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Possible Cancellation of Indeterminism in Quantum Mechanics (Step 3)

The Effective Particle Approach

Version 3.2 (full)

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Contents

1. Abstract
2. Introduction
   1. The Measurement Problem
   2. Randomness in the Detector
   3. Detector Ensemble
3. The Effective Particle Approach
   1. Effective Particle Hypothesis
   2. Scaling Effect
   3. Interim Summary
4. Consequences of the Approach
   1. Consistent Reality
   2. Probability Control
   3. Observer Effect
5. Experiments for Verification
   1. Indirect Experiments
   2. Direct Experiments
6. Mathematical Clarification
7. Conclusion
8. References

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Abstract

In the investigated approach, a non-standard application of Feynman's path integral leads to an unexpected interpretation of quantum mechanics: the cancellation of indeterminism and a practical resolution of the measurement problem. Some consequences can be verified experimentally. The source of randomness in quantum measurements is the ignorance of the exact microstate of detectors at each measurement.

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Introduction

The Measurement Problem

There are two types of randomness: randomness due to ignorance of initial conditions and true quantum randomness (indeterminism). With indeterminism, the knowability of the measurement problem is hindered. When probability is a postulate, it is impossible to imagine under what conditions measurement occurs and under what conditions it does not.

Randomness in the Detector

The wave function (WF) of detectors varies in each measurement. If randomness is due to ignorance of the exact WF of detectors at each measurement, then a question arises: if one detector measured a particle, how does the second detector "know" that it should not measure the particle? With spatially separated detectors, it seems they need superluminal communication. But let us consider the following system.

Detector Ensemble

Imagine that the detector is in a definite quantum state, but we don't know which one. Suppose there exists a statistical ensemble of possible detector states:

• $|\psi _{n}^{1}\rangle$ — states in which the detector will catch the particle with 100% probability
• $|\psi _{n}^{0}\rangle$ — states in which the detector deterministically will not catch the particle

Let $K=2N$ be the number of possible detector states.

Consider a quantum particle incident on two spatially separated identical detector ensembles. What is the probability that both detectors will catch the particle?

Simple summation gives: one detector ensemble will catch the particle with probability $1/2$, both will catch with probability $1/4$.

However, quantum intuition suggests: both detectors will fire only when they are in identical states $|\psi _{n}^{1}\rangle$. States $|\psi _{A1}^{1}\rangle$ and $|\psi _{B2}^{1}\rangle$ can decohere.

The probability of state $|\psi _{n}^{1}\rangle$ equals $1/(2N)$, the probability that both detectors will be in state $n$: $1/(2N)^{2}$.

Probability of simultaneous measurement:

$P_{\text{simul}}={\frac {N}{(2N)^{2}}}={\frac {1}{4N}}$

For macroscopic detectors $N\sim 10^{23}$ (Avogadro's number), and the probability of simultaneous firing is negligibly small.

How can states $|\psi _{A1}^{1}\rangle$ and $|\psi _{B2}^{1}\rangle$ decohere? This is possible in the effective particle approach.

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The Effective Particle Approach

Effective Particle Hypothesis

A dust particle consisting of millions of atoms is often described by a single-particle wave with definite momentum and wavelength. In a photodetector, a flow of electrons arises, which we register. Hypothetically, this flow can be represented as an effective particle with definite energy and wavelength.

Generalization: Any signal from measuring a quantum particle can be represented as an effective quantum particle.

During measurement, the effective particle acquires scale and kinetic energy. The kinetic energy of the electron flow in a photodetector is much greater than the kinetic energy of the measured particle.

In Feynman's path integral, all possible paths of the quantum system are integrated with weight $\exp(iS/\hbar )$, where $S$ is the classical action of the system:

$S=\int (T-U)\,dt$

In the absence of potential energy, the action is determined by kinetic energy.

Feynman Integral:

$A=\int {\mathcal {D}}\varphi \exp \left({\frac {iS[\varphi ]}{\hbar }}\right)$

Consider two paths of the effective particle from the source of the measured particle through detectors to the observer:

• Detector A in state $|\psi _{1A}^{1}\rangle$, effective particle exits with kinetic energy $T_{1A}$
• Detector B in state $|\psi _{2B}^{1}\rangle$, effective particle exits with kinetic energy $T_{2B}$

There is a high probability that one of the kinetic energies is much greater than the other relative to $\hbar$ (Planck's constant).

At the observer, both paths interfere. According to the stationary phase principle, the observer will see the particle with the lowest frequency (kinetic energy).

Consequence: The observer will not see simultaneous firing of two detectors when the states $|\psi _{n}^{1}\rangle$ of the detectors are different. The probability of identical detector states is negligibly small.

