On Jan 5, 2008, at 7:01 PM, Robin van Spaandonk wrote:
In reply to Horace Heffner's message of Sat, 5 Jan 2008 15:57:02
-0900:
Hi,
[snip]
True, but one is not free to choose the radial direction, because
that is
perpendicular to the path of the electron (and hence it's
momentum). IOW
whatever dimension one chooses, both momentum and distance must lie
along the
same vector, but there is no movement in the radial direction,
hence it is
trivially irrelevant.
If that were true then the de Broglie wavelength would be irrelevant
to any consideration and interference would be impossible because the
de Broglie wavelength existence would only be in the direction of
travel. Interference is due to the *lateral* wave extension, not
longitudinal.
A lateral wave is still possible that lies on the surface of the
sphere. De
Broglie himself used a phase criterion in the De Broglie wave to
calculate the
radius of the Hydrogen ground state.
If an electron can specially change its nature just to be in a
hydrino orbital, and become a 2 dimensional object, a magic trick for
which there is no evidence that I have seen, then there is nothing to
prevent the radius of the orbital collapsing to a point.
The HUP limitations apply in any (i.e. every) direction you might
chose, and the de Broli wavelength extends in all directions. If a
particle is constrained to a small volume then it exerts a pressure,
so increasing the confinement results in increasing the pressure,
which requires energy,
and since the situation is constrained by E*
(detla t) = h/(4Pi),
Correction: the above should say: "the time confined to a small
volume is energy limited unless some supply of energy is available to
create the state of confinement."
This is the case. In shrinking to a smaller orbital, electrostatic
potential
energy becomes available. However, if I'm not mistaken the energy/
time form of
the HUP pertains to uncertainties in energy and time, not absolute
values.
The time is a time increment, delta t. The bigger the time increment
the smaller the uncertainty on energy (and thus momentum), and vice
versa.
Since the position of the electron is indeterminate,
The position of the sphere is not indeterminate. You are apparently
attempting a projection of an electron's reality onto a 2 dimensional
surface, but choosing to ignore the fact that surface still exists in
a 3 dimensional space.
so is the time (at any
given point), and hence the uncertainty in the time is also
infinite, resulting
in possible very precise energies.
There is insufficient energy available to compress the orbital. It is
not available because the force between the electron and nucleus is
reduced when the nucleus is within the de Broglie wavelength of the
electron. The uncertainty in position results in an uncertainty in
force direction. If not, then there is nothing to prevent the
spherical surface orbital from collapsing to a point.
The uncertainty of momentum for a particle constrained by distance
delta x is given, according to Heisenberg, by:
(Delta m*v) = h/(2 Pi (delta x))
but since
KE = (1/2) m v2 = (1/(2 m) )* (Delta m*v)^2
(delta KE) = (1/(2 m)) (h/(2 Pi (delta x)))^2
(delta KE) = h^2 /((8 Pi^2 m)*(delta x)^2)
so the more you can confine the position of a particle the more
kinetic energy as well as momentum you statistically observe when you
sample that energy or momentum. The statistically higher momentum in
the reduced volume state results in an outward pressure the keeps the
orbital inflated. When the gravity of a star reaches the point such
pressure can be overcome, then the orbitals collapse and vast
quantities of energy are released as the Coulomb potential energy
becomes available. It seems to me that if stable hydrino orbitals
were available, then stars could gradually shrink, at least to the
size corresponding to all atoms being the smallest hydrino, without
producing supernovas.
The only reason I brought time into the discussion is that I have
suggested the energy to shrink the orbital (and thus the de Broglie
wavelength) into a hydrino sized radius might be momentarily borrowed
via uncertainty, but there is a time limit set by the HUP on the
maximum duration of such a state. My experience doing calculations
relating to this show the energy necessary to form a stable bond
requires inclusion of magnetic binding and very small orbitals.
Horace Heffner
http://www.mtaonline.net/~hheffner/
