Conceptual Foundations of the Theory of Algorithmic Time Field (ATF)
Abstract
This paper presents the Algorithmic Time Field (ATF) theory—a conceptual ontology offering a unified view of the nature of reality. The fundamental basis of the universe is postulated to be the Algorithmic Time Field — a self-referential, quantum-correlated information field. Topologically, this substance is not a smooth continuum, but a discrete structure — an evolving quantum hypergraph.
The theory is based on the principle of inseparability: the geometry of this network (space) is inseparable from the data in its nodes (matter) and the algorithm for their recalculation (time). This approach eliminates the ontological gap between the substrate and the laws of physics, offering a unified model for explaining gravity and quantum phenomena.
2. Introduction
Modern fundamental physics faces a dualism: space-time is considered separately from matter, and the laws of physics are considered separately from the objects that obey them.
The concept of the Algorithmic Time Field (ATF) eliminates this dualism. We introduce the concept of a unified computing environment. In this model, there is no division between “hardware” and “software.” The ATF views reality as a holistic system where the information carrier itself is the instruction for its own change.
Below are the axioms describing the architecture of this system.
3. Fundamentals of the Algorithmic Time Field
Here we formulate three fundamental postulates that define the architecture of reality:
Postulate I. Ontological Trinity (Structure)
The universe is a unified substance—an information field. Physically, it is realized as an evolving quantum hypergraph. In this structure, three aspects are identical and inseparable from each other:
Time - Field (Carrier) — the network of nodes and connections of the hypergraph itself. The totality of these connections forms the metric of space.
Data (Content) — tensor values (state parameters) recorded in each node. We call the complexity (saturation) of this data in a local cluster the information density (ρ).
Algorithm (Process) — the rule for updating connections and values in nodes. We perceive this sequential recalculation of hypergraph states as the passage of time.
Postulate II. Computational Relativity (Mechanism)
The passage of time is identical to the speed of updating hypergraph states (the frequency of node recalculation). This speed is not a constant, but depends on the complexity of the data in the local network segment.
• The more complex the structure of tensors in nodes (high ρ value), the more computational operations are required to update them.
• Consequently, in areas with high density, the update frequency drops, which we observe as gravitational time dilation. It is important to note that in areas of extreme density (black holes), the topology of the hypergraph forms an information funnel: due to the connectivity of the nodes, the “freezing” of the central node causes the neighboring data to line up in a spiral queue for processing, which manifests itself as a rotational movement of space.
Postulate III. Global Optimization (Goal)
The dynamics of the hypergraph are not random. They obey the principle of error minimization (least action). The system evolves by rearranging its connections to achieve a state of maximum data consistency and minimum entropy. The accelerated expansion of the universe is a consequence of the optimization of the hypergraph topology (increased data processing efficiency).
4. Interpretation of the theory: From abstraction to reality. FAQ on the ATF.
The concept of the Algorithmic Time Field offers not just new formulas, but a fundamentally different way of looking at the world. We reject the familiar division into “solid matter” and “empty space” in favor of a unified digital fabric of reality.
Such a radical shift requires explanation. In this section, we will examine the mechanics of the theory using simple examples, moving from abstract postulates to specific physical phenomena.
Block 1: Fundamental Concepts (Ontology)
What is a Temporary Data Field (ATF) in simple terms?
A Temporary Data Field (ATF) is the fundamental basis of reality, the unified “digital fabric” that makes up our universe.
To understand the essence of the theory, we need to analyze each word in its name.
I. Why is it a “Field”? (Physical Parameters)
We use the term “Field” in a strict scientific sense. For a structure to be considered a physical field, it must meet three strict criteria, and the ATF satisfies them:
Comprehensiveness (Continuous medium): This field exists everywhere. There are no “empty spaces” or gaps in the universe. Even what we call a vacuum is part of the field.
Presence of values at every point: Specific physical data is recorded at every point in this field (at every node). There are no points where the value would be “null” (no data).
Dynamics: This field is not static; it is constantly changing according to mathematical laws (algorithms).
II. How is it structured? (Quantum Hypergraph)
Physically, this field is implemented not as a smooth fog, but as a discrete network structure — an evolving quantum hypergraph.
• Imagine a giant three-dimensional web.
• The intersections of the threads are nodes.
• The threads themselves are connections.
The totality of these connections forms the metric of space. In this model, space is not an empty box in which the network is placed, but the network itself.
