The Mystery of Constants
Fundamental physical constants are the "DNA" of reality—unchanging values that appear everywhere in our equations yet seem to have no deeper explanation. Why is Planck's constant ℏ = 1.054571817 × 10-34 J·s and not something else? Why does light travel at exactly 299,792,458 m/s? Why is Newton's gravitational constant G = 6.674 × 10-11 m³/(kg·s²)?
The standard approach in physics treats these as empirical facts: we measure them, plug them into our equations, and move on. But this sidesteps a profound philosophical question: Are these values contingent accidents of our universe, or are they necessary consequences of something deeper?
Some physicists, particularly in string theory, have suggested that constants might not need derivation at all—that they could be part of a "landscape" of possible universes, each with different values. Others seek a theory that would explain why these specific values and no others. ART explores a middle path: these constants aren't arbitrary, but understanding them requires shifting our question from "why these values?" to "why this recursive structure?"
One Measurement to Rule Them All
In 2020, a group of physicists published a fascinating paper arguing that in principle, you only need one type of measurement device to describe everything in the universe: a clock. Building on earlier work by Bill Unruh (who proposed the "three-clock experiment" for measuring distances using special relativity) and the Kibble balance approach to measuring mass, they showed that with sufficiently precise clocks, you could measure distances and masses without needing the speed of light or Planck's constant as separate inputs.
The key insight: time could be the fundamental measurement, with space and mass emerging as derived quantities. Like a musical score that encodes rhythm, pitch, and dynamics in a single notation system, time might be the universal notation for all physical quantities.
ART goes deeper: It's not just that all measurements can be expressed through time—it's that time itself is a projection phenomenon. In the Frequency Domain, there is no time as we experience it. What we call "time" emerges when recursive Archeonic patterns project into the Projection Manifold. The imaginary axis of the 6-dimensional complex space (ℂ³) becomes the temporal dimension we measure.
This suggests that measurement unity isn't just a practical convenience—it's a hint at ontological unity. The constants aren't separate facts about separate aspects of reality; they're different expressions of how recursive identity resolves into projected form.
Planck's Constant and the "Frame Rate" of Reality
Planck's constant ℏ (h-bar) represents the smallest meaningful "step" that physical processes can take—what physicists call the quantum of action. In classical physics, action is energy multiplied by time. But at the quantum level, action comes in discrete chunks of size ℏ. You can't have half a quantum of action, just as you can't play half a beat in music—the fundamental rhythm has a minimum unit.
The ART perspective: From the ontological starting point 0 = 0, reality must express itself through balanced, recursive waveforms—what ART calls Archeons. Each Archeon is defined by Euler's formula: eiθ = cos θ + i sin θ. The minimal nontrivial expression of this identity is one complete phase rotation: Δθ = 2π.
This 2π cycle on the Riemann sphere isn't arbitrary—it's the smallest closed loop that preserves analytic continuity. ℏ emerges as the "cost" of projecting one complete Archeonic phase loop from the frequency domain into spacetime. It's not that ℏ could have been different; it's that one full recursive rotation is the minimum nontrivial way reality can express the identity 0 = 0 as a dynamic process.
Planck Time and Length: The "FPS" of the Universe
From Planck's constant, we can derive the Planck time (tP ≈ 5.39 × 10-44 seconds) and Planck length (lP ≈ 1.62 × 10-35 meters). These aren't just small numbers—they represent the fundamental "grain" of spacetime, the resolution limit of reality itself.
Think of it like the frame rate of a video. A movie might run at 24 frames per second—you can't have a meaningful interval shorter than 1/24th of a second within that medium. Similarly, Planck time is the "FPS of the universe": the shortest duration in which anything meaningful can happen. Below this scale, the very concepts of "before" and "after" become undefined.
Planck length works the same way for space. It's the fundamental pixel size of reality. Just as you can't meaningfully zoom in beyond the pixels on a screen, you can't probe distances smaller than the Planck length without the structure of spacetime itself breaking down.
In ART: These scales aren't arbitrary cutoffs. They're the natural boundaries where projection from the 6D complex manifold reaches its resolution limit. Below the Planck scale, you're no longer dealing with spacetime—you're looking at the pure frequency structure of Archeons before they've been projected. The Planck scales mark the threshold where the "what it appears to be" (spacetime) transitions into the "what it actually is" (recursive harmonic identity).
The Speed of Light: Spacetime's Speed Limit
The speed of light c = 299,792,458 m/s is perhaps the most famous constant in physics. Einstein's relativity revealed that it's not just how fast light travels—it's the maximum speed at which any information or influence can propagate through spacetime. Nothing with mass can reach it; only massless particles like photons naturally move at this speed.
But why this particular value? And why is there a cosmic speed limit at all?
The ART interpretation: The speed of light is the speed limit of the projection manifold itself—the maximum rate at which recursive patterns can propagate through spacetime before they must convert back into pure frequency components.
