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Physical Constants Derived from a Common Foundation

MQ derives fundamental and electromagnetic quantities from a small common set of source measures — the fine structure constant, electron mass, Bohr radius, and the defined speed of light — rather than treating each constant as an unrelated empirical input.

• Fundamental length, mass, and time are derived as related realizations of a common count structure rather than introduced as independent Planck-scale definitions.
• Fine structure constant is resolved in fundamental, Planck-like, and classically realized forms through the Frames mapping after accounting for the MQ predicted non-Lorentz length contraction, aka. the Informativity differential.
• Elementary charge is derived through discrete realization and charge count relations rather than accepted only as a measured or defined quantity (reported concordance with the 2022 CODATA value: 2.30σ agreement).
• Electric constant, ε₀, is reduced to MQ fundamental measures, a function of the Frames mapping between the Internal and System Frames.
• Magnetic constant, μ₀, is independently expressed through the same fundamental measures (reported concordance with the 2022 CODATA value: 1.93σ agreement).
• Coulomb’s constant, kₑ, follows from the same elementary charge and electromagnetic geometry rather than constituting an independent empirical parameter.
• Gravitational constant, G, is reproduced across multiple CODATA releases by accounting for the measurement conditions and the non-Lorentz length contraction effect identified by MQ.
• Across the physical constant solutions, the combined 2022 assessment reports 8.25σ agreement; across all 11 tested implementations of the Frames Principle, the reported aggregate assessment is 8.74σ agreement.

These derivations are numerically implemented equation by equation in the supporting spreadsheets, including intermediate values and uncertainty propagation.

A Common Electromagnetic Interaction Bound

MQ identifies an electromagnetic demarcation: a characteristic count at which electromagnetic realization changes form.

Three independent derivation paths converge on essentially the same result:

• fine structure construction: (n_L = 84.6005457);
• reduced Planck construction: (n_L = 84.6005497);
• elementary charge construction: (n_L = 84.6005499).

The convergence of separate fine structure, quantum action, and charge derivations on the same count provides a common structural link among quantities ordinarily introduced through different branches of physics.

Gravity Derived from Discrete Measurement Structure

MQ interprets gravitation as a realized consequence of finite count measurement geometry rather than as a separately postulated force field.

• The apparent gravitational response is derived from the progressive loss of fractional realizable length — the Informativity differential.
• Newtonian behavior is recovered in the appropriate classical limit.
• The equivalence of inertial and gravitational descriptions follows from the same count-based realization structure rather than being imposed as an independent principle.
• The gravitational coupling and the cosmological term arise from the same MQ action and Frames mapping.
• The Einstein field relation is recovered as the continuum expression of an underlying discrete count geometry.
• Conservation of stress-energy follows from Frames mapping symmetry.
• Curvature is treated as an emergent System Frame description; the underlying Internal Frame is dimensionless and vectorless.

This supplies a route from discrete count relations to the continuum mathematics of general relativity while retaining an explicit physical interpretation of the quantities being mapped.

Galactic Rotation Without Non-Baryonic Dark Matter

MQ derives a parameter-free relation between the Newtonian baryonic velocity and the realized observed velocity of a galaxy.

• Flat rotation curves arise from nonlinear realization geometry rather than from an added dark matter halo.
• The known Newtonian baryonic source law is retained.
• No empirical interpolation function is required.
• No galaxy-specific fitting parameter is introduced by the MQ velocity relation.
• The same expression accounts for high surface brightness spirals, classical disk galaxies, gas-rich dwarfs, and low surface brightness galaxies.
• For the Milky Way comparison, MQ reports an RMS residual of 0.65 km/s, 100% of evaluated points within 1.3%, and a Pearson correlation of 0.99946.
• Across the twelve galaxy analysis, the RMS residual ranges from 0.43 to 2.84 km s^-1, remaining below 3 km s^-1 throughout the sample. The mean absolute error ranges from 0.42 to 11.13 km s^-1, while the mean relative error spans 1.26% for the Milky Way to 13.15% for NGC2976. Six of the twelve galaxies reproduce at least 85% of the sampled radial points within 10% of the published rotation curve, and ten reproduce at least 70% of their sampled radial points within that interval.
• The broader evaluation contains a twelve-galaxy sample spanning materially different galactic morphologies and acceleration regimes.
• The radial acceleration relation and baryonic Tully–Fisher behavior emerge from the same realized velocity expression.
• Gravitational lensing can be evaluated using the standard weak-field relation with the MQ realized gravitational mass, without inserting a separate invisible matter distribution.

The physical claim is therefore not merely that MQ can imitate selected rotation curves, but that galactic “dark matter” behavior may be the observable response of bounded measurement geometry to baryonic gravitation. The equation and data are awaiting completion of peer review.

Cosmic Mass-Energy Fractions from Geometry

MQ derives a closed geometric partition of the universe into realized observational domains.

Reported MQ fractions include:

• dark domain analogue: 68.3624% (Planck ΛCDM comparison: 68.34 ± 0.84%);
• unobserved domain analogue: 26.7887% (Planck dark matter comparison: 26.73 ± 0.82%);
• total observable matter domain: 31.6376% (Planck total matter comparison: 31.66 ± 0.84%);
• visible baryonic domain: 4.8488% (Planck baryonic comparison: 4.97 ± 0.82%).

