| My Version | SomeOther Versions |
| GRW decoherence can be compared to ZizziSelf-Decoherence. |
My version of the GRW mechanism, described here, is not standard.GRW was devised by Ghirardi, Rimini, and Weber to explain why largeobjects behave classically, and not like fuzzy quantumsuperpositions. The GRW model is based on a process of DynamicalDecoherence of Quantum States, whereby every Particle in the Universeacts, once in each time interval of characteristic periodTgrw, to Decohere the Quantum Coherent Superpostion State ofevery particle within characteristic distance a_grw. AdrianKent, in gr-qc/9809026,says: "... The parameters a_grw and Tgrw are to bethought of here as new constants of nature. GRW originally suggesteda_grw = 10^(-5) cm and Tgrw = 10^15 sec ...".
What the time Tgrw means to me is how long a single elementaryparticle can maintain a Quantum Superposition of States before theSuperposition undergoes GRW Decoherence, transforming theSuperposition of States into many States, each of which is anIndependent World of the Many-Worlds,and no longer in superposition with any of the others.
In my version of GRW, a_grw and Tgrw are calculable propertiesof elementary particles.
Since the Electron is the most stable massiveelementary particle, and is widely distributed throughout theplasmas, ions, and atoms of our Universe, it is useful to
The range within which a single Electron can maintain aSuperposition of States is the Micron-Scale spatial range of itsGravitoEM Induction RegionVirtual Gravitons, so that
The time during which a single Electron can maintain aSuperposition of States is also determined by the Micron-Scale rangeof its GravitoEM InductionRegion Virtual Gravitons, not for Gravitons going outward fromthe Compton Radius Boundary of the Electron, but for Gravitons movinginside the Compton Radius Booundary of the Electron.
Since the Compton Radius Vortexstructure of the Electron is the structure of a Kerr-Newman BlackHole, and since at the StaticLimit Outer Boundary of the Ergosphere of the Kerr-Newman BlackHole the Exterior Time dimension becomes Spacelike, anInterior Graviton travelling inside the Static Limit OuterBoundary of the Ergosphere sees time and space interchangedfrom time and space outside the Compton Radius Black HoleElectron.
The speed of light Outside the Ergosphere is the reciprocal of thespeed of light at the Ergosphere, so that Tgrw should be the time itwould take a graviton moving at c_ergosphere to travel, while insidethe Compton Radius Black Hole, the micron distance that is the rangeof the GravitoEM InductionRegion Virtual Gravitons.
Now calculate c_outside in terms of the micron scale of a_grw:
c_outside = 3 x 10^10 cm/sec x (1/a_grw) micron/cm = c/a_grw = 3 x10^14 micron/sec,
Then we have c_ergosphere = 3 x 10^14 sec/micron, so that
Tgrw = c / a_grw = 3 x 10^14 sec
and the Interior Gravitons effectively act as little internalclocks for the Electron.
Take the case of a single particle, and let time flow left toright. Start with a particular State, denoted by -----. Then, let theSuperposition of Possible States build up as illustrated bybifurcation into different possible future worlds, each also denotedby -----, and let the States between the bluelines represent the States at time Tgrw.
During the Superposition before the time Tgrw is reached,the red loops indicate Interactionsamong the States of the Superposition.
At time Tgrw, denoted by the States between theblue lines, the States becomeindependent and are no longer in Superposition, so they are no longerinteracting with each other, so that
after time Tgrw, each State evolves on its own as anIndependent World of the Many-Worlds,and one such Independent State is shown in the above figure (theothers being in Other Worlds).
