On Sunday, November 4, 2018 at 1:42:49 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Sunday, November 4, 2018 at 3:01:50 PM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Sunday, November 4, 2018 at 7:27:12 AM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Sunday, November 4, 2018 at 1:05:36 AM UTC, Philip Thrift wrote:
>>>>
>>>>
>>>>
>>>> On Saturday, November 3, 2018 at 6:21:18 PM UTC-5, agrays...@gmail.com 
>>>> wrote:
>>>>>
>>>>>
>>>>>
>>>>> On Saturday, November 3, 2018 at 9:33:54 PM UTC, Philip Thrift wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Saturday, November 3, 2018 at 3:50:30 PM UTC-5, 
>>>>>> agrays...@gmail.com wrote:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Thursday, November 1, 2018 at 11:22:46 PM UTC, Pierz wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Monday, October 15, 2018 at 9:40:39 PM UTC+11, 
>>>>>>>> agrays...@gmail.com wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On Sunday, October 14, 2018 at 5:08:42 PM UTC, smitra wrote:
>>>>>>>>>>
>>>>>>>>>> On 14-10-2018 15:24, agrays...@gmail.com wrote: 
>>>>>>>>>> > In a two state system, such as a qubit, what forces the 
>>>>>>>>>> interpretation 
>>>>>>>>>> > that the system is in both states simultaneously before 
>>>>>>>>>> measurement, 
>>>>>>>>>> > versus the interpretation that we just don't what state it's in 
>>>>>>>>>> before 
>>>>>>>>>> > measurement? Is the latter interpretation equivalent to 
>>>>>>>>>> Einstein 
>>>>>>>>>> > Realism? And if so, is this the interpretation allegedly 
>>>>>>>>>> falsified by 
>>>>>>>>>> > Bell experiments? AG 
>>>>>>>>>>
>>>>>>>>>> It is indeed inconsistent with QM itself as Bell has shown. 
>>>>>>>>>> Experiments 
>>>>>>>>>> have later demonstrated that the Bell inequalities are violated 
>>>>>>>>>> in 
>>>>>>>>>> precisely the way predicted by QM.  This then rules out local 
>>>>>>>>>> hidden 
>>>>>>>>>> variables, therefore the information about the outcome of a 
>>>>>>>>>> measurement 
>>>>>>>>>> is not already present locally in the environment. 
>>>>>>>>>>
>>>>>>>>>> Saibal 
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> What puzzles me is this; why would the Founders assume that a 
>>>>>>>>> system in a superposition is in all component states simultaneously 
>>>>>>>>> -- 
>>>>>>>>> contradicting the intuitive appeal of Einstein realism -- when that 
>>>>>>>>> assumption is not used in calculating probabilities (since the 
>>>>>>>>> component 
>>>>>>>>> states are orthogonal)? AG 
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think because of interference. Consider the paradigmatic double 
>>>>>>>> slit, with the single electron going through it. It sure looks like 
>>>>>>>> the 
>>>>>>>> electron was in two place at once, doesn't it?
>>>>>>>>
>>>>>>>
>>>>>>> *Yes, that's my assessment how the erroneous interpretation took 
>>>>>>> hold, but only if you restrict yourself to the particle interpretation. 
>>>>>>> If 
>>>>>>> the electron travels as a wave, it can go through both slits 
>>>>>>> simultaneously 
>>>>>>> and interfere with itself. This is my preferred interpretation; the 
>>>>>>> only 
>>>>>>> one that makes sense. AG*
>>>>>>>
>>>>>>> I'm not sure what you mean by "that assumption is not used in 
>>>>>>>> calculating probabilities". 
>>>>>>>>
>>>>>>>
>>>>>>> *If the operator whose eigenvalues are being measured has a well 
>>>>>>> defined mathematical form -- e.g., not like |alive> -- it has specific 
>>>>>>> eigenvectors and eigenvalues, and the state function can be written as 
>>>>>>> superposition of these eigenvectors. It can be shown that eigenvectors 
>>>>>>> with 
>>>>>>> distinct eigenvalues are orthogonal, meaning the Kronecker delta 
>>>>>>> applies to 
>>>>>>> their mutual inner products. Therefore, to calculate the probability of 
>>>>>>> observing a particular eigenvalue, one must take the inner product of 
>>>>>>> the 
>>>>>>> wf with the eigenvector which has that eigenvalue. Due to the 
>>>>>>> orthogonality, all terms drop out except for the term in the 
>>>>>>> superposition 
>>>>>>> which contains the eigenvector whose eigenvalue you want to measure. As 
>>>>>>> you 
>>>>>>> should see, there is nothing in this process of calculating 
>>>>>>> probabilities 
>>>>>>> that in any way implies, assumes, or uses, the concept that the system 
>>>>>>> is 
>>>>>>> simultaneously in ALL component states of the superposition (written as 
>>>>>>> a 
>>>>>>> sum of eigenvectors). AG*
>>>>>>>  
>>>>>>>
>>>>>>>> If you take a sum-over-histories approach it's explicitly assumed 
>>>>>>>> the electron went via all possible paths.
>>>>>>>>
>>>>>>>
>>>>>>> *I don't know that method, but offhand POSSIBLE PATHS might have 
>>>>>>> nothing to do with, and possibly independent of SUPERPOSITIONS OF 
>>>>>>> STATE. AG*
>>>>>>>
>>>>>>> I don't see what the orthogonality of the basis vectors (and hence 
>>>>>>>> component states) has to do with the question of interpretation of 
>>>>>>>> superposition. 
>>>>>>>>
>>>>>>>
>>>>>>> *Explained in detail above. AG*
>>>>>>>
>>>>>>> Clearly the system will be measured in only one state, and this is 
>>>>>>>> what the orthogonal vectors represent. However the quantum state 
>>>>>>>> itself 
>>>>>>>> typically spans more than one dimension of the vector space - that's 
>>>>>>>> what a 
>>>>>>>> superposition is. However I think when physicists say that the 
>>>>>>>> superposition is in all states simultaneously, it's only in a manner 
>>>>>>>> of 
>>>>>>>> speaking - a way of conveying the mathematical situation in natural 
>>>>>>>> language that is inherently classical. 
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> *It's a totally misleading way to discuss the quantum 
>>>>>>> superpositions.  Even classically, say for the vector space of "little 
>>>>>>> pointy things" in a plane, each vector can be expressed in uncountably 
>>>>>>> many 
>>>>>>> bases, both orthogonal and non-orthogonal. So to claim that one basis 
>>>>>>> is 
>>>>>>> somehow preferred, and the vector being expressed as a sum or 
>>>>>>> superposition 
>>>>>>> in that basis, is simultaneously in all components of that particular 
>>>>>>> basis, make no sense whatsoever. AG*
>>>>>>>
>>>>>>> Reading Born's exchange of letters with Einstein (I'm proud to say 
>>>>>>>> Born was my great grandfather), it's clear that Born had a conception 
>>>>>>>> of QM 
>>>>>>>> that was still very realistic in the Einstein sense. Though they 
>>>>>>>> disagreed 
>>>>>>>> significantly and somewhat heatedly, Born still seems to have regarded 
>>>>>>>> QM 
>>>>>>>> probabilities as classical probabilities in disguise.
>>>>>>>>
>>>>>>>
>>>>>>> *Einstein realism seems to have been falsified due to Bell 
>>>>>>> experiments. If that's the case, it would mean that BEFORE measurement 
>>>>>>> of a 
>>>>>>> quantum system, it is not only NOT in all states of a superposition 
>>>>>>> simultaneously for the reasons I have argued (nothing to do with Bell), 
>>>>>>> but 
>>>>>>> ALSO has no local preexisting value. AG*
>>>>>>>
>>>>>>> I don't think he would ever have endorsed the notion that a particle 
>>>>>>>> is truly in all of the states of the superposition simultaneously. 
>>>>>>>>
>>>>>>>
>>>>>>> *Thanks for your input. AG *
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> The (complex-number-weighted) "path"s of the path integral 
>>>>>> (sum-over-histories) formulation are all that are needed to define 
>>>>>> superpositions. 
>>>>>>
>>>>>
>>>>> *Can you flesh that out? How can complex numbers be weighted and 
>>>>> result in superpositions? AG*
>>>>>
>>>>> "Einstein realism" is restored if *retrocausality* (the path futures 
>>>>>> can *stochastically* influence the path pasts) is allowed.
>>>>>>
>>>>>
>>>>> *I don't believe it. I think it has hugely absurd implications. AG *
>>>>>
>>>>>>
>>>>>> - pt
>>>>>>
>>>>>>
>>>> The paths (histories) in a path integral (sum over histories) 
>>>> formulation have complex numbers assigned to them. (That's their 
>>>> "weights".) 
>>>>
>>>>
>>>> http://muchomas.lassp.cornell.edu/8.04/Lecs/lec_FeynmanDiagrams/node3.html
>>>>
>>>> The Feynman formulation of Quantum Mechanics builds three central ideas 
>>>> from the de Broglie hypothesis into the computation of quantum amplitudes: 
>>>> the probabilistic aspect of nature, superposition, and the classical 
>>>> limit. 
>>>> This is done by making the following three three postulates:
>>>>
>>>>
>>>>    1. *Events in nature are probabilistic with predictable 
>>>>    probabilities P.*
>>>>    2. *The probability P for an event to occur is given by the square 
>>>>    of the complex magnitude of a quantum amplitude for the event, Q. The 
>>>>    quantum amplitude Q associated with an event is the sum of the 
>>>>    amplitudes [image: tex2html_wrap_inline1605] associated with every 
>>>> history 
>>>>    leading to the event.*
>>>>    3. *The quantum amplitude associated with a given history [image: 
>>>>    tex2html_wrap_inline1605] is the product of the amplitudes [image: 
>>>>    tex2html_wrap_inline1609] associated with each fundamental process in 
>>>> the 
>>>>    history.*
>>>>
>>>> ...
>>>>
>>>> Postulate (2) specifies how probabilities are to be computed. This item 
>>>> builds the concept of superposition, and thus the possibility of quantum 
>>>> interference, directly into the formulation. Specifying that the 
>>>> probability for an event is given as the magnitude-squared of a sum* 
>>>> made from complex numbers*, allows for negative, positive and 
>>>> intermediate interference effects. This part of the formulation thus 
>>>> builds 
>>>> the description of experiments such as the two-slit experiment directly 
>>>> into the formulation. A *history* is a *sequence* of fundamental 
>>>> processes leading to the the event in question. We now have an explicit 
>>>> formulation for calculating the probabilities for events in terms of the 
>>>> [image: 
>>>> tex2html_wrap_inline1605] , quantum amplitudes for individual 
>>>> histories, which the third postulate will now specify.
>>>> ...
>>>>
>>>> - pt
>>>>
>>>
>>> *Thanks for that. I have a few basic questions about Feynman's 
>>> path-integral formulation of QM. Firstly, IIUC, Bruce wrote that Feynman 
>>> initially believed in a particle-only formulation of QM. but later realized 
>>> this was not possible. Is this true or false? Personally, as I wrote above, 
>>> I don't see how a particle-only theory of slit experiments makes any sense. 
>>> Only using a wave model can we imagine that the "particle" goes through 
>>> both slits simultaneously to produce interference. Secondly, in his 
>>> particle only, or path integral formulation, how does he choose which paths 
>>> to use, given that there exists an uncountable number of direct paths, and 
>>> an uncountable number of paths which loop, go backward, then forward, and 
>>> so on. How does he choose which paths to use? Thirdly, how does he define a 
>>> "fundamental process", which is required to define a "history"? TIA, AG*
>>>
>>
>>
>> This has been written about by the late Victor J. Stenger, Huw Price, Ken 
>> Wharton, ... and me, of course.
>>
>> All are some sort of reification of Feynman paths. 
>>
>> There is the zig-zag particle that goes back and forth in time 
>> ("eventually"going through both slits). There is the reflective path 
>> integral (paths in one time direction mirrored with paths going in the 
>> opposite time direction), etc.
>>
>> - pt
>>
>
> *Seems like a desperate grasping at straws. How does Feynman choose which 
> paths to use, or are all equally required for the theory to make correct 
> predictions? AG*
>


My theory, it's a sort of Darwinian struggle:

*In this sum-over-histories-and-futures interpretation, “decoherence” is 
defined as all histories/futures but one die. (In a 
Darwinian”survival-of-the-fittest analogy, selection is made from a 
“fitness” probability distribution.)*

- https://codicalist.wordpress.com/2018/03/16/mirror-mirror/
- cf. 
https://codicalist.wordpress.com/2018/09/25/retrosignaling-in-the-quantum-substrate/

This may be a sort of version of quantum Darwinism 
[ https://en.wikipedia.org/wiki/Quantum_Darwinism ].

- pt

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