Speed Gamma Boundary Three-Row Scan - Special Relativity: Time, Energy, and Momentum Step by Step

Two finite velocity triangles plus the speed-limit boundary show why gamma grows and then stops being finite. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Speed three gives gamma five fourths

The toy speed limit is 5 m/s. With speed 3 m/s, the quiet leg is 4 m/s, so beta is 3/5 and gamma is 5/4.

3^2+4^2=5^2\quad \gamma=\frac{5}{4}

Speed four raises gamma to five thirds

Increasing only the speed to 4 m/s shrinks the quiet leg to 3 m/s. The denominator of gamma is smaller, so gamma becomes 5/3.

4^2+3^2=5^2\quad \gamma=\frac{5}{3}

At speed five there is no finite gamma

At the speed limit, speed is 5 m/s and the quiet leg is 0 m/s. Gamma would divide by zero, so the checked boundary says no finite gamma.

5^2+0^2=5^2\quad \gamma\ \text{not finite}