The above figure is oversimplified, especially in that each Stateis represented by -----, which appears to be at a fixed time, whilein fact each State is itself an Interaction between the Past Worldsof the Many-Worlds from which it could have come, represented by-----, and the Future Worlds of theMany-Worlds to which it could go, represented by-----, as shown in the followingdiagram:
----- ---------- ----- ----- ---------- ---------- -----... ----- ----- ----- ----- ----- ...----- ---------- ---------- ----- ----- ---------- -----
During the Superposition before the time Tgrw is reached,the red loopInteractions modify the various Basins of Attraction of the QuantumPotential Landscape. This is how Sarfattiback-action of the Configuration on the Quantum Potential occurs.If the Superposition involoves 2^N States, the 2^N States can benaturally described in terms of CliffordAlgebras.
What about other elementary particles?
What about N Particles in Coherent Superposition?
For an Electron with a_grw = 1 micron = 10^(-4) cm and Tgrw = 3 x10^14 sec,
a micron-sized System with Avogadro density of Electrons (as forHydrogen atoms), 6 x 10^23 Electrons/cm^3 = 6 x 10^11Electrons/micron^3, would be Localized by GRW in times on the orderof 200 sec.
Just as an Electron has a_grw = 1 micron = 10^(-4) cm and Tgrw = 3x 10^14 sec,
The Proton Tgrw is:
Jack Sarfattiagrees in part with my view, but (as of 16 December 1998) his viewdiffers from mine in some respects. For instance, he says "...because of the two-way relation between wave and particle, Tgrw isthe time it takes for the coherent landscape to form. As it isforming all of the basins are in nonlocal communication with eachother. ... This co-evolution is erased by any form of environmentaldecoherence which erases the self-organization. If you shield out therandom heat sources you will still eventually erase by the Penroseprocess. ...". From his point of view, the process of co-evolution isincomplete unless it proceeds for the full time Tgrw, and isdestroyed if it is terminated before time Tgrw. Therefore, hemaintains that Abstract Thought Consciousness exists only for Nsmaller than the intersection of the Tgrw and Penrose-Hameroffprocess T_N curves of the QuantumConsciousness TimeGraph. His views are set out more fully on theweb, for example in the Quantum-MindArchive, and the web versions of his views will probably be morecurrent than the above summary as of 16 December 1998.
As of March 2000, JackSarfatti has developed a modellinking GRW with the Hubble constant, resulting in Tgrw = 4 x10^17 sec, which is close to Tgrw for protonsand tubulin-electron cages.
Gisin and Percival have formulated a GRW-type theory interms of a stochastic version of the Schrodinger equation: QuantumState Diffusion: from Foundations to Applications,quant-ph/9701024. The New Scientist of 27 April 1997, pages38-41, has an article by Mark Buchanan entitled Crossing the QuantumFrontier that describes and compares GRW and Quantum State Diffusion(QSD). According to it, "... Ghirardi, Rimini, and Wheeler[GRW] proposed ... [that] very rarely - once every100 million years [about 3 x 10^15 seconds] or so - thewavefunction of a single particle collapses and becomes localised toa tiny region. This change scarcely affects single particles, but hasa huge effect on big things. A ... cat ... contains some 10^27particles. ... There are so many particles that it is overwhelminglylikely that the wave function of at least one particle will collapsewithin just 10^(-12) seconds. ... because the particles ... interactwith one another, their wave functions are entangled ... the collapsein one particle instantaneously triggers a collapse in all theothers. ... in the GRW scheme,. ... it's difficult to imagine whatmight cause [the localizations]. ... Gisin and Percivalsuggest [that the localizations are caused by random fluctuationsand] that the random fluctuations happen over very short periods,so that the state of a quantum system follows a sort of Brownianmotion. ... Just as in the GRW theory, collapse happens veryslowly for single particles, but very quickly for big ones. It worksin much the same way. ... Percival and Gisin believe that it may soonbe possible to detect these fluctuations in the laboratory. ... In1992, Mark Kasevich and Steven Chu of Stanford University directedtwo beams of sodium atoms along different paths some 15 centimeterslong, and found the pattern expected from normal quantum theory. Sothe fluctuations - if present - didn't have noticeable effects. Theseexperiments would be sensitive enough to detect the fluctuations ifthey take place in around 10^(-44) seconds. But the fluctuations maywell be more rapid yet. ... [improved experiments} should providea more sensitive probe within the next few years. ... If the[QSD] fluctuations are detected, these new theories[QSD] will undoubtedly displace ordinary quantum theory,Theoretical physicist Roger Penroseof Oxford University ... points out ... that ... the universe existsin a superposition of states with different mass distributions. ...... a Universe in this [superposition] would be unstable, andwould fall naturally into one state or the other, eliminating thesuperposition ... the decay would be more rapid for superpositionsinvolving more widely differing distributions of mass ... These ideaswould achieve the same ...[results]... as Gisin andPercival's theory, but would also make a real connection to thetheory of gravity. ...".
