The following article:

http://cmathphil.blogspot.com/2008/07/on-penroses-argument-against-density.html

addresses Penrose’s criticism (Penrose, 2004, The Road to Reality) of
the usage of the density operator when dealing with pure quantum
states. The main arguments of Penrose are reviewed, and the reflection
proceeds around the main question: What is the most fundamental
mathematical structure that should be used to describe the quantum
system, and, what is the nature of the physical semantics that this
structure formalizes?

The following reproduces the main text of the article, safe for the
formulas that appear as images (that can be seen in the above link):

On Penrose's Argument Against Density Operators
by Carlos Pedro Gonçalves

What is a quantum state?

Should we speak of a quantum state at all?

Should we speak of quantum states or of quantum processes?

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."

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Dear all,

The enduring discussion on some of my recently posted questions encourages me
to post the following question. (Thank you all!)

1) How the field variables are to be treated in a canonical theory of the
classical elm field?

Some books treat the vector potential, A(r,t), like the position
variable, so that the conjugated momentum reads

P_A = &L/&(&A/&t)

Is this appropriate?

2) What are the correct Hamiltonian eqs. of motion,

&P/&t = - &H/&Q,

or

&P/&t = - &H/&Q + &/&x &H/&(&Q/&x) ?

3) Which is the correct field Lagrangian? In many books, I see

L = E^2 - B^2

Heisenberg & Pauli (1929) and Fock & Podolsky (1932) used

2L = (E^2 - B^2) - (div A + &Phi/&t)

Thank you very much in advance!

Peter

In the original relativity theory of Poincaré and Lorentz, when a
clock and meterstick moves from one inertial frame of reference to
another, the clock ticks at a new rate and the meterstick changes
length but these changes are undetectable. That's a covariant theory.
I interpret an absolute yet undetectable frame of reference to be
equivalent to an axiom of space incommensurability and time
incommensurability.

To assert the converse, that clock rates and meterstick lengths don't
change and that time dilation is a mere consequence of a change in
perspective, is Einstein's theory.

The answer to the question, "Is Einstein's special theory derivable
from the original relativity theory of Poincaré and Lorentz?" seems to
be yes. It only requires a little redefinition and makebelieve,
right?

Shubee
http://www.everythingimportant.org/relativity/special.pdf