The physical comparison comes first

The principal MQ source is the current special-relativity preprint, especially the protocol preceding Equation (22). Choose an inertial observer description and two events on one uniformly moving clock’s path. Synchronized observer clocks assign coordinate times to those events. Their difference defines the observer window, while the moving clock’s own reading difference gives the proper time accumulated along that path. [1]

The at-rest benchmark is the advance that a calibrated clock at rest in the observer’s inertial system would accumulate during a window of the same coordinate duration. It is not an alternative name for the moving clock’s actual proper duration. The benchmark uses local calibration in the source’s reference convention; the observed parameter reports the moving clock’s accumulated advance. [1]

Both physical inertial systems belong to the System Frame. The Internal Frame is MQ’s discrete count-configuration domain. Local and observed subscripts label measurement roles within the physical comparison; they do not turn the observer into one MQ domain and the clock into the other. Two inertial systems can have nonzero relative velocity even when neither is accelerating. [1] [2]

Table 1 records the operational assignments needed before interpreting a time factor. The scalar alone does not say which two events were compared or how their timestamps were obtained. Figure 1 gives a concrete example without requiring the moving clock to return to its starting point.

Count and speed descriptions of the same ratio

Let ${\mathrm{𝑛}}_{\mathrm{𝐿}\mathrm{𝑚}}$ be the dimensionless count associated with motion displacement and ${\mathrm{𝑛}}_{\mathrm{𝐿}\mathrm{𝑐}}$ the positive light-travel count, both accumulated over the same reference interval. Let $\mathrm{𝑣}$ denote the relative speed and $\mathrm{𝑐}$ the speed of light. Common length and elapsed-time reference factors cancel, giving the source relation in Equation (1a). [1]

The common interval is part of the premise. A motion count from one interval and a light count from another cannot be inserted into this ratio without an additional conversion. The light-travel count belongs to the selected interval; it is not a universal dimensionless maximum for every elapsed duration. No momentum, angular or cosmic-age parameter is needed for the present clock comparison. [1]

Let ${\mathrm{𝑡}}_{\mathrm{𝑙}}$ denote the at-rest calibrated benchmark advance and ${\mathrm{𝑡}}_{\mathrm{𝑜}}$ the moving clock’s proper-time advance reported under this fixed-window protocol. Both have units s. Equation (2b) is the source’s multiplying time relation with the equivalent count and speed factors shown together. [1]

The dimensionless counts ${\mathrm{𝑛}}_{\mathrm{𝑇}\mathrm{𝑙}}$ and ${\mathrm{𝑛}}_{\mathrm{𝑇}\mathrm{𝑜}}$ encode these same benchmark and moving-clock advances using the same fundamental time reference. That reference cancels from their ratio, leaving Equation (3c). Their source-specific roles here must not be confused with similarly written counts in quantum-epoch discussions. [1]

The common domain is a positive light reference and a nonnegative motion count strictly smaller than it. In speed language, motion is slower than light. The factor is positive in this domain and equals one at rest. Its formal approach to zero at the equal-count boundary does not describe an inertial rest frame for a massive clock at light speed. Continuous realized outputs need not be independently integer primitive inputs. [1]

Reversing which duration is specified

The source protocol fixes the observer window first. If the question instead gives the moving clock’s actual proper duration and asks for observer duration between those same events, solve Equation (2b) for the benchmark/window parameter. The result has the reciprocal orientation in Equation (4d). This is algebraic rearrangement within the same strictly positive-factor domain, not a different prediction. [1]

Labels (1a)–(4d) belong to this Brief. They correspond to the source’s count ratio in Equation (17), clock relation in Equation (22), count form in Equation (2), and the inverse of the same clock relation. Local and observed roles remain those defined above. Calling both quantities simply time, without stating their event and clock assignments, hides the reason the factor changes position.

Table 2 also checks the roundtrip. Starting with the 10-second observer window gives 8 seconds on the moving clock; using that 8-second duration in the inverse relation returns 10 seconds. Holding 10 seconds fixed in both questions changes the chosen event pair. It does not compare the same two events twice.

Worked clock advances and the speed dependence

Table 3 uses a 10-second observer window and ideal constant speeds. Values are calculated from Equation (2b), with rounded results identified. They are theoretical illustrations, not measured data or evidence that the adopted count normalization is independently verified. Figure 2 plots the same dimensionless advance ratio.

Why units alone do not specify a clock

The source obtains a time-valued scalar relation by dividing the corresponding length measures by light speed. The result retains the same multiplying factor. That is a dimensional and algebraic statement. Identifying one quantity with an at-rest benchmark and the other with a moving clock’s proper-time advance requires the additional protocol already described. [1]

The length comparison has its own prescription. Longitudinal endpoint positions must be simultaneous in the measuring observer’s inertial system. A clock comparison instead uses two events along one clock’s path. Sharing a scalar factor does not make those measurement procedures identical or derive the full Lorentz transformation. The source explicitly supplies Lorentz-compatible kinematics for the interpretation. [1]

MQ’s separate Informativity differential concerns a non-Lorentz finite-count realization effect. It must not be added to, or identified with, the motion factor without a source-supported derivation. The clock account here introduces no intrinsic mechanism operating in a pre-existing physical time inside the dimensionless configuration domain. [1]

What an actual clock test must control

Reporting received ticks is not automatically measuring the proper-time advance in Equation (2b). Signals take time to propagate, and a receiver can see frequency changes from changing separation and Doppler effects. The analysis must relate received data to the specified clock events. Gravitational potential differences and acceleration histories also require their appropriate treatment rather than silent inclusion in a uniform-motion formula. [1]

Independent evidence for relativistic clock behavior predates this MQ source version. Chou and colleagues reported optical-clock measurements in 2010, including motion-dependent shifts at speeds below 10 m/s and a separate height-dependent comparison. Their controlled trapped-ion motion was harmonic; its analysis is not identical to the ideal constant-speed path used in Table 3. The experiment supports relativistic clock effects, not this later MQ-specific count or normalization assignment. [4]

Table 4 separates the established relativistic effect from the proposed count interpretation. A discriminating MQ test would require a separately specified observable consequence beyond the already shared factor, together with the relevant calibration, uncertainty and experimental controls. The broader framework’s publication does not independently certify this clock assignment. [5] [6]

Chronology and interview guidance

October 13, 2026 is the recorded revised source version for this archive entry. This Brief was prepared October 27, 2026 using the current public explanation and operational qualifications. Journal publication of the present MQ special-relativity version is not established. The worked arithmetic is not a new experimental result or a departure from standard relativistic clock behavior.

For an interview, request the two boundary events, synchronization convention, physical clock readings and the interval fixed before calculation. Ask how the source maps fundamental counts to the corrected observable, and which proposed test would distinguish that assignment from ordinary special relativity. A clear protocol makes the claim reportable without treating a familiar-looking factor as a complete physical derivation.