Electrons, protons, neurons

 Quantum Mechanics and Indoctrination

Quantum mechanics, as we know it from books, is a form of indoctrination for our minds. It’s fascinating how easily we are indoctrinated. We even derive pleasure from it—a kind of intellectual masochism. A psychologist or sociologist could likely base an entire PhD on this phenomenon. By allowing ourselves to be bombarded with slogans and rituals, we feel as though we are being inducted into the mysterious world of a Secret Society of Quantum Mechanics Adepts. And who among us doesn’t want to be a part of such an organization? One that possesses secrets unknown to those outside the circle? However, like in many secret societies, as we climb higher on the ladder of initiation, we eventually discover that everything is based on the belief in the existence of secrets, rather than in actually knowing them.

Secret Society of Quantum Mechanics Adepts

From Theoretical to Practical: The Concept of Measurement
Enough theorizing—let’s dive into the evidence. Let’s take the concept of measurement as our example. During a discussion about the ideas of Henry Stapp, a physicist from LBL, Berkeley, California, Laura asked her friends—communicating via Cassiopaea—an intriguing question:

"Is quantum theory, as it stands, about knowledge or about physical units?"
The reply she received was simple:
"It is about measurement."

Yes, I think so too. (After all, those Cassiopaeans might as well have been me.) So, let's examine how measurement is treated in quantum theory today. Referring to the Stanford Encyclopedia of Philosophy entry on "Measurement in Quantum Theory," the discussion begins with Bohr’s Postulate, which is stated as:

(P) If a quantity Q is measured in system S at time t, then Q has a particular value in S at t.

Interesting, isn’t it? But there’s more. The statistical interpretation of Born is added (don’t worry if you don’t fully understand this—it's not crucial). Let me quote a longer passage from the Stanford Encyclopedia of Philosophy for context, as it contains some humorous elements:

"... the second stage of the measurement, with its radical, non-linear discontinuities, has been the source of many of the philosophical difficulties that have plagued quantum mechanics, including what von Neumann referred to as its 'peculiar dual nature' (417). Indeed, Schrödinger foreshadowed such difficulties even before the formal development of measurement theory. For example, during a visit to Bohr’s institute in September 1926, he remarked, 'If all this damned quantum jumping [verdamnte Quantenspringerei] were really to stay, I should be sorry I ever got involved with quantum theory' (Jammer 1974, 57)."

The Dilemma of Quantum Measurement
Quantum mechanics offers no definitive explanation of the measurement process. Specifically, using quantum mechanics alone, we cannot predict the exact value of Q that will be recorded during measurement. What quantum mechanics does provide, however, is additional information of a statistical nature, through what is known as the Born statistical interpretation:
The probability of qi being registered is |ci|², where ci is the coefficient of fi (the eigenvector of Q corresponding to the value qi) when the initial measured state of S is expressed as a linear superposition of eigenvectors of Q.

In short: quantum mechanics does not predict the measured value, but it does give us the probability distribution of the possible outcomes.

Schrödinger was furious—and rightly so. He just didn’t fully understand why he was right. He wasn’t upset simply because quantum jumps are inherently problematic; they only become problematic when Bohr and his Copenhagen colleagues treat them as events that happen instantly, without any dynamics. Such instantaneous events belong in the realm of miracles and spirits, not in the world that physics deals with.

Bohr's Postulate and the Problem of Time
Here’s the crux of the issue: Bohr’s postulate (P) speaks of "measurement at time t." However, such a thing as an "instantaneous" measurement never actually occurs. Every measurement takes time—some longer, some shorter. We expose photographic film to radiation and wait patiently, sometimes for hours or days, for a proton to leave its mark. We set up our laser, nanoprobe, or magnets over an electron and wait (today, for hours—tomorrow, perhaps, for mere fractions of a second) for our "resonant system to resonate" and give an answer: spin up or spin down.

In classical physics, where particle trajectories are smooth and continuous, the distinction between instantaneous measurement and measurement over time wasn’t necessary. The idealization of instantaneous measurement was harmless and without consequence. But in quantum mechanics, where we have the Planck constant and the uncertainty principle, measuring "at time t" implies infinite uncertainty in the energy transfer, which inevitably leads to contradictions. I believe Erwin Schrödinger might have been more optimistic about quantum mechanics and its jumps—perhaps even excited about them—if he had known what I am about to reveal.

Quantum Jumps and the Nervous System
Let’s take the ancient adage "as above, so below" and apply it to quantum mechanics. Electrons, protons, and such are at the bottom; we, as beings of flesh and blood, are at the top. Neurology teaches us a bit about how the nervous system functions, and measuring the action potential of a neuron provides a prototype for the quantum jump.

