Wednesday, July 10, 2024

An introduction to Spiral Wave Theory

Exploring the Spiral Wave Theory: A New Perspective on Quantum Mechanics

Exploring the Spiral Wave Theory: A New Perspective on Quantum Mechanics

When we observe the movement of celestial bodies from an astronomical perspective, we often describe the orbits of planets as elliptical paths around stars. However, considering that our universe is constantly expanding, these elliptical paths are actually part of a larger spiral trajectory through spacetime. This spiral motion can be seen not only in the macroscopic scales of planets and stars but also in the microscopic behavior of particles and waves. By re-examining the laser slit experiments and diffraction patterns through the lens of spiral wave theory, we may find a simpler explanation for the observed interference patterns—without the need to invoke a quantum universe where particles exist in multiple places simultaneously.

1. Introduction to Spiral Wave Theory

The traditional view in quantum mechanics is that particles follow straight-line paths or probabilistic wave-like trajectories. The spiral wave theory challenges this notion by suggesting that particles follow spiral paths in both space and time. This concept can potentially offer new insights into quantum behaviors and the nature of forces.

2. Mathematical Development

To explore the spiral wave theory, we start by defining a spiral trajectory in cylindrical coordinates (r, θ, z), where the z-coordinate represents the spiral's axial progression:

r = r
θ = θ
z = bθ

Here, b is a constant defining the pitch of the spiral. We then modify the time-dependent Schrödinger equation in three dimensions to incorporate these spiral paths.

3. Modified Schrödinger Equation

The time-dependent Schrödinger equation is given by:

iħ ∂ψ(𝐫, t)/∂t = -ħ²/2m ∇² ψ(𝐫, t) + V(𝐫, t) ψ(𝐫, t)

In cylindrical coordinates, the Laplacian ∇² is:

∇² = 1/r ∂/∂r (r ∂/∂r) + 1/r² ∂²/∂θ² + ∂²/∂z²

Substituting z = bθ, we get:

∂/∂z = 1/b ∂/∂θ
∂²/∂z² = 1/b² ∂²/∂θ²

Thus, the Laplacian in spiral coordinates becomes:

∇² = 1/r ∂/∂r (r ∂/∂r) + (1 + 1/b²) 1/r² ∂²/∂θ²

We can then substitute this into the Schrödinger equation and separate variables to obtain differential equations for the radial and angular parts.

4. Solving the Equations

Radial Equation with Harmonic Oscillator Potential

We use the harmonic oscillator potential V(r) = ½ m ω² r² and solve the resulting radial equation numerically.

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

# Parameters for the harmonic oscillator potential
m = 1  # mass (arbitrary units)
omega = 1  # angular frequency (arbitrary units)
hbar = 1  # reduced Planck's constant (arbitrary units)
r_max = 10  # maximum value of r to solve for

# Differential equation for the radial part
def radial_eq(r, R):
    dR_dr = R[1]
    d2R_dr2 = (m² * omega² / hbar²) * r³ * R[0] - (2 * m * hbar * omega / hbar²) * r * R[0]
    return [dR_dr, d2R_dr2]

# Boundary conditions: R(0) should be finite, R(r_max) should be 0
R0 = [1, 0]  # initial guess for R(0) and R'(0)

# Solve the radial equation
r_span = (0, r_max)
r_eval = np.linspace(0, r_max, 1000)
solution = solve_ivp(radial_eq, r_span, R0, t_eval=r_eval)

# Extract the solution
r_values = solution.t
R_values = solution.y[0]

# Plot the radial solution
plt.figure(figsize=(10, 6))
plt.plot(r_values, R_values, label='Radial Solution $R(r)$')
plt.xlabel('$r$')
plt.ylabel('$R(r)$')
plt.title('Radial Solution for the Spiral Wave Model with Harmonic Oscillator Potential')
plt.legend()
plt.grid(True)
plt.show()

Angular Equation

For the angular part, we assume a Fourier series solution and solve:

Θ(θ) = ∑ cₙ e^{inθ}

5. Complete Wavefunction

By combining the radial and angular solutions, we obtain the complete wavefunction:

ψ(r, θ, t) = R(r) (A cos(√k θ) + B sin(√k θ)) e^{-iωt}

6. Visualization

Finally, we visualize the complete wavefunction in a 3D plot.

from mpl_toolkits.mplot3d import Axes3D

# Constants for the angular part
A = 1
B = 1
r = r_values  # Using the solved r values from the radial equation

# Calculate k based on the average r value
k = (m * omega² * np.mean(r_values)⁴ / 2 / (1 + 1/b²) - np.mean(r_values)² * hbar * omega / (1 + 1/b²))

# Generate theta values
theta_values = np.linspace(0, 4 * π, 1000)  # 2 full turns

# Calculate Theta(θ)
Theta_values = A * cos(√k * theta_values) + B * sin(√k * theta_values)

# Create 3D plot
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot(111, projection='3d')

# Calculate z-values for the 3D plot
z_values = b * theta_values

# Plot the spiral wave
ax.plot(r_values * cos(theta_values), r_values * sin(theta_values), z_values, label='Spiral Path')
sc = ax.scatter(r_values * cos(theta_values), r_values * sin(theta_values), z_values, c=np.abs(Theta_values), cmap='viridis', label='Wave Intensity')
fig.colorbar(sc, label='Wave Amplitude')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.setTitle('3D Spiral Wave Model')
ax.legend()
plt.show()

Conclusion

Exploring the spiral wave theory offers a fascinating new perspective on quantum mechanics. While this theory still needs further work, I believe it is one that merits investigation. If I had the funding and time, I could focus on these efforts.

