The next analysis, Dark Matter, will be even more interesting in terms of scale blindness. Because there, for the first time, we will examine the scale relationship between an “observed effect” and an “assumed entity.”
Now we come to one of the most interesting test areas of the scale blindness hypothesis.
The fundamental question here is this:
Is dark matter really a new physical entity?
Or is it a scale blindness that emerges because we try to explain dynamics working at different scales with the same law?
We need to distinguish between these two possibilities.
Step 1: Observation Scale
First, let’s write down what is actually observed.
What is observed:
- Galaxy rotation curves
- Cluster dynamics
- Gravitational lensing
- Large-scale structure formation
That is, what is directly observed are:
magnitudes of the type v(r) and g(r).
What is observed:
Is not a “dark matter particle”.
What is observed:
Is a gravitational effect different from what is expected.
Scale Map
Scale-0
Local observations
- Solar System
- Binary stars
- Planets
Here, Newton and Relativity are very successful.
Scale-1
Galaxy scale
Approximately:
10^20 − 10^21 m scale.
The first anomalies appear here.
Scale-2
Galaxy clusters
Larger scale.
Scale-3
Cosmic web
Large-scale structure of the Universe.
The Emergence of the Problem
Calculation:
Is done with F = (GMm) / r^2.
When visible matter is used:
the expected velocity (v_expected) emerges.
But the measured velocity:
v_measured is larger.
This difference is interpreted as follows:
there is invisible mass called M_missing.
And this turns into dark matter.
The Scale Blindness Question
The critical question here:
Is Newton’s law universal?
Or is the 1 / r^2 behavior valid only at specific scales?
These two interpretations are completely different from each other.
Approach A
Standard Cosmology
Assumption:
The law is correct.
Therefore:
There is missing matter.
That is, the Δg anomaly
↓
is explained as additional mass.
In terms of scale:
The local law is preserved.
A new entity is added.
Approach B
The Possibility of Scale Blindness
Assumption:
No new matter.
The law is scale-dependent.
That is:
It could be g = g(r, λ).
Here:
λ is the scale parameter.
In this case:
The relationship that is correct at the local scale might be changing at the galaxy scale.
Why is MOND Interesting?
MOND (Modified Newtonian Dynamics) was born exactly from this question.
The basic idea:
Newton might change at very low accelerations when a is less than a_0.
This is interesting.
Because for the first time:
not “missing matter”
but “scale transition”
is being questioned.
Scale Blindness Test
The hypothesis can be written as follows:
H0
Dark matter is real.
There is no scale blindness.
H1
At least a portion of dark matter
arises from the misinterpretation of scale-dependent dynamics.
This test can be conducted directly.
Risky Zone in Terms of the Scale Map
Let’s look at this chain:
Local experiment
↓
Local law
↓
Galaxy
↓
Universe
↓
Dark matter
Here, the scale grows at each step.
The scale blindness hypothesis asks this:
How many scales up did we carry the equations calibrated at the local scale?
This is a very important methodological question.
Historical Similarity
This situation is surprisingly similar to the aether problem.
In aether:
There was the assumption “Mechanical wave → Medium is required”.
Here:
There is the assumption “Local gravity → Works the same at every scale”.
Of course, this does not show that dark matter is wrong.
But from the perspective of scale blindness, it produces this warning:
Before accepting an unobserved entity, test the scale transitions themselves.
From a Fractal Perspective
Expressing it closer to my approach:
The standard model assumes this:
G = constant
and
F ∝ 1 / r^2
are valid at every scale.
But in a fractal or multi-scale universe:
It could be G = G(λ)
or
D = D(λ).
That is, the effective dimension or the effective interaction coefficient can change depending on the scale.
If this is the case:
a portion of the effect interpreted as dark matter may actually stem from a scale transition.
Intermediate Conclusion
In terms of scale blindness, the dark matter analysis yields the following result:
| Question | Result |
| Was dark matter observed directly? | No |
| Was an anomaly observed directly? | Yes |
| Can the anomaly be explained with new matter? | Yes |
| Can it be explained with scale-dependent dynamics? | In principle, yes |
| Is it a suitable area for a scale blindness test? | Very suitable |
| Scale blindness risk | Very high |
Among the three analyses we have done so far (Relativity, QFT, Dark Matter), the strongest candidate area for the scale blindness hypothesis, in my opinion, is the Dark Matter problem. Because here, for the first time, there is a direct “scale jump” between the observed effect and the explanation.