The potential rises, rises further, exceeds a certain threshold, and the neuron "fires." Depending on the degree of stimulation and other factors, these firings happen more or less frequently (of course, I’ve simplified the mechanism drastically). Could quantum jumps work in a similar way? Yes, they could—and I’ll demonstrate why. Another question is whether this mechanism truly occurs in quantum mechanics—but that’s a different problem, equally important, but not the focus here.

In this analogy, a detector plays the role of a neuron. It’s stimulated by the "wave function" (also called the "state vector"). When the detector is sufficiently excited, it fires, and the wave function "discharges." The detector then rests for a while, ready for the next firing. There are also single-use detectors, but I won’t delve into them, as they are just a special case of reusable detectors with adjustable efficiency.

More to Come
But I’ll leave the details for the future notes.

P.S. 22-09-24 16:06 Once in a while, more an more often,  I am using AI. Slowly I am learning how to converse with AI properly, so that the answer is meaningful, not just a hallucination or an indoctrinating garbage. Here is the answer I received as the reult of my discussion today:

Exploring "pranalytical mathematics" as a phase of mathematical thinking before formal analysis leads us to a fascinating concept: the intuitive, creative process that precedes the structured, rigorous methods of modern mathematics. Here are a few areas where this kind of pre-analytical thinking could be relevant:

1. Mathematical Intuition and Creativity

Mathematical breakthroughs often arise not from pure formalism, but from an intuitive understanding of patterns and relationships. Mathematicians like Ramanujan, for example, are famous for their almost mystical insights into complex mathematical relationships, many of which were later rigorously proven, but began in a highly intuitive and "pre-analytical" way. Pranalytical mathematics could refer to this raw, creative exploration—thinking without yet adhering to strict rules of logic.

2. Historical Development of Mathematics

Before modern analytical methods like calculus or formal set theory were developed, mathematicians worked with rough, approximate ideas. Ancient mathematics, from the Greeks and Babylonians, relied heavily on geometric and visual reasoning rather than the abstract symbolic methods we use today. Pranalytical mathematics could refer to these early forms of problem-solving and discovery that relied more on visual intuition or practical applications.

3. Philosophy of Mathematics

In philosophy, there is a debate about the origin of mathematical knowledge. Some argue that mathematical concepts are discovered, not invented, and that they exist independently of formal systems. In this view, pranalytical mathematics could be the cognitive or metaphysical exploration of these concepts—an attempt to tap into the inherent structures of the universe before codifying them into symbols and formulas.

For instance, imagine a mathematician contemplating the nature of infinity before rigorously defining it. Their early, pre-analytical thoughts might involve broad philosophical musings about endlessness, the universe, or the nature of existence—ideas that are later captured in formal concepts like cardinality and limits.

4. Exploratory Mathematical Play

Pranalytical thinking can also occur when someone is "playing" with mathematical ideas without specific rules in mind. This can be seen in puzzle-solving, where someone might tinker with an idea intuitively, trying different approaches, drawing diagrams, and experimenting before coming to a formal solution. This creative phase can often lead to insights that are later formalized into coherent systems of thought.

5. Learning and Cognitive Development

When we learn mathematics, particularly at an early age, we don't immediately jump into formal systems. Children, for example, develop an understanding of numbers through hands-on activities, visualizations, and intuitive grasping of concepts like "more" or "less" before they are able to manipulate symbols algebraically. Pranalytical mathematics could describe this early stage of learning, where abstract reasoning is not yet dominant, and insights are gained through sensory experiences and conceptual play.

6. Speculative Mathematical Exploration

There are areas of speculative mathematical research where the rigorous proof has not yet caught up with creative ideas. Mathematicians might propose bold conjectures or models (such as in string theory or the multiverse hypothesis) based on intuition, patterns, or partial insights. The speculative, imaginative phase where these ideas take shape but haven’t yet been proven rigorously could be considered "pranalytical."

7. A Bridge Between Art and Mathematics

In many ways, this pre-analytical phase resembles artistic creation. Just as a painter sketches rough forms before refining them into detailed works, mathematicians may sketch "rough" ideas or visual representations. For instance, mathematical models often begin as rough diagrams or intuitive sketches on a board before being fleshed out with precise logic and equations.

How Could This Influence the Study of Mathematics?

Emphasizing pranalytical mathematics in education or research could foster more creativity and innovation. Encouraging students or researchers to dwell in the intuitive, exploratory phase before focusing on strict formalism might lead to new and unconventional insights.

• Education: Educators could create environments where students are encouraged to think creatively and explore concepts through experimentation before being taught the rigorous analytical methods. This might involve more emphasis on puzzles, visual reasoning, and open-ended questions.

