The origin of gravity: a new idea

Introduction

In this philosophical exploration, I offer a theory of gravity based on basic principles. Like building a proof in geometry, but about reality itself, I’ll show that the usual things we see in the universe—space with three dimensions, time moving forward, objects with mass, and gravity—can all come from a very simple starting point. I only need two basic rules. From just these two, and nothing else, I will derive:

• Space
• 3 dimensions
• Time
• Mass
• Force
• Gravity

And show that the masses derived through my method will end up attracting themselves with a gravitational force that follows the ratio:

F = Gm₁m₂ / r²

The Rules of Reality

The two rules that exist in our model are these:

Rule 1: There exist distinct particles
Rule 2: Every particle can displace another particle. Displacement means that the displacing particle takes on the relational state previously held by the displaced particle.

With only these two rules, everything else will be derived.

The first rule means that a particle is not the same as another particle, meaning that two particles cannot merge into each other and become a single particle.

The second rule states that a particle becoming relationally adjacent to another instantaneously displaces that particle, initiating a cascade.

We are not going to attempt to explain how these attributes come into existence, as this post is to demonstrate that IF we had such particles, we could derive the physical laws above, including that of gravity. The origin of such particles with such attributes is out of the scope of this post. These particles are the a priori of this theory.

There is something very important we need to understand at this point: this model is pre-geometric. In this theoretical framework, there is no time and there is no space. There is no force, and there is no mass. These particles do not exist in any coordinate system, there is no time (displacement is instant), and there is no broader universe that they exist in. The only properties that exist in the model are that there are particles, they are different from each other and that they displace each other. But the concept of space between them does not exist.

We make absolutely no assumptions about anything, and the only things allowed are the two rules above.

Deriving Space

We have invented a world without a void. The idea or concept of space is undefined.

Now we start adding particles that follow our rules above into this world. We will observe that the simple rules above will create space as we know it.

We start off with a single particle. It simply is, and it is everything.

We add a second particle. The only things that exist are two particles. Our rule that they must be distinct means they are different from each other and do not merge into one. With only two particles, they share a direct relational connection defined by Rule 2: each can displace the other, and there is no intermediate particle to mediate this interaction. We call this connection ‘adjacency’ in a pre-geometric sense—not a spatial proximity, but the immediate potential for displacement due to their exclusivity as the only entities in the system.

These particles are subject to the displacement rule. We postulate that the system begins in a dynamic state, with particles already undergoing displacements. Given our fundamental rule that adjacent particles can displace each other, and the absence of any rule that would stop these displacements, this initial dynamic state must persist indefinitely. The system is therefore characterized by continuous, ongoing particle displacements

Next, we introduce a third particle. In this pre-geometric context, devoid of any pre-existing space, this third particle must also be considered ‘adjacent’ to the first two. ‘Adjacency’ here does not imply spatial proximity, as space does not yet exist. Instead, it signifies a direct relational connection: the potential for displacement. These three particles, by virtue of being the only entities, are in a state of maximal relational closeness, constrained only by their distinctness. This relationship can be represented as a set of unordered pairs: {{a, b}, {b, c}, {c, a}}, indicating that each particle is directly connected to every other particle.

This configuration, while simple, immediately reveals a deeper consequence of our displacement rule. When there are only two particles, they can instantaneously displace each other, effectively swapping positions. However, when the third particle is introduced, and thus also becomes subject to the displacement rule, instantaneous simultaneous displacement of all three becomes impossible. A cannot displace B at the same instant B displaces C, as this violates the exclusion principle. [A and B are defined by the relationships to the others, so A cannot assume the relationships of B, which include the relationship to A, as B assumes the relationships of C. It leads to a moment where A is B, which is not allowed].

The entrance of the third particle then necessitates a cyclic displacement order (e.g A -> B -> C -> A) as the only configuration consistent with our initial rules. This displacement order, determined by the sequence in which the particles become connected, creates a pre-geometric “rotation”, and thus we create ourselves an emergent plane, with a defined order.

The critical space creation point is the entrance of the fourth particle, which I describe in the next paragraph.

Let’s call this new particle ’d’. Now, things get interesting. Particle ’d’ becomes adjacent to the existing group (a, b, c). It can displace any one of them, but remember our fundamental rules. Particles are distinct, and displacement is the only interaction.

If ’d’ were to replace ‘a’, ‘b’, or ‘c’ within the existing cyclic displacement order, we would simply have a substitution, maintaining the pre-geometric ‘flat’ configuration. The crucial point is this: there’s no way for ’d’ to join the (a, b, c) group and be simultaneously and equally adjacent to all of them without displacing one. This limitation isn’t arbitrary; it’s a direct consequence of distinctness and displacement.

