Subject: QUANTUM-MIND Digest - 20 Dec 1999 to 24 Dec 1999 (#1999-123)
Date:    Sat, 25 Dec 1999 00:00:35 -0700

There are 10 messages totalling 1044 lines in this issue.

Topics of the day:

  1. [q-mind] Quantum Superluminal Communication and Superposition
     (Experimental aspects) - Fred Thaheld
  2. [q-mind] Three examples for understanding quantum motion - Gao Shan
  3. [q-mind] The hard problem - Chris Lofting
  4. [q-mind] Response to Vecchi re Superpositioning - Scott Bowden
  5. [q-mind]  Reply to G Stone re Human vision - Scott Bowden
  6. [q-mind] Breaking the paradigm - Dave Chamberlain
  7. [q-mind] Beyond rational? (Reply to Nixon) - Peter Mutnick
  8. [q-mind] The Super-Implicate Order (Reply to Lofting) - Peter Mutnick
  9. [q-mind] Bohm theory and motion (Reply to Gao-Shan) - Peter Mutnick
 10. [q-mind] New ideas please - John Cowley

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Date:    Fri, 24 Dec 1999 06:02:20 -0700
From:    Stuart Hameroff <hameroff@U.ARIZONA.EDU>
Subject: [q-mind] Three examples for understanding quantum motion - Gao Shan

>From Gao Shan gaoshan.iqm@263.net

Three examples for understanding quantum motion:
atomic stability, double-slit experiment and Schrodinger's cat

Gao Shan
Institute of Quantum Mechanics
11-10, NO.10 Building,
YueTan XiJie DongLi, XiCheng District
Beijing 100045, P.R.China
E-mail: gaoshan.iqm@263.net

[abstract]
We show that the discontinuous motion of particle can naturally
and objectively explain the atomic stability and double-slit
interference pattern, and solve the Schr\"{o}dinger's cat paradox.

[Introduction]
In order to deeply understand the discontinuous motion of
particle[4,5,6], we will discuss three famous
examples indispensable for understanding quantum mechanics, and
show that the discontinuous motion of particle indeed presents a
clear unified realistic picture for the microscopic world and
macroscopic world.

[Atomic stability]
Fist, we will analyze the origin of the atomic stability, a simple
situation is the base state of Hydrogen atom, its position
distribution density, which can be found through position
measurements, is written as follows:
\begin{equation}\rho(\mathbf{x})=|\psi(\mathbf{x})|^2=\frac{4}{a_0}\cdot{exp(-
\frac{2r}{a_0})}\end{equation}

According to the discontinuous motion of particle, at any instant
the electron will be in only one position in space, but during a
very small time interval $\Delta t $, or even infinitesimal time
interval dt(only for CSTM), the electron will move throughout the
whole space where the above function does not equal to zero, and
its position measure density will be the same as the above
position probability density obtained from the wave function, thus
during a very small time interval $\Delta t $, or even
infinitesimal time interval dt(only for CSTM), the charge
distribution of the whole system will be equivalent to the zero
charge distribution, and there exists no change of the whole
charge distribution either, so it can be easily understood that no
energy is radiated during finite time interval, as well as during
infinitesimal time interval, this is just the objective origin of
the mysterious stability in the atomic world.

[Double-slit experiment]
The second example is double-slit experiment, people have been
trying to understand the formation process of the double-slit
interference pattern objectively, but few people can give a clear
ontological description for it, which bases only on the motion of
particle, the essential reason, as we think, is that most people
ignored the essential difference between instant and infinitesimal
time interval or finite time interval.

By means of the discontinuous motion of particle, the mystery of
this process can be disclosed, the real process should be that the
particle undergoing the discontinuous motion passes through both
slits in the double-slit experiment, this means that the particle
is still in only one of the two slits at any instant, but during a
very small time interval $\Delta t $, or even infinitesimal time
interval dt(only for CSTM), the particle moves throughout both
slits and passes through them, and the position measure density of
the particle always satisfies the function
$\rho(\mathbf{x},t)=|\psi(\mathbf{x},t)|^2$, which is finite in
both slits, since the particle undergoing the discontinuous motion
can pass through both slits in this objective way, we can
understand the formation of the double-slit interference pattern,
which is not a simple mixture of two one-slit interference
patterns.

[Schr\"{o}dinger's cat]
Since the evolution of the discontinuous motion of particle will
naturally result in the dynamical collapse process of the wave
function describing the discontinuous motion[5,6], the
Schr\"{o}dinger's cat paradox will be objectively solved in terms
of the discontinuous motion of particle.

As we know, cat is a macroscopic complex open system, the energy
difference $\Delta E$ between different space branches of its wave
function, for example, the living branch and dead branch, will be
very large due to the environmental effects such as thermal energy
fluctuations, thus according to the evolution law of the
discontinuous motion (DSTM), the collapse time will be $\tau_{c}
\cong \frac{\hbar E_{p}}{(\Delta E)^{2}}$  (This result has
also been obtained by Hughston[7] and Fivel[3] from different point of
views, and
discussed by Adler etc[1,2]),  and the superposition of the
living branch and dead branch will collapse to one of the branches
very soon owing to the very large value of $\Delta E$, say when
$\Delta E \approx 7Gev$ we have $\tau_{c}\approx 10^{-6}s$, then
the cat can only be in the living state or dead state, and its
superposition state hasn't even been completely formed before the
collapse process finished, this solves the Schr\"{o}dinger's cat
paradox.


[Conclusions]
We show that the stability of atom and formation of double-slit
interference pattern can be objectively explained, and the
Schr\"{o}dinger's cat paradox can be naturally solved in terms of
the discontinuous motion of particle.

[1]S.L.Adler, L.P.Horwitz, e-print quant-ph/9904048, (1999)
[2]S.L.Adler, L.P.Horwitz, e-print quant-ph/9909026, (1999)
[3]D.I.Fivel, e-print quant-ph/9710042, (1997)
[4]Gao Shan, e-print physics/9907001, (1999)
[5]Gao Shan, e-print physics/9907002, (1999)
[6]Gao Shan, Quantum-Mind Digest, 20 Dec 1999 (1999)
[7]L.P.Hughston, Proc.Roy.Soc.Lond.A, 452,953 (1996)

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