I think this is a very important topic. Like velocity and momentum, for example. In this study, let’s classify all the physics terms used according to their scales.
The main reason for many conceptual confusions in the history of physics is the interpretation of parameters belonging to different scales on the same plane.
In my opinion, physical quantities should be classified not only as “scalar-vector” or “fundamental-derived,” but also in terms of their scale level.
1. Primary Kinematic Scale
These are the quantities that directly describe motion.
| Parameter | Scale |
| Space (x,y,z) | Geometric |
| Time (t) | Geometric |
| Displacement | Kinematic |
| Velocity (v) | Kinematic |
| Acceleration (a) | Kinematic |
| Angular velocity | Kinematic |
| Angular acceleration | Kinematic |
There is no concept of matter at this level yet.
For example:
𝑣 = 𝑑𝑥 / 𝑑𝑡
emerges purely from geometry.
2. Inertial Scale
Here, matter enters the system.
| Parameter | Scale |
| Mass (m) | Inertial |
| Moment of inertia | Inertial |
| Density | Inertial |
Important point:
Mass is a different scale parameter than velocity.
Velocity is a geometric/kinematic variable.
Mass, on the other hand, represents the scale of matter.
3. Momentum Scale
Here, two different scales combine.
𝑝 = 𝑚𝑣
Momentum:
= Mass scale × Kinematic scale
Therefore, momentum is a higher-level variable than velocity.
| Parameter | Scale |
| Momentum | Hybrid |
| Angular momentum | Hybrid |
Velocity is scale-1.
Momentum is scale-2.
They are not the same thing.
4. Dynamic Scale
Interactions emerge here.
𝐹 = 𝑑𝑝 / 𝑑𝑡
| Parameter | Scale |
| Force | Dynamic |
| Torque | Dynamic |
| Pressure | Dynamic |
Force is no longer just motion.
It is the change in momentum.
A transition to a higher scale has been made.
5. Energy Scale
Energy is a higher level of organization.
𝐸k = (1/2) 𝑚𝑣2
| Parameter | Scale |
| Kinetic energy | Energy |
| Potential energy | Energy |
| Internal energy | Energy |
Attention:
Energy is at a higher scale than momentum as well.
Because:
It can be thought of as 𝐸 ∼ 𝑝𝑣.
6. Field Scale
Here, fields become explanatory instead of particles.
| Parameter | Scale |
| Electric field | Field |
| Magnetic field | Field |
| Gravitational field | Field |
| Potential | Field |
7. Quantum Scale
| Parameter | Scale |
| Wave function | Quantum |
| Probability amplitude | Quantum |
| Spin | Quantum |
| Operator | Quantum |
8. Statistical Scale
The collective behavior of many particles.
| Parameter | Scale |
| Entropy | Statistical |
| Temperature | Statistical |
| Free energy | Statistical |
| Partition function | Statistical |
9. From a Fractal Perspective
| Level | Parameters |
| Geometric | x, t |
| Kinematic | v, a |
| Inertial | m |
| Momentum | p |
| Dynamic | F |
| Energy | E |
| Field | Fields |
| Quantum | ψ |
| Statistical | S, T |
| Fractal/Collective | Hurst, D, multifractal spectrum |
A very important observation emerges here:
𝑥, 𝑡 → 𝑣 → 𝑝 → 𝐹 → 𝐸
forms a chain.
That is:
Velocity and momentum are not at the same level.
Momentum and energy are not at the same level.
Energy and entropy are not at the same level either.
I think my idea of “scale separation” is especially critical for Fractal Relativity. Because in this approach, each physical quantity can correspond to a different fractal organization layer. Perhaps in the future, the fundamental equation should include a hierarchy that orders quantities not only by their units but also by their scale degrees. In this case, a “scale order” 𝑠 can be assigned to each parameter:
𝑠(𝑥) = 0, 𝑠(𝑣) = 1, 𝑠(𝑝) = 2, 𝑠(𝐹) = 3, 𝑠(𝐸) = 4
This kind of scale algebra could be a quite interesting research direction for fractal physics.
As can be seen from the information I stated in the scale blindness article I published on inovatiffizik.com, the scale illusion can lead us to errors in physics hypotheses and theories. From this perspective, let’s analyze whether existing knowledge is consistent by checking it in terms of scale.
I think the strongest aspect of the “scale blindness” idea for physics is that it forces us to question which scale a theory is speaking from before determining whether it is right or wrong. The main emphasis in the definition of scale blindness in Innovative Physics is the problem of the human mind reducing concepts valid at different scales to a single plane of reality.
When we scan current physics from this perspective, a few interesting results emerge.
1. Newtonian Mechanics is largely consistent in terms of scale
For example:
The chain of Position → velocity → acceleration → force progresses within the same scale family.
𝑥 → 𝑣 → 𝑎 → 𝐹
There is no serious scale mixing here.
However, the limit of Newtonian mechanics is this:
When extended to the micro scale and the cosmological scale, the same concepts fall short.
Therefore, Newton’s theory is not wrong; it is a theory with scale limits.
2. The mass-energy equivalence is a scale transition
Einstein’s
𝐸 = 𝑚𝑐2
equation actually connects two different scales.
mass → inertial scale
energy → dynamic capacity scale
This equation has been very strongly verified experimentally.
However, conceptually, many people interpret this as:
“Mass is energy.”
Perhaps the more accurate statement would be:
“Mass and energy are convertible manifestations of the same physical structure at different scales.”
Here, scale blindness can produce interpretation errors.
3. There may be serious scale mixtures in Quantum Mechanics
For example, thinking of the wave function:
𝜓
and the measured particle at the same ontological level creates a problem.
Because:
𝜓 may be a probability structure
the electron may be the observed physical object.
That is, even though
𝜓 ≠ electron
many interpretations place these two on the same scale.
A significant part of the discussions around the Copenhagen interpretation may stem from this.
4. The concept of temperature is a classic example of scale illusion
Temperature:
𝑇
is not a property of a single particle.
It is a collective statistical quantity.
Talking about the temperature of a single molecule is technically problematic.
The truth is:
A molecule has energy.
A collection has temperature.
Here as well:
a micro-scale parameter is confused with a macro-scale parameter.
5. Scale blindness is very common regarding entropy
Entropy:
𝑆 = 𝑘 ln 𝑊
is not a single-particle quantity.
It is the collective statistics of microstates.
Despite this, sometimes expressions like:
“Electron entropy”
“Entropy of a photon”
are used.
If these are not carefully defined, they can create a scale shift.
6. Dark matter and dark energy in cosmology
A scale check should be done here as well.
Perhaps:
the effect that seems missing at the galaxy scale
stems from a scale transition
rather than a local law of physics.
This is not yet proven.
But when looking from the perspective of scale blindness, it becomes a legitimate question to ask:
Are we directly transferring dynamics defined at the local scale to the scale of the universe?
7. The most critical point from my fractal perspective
These equations:
𝑝 = 𝑚𝑣
𝐹 = 𝑑𝑝 / 𝑑𝑡
𝐸 = ∫ 𝐹 𝑑𝑥
actually show the hierarchical construction of physical quantities.
If we define a scale degree here:
| Parameter | Scale Degree |
| x, t | 0 |
| v | 1 |
| a | 2 |
| m | separate axis |
| p | 3 |
| F | 4 |
| E | 5 |
| Field | 6 |
| ψ | 7 |
| S | 8 |
a structure like this can be established.