In ART's framework, spacetime is not a fundamental arena but a projected slice of a 6-dimensional complex manifold (ℂ³). Each spatial dimension is paired with an imaginary orthogonal axis: (x + ix′), (y + iy′), (z + iz′). What we experience as "spacetime" is the real projection of this complex geometry.
Motion through space involves rotation through this complex manifold. As an object moves faster, its projection gradient tilts more steeply through the real-imaginary axes. At the speed of light, the projection reaches maximum tilt—the boundary where the pattern can no longer maintain coherent form in spacetime and must exist purely as frequency propagation.
This is why massless particles travel at c: they have no rest frame in spacetime. A photon is pure frequency propagation, a ripple in the projection manifold that never "settles" into a stable projected form. Massive particles, by contrast, have internal recursive structure (rest mass) that requires a stable projection, which is only possible below c.
The speed of light thus connects spacetime to the frequency domain: it's the conversion factor between being-in-time and being-as-frequency. Not a speed of travel, but the rate at which projected identity can propagate before losing its grip on spacetime.
The Gravitational Constant: How Reality Bends
Newton's gravitational constant G = 6.674 × 10-11 m³/(kg·s²) determines the strength of gravity: how much spacetime curves in response to mass-energy. It appears in both Newton's law of gravitation and Einstein's field equations, acting as a conversion factor between matter and geometry.
Interestingly, G is the least precisely measured of the fundamental constants—we know it to only about 5 significant figures, compared to 9 or 10 for others. This isn't because physicists aren't trying; gravity is simply extraordinarily weak compared to other forces, making precision measurements challenging.
In ART's framework: G isn't fundamentally about force or attraction. It's the curvature–response coefficient—a measure of how much Archeonic phase curvature (in the 6D complex manifold) translates into spacetime curvature when projected.
Think of it like a spring constant: if you compress a spring, how much does it push back? Similarly, G tells you: if you concentrate recursive tension (what we perceive as mass-energy) in a region, how much does spacetime bend in response? The value of G reflects the "stiffness" of the projection manifold—how resistant it is to geometric deformation.
In ART's view, gravity isn't a force between masses but an alignment phenomenon: matter is Archeonic structure with high phase coherence, and this coherence creates gradients in the projection manifold that other structures naturally follow. G quantifies this gradient-response relationship.
The Unity of Constants: An Open Exploration
What's striking about ℏ, c, and G is how they interweave. Combine them in various ways and you get the Planck scales—the fundamental units of time, length, mass, and energy. These aren't independent facts; they're facets of a unified structure.
For example:
- Planck time: tP = √(ℏG/c⁵)
- Planck length: lP = √(ℏG/c³)
- Planck mass: mP = √(ℏc/G)
- Planck energy: EP = √(ℏc⁵/G)
These relationships hint that ℏ, c, and G aren't truly independent. They're different expressions of the same underlying geometry.
ART's approach: Rather than treating these as separate mysteries to solve, ART explores how they might emerge together from the structure of recursive identity projected through a 6-dimensional complex manifold. The method is still being developed—similar to how string theory continues to explore whether constants can be derived or whether they're landscape parameters.
The journey is open. What ART offers is not a completed derivation but a framework for thinking about these questions: ℏ as the quantum of recursive action, c as the projection manifold's coherence limit, and G as the curvature-response coefficient. Whether these can be fully derived from first principles, or whether they're structural parameters of our particular projection, remains to be determined.
Why This Matters
The question "why these constants?" is ultimately a question about the nature of explanation itself. What would it mean to truly explain why ℏ, c, and G have the values they do?
For some physicists, the answer might be anthropic: these values are what they are because if they were significantly different, we wouldn't be here to ask. For others, it's a matter of finding the right mathematical structure—perhaps string theory's additional dimensions, perhaps something else—from which the values follow necessarily.
ART offers a third path: shift the question from "why these values?" to "why this recursive structure?" Instead of asking why ℏ = 1.054... × 10-34, ask why reality expresses itself through phase cycles, projection, and recursive closure. The specific numerical values emerge from translating ontological structure into measurement units (meters, seconds, kilograms), but the deeper question is about the geometry of identity itself.
This is a philosophical stance as much as a physical one. It suggests that the constants aren't arbitrary contingencies but also aren't necessarily derivable in the way we might first imagine. They're more like the axioms of geometry—not arbitrary, yet not provable from something more basic, because they define the structure within which "proof" has meaning.
The exploration continues. What ART contributes is a framework for thinking about these deep questions, connecting physical measurement to ontological structure in a way that might, eventually, help us understand not just the "how much" but the "why" of fundamental constants.
To see how ART approaches other fundamental questions and makes specific predictions about observable phenomena, explore ART's testable predictions and how this framework attempts to address the unification problem in physics.