Why Quantum Mechanics Feels Like a Cosmic Prank (But Also, Maybe Not?)

 This post explores the second "sin" of quantum mechanics—the apparent non-causal nature of the universe at a microscopic level. Understanding this oddball feature can change how we see everything from science to philosophy, and even life itself. Plus, it's always fun to ponder if we're all just cosmic dice throws, right?

God playing dice?

A Recap: Quantum Mechanics and its "Sins"

In my earlier post, Quantum Sins: Why I'm Not Sold on the Uncertainty of It All, I dug into one of quantum mechanics' gravest offenses—its inherently probabilistic nature. According to the book The Emerging Quantum: The Physics Behind Quantum Mechanics by Luis de la Peña, Ana María Cetto, and Andrea Valdés Hernández, this world, full of chaotic energy fields and quantum fuzziness, is driven by probabilities. You just have to accept that and move on (shut up and calculate, they say).

But there’s more to the story. In their view, these quantum oddities might stem from fluctuations in the "aether"—or as they cautiously term it, the "zero-point energy field." Yes, that mysterious "beast" that no one quite understands. While it doesn't answer all our burning questions, it gives us something more to work with, even though with this alternative view the world appears to be even more complex than we would wish.

Zero-point energy field

Note: By the way: you can find a nice and informative literary/journalistic exposition of the zero-point energy field concept  in the book "The Field" by Lynne McTaggart.

A really pleasant read, with a window into the paranormal world, and with lot of references.

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Enter the Second Sin: Non-Causality

And now, dear reader, brace yourself for Quantum Sin #2—non-causality as the authors of "The Emerging Quantum" term it. Yep, quantum mechanics is a rebel without a cause. One shining example of this noncausality is the famous Heisenberg Uncertainty Principle. If you've ever wanted to pin down the trajectory of an electron, forget about it. Heisenberg's inequalities imply that there are inevitable quantum fluctuations (whatever it means)", trajectories simply do not exist (and it is not made clear what it is that "exist", beyond the "math" and the mysterious "observer", who is not even a part of the theory),  and to make things weirder, the theory itself provides no reason why they happen.

Heisenberg Uncertainty

It's as if quantum mechanics decided, "Let’s just say things happen randomly. No need to explain further." Naturally, this has led to fierce debates among physicists—some argue it's just ignorance on our part, while others think it's the universe keeping its secrets well-hidden, like a magician refusing to reveal how the rabbit got into the hat.

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The Story of Heisenberg's Fluctuations (Minus the Observers)

Now, if you’ve heard the textbook explanation for the Uncertainty Principle, it probably involved an electron being disturbed by an observer. You know, the whole "Schrödinger’s cat is dead AND alive" until-someone-looks situation. But the real kicker is that Heisenberg’s inequalities follow mathematically from quantum theory, no observers necessary! "Observers" undefined within the formalism. It's like a party that happens whether or not anyone shows up.

The uncertainties (or “indeterminacies” if we’re feeling fancy) are woven into the fabric of reality. And here's the fun part—try explaining that one at a cocktail party.

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Energy-Time Inequality: A Special Kind of Weird

If you thought the regular Uncertainty Principle was trippy, wait till you get to the energy-time inequality. This one's even more out there because it doesn’t fit nicely into the usual quantum mechanics toolkit. It is there, and it is not! Over the years, various theorists have tried to patch this up with new proposals, and some (including the author of this post) have even played with the idea of introducing a "time operator" (cue dramatic music).

Still, most physicists wave their hands and say, "Eh, it's spontaneous!" It's like they’ve decided that quantum fluctuations are the universe's equivalent of spontaneous combustion—no cause needed, just sit back and enjoy the chaos. Or, perhaps, it is just God playing invisible dice?

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A Different Take: My Event Enhanced Quantum Theory (EEQT)

Now, if you’re tired of all this quantum uncertainty and complementarity, let me offer you a little ray of hope. In Event Enhanced Quantum Theory (EEQT), the child of Ph. Blanchard and myself, things are a bit more grounded (but still pretty wild). The Heisenberg Uncertainty Principle holds true, but we add a twist. EEQT allows for the simultaneous (and even continuous)  measurement of variables that are usually incompatible—things like position and momentum or different spin components. Moreover, EEQT has the concept of "measurement" included in its extended math formalism!

Of course, chaos reigns in this world too, but it’s a chaos you can simulate on a regular old classical computer. And sometimes, amidst the madness, patterns emerge—beautiful, sometimes terrifying, quantum fractals. In fact, I wrote a whole book about these fractals, aptly titled Quantum Fractals. It's full of eye candy and scientific intrigue. Think of it as a fusion of quantum mechanics and abstract art—minus the pretentious gallery openings.

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Merging Worlds: EEQT Meets the Zero-Point Field?

Here’s where things get even more interesting (or insane, depending on your perspective). I’ve got this wild idea to merge EEQT with the zero-point energy field theory promoted by de la Peña and friends. It’s pure speculation at this point, but something deep inside tells me this could work. Maybe it’s a whisper from a benevolent angel, or perhaps it’s the trickster devil egging me on. Who knows? Either way, I won't know until I try.

