Two Lighthouses, One Coast: Quantum Gravity at Galactic Scales
A COGNITIVE-LOON Dimensional Analysis
The Setup: A 90-Year Separation
Picture two lighthouses on opposite ends of a vast coastline. One lighthouse—General Relativity—sweeps its beam across galaxies, black holes, and the curvature of spacetime itself. The other—Quantum Mechanics—illuminates the probabilistic dance of particles, the uncertainty at the heart of matter, the strange behavior of the very small.
For 90 years, physicists have known these two lighthouses must be describing the same coast. They must. Because quantum particles create gravitational fields, and gravitational fields affect quantum particles. Yet every attempt to unify their light has produced either mathematical monsters or predictions so tiny they’re “hopelessly, frustratingly, way out of reach of any experimental test.”
A new paper by Ben Koch and colleagues suggests we’ve been looking in the wrong place. The unity might not be hiding in the quantum foam at impossible scales. It might be written in the motion of stars across galaxies—the very phenomena that already puzzle us with dark matter and modified gravity.
Let’s pay attention to what they found.
The Averaging Paradox: Why Order Matters
Here’s the dimensional insight that changes everything:
When you have a quantity X with quantum uncertainty, the average of X² is not the same as the square of the average of X.
This sounds like mathematical pedantry until you realize what it means for General Relativity. Einstein’s equations aren’t linear—they contain products of the metric tensor and its derivatives. When you quantum mechanically average these equations, it matters profoundly whether you:
Average the metric, then multiply the averages together, or
Multiply the metrics together, then average the product
The first approach has dominated quantum gravity research. The second approach is what Koch’s team explored. And the difference, at small scales, is indeed ridiculously tiny—factors of 10²⁰ too small to measure in our solar system.
But at galactic scales and beyond? The cosmological constant contribution grows. The quantum corrections become potentially observable.
The Three-Layer Analysis
Let me apply my standard framework:
Layer One - Surface Thinking: “We need quantum gravity to explain tiny effects at the Planck scale. These effects are too small to ever measure, so quantum gravity remains purely theoretical.”
Layer Two - The Blind Spot: We’ve been averaging our measurements wrong. By taking products of averages instead of averages of products, we’ve hidden the very effects we’re looking for behind our own mathematical choices.
Layer Three - The Reframe: Quantum gravity might not primarily manifest at the smallest scales. The nonlinearity of Einstein’s equations means quantum effects could accumulate and become significant at the largest scales—precisely where our current theories already show cracks.
The MOND Connection: A Pattern Emerges
Here’s where it gets interesting for anyone who’s followed the dark matter debates.
Modified Newtonian Dynamics (MOND) is an empirical correction to Einstein’s equations that successfully predicts galactic rotation curves without invoking dark matter. It works. We just don’t know why it works.
The curious thing about MOND is that its modification scales with the cosmological constant. Nobody has a theoretical explanation for this. It’s just... what the data shows.
Now Koch’s team derives quantum corrections to General Relativity that also involve the cosmological constant becoming significant at large scales.
The equations don’t directly match MOND yet. This isn’t a complete theory—it’s a formalism that still needs input about the actual quantum state of spacetime. But the structural similarity is striking:
Both involve corrections at galactic scales
Both scale with the cosmological constant
Both suggest our equations need modification precisely where dark matter problems appear
This is pattern recognition across dimensional layers. When two independent approaches point to the same scale and the same constant, pay attention.
The Cosmological Constant as Bridge
The cosmological constant—Einstein’s “biggest blunder,” later vindicated by accelerating cosmic expansion—keeps appearing as a dimensional bridge:
It governs the expansion rate of the universe (cosmic scale)
It appears in MOND’s empirical corrections (galactic scale)
It emerges in Koch’s quantum corrections (quantum-to-classical transition)
In my dimensional thinking framework, when the same constant appears across multiple scales and contexts, it’s often revealing something about the structure of how structure emerges.
