SCIENCE · INVESTIGATE AND EXPLAIN

Conserve four-momentum rather than a sum of rest masses

The original isolated collision joins a moving unit-rest-mass body to a stationary target of mass m2. All products remain in one composite, with no escaping radiation. Energy and momentum must be added in a common frame before the final invariant mass is computed.

Learning outcome: Close total energy and momentum, independently reconstruct the composite velocity and mass, and partition the incoming kinetic energy before changing the target mass.

Starting recap

Name event pairs, frame signs and c=1 units; retain simultaneity, worldline integration, four-momentum and unused evidence boundaries.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

For v=0.6 and target mass 1, total E=2.25 and p=0.75. Composite M=sqrt(4.5)≈2.121320 and speed 1/3. Internal increment is about 0.121320 and bulk kinetic energy 0.128680, summing to the incoming kinetic energy 0.25.

Open the experiment

Predict

Why is summing the incoming invariant masses insufficient to obtain the final composite invariant mass?

Your prediction and reason

Experiment

Close total energy and momentum, independently reconstruct the composite velocity and mass, and partition the incoming kinetic energy before changing the target mass.

Infer the composite invariant mass

Worked teaching model · synthetic values · Original one-dimensional perfectly inelastic isolated collision: incoming rest mass1, target rest mass b at rest, c=1. All products retained in one composite with internal energy; no radiation escapes. Sum four-momentum, not the incoming rest masses, is conserved.

Incoming unit-mass speed: 0.6 c Stationary target rest mass: 1 reference mass

Reset keeps your prediction, captures and practice history.

Four-momentum closes while part of the incoming kinetic energy appears as internal energy and composite invariant mass.

Original one-dimensional perfectly inelastic isolated collision: incoming rest mass1, target rest mass b at rest, c=1. All products retained in one composite with internal energy; no radiation escapes. Sum four-momentum, not the incoming rest masses, is conserved.

Original conditional ledger; reference units retain their distinct meanings
Quantity	Value	Unit
Initial and final total energy	2.250000	reference mass × c²
Initial and final total momentum	0.7500000	reference mass × c
Composite invariant mass	2.121320	reference mass
Composite velocity	0.3333333	c
Sum of incoming rest masses	2	reference mass
Retained internal-energy mass increment	0.1213203	reference mass
Composite bulk kinetic energy	0.1286797	reference mass × c²
Incoming kinetic energy	0.2500000	reference mass × c²

These original virtual events and collision records are not an actual clock, accelerator, photon-source or practical experiment. No physical apparatus operation is assigned.

Four-momentum closes while part of the incoming kinetic energy appears as internal energy and composite invariant mass.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define events, frames and conserved quantities

Initially E=γ+m2 and p=γv. The composite mass satisfies M²=E²−p²=1+m2²+2m2γ. Its speed is p/E, and substituting that speed into γfinal M reconstructs its total energy. These are consequences of one conserved four-momentum, not separate fitted rules.

Except at zero relative speed, M exceeds 1+m2. The difference represents retained internal energy in the composite rest frame. This does not violate energy conservation or imply that the original particles changed rest mass merely because they moved. The final object is a different internally excited system.

The incoming kinetic energy divides between composite bulk kinetic energy E−M and internal-energy mass increment M−1−m2 in c=1 units. If radiation escaped, the final composite alone would not carry the full initial four-momentum; that would be a different model and must include the outgoing radiation explicitly.

2. Reconstruct the original case

3. Predict and investigate

Why is summing the incoming invariant masses insufficient to obtain the final composite invariant mass?

Close total energy and momentum, independently reconstruct the composite velocity and mass, and partition the incoming kinetic energy before changing the target mass.

Transfer the event construction

For the same v=0.6 but target mass 2, find composite invariant mass and speed.

Retain the chosen events, frame convention and intermediate reasoning before opening public feedback.

Compare a worked response

E=3.25, p=0.75, M=sqrt(10)≈3.162278 and speed 3/13≈0.230769. The internal increment is about 0.162278; the target changes both the center-of-momentum motion and internal-energy account.

Primary mechanism context. Checked 31 October 2026. Original derivations, records and diagrams; no physical apparatus operation or actual independent clock/particle measurement is claimed. Retain first reasoning and public-feedback exposure in the course evidence workspace when registered.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

For the same v=0.6 but target mass 2, find composite invariant mass and speed.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Recover invariant mass and bound a low-speed approximation Next: Derive photon energy with the emitter recoil retained

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