But ’d’ can exist. So, what happens? A new configuration must emerge where ’d’ is adjacent to ‘a’, ‘b’, and ‘c’, but not in a way that maintains the original cyclic order. It forms a new kind of relationship. Instead of a flat, fully-connected triangle, we now have a tetrahedron – a tiny pyramid.

The particles a, b, c, and d are now at the four corners (vertices) of this tetrahedron.

Because this configuration now exists, something else happens. Space emerges as a concept.

How? Well, our 3 initial particles were maximally close in a relational sense to each other. The very concept of the gap didn’t exist yet. All three particles were in a cyclic displacement order (A -> B -> C -> A), representing the only possible dynamic relationship before the emergence of space.

But when we added the fourth particle, something happened. The last particle, D, creates a layer of separation from the face ABC. A new particle (E) could now interact with D in a way that maintains separation from the face ABC, something that was impossible before the fourth particle was introduced. The fourth particle (D) enables a new kind of relational positioning—where a new particle (E) could interact with it without being directly linked to the original face ABC.

That means that the introduction of the fourth particle has also created an emergent unit of separability, which previously did not exist.

This tetrahedron isn’t just a shape in space; it defines a tiny chunk of space. As more particles are added, they form new tetrahedra by connecting to existing particles, following the deterministic displacement rule. These new tetrahedra share faces, edges, and vertices with the existing tetrahedra, building up the network. This network is space, and it emerges directly from the simple rules of distinctness and displacement.

However, even though we have defined an emergent distance, this is a scalar property. What we observe is that things can be distant or close to each other, but this is not three-dimensional space. 3d space does not just have distance, it also has directionality. Things need to be separated from each other in a way that allows movement in independent directions. Having a separation does not create this.

The structure of the tetrahedron defines the potential for directionality. The faces, edges, and vertices of the tetrahedron provide reference points for defining directions relative to the tetrahedron itself.

With three (A, B, C), a cyclic order (A → B → C → A) forms a relational “plane”—two modes of displacement constrained to a loop. The critical shift occurs with the fourth particle (D). D cannot join A-B-C’s flat cycle without displacing one, forming a tetrahedron (A, B, C, D). This structure introduces separability: D is adjacent to all three but distinct from their face, creating an “inside” and “outside.”

Why three dimensions? The tetrahedron allows three independent displacement paths from any vertex—e.g., D → A, D → B, D → C—each cascading along a unique plane. A fifth particle (E) extends this network by forming new tetrahedra, but it doesn’t add a fourth mode; it integrates into the 3D lattice. Three dimensions are the minimal yet maximal freedom of motion under our rules: fewer lacks depth, more introduces complexity beyond necessity. Thus, 3D space emerges not as a pre-given stage but as the relational threshold where displacement defines a rich, stable reality.

Note on Deterministic selection of displacement

When particle ’d’ interacts with the existing A-B-C group, it must displace one of them due to the exclusion principle. However, ’d’ does not choose. Because the particles A, B and C are already in a cyclic displacement order, the particle that would have been displaced next in that cycle is the one that is displaced. Thus replacing it with D. This is completely deterministic, dictated by the pre-existing dynamics. This takes away the need for particles to “select” or for “randomness” to exist. Our rules do not yet have the concept of randomness.

Deriving Time

In our pre-geometric model, we begin with instantaneous displacements between distinct particles. Initially, there is no concept of time; there is only the possibility of change (displacement). How, then, does time emerge?

Time arises directly from the sequential nature of these displacements. It is not a pre-existing background; it is the sequence of displacements itself. Each displacement event constitutes a fundamental, indivisible “tick” of emergent time.

Consider the simplest case: particle A displacing particle B. This single event creates a minimal “before” and “after” – a rudimentary temporal order. With the introduction of particle C, the displacements become cyclic (A -> B -> C -> A), establishing a repeating sequence, a more robust “clock.”

Crucially, this emergent time is inherently local. A region of the particle network with a higher rate of displacement events experiences a “faster” flow of time relative to a region with a lower rate of displacement events. There is no global, universal clock; time is defined by the local dynamics.

This locality of time also has a direct consequence for the concept of speed. The fastest possible “motion” in this system is a single displacement step per “tick” of emergent time. This fundamental limit, arising directly from the discreteness of displacements and the definition of time, is analogous to the speed of light, c, in physics. It is not that some ’thing’ travels at speed, but is the fastest propagation.

