User:Unitfreak/Quantum Variables

Stone speed = 0 Stone speed = ⅓ c Stone speed = ⅔ c Photon speed = c
The objects depicted in the above animations appear to progress through a series of color shades. This color progression is intended to represent the phase progression of a quantum wave function. The left side of each animation represents the object in three-dimensional space, with the x and y axes respectively running horizontally and vertically. The right side represents the object in spacetime, with the x-axis running horizontally and time running vertically. The horizontal line through each animation represents the x-axis.

The images immediately above are still frames taken from the animations far above. The following physical variables have been marked on the images: $V_{0}$ : the "rest volume" of the stone (volume when not moving). $V$ : the volume of the stone when in motion. $\lambda$ : the quantum wavelength (Planck constant / momentum). $\tau _{0}$ : the "rest period" of the stone (Planck constant / rest energy). $\tau _{H}$ : the Hamiltonian period (Planck constant / total energy ). $\tau _{L}$ : the Lagrangian period. As the stone's speed approaches the speed of light, the stone's volume decreases (shrinks in the direction of motion) due to relativistic length contraction. Motion also causes the wavelength to decrease (reflecting an increase in momentum) and the Hamiltonian period to decrease (reflecting an increase in kinetic energy). The Lagrangian period increases with speed.