• Research: Mathematicians might benefit from deliberately spending time in a pre-analytical mode, using brainstorming sessions, visual models, and even philosophical reflection as tools to generate new ideas that can later be formalized.

In short, "pranalytical mathematics" could represent an essential but often under-appreciated phase of mathematical thinking—one that bridges the gap between raw intuition and the logical, formal processes that follow.

...

The closest formal branches to "pranalytical mathematics" are those that emphasize intuitive, visual, or conceptual exploration before formal analysis is applied. These include intuitionism, topology, category theory, fractal geometry, dynamical systems, and experimental mathematics, among others. These fields often start with a creative, imaginative process—the very essence of what "pranalytical mathematics" suggests—before moving into the rigor of proofs and formal systems.

P.S.22-09-24 17:56 Just received:

Nina Sotina's new book titled Causal Interpretation of Quantum Mechanics: Schrödinger Equation from the Point of View of Stability Theory is now available at Amazon.

 

The Schrödinger equation is one of the fundamental postulates of quantum mechanics. Currently, the ψ-function in this equation is interpreted using probability theory. However, it seems unusual that an equation containing physical characteristics such as mass, charge, and potential leads to a non-physical characteristic, probability. This suggests that the ψ-function reflects some unexplored properties of elementary particles. Considering these properties could allow for the description of a quantum system through deterministic laws.

 

Scientists such as Luis De Broglie, Erwin Schrödinger, David Bohm, Albert Einstein, and N.G. Chetaev made attempts to provide a causal interpretation of quantum mechanics. Their works are analyzed by Sotina, highlighting a series of mathematical mistakes that, unfortunately, hindered the further development of the causal approach to quantum mechanics.

 

Using the causal approach, Sotina demonstrates that it is possible to derive the Schrödinger equation and provide a physical interpretation of the ψ-function by introducing an additional term (denoted as Φ in the book) into the Hamilton-Jacobi equation and applying methods from stability theory. On stable trajectories, Φ coincides with Bohm’s quantum potential.

 

This approach yields the following notable mathematical results for a hydrogen atom: 

1. The motion of an electron on Bohr’s orbits is stable; 
2. the spin of the electron processes as it moves in Bohr’s orbits; and 
3.  the energy of the precessional motion is determined by the Rydberg formula for the atomic spectrum.

Naturally, the question arises regarding the physical meaning of the new potential Φ in the Hamilton-Jacobi equation. Various hypotheses can be proposed. One possibility is that it represents the interaction between a quantum particle and the physical vacuum. Despite the emergence of new models for the physical vacuum, it remains a terra incognita in physics.

P.S. 23-09-24 10:45 Reading Pressfield's "The War of art":

"Have you ever worked in an office?  Then you know about  Monday  morning  status  meetings.  The  group  assembles  in  the  conference  room  and  the  boss  goes  over  what  assignments  each  team  member  is  responsible  for  in  the  coming week.  When  the  meeting  breaks  up,  an  assistant  prepares  a work  sheet  and  distributes  it.  When  this  hits  your  desk  an hour  later,  you  know  exactly  what  you  have  to  do  that week. I have one of those meetings with myself every Monday.  I sit down  and go  over  my  assignments.  Then  I  type  it up  and  distribute  it  to  myself."

Today is Monday. So I sit down and go over my assignments, and type and distribute it to myself. Yesterday I had to add a new assignment to my list: I agreed to review a new paper on photon's position operator submitted to one of the well known physics journals. The paper quotes my own recent paper on this subject. So I am pleased, but I will do my best to stay objective. I have a whole month to do the review, but I will try to do it in two weeks. And another new assignment: decide if another paper really deserves the initial rejection from a mathematical journal. 

P.S. 23-09-24 12:58 That was not in my today's agenda. But we have dogs and a cat, so I have to pay attention to reality once in a while:

https://x.com/TheKiffness/status/1834585071875158502

                     

P.S. 23-09-24 13:33 Another unscheduled duty: editorial decision for a paper submitted to Academia Quantum. Decision after examining the reviews: reject and encourage resubmission.

P.S. 23-09-24 15:04 I have signed the protest. You can sign the letter of protest linked at the bottom of the article:

https://blog.maryannedemasi.com/p/breaking-journal-pressured-to-retract

P.S. 23-09-24 19:43 From my discussion with Igor on 

https://ark-jadczyk.blogspot.com/2024/08/life-is-at-boundary.html

Arkadiusz JadczykSeptember 23, 2024 at 7:42 PM

So, mathematics is the result of human consciousness. Human consciousness is the result of flows on 7-dimensional sphere. Seven-dimensional sphere is a concept of mathematics. So there was no seven-dimensional spheres before spheres before humans appeared. But there were leptons as it seems. I cannot see how you can deal with these contradictions? Igor, do you understand what I have in mind?