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Oscillating Spacetime: The Foundation of the
universe
The simplified electron and
muon model
The simplified electron and
muon model
John A. Macken
Revised – May 22, 2024
Oscillating Spacetime: The Foundation
of the Universe
This theory is written by John A. Macken
formerly entrepreneur, inventor and company
president
jmacken@stmarys-ca.cedu
Content:
1) Unveiling the True Nature of Electrons' Wave Essence
2) Quantum Whirlpools Resonating
3) The beautiful harmony of spacetime symphony
resonates perfectly
4) Exploring the Dual Nature of the Electron's
Wave-Based Model
5) Exploring the Mysterious Core Wave
6) Exposing Mistakes in Depiction.
7) Exploring Time Changes in the Core Wave.
8) Exploring the Mysterious World of the Electron's Core
Wave
9) Unraveling the Mystery of Dipole Waves in Spacetime
10) Unveiling the Amplitudes of Waves in a New
Light
11) References of this e-book
12) Colclusion
13) Glossary
When delving into the world of fermionic entities
and the oscillating spacetime they inhabit, a
fascinating paradigm emerges. It reveals that the
very essence of an electron, along with other
fermions, lies in the intricate dance of rotating soliton
waves. This fundamental concept uncovers a
profound truth about these particles, emphasizing
their inherent wave-like character woven into the
fabric of spacetime.
Our journey commences with the electron, the
simplest yet most significant manifestation of this
wave-based fermion. Within the vast expanse of
spacetime, the electron's wave takes on countless
forms, shaped by its interactions with other fermions
and the boundaries of its existence. Thus, we begin
our exploration by focusing on the quintessence of
the electron, capturing its purest and most isolated
state.
Unveiling the True Nature of
Electrons' Wave Essence
1
To unravel the mysteries of the electron, we must
construct a simplified model that encapsulates its
essence in a compact form. Within this model lie the
keys to calculating its energy, understanding its
wave properties, and comprehending the forces that
govern its behavior.
But our journey doesn't end there. In Section 18 of
“Oscillating Spacetime: The Foundation of the
Universe”, we catch a glimpse of the dynamic nature
of this quantized wave. Here, we embark on a brief
discourse that sheds light on how this foundational
wave entity gracefully expands and contracts,
assuming various sizes and shapes. This further
enriches our understanding of the electron's
enigmatic essence within the vast symphony of
oscillating spacetime.
2
The concept of a wave-based model for electrons and a
rotating quantum vortex has been compared. In Figure 1, it
was explained that when angular momentum is added to
the superfluid Bose-Einstein condensate, it creates
rotating vortices. These vortices are soliton waves that
possess quantized angular momentum with the value of ħ.
Interestingly, these quantum vortices arrange themselves
in a specific pattern, suggesting that each vortex pushes
away its neighboring vortices by distorting the
surrounding superfluid.
Quantum Whirlpools Resonating
3
The beautiful harmony of
spacetime symphony resonates
perfectly
In the vast cosmic dance of oscillating spacetime, a
fascinating comparison emerges: it acts like a flawless
superfluid, always moving yet perfectly coherent. When
infused with quantized angular momentum, this ethereal
medium orchestrates a captivating show—a rotating soliton
wave, similar to the quantum vortices shown in Fig. 1.
Resonances in oscillating spacetime, like harmonious
melodies, come together to create stable or semi-stable
rotating waves at specific frequencies. In our discussion, we
focus on electrons and muons, the basic building blocks of
our universe.
4
The core of an electron's being lies in the creation of a
rotating wave, intricately connected to its environment. To
exhibit the well-known de Broglie wave properties, this
rotating wave must carve out standing waves within the
fabric of oscillating spacetime. Examination indicates that an
electron's de Broglie wave nature suggests the presence of
spherical standing waves resonating at a frequency
precisely matching an electron's ωc = 7.76×10^20 rad/s.
Therefore, a fascinating possibility arises: these standing
waves likely originate from the rhythmic movements of a
wave rotating at an electron's ωc. A peek into the simplest
form of an electron reveals a model of graceful simplicity—a
rotating wave, encompassing about one Compton
wavelength in circumference. This tiny cosmic performance
showcases a radius equal to an electron's Compton radius
(rc = ħ/mec = 3.86×10^-13 m), echoing the harmonious
symphony of oscillating spacetime. This radius also
corresponds to an electron's Compton angular wavelength
(rc = λc = ħ/mec), highlighting the intricate relationship
between wave and particle that defines the essence of an
electron. This simplified wave-based model of an electron is
visually represented below, a tribute to the exquisite beauty
woven into the fabric of our universe.