So, that’s one of the many projects on my drawing board—a quantum adventure waiting to unfold.

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The Final Thought: The Dance of Quantum Chaos

In the end, quantum mechanics may feel like the ultimate cosmic prank, where things just "happen" without rhyme or reason. Yet, there’s something undeniably beautiful about it too. We may not understand the cause behind the quantum curtain, but we can still marvel at the dance it creates. And who knows? Maybe that very uncertainty is what makes life—and the universe—so full of wonder.

Monkeys, UFOs, and Quantum Fractals: A Mind-Bending Journey through Relativity and Imagination

The Quantum Sky and UFOs: A Puzzling Connection

Picture this: the mathematical world of quantum fractals applies not just to abstract quantum state vectors, but also to something as vast and visible as the sky. Yes, the actual sky. Quantum mechanics and Special Relativity share a hidden bond, one that links the rotation of quantum spin states on the Bloch sphere to the way light behaves in the heavens. Mind-blowing, isn’t it?

While this might sound like a leap from the purely theoretical to the outlandish, it’s grounded in rigorous formalism. You can almost see it—those elusive patterns in the cosmos that bend both light and logic. Let me take you further down the rabbit hole with a thought experiment that will stretch your imagination.

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UFOs, Aberrations, and Lawrence Krauss

Let’s first rewind to a passage from Lawrence M. Krauss's Beyond Star Trek:

“The traditional notion has been that UFOs don’t behave like rockets or planes (this is, after all, what makes them UFOs)... turning at 90-degree angles on a dime."

It’s a tantalizing idea. UFOs not only defy gravity but also physics as we know it, performing maneuvers that mock conventional aerodynamics. And let’s take it a step further—not just 90 degrees, but any angle, at any speed. All with a flick of a switch.

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Enter: The Monkey Pilot

Now, here’s where things get surreal. Imagine a monkey at the controls of one of these UFOs. Yes, a monkey. This primate has a joystick with 24 different positions, each pre-programmed for a specific, instantaneous maneuver. Every flick of the joystick sends the UFO into a new rotation or sudden acceleration.

 This primate has a joystick with 24 different positions

But this isn’t just about the ship’s wild movements. The monkey is also tracking a distant star—say, Betelgeuse—on a hemispherical dome. Every time the joystick moves, the star appears to shift on the dome due to the UFO’s motion and the relativistic aberration of light. The monkey repeats this process a hundred thousand times—randomly, relentlessly.

And then something bizarre happens. A pattern begins to emerge on the dome, as if the universe is leaving behind a cryptic signature for the monkey to discover.

Fractal pattern created by the monkey

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Science Fiction Today, Reality Tomorrow?

Today, this scene feels perfect for a sci-fi blockbuster, an absurd twist of logic and physics. Krauss would tell you that such maneuvers are impossible with our current understanding of science and technology. And he’d be right.

But tomorrow? Who knows? Science has a way of catching up with the impossible. The boundaries of reality bend when human beings refuse to accept limitations. What is fiction today might become the next experiment tomorrow.

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Quantum Fractals: From Monads to the Sky

This entire thought experiment stems from the idea in my book Quantum Fractals.

 In it, I delve into "qubits," the elementary quantum systems that, like Leibniz’s monads or modern digital bits, form the foundation of everything. But if the micro reflects the macro, as many believe, should we be surprised that the smallest quantum fractals can echo into the vastness of the cosmos?

From the quantum to the celestial, the patterns are there, waiting to be discovered—or maybe even flown through by a monkey in a UFO.

Parabolic quantum fractal on the Bloch sphere

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What’s left is for us to stretch our minds beyond the confines of current knowledge. After all, as the saying goes: "As above, so below."

Matrix=womb

 Wikipedia has an article "Pythagorean triple". 

It contains a lot of useful information, but what draws my particular attention is this sentence in the section "Spinors and the modular group":

The group Γ(2) is the free group whose generators are the matrices

Consequently, every primitive Pythagorean triple can be obtained in a unique way as a product of copies of the matrices U and L.

We will call these matrices U₂ and L₂. I really like the matrix U₂. Here is a piece from page 96 of my book Quantum Fractals.

The matrix U2 actively participated in creation of the cover image of my book

It deserves our special attention. And yes, it has to do with spinors, and it has to do with light. And, of course, with Pythagorean triples and quadruples, and even quintuples. There is a whole saga that needs to be told. But first things first. Step by step.

We will be dealing with matrices. While it is a plausible hypothesis that God created the integers (see my previous post "The magic of numbers 3,4,5", it is not clear who invented matrices  with their noncommutative multiplication rule. Till now nothing is known about matrices being featured in the Bible, Talmud or Babylonian tablets. The online paper "When was Matrix Multiplication invented?" informs us that:

1850 Sylvester first use of term "matrix" (matrice=pregnant animal in old french or matrix=womb in latin as it generates determinants)

1858 Cayley matrix algebra [7] but still in 3 dimensions [14]

1888 Giuseppe Peano (1858-1932) axioms of abstract vector space [12]

The Matrix is a womb. Billy Carson

I will assume that the Reader is acquainted with matrix multiplication. We will be dealing here first with 2x2 matrices: two rows and two columns. Then with 3x3 matrices, then with 4x4 matrices, then ... the future will tell. Matrices will have real or complex entries, but we will will be particularly interested in matrices with integer entries. The matrix U₂ above  has integer entries 0,1,2. Our cat Pikabu knows this matrix pretty well. 

