I would like to present the example of the Harmonic Oscillator as a means to 
demonstrate the importance of matter waves. This is a continuation of MEaT, 
the theory of Matter, Energy and Time. In this theory matter has two states, 
particles which are stationary and exist in real time, and matter waves 
which travel at the speed of light and exist in imaginary time. The 
multidimensionality of time is necessary for the conservation of Matter, 
Energy and Time. Time dilation of the particle state is the natural 
evolution of multidimensionality of time. The motion of matter occurs only 
as waves of matter in imaginary time.

An object of mass travels at an apparent speed v by having a percentage of 
its mass in wave state. The normalized velocity is given by b = v/c, and the 
amount of mass in wave state is given by the relation m = M*b, where M* is 
the rest mass. The amount of mass remaining in the particle state is M*(1 - 
b^2)^.5. This relation for the particle mass is a result of the 
multidimensionality of time. An expression of this mass as a complex number 
is

M = M*{(1-b^2)^.5 - ib}. The -i in this equation implies that the wave state 
lags the particle state by a phase of pi/2 of its conversion cycle in time, 
and that the wave state exists in imaginary time. Time has two factors, rate 
and duration. Time dilation implies that it is the rate of time which is 
conserved, not its duration: w = w*{(1-b^2)^.5 - ib}, where w is defined by 
the relation

w*h-bar = M*c^2, where h-bar is Plank's constant divided by 2pi. It is seen 
that M^2 and w^2 are constants of the motion. When a particle is converted 
to a wave its mass is transferred to imaginary time, and its rate of time is 
transferred with it. The rate of time for the remaining particles is thereby 
reduced. This is the cause for time dilation, and the reduced mass in the 
particle state for a body in motion. I would also like to point out that the 
term b is also b = n/N, where n is the number of particles which have been 
converted to waves, and where N is the number of particles for the rest 
mass. It can be seen that b = v/c represents a time average for the apparent 
speed of the body, while b = n/N is an ensemble average. MEaT is the only 
representation for Matter, Energy and Time that allows for the proof that 
time averages are equal to ensemble averages; until now this equality has 
only been assumed, and never proved. We are now at a point where an analysis 
of the Harmonic Oscillator can be understood.

The Hamiltonian for the Harmonic Oscillator is given by

H = M*((1-b^2)^.5)(w^2)(x^2)/2 + (p^2)/2M*

where the mass term reflects the stationary particle state and the momentum 
refers to the wave momentum, p=mc, where m is the mass of the wave state. It 
is instructive at this point to factor the Hamiltonian into Creation and 
Annihilation operators as follows:

H = {((M*((1-b^2)^.5)/2)^.5)wX + iP/(2M*)^.5}{((M*((1-b^2)^.5)/2)^.5)wX - 
iP/(2M*)^.5}

+ i{X,P}(w/2)((1-b^2)^.25)

H = aa* - (wh-bar/2)((1-b^2)^.25)

where a is the Annihilation operator and a* is the Creation operator. The 
Hamiltonian operator and its commutator operate on a wave function on its 
right (not shown). The Creation operator operates first, raising the energy 
state of the system by one energy level, wh-bar, by causing a particle to 
change state into a wave, then the Annihilation operator reduces the energy 
state of the system by one level, by causing a wave to change state into a 
particle, obtaining the original system energy. The commutator represents 
the energy emitted by the wave state when it is converted to a particle; the 
term (1-b^2)^.25 represents the time dilation of the energy rate due to the 
apparent motion of the body. This commutator has always previously been 
considered to be the ground state energy of the system. This is seen to be 
incorrect. The ground state energy of the system is the energy of the 
particle state, (M*((1-b^2)^.5)c^2)/2. Note that this isn't Einstein's 
relation E=M*c^2. Einstein's relation for E is the energy of the wave state 
for the body traveling at the speed of light; E=mc^2 is the energy of the 
wave state. Also note that the term for the ground state energy is divided 
by 2; the other half of the energy for the wave state comes for the 
potential energy field. The conservation of the energy of the wave state 
comes from the application of the commutator energy being put back into the 
system by causing another particle to convert to a wave, etc. This is the 
mechanism by which energy is conserved. A change of the energy state of the 
system is conducted by the potential energy field. The observant reader 
should realize that the motion of the body can be altered by shining photons 
with the frequency given by the commutator onto the body ( you might call 
this the principle for artificial gravity, or a new principle for mass 
engines.) The reader should also note that MEaT provides an explanation for 
the quantization of energy (i.e. the energy of the wave states are 
quantized.) MEaT describes reality accurately with one theory, instead of 
requiring many theories which don't agree with each other.