5
Exploring the Dual Nature of the
Electron's Wave-Based Model
In breaking down the proposed wave-based model of an
electron, we uncover a split in its essence, revealing two
interconnected components:
1. The Core Wave:
At the center of this model is a core wave, spinning
harmoniously at the electron's characteristic frequency, ωc.
Unlike traditional beliefs of clear-cut boundaries, this core
wave possesses a fluidity that challenges standard
definitions. However, in the realm of calculations, it is
enclosed by a "mathematical radius," labeled as rc. This
mathematical concept acts as a crucial point for theoretical
examinations, allowing for precise calculations of the
electron's characteristics.
2. Surrounding Standing Waves:
Surrounding the core wave are complex patterns of
standing, rotating waves. These waves, resembling celestial
performers, encircle the core with elegance and accuracy,
molding the electron's cosmic presence.
6
Beyond the rc boundary, an electric field of significant
strength is formed, containing energy measured as Eext =
αħc/2rc, approximately 3×10^-16 J. Notably, this energy
source makes up only a small portion—around 0.4%—of the
electron's total energy. Additionally, a magnetic field of
similar intensity accompanies this electric field, further
enhancing the electron's energetic framework.
Therefore, within this model's framework, a remarkable
discovery emerges: over 99% of an electron's energy is
housed within its rotating core, while the electric and
magnetic fields combined hold less than 1%. This unique
distribution emphasizes the importance of the core wave in
shaping the electron's essence, while showcasing the
intricate relationship between its core and surrounding
fields.
7
“The electron does not have a sharp boundary or surface.
There is no such thing as an electron sitting still with a sharp
boundary. We can think of it as a spread-out fuzzy 'cloud'
surrounding the nucleus, whose 'edge' is fuzzy.”
Exploring the Mysterious Core
Wave
Trying to understand the heart of the electron model, Figure
4 shows us a visual journey into unknown territory. Here we
have two different but connected attempts to represent the
mysterious core wave—an entity so unique that it
challenges our traditional understanding. This core wave, a
4-dimensional soliton, moves in a complex way within the
fabric of oscillating spacetime, revealing dimensions beyond
what we usually perceive.
8
The high resistance of this medium, with a value of c^3/G =
4×10^35 kg/s, allows for the creation of a wave with a very
small displacement amplitude—a mere Planck length/time.
Despite its tiny size, this wave has the potential to form a
concrete electron model that can be tested in experiments.
Figure 4 A focuses on the spatial aspect of the electron's
core wave, showing us its spatial complexities and
geometries. On the other hand, Figure 4B explores the
temporal side, capturing the essence of its temporal
dynamics. Together, these two parts come together
smoothly to create a single entity—a 4-dimensional rotating
wave that represents the electron in its entirety.
9
In seeking to depict the core wave of the electron model,
Figure 4 serves as a visual exploration into uncharted realms,
endeavoring to unravel the mysteries of this 4-dimensional
soliton wave within the dynamic framework of oscillating
spacetime.
Exposing Mistakes in Depiction.
In this study, Figure 4 takes us on a fascinating journey into
the enigmatic core wave of the electron model. Its aim is to
shed light on a phenomenon that has puzzled scientists for
a long time. This core wave, known as a 4-dimensional
soliton, gracefully maneuvers through the complexities of
oscillating spacetime, defying conventional understanding
with its unique properties.
The medium in which this wave exists presents a significant
challenge, as it is quantified by an astonishing value of
c^3/G = 4×10^35 kg/s. This formidable impedance allows
for the emergence of a wave that has an imperceptible
displacement amplitude, measuring only a mere Planck
length/time. Despite its ethereal nature, this wave holds the
potential to manifest as a tangible electron model that can
be empirically validated.
Figure 4A takes a deep dive into the spatial intricacies of the
electron's core wave, capturing its essence within the fabric
of space. On the other hand, Figure 4B explores the wave's
temporal dynamics, showcasing its rhythmic oscillations
through time.
10
Together, these two components merge into a unified entity
—a 4-dimensional rotating wave that encapsulates the very
essence of the electron.
Exploring Time Changes in the
Core Wave.
Figure 4A, although a brave attempt to represent the spatial
aspect of the electron's core wave, contains several
inaccuracies that require careful examination and
improvement. These subtle differences provide valuable
insights into the complex nature of the electron model,
prompting a deeper exploration into its manifestation.
11
1) Spatial Amplitude Discrepancy:
The depiction in Figure 4A exaggerates the height of the
wave, mainly due to the significant difference between the
spatial amplitude of the Planck length (Lp) and an electron's
Compton radius. Since the Lp spatial amplitude is
approximately 10^22 times smaller than the Compton
radius, the portrayed wave's size is inflated beyond its
actual proportions.
2) Incorporation of the Fine Structure Constant:
An interesting anomaly arises when considering the fine
structure constant, which introduces a slight distortion
within the electron's core. However, this distortion is not
accounted for in Figure 4, indicating the intricate relationship
between fundamental constants and the electron's inherent
properties. Although we only partially understand this
mysterious effect, it deserves further investigation in
subsequent sections.
12
3) Misrepresentation of Rotation:
Figure 4 mistakenly suggests a simplistic rotation
representation, implying a unidirectional and planar motion.
In reality, the rotating wave that forms the electron's core
operates within a turbulent sea of spatial and temporal
fluctuations at the Planck scale. This chaotic environment
challenges conventional notions of causality, resulting in an
expectation of rotational direction and axis amidst a
symphony of probabilistic fluctuations. These nuances
challenge our understanding of rotational dynamics and
highlight the complexities of the electron's core wave.
By examining these inaccuracies, we open the door to a
more nuanced comprehension of the electron model,
unraveling layers of complexity that are at the forefront of
scientific inquiry.
13
Exploring the Mysterious World of
the Electron's Core Wave
As we venture further into the mysterious realm of the
electron's core wave, a fascinating discovery emerges: its
influence extends beyond just space, reaching into the
intricate fabric of time itself. In this explanation, we embark
on a visual journey, using shades of blue and yellow in
Figure 4B to unravel the subtle details of temporal
modulation.
Imagine the blue section in Figure 4B as a domain where
time moves faster than the local norm, while the yellow
section represents a realm where time slows down. This
temporal distortion appears as a shift of ± Planck time (±
5×10^-44 s) along the time dimension, giving us a glimpse
into the complex interaction between the core wave and the
temporal fabric.
For every rotation of the wave, a hypothetical clock in the
blue section gains one unit of Planck time (∿10^-43 s),
while its counterpart in the yellow section experiences a
corresponding loss. This small difference has significant
implications when compared to the local norm.
14
With the wave rotating at ωc = 7.76×10^20 rad/s, the blue
section experiences time at a faster rate, approximately
Tpωp = 4.18×10^-23 seconds per second, compared to the
local norm. At the same time, the yellow section
experiences a decrease in time.
Although this temporal difference may seem imperceptible,
it highlights the intricate tapestry of temporal modulations
within the core wave. To put this phenomenon into
perspective, imagine two perfectly synchronized clocks that
differ by this tiny interval. Over the age of the universe, they
would only diverge by approximately 40 microseconds—a
minuscule yet profound testament to the subtle
complexities of temporal dynamics within the electron's
core wave.
15
"Time is what prevents everything from happening at once."
— John Archibald Wheeler
Unraveling the Mystery of Dipole
Waves in Spacetime
Deep within the core of an electron lies a fascinating
phenomenon known as a "dipole wave in spacetime," which
challenges our conventional understanding of the universe.
According to the principles of general relativity, the
existence of macroscopic dipole waves is considered
impossible, as it goes against the fundamental constraints
of our universe. This notion is extensively discussed in texts
on general relativity, like (1), where they explain that mass
dipole radiation is nullified due to the second time derivative
of mass dipole being zero.
In a larger context, the presence of dipole waves in
spacetime would violate the principle of momentum
conservation, a fundamental rule in the cosmic symphony.
However, an intriguing idea emerges: could the uncertainty
principle hold the key to unraveling the mystery of dipole
waves within spacetime?
16
Herein lies a paradoxical reconciliation: while general
relativity sets up barriers against the existence of
macroscopic dipole waves, the uncertainty principle opens
the door for their covert presence. Theoretical foundations,
ranging from [2] to [3], emphasise the impossibility of
achieving measurements accurate to the Planck length (Lp)
or Planck time (Tp). It is within this realm of uncertainty that
quantum mechanics finds its place, allowing for the hidden
existence of dipole waves in spacetime—a crucial element
for the wave-based model of fermions.
Thus, in the intricate interplay between uncertainty and
possibility, the enigmatic nature of dipole waves in
spacetime finds solace, providing us with a captivating
glimpse into the paradoxes that form the very fabric of our
reality.
17
Unveiling the Amplitudes of Waves
in a New Light
18
When it comes to the world of sound, understanding the
amplitude of a sound wave is crucial. It refers to the
maximum distance that vibrating particles move away from
their average position. This measurement, known as
"displacement amplitude (Ad)," is expressed in meters and
helps us gauge the strength of sound waves.
However, in the realm of wave dynamics, there is another
way to look at amplitudes. Instead of focusing on length, we
can examine strain amplitude (As), which represents the
dimensionless maximum slope of a sine wave. This abstract
concept allows us to gain a deeper understanding of wave
behavior, going beyond traditional measurements and
capturing the true essence of wave dynamics.
Taking this idea further, let's consider the rotating wave that
forms the core of an electron. Here, we introduce the
concept of "electron's strain amplitude (Ae)," which is
calculated to be 4.185×10^-23. This dimensionless value is
obtained by dividing the electron's displacement amplitude
(Lp) by its Compton angular wavelength (ƛc = ħ/mec =
3.86×10^-13). It encapsulates the dynamic behavior of the
electron in a concise form.
What's fascinating is that this dimensionless number serves
as a universal descriptor for all of the electron's properties,
except for its electromagnetic properties. It is expressed in
dimensionless Planck units, offering us a way to unravel the
complexities of wave dynamics and gain a deeper
understanding of the fundamental properties of particles
and waves.
19
References of this e-book
[1] Misner CW.: Thorne KS, Wheeler JA.: Gravitation. W.
H. Freeman and Company. 1200 – 1203, (1973)
[2] Garay LJ.: Quantum gravity and minimum length.
International Journal of Modern Physics A, 10(02), 145-
165. (1995)
[3] Baez JC.: Olson, S. J. Uncertainty in measurements
of distance. Classical and Quantum Gravity, 19(14),
L121. (2002)
[4] Calmet X.: Graesser M, Hsu, SD.: Minimum length
from quantum mechanics and classical general
relativity. Physical review letters, 93(21), 211101 (2004)
45
[5] Calmet X.: On the precision of a length
measurement. The European Physical Journal C.;
54:501-5 (2008)
Conclusion
To sum up, delving into the simplified electron and muon
model from the theory of oscillating spacetime has revealed
an intriguing story of wave-based fermions. From the
mysterious core wave swirling inside the electron to the
intricate manipulation of temporal dynamics, each aspect of
this model provides deep insights into the basic essence of
particles and waves. Looking through the lens of uncertainty
and potential, we've explored spatial and temporal
dimensions, discovering the elegant simplicity that lies
beneath the intricate structure of our universe. Reflecting on
the journey taken, it's evident that the quest for knowledge
is a continuous pursuit—one that encourages us to
constantly push the boundaries of our comprehension and
embrace the beauty of the unknown.
20
Glossary:
Displacement Amplitude (Ad): The maximum displacement
of vibrating particles from their mean position in a sound
wave, measured in meters.
Strain Amplitude (As): The dimensionless maximum slope
of a sine wave, representing the magnitude of strain in wave
dynamics.
Electron's Strain Amplitude (Ae): A dimensionless number
derived from dividing the electron's displacement amplitude
by its Compton angular wavelength, representing the
dynamic behaviour of the electron in a compact form.
Planck Length (Lp): The scale at which classical ideas
about gravity and space-time cease to be valid, and
quantum effects dominate, approximately 1.616 × 10^-35
meters.
21
Compton Angular Wavelength (ƛc): The wavelength
associated with the momentum of a particle, calculated
using the Compton wavelength formula, approximately
3.86 × 10^-13 meters for an electron.
Oscillating Spacetime: A theoretical framework proposing
that spacetime undergoes oscillatory fluctuations at the
smallest scales, influencing the behaviour of particles and
waves.
Dimensionless Planck Units: Units of measurement based
on fundamental constants such as the Planck length, Planck
time, and Planck mass, providing a scale for quantum
phenomena.
22

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The simplified electron and muon model, Oscillating Spacetime: The Foundation of the Universe

  • 1. Oscillating Spacetime: The Foundation of the universe The simplified electron and muon model The simplified electron and muon model John A. Macken Revised – May 22, 2024
  • 2. Oscillating Spacetime: The Foundation of the Universe This theory is written by John A. Macken formerly entrepreneur, inventor and company president jmacken@stmarys-ca.cedu
  • 3. Content: 1) Unveiling the True Nature of Electrons' Wave Essence 2) Quantum Whirlpools Resonating 3) The beautiful harmony of spacetime symphony resonates perfectly 4) Exploring the Dual Nature of the Electron's Wave-Based Model 5) Exploring the Mysterious Core Wave 6) Exposing Mistakes in Depiction. 7) Exploring Time Changes in the Core Wave. 8) Exploring the Mysterious World of the Electron's Core Wave 9) Unraveling the Mystery of Dipole Waves in Spacetime 10) Unveiling the Amplitudes of Waves in a New Light 11) References of this e-book 12) Colclusion 13) Glossary
  • 4. When delving into the world of fermionic entities and the oscillating spacetime they inhabit, a fascinating paradigm emerges. It reveals that the very essence of an electron, along with other fermions, lies in the intricate dance of rotating soliton waves. This fundamental concept uncovers a profound truth about these particles, emphasizing their inherent wave-like character woven into the fabric of spacetime. Our journey commences with the electron, the simplest yet most significant manifestation of this wave-based fermion. Within the vast expanse of spacetime, the electron's wave takes on countless forms, shaped by its interactions with other fermions and the boundaries of its existence. Thus, we begin our exploration by focusing on the quintessence of the electron, capturing its purest and most isolated state. Unveiling the True Nature of Electrons' Wave Essence 1
  • 5. To unravel the mysteries of the electron, we must construct a simplified model that encapsulates its essence in a compact form. Within this model lie the keys to calculating its energy, understanding its wave properties, and comprehending the forces that govern its behavior. But our journey doesn't end there. In Section 18 of “Oscillating Spacetime: The Foundation of the Universe”, we catch a glimpse of the dynamic nature of this quantized wave. Here, we embark on a brief discourse that sheds light on how this foundational wave entity gracefully expands and contracts, assuming various sizes and shapes. This further enriches our understanding of the electron's enigmatic essence within the vast symphony of oscillating spacetime. 2
  • 6. The concept of a wave-based model for electrons and a rotating quantum vortex has been compared. In Figure 1, it was explained that when angular momentum is added to the superfluid Bose-Einstein condensate, it creates rotating vortices. These vortices are soliton waves that possess quantized angular momentum with the value of ħ. Interestingly, these quantum vortices arrange themselves in a specific pattern, suggesting that each vortex pushes away its neighboring vortices by distorting the surrounding superfluid. Quantum Whirlpools Resonating 3
  • 7. The beautiful harmony of spacetime symphony resonates perfectly In the vast cosmic dance of oscillating spacetime, a fascinating comparison emerges: it acts like a flawless superfluid, always moving yet perfectly coherent. When infused with quantized angular momentum, this ethereal medium orchestrates a captivating show—a rotating soliton wave, similar to the quantum vortices shown in Fig. 1. Resonances in oscillating spacetime, like harmonious melodies, come together to create stable or semi-stable rotating waves at specific frequencies. In our discussion, we focus on electrons and muons, the basic building blocks of our universe. 4
  • 8. The core of an electron's being lies in the creation of a rotating wave, intricately connected to its environment. To exhibit the well-known de Broglie wave properties, this rotating wave must carve out standing waves within the fabric of oscillating spacetime. Examination indicates that an electron's de Broglie wave nature suggests the presence of spherical standing waves resonating at a frequency precisely matching an electron's ωc = 7.76×10^20 rad/s. Therefore, a fascinating possibility arises: these standing waves likely originate from the rhythmic movements of a wave rotating at an electron's ωc. A peek into the simplest form of an electron reveals a model of graceful simplicity—a rotating wave, encompassing about one Compton wavelength in circumference. This tiny cosmic performance showcases a radius equal to an electron's Compton radius (rc = ħ/mec = 3.86×10^-13 m), echoing the harmonious symphony of oscillating spacetime. This radius also corresponds to an electron's Compton angular wavelength (rc = λc = ħ/mec), highlighting the intricate relationship between wave and particle that defines the essence of an electron. This simplified wave-based model of an electron is visually represented below, a tribute to the exquisite beauty woven into the fabric of our universe. 5
  • 9. Exploring the Dual Nature of the Electron's Wave-Based Model In breaking down the proposed wave-based model of an electron, we uncover a split in its essence, revealing two interconnected components: 1. The Core Wave: At the center of this model is a core wave, spinning harmoniously at the electron's characteristic frequency, ωc. Unlike traditional beliefs of clear-cut boundaries, this core wave possesses a fluidity that challenges standard definitions. However, in the realm of calculations, it is enclosed by a "mathematical radius," labeled as rc. This mathematical concept acts as a crucial point for theoretical examinations, allowing for precise calculations of the electron's characteristics. 2. Surrounding Standing Waves: Surrounding the core wave are complex patterns of standing, rotating waves. These waves, resembling celestial performers, encircle the core with elegance and accuracy, molding the electron's cosmic presence. 6
  • 10. Beyond the rc boundary, an electric field of significant strength is formed, containing energy measured as Eext = αħc/2rc, approximately 3×10^-16 J. Notably, this energy source makes up only a small portion—around 0.4%—of the electron's total energy. Additionally, a magnetic field of similar intensity accompanies this electric field, further enhancing the electron's energetic framework. Therefore, within this model's framework, a remarkable discovery emerges: over 99% of an electron's energy is housed within its rotating core, while the electric and magnetic fields combined hold less than 1%. This unique distribution emphasizes the importance of the core wave in shaping the electron's essence, while showcasing the intricate relationship between its core and surrounding fields. 7 “The electron does not have a sharp boundary or surface. There is no such thing as an electron sitting still with a sharp boundary. We can think of it as a spread-out fuzzy 'cloud' surrounding the nucleus, whose 'edge' is fuzzy.”
  • 11. Exploring the Mysterious Core Wave Trying to understand the heart of the electron model, Figure 4 shows us a visual journey into unknown territory. Here we have two different but connected attempts to represent the mysterious core wave—an entity so unique that it challenges our traditional understanding. This core wave, a 4-dimensional soliton, moves in a complex way within the fabric of oscillating spacetime, revealing dimensions beyond what we usually perceive. 8
  • 12. The high resistance of this medium, with a value of c^3/G = 4×10^35 kg/s, allows for the creation of a wave with a very small displacement amplitude—a mere Planck length/time. Despite its tiny size, this wave has the potential to form a concrete electron model that can be tested in experiments. Figure 4 A focuses on the spatial aspect of the electron's core wave, showing us its spatial complexities and geometries. On the other hand, Figure 4B explores the temporal side, capturing the essence of its temporal dynamics. Together, these two parts come together smoothly to create a single entity—a 4-dimensional rotating wave that represents the electron in its entirety. 9 In seeking to depict the core wave of the electron model, Figure 4 serves as a visual exploration into uncharted realms, endeavoring to unravel the mysteries of this 4-dimensional soliton wave within the dynamic framework of oscillating spacetime.
