Deeper Relativity Budget Scans

Opposite Momentum Ledger Three-Step Audit

signs cancel, energies add

A pair ledger separates signed momentum conservation from additive positive energy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The left particle carries fifteen momentum units

The left-moving ledger entry is momentum 15 kg m/s and energy 125 J. Momentum keeps a direction sign; energy is a positive budget.

15 kg m/sEL=125 J15\ \mathrm{kg\,m/s}\quad E_L=125\ \mathrm{J}
Opposite momentum ledgerOpposite momenta cancel while energies add.left momentumright momentumtotal momentumtotal energy

The right particle carries negative fifteen momentum units

The other entry has momentum -15 kg m/s and energy 125 J. The sign records opposite direction; it does not make energy negative.

−15 kg m/sER=125 J-15\ \mathrm{kg\,m/s}\quad E_R=125\ \mathrm{J}
Opposite momentum ledgerOpposite momenta cancel while energies add.left momentumright momentumtotal momentumtotal energy

Momentum cancels while energy adds

Adding the two signed momenta gives 0 kg m/s. Adding the two positive energies gives 250 J. The ledger is conserved by signed momentum and additive energy.

15+(−15)=0125+125=25015+(-15)=0\quad125+125=250
Opposite momentum ledgerOpposite momenta cancel while energies add.left momentumright momentumtotal momentumtotal energy