Neo's Best Moments| The Matrix Trilogy | Max

There is a particular matrix with integer entries, we call it E. Wikipedia calls it the identity matrix and denotes it by the capital letter I:

The identity matrix is often denoted by ${\displaystyle {�}_{�}}$, or simply by ${\displaystyle �}$ if the size is immaterial or can be trivially determined by the context.^[1]

If A and B are square (the same number rows and columns) their matrix product (in the order written) is denoted AB. In general AB is not the same as BA. For an arbitrary matrix A and the identity matrix we have though AE=EA=A. If A,B are two matrices and AB=E, one can prove that then also BA=E. The matrix B with this property is unique and called the inverse A.  Quoting Wikipedia again:

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that

where I_n denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.^[1] If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A⁻¹. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

 Here Wikipedia is using bold letters to denote matrices. We will use normal letters. We will also need the concept of the determinant and trace. Exploiting the handy  Wikipedia again:

The determinant of a 2 × 2 matrix is

The trace Tr(A) of the matrix A is simply the sum of all its diagonal elements. In the acse of the 2x2 matrix above

Tr(A ) = a+d. 

There is a beautiful little paper by Roger C. Alperin "The Modular Tree of Pythagoras", p.807,  we notice the following interesting sentence

Order out of chaos. Fractals out of qubits

 Looking for an empty USB stick, by pure chance, of course, I have stumbled upon my old presentation. I must say I liked it! Not a bad one. So I will share it here today.

It is much like I am reading now my old papers about conformal infinity. I am trying to understand them and I can't stop wondering: 

-Who wrote this?  

-Was it me?

- Wait a moment, if it was me, why did I write that "it can be easily verified that the whole represented body is contained inside a sphere of radius 1"? 

I open Mathematica, write a line of code:

FindMaximum[{x1^2 + x2^2 + x4^2 + x5^2, x1^2 + x2^2 + x5^2 == 1, 

  x4^2 + x5^2 == 1}, x1, x2, x4, x5]

and look at the result:

{2., {x1 -> 0.707107, x2 -> 0.707107, x4 -> 1., x5 -> 5.71313*10^-10}}

and instantly see that it should be square root of 2 and not 1 as in the paper. Well, it does not matter in this case, but the author (me?) was certainly lousy!

Anyway, here is the presentation I have found this morning:

 

And on the same stick (as you see not quite an empty one) I have found also an mp4 file with this video that I have painfully made from thousands of separate frames: 

Parabolic quantum fractal

So the USB was not empty. It also contains high resolution graphics from the presentation. Like these:

And I have completely forgotten.

Now back to the conformal infinity - the nonlinear cap of our linear Minkowski space.

P.S.1. I asked my friend in Novosibirsk if he knows someone who can help me with my problems with the conformal infinity. Today I received his answer: I should contact Vasily Gorbunov. I have checked the webpage with some of his papers and I am amazed! Before asking my questions I should work really hard to prepare them. The better, I prepare my questions, the more I will be able to get from forthcoming replies. So, this is what I will be doing for next few days: making sure that I am asking questions to which I am not able to find answers all by myself!

P.S.2. I have used Povray to render the above graphics. Of course first I had to do all the necessary algebra by hand and using Mathematica. And, of course, I had to learn (though only superficially) how to use the software. It took me a while.

P.S.3. Yesterday (it was Tuesday)  I was afraid that I have made a mistake representing the doubled infinity as on this picture:

Double conformal infinity

I was thinking that the two singular points may be artefacts of the projection. Today it seems to me that they are really singular. But I am not yet 100% sure. Working on it. Need to understand how light travels when trapped in infinity. Then write another paper on the subject, this time doing everything right. 

But first I have to learn Projective Geometry - the subject I know about next to nothing!

P.S.4. Few days ago I have asked Masahito Saito, a topologist from the University of South Florida in Tampa,  for help with my double infinity. This morning I have received his kind reply. For a topologist the answer is simple: these are just two spheres touching at two points: north and South Poles:

"... So, topologically it seems to be two spheres with two pairs of points identified separately...."

 Can you see it? Can you see these two spheres?

P.S.5. Also this morning one of the authors (RI) of 

"A Mathematica Package for Visualizing Objects Inmersed in R4"

kindly provided me with their package. I still have to learn how to use it and see if it will be of some help.

P.S.6. Saturday 14-01-23, 11:36 AM. Patience, please. Started to write a new post, but had to pause, I am still working on a satisfactory understanding the whole situation. I am not satisfied yet. In fact - very far from being satisfied. Many questions without answers. Thus happiness (because there is so much work needed, and it is clear what kind of work), but no satisfaction - thus excitement.