Dist Babble

  Example Calculation: Single Temporal Quantum in a Harmonic Potential Step 1: Define the Harmonic Potential Let's start with a simple harmonic potential defined as: V ( ϵ ) = 1 2 k ϵ 2 V(\epsilon) = \frac{1}{2} k \epsilon^2 V ( ϵ ) = 2 1 ​ k ϵ 2 where k k k is the spring constant. For this example, we'll use a common value for k k k . Assume : k = 1   N/m k = 1 \, \text{N/m} k = 1 N/m (as an example). Step 2: Write the Hamiltonian The Hamiltonian for our single temporal quantum can be expressed as: H = 1 2 ( d ϵ d t ) 2 + 1 2 k ϵ 2 H = \frac{1}{2} \left(\frac{d \epsilon}{dt}\right)^2 + \frac{1}{2} k \epsilon^2 H = 2 1 ​ ( d t d ϵ ​ ) 2 + 2 1 ​ k ϵ 2 Step 3: Schrödinger Equation The corresponding time-independent Schrödinger equation is given by: − ℏ 2 2 m d 2 Ψ ( ϵ ) d ϵ 2 + 1 2 k ϵ 2 Ψ ( ϵ ) = E Ψ ( ϵ ) -\frac{\hbar^2}{2m} \frac{d^2 \Psi(\epsilon)}{d \epsilon^2} + \frac{1}{2} k \epsilon^2 \Psi(\epsilon) = E \Psi(\epsilon) − 2 m ℏ 2 ​ d ϵ 2 d 2 Ψ ( ϵ ) ​ + 2 1 ​ k ϵ 2 Ψ ( ϵ ...

 Modified Gauss's Law in Temporal Physics 1. Assumptions Temporal Flow Representation : We define temporal flows using the function τ ( t ) \tau(t) τ ( t ) , which captures the flow of time as a dynamic quantity. Limitations of Time Flow : The maximum flow of time is bounded by the speed of light c c c . This is a fundamental principle from relativity, implying that no information or matter can travel faster than light. Planck Time Significance : The Planck time t P ≈ 5.39 × 1 0 − 44 t_P \approx 5.39 \times 10^{-44} t P ​ ≈ 5.39 × 1 0 − 44 seconds represents the smallest meaningful unit of time in quantum mechanics, providing a lower bound for temporal interactions. Influence of Temporal Flows on Electric Fields : We hypothesize that electric fields are influenced by temporal flows, leading to modifications in the classical laws of electromagnetism. 2. Classical Gauss's Law We start with the classical form of Gauss's Law, which states: ∇ ⋅ E = ρ ϵ 0 \nabla \cdot \mathbf{E}...