Keeping one checked gamma triangle shows lab time scaling with proper time.
Keeping one checked gamma triangle shows lab time scaling with proper time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Four proper seconds become five lab seconds
Gamma 5/4 multiplies proper time 4 s into lab time 5 s.
4⋅45=5
Eight proper seconds become ten lab seconds
Doubling the proper interval to 8 s doubles the lab interval to 10 s because gamma is unchanged.
8⋅45=10
Twelve proper seconds become fifteen lab seconds
The third row keeps the same triangle and changes only the moving-clock reading. Proper time 12 s gives lab time 15 s.