Entanglement Question

  • #51
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What interpretations fix the preferred basis issue (definite outcomes I think you call it)?
Why do you think its interpretation dependant?

But aside from that it might be a good idea not to derail this thread with a side issue.

Thanks
Bill
 
  • #52
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Why do you think its interpretation dependant?

But aside from that it might be a good idea not to derail this thread with a side issue.

Thanks
Bill
You said:"It doesn't matter what issue particularly worries you there is an interpretation that fixes it." I just gave an example of an issue, and you just have to say what interpretation fixes it. Otherwise it means your assertion was false.
 
  • #53
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I tried. In this lecture Susskind refers to some paper so I assume it makes no sense to view this lecture if you don't know the paper.
But I watched anyways and got to the point where two people from two non-interacting worlds are jumping into the blackhole and meeting in the middle. And I do not understand what I was supposed to take from this lecture.
It's worth following it to the end, even if you don't fully understand it. The conjecture at the end, is that entangled particles are connected by Planck scale wormholes.

In Quantum Gravity space and time are much more complicated than in Quantum Mechanics.

I'm not directing this at you. Your comment was just a recent comment along the relevant vein of discussion, but more generally, the point I'm making is that we shouldn't dismiss something which we do not understand as crazy, cranky, crack-pottery etc. We've all been there. When we know a little bit about a subject, we presume to know more than we do. It might seem like it makes us appear more knowlegable or more scientific, but that's not how science works and it's not a good example to set others.
 
  • #54
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\Otherwise it means your assertion was false.
Decocherence is interpretation independent and it explains the preferred basis part of the measurement problem. It doesn't explain all the other parts - but it does that one.

Thanks
Bill
 
  • #55
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The essential property follows from the definition of a wave-function being the expansion of the state in terms of position eigenstates - it has nothing to do with Scrodingers equation.
Staye of what? Eigenstates of what? The reason is that you discuss the wave function without referring to the equation that it is the solution of (!),
is that you tacitly presuppose the QM formalism. My point is that we do understand the formalism, but not QM.
 
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  • #56
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Staye of what? Eigenstates of what? The reason is that you discuss the wave function without referring to the equation that it is the solution of (!), is that you tacitly presuppose the QM formalism. My point is that we do understand the formalism, but not QM.
It's as I said - position eigenstates. Why didn't you note the key word I said before eigenstate?

The problem is you have got the cart before the horse. What a wave-function is has nothing to do with Schroedinger's equation - its got to do with the foundational axioms of QM which are (as per Ballentine):

1. To every observation there exists a Hermitian operator O such that the possible outcomes are the eigenvalues of the observation.

2. There exists a positive operator P, of unit trace, called the state of the system, such that the expected outcome of an observation O, E(O), is E(O) = Trace (PO). This is called the Born Rule.

Axiom 2 is to some extent determined by axiom 1 via Gleason's theorem (you have to add non contextuality to it).

States of the form P= |u><u| are called pure and because Trace (|u><u|) = 1, <u|u> = 1, hence they are of unit length, which is the normalisation condition you were talking about. It follows directly from the Born Rule.

Consider the eigenvectors |xi> of the position operator X. These, by definition, are position eigenstates. Then, by the properties of Hermitian operators (ie its eigenvectors form an orthonormal basis) we have |u> = Σ |xi>< xi|u> with what I said in the previous post following.

That the wave-function is normalised to 1 and |< xi|u>|^2 is the probability of getting position xi follows directly from the axioms of QM. The Schroedinger equation is not involved.

Where the Schroedinger equation comes from is that the probabilities defined by the Born Rule should not depend on the frame.

I think you are a bit confused about understanding in science. In science you understand something when its explained by known premises - which is exactly what we have in QM. The two axioms I gave are the known premises from which we explain QM phenomena.

The issue here is they are not premises in the mould of the usual ones in physics. That's why people say no one understands QM. But what they really mean is no one understands it in terms of everyday intuitive pictures. That is different from understanding - and why I say - We have met the enemy and he is us.

Thanks
Bill
 
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  • #57
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Decocherence is interpretation independent and it explains the preferred basis part of the measurement problem. It doesn't explain all the other parts - but it does that one.

Thanks
Bill
In the interest of not confusing people you should add that there is no agreement in the quantum foundations community about decoherence explaining preferred basis and that basically only proponents of the Everett approach like Zurek claim that decoherence solves the issue.
 
  • #58
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In the interest of not confusing people you should add that there is no agreement in the quantum foundations community about decoherence explaining preferred basis and that basically only proponents of the Everett approach like Zurek claim that decoherence solves the issue.
Where did you get that from? It wasn't from my text on the matter:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

See page 83 to 85.

Thanks
Bill
 
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  • #59
zonde
Gold Member
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It's worth following it to the end, even if you don't fully understand it. The conjecture at the end, is that entangled particles are connected by Planck scale wormholes.
Reasoning along the lines of black holes, wormholes, parallel worlds and such is armchair science in n-th iteration. You have to have quite specific beliefs to consider it interesting.
You have to believe that mathematics is not just very useful baseline for describing real world but that mathematics is some sort of super reality that determines how reality is "functioning". And this is without considering poor assumptions and erroneous applications of math.
Well, I don't have these beliefs so I don't consider that kind of reasoning worth following.

I'm not directing this at you. Your comment was just a recent comment along the relevant vein of discussion, but more generally, the point I'm making is that we shouldn't dismiss something which we do not understand as crazy, cranky, crack-pottery etc. We've all been there. When we know a little bit about a subject, we presume to know more than we do. It might seem like it makes us appear more knowlegable or more scientific, but that's not how science works and it's not a good example to set others.
The problem is not in understanding of the idea but it's relevance to reality.
 
  • #60
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  • #61
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Your text is from Zurek.
Errrrr. I don't know what to say.

Do you actually read references?

It isn't of course - but that you would confidently say it is, is to say the least, rather a concern.

I think I will take my leave of this thread - there is really no more to say anyway.

Thanks
Bill
 
  • #62
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Errrrr. I don't know what to say.

Do you actually read references?

It isn't of course - but that you would confidently say it is, is to say the least, rather a concern.
Don't worry. I know the book is not authored by Zurek, I was referring to the text pages you highlighted, they refer to the concept of einselection, that comes from Zurek.
Nevermind, it is obvious you don't want to discuss physics.
 
  • #63
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It's as I said - position eigenstates. Why didn't you note the key word I said before eigenstate?

The problem is you have got the cart before the horse. /QUOTE]
The problem is that you are somewhat pedantic.
I read and met Ballentine about 25 years ago. I subscribe to his approach to quantum mechanics.
Yet, you can axiomatize QM all you want, it is not the same as understanding it.
And, imo a no-brainer, a wave function requires a wave equation.
Get out of that box.
 
  • #64
Nugatory
Mentor
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It's time to end this thread. Now.
 

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