Does Decoherence Solve the Measurement Problem Completelyby Prathyush Tags: measurement, quantum mechanics 

#55
Nov2812, 07:43 PM

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#56
Nov2812, 08:06 PM

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Belief in indeterminism is to me exactly like solipsism, sure I can never prove it wrong, it's logically coherent, but it explains nothing and I have no reason to think it's true. For anyone believing in indeterminism, I wonder how you can justify the Born Rule. What sort of sense would it make for a genuinely indeterminate universe to care about a statistical rule like that of Born? Why wouldn't particles just do whatever the hell they want at all times without obeying any laws what so ever. The fact that we observe a "rule" is to me philosophically requiring an explanation. To me "random" is JUST as likely as inventing a God. So when you ask "why did the cat die?" I would say "God became allergic to felines" and take that just as seriously as "it just happened out of randomness". If you followed up with "but why would God kill cats according to what we percieve as the Born Rule?" I would tell you: "God works in mysterious ways" and claim a Nobel Prize. It's incoherent, stupid and not science. Science seeks explanations, if we had given up when we hit something that seems random we would have given up on trying to model ANYTHING, because EVERYTHING seems incomprehensible at first sight. Imagine the first time someone pondered the rain, it would have to have seemed completely random, which is why most societies at the time believed in weather Gods, they saw no other explanation. I am 100% confident that reality is not indeterministic 



#57
Nov2812, 08:10 PM

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So it's wrong in the same sense that Newtonian gravity is wrong. It works but it's not the final and fundamental model. This is the same way I percieve QM given the fact that there is no way to make sense of QM unless you are willing to accept antirealisticindeterminism on par with solipism, Bohm (nonlocal and surrealistic trajectories) or Many Worlds and be able to get the Born Rule out of Many Worlds. 



#58
Nov2812, 08:22 PM

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Later harder to evade theorems such as Gleasons also came along that also justifies it  but of course that is also evadeable since it rests on a crucial assumption of noncontextuality. I think contextuality is pretty weird but if you want determinism that's what you need. I hasten to add me thinking the additivity of expectation values natural and contextuality wierd means Jack Shite  nature does not have to respect my or anyone else's aesthetics. Oh and since PBR has been mentioned I am glad I got the chance to post Schlosshauer's analysis of it which shows like contextuality and Von Neumann's theorem it also rests on hidden assumptions. Its very interesting how given a theory/interpretation that PBR applies to one can always construct one where it doesn't  and conversely. Its just goes to show how weird nature really is. Thanks Bill 



#59
Nov2912, 12:37 AM

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An agnostic view regarding (1) would be that QM allowes us to predict experimental results  endofstory. I agree that this seems to be incomplete b/c there is not reason "why" this works, there is no idea regarding reality or regarding a relation between the QM formalism and reality. And there it always a kind of 'interpretation' in the sense of "given this apparatus and an electron I have to use that formula with the following initial conditions". All what I am sying is that these missing pieces  and I agree that this agnostic view is unsatisfactory and that there are missing pieves  are not on the level of (1). Let's make a simple example: in classical mechanics we can count dead cats and alive cats (and such things) using Peanos axioms. Their consistency or inconsistency in the sense of Hilbert's second problem is to be discussed on the level of (1), the reason "why" we can use them is beyond level of (1). Btw.: we never ask the question "why" things work as they do in classical mechanics. Why do we not ask this question? Why do we ask this question in QM? Is it really true that we have a full understanding of these ideas in classical mechanics? I am sure the answer is "no". 



#60
Nov2912, 12:51 AM

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All what I am saying is that these problems are strictly speaking not on the level of (1) as a pure mathematical formalism but beyond that level. And it is not clear that your interpretation of science (it's an interopretation, not a definition) is not the common view, at least not in quantum mechanics; many will agree that QM is not about "why" and not about "explanations". That does not mean that QM in the sense of (1) is incomplete or wrong. It just means that there are good reasons to go beyond (1)  and to be very careful when we should stop calling something science and when it becomes metaphysics (not with any negative connotation). I think we should remeber where this discussion started. It was about the question regarding decoherence and the measurement problem. This thread (and many others) show that one problem is that decoherence comes with some context (interpretations, measurement problem, ...) and that in many presentations the facts (decoherence) and the context are presented as the same thing. So all what did was to decompose "decoherence as presented or perceived" in "decoherence as a fact derived from QM and demonstrated by experiments" and "context and interpretation of decoherence like measurement, many worlds, ...". 