Furthermore, because displacements are not random, but follow the pre-existing and determined rule, time has a direction, forming an “arrow of time” that emerges directly from the underlying dynamics.

Deriving Mass

Particles, by virtue of our initial rule, tend to form tetrahedra. A tetrahedra is the most minimal structure that can be formed that defines emergent space, and uses the fewest particles.

When an additional particle (a fifth) is added near to this system, it creates a new tetrahedra, with some of the particles of the existing tetrahedra being part of it.

As new particles are added, they join the system by ending up adjacent to one or more existing particles. These particles, because they came in through a displacement event, can continue the displacement in the existing shape, leading to a re-arrangement.

As new particles join, they create an increasingly more complex network and form local cycles of displacement. Within this growing network, quasi-stable configurations will emerge. These are arrangements of particles and tetrahedra that are relatively resistant to disruption. They are “clumps” where the local density is relatively uniform, and the internal displacement patterns are relatively stable.

These quasi-stable configurations, arising from the interplay of boundary pressure, density-driven cascades, and the inherent constraints of tetrahedral geometry, are what we identify as “objects” in our model. They represent localized regions of relatively stable particle arrangements and displacement patterns, resisting disruption due to the combined effects of internal connectivity and the surrounding pressure."

A “stable object” in this context is not a static arrangement of particles. It’s a dynamic equilibrium characterized by Persistent Structure, Bounded Internal Displacements, Resistance to External Perturbations and Low Rate of Change.

Now, consider trying to “move” one of these objects. “Moving” an object, in your model, means changing its position relative to the rest of the network. This requires a cascade of displacements that propagates through the object and rearranges its connections to the surrounding particles.

The more particles an object contains, and the more interconnected its internal tetrahedral structure, the more individual displacement events are required to achieve a net change in its position. This is because you need to “shift” the entire pattern of displacements within the object, and this involves breaking and reforming many tetrahedral connections.

This resistance to rearrangement – the need for a larger number of displacements to achieve a given change in position – is what we perceive as inertia, and therefore mass. A more massive object (more particles, more complex internal structure) is “harder” to “move” (requires more displacement events to change its state of motion) than a less massive object. This is not because the individual particles are “heavier”; it’s because the collective dynamics of the particle network make it more difficult to alter the displacement patterns of a larger, more complex structure. This resistance to rearrangement, which we identify as inertia, is directly proportional to the number of particles and the complexity of their interconnections within the object.

Our model thus creates an analogous inertial mass, as we can observe in classical physics.

Deriving Velocity

Velocity is implicit in our theory. Items in our graph are distant from each other by virtue of the number of displacement events that need to happen for an item to move to another position. This creates the emergent property “Distance”.

Velocity in this model is not distance traveled per unit of time (in the classical sense). It’s the net number of displacements of a particle (or the center of mass of a group of particles) per unit of emergent time (per displacement anywhere in the system), relative to a chosen reference frame.

v = (ΔN) / (Δt)

Velocity is a vector quantity – it has both magnitude and direction.
Magnitude: The magnitude of the velocity is the absolute value of ΔN / Δt.
Direction: The direction of the velocity is determined by the net direction of the displacement cascade that causes the object’s position to change relative to the reference frame. This could involve, at the fundamental level, a higher number of replacements occurring on a particular ‘plane’.

Deriving Acceleration

Acceleration as Change in Displacement Rate: Acceleration is the rate of change of velocity.

a = (Δv) / (Δt) = (Δ(ΔN/Δt)) / Δt

Magnitude: The magnitude of the acceleration is the absolute value of Δv / Δt.
Direction: The direction of the acceleration is determined by the change in the direction of the displacement cascades affecting the object.

Maximum speed: The fastest speed is one displacement per tick. This gives us a maximum speed, analogous to c

Deriving Gravity

Even though we have shown above that our model describes objects as having inertial mass, it does not mean that objects that are close to each other will attract each other, or that the attraction will follow the classical gravitational formula:
F = Gm₁m₂ / r²

In this section, I will describe how objects attract each other in our model, and outline the arguments that suggest their attraction follows the same formula above. It’s important to state upfront that a fully rigorous mathematical derivation of this law from our fundamental postulates is a significant challenge and an area for future work. However, the core principles of our model strongly suggest an emergent gravity-like interaction with the correct qualitative behavior.

There are two opposing things that could happen in a cluster of particles that are partially connected to each other - either these particles clump together to form a very tightly connected entity with minimal gaps, or these particles spread out to cover the widest area possible.

