On 11/3/2015 8:15 PM, Bruce Kellett wrote:
On 4/11/2015 1:26 pm, Russell Standish wrote:
On Wed, Nov 04, 2015 at 11:59:41AM +1100, Bruce Kellett wrote:
I disagree. I do not think the quantum mechanics /ab initio/ is in
any way possible.
This is what I do in appendix D of my book. It then behooves you to
point out where exactly that is wrong.
You don't actually derive QM /ab initio/ there: you know where you
want to get and then make a series of appropriate assumptions. You
postulate that the observer can choose an observable, which has a
discrete set of possible outcomes. You then assume a probability
interpretation. The relationship to observations is simply assumed. I
do not see any derivation of the fact that possible outcomes of
measurements are the eigenvalues of the corresponding operator. You
have a major basis problem because the best you have is that a state
(vector) is a linear sum over some complete basis set, but you don't
know what that basis set might be, or what it might represent.
The derivation of a time evolution equation depends on the assumption
of a classical time variable, which you assume is uniform and
universal. You do not demonstrate that the 'Hamiltonian' you have in
your time evolution equation is the energy operator. In fact you show
nothing at all about H, or about any dynamics -- which presumably you
take over from classical mechanics or something similar.
This scarcely counts as a derivation of any useful physics at all,
much less of quantum mechanics that relates to observational results.
Bruce
It's interesting that there seem to be many different ways to "derive"
QM. Vic Stenger, in his book "The Comprehensible Cosmos" derives it as
a gauge transformation.
http://www.colorado.edu/philosophy/vstenger/Nothing/Laws.pdf
Scott Aaronson in his book "Quantum Computing Since Democritus" derives
it as the natural extension to probability theory that allows negative
probability. Of course partly this is possible because QM isn't really
a physical theory, it's a schema for theories or a kind of meta-theory
the way classical mechanics is a meta-theory of mechanisms.
Brent
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