Re: Derivation of Heisenberg Uncertainty from Kaluza Klein Geometry
- From: "Sue..." <suzysewnshow@xxxxxxxxxxxx>
- Date: Fri, 21 Mar 2008 01:37:09 -0700 (PDT)
On Mar 20, 10:21 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
For those who have followed my Kaluza-Klein (KK) work, I believe that it
is now possible to derive not only intrinsic spin, but Heisenberg
uncertainty directly from a fifth, compactified dimension in Kaluza
Klein. This would put canonical quantum mechanics on a strictly
geometric foundation which -- as a side benefit -- unites gravitation
and electromagnetism.
I need to consolidate over the next few days, but here is the basic
outline. First, take a look at:
http://jayryablon.files.wordpress.com/2008/03/intrinsic-spin-20.pdf
where I show how intrinsic spin is a consequence of the compactified
fifth dimension. This paper, at present, goes so far as to sow how the
Pauli spin matrices emerge from KK.
Next, go to the two page file:
http://jayryablon.files.wordpress.com/2008/03/spin-to-uncertainty.pdf
This shows how one can pop Heisenberg out of the spin matrices.
Finally, go to the latest draft paper on KK generally, at:
http://jayryablon.files.wordpress.com/2008/03/non-linear-qed.pdf
<< But with the non-linear (13.6) in hand, we should be able
to do a similar thing based on the gravitational field MN g
(really MN f ) rather than the electromagnetic field potential
M A , and based on the source energy tensor MN T rather than the
source
vector current M J . We shall not attempt the full
calculation of this, but will develop the first step. >>
Page 40
I remain skeptical about this notion. There is a finite
probability a path will be effective for the transfer
of energy from one atomic oscillator to another. (QED)
But an energy conservative force or localised current
can exist, even when the probabilty of energy transfer
is zero.
<< While virtual particles obey conservation of energy
and momentum, they can have any energy and momentum,
even one that is not allowed by the relativistic
energy-momentum relation. Such a particle is called
off-shell. When there is a loop, the momentum of the
particles involved in the loop is not uniquely determined
by the energies and momenta of incoming and outgoing
particles. A variation in the energy of one particle in
the loop can be balanced by an equal and opposite variation
in the energy of another particle in the loop. >>
http://en.wikipedia.org/wiki/Renormalization
A "Gaussian integral underlying the path integral"
is a valiant attempt. But what is the event whose
probabilty is represented by the Gaussian curve?
None I can identify.
It might be possible to make the false assumption
that only luminous bodies exhibit gravitational
attraction.
(infrared, ultraviolet divergence)
You are perhaps trying something like
that down through equation 14.4.
<< The physical constant e, the electron's charge,
can then be defined in terms of some specific experiment;
we set the renormalization scale equal to the energy
characteristic of this experiment, and the first term
gives the interaction we see in the laboratory
(up to small, finite corrections from loop diagrams,
providing such exotica as the high-order corrections
to the magnetic moment). The rest is the counterterm.
If we are lucky, the divergent parts of loop diagrams
can all be decomposed into pieces with three or fewer
legs, with an algebraic form that can be canceled out
by the second term (or by the similar counterterms that
come from Z0 and Z3). In QED, we are lucky: the theory
is renormalizable. >>
http://en.wikipedia.org/wiki/Renormalization
Let us be more concrete and consider a magnetic system
(e.g.: the Ising model), in which the J coupling constant
denotes the trend of neighbour spins to be parallel.
Physics is dominated by the tradeoff between the ordering
J term and the disordering effect of temperature. For
many models of this kind there are three fixed points:
[A,B,C]
So, if we are given a certain material with given
values of T and J, all we have to do in order to find
out the
*large scale behaviour*
of the system is to
iterate the pair until we find the corresponding fixed point.>>
http://en.wikipedia.org/wiki/Renormalization_group
C. P. Kouropoulos
http://arxiv.org/abs/physics/0107015
describes a plausible *large scale behaviour*
but none of A,B,C is a good fit for coherent matter.
The
http://en.wikipedia.org/wiki/Ferromagnetic phase
described in A is probably closest.
Thanks for the liberal application of words.
I get tangeled up in the squiggles. :o)
Kind regards,
Sue...
This lay out the full context in which I am developing this work.
Please note that the discussion on intrinsic spin in the third link is
superseded by the discussion thereof in the first link.
Best to all,
Jay.
____________________________
Jay R. Yablon
Email: jyab...@xxxxxxxxxxxx
co-moderator: sci.physics.foundations
Weblog:http://jayryablon.wordpress.com/
Web Site:http://home.nycap.rr.com/jry/FermionMass.htm
.
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