Breakdown of Unitarity in Large Systems
The problem is that micro-quantum theory breaks down for macro-systems. I mean key rules like unitarity are lost with order parameters! The phase of the order parameter is rigid. It does not collapse like a micro-wave. It is local. Does it still entangle? Probably a tradeoff. The key term is |psi|^2phi (mean field Hartree)
Does the entangled
PSI(x)PSI(x') + PSI(x)'PSI(x')'
make sense where PSI & PSI' are two different macro-quantum solutions of the nonunitary local Landau-Ginzburg eq.
There is generally no macro-quantum order parameter in configuration space like for micro-quantum waves.
The macro-quantum coherent states are not eigenstates of a Hermitian operator.
The effective Hamiltonian density for the time evolution of macro-quantum order parameters is not a linear Hermitian operator in a Hilbert space.
H = a|GradPSI|^2 + b|PSI|^2 + c|PSI|^4
It's real, but it's a c-number. All of the linear Hilbert space structure is lost.
The basic differential equation is not linear like in micro-quantum theory where
H = a(Grad)^2 + V is a linear operator on a linear Hilbert space of functions.
The squared modulus of the order parameter is not scalable like for a micro-quantum wave function.
You lose the projective ray symmetry under |psi> --> z|psi> (Dirac, Quantum Mechanics)
On Oct 2, 2005, at 9:04 AM, Gary S. Bekkum wrote:
David Deutsch did note the apparent special status of living systems in the multiverse, as they create unique structures across vast regions of the multiverse - what Daid calls multiversal objects.
Please note Deutsch: "Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned."
The Structure of the Multiverse
Authors: David Deutsch
Comments: 21 pages, 3 illustrations
The structure of the multiverse is determined by information flow.
Machines, Logic and Quantum Physics
Authors: David Deutsch, Artur Ekert, Rossella Lupacchini
Categories: math.HO quant-ph
Comments: 19 pages, 8 figures
Subj-class: History and Overview
MSC-class: 00A30; 03-01
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Signal non-locality is only in living systems.
From: Jack Sarfatti [mailto:firstname.lastname@example.org]
Sent: Saturday, October 01, 2005 6:32 PM
To: Dan Smith
Subject: Dan Smith's Golden Calf
On Oct 1, 2005, at 2:46 PM, Dan Smith wrote
Computability is ambiguous.
1. It's obvious that Mandelbrot Set is effectively computable to sufficient human perceptual resolution by computers as the pictures show.
2. An algorithm is a retarded machine operating one-way past to future without any TELOS advanced signal nonocality from future back to past as in presponse. BTW Hameroff has done a fairly good recent review of that issue.
Also the no-cloning theorem is not as big a barrier as once thought (April 2005 Rev Mod Physics on Quantum computing with continuous variables) just as Hawking's "chronology protection" barrier against time travel to the past is wrong (e.g. Gott's 1997 paper before discovery of dark energy mind you!).
No-cloning arbitrary quantum states perfectly of course, but one can do a good enough job with MACRO-QUANTUM Gaussian states of continuous variables allowing the effective signal nonlocality of presponse & Remote Viewing!
3. No conscious process can be purely retarded i.e. effectively algorithmic.
4. Consciousness like gravity is an emergent "More is different" property from the combination of
I. Local gauge invariance
II Spontaneous breakdown of symmetry G to subgroup H of ground state manifold G/H
5. The conscious mind field is a local giant ground state order parameter in the BRAIN. It is immune from environmental decoherence via "holographic field phase rigidity". All this is in my book Super Cosmos http://amazon.com
You cannot point to a mechanical algorithm like MB Set even if it is a boundary of a non-computable Julia Set and imbue it in your Wish Fullfilment Majic Thinking as the Mind of God with Cosmic Consciousness as you seem to do. ;-)
But anyway, your source below agrees with me that the MB is not computable in the classical, i.e. strict, sense of that term
What more can I say? QED.
The strict sense is not relevant to the actual physics of consciousness.