence, the measurement problem, and interpretations of quantum mechanics" (Rev. Mod. Phys. 76, 2005) and "Decoherence and the quantum-to-classical transition" (Springer, 2007). The consensus indicates that while decoherence plays a significant role, it does not fully resolve the measurement problem.

PREREQUISITES
  • Understanding of the Born rule in quantum mechanics
  • Familiarity with decoherence theory
  • Knowledge of the measurement problem in quantum mechanics
  • Awareness of the Many-Worlds Interpretation (MWI)
NEXT STEPS
  • Read Steven Weinberg's "Lectures on Quantum Mechanics" focusing on pages 90-92
  • Study M. Schlosshauer's "Decoherence, the measurement problem, and interpretations of quantum mechanics" (Rev. Mod. Phys. 76, 2005)
  • Explore M. Schlosshauer's "Decoherence and the quantum-to-classical transition" for deeper insights
  • Investigate the Many-Worlds Interpretation (MWI) and its implications for quantum mechanics
USEFUL FOR

Quantum physicists, students of quantum mechanics, and researchers interested in the foundations of quantum theory and the implications of decoherence on the measurement problem.

Jamister
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TL;DR
measurement problem (i.e born rule) is solved by decoherence
Weinberg says in his book "Lectures on Quantum Mechanics" that the born rule can be deduced from decoherence, and this solves the measurement problem. I'm looking for reference, book or article, to understand this better.
Thank you
 
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Maybe he means in the MWI.
 
EPR said:
Maybe he means in the MWI.
What is MWI?
 
orisomech said:
Summary:: measurement problem (i.e born rule) is solved by decoherence

Weinberg says in his book "Lectures on Quantum Mechanics" that the born rule can be deduced from decoherence, and this solves the measurement problem.
Decoherence does not solve the measurement problem.
 
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Jamister said:
Weinberg says in his book "Lectures on Quantum Mechanics" that the born rule can be deduced from decoherence, and this solves the measurement problem.
Can you quote his exact statement? Because I don't think that that's exactly what he says.
 
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Demystifier said:
Can you quote his exact statement? Because I don't think that that's exactly what he says.
Well, it's hard to quote one sentence, because it is on entirely 3 pages.
one of the quotes is this (on page 92):
1601288538002.png

and another one is this (on page 91):
1601288039347.png

but I also attach the book itself where this claim is on pages 90-92.

[Mentor Note -- Copyrighted PDF copy of the book has been removed]
 
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The measurement problem is different from the Born rule, but anyway:

For any given experiment, the possible measurement results must decohere if they are to be resolved by an experiment. If they do not decohere, they cannot be resolved by an experiment.
 
Jamister said:
Well, it's hard to quote one sentence, because it is on entirely 3 pages.
one of the quotes is this (on page 92):
View attachment 270117
and another one is this (on page 91):
View attachment 270116
but I also attach the book itself where this claim is on pages 90-92.
Well, he says
So where does the Born rule come from? There are two main approaches to this question, that are often called instrumentalist and realist, each with its own drawbacks.
you said that he claims that the Born rule can be deduced from decoherence. I think you need to read more carefully.
 
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Jamister said:
Well, it's hard to quote one sentence, because it is on entirely 3 pages.
one of the quotes is this (on page 92):
View attachment 270117
and another one is this (on page 91):
He says that there is a widespread impression that decoherence solves the problem, then he goes on to point out why it only seems so, but in fact is not a solution.
 
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  • #11
Jamister said:
Well, it's hard to quote one sentence, because it is on entirely 3 pages.
one of the quotes is this (on page 92):
View attachment 270117
and another one is this (on page 91):
View attachment 270116
but I also attach the book itself where this claim is on pages 90-92.
In those quotes he never says that it explains the Born rule. And concerning the claim that decoherence solves all problems, he uses phrases "there seems to be a wide-spread impression" and "has to do with". So it's far from a definite statement that decoherence solves the problems.

And by the way, it's illegal to attach the whole book. Next time attach only a few relevant pages.

For more on decoherence, you might want to see my lecture
http://thphys.irb.hr/wiki/main/images/5/50/QFound3.pdf
 
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  • #12
Thank you for the replies. I respond to - Demystifier , martinbn,
A. Neumaier. I didn't mean that decoherence solves the problem of born rule completely, but I didn't understand his point in the book and I want to read more about it. Do you know a good source for it?
 
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Jamister said:
I didn't mean that decoherence solves the problem of born rule completely, but I didn't understand his point in the book and I want to read more about it. Do you know a good source for it?
  • M. Schlosshauer, Decoherence, the measurement problem, and interpretations of quantum mechanics, Rev. Mod. Phys. 76 (2005), 1267–305.
  • M. Schlosshauer, Decoherence and the quantum-to-classical transition, Springer, New York 2007.
 
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  • #15
Jamister said:
from your presentation
Why do you say that :
View attachment 270125
how did you get there?
If you understood everything before that claim, then you should understand that claim as well. To have a coherent superposition one should know the phases in front of the two terms, but as explained in the lecture the phases are "eaten up" by the environment.
 

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