| My Version | Some Other Versions |
| GRW decoherence can be compared to Zizzi Self-Decoherence. |
My version of the GRW mechanism, described here, is not standard. GRW was devised by Ghirardi, Rimini, and Weber to explain why large objects behave classically, and not like fuzzy quantum superpositions. The GRW model is based on a process of Dynamical Decoherence of Quantum States, whereby every Particle in the Universe acts, once in each time interval of characteristic period Tgrw, to Decohere the Quantum Coherent Superpostion State of every particle within characteristic distance a_grw. Adrian Kent, in gr-qc/9809026, says: "... The parameters a_grw and Tgrw are to be thought of here as new constants of nature. GRW originally suggested a_grw = 10^(-5) cm and Tgrw = 10^15 sec ...".
What the time Tgrw means to me is how long a single elementary particle can maintain a Quantum Superposition of States before the Superposition undergoes GRW Decoherence, transforming the Superposition of States into many States, each of which is an Independent 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 properties of elementary particles.
Since the Electron is the most stable massive elementary particle, and is widely distributed throughout the plasmas, ions, and atoms of our Universe, it is useful to
The range within which a single Electron can maintain a Superposition of States is the Micron-Scale spatial range of its GravitoEM Induction Region Virtual Gravitons, so that
The time during which a single Electron can maintain a Superposition of States is also determined by the Micron-Scale range of its GravitoEM Induction Region Virtual Gravitons, not for Gravitons going outward from the Compton Radius Boundary of the Electron, but for Gravitons moving inside the Compton Radius Booundary of the Electron.
Since the Compton Radius Vortex structure of the Electron is the structure of a Kerr-Newman Black Hole, and since at the Static Limit Outer Boundary of the Ergosphere of the Kerr-Newman Black Hole the Exterior Time dimension becomes Spacelike, an Interior Graviton travelling inside the Static Limit Outer Boundary of the Ergosphere sees time and space interchanged from time and space outside the Compton Radius Black Hole Electron.
The speed of light Outside the Ergosphere is the reciprocal of the speed of light at the Ergosphere, so that Tgrw should be the time it would take a graviton moving at c_ergosphere to travel, while inside the Compton Radius Black Hole, the micron distance that is the range of the GravitoEM Induction Region 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 x 10^14 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 internal clocks for the Electron.
Take the case of a single particle, and let time flow left to right. Start with a particular State, denoted by -----. Then, let the Superposition of Possible States build up as illustrated by bifurcation into different possible future worlds, each also denoted by -----, and let the States between the blue lines represent the States at time Tgrw.
During the Superposition before the time Tgrw is reached, the red loops indicate Interactions among the States of the Superposition.
At time Tgrw, denoted by the States between the blue lines, the States become independent and are no longer in Superposition, so they are no longer interacting with each other, so that
after time Tgrw, each State evolves on its own as an Independent World of the Many-Worlds, and one such Independent State is shown in the above figure (the others being in Other Worlds).
The above figure is oversimplified, especially in that each State is represented by -----, which appears to be at a fixed time, while in fact each State is itself an Interaction between the Past Worlds of the Many-Worlds from which it could have come, represented by -----, and the Future Worlds of the Many-Worlds to which it could go, represented by -----, as shown in the following diagram:
----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ... ----- ----- ----- ----- ----- ... ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
During the Superposition before the time Tgrw is reached, the red loop Interactions modify the various Basins of Attraction of the Quantum Potential Landscape. This is how Sarfatti back-action of the Configuration on the Quantum Potential occurs. If the Superposition involoves 2^N States, the 2^N States can be naturally described in terms of Clifford Algebras.
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 x 10^14 sec,
and
a micron-sized System with Avogadro density of Electrons (as for Hydrogen atoms), 6 x 10^23 Electrons/cm^3 = 6 x 10^11 Electrons/micron^3, would be Localized by GRW in times on the order of 200 sec.
Just as an Electron has a_grw = 1 micron = 10^(-4) cm and Tgrw = 3 x 10^14 sec,
The Proton Tgrw is:
Jack Sarfatti agrees in part with my view, but (as of 16 December 1998) his view differs from mine in some respects. For instance, he says "... because of the two-way relation between wave and particle, Tgrw is the time it takes for the coherent landscape to form. As it is forming all of the basins are in nonlocal communication with each other. ... This co-evolution is erased by any form of environmental decoherence which erases the self-organization. If you shield out the random heat sources you will still eventually erase by the Penrose process. ...". From his point of view, the process of co-evolution is incomplete unless it proceeds for the full time Tgrw, and is destroyed if it is terminated before time Tgrw. Therefore, he maintains that Abstract Thought Consciousness exists only for N smaller than the intersection of the Tgrw and Penrose-Hameroff process T_N curves of the Quantum Consciousness TimeGraph. His views are set out more fully on the web, for example in the Quantum-Mind Archive, and the web versions of his views will probably be more current than the above summary as of 16 December 1998.
As of March 2000, Jack Sarfatti has developed a model linking GRW with the Hubble constant, resulting in Tgrw = 4 x 10^17 sec, which is close to Tgrw for protons and tubulin-electron cages.
