🚀 go-pugleaf

The last line in first version that I may not have aborted was mistyped.
This is the corrected version.
I will now lay to rest forever the bogus objection made by Mike Gallis,
Carlton Caves, Keith Ramsay et-al that my gedankenexperiment requires
violation of local unitarity in which a finite norm superposition is
transformed into a zero-norm superposition.

|a,b>  = {|a,e,+>|b,e,+> + |a,e,->|b,e,->}/sqrt2

|a,b>' = {e^iphi|a,e,+>|b,e,+> + |b,e,->|a,o,+>}/sqrt2

note that |<a,e,+|a,o,+>| = 1

|a,e,+> = e^ix |a,o,+>

<a,e,+|a,e,-> = 0

<a,o,+|a,o,-> = 0

There is no need to use a transformation that brings two orthogonal states
into the same state which would violate invariance of inner products and
norms.  The half-wave plate transformation H(o) is

H(o)|a,o,-> = |a,o,+>

H(o)|a,o,+> = |a,o,->

H(o)|a,e,+> = |a,e,+>

H(o)|a,e,-> = |a,e,->

H(o){|a,o,-> - |a,e,+>} = |a,o,+> - |a,e,+> = |a,o,+>[1 - ei^x]

[<a,o,-| - <a,e,+|][|a,o,-> - |a,e,+>]

= <a,o,-|a,o,-> + <a,e,+|a,e,+> - <a,o,-|a,e,+> - <a,e,+|a,o,->

= 1 + 1 - 0 - 0 =2

<a,o,-| - <a,e,+|H(o)*H(o)|a,o,-> - |a,e,+> = |1 - eix|^2 = 2(1 - cosx)

therefore, local unitarity of H(o) (i.e. invariance of inner product)
requires that x = pi/2

* so that |a,e,+> = i|a,o,+>

(this was mistyped in first version)

QED

There is no violation of local unitarity in my quantum connection signal
gedankenexperiment in the specific sense falsely claimed by skeptics.