Connections among the papers · Modern synthesis
One pulse, three questions.
What is its quantum energy? What does another observer measure? What changes when a body emits light?
The light-quanta paper does not establish relativity. The September mass–energy argument does not require quanta. This laboratory connects their consequences without turning one paper’s conclusion into another’s hidden premise.
One pulse · Three distinct questions
Follow the energy without confusing the claims
This is a modern comparison using the exact modern SI definitions of h and c, not a reconstruction of what was measured in 1905. A programmed consequence is not experimental confirmation.
Predict before changing the observer
Keep the source frequency and pulse energy fixed. Will a receding observer report less energy per quantum, fewer quanta, or both? Compare E/(hν) in the two frames after changing β. No answer is required to continue.
Accepted settings: ν = 500000000000000 Hz; E = 1 J per pulse; β = 0.6; source-frame angle = 0°. Changing only β changes the observer, not the emitted pulse.
Bookmark these accepted settings
1. Light quanta: an energy scale, not a proof of relativity
In modern notation the quantum energy is hν. Total pulse energy E and frequency ν are independent settings. E/(hν) is shown without rounding: an energy ratio is not an independently measured integer photon count.
| Quantity | Value | Unit |
|---|---|---|
| Frequency in the source frame | 500000000000000 | Hz |
| Pulse energy in the source frame | 1 | J |
| hν in the source frame | 3.313e-19 | J |
| E/(hν) in the source frame | 3.0184e18 | 1 |
Read the light-quanta argument, §6 · Compare the entropy coefficients
2. Relativity: energy and frequency change together
For the same pulse, the wave owners evaluate ν′/ν and E′/E. Both follow q = γ(1 − β cos θ), so the modern comparison E′/(hν′) equals E/(hν), apart from numerical rounding. This equality compares two computed consequences; it does not independently establish light quanta.
| Quantity | Value | Unit |
|---|---|---|
| Frequency transformation factor | 0.5 | 1 |
| Energy transformation factor | 0.5 | 1 |
| Frequency in the moving frame | 250000000000000 | Hz |
| Pulse energy in the moving frame | 0.5 | J |
| hν in the moving frame | 1.6565e-19 | J |
| E′/(hν′) in the moving frame | 3.0184e18 | 1 |
3. Mass–energy: first specify the system
A unidirectional light pulse has zero invariant mass. Its energy divided by c² is not its rest mass. To connect to the September argument, now add a distinct, equal pulse traveling in the opposite direction. Their total source-frame energy is 2E and their momenta cancel.
| Quantity | Value | Unit |
|---|---|---|
| Pulse energy divided by c² (not its rest mass) | 1.1127e-17 | kg |
| Invariant mass of a unidirectional light pulse | 0 | kg |
| Opposite equal pulse: moving-frame energy | 2 | J |
| Balanced pair: source-frame energy | 2 | J |
| Balanced pair: moving-frame energy | 2.5 | J |
| Balanced pair: invariant mass | 2.2253e-17 | kg |
| Body's mass decrease for balanced emission | 2.2253e-17 | kg |
For a body initially at rest that emits this balanced pair without recoil, the mass decrease is 2E/c². The displayed system invariant mass is a later interpretation. The historical argument instead compares two energy ledgers and uses the low-speed kinetic-energy premise. It does not require quanta, and we have not assigned the unknown initial body energy E₀ = Mc².
Read the September paper · Follow the two ledgers · Inspect the low-speed coefficient
Model limits and the code behind the numbers
The idealization is a unidirectional, monochromatic vacuum pulse between inertial frames. This does not model finite spectral bandwidth, diffraction, media, gravitational shifts, detector response, or the recoil caused by unbalanced single-pulse emission. The control bounds are numerical admission limits, not claims of physical impossibility.
The frequency and energy factors come from the existing relativistic wave owners. One accepted, instance-scoped snapshot supplies every displayed quantity. No FrankenSim/WASM execution is claimed.
Wave owners · Cross-paper calculation · Snapshot publication