Class Relativity

java.lang.Object
org.episteme.natural.physics.relativity.Relativity
public class Relativity extends Object
Special and General Relativity.

Lorentz transformations, time dilation, length contraction, relativistic dynamics.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Summary

    Constructors
    Constructor
    Description
    Relativity()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static Real
    energyFromMomentum(Real momentum, Real restMass)
    Energy-momentum relation: E² = (pc)² + (m₀c²)² Returns total energy from momentum
    static Real
    escapeVelocity(Real mass, Real radius)
    Escape velocity: v_esc = √(2GM/r) = c√(r_s/r)
    static Real
    gravitationalTimeDilation(Real properTime, Real radius, Real schwarzschildRadius)
    Gravitational time dilation: t = t₀/√(1 - r_s/r) Near massive object at distance r
    static Real
    lengthContraction(Real properLength, Real velocity)
    Length contraction: L = L₀/γ Returns contracted length in moving frame
    static Real
    lorentzFactor(Real velocity)
    Lorentz factor: γ = 1/√(1 - v²/c²)
    static Real
    photonSphereRadius(Real mass)
    Photon sphere radius: r_ph = 3GM/c² = 1.5 r_s
    static Real
    relativisticDoppler(Real sourceFreq, Real velocity, boolean approaching)
    Doppler effect (relativistic): f = f₀√((1-β)/(1+β)) For source moving directly away (β = v/c)
    static Real
    relativisticKineticEnergy(Real restMass, Real velocity)
    Relativistic kinetic energy: KE = (γ - 1)m₀c²
    static Real
    relativisticMomentum(Real restMass, Real velocity)
    Relativistic momentum: p = γm₀v
    static Real
    schwarzschildRadius(Real mass)
    Schwarzschild radius: r_s = 2GM/c² Event horizon radius for black hole
    static Real
    timeDilation(Real properTime, Real velocity)
    Time dilation: Δt = γΔt₀ Returns dilated time for moving observer
    static Real
    totalEnergy(Real restMass, Real velocity)
    Total relativistic energy: E = γm₀c²
    static Real
    velocityAddition(Real v1, Real v2)
    Velocity addition formula: v = (v₁ + v₂)/(1 + v₁v₂/c²)

    Methods inherited from class Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Relativity

      public Relativity()

  • Method Details

    • lorentzFactor

      public static Real lorentzFactor(Real velocity)
      Lorentz factor: γ = 1/√(1 - v²/c²)

    • timeDilation

      public static Real timeDilation(Real properTime, Real velocity)
      Time dilation: Δt = γΔt₀ Returns dilated time for moving observer

    • lengthContraction

      public static Real lengthContraction(Real properLength, Real velocity)
      Length contraction: L = L₀/γ Returns contracted length in moving frame

    • relativisticMomentum

      public static Real relativisticMomentum(Real restMass, Real velocity)
      Relativistic momentum: p = γm₀v

    • relativisticKineticEnergy

      public static Real relativisticKineticEnergy(Real restMass, Real velocity)
      Relativistic kinetic energy: KE = (γ - 1)m₀c²

    • totalEnergy

      public static Real totalEnergy(Real restMass, Real velocity)
      Total relativistic energy: E = γm₀c²

    • energyFromMomentum

      public static Real energyFromMomentum(Real momentum, Real restMass)
      Energy-momentum relation: E² = (pc)² + (m₀c²)² Returns total energy from momentum

    • velocityAddition

      public static Real velocityAddition(Real v1, Real v2)
      Velocity addition formula: v = (v₁ + v₂)/(1 + v₁v₂/c²)

    • relativisticDoppler

      public static Real relativisticDoppler(Real sourceFreq, Real velocity, boolean approaching)
      Doppler effect (relativistic): f = f₀√((1-β)/(1+β)) For source moving directly away (β = v/c)

    • schwarzschildRadius

      public static Real schwarzschildRadius(Real mass)
      Schwarzschild radius: r_s = 2GM/c² Event horizon radius for black hole

    • gravitationalTimeDilation

      public static Real gravitationalTimeDilation(Real properTime, Real radius, Real schwarzschildRadius)
      Gravitational time dilation: t = t₀/√(1 - r_s/r) Near massive object at distance r

    • escapeVelocity

      public static Real escapeVelocity(Real mass, Real radius)
      Escape velocity: v_esc = √(2GM/r) = c√(r_s/r)

    • photonSphereRadius

      public static Real photonSphereRadius(Real mass)
      Photon sphere radius: r_ph = 3GM/c² = 1.5 r_s