Re: E = wLF Derived By Modified Quantum Logic

From: OsherD (mdoctorow_at_comcast.net)
Date: 01/24/05 

Date: 23 Jan 2005 16:02:59 -0800

What about an application to physics in the rather simple cases of
expanding and/or accelerating universes including the early
inflationary period, with the resultant one-dimensional forces being
gravitational versus expansion (the latter can be the Cosmological
Constant, Dark Energy-based, Quintessential (partly contained in the
first), etc.)?

One might first be tempted to deny the accuracy of E = wLF based on the
fact that gravitational potential energy (PE) is:

1) PE = -km1m2/r

where m1, m2 are the two masses involved and r is the distance between
them and k is constant. The potential energy is supposedly assigned to
the system of two masses rather than to either one individually, which
makes one wonder about the accuracy of the assignment, but we will
ignore this slight problem. Work is then defined as the difference of
two potentials at two points (supposedly attributed to one of the
original pair of point masses).

The force field on a unit mass m1 = 1 exerted by a
central mass m2 = M at the origin (0, 0, 0) in Euclidean/rectangular
coordinates gravitationally with magnitude GM/r^2 for Newton's
gravitational constant G is:

2) F(x,y,z) = -GM(x,y,z)/(x^2 + y^2+ z^2)^(3/2)

where (x, y, z) is the vector r = (x, y, z). The work done by force F
in moving a unit mass from point
(x1,y1,z1) to (x2,y2,z2) is:

3) -grad(F)(x1,y1,z1) -(-grad(F)(x2,y2,z2) =
MG(1/r2 - 1/r1)

with F = -grad(-MG/r) where PE is -MG/r since the force is
irrotational.

Thus, it looks as though work W = LF1 - LF2 where
L is proportional to 1/r, and so as in the earlier
posting it is the difference in energies rather than
the energy which is proportional to the work times
the displacement.

Nevertheless, it makes sense to attribute an energy
E = LF to each point mass even in this case, which
also resolves the quandary about only assigning
a gravitational potential to the system and not to
each point mass (and similarly for string masses)
and can be easily extended to an expansive force
like Dark Energy's force as well.

To see this, it is useful to read the machinery of my
arguments that P(A-->B) is a proximity function
which is a one-sided partial inverse of the Euclidean-like metrics. I
developed this over several years at geometry.research through the Math
Forum site, although within the last few months I moved from there to
almost exclusively the sci.stat.math site.
It is one-sided in the sense that everything is
ordered by cause vs effect. For example, in one
dimension if x is the cause and y the effect, then
p(x,y) = 1 + y - x is the proximity between x and y, and it is not
reflexive since it does not equal 1 + x - y, but it is nonnegative and
between 0 and 1 and has some other interesting features. You might try
to begin with p(x,y) - 1 and examine its properties.
Notice that when the distance d(x,y) = /x - y/ = 0
with the ordered condition y < = x, we have 1 + y - x = 1 and when
d(x,y) = 1 with y < = x we can only have x - y = 1 which for x, y in
[0, 1] and y < = x implies x = 1 and y = 0 so p(x,y) = 1 + y - x = 1 +
0 - 1 = 0! As expected, proximity goes up when Euclidean-like
distance goes down in the unit n-hypercube. pn(x, y) for x, y
n-dimensional is defined as 1 + average of x-coordinates - average of
y-coordinates.

Osher Doctorow

Relevant Pages

  • Re: Calculating Newtons in Joules and Joules/s
    ... Momentum and energy are separately conserved. ... If the 3 kg mass were to get all of the momentum of the ... Make it two 4 kilogram masses instead of two 3 kg masses. ... kinetic energy is conserved. ...
    (sci.physics)
  • Re: Mass and Energy
    ... No mass is converted to energy. ... I understand the phenomenon of "binding energy" very well. ... The "binding energy" of an atomic nucleus is the amount of energy ... between the sum of the rest masses of the constituent "particles" ...
    (sci.physics)
  • Re: Question on GR sources
    ... At least one of the masses therefore has kinetic energy. ... simply use the rest mass of each as the energy, ...
    (sci.physics.relativity)
  • Re: Questions (Space)
    ... about the masses of elementary particles, such as the photon, they ... energy goes into additional mass instead of additional speed. ... speeds, anything you or I would ever personally experience, the ...
    (rec.arts.sf.composition)
  • Re: Where is the mass?
    ... less than tha sum of the masses of the proton and electron from which it was ... All of the mass of the atom (inclusive of the negative potential energy) ... is localised in the two particles. ...
    (sci.physics.research)