On Thursday, October 10, 2019 at 9:53:29 PM UTC-6, Brent wrote:
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> On 10/10/2019 6:55 PM, Alan Grayson wrote:
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> On Thursday, October 10, 2019 at 3:37:13 PM UTC-6, Alan Grayson wrote: 
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>> On Thursday, October 10, 2019 at 3:27:58 PM UTC-6, Brent wrote: 
>>>
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>>> On 10/10/2019 8:02 AM, Alan Grayson wrote:
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>>> On Wednesday, October 9, 2019 at 4:21:50 PM UTC-6, Brent wrote: 
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>>>>
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>>>> On 10/9/2019 3:52 AM, Alan Grayson wrote:
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>>>> On Wednesday, October 9, 2019 at 12:28:38 AM UTC-6, Brent wrote: 
>>>>>
>>>>>
>>>>>
>>>>> On 10/8/2019 9:20 PM, Alan Grayson wrote: 
>>>>> > I've argued this before, but it's worth stating again. It's a 
>>>>> > misintepretation of superposition to claim that a system described 
>>>>> by 
>>>>> > it, is in all the component states simultaneously. As is easily seen 
>>>>> > in ordinary vector space, an arbitrary vector has an uncountable 
>>>>> > number of different representations. Thus, to claim it is in some 
>>>>> > specific set of component states simultaneously, makes no sense. 
>>>>> Thus 
>>>>> > evaporates a key "mystery" of quantum theory, inclusive of S's cat 
>>>>> and 
>>>>> > Everett's many worlds. AG 
>>>>>
>>>>> No.  It changes the problem to the question of why there are preferred 
>>>>> bases. 
>>>>>
>>>>> Brent 
>>>>>
>>>>
>>>> Who chose Alive and Dead, or Awake and Sleeping for the S. cat? Wasn't 
>>>> it the observer? 
>>>>
>>>>
>>>> Could the observer have chosen |alive>+|dead> and |alive>-|dead> as a 
>>>> basis?
>>>>
>>>> Brent
>>>>
>>>
>>> *That's a great question and the answer is No, because, as you would 
>>> say, the pair (|Alive>, |Dead>), forms a "preferred" basis. We can only 
>>> measure Alive or Dead. However, the other pair you have above is a 
>>> perfectly valid state of the S cat system, a vector in the Hilbert Space of 
>>> the system, and presumably there is an uncountable set of other valid 
>>> states in Hilbert Space. This means that the interpretation of a 
>>> superposition of the first pair is just as valid as the interpretation of 
>>> any other pair; namely, that the system is in both components 
>>> simultanously. But this is obvious nonsense given the plethora of valid 
>>> bases, so the interpretation fails. THIS is my point. Am I mistaken? AG*
>>>
>>>
>>> The way I read what you posted above is that it would "make no sense" to 
>>> say a ship on a heading of 345deg is simultaneously moving on a 270deg and 
>>> 90deg heading.  I think that does make sense.   The interesting question is 
>>> could it be moving on some other heading?  The answer might be no, it's in 
>>> the Panama Canal.  In other words there may be something else in physics 
>>> that determines  perferred basis, even thought he bare Schrodinger equation 
>>> doesn't seem to.
>>>
>>> brent
>>>
>>
>> No, not what I meant. Rather, a ship with a heading of 345 deg, could be 
>> represented as moving on a 270deg and 90deg heading, *as well as an 
>> uncountable combination of other headings.*  I think this fundamental 
>> misinterpretation of superposition of states leads to the MWI and a host of 
>> other "mysteries" alleged in QM. AG 
>>
>
> IOW, you can think of the wf representing a heading of 345deg, and since 
> the basis in Hilbert Space is *not* unique, you can imagine that very 
> *same* wf composed of *different* components. Thus, if it's claimed that 
> one set of basis components simultaneously represents the wf, one can also 
> find another, *different* set of basis components to simultaneously 
> represent the wf. It therefore makes no sense to claim that any set of 
> basis components simultaneously represents the wf. Specifically, the 
> quantum claim that a system can be in several component states 
> simultaneously, is bogus, since the components are *not unique*. AG
>
>
> But my example of the ship shows that it's a commonplace that a vector can 
> be represented as a sum of components in infinitely many ways...it's a 
> trivial result of being a vector space.  It's just your prejudice that 
> there has to be a unique "really, really real" representation.
>
> Brent
>

I have no prejudice. I do *not* insist on a unique representation; nor do I 
believe that. Rather, I am saying that SINCE there is no unique 
representation, it's a fallacy to take, say one representation, and assert 
that the components in one representation, simultaneously represent the wf. 
So, for example, in the case of S's cat, it's a fallacy to assert that the 
cat is simultanously Alive and Dead. It's the lack of recognition of the 
NON-UNIQUENESS that is responsible for the misinterpretation of the 
superposition and many (not all) alleged weird interpretations of QM. AG 

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