No way to make the equivalent of the encoding Heisenberg microscope in the situation studied by Sanders.
Basically (z1a'|z3a') is a fixed parameter made by the Kerr cell equally affecting both a' and b' outputs as a local common past cause.
No way to change it locally at a'.
If so, that generalizes Stapp's theorem even to the case of entangled coherent Glauber states without needing to assume that the inner products must small.
However, in that case it's hard to see how John Cramer's device would work - though his argument is intuitively plausible.
Avshalom Elitzur says entanglement signals when ftl violate Second Law of Thermodynamics. Of course some of the people at USD AAAS in a parallel session claimed that.
What immortal hand or eye dare break thy fearful symmetry?
See the paper on entangled Schrodinger Tigers I just uploaded to the Library Quantum Computing Section.
Jack Sarfatti
Debate with Zielinski on the physics of over-complete non-orthogonal eigenfunctions http://bit.ly/q3YVeX
23 hours ago via AutoTweet Connector · Like ·
Zohar Ko PZ is obviously right.
Jack Sarfatti How much did Zielinski pay you to say that? ;-) Polemics are inappropriate here. Before I delete your remark, defend it so I can see if you know what you are talking about or merely trying to pi$$ me off.
Jack Sarfatti There is nothing "obvious" about Z's generally dark remarks.
Jack Sarfatti If you think Z is correct then you do not understand quantum measurement theory of Bohr to von Neumann. A switch in the base eigenfunctions is not a passive formal affair, but is a real change in Bohr's "total experimental arrangement" e.g. changing relative orientations of Stern-Gerlach magnets, introducing quarter-wave plates etc.
Zohar Ko It's the first axiom of QM that everybody learns in school: physics is independent of the basis, orthogonal or not.
Jack Sarfatti You are a good example of the saying a little bit of knowledge is a dangerous thing.
Jack Sarfatti The invariance of the trace of the density matrix with operators is only for unitary transformations that preserve inner products with similarity transformations on the operators.
Jack Sarfatti In particular, unitary transformations on an orthogonal basis will give a new orthogonal basis. However, unitary transformations on a non-orthogonal basis will give a new nonorthogonality basis - actually they are in same unitarily equivalence class.
Jack Sarfatti However, a non-unitary transformation is needed to connect an orthogonal basis with a non-orthogonal basis. Therefore, the traces of density matrices with operators in a non-orthogonal basis are different from those with those operators in an orthogonal basis. We have two different non-overlapping unitarily equivalent equivalence classes. In particular there is entanglement signaling in entangled systems with a physically demanded non-orthogonal basis, and none in those with physically demanded orthogonal basis.
Jack Sarfatti Let U be a unitary transformation. Let N be a non-unitary transformation.
UU* = U*U = 1
NN* =/= 1
Let {|Oi)} = orthogonal basis
(Oi|Oj) = 0 , i =/= j
Let {|Zi)} be a non-orthogonal basis
|Z) = N|O)
For any operator A
A' = UAU^-1
For the appropriate density matrix R
(A) = Tr{RA}
R = sum over eigenvalues P(oj)|Oj)(Oj|
P(oj) = probability to find oj in a statistical mixture
R' = URU^-1
(A') = Tr{R'A'} = Tr{RA} = (A)
i.e. invariance under unitary transformations of all physical expectation values.
On the other hand
S = NRN^-1 is a completely new physical object that is not unitarily equivalent to R - it means the emergence of qualitatively new physics.
In particular for the same operator A
Tr{SA} =/= Tr{RA}
However, under a unitary U
S' = USU^-1 = UNRN^-1U^-1
TrS'A' = TrSA
In particular if A describes a nonlocal signal
Tr{RA} = 0
Tr{SA} =/= 0
Probably best to start with the globally rigid conformal de Sitter group i.e. 16 parameters including / =/= 0. There is no gravity, i.e. no dynamical curvature until you localize at least its T4 subgroup.
The 4 tetrads e^I and the 6 spin-connections w^I,^J formally live on a non-dynamical Minkowski space-time (at least when / = 0).
Geometrodynamic field (e^I, w^I^J) is on equal ontological par with U1xSU2 & SU3 forces.
From: Paul Zielinski
To: Jack Sarfatti
Sent: Wed, July 6, 2011 2:45:56 PM
Subject: Re: de Broglie waves as the generator of spacetime
Regarding (5), if you start with Minkowski spacetime as an axiom, then how can you end up with emergent curved spacetime geometry and no background?
Don't you mean that you start with de Sitter space in the complete absence of gravitating matter?
Or are you taking about SR kinematics?
I don't understand either version.
Look I think you are confused over the difference between mathematics and theoretical physics.
In pure math you can do anything you like.
Quantum theory (OQT) used pure math with additional constraints linking symbols to operational procedures.
In particular OQT assumes only Hermitian operators with real eigenvalues and orthogonal eigenfunctions. These eigenfunctions correspond to Bohr's "total experimental arrangement" of detectors at the classical level.
A unitary change of basis is an actual change in the configuration and settings of the detectors. It leaves inner products invariant and it requires similarity transformations of the operators.
A non-orthogonal set of eigenfunctions will correspond to some new physical conditions e.g. laser beams, phase transitions with new order parameters etc.
Henry Stapp may want to say this is new physics beyond OQT?
The observables need not be Hermitian, if the Hamiltonian is not Hermitian then it generates a non-unitary time evolution with imaginary energy part i.e., dissipation & pumping - open not closed systems. decaying states, and growing states & dissipative meta-stable structures - far from thermal equilibrium etc.
We have seen in the density matrix formalism for an entangled system the use of a non-orthogonal basis allows entanglement signaling - there must be a physical reason why the non-orthogonal basis MUST be used. It's not an abstract formal whim the way Zielinski believes.
From: Paul Zielinski <iksnileiz@gmail.com>
To: Jack Sarfatti <sarfatti@pacbell.net>
Sent: Wed, July 6, 2011 3:22:55 PM
Subject: Re: OK I think I see where Zielinski makes his false premise on physical meaning of base eigenvectors in quantum theory
Change to:
"My point is that the physical motivation for the choice of non-orthogonal state vectors to represent the physical states of a QM system does not legitimize the
use of non-orthogonal bases for the direct computation of observable quantities from the associated Hilbert space operators."
On 7/6/2011 3:19 PM, Paul Zielinski wrote:
My point is that the motivation for the choice of state vector to represent the physical
state of a QM system does not legitimize the use of a non-orthogonal basis for the direct computation of observable quantities from the associated Hilbert space operators.