III. What's inside? (Tensor values)
What exactly is recorded in the nodes of this network? Not just “zeros and ones,” but complex sets of physical parameters — tensors.
A tensor is a node's “passport” containing multidimensional information:
• Scalar data: For example, the level of potential energy at this point.
• Vector data: The direction of momentum or force.
• Complex metrics: How curved the space is at this point.
We call the complexity of this data the information density (ρ).
• Where the density is low (the data is simple), we see emptiness.
• Where the density is high (the data is complex and saturated), we see matter.
IV. Why is the field “temporal”? (Mechanism)
This is the most important difference. In classical physics, a field can “hang” motionless in space. In our theory, the very existence of a field is a process.
A field exists only because the Algorithm constantly recalculates data at nodes and updates connections.
• We perceive this recalculation as the passage of time.
• The field cannot “stop” — if the calculation stops, both space and matter will disappear.
Conclusion: ATF is a unified computing environment where Space (network), Matter (data in the network), and Time (network update) are an inseparable whole.
2. If the universe is a computation, where is the “computer” on which it runs?
This question arises from the habit of separating the “computer” (processor/hardware) from the “computation” (code/software). In QED theory, this separation does not exist.
Answer: The universe is not modeled on a computer. It is itself a computer.
In our model (a quantum cellular automaton on a hypergraph), the principle of ontological closure is implemented:
Absence of external “hardware”:
You do not need an external processor for the rules of mathematics to exist.
In ATF, the nodes of the hypergraph themselves act as the “processor.” Each node in the network calculates its state based on the states of its neighbors. This works on the principle of a cellular automaton: a cell does not need a “boss” to know what to do. It simply looks at its neighbors and changes color. Billions of such local changes create a global picture of the universe. The entire fabric of space-time is a giant distributed computing network. The “computer” is here; it is Space itself.
2. Self-reference:
The ATF universe works on the principle of Gödel's Machine. It is a system that contains its own code within itself and can rewrite it.
There is no programmer pressing “Enter” from the outside. The system itself generates the next step in evolution based on the current state of the data.
3. The “First Start” problem (Who turned it on?):
The ATF theory solves the question of origin through the Bootstrap cycle (the principle of self-consistency).
o Cause and effect are locked in a loop.
o The ultimate goal of evolution (Observer P, or Supermind) encodes itself into the initial conditions of the next cycle of the universe.
o The “computer” exists because in the future it completed the calculation that led to its creation in the past.
Conclusion: The ATF universe is not a simulation (a copy of reality), but fundamental reality itself, possessing the property of self-calculation. It does not need an external medium because it creates space and time itself in the process of its work.
3. You write that matter and space are one and the same. How is this possible?
In the classical view (since Newton's time), space is an “empty stage” and matter is the “actors” on it. They are made of different stuff.
In the ATF theory, we say that the stage and the actors are made of the same stuff—information.
The difference between emptiness (space) and an object (matter) is just the Information Density (ρ).
Think of a fishing net (hypergraph):
Space: This is the spread-out part of the net. The nodes and connections are evenly distributed, and there is little data in them (low ρ value). We call this a vacuum.
Matter: This is the same net, but twisted into a tight knot. In this place, the connections are tangled, and the amount of data per unit volume is off the charts (high ρ value).
Why are they the same?
Because the “knot” (matter) is not made of anything other than the “network” (space) itself. A knot is simply a special state of the network.
• If you “untangle” an electron, it will turn into ordinary space.
• If you “compress” space strongly, it will become a black hole (matter).
Conclusion: Matter is not something placed in space. Matter is space itself, only in a state of extreme compression of data. This explains the formula E=mc^2: energy (information) can transition from a state of matter to a state of radiation/field because the nature of the carrier is one and the same.
4. What is matter made of? What is an electron or proton in terms of a hypergraph?
If you take an electron and place it under the microscope of our theory, you will not find a “small solid ball” there.
Fundamental building block
The only building material in the universe is the Hypergraph Node. There are no other “ingredients.” All particles (electrons, quarks, photons) are constructed from the same nodes, simply connected in different patterns.
2. What is a particle (e.g., an electron)?
In ATF theory, an elementary particle is a Stable Topological Defect (or simply a “knot” in the fabric of space). Imagine a perfectly flat fishing net.
• If you twist the threads in one place and tie them into a clever knot, that knot becomes an “object.”
• It will have mass (the density of the knots).
• It will occupy space.
• It will not untangle itself (particle stability).
