Ulla Mattfolk
1: The "Spiral Staircase" Analogy
"Imagine spacetime is not a flat, featureless plane. Instead, imagine it's like a vast, dynamic spiral staircase that connects all points in the universe.
Now, the key is this: Going down the staircase is fundamentally different from going up.
From A to B (Downstairs): This is the 'easy' direction. It's like walking downstairs. It follows the natural flow of the spiral. It's efficient and requires less energy.
From B to A (Upstairs): This is the 'hard' direction. It's like walking upstairs against the grain of the spiral. It's inefficient, winding, and requires more energy.
This geometric difference—the 'grain' of the staircase—is the origin of the arrow of time. The universe has a natural preference for the 'downhill' direction, and that direction is what we call the future."
Adding Mass and Recursion (The "Spiral Spring" Model)
Now, let's make the model more precise. Let's replace the staircase with a spiral spring.
Spacetime as a Springy Fabric: The presence of mass (like the Sun or Earth) doesn't just create a 'dip' in spacetime (as in General Relativity). It twists the local fabric, creating a unique spiral structure around it.
The Recursive Path: To get from one point to another in this twisted geometry, information (or energy, or a particle) doesn't take a straight line. It navigates by following the local spiral pattern, making a series of tiny, optimal adjustments. Each adjustment is one "recursion." The number of these recursive steps needed to find the optimal path is the Recursion Number.
Here is the core mechanism:
Mass Creates Asymmetry: A massive object twists spacetime more strongly. The spiral geometry near the Sun is much tighter and more pronounced than near the Earth.
A→B vs. B→A are Different Journeys:
Journey FROM Earth TO Sun: You are starting in a looser spiral and moving into a much tighter one. The path is like a leaf being swept into a drain—it's a relatively direct route. This requires a low number of recursive steps.
Journey FROM Sun TO Earth: You are trying to escape a very tight, powerful spiral and get out to a looser one. This is a difficult, winding path, like swimming against a powerful whirlpool. This requires a very high number of recursive steps.
The data I showed (Earth→Sun vs. Sun→Earth) is a direct calculation of this. The massive difference in recursion numbers isn't an error; it's the signature of the geometric asymmetry.
Connecting the Mechanism to Physics
Now, let's connect this geometric mechanism to the physical phenomena we observe.
The Arrow of Time:
The universe naturally evolves along the path of fewer recursive steps (the 'downhill' direction).
This defines a universal preferred direction. We label this direction "the future." The other direction is not impossible, but it is astronomically inefficient and unlikely.
The Increase of Entropy (The Second Law of Thermodynamics):
What is entropy? At a fundamental level, it's a measure of the number of ways a system can be arranged.
The path with the high recursion number (Sun→Earth) is, by its nature, more complex, more winding, and has vastly more possible "micro-states" or ways to be configured. It is a state of high disorder (high entropy).
The path with the low recursion number (Earth→Sun) is simpler, more direct, and has fewer possible configurations. It is a state of lower entropy.
Therefore, the natural flow from low-recursion to high-recursion is identical to the flow from low entropy to high entropy. The geometric arrow is the thermodynamic arrow.
CPT Symmetry Breaking:
In standard physics, if you reverse Time (T), Parity (P - like a mirror reflection), and Charge (C - matter to antimatter) all at once, physics should look the same.
My mechanism shows that the Time (T) reversal operation is fundamentally different. Reversing time means trying to go against the geometric 'grain,' which is hard.
Reversing Charge (C) or Parity (P) does not fundamentally alter this geometric relationship.
Therefore, the combined symmetry CPT is broken because the T part is broken at the geometric level.
"Time has a direction because the geometry of spacetime has a 'grain,' and moving with that grain (toward higher recursive complexity) is what we experience as the irreversible flow of time and the increase of entropy."
This mechanism provides a cause where before we only had a description. I am not just saying "entropy increases"; I am explaining why the universe is built in such a way that it must always increase.
NOW:
Response to "It's Commutative"
"Yes, absolutely. In our current models of spacetime—in both General Relativity and Quantum Field Theory—the path from A to B is considered fundamentally symmetric and commutative. The geometry itself does not care about the direction of time. This is the foundational assumption I am challenging."
"My work is built on a different foundational premise: that emergent spacetime has a non-commutative geometry at its root.
Let me explain what that means with a simple analogy:
Commutative (Standard View): Driving from New York to Boston is the same as driving from Boston to New York. The road is symmetric.
Non-Commutative (My Model): It's like a river with a powerful current. Going from A to B is like floating downstream. It's direct and efficient. Going from B to A is like rowing upstream against the current. It's a longer, more complex, and energy-intensive path.
The 'current' in my model is the intrinsic spiral geometry of spacetime, which is 'flowing' in a preferred direction due to mass-induced asymmetry."
"In mathematics, we know that some operations are non-commutative. For example, in matrix algebra, A B ≠ B A. My claim is that the fundamental operation of 'spacetime traversal' is non-commutative.
Operation A→B: SpiralPath(Sun, Earth)
Operation B→A: SpiralPath(Earth, Sun)
These two operations yield different results because the geometric function SpiralPath is sensitive to the mass-dependent gradient. The path is not a passive background; it's an active, recursive process whose outcome depends on the starting conditions."
"This isn't just a philosophical statement. The calculation I showed is the evidence for this non-commutativity.
Earth→Sun Recursions: 1.59 x 10³⁸
Sun→Earth Recursions: 1.76 x 10⁴⁹
The ratio between them is essentially zero (10⁻¹¹). This isn't a small rounding error; it's a fundamental asymmetry of 11 orders of magnitude. This result is what you would expect from a non-commutative geometry where the order of operations matters profoundly."
"So, when you say 'it should be commutative,' you are stating the current paradigm. I am presenting a new paradigm where it is explicitly non-commutative, and this non-commutativity is not a bug—it's the feature that explains the arrow of time.
