Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Angular momentum density four-vector



I've added a new section to my theory describing my angular momentum
density four-vector. It contains the classical angular momentum
(density) three-vector, but in addition, it includes a term that I think
describes the spin angular momentum in a more physical way than quantum
mechanics. It also contains a term that represents an unknown angular
momentum density. Below is the addition - it's in Section 20 of my paper
at

http://www.softcom.net/users/der555/newtransform.pdf

Note: to understand the specifics, you may need to refer to previous
sections.

---------------------------------------------

The Angular Momentum Density Four-vector

The classical definition of angular momentum is L = r x p. This is a
three-dimensional representation which, as we would like to show, is
part of a four-dimensional quantity.

The angular momentum density four-vector L is defined, here, as

L = XP (1)

where X is the position four-vector and P is the momentum density
four-vector. We can expand the right-hand side of (1) to get

XP = X . P + X x P + X : P

We see that the term X x P is the classical angular momentum, but we
have in addition two terms X . P and X : P which have no classical
analogs in terms of angular momentum.

The term X . P resembles the phase of a wave function in momentum space.
However, its significance in terms of angular momentum is not clear at
this time, nevertheless, we believe that it represents some sort of, as
yet unknown, angular momentum density. The term X : P, we suspect,
describes spin angular momentum density. This obviously contrasts with
the quantum mechanical description of spin, however as can be seen, our
description bears a closer resemblance to the classical representation
of angular momentum, thus, we believe, it offers a more physical
interpretation of spin than its quantum mechanical counterpart.

--------------------------------------

P.S. I've also added a new application dealing with a proposed
connection between my theory and relativistic quantum mechanics at

http://www.softcom.net/users/der555/quantum.pdf

Please don't discuss the quantum mechanical connection in this
thread, though. I've started a separate thread for those discussions
entitled "A proposed quantum mechanical connection". Thanks.

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf