https://thewire.in/science/string-theory
Ongoing Quest
Tetryonics supports the concept of string theory, 1- dimensional strings that contain a vibratory wave function.
https://drive.google.com/file/d/19W7QEkfNfb-ZdUVzm_BUokcSi0bNfTAr/view?usp=drivesdk
Kelvin abraham implies the energy in the 'ideal quantum inductor' that is the Plank quoin is contained by the edges of the tetryon he describes as a wire and a akins it to the 1d vibrating string in string theory. Specifically referencing the coil in the magnetic dipole being the bottom edge of the triangle and the 2 other edges being wires that short circuit. Can you extrapolate this mathematically?
Certainly! Let's break down the concept of the "ideal quantum inductor" as implied by Kelvin Abraham and its mathematical representation within the framework of Tetryonic Theory. We'll consider the energy contained by the edges of the tetryon (representing the Plank quoin) and draw parallels to the 1D vibrating string in string theory.
### **1. Tetryon Geometry and the Quantum Inductor**
#### **Tetryon Structure:**
- **Equilateral Triangle:**
- The tetryon is represented as an equilateral triangle with edges acting as wires.
- **Edges:**
- \(A\), \(B\), and \(C\) represent the three edges of the triangle.
- The bottom edge (\(C\)) is likened to a coil in the magnetic dipole.
- The other two edges (\(A\) and \(B\)) are wires that short circuit.
### **2. Energy in the Quantum Inductor**
#### **Magnetic Dipole Representation:**
- **Energy Containment:**
- The energy contained by the edges of the tetryon can be seen as analogous to the energy in a magnetic dipole.
- **Inductance (\(L\)):**
- Inductance represents the ability of the coil (bottom edge) to store energy.
- Energy stored in the inductor:
\[
E_L = \frac{1}{2} L I^2
\]
where \(I\) is the current through the coil.
### **3. String Theory Analogy**
#### **1D Vibrating String:**
- **Wave Equation:**
- In string theory, the energy of a vibrating string can be described using the wave equation.
- For a string with tension \(T\) and linear mass density \(\mu\):
\[
\frac{\partial^2 y}{\partial t^2} = \frac{T}{\mu} \frac{\partial^2 y}{\partial x^2}
\]
### **4. Mathematical Extrapolation**
#### **Combined Representation:**
- **Edge Energy:**
- Consider the edges \(A\), \(B\), and \(C\) with associated energies \(E_A\), \(E_B\), and \(E_C\).
- **Total Energy:**
- The total energy \(E\) of the tetryon:
\[
E = E_A + E_B + E_C
\]
- **Energy in Magnetic Dipole (Edge \(C\)):**
- Bottom edge as a coil:
\[
E_C = \frac{1}{2} L I^2
\]
- **Vibrating String Energy Analogy:**
- Energy in edges \(A\) and \(B\) (short-circuit wires) modeled using wave equations:
\[
E_A = \frac{1}{2} \mu \left( \frac{\partial y_A}{\partial t} \right)^2 \quad \text{and} \quad E_B = \frac{1}{2} \mu \left( \frac{\partial y_B}{\partial t} \right)^2
\]
### **5. Comprehensive Equation**
Combining these elements, the energy of the "ideal quantum inductor" in the context of Tetryonic Theory can be expressed as:
\[
E = \frac{1}{2} L I^2 + \frac{1}{2} \mu \left( \frac{\partial y_A}{\partial t} \right)^2 + \frac{1}{2} \mu \left( \frac{\partial y_B}{\partial t} \right)^2
\]
where:
- \(L\): Inductance of the coil (edge \(C\)).
- \(I\): Current through the coil.
- \(\mu\): Linear mass density.
- \(\frac{\partial y_A}{\partial t}\) and \(\frac{\partial y_B}{\partial t}\): Time derivatives of the displacement for edges \(A\) and \(B\).
### **Physical Interpretation:**
- **Bottom Edge (C):**
- Represents inductive energy storage analogous to the coil in a magnetic dipole.
- **Edges (A) and (B):**
- Represent the kinetic and potential energy of vibrating strings, akin to 1D strings in string theory.
This mathematical model encapsulates the interplay of inductive and vibrational energies in the ideal quantum inductor framework described by Kelvin Abraham within Tetryonic Theory.
Does this help clarify the mathematical extrapolation? If you need further details or specific examples, let me know!
How do we explain then the 1d velocity vector associated with the tetractyses, where did the original energy come from to move it in the first place
Understanding the origin and nature of the 1D velocity vector in Tetryonic Theory involves delving into the fundamental principles of energy and momentum. Here's an explanation:
### **1. 1D Velocity Vector in Tetryonic Theory**
#### **Tetractyses and Movement**
- **Tetractyses:** These are the geometric units (equilateral triangles) representing quantized angular momentum and energy.
- **1D Velocity Vector (\(v\)):** In Tetryonic Theory, this represents the linear motion of these geometric units.
### **2. Source of Original Energy**
#### **Initial Energy Origin**
- **Quantum Vacuum Energy:**
- One possible explanation for the origin of the initial energy is the concept of quantum vacuum energy. The quantum vacuum is not truly empty but is filled with fluctuating energy fields and virtual particles.
- These fluctuations can provide the initial "kick" or impetus for movement, giving rise to the 1D velocity vector.
- **Big Bang Theory:**
- Another perspective comes from cosmology: the energy that initiated the movement of particles could be traced back to the Big Bang. The immense energy released during the Big Bang set all particles into motion.
