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`

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'" = "time"/root()(1-v^2/c^2) " or " t' = gammat`
`"length'" = "length"/root()(1-v^2/c^2) " or " l' = gammal`
`"energy'" = "energy"/root()(1-v^2/c^2) " or " e' = gammae`
`"gravity'" = "gravity"/root()(1-v^2/c^2) " or " g' = gammag`

Velocity Time Dilation Playground

Frame
Time:     
Length:
Energy:
Gravity:

β:   Δ Velocity in km/s:     γ (Gamma):
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)`
Schwarzschild radius
`r_s = (2GM)/c^2`

Gravitational Time Dilation Playground

Outside the gravity field
Time:     
Length:

Object

Units:  

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

Bekenstein bound and Shanon Entropy

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)`






Important Concepts

Major Interesting or Surprising Things

Minor Interesting or Surprising Things

Learning Resources

Minor Learning Resources

Tools

Interesting Papers

Other Topics

Alternatives







Scratch Pad

`"ge" = (GMtc)/(root()(c^2-v^2) * r)`


`"ge" = (GMgamma)/r^2`


`"ge" = (GMt')/r^2`


`"ge" = (GMtroot()(c^2* r - 2GM))/(cr^2root()(r))`

`ϟ = g*A`
`ϟ = (GMA)/r^2`





TODO:

  • Gravitational Redshift Calculator (give mass, r, distance and get redshift)
  • Below surface gravitational time dilation (give m, r, and distance get t)
  • Above surface gravitational time dilation (give m, r, and distance get t)