I was messing around with the relativistic energy equation and stumbled upon something that looks like the spacetime interval equation. So, I'm wondering if there is some deeper connection there, or if it's just an interesting coincidence. I'll just go through it really quickly. E2 = m2c4 + p2c2 m2c4 = E2 - p2c2 m2c4 = (γmc2)2 - (γmu)2c2 m2c4 = (γmc2)2 - (γm Δx/Δt)2c2 Divide all terms by m2γ2 c4/γ2 = (c2)2 - (Δx/Δt)2c2 Divide all terms by c2/Δt2 (cΔt)2/γ2 = (cΔt)2 - (Δx)2 And that looks suspiciously like the spacetime interval with the (+ - - -) sign convention if (Δs)2 = (cΔt)2/γ2. (cΔt)2/γ2 = (cΔt)2 - (Δx)2 (Δs)2 = (cΔt)2 - (Δx)2 So the spacetime interval is really (cΔt)2/γ2? Basically it looks like rest mass corresponds to the spacetime interval, energy corresponds to time, momentum corresponds to space, and the spacetime interval is a function of the Lorentz factor: (Δs) ∝ γ-1. (The time and space things makes sense to me since I've seen a proof that conservation of energy is related to time translations and conservation of momentum is related to space translations/rotations). Is this a coincidence or is there a reason for it? Thanks!