Friday, November 10, 2023

My Journey with Print on Demand and Artificial Intelligence Art

So I have to be honest. this past year. I decided to join the Print on Demand and AI revolution trend. I ended up creating a site called Alchemystics.org .  Here I will tell you a bit about my journey, some of the lessons I have learned, and will even give you some of my trade secrets (obviously as affiliate links).

But first, let me tell you a little backstory on my life. I used to run a small online record store called Chaos Existence. At the time, chaos existence was actually a fairly innovative site and I was able to not only provide full audio samples but a dynamic inventory website linked to a database. In addition, I wrote all of the code necessary for this ecommerce platform.  Calling it a platform might be a bit of a stretch. However, the site was capable of integrating with our suppliers and pulling in their inventory via electronic data interchange as well as pushing our entire catalog to other aggregator sites. Although perhaps some other e commerce platforms with a lot more doing something similar (perhaps), I came up with the idea myself and implemented all the necessary code for these projects.

I have a certain fondness for these days. And even though the the music landscape was quickly changing with MP3's. I did not close the store for lack of business. In the end, i learned a lot about cashflow. I Ended up with way too much money stuck in failed special orders which meant I had a large inventory of things hardly anyone wanted.  😅 

Now fast forward to other entrepreneurial ventures and and several career moves to about February of this year, when I decided to launch metazen minerals after going to the Tucson Gem show. I had a small side hustle of trading minerals and silver jewelry i had made a few years back.  However with the changing financial landscape and unfortunately being newly single again I found a need ro find some new clothing as I started to socialize again.  However, I was not finding the style or art that I wanted. Sure,  I probably did not look as hard as I could of, but my local artisan friends and old tried and true websites were either oversaturated or out of business at this point.

The timing of this also coincided with the artificial intelligence breakthrough. in March of of 2023 chat G. P. T was all over the news and subsequently other projects such as mid journey we're at the top of everyone's mind and all over the news. 

Being a technological artist, I decided to start playing with. The technology's myself and in turn create some of my own art.

 These experiments led me to some results that I wanted to put on t shirts myself. Side note, eventually lead me back to brush up on my photoshop and illustrator skills. 

Now Meta Zen Minerals was not a great name that could also include apparel... and I happened to already own the alchemystics.org domain.  As you can guess, this lead to the transition to thr alchemystics art collective and website. 

I think this is a good time to break as part one of a story series. And I will continue as I get more time.


 


Thursday, June 13, 2013

Happy Birthday


hanging head in shame,
you know the name
of this drill
one day
you'll come back and want to feel
what is a next level deal.
Your happy birthday gift
... so swift,
Didn't know that you would do
something like this...
no wonder it was
that I also have
things I miss
in this entangled deadly kiss.
So sweet and soft to the touch,
but delivery poisonous -truth
venemous -much
with your serpentine long lists
of previous heart eclipses
many tainted
while mine, in one hand painted.
Align your mind to the truth
and you will view
that I just merely asked
for bare minimum,
just be there for me
when I need someone.
You make it out to be
that I control thee...
but I give you freedom to be
and just wish to
communicate
occassionally.
Nurture I do,
nature I am,
perfect am not,
but you broke this dam.
You make me see
something lacking honesty,
while you see some one and
and still planned to move in with me.
You tell my friends one thing,
while my family another.
Straight to my face and
even my mother..
Now look within yourself,
and tell me all you seek.
Seems like a fallacy
when your will is weak.


Friday, June 7, 2013

Forum


although not a saint
truth I will paint
and stroke this brush
when you tell me to hush
you decree publicly
what you can't say to me
but I call it out
and mutual friends turn about
hypocrisy
instilled by thee
when you decide
to hurt me
in front of our community
I merely say you what you are doing
apparenty
pain is what you find alluring
in a public forum
I point out your decorum
and I am the one to blame?
and I should be the one to contain?
when I am willing to give you my hand
but instead you want to disband
behaving dishonestly
for this I cannot stand