#61
Nov2912, 01:13 AM

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#62
Nov2912, 01:42 AM

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#63
Nov2912, 01:58 AM

P: 79

My understanding of the usual formulation of the quantum measurement problem is that it has to do with an apparent contradiction between the dynamics of quantum theory as described by the Schrodinger wave equation (and its wavefunction solutions), and the Born measurement axiom or postulate.
I call this the pseudo quantum measurement problem because I don't see any logical contradiction there. That the underlying reality has something to do with wave shells expanding in media of unknown structure seems to me to be a most reasonable assumption. This is what the wave equation and wavefunctions have 'something' to do with (in the sense that they might be conceptually associated with an underlying reality), imo. We place obstructions in the paths of the expanding wave shells and posit that the probability of whether or not a detection is recorded will be in direct proportion to the amplitudes (specifically, the squares of the amplitudes) of the wave fronts as they contact the obstructions. No problem there. This applies to waves in both particulate and nonparticulate media, and is understandable in terms of our limited sensory apprehension of nature. What's less understood, or, not really understood at all, is the qualitative nature of the apparent particlelike properties of individual quantum detection results, which, in my view, is part of the real quantum measurement problem. Decoherence cannot, imo, solve what I consider to be the real quantum measurement problem. 



#64
Nov2912, 02:12 AM

P: 79

By the way, thanks to all commenters, especially tom.stoer, bhobba, Quantumental, eloheim and bohm2 (apologies if I failed to mention other substantial commenters). I'm a recent graduate with a more than passing interest in the foundations of quantum theory, and modern physics in general. I've been doing a little homework and, for your convenience and amusement, here's a sampling of some of the reading and viewing that I've been doing with the help of the internet.
Some of it is beyond my current ability to fully understand (or maybe I'm just trying to read too fast). So, expect some questions ... and I hope they don't sound too naive. http://mattleifer.info/2011/11/20/ca...statistically/ http://mattleifer.info/2012/02/26/qu...epbrtheorem/ http://www.aps.org/units/gqi/newslet...d/vol6num3.pdf http://mattleifer.wordpress.com/2007...ationsdebate/ http://pirsa.org/displayFlash.php?id=12050021 http://dabacon.org/pontiff/?p=5912 http://science.slashdot.org/story/11...hysicalobject http://blogs.discovermagazine.com/co.../#.ULb27oY4eso http://www.physicsforums.com/showthr...551554&page=17 http://www.nature.com/news/quantumt...dations1.9392 http://motls.blogspot.com/2011/11/na...paperby.html Distinct Quantum States Can Be Compatible with a Single State of Reality http://arxiv.org/abs/1201.6554 On the reality of the quantum state http://arxiv.org/abs/1111.3328 Exponential complexity and ontological theories of quantum mechanics http://arxiv.org/abs/0711.4770 Strengths and Weaknesses of Quantum Computing http://arxiv.org/abs/quantph/9701001 Einstein, incompleteness, and the epistemic view of quantum states http://arxiv.org/abs/0706.2661 In defense of the epistemic view of quantum states: a toy theory http://arxiv.org/abs/quantph/0401052 The paradigm of kinematics and dynamics must yield to causal structure http://arxiv.org/abs/1209.0023 Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference http://arxiv.org/abs/1107.5849 



#65
Nov2912, 03:23 AM

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The book to get is Ballentine  Quantum Mechanics  A Modern Development: http://www.amazon.com/QuantumMechan.../dp/9810241054 Here you will find QM developed from just two axioms and Schrodengers equation derived (yes derived  not assumed) from its true basis  Galilean Invariance. Take your time, go through it carefully, and you will come away with a really good understanding. Thanks Bill 