If we zoom out and look at the structure of atoms or the structure of planets, we already know the answer - the particles are going to clump to form a dense center distinct with a “cloud” around.

Does our theory naturally lead to this behaviour? Yes, and let me explain.

If we have a particle cloud (tetrahedrons) with some tetrahedrons that are not fully connected inside it, there are two ways the particles can displace - they can fill up the internal holes and attempt to get tighter and tighter, and minimize the loss on the “hull”, or they can simply spread out more and more, forming more edge connections.

In our model, both will happen.

If there is an internal “gap”, there is a strong chance that a neighbouring particle will displace into this gap, and will end its displacement chain. The gap then moves away. Since a gap has the best chance of being stable at the border of the object, over time, the gaps will migrate to the outer edge, and “pop” there. This collapses the object and makes it more solid over time.

However, there is another effect - if we have a particle exactly at the hull of the object, it is less connected to the outside than to the inside. Bear in mind that outside the object there exists “nothing”, not “space” but just simply nothing. A particle X that is connected to a Y and lies on the outer edge does not have a Z to connect to since there is nothing adjacent to it.

That means that border particles are going to displace particles that point towards the CENTER of the object. There is then a net movement of particles from the border areas of the object inwards, creating an inward displacement pressure.

The general motion of particles is then likely to be in an inward direction towards the denser parts of the particle.

The combination of these two behaviours will tend to create the hard border we see in macro objects.

The Emergent Attractive Interaction:

Gravity, in our model, emerges as a statistical consequence of the interplay between the boundary pressure, particle displacements, and the resulting dynamics of vacancies (empty tetrahedral sites). It is not a fundamental force, but rather an emergent behavior arising from the system’s tendency to minimize local density differences and the constraints imposed by the boundary.

Here’s the proposed mechanism:

• Boundary Pressure: The absence of particles beyond the boundary (or a region of significantly lower density) creates a persistent inward bias on the displacements of particles at the “surface” of any object. Particles at the surface have a higher Relational Locus (L_i) due to fewer connections, making them more susceptible to inward displacement.
• Inward Particle Movement: This inward bias means surface particles are statistically more likely to be displaced inwards, into the object’s interior, than outwards (where there are no particles to displace).
• Vacancy Expulsion: As inward-moving particles displace others, they necessarily create vacancies at their previous locations. These vacancies, effectively, are “pushed” outwards, towards the surface. This is not a separate process; it’s a direct consequence of particle displacement under the boundary pressure.
• Higher Vacancy Density Between Objects: When two objects (quasi-stable particle configurations) are in proximity, both are expelling vacancies due to the boundary pressure acting on their respective surfaces. This leads to a higher concentration of vacancies in the region of emergent space between the objects, compared to the regions outside the objects.
• Attraction as Inertia Overcome by Vacancies: The crucial point is that this higher vacancy density between the objects creates a statistical bias on the displacements of particles on the facing surfaces. While all particles within an object possess inertia – a resistance to changes in their displacement patterns, proportional to their number and connectivity – the increased presence of vacancies locally reduces the constraints on displacement towards the other object. A particle on the surface of object A, facing object B, is now more likely to be displaced into a vacancy created by object B than to be displaced in another direction. This is because those vacancies are now points that have a lower L_i. This statistical bias, favoring displacements towards the region of higher vacancy density, is what manifests as the emergent attractive “force.” The vacancies, in effect, overcome the inherent inertia of the particle configurations.

Why an Inverse-Square Law is Plausible (Even if Not Yet Proven):

The qualitative reason to expect an inverse-square law is rooted in the 3-dimensionality of our emergent space, which itself arises from the tetrahedral connections. The “influence” of each object – the bias on displacement probabilities caused by vacancy expulsion – can be thought of as spreading out through the network. Because this network is three-dimensional, as a direct consequence of its construction from interconnected tetrahedra, this influence is ‘diluted’ proportionally to the surface area of a sphere (4πr²). A particle at distance ‘r’ (measured in displacement steps) from the source is less likely to be affected by a displacement cascade originating from the source, and this probability decreases with the square of the distance

F = Gm₁m₂ / r²

We would see an attractive relationship between objects that is analogous to the classical gravitational formula.

Emergent Gravitational Constant (G):

The constant ‘G’ in Newton’s formula would not be a fundamental constant in our model. It would be an emergent quantity, determined by the details of the displacement rule, the boundary pressure, and the tetrahedral geometry. Determining the precise relationship between G and the fundamental parameters of the model is a key area for future work.