| 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:

- the GRW time used by Jack Sarfatti in his model of universe/human consciousness connection; and
- the GRW time for the nanometer range-scale of tubulin-electron cages in the tubulin-electron models of consciousness in the human brain.

**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 ...".

......