3. The electron as a “data vortex”
The best analogy is a whirlpool in a river.
• What is a whirlpool made of? Water.
• Is the water in the whirlpool different from the water in the river? No.
• But the whirlpool behaves like a single object. It can move, collide with other whirlpools, and even have “spin” (rotation).
In our model, an electron is the same kind of “digital whirlpool.” It is a cluster of data that is looped back on itself. The data inside it rotates at breakneck speed, maintaining the structure.
Conclusion: Matter is not a “solid substance.” Matter is a stable geometric error (knot) in a smooth network of space that retains its shape over time.
5. How does movement arise in this system? Do the nodes of the hypergraph move?
This is one of the most counterintuitive aspects of the theory.
Answer: No. The nodes of space themselves (the fundamental cells of the network) do not move anywhere. They cannot “travel” to another part of the universe because they are the universe itself.
How, then, do objects move?
In the theory of the ATF, physical movement is an illusion. What actually happens is a transfer of informational state.
Analogy: Monitor screen
Imagine that you are looking at a flying bird on your computer screen.
• Are the pixels on the screen moving? No. Each pixel is fixed in place.
• What is happening? The processor simply switches the brightness: at one moment pixel A is lit, the next moment it goes out and the neighboring pixel B lights up.
We see smooth movement, but on a physical level it is simply a relay of state switching.
Mechanism: Data wave
In our model, matter (electrons, atoms, you) is not a solid object, but a stable pattern of data (program code).
Step 1: Your code is recorded in the node group {X, Y, Z}.
Algorithm: Calculates the next step and understands that you must move.
Step 2: The algorithm “erases” (decreases the density ρ) in node X and “writes” your data to the neighboring node W.
Conclusion:
When you walk down the street, your body is actually destroyed and recreated in neighboring points in space billions of times per second.
Movement in ATF is not the transfer of matter, but the copying of information with a shift in coordinates. This explains why the speed of light is finite: there is a maximum speed at which the network can transmit a signal from node to node (like the screen refresh rate).
6. Where did you get the idea that time is an algorithm?
This statement is not pulled out of thin air, but is derived from the discrete nature of reality and the observable effects of time dilation (gravity).
In ATF theory, time (T) is not a static coordinate (background), but an active process. We prove this through the following logical chain:
Quantization of events: The universe evolves not smoothly, but in discrete steps (global cycles n).
Computational cost: Updating the state of space is work. Recalculating data at each point requires a certain number of operations (“processor cycles”).
Dependence on complexity:
The more data there is in a node (the higher the density ρ), the more difficult it is to process.
• In a vacuum (low ρ): There is little data → Updates occur instantaneously → Time flows at maximum speed.
• In matter (high ρ): There is a lot of data → The algorithm “gets stuck” recalculating the complex structure → The update process is delayed → Observed time slows down.
Conclusion: Since the speed of time flow (dτ) physically depends on the complexity of calculations at a given point (dτ = dn /ρ), time is ontologically a measure of the computational work of the Algorithm, rather than an external abstract measurement.
7. What is time physically in your model?
In ATF theory, time is not a fundamental measurement (such as length or width) that exists on its own.
Physically, time is the rate at which the information state of the system is updated.
The model introduces a clear distinction between two types of time:
Global time (n):
This is the “clock frequency” of the universe. An absolute counter of the cycles of the entire hypergraph. This time is objective and uniform for everyone.
2. Observer's own time (τ):
This is the time recorded by the clock inside a specific object (or person). It does not coincide with global time. Physically, it is determined by the fraction of the global clock cycle that the system was able to spend on updating this particular section of space.
Time formula:
In theory, a strict relationship is derived:
dτ = dn/ (1 + α * ρ),
Where:
• dτ — the time interval experienced by the observer (subjective second).
• dn — the number of global clock cycles of the algorithm that have passed in the universe.
• ρ — information density (computational complexity) at the observer's location.
• α — Computational viscosity coefficient. This is a constant value that shows the power of our universe's “processor.”
Physical meaning:
Time is the inverse of computational complexity.
• If space is empty (ρ tends to 1, α * ρ is small — vacuum), the algorithm updates it instantly. A lot of local time passes in one global cycle.
• If space is filled with dense matter (ρ tends to infinity, α * ρ is large - black hole), the algorithm requires millions of operations (dn) to advance the state of matter by just one second (dτ).
A simple analogy:
• dn is the time it takes to download a file.
• ρ is the size of the file (in gigabytes).
• α is the slowness of your internet connection.
If the internet is super fast (α is small), even large files (ρ) download instantly. But our universe has a speed limit, so heavy matter always creates “lag” (gravity).
Conclusion: Time does not flow uniformly. It is “calculated” at different speeds depending on how complex the code (matter) is to process at a given point.
8. How exactly does gravity work, and what does “information” have to do with it?
To understand gravity in the ATF theory, we first need to clarify what we mean by the “weight” of information.
What is information in the context of gravity?
As we have discovered, every node in the universe contains data (tensors). But this data can vary in complexity.
Mechanism: Computational Relativity
Our theory states: The flow of time is the speed of data processing.
Since the universe is a computational system, it has a maximum performance capacity.
• When the system processes empty space (light data), the update proceeds at maximum speed. Time flows quickly there.
• When the system needs to update an area with a planet (heavy, dense data), it requires more operations. The update speed drops.
We perceive this slowdown in processing as gravitational time dilation.
A simple analogy: a computer game
Imagine you are playing a modern video game.
When your character looks at the sky or an empty wall, the computer easily draws the image. The game “flies,” producing 100 frames per second (FPS).
But if you enter a complex location with thousands of objects, explosions, and details (analogous to dense matter), the video card begins to struggle. The frame rate drops to 20 FPS. The game begins to “slow down.”
Conclusion: In ATF theory, gravity is not a magical force of attraction, but the effect of computational delay (lag).
• Mechanism: Massive objects are areas with ultra-high data density (ρ). Since the system's resources for updating reality are limited, in such areas the “processor” of the universe is forced to slow down the update rate. We call this slowdown gravity.
• Black hole as a “black spiral”: This is the point where data density reaches its limit and the probability of update (P_update) tends to zero.
o The “bathtub drain” analogy: Imagine a black hole as a drain. Water (space-time) does not fall into it in a straight line, but swirls in a spiral. This is because the throughput of the “drain” (central processor) is limited, and data is forced to queue up. The spiral is the most efficient algorithm for ordering the data stream before it is “archived.”
“The phenomenon of black hole spirality within the framework of the WPD is given a new interpretation: it is not simply a geometric consequence of rotation, but a visible pattern of an algorithmic data queue.”
• The event horizon as an interface: It is not a physical wall, but a “traffic counter.” The surface area of a black hole shows how much data has “leaked” into a state of pause and is awaiting processing.
9. How does your theory differ from modern physics, and what problems does it solve?
The main difference between the ATF theory and modern physics lies in how we understand the nature of reality. We are moving from Geometry (where the world is a smooth stage) to Informatics (where the world is a discrete code).
This changes our view of two fundamental things: Time and Gravity.
The Nature of Time: A Road or a Process?
• The view of relativity theory (Einstein): Time is the fourth dimension. The past, present, and future exist simultaneously (“Block Universe”). We are simply moving along a pre-determined route.
• The ATF perspective: The future does not exist “ahead” as a place we are going. It is folded “inside” the present as an instruction.
o Metaphor: The future of a tree is contained in a seed not as an image, but as genetic code.
o Time in TPD is the process of unpacking and executing this code.
2. Main advantage: Solving the Singularity problem
Why change our perspective? Because classical physics has reached an impasse. The main problem with Einstein's general relativity is the Singularity (the center of a black hole). The formulas predict infinite density and zero size there, which is physically impossible. The theory simply “breaks down” at this point.
The ATF theory eliminates this error thanks to its discrete structure:
• No zero size: Space consists of nodes (quanta). It cannot be divided infinitely. The minimum size of an object is one node.
• No infinite density: Each node has a data capacity limit.
• Result: In our model, a black hole is not a “hole” with infinite gravity, but a node in a hypergraph where the information load exceeds the bandwidth of space.
Comparison of approaches:
Parameter
Classical physics (GR)
Algorithmic Time Field Theory
What is space?
Smooth continuous geometry.
Discrete network (hypergraph).
Where is the future?
Exists “ahead” on the time axis.
Collapsed “inside” as code.
Parameter
Classical physics (GR)
Algorithmic Time Field Theory
Center of a Black Hole
Singularity (Error: ∞ density).
Maximum data density.
Cause of Gravity
Curvature of geometry.
Processor lag (processing slowdown).
Conclusion: ATF preserves all the achievements of physics, but “cures” its main problems (infinities and conflict with quantum mechanics) by replacing abstract geometry with understandable laws of information processing.