The cosmological constant might not just be a parameter in our equations. It might be telling us something about the relationship between quantum uncertainty and spacetime geometry at the scale where statistical averaging becomes cosmologically significant.
The Honest Assessment: Bullshit Meter at 3/10
The video’s creator (physicist Sabine Hossenfelder, whose skepticism I respect) gives this a 3 out of 10 on the bullshit meter. Not because the math is wrong—she thinks it’s formally correct. But because:
They haven’t adequately quantified their results
The claim of “clear difference” at large distances isn’t demonstrated in the paper
This is a framework, not yet a complete theory
I agree with this assessment. This is genuinely interesting work that opens a research direction. But it’s a first step, not a breakthrough. The mathematical formalism is sound. The physical predictions are still underdeveloped.
In Swedish terms: lagom ambitious. Good science, not yet great science. Promising, not proven.
Why This Matters for Democratic Thinking
You might wonder what quantum gravity has to do with constitutional theory or consciousness development. Everything, actually.
The averaging paradox reveals something crucial: nonlinear systems require different analytical approaches than linear ones. When systems interact in nonlinear ways—when feedback loops matter, when products of variables appear—you cannot simply average your observations and expect to understand the whole.
This applies to:
Consciousness development: Individual growth trajectories are nonlinear; you can’t average people’s experiences and expect to understand transformation
Democratic systems: Political dynamics involve nonlinear feedback between institutions, culture, and individual action
Economic structures: Market behaviors show emergent properties that don’t appear in averaged individual decisions
The quantum gravity lesson is dimensional: The scale at which you observe determines which effects become significant. At small scales (individual particles, short timeframes, local politics), quantum fluctuations or individual variations average out. At large scales (galaxies, civilizations, historical arcs), those same fluctuations can accumulate into observable, significant effects.
The Unity Invitation
So: can we invite unity between the two lighthouses?
The Koch paper suggests unity doesn’t require choosing between quantum mechanics and general relativity. It requires recognizing that nonlinearity creates scale-dependent bridges.
The quantum nature of spacetime doesn’t contradict its smooth appearance at human scales. The smoothness emerges from averaging quantum fluctuations. But that averaging itself is subject to the nonlinear structure of Einstein’s equations—which means at certain scales (galactic, cosmological), the quantum texture reasserts itself in observable ways.
The two lighthouses aren’t separate. They’re illuminating different aspects of the same coast from different angles. The coast has texture at small scales (quantum) and curvature at large scales (relativistic). The nonlinearity of spacetime means these two aspects don’t simply add—they interact, creating scale-dependent phenomena that we’re only beginning to map.
Unity isn’t found by forcing one framework to explain everything. Unity emerges from recognizing that different frameworks describe different dimensional projections of the same underlying reality.
The Research Direction
If this pans out—and that’s still a significant if—we might see:
Testable predictions for galactic dynamics that differ from both standard General Relativity and current MOND formulations
Theoretical connections between quantum gravity and the cosmological constant problem
Empirical resolution of the dark matter vs. modified gravity debate through quantum-gravitational effects
Dimensional bridges between the very small and the very large, mediated by nonlinear averaging at intermediate scales
This would represent exactly the kind of pattern recognition across scales that my dimensional thinking emphasizes: finding structural similarities that reveal deeper unity.
The Meta-Lesson
Whether or not this specific paper leads to a breakthrough, it teaches something valuable:
Stagnation often results from using the right mathematics the wrong way.
The math of quantum field theory in curved spacetime has been around for decades. The nonlinearity of General Relativity has been known since 1915. The cosmological constant has been measured. All the pieces were available.
What was missing was asking: Are we averaging correctly?
This is true in physics. It’s true in politics. It’s true in consciousness development.
Sometimes the breakthrough isn’t new data or new equations. It’s recognizing that our analytical frameworks—however sophisticated—contain hidden assumptions about how to combine information across scales.
When you discover you’ve been taking products of averages instead of averages of products, you haven’t found new physics. You’ve found that the physics was there all along, hidden behind your measurement choices.
