Zamicol's Relativity Playground

Name	Symbol	Value
Gravitational Constant	G	`6.67408 × 10^-11 m^3 kg^-1 s^-2`
Speed of Light	c	299,792,458 m/s
Plank Constant	h	`6.62607015 × 10^-34 J⋅s`
Fine-structure constant	α	`\alpha =e^2/(2\varepsilon _{0}hc)` which is `0.00729735 = 1/137.03600`

Special Relativity, Lorentz Transformation, and Velocity Time Dilation

Lorentz factor
`gamma = 1/root()(1-v^2/c^2)`

Relative velocity
`β = v/c`

Relativistic mass
`m = root()(E^2 - (p^2c^2)/c^2`

Rest mass energy equivelence
` E = mc^2`

Time, relativistic mass, energy, luminosity, and more.
`"time'" = "time"/root()(1-v^2/c^2) " or "t' = gammat`

Length
`"ℓ'" = "ℓ"root()(1-v^2/c^2) " or "ℓ' = ℓ/gamma`

`"gravity'" = "gravity"/root()(1-v^2/c^2) " or "g' = gammag`

Velocity Time Dilation Playground

General relativity, Gravitational Time Dilation, Escape Velocity, and Schwarzschild radius

Einstein field equations `G_(munu) + Lamdag_(munu) = (8piG)/c^4T_(munu)`

Einstein gravitational constant
`kappa = (8piG)/c^4`

Newton's gravity
`g = (GM)/r^2`

Gravitational Time Dilation
`t' = troot()(1-(2GM)/(rc^2))`

Escape velocity
`v_e = root()((2GM)/r)`

Inverse Square Law
`I = P/(4pir^2)`

Schwarzschild radius
`r_s = (2GM)/c^2`

Gravitational Time Dilation Playground

Information theory - Entropy, Bekenstein bound, Shanon entropy, Landauer's principle, and Kolmogorov complexity

Black hole entropy and surface area
`S = A/(4Gℏ)`

Bekenstein bound
`S ge (2pikRE)/(ℏc)`

Entropy
`H(X) = -sum_(i=1)^n P(x_i)logP(x_i)`

Landauer limit
`E = k_b T ln 2`

Boltzmann entropy
`S = k_b ln W`

Important Concepts

Major Interesting or Surprising Things

Minor Interesting or Surprising Things

Learning Resources

Minor Learning Resources

Tools

Interesting Papers

Other Things

Alternatives

Entropic Gravity

MOND