#66
Nov2912, 03:27 AM

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#67
Nov2912, 03:33 AM

P: 127

So for those who think that QM is *the* fundamental theory, they have to explain why everything occurs really. If you ask why and their reply is simply: indeterminism!, then that suggests to me that they are not really interested in knowing why, but rather just want the math to work. That's fine if you are going to do technical work, but if you are seeking truth you can never be satisfied with "it just happens" 



#68
Nov2912, 03:49 AM

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http://en.wikipedia.org/wiki/Gleason's_theorem Gleason's theorem highlights a number of fundamental issues in quantum measurement theory. The fact that the logical structure of quantum events dictates the probability measure of the formalism is taken by some to demonstrate an inherent stochasticity in the very fabric of the world. To some researchers, such as Pitowski, the result is convincing enough to conclude that quantum mechanics represents a new theory of probability. Alternatively, such approaches as relational quantum mechanics make use of Gleason's theorem as an essential step in deriving the quantum formalism from informationtheoretic postulates. The theorem is often taken to rule out the possibility of hidden variables in quantum mechanics. This is because the theorem implies that there can be no bivalent probability measures, i.e. probability measures having only the values 1 and 0. Because the mapping is continuous on the unit sphere of the Hilbert space for any density operator W. Since this unit sphere is connected, no continuous function on it can take only the value of 0 and 1. But, a hidden variables theory which is deterministic implies that the probability of a given outcome is always either 0 or 1: either the electron's spin is up, or it isn't (which accords with classical intuitions). Gleason's theorem therefore seems to hint that quantum theory represents a deep and fundamental departure from the classical way of looking at the world, and that this departure is logical, not interpretational, in nature. Of course it doesn't prove anything but for sure it is far from certain that indeterminism can not be fundamental  not certain at all. Thanks Bill 



#69
Nov2912, 06:40 AM

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the reason why we don't in classical mechanics is that classical mechanics fits to our perception whereas QM doesn't; QM was the first physical theory to which no Platonism, Aristotelism, Kantianism or any other XYZism had an answer; QM does not fit to the categories of our perception;
now there are two options 1) change nature 2) change our ideas about nature for me 2) is acceptable, but that's a matter of taste ;) 



#70
Nov2912, 07:10 AM

P: 127

Hell we can make it even more absurd. Why should you assume that existence existed before you? Sure you might say "well my observations seem to be best accounted for by postulating that things were around before me." After all, it makes little sense that existence surrounding you should try to decieve you into thinking that old things have been around for a long time if they hasn't. But the same applies to Born Rule, there is no reason why something that is truly indeterminate should follow a statistical rule... So with the same logic you reject the "the universe came into existence with me" hypothesis, I reject the "magic is the reason Born rule exists." 



#71
Nov2912, 08:08 AM

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I am not sure whether you understand what I am saying.
QM tells us a lot about nature; it makes experimentally provable and correct predictions, something that was not the case with classical mechanics! There is no single experiment which tells us that QM (in the sense of its predictions is wrong)! Problems appear on the level of interpretation and the completeness of the formalism. Therefore my conclusion is to doubt the interpretation. 



#72
Nov2912, 09:22 AM

P: 127

Noone is arguing that the results we have from QM is correct, that would be as dumb as denying gravity after you've fallen off a cliff. But this doesn't prove anything about indeterminism. Classical mechanics DID indeed give right answers to a lot of questions, it was only when we probed deeper and needed more fundamental answers that it didn't suffice. And due to the unacceptable indeterminism, this means QM is not fundamental, or you have to accept MWI or dBB and solve the problems facing them, which seems impossible without postulating some new kind of physics. It seems you think that indeterminism is ok because we don't have a explanation that works 100% yet and I think that's a defeatus mentality, because anywhere in history we could've said the same. "How does leafs get their green color? **** it I'm living 10 000 years B.C. how the **** am I suppoed to know? It's random!" 


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