Natural Science Forum / Physics / Research / March 2010

[[Mod. note -- Most discussion of the author's theory would likely
violate the newsgroup charter's prohibition on "excessively speculative"
theories, so followups should be by E-mail to the poster (which I
have set to be the default) unless you genuinely believe that you

1)  It is well known that the inner product of position and momentum
eigenvectors:
<x|p> = exp[i pq]   (1)
Is there some simplified expression for the outer product:

======      Moderator's note =================================
Relativistic bicycles? I wonder, how fast you want to make them ;-))
SCNR, HvH.
==============================================================

Suppose a single photon polarized by a polaroid set at the angle 30
arrives at a polaroid at the angle zero – as in Fig. 11-3 [1]. Quantum
mechanics tells us, the photon, as a whole, will get through 3/4 of
the time, and 1/4 of the time it will heat the polaroid by being

By "motion molehill" I mean a hypothetical version of motionmountain.net
aimed more or less at third grade level.  That thought occurred to me
after reading (and contributing a little to) a 362-post (currently)
thread in a private newsgroup hierarchy (panix.questions) about teaching

I'm doing some individual study about GR and have this basic question.
In the Twins Paradox, the twin who stays fixed ages more than the twin
who travels and then comes back.  My question is this: is it the
acceration of the travelling twin that causes the dilation, or does

I have a complicated diffusion equation with various
slowly changing time dependent parameters.
Does anyone know if there is an analogue of
the adiabatic approximation that would apply

I have a one dimensional quantum
mechanics problem where x is
the coordinate operator and p
the momentum operator (so [x,p]=i).

In the case of atoms, there is a rough correlation that gives the
radius for different n values: R ~ n^2 a, where a = the Bohr radius.
Atoms can range in size by a factor of at least 300^2, and radiation
from huge Rydberg atoms with n ~ 300 has been observed in space.

I have read this on wikipedia about the exclusion principle, without
any reference:
"In relativistic quantum field theory, the Pauli principle follows
from applying a rotation operator in imaginary time to particles of

In his development of the path integral at:
http://jayryablon.files.wordpress.com/2009/12/sakurai-and-zee.pdf
professor A. Zee has two errata which he has corrected at:
http://www.kitp.ucsb.edu/~zee/nuts.html.  One is a missing factor of

The Big Bang & Variable Light Speed
I'm going to offer an interesting perspective on the FW cosmology -- a
different take that brings to light (pun intended) what's hiding in
plain sight.

Please take a look at http://en.wikipedia.org/wiki/Lie_product_formula.
Would this formula, which is stated to apply to NxN matrices, also apply
to an infinite-dimensioned operator / matrix?  Why or why not?
Thanks,

Consider a metric for a 2-dimensional manifold in the form:
ds^2 =dt^2 - dx^2/ c^2
How can I tell PHYSICALLY whether c is a constant or is some non -
constant function.

I am reading Luminet's paper titled "Time, Topology and the Twin
Paradox" available at:
http://arxiv.org/ftp/arxiv/papers/0910/0910.5847.pdf
The author is deriving the equation for proper time and compares