These fractions arise from MQ count geometry rather than being independently adjusted cosmological density parameters. MQ consequently offers a physical interpretation of why the ΛCDM fractions take their observed approximate values, while differing from the ΛCDM interpretation of those fractions. MQ recognizes that all expanding frames have visible, observable, unobserved and dark fractions which are constant over time. Those fractions - in part - correspond to the same ΛCDM fractions, the latter derived as distinct material and/or energy components.

A Frame-Based Resolution of the Hubble Tension

MQ treats the differing determinations of the Hubble constant as distinct realizations of one underlying scalar expansion.

• The CMB-like determination corresponds to the continuous System Frame realization.
• The distance ladder-like determination corresponds to a differently mapped realization associated with the Internal Frame count structure.
• The two observational branches are therefore not required to estimate one identical primitive parameter.
• MQ predicts the lower branch at H_sys = 68.259(19) km s^-1,Mpc^-1.
• MQ predicts the upper branch at H_int = 73.508(21) km s^-1,Mpc^-1.
• The reported comparison of the MQ frame dependent branches with the SPT-3G and PANTHEON+ observational determinations yields a 3.35σ agreement.

The Hubble tension is thus recast as evidence that observational channels sample different frame realizations of the same expansion phenomenon.

Cosmic Microwave Background Predicted from Expansion Geometry

MQ derives the present cosmic microwave background temperature from the universe’s count geometry, expansion history, mass-energy allocation, and the standard blackbody relation.

• MQ present-day CMB temperature: 2.72509 ± 0.00058 K.
• Comparison measurement: 2.72548 ± 0.00057 K.
• MQ present-day radiation energy density: 4.1750 x 10^-14 J,m^-3.
• Observed radiation energy density: 4.17 x 10^-14 J m ^-3.
• MQ quantum epoch effective duration: 363,312 years.
• Comparison recombination era estimate: 379,000 years.

Because the CMB temperature is calculated without fitting the measured CMB temperature itself, MQ presents this result as an independent physical consistency test of its expanding frame geometry.

A Physical Model of Universe Initiation

MQ develops a count-based cosmogenesis in which length, mass, and time not assumed to exist before the universe.

• The pre-physical configuration domain is distinguished from the later Internal Frame of the realized universe.
• Universe initiation follows from a defect in the otherwise uniform configuration domain. Defects are a required mathematical outcome of all open systems.
• A minimum admissible three dimensional structure is derived.
• The quantum epoch has a finite effective duration and terminates according to a discrete geometric condition, a minimum radial length count at which internal referencing first becomes possible.
• Physical length, mass, and time emerge only through the subsequent Frames mapping into the System Frame.
• Expansion, mass allocation, CMB formation, and the present observable domains are developed as stages of the same realization process.
• Singular initial density and an externally imposed inflation field are not required as primitive assumptions.

This provides a physically ordered account of how dimensionless configuration can precede measurable physical quantities without assigning physical units to the pre-physical domain.

Quantum Behavior from Realization and Availability

MQ extends its count-based framework into the foundations of quantum mechanics.

• Quantum probabilities arise from normalized realization availability rather than from intrinsically indeterminate physical objects.
• The Born-rule structure is recovered from the normalization of admissible realized outcomes.
• Complex amplitudes and Hilbert space descriptions emerge as System Frame encodings of the underlying realization structure.
• The Schrödinger and Madelung forms are connected to the mapped availability density and its evolution.
• Measurement outcomes correspond to stable, mutually exclusive realized record states.
• Gauge structure emerges from gradients in System Frame availability rather than being inserted into the Internal Frame.
• The approach preserves quantum statistics while proposing a deterministic configuration-level foundation beneath the probabilistic observable description.

MQ therefore addresses not only the numerical application of quantum equations, but the physical origin of probability, measurement outcomes, and the classical–quantum divide.

One Framework Across Multiple Scales

Taken together, the MQ research program has produced a common mathematical and physical construction that has been applied to:

• the fundamental units of length, mass, and time;
• Heisenberg’s uncertainty principle;
• the fine structure constant and elementary charge;
• the electric, magnetic, Coulomb, gravitational, Planck, and Hubble constants;
• Newtonian gravitation and the equivalence principle;
• general relativity and the cosmological term;
• quantum probability and measurement;
• galactic rotation and gravitational lensing;
• cosmic mass-energy fractions;
• the Hubble tension;
• the origin, age, expansion, and measurable domains of the universe;
• the present cosmic microwave background temperature.

The central result is not any one numerical agreement. It is that the same distinction between a dimensionless, count-based Internal Frame and the physically realized System Frame repeatedly generates testable expressions across phenomena ordinarily treated as separate problems.

Examine the Evidence

MQ makes unusually broad claims, and those claims should be evaluated quantitatively. The Institute therefore provides the underlying publications, derivations, appendices, uncertainty calculations, and equation-by-equation spreadsheets so that each result can be independently inspected, reproduced, challenged, or improved.

Explore the research by subject:

• Physical constants and fundamental measures
• Gravity and general relativity
• Quantum foundations
• Dark matter and galactic rotation
• Cosmology and the Hubble tension
• Universe initiation and the CMB
• Publications, preprints, and supporting calculations