One more Copernican revolution: reconsidering scale-centrism

The Copernican Revolution famously displaced Earth from the center of the cosmos, forcing humanity to confront its non-privileged position in space. However, I propose that we may need another revolution—one that challenges our implicit assumption that our particular spatiotemporal scale occupies a privileged position in physical theory. Just as we no longer consider ourselves spatially central, perhaps we should question whether our scale of observation is fundamentally special.

Scale symmetry as a fundamental principle

What if we adopt the perspective that every scale is equally “central” to understanding reality? This represents a radical extension of the Copernican principle: not only is our spatial location non-privileged, but our temporal and spatial scale of observation may also be arbitrary.

When we observe the universe, we notice a pattern: entities larger than us tend to evolve more slowly, while smaller entities change more rapidly. Galaxies evolve over billions of years, human affairs over decades or centuries, cellular processes over minutes or hours, and subatomic interactions over infinitesimal fractions of a second. This pattern suggests an intriguing possibility: perhaps each scale of reality has its own equivalent of “cosmology” and “particle physics.”

From this perspective, our human-scale physics might be the “particle physics” of larger-scale structures and simultaneously the “cosmology” of smaller-scale entities. The physics we observe at any given scale would represent only a cross-section of a multi-scale reality.

Experimental implications

This philosophical shift has practical implications. If all scales are equally fundamental, we should expect to find “complete” physics at every scale—including emergent principles that aren’t obviously derivable from smaller scales. Rather than assuming that the most fundamental theories must be at the smallest scales (the reductionist view), we might expect fundamental principles to emerge at every scale.

Some experimental signatures might include:

  • Emergent symmetries at macroscopic scales that aren’t present microscopically
  • Physical laws that take the same form across widely different scales (genuine scale invariance)
  • Phenomena that resist complete reduction to more microscopic descriptions

Mathematical formalism

To formalize this philosophical stance, I’ve been developing a mathematical framework that treats scale transformations as a form of coordinate transformation, similar to how relativity treats reference frame shifts.

The core idea is to define a “scale connection” that determines how physical quantities transform across scales. This is analogous to the metric connection in general relativity, which determines how vectors transform across curved spacetime.

Consider a physical quantity $A(x,s)$ that depends on both position $x$ and scale $s$. Its total scale derivative would be:

\[\frac{D A}{D s} = \frac{\partial A}{\partial s} + \Gamma^A_{BC} \frac{\partial B}{\partial s} C\]

Where $\Gamma^A_{BC}$ is the scale connection that encodes how quantities couple across scales.

Cosmological speculations

This framework has intriguing cosmological implications. If the universe is genuinely scale-symmetric in some deep sense, then perhaps the apparent asymmetry between cosmic scales is itself an emergent phenomenon—analogous to how the apparent asymmetry between space directions in our everyday experience emerges from symmetric underlying physics.

One speculative possibility is that the arrow of time and the apparent “direction” of causality from micro to macro scales might be related phenomena, both emerging from more fundamental scale-symmetric dynamics.

Research directions

I’m currently pursuing several research directions based on this framework:

  1. Developing a more rigorous mathematical formulation of scale connections
  2. Investigating whether certain puzzling quantum phenomena (measurement, entanglement) might be reinterpreted through a scale-symmetric lens
  3. Exploring connections to renormalization group theory and effective field theories

Philosophical significance

Beyond its potential scientific value, this perspective offers a philosophically satisfying worldview that reconsiders our implicit scale-centrism. Just as the Copernican revolution humbled humanity by removing Earth from the cosmic center, perhaps this “scale revolution” can humble us further by suggesting that our particular scale of observation isn’t privileged either.

If successful, this approach might help bridge the seemingly disparate worlds of quantum mechanics and general relativity by suggesting that both represent valid perspectives from different scales, neither more fundamental than the other.

The cosmos remains the same, but our perspective shifts—understanding that our view from this particular scale is just one of infinitely many equally valid perspectives on reality.