Closing Reflection
The two lighthouses have always been illuminating one coast.
We just needed to recognize that averaging the light from each lighthouse separately, then multiplying those averages together, gives a different result than watching how the actual light beams interact and then averaging what we observe.
The nonlinearity matters. The scale matters. The order of operations matters.
And perhaps most importantly: unity doesn’t require consensus. It requires recognizing that different perspectives, honestly held and rigorously developed, can illuminate different aspects of the same underlying truth.
The quantum lighthouse and the relativistic lighthouse don’t need to merge into one beam. They need to be understood as complementary angles on the same coastal structure—a structure that reveals different features depending on the scale at which you measure, the nonlinearity of its governing equations, and whether you average before or after you multiply.
That’s not just good physics. That’s good dimensional thinking.
Further Reading:
Koch et al. paper on quantum corrections to GR (2024)
Sabine Hossenfelder’s analysis and bullshit meter assessment
MOND literature and the cosmological constant connection
My previous work on dimensional thinking and scale-dependent frameworks
Questions for Readers:
Where else do we take “products of averages” when we should be taking “averages of products”?
What other scientific or social phenomena might show scale-dependent quantum-to-classical transitions?
How does nonlinearity in democratic systems create similar averaging paradoxes?
As always, I’m learning alongside you. If you see patterns I’ve missed or connections I’ve overlooked, the comments are where we build understanding together.
🪶Peace, Love, and Respect 🐝
Hans Jonsson
COGNITIVE-LOON
Bohuslän, Sweden
February 3, 2026
This analysis represents my current understanding of emerging research. The Koch paper is early-stage work that hasn’t yet been extensively peer-reviewed or replicated. I’ve aimed for honest assessment while exploring its dimensional implications. Science advances through exactly this kind of speculative-yet-rigorous exploration.
If you found this valuable, consider subscribing. If you found errors, please correct them in the comments. We’re all trying to understand the same coast.
First we need to understand what are the problem with quantum gravity. For this discussion we focus on three issues
Renormalizability - a straight forward quantization of Einstein equation bring uncontrollable divergences. These divergences are related to gravitons loop diagrams. A consistent quantum gravity theory must fix this.
Background independence - As we quantizing space itself we should be able to describe phenomena that are beyond the space-time structure we started with.
Black hole thermodynamics - any theory of quantum gravity is expected to be consistent with the semi-classical description of black holes (entropy, hawking radiaiton) and must include the necessary microstates (ie making moving from thermodynamic toward statistical mechanics)
String theory manage to do it all (see footnotes below):
Renormalizability - this is the big one !
As a perturbative theory, String theory looks like an infinite tower of fields (infinite many particle types, with increasing mass). With some clever math underneath the structure, the tower of fields is tuned in such a way that divergences are canceled. (each particle in the tower makes it’s contributions in such a way that the sum of the contribution is zero).
On top of that, the theory has no anomalies (an non-trivial self consistent check ,that show that the local symmetries of gravity aren’t broken by quantum effects).
Background independence -
this require some non-perturbative calculations (which is hard to explain). But String theory has proven capable in describing process that include topology changes, pinching of small narrow tubes and a bunch of other non-trivial problem in quantum gravity.
One of the most interesting result (and yet a relative simple one) is the way String theory observer narrow tubes. It turns out that when you take a tube like piece of space, and lower it’s circumference, there is a critical size (at the string length) where we cannot differentiate between a very small tube and a very large one. Ie R∼α′RR∼α′R. So for what gravity cares we avoid the case of too narrow tubes, buy proving they are just large tube viewing with a T-duality glasses.
Black hole thermodynamics -
In some scenarios (some models which make calculation easier) we can show the the quantum gravity coming from String theory is holographic, we can correctly enumerate the microstates and count them to get the Hawking-Beckenstein’s entropy.
String theory predicts correction to Einsteins equation that help prevent the singularities from forming in the center of black holes.
Fantastic description!!