To all:

With some good advice along the way from Nuropulp, I believe I have
found a solution to the "perplexity" known since the time of Dirac, that
the eigenvalues of the velocity operator are equal to the speed of
light, and have therefore been taken as suggestive that fermions must
travel at the speed of light (subject then, to Zitterbewegung and the
like).

In particular, following an earlier comment inn which Nuropulp stated
"But in your transformed H = beta sqrt(m^2 + p^2), dH/dp_i is not
obviously the same as your transformed v," I have tried to ferret out
the cause of this inconsistency.

In the new, brief, 6.5-page draft paper posted below:

http://jayryablon.files.wordpress.com/2008/07/correcting-newton-wigner.pdf

Only visit:
http://hvansari.googlepages.com or
http://www.geocities.com/hamid_vasigh

http://plus.maths.org/latestnews/may-aug08/sawyer/index.html

Prof. Sawyer was my friend, mentor and tutor,
and is acknowledged as a world famous teacher.
While a high school student (1968...) he invited me
to his home numerous times and we'd discuss
math, physics and relativity. His favorite subjects
were the Curl and spacetime.

Modern SpaceTime evolved from our discussions.
http://physics.trak4.com/
and yielded an alternative (++++) metric signature,
though nonorthogonal, that he suggested, he was a
genius who often used imaginary and oblique CSs.
Subsequently that metric has proven itself to be an
extremely powerful tool in GR.

That's why I keep an ear open for unconventional
approaches.

Cheers Dr. Sawyer!
Ken S. Tucker

I used to think I knew what the uncertainty principle was, but have
recently become confused by a statement at SPResearch (supported by
wiki) to the effect that the product of the uncertainties is greater
or equal to Planck's reduced constant / 2.

That is not the minimum value I learned, and not the minimum value I
have used in the past. I have checked in 2 of my old university
textbooks and both indicate the minimum value is Planck's reduced
constant (i.e. twice as large). The second textbook even claims to
prove it.

Wiki claims the 'modern' value of half this was derived in 1927.
However, both my books (Eisberg, and Pauling & Wilson) were required
reading in the late 60's, and the second was first published in that
decade.

So, which figure is correct, how did this discrepancy arise, and where
does this leave us for physical interpretations, such as in the
spontaneous creation and annihilation of virtual pairs within the
uncertainty constraint?

Following up on a recent post by Neuropulp four threads down from this,
I have come upon an interesting paradox which relates to her statement
"But in your transformed H = beta sqrt(m^2 + p^2), dH/dp_i is not
obviously the same as your transformed v.":

Consider the usual Dirac Hamiltonian:

H = alpha dot p+beta m (1)

in contrast to the Foldy-Wouthuysen Hamiltonian:

H'=beta sqrt(m^2+p^2). (2)

The Foldy-Wouthuysen transformation is itself the unitary operator:

U = exp[beta alpha dot (p/|p|) theta] (3)

Now, consider a Fermion "at rest," p=0. In that case, from (1) and (2):

H = H' = beta m (4)

which means that the FW transformation leaves the Hamiltonian of an "at
rest" Fermion unchanged.

Now, try to form the velocity operator from (1) and (2) and (4). From
(4), for an "at rest" fermion,

dH/dp=dH'/dp=0 (5)

But from (1),

dH/dp = alpha (6)

(I have already submitted a similar posting to SPR under a different
title. However, the second question below does seem ideal for SPF.)

On repeating Einstein's rotating disk experiment, I find redshift of
rim is given by

1/(1+z) = sqrt(1 - [v/c]^2) = sqrt(1 - [wr/c]^2)
= sqrt(1 - 2.integral[ w^2 r]dr/[c]^2)
= sqrt(1 - 2.del phi/c^2)
where w = angular velocity, and del phi is gravitational potential
energy of rim relative to observer located at middle of disk.

Clearly, from the binomial expansion, this is only equal to the
traditional gravitational Doppler shift factor (1 - del phi/c^2), to a
first approximation.

Is there any more subtle relativistic effect here that I have missed?

If not, does Einstein's general principle thus establish that the
following statement is, consequently, a general law of nature:

"A gravitational Doppler shift factor of 1 - del phi/c^2, is only
generally valid to a first approximation."

X-No-archive: yes

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