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Principle of Causality

Causality is the principle that cause and effect has an objective time-sequence which is independent of the frame of reference. That is, an observable effect always occurs (in time) after its observed cause, no matter what frame is chosen for the observations. Thus, if an event occurring at (x₁, t₁) causes an effect (another event) at (x₂, t₂), then t₂ > t₁. The time-interval occurs because the influence of cause takes some time to reach x₂ (from x₁); the influence (or signal) moves with a finite velocity v, so that

Observed from another Lorentz frame, the time interval is given by

t₂’ – t₁’ = [(t₂ – x₂ v/c₂) – (t₁ – x₁ v/c₂)]

= (t₂ – t₁) (1 – vv_s/c₂)

Causality implies that t₂’ > t₁’, or vv_s < c₂.

The Lorentz transformations are valid iff v < c. Hence, to absolutely ensure above inequality, we find,

v_s < c

Thus the physical implication of causality principle is that no physical influence or signal can propagate with velocity with velocity faster than that of light in free space (vacuum).