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
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

Frame
Time:
Length:
Energy:
Gravity:

β:   Δ Velocity km/s:     γ :
Slow
Fast
Frame 1
Time':
Length':
Energy':
Gravity':
Frame 2
Time':
Length':
Energy':
Gravity':

## 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)
r_s = (2GM)/c^2

## Gravitational Time Dilation Playground

Outside the gravity field
Time:
Length:

Object

Units:

Mass:
Tiny
Massive
Small
Large
Inside the gravity field
Time':    1
Length':    1
Gravity: 1
Escape Velocity: 1
Schwarzchild Mass: 1

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

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