I would like to include in this paper another example of the wave nature of 
matter. It is known that the two states of charge, the stationary particle 
state and its wave state, emit fields whose characteristics are particular 
to its state of motion; Particles of charge emit E fields and their waves 
emit B fields. It is rather naive to think that other types of matter don't 
have similar characteristics. Particles of mass attract other particles of 
mass, and waves of mass attract other waves of mass; this is called Gravity. 
Until now the wave state of matter has been ignored and about 96% of the 
gravity within a Galaxy has gone unaccounted for. The part of gravity which 
has gone missing is the Lorentz force. It is obvious that the gravity 
generated by the Black Hole at the center of a Galaxy emits an axially 
symmetric gravitational field; this should lead someone to think that the 
Black Hole just might be made of matter waves, and not by a singularity of 
particles. The E and B fields of mass are solved by Maxwell's equations with 
a negative source of mass for the E field, and a positive source of mass for 
the B field. Some questions about Faraday's Law for mass should arise which 
can be settled measurements of gravity waves. Do you remember Joe Weber? I 
think that if he had used gyros instead of a block mass he might have had 
better luck in finding gravity waves. Anyway, there are some nice pictures 
from the Hubbell telescope of gravity waves which should be enlightening. To 
continue, consider the orbit of stars, planets and other matter about the 
center of a galaxy. The motion of these objects imply that they have a 
percentage of their matter in wave state. The closer you get to the center 
of the galaxy the faster this matter moves (conservation of angular 
momentum) and the greater will be the percentage of its mass in wave state. 
There will be a radius from the galactic center where all objects will be 
completely in wave state. This is the radius where the Black Hole begins. A 
Black Hole is made entirely of matter waves which exist in imaginary time. A 
Black Hole is black (invisible) because it exists in imaginary time. Dark 
matter (matter waves) is dark because it also exists in imaginary time. 
Matter waves constitute a vector potential, and the curl of this vector 
potential defines a matter (mass) wave B field centered at the galaxy's 
center, the center of the Black Hole. You can imagine that this is a B field 
of incredible magnitude. Strong enough to influence alignment and motion of 
any rotating (spinning) matter within its domain. The Black Hole and all the 
spinning stars and planets within the Galaxy act like magnets of matter 
(mass) whose structure and order are dictated by the Black Hole at its 
center and the motion of the rest of the Galaxy. The Sun and all the planets 
of the Solar system, and all other star systems, have their axis of rotation 
aligned to the Black Hole, and not to the Sun. For the three planets which 
are in question one must consider the possibility that they have rotating 
cores, which we know do exist. One can also imagine that the B fields of the 
Galaxy and its Black Hole might have an effect on the motion of weather, and 
in particular Hurricanes. I would like to note that the Lorentz force does 
not tell us anything about the forces between particles and waves, if they 
do exist. Also, the mutual attraction of particles is a potential energy 
field which affects the transition of particles into waves, which then come 
under the influence of other waves.

So, Physics has gone wrong somewhere, sometime, when Physicists decided to 
ignore the wave nature of matter. Modern Physics will only begin when the 
wave nature of matter waves is finally recognized.

Ron Poteet

7/15/05