### Wave Function and Lorentz Transformation

According to the Lorentz equation, the length of a particle decreases at higher speeds (length contraction). We may write Lorentz transformation equation for linear motion as follows:

L = L_{0}√ (1-v^{2}/c^{2})

In velocities greater than the speed of light (v>c), the Lorentz transformation equation moves us to the imaginary domain, because (1-v^{2}/c^{2}) turns into a negative number.

L = √-n.^{9}

In this model imaginary domain is related to the proposed singularity; hence I conclude that any particle that exceeds the speed of light moves to singularity.

The above interpretation of wave function suggests a reason for using complex numbers to define wave function in the Schrodinger’s equation, mentioned above. While the real number corresponds to the particle in space-time, its imaginary portion relates to the trace of particle in singularity. That is one way to describe wave function by complex numbers.**Water Waves**

Water waves offer an analogy for the above concept. As the water molecules rise from the surface, we see them as wave. When they fall, they join the sea of water again. And then the cycle repeats itself. What we see are waves at the surface, but in reality, the waves are extension of the sea. They take a specific shape while in action.

The main factors, which are hidden here, are the energy field, which is moving the water molecules, and the data, which regulates the movement and shapes of the wave’s motions. The collective action of the field (data and energy), which is not observable, and the water molecules, which are observable, form the visible waves. It is not a sound strategy to preoccupy oneself with the shape of the waves while ignoring and normalizing contributory factors from the underlying sea.

### Dirac’s Electron

The Dirac equation for electron can be written as follows:

Ψ = (a A, b A’ )

This represents a pair of 2-spinors. We can interpret its physical reality as follows. An electron actually consists of two separate particles (aA and bA’). They are called particle and anti-particle. These two particles have opposite charges and are continually converting into each other.

In Dirac’s electron wave model, the anti-particle is represented in second portion of the phase. The anti-particle of electron is positron. The birth and rebirth of the Dirac’s electron is in line with this model. However, the instantaneous speed of Dirac particles is always constant and equal to the speed of light. The variation in propagation speed comes from the zigzag motion of two components as they average out. In this model, I have proposed that the speed along the propagation line is constant but that the instantaneous speed of the particle changes between the propagation speed and the speed of light in a two-dimensional wave plane. The disappearance and rebirth of the particle comes by its entering and rising from the proposed singularity.