Everything in Discrete Space

I'm working through the implications of discrete space and am starting to build some intriguing intuitions. I am trying to reduce the physical world down to a bunch of geometric atoms changing state—essentially, to a grid of voxels.

I don't claim the following is true, only that it's a coherent way to explain a bunch of concepts, including motion, mass, fields (gravity and electromagnetism), local and non-local interaction, fluid dynamics, and even exotic things like quantum tunneling and time dilation. All of these phenomena follow from a simple model with a simple axiom.

Model: The physical world is composed of discrete atoms of space ("voxels") in particular states. These states are called "bits." In the simplest model, there are only two possible states—off or on, 0 or 1, empty or full.

Axiom: Two bits cannot occupy the same space.

That's the setup. Let's see how far we can push it.

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The basics:

"Motion" is a transmission of bits through the grid. The voxels themselves do not move; instead, their bit state transfers.

Local interaction happens when there is a local "collision" of these bits.

Non-local interaction happens when bit states are connected at a distance.

Mass is a type of geometric structure in the grid. It is a pattern of voxels.

Relative to the individual voxel, objects like atoms are incredibly large, dense structures.

Fields, like mass, are a type of structure in the grid. The difference between mass and fields is only the configuration of their voxels. These different configurations produce different patterns when interacting with the world—e.g. the gravitational and electromagnetic fields create different "forces" because they are different geometric structures. Your car acts differently whether it's driving on gravel or asphalt, going uphill or down.

Objects as Extended Structure:

Where are the boundaries of objects?

In this model, the totality of an object includes all its geometric structure—both its mass and fields. It's helpful to think of mass as "macrostructure" and fields as "microstructure". A gravitational field, then, could be considered as part of the extended structure of an object—reaching beyond its dense atomic structure to interact with distant objects. So for example, the mass of your body affects the motion of the sun; therefore, your extended body reaches to the sun.

Fields and Biased Motion:

Motion is the transmission of bits through the grid. As the bits move, they must interact with the existing structures in the grid. This includes macrostructures (atoms) and microstructures (fields).

The gravitational field is simply a microstructure that biases motion towards its center of mass.

Take bowling as an analogy. You throw the bowling ball down the lane, towards a triangular structure of pins. If it lands on the left side of the triangle, it will bounce off to the left. If the ball lands on the right side, it will bounce towards the right. So we could say the triangular structure of the pins is biasing the motion of the ball (preventing it from moving straight).

With a gravitational field, if it's actually just a microstructure in a grid, we could say it has an inward bias. The greater the mass, the denser the field, the stronger the bias.

If this is correct, then we could say gravity has a shape. That is, there's a micro-structure that we call "gravity" which forms a field that interacts with passing bits and nudges them towards a center mass. Rather than space itself being distorted, gravity is a structure in space that distorts motion.

Electromagnetic fields are more complex. Instead of simply nudging bits towards a center mass, they bias motion depending on other factors like charge and velocity (which can also be interpreted geometrically). "Field lines" would then map real biases generated by underlying geometric structures.

Exotic Intuitions

This model also gives a plausible reason for “time dilation.” Larger masses create denser microstructures in the field, which increases the interactions encountered by propagating bits. These interactions effectively slow the transmission of states, resulting in an observable time dilation effect—akin to moving through a denser medium.

And the “quantum tunneling” phenomenon has a perfect explanation. In discrete space, objects have jagged edges, which means the "energy barriers" between boundaries are neither uniform nor smooth. This means, for purely geometric reasons, some bits can “hop” across boundaries effortlessly. In fact, in discrete space, lines can “intersect” without even sharing a common point!

If space is discrete, we would expect to see tunneling. I consider the empirical discovery of tunneling to be evidence of the discreteness of space. (Imagine making such a prediction prior to the discovery of tunneling—people would think it’s ridiculous and impossible!)

A Conceptual Toolbox

I am early in my journey through theoretical physics and still playing with ideas. I only have a handful of strong beliefs. However, I’m slowly growing my conceptual toolbox, and I suspect some of these tools will be handy indeed.