  • 13. Exposing Mistakes in Depiction. In this study, Figure 4 takes us on a fascinating journey into the enigmatic core wave of the electron model. Its aim is to shed light on a phenomenon that has puzzled scientists for a long time. This core wave, known as a 4-dimensional soliton, gracefully maneuvers through the complexities of oscillating spacetime, defying conventional understanding with its unique properties. The medium in which this wave exists presents a significant challenge, as it is quantified by an astonishing value of c^3/G = 4×10^35 kg/s. This formidable impedance allows for the emergence of a wave that has an imperceptible displacement amplitude, measuring only a mere Planck length/time. Despite its ethereal nature, this wave holds the potential to manifest as a tangible electron model that can be empirically validated. Figure 4A takes a deep dive into the spatial intricacies of the electron's core wave, capturing its essence within the fabric of space. On the other hand, Figure 4B explores the wave's temporal dynamics, showcasing its rhythmic oscillations through time. 10
  • 14. Together, these two components merge into a unified entity —a 4-dimensional rotating wave that encapsulates the very essence of the electron. Exploring Time Changes in the Core Wave. Figure 4A, although a brave attempt to represent the spatial aspect of the electron's core wave, contains several inaccuracies that require careful examination and improvement. These subtle differences provide valuable insights into the complex nature of the electron model, prompting a deeper exploration into its manifestation. 11
  • 15. 1) Spatial Amplitude Discrepancy: The depiction in Figure 4A exaggerates the height of the wave, mainly due to the significant difference between the spatial amplitude of the Planck length (Lp) and an electron's Compton radius. Since the Lp spatial amplitude is approximately 10^22 times smaller than the Compton radius, the portrayed wave's size is inflated beyond its actual proportions. 2) Incorporation of the Fine Structure Constant: An interesting anomaly arises when considering the fine structure constant, which introduces a slight distortion within the electron's core. However, this distortion is not accounted for in Figure 4, indicating the intricate relationship between fundamental constants and the electron's inherent properties. Although we only partially understand this mysterious effect, it deserves further investigation in subsequent sections. 12
  • 16. 3) Misrepresentation of Rotation: Figure 4 mistakenly suggests a simplistic rotation representation, implying a unidirectional and planar motion. In reality, the rotating wave that forms the electron's core operates within a turbulent sea of spatial and temporal fluctuations at the Planck scale. This chaotic environment challenges conventional notions of causality, resulting in an expectation of rotational direction and axis amidst a symphony of probabilistic fluctuations. These nuances challenge our understanding of rotational dynamics and highlight the complexities of the electron's core wave. By examining these inaccuracies, we open the door to a more nuanced comprehension of the electron model, unraveling layers of complexity that are at the forefront of scientific inquiry. 13
  • 17. Exploring the Mysterious World of the Electron's Core Wave As we venture further into the mysterious realm of the electron's core wave, a fascinating discovery emerges: its influence extends beyond just space, reaching into the intricate fabric of time itself. In this explanation, we embark on a visual journey, using shades of blue and yellow in Figure 4B to unravel the subtle details of temporal modulation. Imagine the blue section in Figure 4B as a domain where time moves faster than the local norm, while the yellow section represents a realm where time slows down. This temporal distortion appears as a shift of ± Planck time (± 5×10^-44 s) along the time dimension, giving us a glimpse into the complex interaction between the core wave and the temporal fabric. For every rotation of the wave, a hypothetical clock in the blue section gains one unit of Planck time (∿10^-43 s), while its counterpart in the yellow section experiences a corresponding loss. This small difference has significant implications when compared to the local norm. 14
  • 18. With the wave rotating at ωc = 7.76×10^20 rad/s, the blue section experiences time at a faster rate, approximately Tpωp = 4.18×10^-23 seconds per second, compared to the local norm. At the same time, the yellow section experiences a decrease in time. Although this temporal difference may seem imperceptible, it highlights the intricate tapestry of temporal modulations within the core wave. To put this phenomenon into perspective, imagine two perfectly synchronized clocks that differ by this tiny interval. Over the age of the universe, they would only diverge by approximately 40 microseconds—a minuscule yet profound testament to the subtle complexities of temporal dynamics within the electron's core wave. 15 "Time is what prevents everything from happening at once." — John Archibald Wheeler
