Mass–Energy · System Boundaries & Empirical Checks
System boundaries
and the energy ledger.
When energy leaves a body as radiation, which system loses mass, and which does not? Drag a thermodynamic boundary around the components and inspect what energy crosses it.
System boundary energy ledger · reference model, host calculation
ME-03: System-boundary energy ledger with cited energy-source cards
Energy that leaves a body takes mass with it. Draw the line around the body and its light together, and nothing is lost.
Case Study Facts: Radium-226 Alpha Decay
Citation: NuDat 3.0 / Evaluated Nuclear Structure Data File (ENSDF), Brookhaven National Laboratory (226Ra Q-alpha = 4.871 MeV).
- 1. System before:
- Radium-226 nucleus at rest
- 2. System after:
- Radon-222 nucleus and alpha particle after heat emission
- 3. Matter crosses boundary:
- No (Closed system: The radon-222 nucleus and the alpha particle both stay inside the boundary.)
- 4. Radiation disposition:
- escapes (The decay energy leaves as heat.)
- 5. Reference frame:
- Rest frame of parent nucleus
- 6. Energy figure:
- 4.871 MeV (decay-energy-per-event)
Predict before inspecting the sealed box:
A sealed box holds a battery-powered lamp and a mirror. When the lamp lights up inside, does the box's total mass change?
Show the reference code & kernel bindings
Reference evaluator: src/physics/reference/massEnergy.ts
// evaluateBoundaryLedger
const bodyDeltaM = -emittedEnergy / (c * c);
const sysDeltaM = disposition === "retained" ? inputEnergy / (c * c) : 0;
// evaluateFourMomentum
const mSquared = (totalEnergy / c)^2 - p^2;
const invariantMass = Math.sqrt(Math.max(0, mSquared));The physics of the boundary
Three thermodynamic boundaries
Einstein concludes that if a body gives off the energy L in the form of radiation, its mass diminishes by L/V² (or in modern notation L/c²):
The total energy of an isolated system is strictly conserved. If the boundary is drawn around the emitting body and the radiation together inside a sealed container, no energy escapes, and the total mass of the enclosure remains completely unchanged:
Closed systems versus isolated systems
A system is closed if no matter crosses its boundary. It is isolated only if neither matter nor energy crosses its boundary. A radioactive radium salt sealed in an ampoule exchanges heat with its surroundings without losing matter; its mass decreases only as that heat leaves the container.
Modern four-momentum invariant mass
In modern relativistic mechanics, the invariant mass m of any system of particles or photons is the Lorentz norm of its total four-momentum P^μ = (E/c, p):
While a single light pulse has |p| = E/c and is therefore massless (m = 0), two equal and opposite light pulses have total momentum p = 0 and carry a nonzero system invariant mass: