User:SangYoungJoo/sandbox

Relative Energy of Wave and Particle
Modifying Lorentz factor $$\gamma=1/\sqrt{1-\beta^2}$$ slightly, we can write it like this:

$$\beta^2+1/\gamma^2=(P_p/P)^2+(P_w/P)^2=1$$

Here, $$P_p$$ is the momentum in the gravitational direction, $$P_w$$ is the momentum in the direction perpendicular to that, and P is the total momentum in subatomic world. It also means mass (gravitational potential) and charge (electromagnetic potential).

Velocity of Light
This also applies to the velocity of light, which is as follows.

$$\vec{v}=c(\cos\theta\vec{e_r} + \sin\theta\vec{e_\theta})$$

($$\theta=\frac{GM}{rc^2}$$, $$c$$: light speed)

Here, unit vectors are tangent-normal coordinate system. Unit vector $$\vec{e_r}$$ is longitudinal wave of gravitational field and $$\vec{e_\theta}$$ is transverse waves of electromagnetic fields. The derivative of light velocity becomes the source of gravity and electomagnetic force like this.

$$\vec{F}/m=\frac{d\vec{v}}{dt}=>-\frac{GM}{r^2}(\cos^2\theta\vec{e_r} - \sin^2\theta\vec{e_\theta})$$

Gravitational Field Equation
In the process of deriving the force, the following equation is derived, which expresses the gravitational field without electromagnetic effects.

$$\frac{dv}{dt}=\frac{v^2}{r}$$

If we apply the Lorentz factor due to electromagnetism again, it becomes as follows.

$$\int{\frac{c}{r}}dt=-\frac{1}{\beta}-\ln{\gamma(1+\beta)}+C=\ln(\Phi/c^2)$$

$$1/\beta$$ represents gravitational potential, $$\ln\gamma(1+\beta)$$ represents electromagnetic potential.

Momentum, Force and Energy
$$Fdr=cdP$$ in subatomic field including photon.

$$Fdr=vdP+Pdv$$ in non-subatomic field.

In the subatomic world, $$P$$ is $$mv$$ and in the electromagnetic, gravitational field, it is $$\gamma{mv}$$. $$Pdv$$ is considered to be an effect of the amount of charge and becomes 0 if there is no charge. The relativistic force in the gravitational field can be defined as $$\gamma^3{mdv/dt}$$ and is identical to centrifugal force. $$r$$ represents the direction in which acceleration occurs. Considering only natural forces, $$r$$ can be seen as representing a centripetal direction such as gravity or electromagnetic force, and when considering artificial forces, $$r$$ represents a virtual centripetal point. In cases where the change in momentum and acceleration are constant (e.g. orbital motion), it can be written as follows.

$$F=\frac{c}{r}P$$ in subatomic field including photon.

$$F=\frac{v}{r}P$$ in non-subatomic field.

Atomic physics and chemistry

 * Relativistic quantum chemistry
 * Breit equation
 * Electron spin resonance
 * Fine-structure constant

Mathematical physics

 * Relativistic quantum mechanics
 * Quantum spacetime
 * Spin connection
 * Spinor bundle
 * Dirac equation in the algebra of physical space
 * Casimir invariant
 * Casimir operator
 * Wigner D-matrix

Particle physics and quantum field theory

 * Zitterbewegung
 * Two-body Dirac equations
 * Relativistic Heavy Ion Collider
 * Symmetry (physics)
 * Parity
 * CPT invariance
 * Chirality (physics)
 * Standard model
 * Gauge theory
 * Tachyon
 * Modern searches for Lorentz violation