Natural Science Forum / Physics / Research / April 2008

Hello to all:

I'd like to get some advice on a problem I am presently considering.

Let's consider a Dirac spinor u(p), and for a concrete example, let's
take the u^(1) for an spin up electron, where N is the usual
normalization factor:

         /      1      \
        |       0       |
u^(1)=N |   p_z / E+m   |       (1)
         \   p_+/E+M   /

To place this "at rest," we set p=0 and E=m, so that:

         /      1     \
        |       0      |
u^(1)=N |       0      |       (2)
         \      0     /

But, because of the uncertainty principle:

delta t delta E >= (1/2) hbar     (3a)
delta x delta p >= (1/2) hbar     (3b)

there is really no such thing as a "zero" momentum p=0, or E=m, only the
expected values <p>=0, <E>=m.  How, therefore, might one write u^(1) for
an electron "at rest," in light of uncertainty?

Specifically, can we ever really have the state (2) in light of
Heisenberg, or, does one need to take the p and E in (1) and use in
their place, the expected values <p> and <E>, and / or the Root mean
square deviations delta p and delta E?  For example, might one use, at
rest:

E  -->  m +/- delta E   (4a)
p  -->  0 +/- delta p   (4b)

or some such expression other than p=0, or E=m.

Thanks.

Jay.
____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm