How is the Born rule deduced from decoherence?

In summary: And if you don't have a coherent superposition, then you don't have interference. And if you don't have interference, then you don't have different probabilities for different outcomes.
  • #1
Jamister
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TL;DR 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. I'm looking for reference, book or article, to understand this better.
Thank you
 
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  • #2
Maybe he means in the MWI.
 
  • #3
EPR said:
Maybe he means in the MWI.
What is MWI?
 
  • #5
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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  • #6
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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  • #7
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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  • #8
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.
 
  • #9
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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  • #10
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?
 
  • #14
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.
 

1. How does decoherence relate to the Born rule?

Decoherence is a process that explains how a quantum system becomes entangled with its environment, leading to the "collapse" of its wave function. The Born rule, on the other hand, is a mathematical formula that predicts the probability of obtaining a particular measurement outcome in a quantum system. Decoherence provides a physical explanation for why the Born rule holds true.

2. Can the Born rule be derived from first principles?

No, the Born rule cannot be derived from first principles. It is a fundamental postulate of quantum mechanics, meaning that it is assumed to be true without proof. However, decoherence provides a physical explanation for why the Born rule is necessary in quantum mechanics.

3. How does decoherence affect the measurement process in quantum mechanics?

Decoherence causes a quantum system to interact with its environment, leading to the entanglement of the system and the environment. This interaction causes the system to lose its quantum coherence and behave classically, allowing for the measurement process to take place. The Born rule then predicts the probability of obtaining a particular measurement outcome.

4. Are there any alternative explanations for the Born rule?

There are some alternative theories that attempt to explain the Born rule, such as the many-worlds interpretation and the spontaneous collapse theory. However, these theories are not widely accepted and do not have as much empirical support as decoherence.

5. How important is the Born rule in quantum mechanics?

The Born rule is a fundamental principle in quantum mechanics and is essential for making predictions about the behavior of quantum systems. Without the Born rule, it would be impossible to make accurate predictions about measurement outcomes in quantum systems, making it a crucial aspect of the theory.

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