Gisin says, in the Gisin-Percival paper: "... the quantum worldtakes advantage of random chance to evolve into one, among manypossible, classical looking state of affair ... Notice the similaritywith biological evolution: there the randomness is provided by theaccidental (another world for random) mutations and Nature takesadvantage of these fluctuations to produce order ... in a stochasticversion of the Schrodinger equation the fluctuations ... could beindependent of the environment, the latter taking advantage of thefluctuation to shape the physical system. ..."
Percival says, in the Gisin-Percival paper: "... The stochastictheories of quantum mechanics, like quantum state diffusion, areanalogous to the mathematical theories of biological evolution of the1940s. In each case the mechanism is clear, but the cause of thestochastic fluctuations is not. ...".
Adrian Kent, in gr-qc/9809026,says: "... Griffiths, Omnes, Gell-Mann and Hartle ... have set out aconsistent (or decoherent) histories interpretation of quantum theorybased on particular choices of criteria ... considered as a finishedproduct, the consistent (or decoherent) histories interpretationmust, I believe, be judged a failure as a scientific theory. ... itis unable to account for the simplest predictions or retrodictions,or to explain the success of Copenhagen quantum mechanics orclassical mechanics. ... The key scientific problem in quantumhistories approaches is to find some set selection rule,probabilistic or deterministic, sufficiently strong that it allowsclassical mechanics, Copenhagen quantum mechanics, and quantum fieldtheory to be derived within characterisable domains of validity....
... [B]y going outside the consistent histories framework,and deviating from standard quantum mechanics, a solution to thenonrelativistic set selection problem can be found, by reinterpretingdynamical collapse models of Ghirardi-Rimini-Weber type in theframework of quantum histories. Encouragingly from the point of viewof relativistic generalisation, the quantum histories frameworkincludes covariantly defined notions of event. ... A covariantlydefined set selection rule, which picks out generally inconsistentsets and reduces to something resembling a dynamical collapse modelin the non-relativistic limit, would be a particularly attractive wayof solving the deep problem of interpreting quantum theory in thecosmological context, since it need not necessarily require any greatconceptual revolution that threatens the successes of our presenttheories or (most of) their fundamental principles. It would, ofcourse, disagree at least subtly with the predictions of standardquantum theory ... but then, if nature really has chosen to makefundamental use of the notion of a quantum event, it would seemuncharacteristically tasteless to have done so in a way that leavessuch events entirely undetectable. ...
... Ghirardi-Rimini-Weber's spontaneous localisation or quantumjump model ... is the ur-model of modern dynamical collapse theories.In an appropriate limit, it leads to one of a class of Markovianstochastic differential equations which define testablealternatives to the Schrodinger equation. ...
... the GRW model defines a probabilistic set selection rule for aquantum histories formulation based on unsharp events. The set isselected by the choice of decompositions together with the randomchoice of Poisson times; its histories are given by sequences ofunsharp events ... at the chosen times. ... The selected sets ... arenot consistent ... which is why the models disagree with standardquantum theory. ...
"... The parameters a_grw and Tgrw are to be thought of here asnew constants of nature. GRW originally suggested a_grw = 10^(-5) cmand Tgrw = 10^15 sec ...".