On 7/10/2018 7:04 PM, [email protected] wrote:
On Tuesday, July 10, 2018 at 5:08:30 PM UTC-6, Brent wrote:
On 7/10/2018 3:30 PM, [email protected] <javascript:> wrote:
*More and more, Dirac's claim seems to be an illusion that most
everyone has fallen in love with. Consider the example of a
vector in a plane decomposed as a superposition of unit vectors
in some orthogonal basis, Not an exact analogy to the quantum
superposition of course, but worth thinking about. How many
decompositions are possible? Well, rotations of the original
orthogonal basis give an uncountable number of DIFFERENT
decompositions. In fact, the set of NON orthogonal pairs define
another uncountable set of bases, each of which results in a
DIFFERENT decomposition. So in this example, it makes no sense to
say the original vector is in two states simultaneously in some
basis, when an uncountable set of other bases exist, each with a
different decomposition. In the quantum case, it is natural and
convenient to restrict ourselves to the basis in which the system
is being measured. But even here, other bases exist which allow
other, different, decompositions of the system into
superpositions, sometimes countable, sometimes not, depending on
the system. *
All true. True of any vector space. SO WHAT?
*The "SO WHAT?" is that since many superpositions exist, it makes
little sense to single out one, even if it seems natural and
convenient (say, in the basis being measured), and assert the system
is in both component states simultanoeusly prior to measurement. AG
*
Where does Dirac say anything about singling out states. His
description is completely arbitrary and applies to any states. Does it
make little sense to single out North and East directions? After all
there are infinitely many other coordinate systems that could be used.
Brent
*So, IMO, Dirac's claim fails, not to mention the fact that his
"argument" in favor of simultaneity*
"simultaneity" doesn't appear in Dirac's paragraph. So your rant
is unclear.
*of superposition states prior to measurement, is really just an
assertion. AG*
Instead of picking on a paragraph of Dirac taken out of context,
why don't you go read a modern version. Try Asher Peres, "Quantum
Theory: Concepts and Methods" pp 50, 116-117
Brent
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