Gisin and Percival have formulated a GRW-type theory in terms of a stochastic version of the Schrodinger equation: Quantum State Diffusion: from Foundations to Applications, quant-ph/9701024. The New Scientist of 27 April 1997, pages 38-41, has an article by Mark Buchanan entitled Crossing the Quantum Frontier that describes and compares GRW and Quantum State Diffusion (QSD). According to it, "... Ghirardi, Rimini, and Wheeler [GRW] proposed ... [that] very rarely - once every 100 million years [about 3 x 10^15 seconds] or so - the wavefunction of a single particle collapses and becomes localised to a tiny region. This change scarcely affects single particles, but has a huge effect on big things. A ... cat ... contains some 10^27 particles. ... There are so many particles that it is overwhelmingly likely that the wave function of at least one particle will collapse within just 10^(-12) seconds. ... because the particles ... interact with one another, their wave functions are entangled ... the collapse in one particle instantaneously triggers a collapse in all the others. ... in the GRW scheme,. ... it's difficult to imagine what might cause [the localizations]. ... Gisin and Percival suggest [that the localizations are caused by random fluctuations and] that the random fluctuations happen over very short periods, so that the state of a quantum system follows a sort of Brownian motion. ... Just as in the GRW theory, collapse happens very slowly for single particles, but very quickly for big ones. It works in much the same way. ... Percival and Gisin believe that it may soon be possible to detect these fluctuations in the laboratory. ... In 1992, Mark Kasevich and Steven Chu of Stanford University directed two beams of sodium atoms along different paths some 15 centimeters long, and found the pattern expected from normal quantum theory. So the fluctuations - if present - didn't have noticeable effects. These experiments would be sensitive enough to detect the fluctuations if they take place in around 10^(-44) seconds. But the fluctuations may well be more rapid yet. ... [improved experiments} should provide a 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 Penrose of Oxford University ... points out ... that ... the universe exists in a superposition of states with different mass distributions. ... ... a Universe in this [superposition] would be unstable, and would fall naturally into one state or the other, eliminating the superposition ... the decay would be more rapid for superpositions involving more widely differing distributions of mass ... These ideas would achieve the same ...[results]... as Gisin and Percival's theory, but would also make a real connection to the theory of gravity. ...".
Gisin says, in the Gisin-Percival paper: "... the quantum world takes advantage of random chance to evolve into one, among many possible, classical looking state of affair ... Notice the similarity with biological evolution: there the randomness is provided by the accidental (another world for random) mutations and Nature takes advantage of these fluctuations to produce order ... in a stochastic version of the Schrodinger equation the fluctuations ... could be independent of the environment, the latter taking advantage of the fluctuation to shape the physical system. ..."
Percival says, in the Gisin-Percival paper: "... The stochastic theories of quantum mechanics, like quantum state diffusion, are analogous to the mathematical theories of biological evolution of the 1940s. In each case the mechanism is clear, but the cause of the stochastic fluctuations is not. ...".
Adrian Kent, in gr-qc/9809026, says: "... Griffiths, Omnes, Gell-Mann and Hartle ... have set out a consistent (or decoherent) histories interpretation of quantum theory based on particular choices of criteria ... considered as a finished product, the consistent (or decoherent) histories interpretation must, I believe, be judged a failure as a scientific theory. ... it is unable to account for the simplest predictions or retrodictions, or to explain the success of Copenhagen quantum mechanics or classical mechanics. ... The key scientific problem in quantum histories approaches is to find some set selection rule, probabilistic or deterministic, sufficiently strong that it allows classical mechanics, Copenhagen quantum mechanics, and quantum field theory 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 the nonrelativistic set selection problem can be found, by reinterpreting dynamical collapse models of Ghirardi-Rimini-Weber type in the framework of quantum histories. Encouragingly from the point of view of relativistic generalisation, the quantum histories framework includes covariantly defined notions of event. ... A covariantly defined set selection rule, which picks out generally inconsistent sets and reduces to something resembling a dynamical collapse model in the non-relativistic limit, would be a particularly attractive way of solving the deep problem of interpreting quantum theory in the cosmological context, since it need not necessarily require any great conceptual revolution that threatens the successes of our present theories or (most of) their fundamental principles. It would, of course, disagree at least subtly with the predictions of standard quantum theory ... but then, if nature really has chosen to make fundamental use of the notion of a quantum event, it would seem uncharacteristically tasteless to have done so in a way that leaves such events entirely undetectable. ...
... Ghirardi-Rimini-Weber's spontaneous localisation or quantum jump model ... is the ur-model of modern dynamical collapse theories. In an appropriate limit, it leads to one of a class of Markovian stochastic differential equations which define testable alternatives to the Schrodinger equation. ...
... the GRW model defines a probabilistic set selection rule for a quantum histories formulation based on unsharp events. The set is selected by the choice of decompositions together with the random choice of Poisson times; its histories are given by sequences of unsharp events ... at the chosen times. ... The selected sets ... are not consistent ... which is why the models disagree with standard quantum theory. ...
"... The parameters a_grw and Tgrw are to be thought of here as new constants of nature. GRW originally suggested a_grw = 10^(-5) cm and Tgrw = 10^15 sec ...".
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