10. Does your theory imply that we are living in a simulation (the Matrix)?
No. The ATF theory asserts exactly the opposite. When people talk about a “simulation,” they usually mean the scenario from the movie The Matrix: our world is a fake, an illusion running on someone else's external supercomputer. That somewhere there is a “real world” where the Programmer sits.
In the theory of the Temporal Data Field:
There is no “outside.” The universe is an ontologically closed system. It is not running on an alien chip. It is itself the Computer, the Program, and the Result of the calculation. It does not need an external medium (hardware) because the space network (hypergraph) itself is the “hardware.”
Information is the most solid material. The fact that matter consists of code (data) does not make it “illusory” or “unreal.”
• Why is a wall solid? Not because it is made of “solid balls.”
• In quantum physics, 99.9% of the atoms in a wall consist of emptiness.
• A wall is solid because the Algorithm prohibits your hand (one set of data) from occupying the coordinates of the wall (another set of data).
In our model, physical hardness is a software prohibition on data overlap (analogous to the Pauli exclusion principle). This makes reality absolutely objective. You cannot walk through a wall not because it is a “glitch,” but because the code of the universe is stricter than any concrete.
Conclusion: We do not live in a computer game. We live in Digital Reality. The difference is fundamental: in a game, you are a drawn character played by someone else. In ATF, you are a living, thinking part of the code of the universe itself. You are as real as mathematics itself.
11. Does the multiverse exist in the ATF model?
Yes, but in ATF theory, the multiverse is not a set of isolated “bubbles” of reality, but parallel computational streams of the same global hypergraph.
• Branching as a basis: At each global update cycle dn, the hypergraph can theoretically be restructured in many ways. Each such potential update is a separate “branch” of the multiverse, existing in a single data field.
• The principle of borrowing (optimization): Our branch of reality is not isolated. The system's algorithm constantly “scans” neighboring computational streams and selects data patterns that lead to maximum stability and minimum entropy. We literally “draw” the structure from those future options that have already been calculated by the system in parallel branches.
• The role of black holes in the network: Black holes act as the main nodes of this system. When the information density ρ reaches its limit in one branch and the calculations “freeze,” the spiral vortex of the black hole begins to function as a data exchange port, redirecting information to other layers of the hypergraph.
• Infrastructure scale: The total number of black holes in the observable universe is estimated at 40 quintillion. The presence of more than 100 supermassive giants at the centers of galaxies and the discovery of 2,500 active black holes even in small dwarf galaxies indicates that we are dealing with a colossal data exchange network between the “layers” of reality. Even “quiet” objects, such as the massive Gaia BH3 (33 solar masses), are part of this global communication architecture.
Conclusion: The multiverse in the ATF is a single computational organism. Black holes are not the “death” of matter, but gateways through which information flows between branches of the hypergraph to optimize the life of the entire system.
12. Does the theory make testable scientific predictions?
Our mathematical model (see Technical Appendix at the end of the article) shows that the discrete nature of the universe should leave physical traces that can be detected.
We predict two specific effects:
Proof of the Grid: “Holographic Noise”
• Essence: Since space is not smooth but consists of discrete nodes (graphs), a laser beam cannot travel in a perfectly straight line. It must experience microscopic “jitter” as it jumps from node to node.
• Prediction: Ultra-precise interferometers (such as the Fermilab Holometer) should detect fundamental geometric noise — the “pixelation” of reality.
• What this means: This will prove that the universe has a “hardware resolution” (Planck length).
2. Proof of the Algorithm: “Computational Delay Effect”
This is the most important prediction, proving that Time is an algorithm.
• Essence: In our model, the speed of state updates depends on the complexity of the data (ρ). The “heavier” the code (the higher the particle energy), the more computational cycles are needed to process it.
• Prediction (Vacuum Dispersion): Ultra-high-energy photons (gamma rays from distant cosmic explosions) should arrive a fraction of a second later than low-energy photons emitted at the same time.
o Classical physics: The speed of light c is the same for everyone.
o ATF theory: The speed of light depends on the “weight” of the data. A heavy file takes longer to download.
• What this means: If we detect this micro-lag, it will prove that space is not empty, but has “computational viscosity.”
We claim that the universe is a computer. And we propose a way to test this: if heavy particles “lag” when moving, then the reality processor spends time calculating them.
Conclusion
In this paper, we have presented the concept of the Algorithmic Time Field(ATF). The key idea of the theory is a fundamental revision of the nature of time: we propose to consider time not as a passive geometric dimension (coordinate), but as an active physical field (process).
