On 10/10/2019 6:55 PM, Alan Grayson wrote:
On Thursday, October 10, 2019 at 3:37:13 PM UTC-6, Alan Grayson wrote: On Thursday, October 10, 2019 at 3:27:58 PM UTC-6, Brent wrote: On 10/10/2019 8:02 AM, Alan Grayson wrote:On Wednesday, October 9, 2019 at 4:21:50 PM UTC-6, Brent wrote: On 10/9/2019 3:52 AM, Alan Grayson wrote: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. AGIOW, 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.
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