| Topic: |
Science > Physics |
| User: |
"purrcy" |
| Date: |
15 Jul 2005 03:26:25 PM |
| Object: |
Harmonic Oscillator and Graviry |
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
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