P-adic Entanglement

As you probably know science today can't explain Quantum Entanglement.

I invented an explanation to the hidden mechanism behind Quantum Entanglement!

The problem - "spooky action at a distance"

If we "connect" (entangle) two small (quantum) particles in a special way, then after we "connected" them, we can separate them over very large distance, even two opposite sides of the universe,

but still each of the particles will "know" what happens to the other one IMMEDIATELY, in spite the fact that they can't communicate between them. (such communication would take them years).

Einstein hated it and called it "spooky action at a distance".

The solution - "common action at a proximity"

In a nutshell, my theory takes the "spookiness" out of the particles and puts it into the structure of space itself.

First of all please allow me to establish a few simple ideas that are unrelated to each other.

Later, we will build on these ideas some more complicated ideas and tie them together.

Metaphor I - Chessboard

The idea came to me from Richard Feynman's Lectures on Physics, Lecture 2 Basic Physics Section 1 - Introduction:

In the game of chess, if a bishop starts on light color squares, then it will be on the same light color squares throughout the chess game. If it starts on dark sqaures, it will always be on dark squares.

Metaphor II - Pixels

When I was a teenager, I liked to program graphics in DOS. Each tiny "square" of light on the screen is called a pixel. The screen resolution in DOS is very grainy: 320 pixels across, and 200 pixels down.

Let's say we want to rotate a point of light (pixel) around the center of the screen. We would hold the real accurate coordinates (floating point numbers with decimal precision) in the memory all the time,

Then we would do some calculations (sines, cosines) with these accurate floating point coordinates, to figure out what is the next position for our rotating point, but not drawing anything yet.

Now we "translate" (round up or down) the accurate floating point coordinates in the memory, into not accurate at all integer (whole numbers) coordinates on the screen, and we draw in the integers coordinates.

Metaphor III - Distorting mirror

You've probably seen a distorting mirror in a carnival fair "mystery room" or in a science museum "optical illustions" room. Let's think of a mirror that makes you look very tall and thin.

If we would hold a "measuring tape" or a ruler in front of that distorting mirror, we would see the number line "compressed" together.

We can think of another form of distorting mirror that is curved in its sides more than its middle, so it's distorting non-uniformally: the more you move to the side the more the numbers are close together.

P-adic numbers and ultrametric space

I'll try to explain here what P-adic numbers are, but do yourself a favor and read the friendly introduction in Wikipedia.

P-Adic numbers

In p-adic numbers, the closer you are the further you are, and the further you are the closer you are.

The world of p-adic numbers is "upside down" in the sense that instead of the difference,

we look at the reciprocal of the difference (one over the difference) like so:

Example I

With "normal" numbers, 0.005 is close to 0.004 because the difference is 1/1000 (one thousandth)

With "p-adic" numbers, 0.005 is far from 0.004 because the difference is 1000 (one thousand)

Example II

With "normal" numbers, 5000 is far from 4000 because the difference is 1000 (one thousand)

With "p-adic" numbers, 5000 is close to 4000 because the difference is 1/1000 (one thousandth)

Example III

With "normal" numbers, 5000000 is very far from 4000000 because the difference is 1000000 (million)

With "p-adic" numbers, 5000000 is very close to 4000000 because the difference is 1/1000000 (millionth)

This isn't correct, but it gives you the correct "feeling" of what p-adic numbers behave like.

Also know that it's possible to do Calculus and Complex Numbers and everything with p-adic numbers.

Ultrametric space

If you look up ultrametric space in Wikipedia, its formal definition is:

A space where every triangle is a Isosceles triangle which is taller and thinner than a Equilateral triangle with the same base. Meaning the base of every triangle is "squeezed" to be slim.

But that doesn't help very much, so a better "definition" from StackExchange question about "Visualizing Balls in Ultrametric Spaces" and especially Mirko's answer there:

Think of the Cantor set and its basic closed-and-open intervals, ... Note that for any two such intervals, they either do not intersect, or one is contained in the other.

The reason that I'm bringing talking about the "Ultrametric Space" is :

(1) The p-adic numbers form a complete ultrametric space.

(2) This fractal like structure creates "dust" that is spread evenly and yet not continously but discretely throughout space (in the case of p-adic numbers: throughout the number line).

Another application (example) of an "ultrametric space" "Tree of Life" in biology, also called "Phylogenetic Tree".

The distance from the root to the end of every leaf is the same. (The Cantor Set middle points are also shown like a binary tree (in red color) with this property in one of the pictures in Wikipedia)

Discrete Space

OK, so now after a long (and hopefully gradual) preperation we are getting to my theory:

My first step is that I think space is not continous but instead space is discrete.

This isn't as bizarre as it sounds, you can read in Wikipedia - Quantum Spacetime.

One set of rounded coordinates

I think that the space that we see is like the pixels on the screen metaphor.

Of course instead of 2-D pixels Mother Nature uses 3-D voxels, and she has better hardware than a personal computer.

The "display" coordinates are the only type of coordinates that we can see. They are like the integer values of the little "squares".

The real calculations of movement (before being rounded for the display squares) are done in two other systems of coordinates which are a lot more accurate:

Two sets of accurate coordinates

Most people know about the rational numbers (something divided by something else).

But what most people are unaware of is that these numbers come in two "flavors": "normal" and p-adic.

But we know the p-adic numbers are just as good, and they also have their special property of "flipped" distance.

So I claim that "normally" all the particles are on the "normal" rational coordinates.

But when we "entangle" two particles, what we are actually doing is giving them a little "nudge" and push them onto p-adic coordinates.

To us they still look the same because we only see the rounded display coordinates, and the two accurate coordinates are doing rounding in the same way;

But in fact the two "entangled" particles are close to each other because in p-adic world the further apart they are, the closer they get.

Distorted mirror interpretation

If the p-adic distance behavior still makes no sense think about the following model:

in every "normal" coordinate on the number line we put a normal glass window so what is near looks near; what is far looks far.

in every "p-adic" coordinate on the number line we put distorted glass window so what is near looks near; and what is far also looks near.

remember: it "shrinks" the number line horizontally so that even the opposite ends of the universe become near.

Distorted chessboard interpretation

Let's say that the light color squares are the "normal" rational coordinates. The dark color squares are the p-adic coordinates.

Once the two bishops were pushed slightly to the dark squares, the other pieces are transparent for them - the two bishops have a clear line of sight to act on each other.

What's more - the special structure of the p-adic space means that while the light color "normal" coordinates grid remains rigid and flat, the dark color p-adic coordinates are curved so that very far away ends become close together.

This is like the situation on the ball we live on - planet Earth - when you walk a long distance from where you are (far), you eventually return to the same place (close).

Visualization with wooden chessboard

This chessboard is very dear to me: It was hand-made by my father when he was a boy! On the other side it closes like a box for the pieces and also has backgammon triangles.

1. How it looks to us

2. Discrete space

3. Entangled bishops colored in black

4. Curved space

5. Entangled bishops on ball

Proper disclosure

AFTER I thought about this MYSELF I found a physicist named Tim Palmer who have a similar theory!

(At least I think it's similar, because I can't understand the "hardcore" mathematics).

A link to the non-technical article in the magazine New Scientist:


A link to the full article here - thank you Stealth Skater!


You can read about Tim Palmer in Wikipedia - he's very impressive!

and also about his theory: Invariant set postulate

And also this technical article by Tim Palmer that really sounds like what I'm saying (at least the headline - the rest I can't understand)

p-adic Distance, Finite Precision and Emergent Superdeterminism: A Number-Theoretic Consistent-Histories Approach to Local Quantum Realism

See also:

P-adic Quantum Mechanics