Tuesday, June 4, 2013

You will realize

in the long run
your time of fun
will run dry
and you will cry
over what was lost
and what was offered
and how it was
that i have suffered
you will then realize
that i am the prize
with infinite potential
but you merely thinking
that I was mental
instead,
a true genius inside
you should have stayed
in my pocket
and by my side

i will
conquer my fears
and wipe my tears
this window is closed
and the truth appears
you lie to yourself
and then to me
your overlap of love
and the timing you said...
is just
a complete fallacy
you tell me your side and
then your reasons
but your actions don't align
and i see
winter's your season
cold hearted you are
and how you treated me
 as you leave 
someone who loves you
infinitely
when you knew i needed love
and you couldn't pass a test
to be my girlfriend
or my partner
so i put it to rest
you left during the bad
and soon i will be good
you don't deserve me
because you treat me
 not as you should

with your friends telling you
they don't see what you see
focusing mostly
on negativity
to justify your actions
merely to quench
your own physical satisfactions
now i sit on the bench
and i will then disappear
and this will be clear
that you threw me away
when you should have stayed
for my love is epic
and my future is golden
fool you are
you might be lonely and old then
and though my heart is shattered
and pride i've swallowed
i see 
you don't know what truly mattered

you left before
a chance we both deserved
i suspect one day soon
you will get served
a dose of your karma
so huge
much it will hurt
even though you feel 
that I am the jerk

I tell it it how it is
calling out you and your man
you have no integrity
for ruining our plan
and i see your dishonesty
because you felt differently
from what you told me
i wish this was a figment, see
we were to move in together
you requested the changes
while I accepted you
unconditionally
knowing your dangers
all the things we forgave
while I was your slave
but now i will find
someone who will return
all that love that i gave.

Monday, June 3, 2013

Apologies


trying to make my peace
by saying my piece...
at least
try...
to make my wrong right
at least
try...
to say goodnight
to pasts we had
and as time passes
align
converge
and emerge
now,
here's my invitation
to break bread
starting new patterns
leaving behind
what we had instead

Confession of Love (Followed by Rejection)

 have a hard time
holding back
what is in my heart 
as it attacks 
my logicaI mind
as it unwinds
falls apart
and then comes back 
and its not my intent
maybe you're right
maybe I'm sick
but I am who I am
and try as I might
I find myself
seeking the light
the answers
and truth 

wish you you would see
the light within me
and realize my sorrow
is not unfounded
but also
would not be there tomorrow
if I were still in your pocket
and had you by my side
to help me heal
so in you I can confide

so many things I want to say
but my pride gets in the way
for I am to come back soon
and I wish upon a star
and I look up at the moon
now I give up on my will
and tell how you I feel
simply put
that I love you still

Monday, May 20, 2013

its all the same


i give up,
i give in...
i lost when "all in"
Nothing left to lose,
nothing left to gain...
nothing left at all...
its all the same,
now i have shattered pieces
scattered about,
like a child, i scream,
and cry out.
in anger, in pain..
frustrations are
driving me insane
whie expecting different results
from doing the same
now...
trying to break that spell
that I know too well. 
trying to break
that mental jail
find the positive
in what remains
but when you have nothing...
it's all the same.

Saturday, August 18, 2012

Silence


Distance increases
our hearts:
shattered, broken pieces.
As we
lay down alone,
creating new homes
wondering, wandering, longing
to each, neither are belonging
even though
abundance of love abound
we are forming
dominoes falling down
but for you- my love remains still
nothing, even if you will
or won't....
send me a thought
through these telecommuncation
toys that i've bought.
Even if you judge,
you won't make me budge.
Because true love
is infinite and eternal
and remains
ever so..
even through
our minutia complains.
those are the thoughts
which we write in our journals

and so...
I wish you were happy
with me.
But that thought ceases
when I see reality...
and I hope that if you were to let me go
.. I hope you would at least let me know
so that I fall with grace.
But know this:
no matter what,
for you,
in this heart,
there is a place.
That I will be there still
even if you disagree
with what is my will...
and how I proceed
And know
that it is you in my life that I need
one way or another
as sister and brother,
but preferably more my lover
to stand by my side
so in you I can confide...
and have you embrace me again

Wednesday, June 13, 2012

Lost and Found

clear minded-
and balanced 
I find it surreal,
i still will-
 try to pick up the pieces-
at least what is
left
 ...  right?
the straight is askew
and I ask you
don't you realize
that I'm a prize?
even broken
tattered
heart shattered
unwound
and unfound
my light within
is all around
a shining beacon
amongst a sea
of dark
it matters not
i am radiating
aimlessly in a chase
racing through amazing mazes
mentally distracted
heart retracted
lost...in space yes
why won't you
spark my fire
i will solve the puzzle
i'll be inspired
go from lost to found
abound
in abundance
of treasures from my soul
glistening with love to be shared
it is my goal
but I need fuel to feed my flame
but it is not just for anyone
it is for someone that is the same:
stimulating
titillating
facilitating reciprocating
I rather be alone
if all I have is gone
from not filling my cup
lonely I became
since it's only me
for life is to be shared
can't seem to break free
from my own shackles
that i can't seem to bare
now i look up
let me see
what is right,
not just what was
left...
let me be
rise
independently
for no one else
is there at the end
it is only me...
my best friend