Questions about hydrogen in SMM/DTT

The material here establishes detailed consequences of a declared Coulomb model and explains the proposed temporal construction leading toward it. The central source-to-Hamiltonian correspondence remains an open obligation in Paper 12. The status page distinguishes that task from the completed atomic calculations and from the further spin, radiative and nuclear terms. [Hydrogen II]

It connects several parts of the programme through one explicit physical system. The same coefficients must determine the atom’s size, binding energy, spectrum and response. That gives collaborators concrete quantities to derive together, and helps readers identify where an interpretation has become a mathematical or physical claim.

The presentation uses six nested inner generative roles and a seventh outer completion. Their role is hierarchical. A physical correspondence must explain how the completed records support the familiar spatial and clock observables. It should also explain how the atomic quantum numbers arise, rather than equating those labels with generative levels by naming alone.

The stationary 1s benchmark is described by a normalized wavefunction, not a specified circular trajectory. Its probability density is spherically symmetric and its probability current vanishes for the usual real spatial wavefunction, while momentum variance remains nonzero. Circular Bohr orbits can illustrate certain historical scale relations, but they are not the full quantum ground-state description. [Relative-speed derivation]

They describe different quantities. The position density is probability per unit volume. The radial distribution multiplies that density by the shell area, 4πr², to give probability per unit radius. For 1s the density is largest at zero, while the radial distribution peaks at r = aμ. Use the probability explorer to compare both with cumulative probability.

For the 1s relative-coordinate state, the probability inside one characteristic length is 1 − 5exp(−2), approximately 0.3233. A radial peak therefore does not imply that half the probability lies inside that radius. The mean radius is 1.5aμ and other measures of atomic size answer different questions. The ground-state article derives these results.

Neutrality fixes a charge relation. Binding concerns the spectrum of a physical energy operator relative to a separation threshold. A neutral pair without an attractive interaction need not have a bound state. A temporal construction must supply the interaction and dynamics in addition to a cancelling charge character. [Hydrogen I]

It means the proposed initial record construction is defined without using the measured fine-structure constant or spectroscopy-derived scales as inputs. It does not mean the physical hydrogen atom has no electromagnetic interaction. The later correspondence must explain how the independently supplied charged-sector response enters the effective atom. [Hydrogen I]

The structural integer and the physical coupling are separate results. The supplied canonical-complexification draft introduces a matching problem and a correction slot beyond the exact count. A physical prediction needs the relevant electromagnetic sector, its normalization and a calculated correction in a stated convention. Fitting an offset to hydrogen data would make that datum part of the calibration. [Canonical complexification]

For the Coulomb model, the relative RMS speed in a level with principal number n is αc/n. In the centre-of-mass frame, the electron RMS speed has an additional μ/mₑ factor. These statements concern momentum variance and the declared nonrelativistic model; they do not assert a literal circular trajectory for every state.

Both constituents move. Separating their free centre-of-mass motion leaves a relative-coordinate kinetic term containing μ = mₑmₚ/(mₑ + mₚ). Taking the proton mass to infinity recovers μ = mₑ. The scale explorer shows how this finite-mass correction changes the characteristic radius and the gross binding energies together.

An energy difference supplies a possible photon energy, but a transition requires an interaction with a nonzero relevant matrix element. The leading one-photon electric-dipole approximation has angular and parity selection rules. The 2s-to-1s interval, for example, is not an allowed E1 transition; a two-photon process requires a different calculation. [MIT quantum physics]

First check the convention. The explorer calculates vacuum wavelengths using a gross reduced-mass model. A table may quote air wavelengths, a resolved fine-structure component or an unresolved multiplet. Precision comparison also needs radiative, recoil, nuclear and other relevant contributions. A difference between unlike quantities is not a new-physics residual. [NIST lines] [NIST data notes]

The section explains the radiative problem and the required physical ingredients. The supplied radiative draft identifies important coefficient calculations as targets or open work. A dimensional estimate or the form of a logarithm does not supply all coefficients, finite terms and cancellations needed for a complete result. [Hydrogen III]

A contact-like contribution may vanish in the upper D state while remaining in a lower S state. For an interval a→b, the change is (δEᵦ − δEₐ)/h. Thus a 2S-to-nD interval retains minus the 2S contribution in the simple model. The residual explorer makes this endpoint dependence explicit.

No. They are synthetic values generated by the displayed level-shift rule and user-chosen amplitude. Their purpose is to demonstrate correlated interval changes, endpoint subtraction and cycle closure. Interpreting an actual anomaly would additionally require a complete reference calculation, experimental uncertainties and a derived physical correction model.

Yes. If changing another allowed parameter produces the same vector of interval changes, the chosen observables do not distinguish those explanations. A short-range S-state effect can overlap with finite-nuclear-size contributions. The differential article explains this using response vectors and projection away from nuisance directions. [Differential programme]

Philosophy can clarify the relation between generative ontology, physical clocks, quantum states and completed observations. It can ask what an explanation adds beyond its effective equations and which claims depend on a successful source correspondence. Those questions become sharper when attached to explicit atomic calculations and hypotheses.

Choose a definite target: reproduce a calculation, identify a counterexample, improve a convergence argument, develop an interaction model or clarify an explanatory claim. State the hypotheses and the exact result. The collaboration page welcomes work from physics, mathematics and philosophy and links to the main contact page.

Cite the website when referring to its explanation, explorer or worked example, using the page citation and revision date. Cite the original paper when discussing a result attributed to that paper, identifying its version and section. The reference library labels supplied manuscripts as working drafts and links separately to related journal records.