Did Einstein ever question the constancy of the gravitational constant 'G'? The answer, surprisingly to some, is yes—at least in principle.

While standard General Relativity (GR) treats 'G' as a fixed universal constant, Einstein, particularly in the later stages of his work, remained open to the idea that such constants might not be fundamental. In Kaluza–Klein theories, where gravity and electromagnetism are unified in higher dimensions, 'G' could emerge from the geometry of extra spatial dimensions. Likewise, Mach’s Principle, which deeply influenced Einstein, suggested that local physics (including inertia and gravitation) might depend on the large-scale distribution of matter—hinting at a variable 'G' in different cosmic regimes.

Later thinkers advanced this idea more formally. Dirac's Large Numbers Hypothesis (1937) proposed that 'G' might decline over cosmological time. Brans–Dicke Theory (1961), a scalar-tensor framework, allowed 'G' to vary with a scalar field, aligning more fully with Machian ideas Einstein appreciated but did not implement in GR.

In short: while Einstein never formalized a variable 'G', he did consider that such constants might arise from deeper unifying principles, and thus could vary under extreme or cosmological conditions.

ECM and the Reframing of Time and Motion

From the standpoint of Extended Classical Mechanics (ECM)—a contemporary framework challenging some relativistic assumptions—this openness is pivotal. ECM builds a broader picture where frequency, not time, is the primary physical quantity.

This shift is crucial in addressing the so-called "twin paradox" from special relativity, where a traveling twin is predicted to age more slowly than a stationary one due to time dilation.

In ECM, this scenario is reinterpreted. Rather than invoking metaphysical "dilation" of time, ECM explains that what actually occurs is time distortion—a measurable shift in the behaviour of physical clocks due to frequency and phase change, governed by:

Δt =x°/(360°f)

Here, 'f' is the physical oscillation frequency, and 'Δt' arises from accumulated phase shift. Importantly, cosmic time in ECM is absolute and unaffected by motion or gravity; it is the clocks—physical systems subject to deformation, acceleration, or field variation—that experience distortion. Hence, no true aging difference occurs between the two observers—only a discrepancy in recorded time due to altered oscillatory behaviour.

Reclaiming Physical Realism

Einstein's contributions rightly revolutionized physics, but ECM urges a re-visitation: what if time is not a fluid that bends, but a reconstruction from periodic phenomena? What if frequency, phase continuity, and energy dynamics provide a more foundational grasp of what clocks measure?

Rather than dismissing Einstein, ECM builds upon the same instinct that led him to question Newton’s absolute space—and later, even the constancy of 'G'—to suggest that 'our understanding of time itself may need to evolve.'

For ongoing research on ECM and its foundational propositions, see:

Technical Report Appendix 24: The Physical Primacy of Frequency over Time -Ti...

DOI: https://doi.org/10.13140/RG.2.2.30764.17288

Regards

Soumendra Nath Thakur