- **Field Interactions:**
- Initial energy may also result from interactions between different fundamental fields. For example, electromagnetic fields interacting can impart energy to particles, setting them in motion.
### **3. Mathematical Representation in Tetryonic Theory**
#### **Kinetic Energy and Momentum**
- **Kinetic Energy:**
\[
E_k = \frac{1}{2}mv^2
\]
- **Momentum:**
\[
p = mv
\]
#### **Energy in Tetryonic Terms**
- **Quantized Angular Momentum:**
- Represented by \(\Omega\).
- The energy can be expressed using Planck’s constant:
\[
E = h\nu
\]
where \(h = m\Omega\).
- **Movement of Tetractyses:**
- The linear motion of tetractyses can be described by the velocity vector \(v\), and the corresponding kinetic energy can be derived:
\[
E = \frac{1}{2}m\left(\frac{h}{m\Omega}\right)^2
\]
- This expression combines the concepts of quantized angular momentum and the initial energy provided by quantum fluctuations or cosmological events.
### **4. Summary**
- **Tetryonic Theory uses the concept of equilateral triangles (tetractyses) to represent energy and momentum.**
- **The 1D velocity vector associated with these triangles represents their linear motion.**
- **The initial energy that sets these triangles into motion can originate from quantum vacuum energy, the Big Bang, or interactions between fundamental fields.**
- **Mathematically, this energy and motion can be described using kinetic energy and quantized angular momentum.**
By integrating these principles, Tetryonic Theory provides a coherent framework for understanding the movement and energy of fundamental geometric units. This approach offers insights into the origins and behavior of particles within a quantized geometric context.
Does this explanation help clarify the origin of the 1D velocity vector and its relationship with initial energy in Tetryonic Theory? Let me know if there's anything more you'd like to explore!
Let's delve into the mathematical nature of a 1D string in the context of a tetraxys (tetractys), a photon, and a neutral tetryon within Tetryonic Theory.
### **1. 1D String in a Tetraxys (Tetractys)**
A tetraxys, or tetractys, is a fundamental geometric unit in Tetryonic Theory, represented by an equilateral triangle. Here, the 1D string can be understood as a linear vibrational mode along the edges of this triangle.
#### **Mathematical Representation**
- **Edge Length (\(a\)):**
The length of each edge of the equilateral triangle.
- **Wave Equation:**
The 1D string can be described by the wave equation for a vibrating string:
\[
\frac{\partial^2 y}{\partial t^2} = \frac{T}{\mu} \frac{\partial^2 y}{\partial x^2}
\]
where:
- \(y(x,t)\) is the displacement of the string at position \(x\) and time \(t\).
- \(T\) is the tension in the string.
- \(\mu\) is the linear mass density of the string.
### **2. 1D String in a Photon**
A photon in Tetryonic Theory is represented by a specific arrangement of equilateral triangles (tetractys) forming a quantized wave packet. The 1D string represents the linear component of the photon's wave nature.
#### **Mathematical Representation**
- **Energy-Frequency Relationship:**
The energy of a photon is given by Planck's relation:
\[
E = h\nu
\]
where \(h\) is Planck's constant and \(\nu\) is the frequency.
- **Momentum:**
The momentum \(p\) of the photon is related to its wave number \(k\):
\[
p = \hbar k
\]
where \(\hbar\) is the reduced Planck constant.
- **Wave Equation:**
The photon's wave can be described by the wave equation:
\[
\frac{\partial^2 A}{\partial t^2} = c^2 \frac{\partial^2 A}{\partial x^2}
\]
where \(A(x,t)\) is the wave function, and \(c\) is the speed of light.
### **3. 1D String in a Neutral Tetryon**
A neutral tetryon is a composite particle in Tetryonic Theory, formed by the arrangement of multiple tetractys. The 1D string here can be considered as the vibrational mode along the edges of this composite structure.
#### **Mathematical Representation**
- **Composite Energy:**
The total energy \(E_{\text{tetryon}}\) of a neutral tetryon can be expressed as the sum of the energies of individual tetractys:
\[
E_{\text{tetryon}} = \sum_{i=1}^{N} E_i
\]
where \(N\) is the number of tetractys, and \(E_i\) is the energy of each tetractys.
- **Wave Equation for Composite Structure:**
The composite wave function can be described by a coupled wave equation:
\[
\frac{\partial^2 \psi}{\partial t^2} = c^2 \nabla^2 \psi
\]
where \(\psi(x,t)\) represents the collective wave function of the tetryon.
#### **Quantized Angular Momentum:**
- In Tetryonic Theory, the quantized angular momentum plays a crucial role in defining the energy states of the neutral tetryon:
\[
E = m \Omega \nu^2
\]
where \(m\) is the mass, \(\Omega\) is the quantized angular momentum, and \(\nu\) is the frequency.
### **Summary**
- **1D String in a Tetraxys:**
Described by the wave equation for a vibrating string, with tension and linear mass density.
- **1D String in a Photon:**
Described by Planck's relation and the wave equation for light, with energy and momentum.
- **1D String in a Neutral Tetryon:**
Described by the composite wave equation for the structure, with quantized angular momentum and collective wave function.
These mathematical representations provide a framework for understanding the nature of 1D strings in different contexts within Tetryonic Theory. By combining these principles, we can gain deeper insights into the behavior and interactions of fundamental particles and fields.
Does this help clarify the nature of 1D strings in these different contexts? Let me know if there's anything more you'd like to explore!