  • 19. Unraveling the Mystery of Dipole Waves in Spacetime Deep within the core of an electron lies a fascinating phenomenon known as a "dipole wave in spacetime," which challenges our conventional understanding of the universe. According to the principles of general relativity, the existence of macroscopic dipole waves is considered impossible, as it goes against the fundamental constraints of our universe. This notion is extensively discussed in texts on general relativity, like (1), where they explain that mass dipole radiation is nullified due to the second time derivative of mass dipole being zero. In a larger context, the presence of dipole waves in spacetime would violate the principle of momentum conservation, a fundamental rule in the cosmic symphony. However, an intriguing idea emerges: could the uncertainty principle hold the key to unraveling the mystery of dipole waves within spacetime? 16
  • 20. Herein lies a paradoxical reconciliation: while general relativity sets up barriers against the existence of macroscopic dipole waves, the uncertainty principle opens the door for their covert presence. Theoretical foundations, ranging from [2] to [3], emphasise the impossibility of achieving measurements accurate to the Planck length (Lp) or Planck time (Tp). It is within this realm of uncertainty that quantum mechanics finds its place, allowing for the hidden existence of dipole waves in spacetime—a crucial element for the wave-based model of fermions. Thus, in the intricate interplay between uncertainty and possibility, the enigmatic nature of dipole waves in spacetime finds solace, providing us with a captivating glimpse into the paradoxes that form the very fabric of our reality. 17
  • 21. Unveiling the Amplitudes of Waves in a New Light 18 When it comes to the world of sound, understanding the amplitude of a sound wave is crucial. It refers to the maximum distance that vibrating particles move away from their average position. This measurement, known as "displacement amplitude (Ad)," is expressed in meters and helps us gauge the strength of sound waves. However, in the realm of wave dynamics, there is another way to look at amplitudes. Instead of focusing on length, we can examine strain amplitude (As), which represents the dimensionless maximum slope of a sine wave. This abstract concept allows us to gain a deeper understanding of wave behavior, going beyond traditional measurements and capturing the true essence of wave dynamics. Taking this idea further, let's consider the rotating wave that forms the core of an electron. Here, we introduce the concept of "electron's strain amplitude (Ae)," which is calculated to be 4.185×10^-23. This dimensionless value is obtained by dividing the electron's displacement amplitude (Lp) by its Compton angular wavelength (ƛc = ħ/mec = 3.86×10^-13). It encapsulates the dynamic behavior of the electron in a concise form.
  • 22. What's fascinating is that this dimensionless number serves as a universal descriptor for all of the electron's properties, except for its electromagnetic properties. It is expressed in dimensionless Planck units, offering us a way to unravel the complexities of wave dynamics and gain a deeper understanding of the fundamental properties of particles and waves. 19 References of this e-book [1] Misner CW.: Thorne KS, Wheeler JA.: Gravitation. W. H. Freeman and Company. 1200 – 1203, (1973) [2] Garay LJ.: Quantum gravity and minimum length. International Journal of Modern Physics A, 10(02), 145- 165. (1995) [3] Baez JC.: Olson, S. J. Uncertainty in measurements of distance. Classical and Quantum Gravity, 19(14), L121. (2002) [4] Calmet X.: Graesser M, Hsu, SD.: Minimum length from quantum mechanics and classical general relativity. Physical review letters, 93(21), 211101 (2004) 45
  • 23. [5] Calmet X.: On the precision of a length measurement. The European Physical Journal C.; 54:501-5 (2008) Conclusion To sum up, delving into the simplified electron and muon model from the theory of oscillating spacetime has revealed an intriguing story of wave-based fermions. From the mysterious core wave swirling inside the electron to the intricate manipulation of temporal dynamics, each aspect of this model provides deep insights into the basic essence of particles and waves. Looking through the lens of uncertainty and potential, we've explored spatial and temporal dimensions, discovering the elegant simplicity that lies beneath the intricate structure of our universe. Reflecting on the journey taken, it's evident that the quest for knowledge is a continuous pursuit—one that encourages us to constantly push the boundaries of our comprehension and embrace the beauty of the unknown. 20
  • 24. Glossary: Displacement Amplitude (Ad): The maximum displacement of vibrating particles from their mean position in a sound wave, measured in meters. Strain Amplitude (As): The dimensionless maximum slope of a sine wave, representing the magnitude of strain in wave dynamics. Electron's Strain Amplitude (Ae): A dimensionless number derived from dividing the electron's displacement amplitude by its Compton angular wavelength, representing the dynamic behaviour of the electron in a compact form. Planck Length (Lp): The scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate, approximately 1.616 × 10^-35 meters. 21
  • 25. Compton Angular Wavelength (ƛc): The wavelength associated with the momentum of a particle, calculated using the Compton wavelength formula, approximately 3.86 × 10^-13 meters for an electron. Oscillating Spacetime: A theoretical framework proposing that spacetime undergoes oscillatory fluctuations at the smallest scales, influencing the behaviour of particles and waves. Dimensionless Planck Units: Units of measurement based on fundamental constants such as the Planck length, Planck time, and Planck mass, providing a scale for quantum phenomena. 22