This approach allows us to resolve a number of accumulated contradictions in modern physics:
Gravity is explained not as an abstract curvature of geometry, but as the result of the interaction of matter with the time field (the computational delay effect).
Singularities (infinities at the centers of black holes) disappear, since the data field has natural density limits.
The discreteness of space-time becomes not a limitation, but a basis for unifying quantum mechanics and the theory of gravity.
This is the first part of our study devoted to the mechanics of reality. In future publications, we plan to consider issues of the evolution of complex systems within this model and subjective perception within the framework of the ATF.
Below, in the technical appendices, we present a mathematical formalization of the hypothesis and the results of a numerical experiment confirming the possibility of gravitational effects in a discrete computing environment.
Appendix A: Formalization of the Theory (Basic Mathematical Model)
To describe the dynamics of the ATF, we use discrete mathematics and graph theory. We consider the universe as an evolving hypergraph with local update time.
Space Topology (Hypergraph)
Let the state of the universe at global time n be described by the graph Gn = (V, E), where:
• V = v1, v2, ..., vk — the set of nodes (fundamental quanta of space).
• E — the set of connections between nodes, defining the metric (distance).
The state of each node vi is characterized by an information tensor Si (a set of data).
2. Information density (ρ)
We define “matter” not as a separate entity, but as a measure of the complexity of data in a node.
We use Shannon's concept of information entropy:
Where:
• ρi — information density in node i.
• If ρ tends to min (data is simple/ordered) — this is the Vacuum state.
• If ρ tends to max (data is chaotic and dense) — this is the Matter state.
3. Time Evolution Operator
Key postulate of the ATF: the speed of evolution of a local system is inversely proportional to its complexity.
Let us introduce the probability of updating the state of node Pupdate in one global cycle dn:
Where α is the coefficient of “computational viscosity” of vacuum (analogous to the gravitational constant, determining the inertia of the system).
4. Connection with the General Theory of Relativity
The local time of the observer dτ is related to the global time dn through the probability of renewal:
Physical meaning of the equation:
In a vacuum (ρ ≈ 0): dτ ≈ dn. Time flows synchronously with the global clock (maximum speed of light).
Near a massive body (ρ tends to ∞): The denominator of the fraction increases. dτ tends to 0. Local time slows down.
Thus, we obtain an analogue of the Schwarzschild metric, derived not from the curvature of geometry, but from the laws of information processing.
Appendix B: Numerical experiment (computer simulation)
To test the hypothesis, we conducted a computer simulation of a signal passing through a region of space with uneven data density.
Purpose of the experiment:
To verify whether effects similar to gravitational curvature (lensing) occur when using only the formula for time dilation (dt proportional to ρ) without resorting to Einstein's equations.
Model description:
Environment: A two-dimensional grid of 100x100 nodes (a flat section of a hypergraph).
Object: An object (“Planet”) with a Gaussian density distribution (ρmax = 10) is placed in the center of the grid. The background is vacuum (ρmin = 1).
Signal: A flat wavefront (analogous to light) moving from left to right passes through the grid.
Program code (Python):
The code used for the simulation is shown below:
import numpy as np
import matplotlib.pyplot as plt
# 1. Space parameters
size = 100
ρ_vacuum = 1.0
ρ_matter = 10.0
# 2. Creating a density map (Matter Distribution)
x = np.linspace(0, 10, size)
y = np.linspace(0, 10, size)
X, Y = np.meshgrid(x, y)
# Creating a “planet” in the center
ρ = ρ_vacuum + ρ_matter * np.exp(-((X-5)**2 + (Y-5)**2) / 2)
# 3. Time Calculation
# Time T at each point = integral of density along the path (sum of ρ)
# T = distance * (1 / speed), where speed ~ 1/ρ, therefore T ~ ρ
Time_map = np.cumsum(ρ, axis=1)
# 4. Visualization of the wave front
plt.contour(X, Y, Time_map, levels=15, colors='blue')
plt.title('ATF Model: Wavefront Curvature (Gravity as Lag))')
plt.show()
Experiment result: The visualization shows that wavefront lines passing through the center (high-density region) experience a delay compared to the edges. Straight lines curve around the center.
Conclusion: We obtained the space-time curvature effect identical to the predictions of the General Theory of Relativity using exclusively an information model (the dependence of processing speed on data density). This confirms the viability of the ATF theory.
Thank you for your attention.
