Fermion Waves and Boson Waves

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Understanding Temporal Wave Dynamics

I question why a wave with a positive value might travel in the negative direction of time, and vice versa. I believe this relates to a sequence of events where larger values propagate smaller values in the direction of the wave.

Temporal Flow Hamiltonian

The fundamental concept here is represented by the Temporal Flow Hamiltonian:

  • Let TiT_i represent the temporal flows.
  • Let ωi\omega_i denote their respective frequencies.

Wave Propagation

Temporal waves are described as Ψ(t)\Psi(t), which evolve according to the Hamiltonian H(t)H(t):

H(t)=∑iTi⋅ωiH(t) = \sum_i T_i \cdot \omega_i
  • Amplitude Influence: The amplitude in Ψ(t)\Psi(t) indicates energy levels. Higher amplitude values signify regions of higher energy, influencing the propagation of lower energy (smaller amplitude) regions. In this model, larger values dominate interaction dynamics.

Wave Interaction

  1. Fermions: Represented by anti-symmetric wave functions, fermions lead to destructive interference:

    Ψfermion=12(ψ1−ψ2)\Psi_{\text{fermion}} = \frac{1}{\sqrt{2}} \left( \psi_1 - \psi_2 \right) 

    This means that higher positive values can cancel out higher negative values.

  2. Bosons: Exhibiting symmetric wave functions, bosons result in constructive interference:

    Ψboson=12(ψ1+ψ2)\Psi_{\text{boson}} = \frac{1}{\sqrt{2}} \left( \psi_1 + \psi_2 \right) 

    This amplification enhances the overall energy of the wave.

Propagation Mechanism

  • Larger Values Propagating Smaller Ones: Higher amplitude (energy) values exert a directional influence, effectively pushing lower amplitude values along the wave's direction. This is consistent with energy transfer in wave mechanics.

  • Wave Superposition: The interaction of waves—constructive for bosons and destructive for fermions—affects energy propagation within the system.

Practical Implications

  • Fermions: Destructive interference maintains distinct quantum states by ensuring higher energy states disperse or neutralize lower energy states.

  • Bosons: Constructive interference allows higher energy states to amplify and stabilize lower energy states, leading to coherent states.

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