CONTINUUM FROM DISCONTINUUM

Discontinuing The Continuum, Replacing It By Quantum Entanglement Of Granular Substrate:

Is the universe granular? Discontinuous? Is spacetime somehow emergent? I do have an integrated solution to these quandaries, using basic mass-energy physics, and quantum entanglement. (The two master ideas I use here are mine alone, and if I am right, will change physics radically in the fullness of time.)  

First let me point out that worrying about this is not just a pet lunacy of mine. Edward Witten is the only physicist to have got a top mathematics prize, and is viewed by many as the world’s top physicist (I have met with him). He gave a very interesting interview to Quanta Magazine: “A Physicist’s Physicist Ponders the Nature of Reality.

Edward Witten reflects on the meaning of dualities in physics and math, emergent space-time, and the pursuit of a complete description of nature.”

Witten ponders, I answer.

Quantum Entanglement enables to build existence over extended space with a wealth exponentially growing beyond granular space

Witten: “I tend to assume that space-time and everything in it are in some sense emergent. By the way, you’ll certainly find that that’s what Wheeler expected in his essay [Information, Physics, Quantum, Wheeler’s 1989 essay propounding the idea that the physical universe arises from information, which he dubbed “it from bit.” He should have called it: “It from Qubit”. But the word “Qubit” didn’t exist yet; nor really the concept, as physicists had not realized yet the importance of entanglement and nonlocality in building the universe: they viewed them more as “spooky” oddities on the verge of self-contradiction. ..]

Edward Witten: As you’ll read, he [Wheeler] thought the continuum was wrong in both physics and math. He did not think one’s microscopic description of space-time should use a continuum of any kind — neither a continuum of space nor a continuum of time, nor even a continuum of real numbers. On the space and time, I’m sympathetic to that. On the real numbers, I’ve got to plead ignorance or agnosticism. It is something I wonder about, but I’ve tried to imagine what it could mean to not use the continuum of real numbers, and the one logician I tried discussing it with didn’t help me.”

***

Well, I spent much more time studying logic than Witten, a forlorn, despised and alienating task. (Yet, when one is driven by knowledge, nothing beats an Internet connected cave in the desert, far from the distracting trivialities!) Studying fundamental logic, an exercise mathematicians, let alone physicists, tend to detest, brought me enlightenment. mostly because it shows how relative it is, and how it can take thousands of years to make simple, obvious steps. How to solve this lack of logical imagination affecting the tremendous mathematician cum physicist Witten? Simple. From energy considerations, there is an event horizon to how large an expression can be written. Thus, in particular there is a limit to the size of a number. Basically, a number can’t be larger than the universe.

https://patriceayme.wordpress.com/2011/10/10/largest-number/

This also holds for the continuum: just as numbers can’t be arbitrarily large, neither can the digital expression of a given number be arbitrarily long. In other words, irrational numbers don’t exist (I will detail in the future what is wrong with the 24 century old proof, step by step).

As the world consists in sets of entangled quantum states (also known as “qubits”), the number of states can get much larger than the world of numbers. For example a set of 300 entangled up or down spins presents with 2^300 states (much larger than the number of atoms in the observable, 100 billion light years across universe). Such sets (“quantum simulators”) have been basically implemented in the lab.

Digital computers only work with finite expressions. Thus practical, effective logic uses already only finite mathematics, and finite logic. Thus there is no difficulty to use only finite mathematics. Physically, it presents the interest of removing many infinities (although not renormalization!)

Quantum entanglement creates a much richer spacetime than the granular subjacent space. Thus an apparently continuous spacetime is emergent from granular space. Let’s go back to the example above: 300 spins, in a small space, once quantum entangled, give a much richer spacetime quantum space of 2^300 states.

Consider again a set S of 300 particles (a practical case would be 300 atoms with spins up or down). If a set of “particles” are all entangled together I will call that a EQN (Entangled Quantum Network). Now consider an incoming wave W (typically a photonic or gravitational wave; but it could be a phonon, etc.). Classically, if the 300 particles were… classical, W has little probability to interact with S, because it has ONLY 300 “things”, 300 entities, to interact with. Quantum Mechanically, though, it has 2^300 “things”, all the states of the EQN, to interact with. Thus, a much higher probability of interacting. Certainly the wave W is more likely to interact wit2^300 entities than with 300, in the same space! (The classical computations can’t be made from scratch by me, or anybody else; but the classical computation, depending on “transparency” of a film of 300 particles would actually depend upon the Quantum computation nature makes discreetly, yet pervasely!

EQNs make (mathematically at least) an all pervasive “volume” occupying wave. I wrote “volume” with quote-unquote, because some smart asses, very long ago (nearly a century) pointed out that the Quantum Waves are in “PHASE” space, thus are NOT “real” waves. Whatever that means: Quantum volumes/spaces in which Quantum Waves compute can be very complicated, beyond electoral gerrymandering of congressional districts in the USA! In particular, they don’t have to be 3D “volumes”. That doesn’t make them less “real”. To allude to well-established mathematics: a segment is a one dimensional volume. A space filling curve is also a sort of volume, as is a fractal (and has a fractal dimension).

Now quantum entanglement has been demonstrated over thousands of kilometers, and mass (so to speak) quantum entanglement has been demonstrated over 500 nanometers (5,000 times the size of an atom). One has to understand that solids are held by quantum entanglement. So there is plenty enough entanglement to generate spaces of apparently continuous possibilities and even consciousness… from a fundamentally granular space.

Entanglement, or how to get continuum from discontinuum. (To sound like Wheeler.)

The preceding seems pretty obvious to me. Once those truths get around, everybody will say:’But of course, that’s so obvious! Didn’t Witten say that first?’

No, he didn’t.

You read it here first.

Granular space giving rise to practically continuous spacetime is an idea where deep philosophy proved vastly superior to the shortsightedness of vulgar mathematics.

Patrice Ayme’