A Unified Road to Reality

[Postulates]
Space and time are discrete, and their quanta are respectively denoted by the space unit Lu and the time unit Tu. Motion is discontinuous and random, and its quantum is denoted by the unit of motion hbar.
The random discontinuous motion in discrete space and time is called quantum motion.

[Deductions] 
1. Dynamical wavefunction collapse and quantum theory

In the nonrelativistic domain, the evolution equation of quantum motion includes two parts: the linear Schrödinger evolution term and the nonlinear stochastic evolution term. The former corresponds to Schrödinger's equation in quantum mechanics, and the latter describes the dynamical collapse of the wave function. This provides a complete quantum theory.

2. Constancy of the speed of light and special relativity

The speed of light can be expressed by the space unit Lu and the time unit Tu, namely c=Lu/Tu. The discreteness of space and time will lead to the maximum and constancy of the speed of light. This provides a logical foundation for special relativity. As a result, special relativity will be replaced by the theory of special relativity in discrete space and time.

3. Gravitational constant and general relativity

The gravitational constant can be expressed by the space unit Lu, the time unit Tu and the unit of motion hbar, namely k=2pi*LuTu/hbar. This expression implies that gravity may exist only in discrete space and time. As a result, general relativity will be replaced by the theory of general relativity in discrete space and time.

4. Unification of quantum and gravity

The conflict between quantum theory and general relativity can be settled with the help of quantum motion. As a result, the theory of quantum motion may provide a consistent framework for the unification of quantum and gravity.

5. Charges and interactions

A basic charge can be constructed by using the space unit Lu, the time unit Tu and the unit of motion hbar, namely C=(Eu*Lu)^1/2=(hbar*c)^1/2, and its interaction potential energy is in inverse proportion to the distance between the charges. The charge of the electromagnetic interaction can be expressed as a multiple of the basic charge, namely e=(alpha*bar*c)^1/2=(alpha)^1/2C, where alpha~1/137 is the fine structure constant. Similarly, the charges of weak interaction and strong interaction can also be expressed as a certain multiples of the basic charge. The multiple denotes the coupling strength of the interaction, and may be determined by the interplay of the charge and the actual vacuum.

6. Dark energy and the fate of our universe

The dark energy may originate from the quantum fluctuations of the discrete space-time limited in our universe. The real form of dark energy will determine the future of our universe.

7. Unit of mass and the essential elements of matter

A unit of mass can be expressed by the space unit Lu, the time unit Tu and the unit of motion hbar, namely Mu=hbar/(Lu*c)=hbar*Tu/Lu^2. The size of a particle with a unit of mass is the space unit Lu. Considering the size limitation of discrete space-time, the fundamental particles with a unit of mass may be the essential elements of matter.

[*] Most of the above deductions are detailedly discussed in the book Quantum Motion.