Originally posted by Agerg
Why should not-lying be more perfect than lying!? ... setting aside the fact that we may not like being lied to, the act of a lie, paraphrasing you slightly, is to deliberately convey information which is believed to be not true in order to gain an end (and end which may be a positive one or a negative one (No kind Nazi ... no jews in my basement!)). In some ...[text shortened]... t even be sure you stated it correctly). I'm sorry but I cannot follow you on this argument yet.
I don't see the lying is imperfect thing either. Although in the case of God a white lie would be unnecessary as they could just protect the jews in the basement by making the Nazis forget to search.
I didn't derive anything I just wrote it down. One can always (at least in the theory) prepare states in linear combinations of eigenstates. Really each term should have a complex coefficient c(+/- 1/2) with the rule |c(1/2)|^2 + |c(-1/2)|^2 = 1. But for the terms of this discussion the equation I wrote down is good enough.
An alternative example is a particle in a 1 dimensional box. The wave equation is (Using f for the wavefunction as phi is unavailable):
Ef(x) = -h^2/2m * d^2f(x)/dx^2 + V(x)f(x)
V(x) = 0 if 0 < x < 1, and is infinite elsewhere. h is the reduced Planck's constant. This is solved by:
f(x) = ASin(kx), where k = pi*n = 1, 2, 3, ... ; is deduced from the boundary conditions, and fixes the energy. E = h^2k^2/2m. So let's measure the (vector) momentum. In terms of momentum eigenstates the wavefunction is:
f(x) = A/2i * (exp(ikx) - exp(-ikx)), or in Dirac notation where <x|k> = e(ikx), we have:
|f> = A/2i * (|k> - |-k> ).
So (up until the moment the momentum is measured) a particle in definite state of energy has momentum +k
and momentum -k. Some real damage is done to the law of non-contradiction in quantum theory. What is the case is that the result of the measurement must be one or the other, so we can't measure the particle to simultaneously have two momenta. The problem lies in trying to use classical logic where one shouldn't.