Relativity

Spacetime, Lorentz · 8 formulas

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Lorentz Factor

γ=11−v2/c2\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}

Quantifies how much time, length, and mass distort as velocity approaches c.

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Time Dilation

Δt=γΔt0\Delta t = \gamma \Delta t_0

A moving clock ticks slower than a stationary one, as seen by an outside observer.

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Length Contraction

L=L0/γL = L_0 / \gamma

Objects in motion appear shorter along their direction of travel.

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Relativistic Momentum

p=γmvp = \gamma m v

Momentum diverges as velocity approaches c, preventing massive objects from reaching light speed.

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Energy–Momentum Relation

E2=(pc)2+(mc2)2E^2 = (pc)^2 + (mc^2)^2

The full relativistic relation linking total energy, momentum, and rest mass.

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Relativistic Velocity Addition

u=u′+v1+u′v/c2u = \frac{u' + v}{1 + u'v/c^2}

Velocities don't simply add at high speeds; the result never exceeds c.

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Relativistic Doppler Effect

f=f01−β1+βf = f_0 \sqrt{\frac{1 - \beta}{1 + \beta}}

Receding sources redshift, approaching sources blueshift — with a relativistic gamma correction.

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Schwarzschild Radius

rs=2GMc2r_s = \frac{2GM}{c^2}

The radius at which escape velocity equals c — the event horizon of a non-rotating black hole.