Resolution of the measurement problem:

1. Quantum detectors are in a random initial state. The randomness of measurement is a consequence of detector randomness.
2. Why do we see one variant of quantum measurement? Partially resolved. On one hand, the alternative measurement variant simply does not exist — the detector is in a definite state, and the "particle + detector" system evolves deterministically without any alternative variants. But simultaneous measurement by two detectors is allowed, we just don't see it. This is another variant of the many-worlds interpretation.

Remark: The signal to the observer might look like this: Bob measured the particle and called Wigner that the particle was in state B. The call is a signal to which it is difficult to attribute an effective particle with some momentum and energy. Is the effective particle hypothesis wrong? No, it's just unnecessary, but useful for associations.

The path integral applies to any quantum system. It's not necessary to consider an effective particle. It's sufficient to specify the initial state of particles and detectors, their action function, and consider the evolution paths of the system. Only the scaling effect and a large difference in energies at the detectors are mandatory.

Scaling Effect

We cannot see a quantum particle directly — its interaction with us is too small. Signal amplifiers are needed — quantum detectors.

The particle signal scales from weak to an avalanche of macroscopic effects. The kinetic energy of the system along the path through the detector grows.

Clarification: Kinetic energy may not grow (as in an astronaut's eye when hit by a cosmic particle), but it must be large and vary on each possible path.

Example: A cosmic particle hit both eyes of an astronaut, but in one eye there is one kinetic energy of "stars," and in the other — another. The astronaut sees stars in one eye.

Conclusion: Kinetic energy does not necessarily increase. The main thing is that it be large and there be a large difference in alternative paths.

Interim Summary

For the approach to work, the following are necessary:

1. Path integral
2. Random initial microstate of the system (in the considered case — random microstate of detectors)
3. Scaling effect and/or large difference in kinetic energies along paths

The approach is called the effective particle approach.

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Consequences of the Approach

Consistent Reality

Consider a quantum system consisting of a measured particle, observers Alice and Bob with detectors A and B, and observer Wigner, to whom Alice and Bob report measurement results.

Question: Can Alice and Bob simultaneously report that they registered the particle (assuming they always tell the truth)?

This system can be reduced to the one considered above, treating Alice and Bob with their detectors as two detectors (detector Alice and detector Bob). In the effective particle approach, Wigner can observe that only detector Alice or only detector Bob fired. Both firings simultaneously are negligibly probable.

If Alice calls Wigner and says "I caught the particle," and Wigner calls Bob and says "Alice caught the particle," can Bob discover that his detector fired?

Answer: No, because Bob's detector and the chain "Alice's detector — Alice — Wigner" can be considered as alternative paths of observer Bob. Similarly, all other call chains can be considered: Alice-Bob, Alice-Bob-Wigner.

Consistency principle: From the point of view of an arbitrarily chosen observer, all alternative paths must lead to one measurement result. All measurement results of other observers must be consistent with this observer's result. For each observer, the path with minimum action wins.

Many-worlds interpretation: Without considering that minimum action wins, one can say that there exist alternative worlds of observers with different measurement results.

Note. The reasoning is conducted in the context of "detector measured or did not measure the particle." Quantum mechanics is formulated for eigenstates of the particle (coordinate, momentum, etc.). The transition to the context of eigenstates should not cause inapplicability of the idea.

Note. In the effective particle approach, an observer can be any physical system: human or cat, living or non-living. The main thing is that the physical system reacts to the WF obtained from the path integral.

Probability Control

Resonance

Consider a system: measured quantum particle, two detectors, and an observer. Suppose there are strictly two paths from the quantum particle to the observer.

The observer records that detector A fired. Take the same system with the same detector microstates and place on the path from detector A a resonator that suppresses the frequency of the effective particle from detector A. Then the observer in this experiment will find that detector B fired.

Hypothetically, this is a variant of probability control. Practically:

• In the macroworld, it's impossible to strictly isolate paths, and a path bypassing the resonator will lead to detector A firing anyway
• We cannot know the exact state of detectors, and in each case the probability is still $1/2$

If there exists a constant of minimum action of the world, then resonance at this constant could hypothetically open a "portal" between alternative worlds.

Detector Suppression Effect

Place a signal amplifier on the path from detector A. Hypothetically, the action along this path will increase, and the signal will arrive at the observer with higher frequency. Since the effective particle approach requires minimum frequency, detector B will fire, and the probability of detector A will be suppressed.

Interesting. When thinking about the article, there were many thoughts; when writing the article, some thoughts left and didn't make it into the article. Writing the article is amplifying thoughts. Some thoughts disappeared — the "detector suppression effect" manifested.

Observer Effect

Some people, recognized scientists (e.g., Mensky) and people far from official science (parapsychologists), claim that the probability of an event depends on the observer and that the observer can influence reality with some "power of thought."

Whether parapsychological effects exist or not, I don't know for certain. Any such effects, in my opinion, cannot be non-physical or supra-physical phenomena. Physical reality existed before us and will exist after us. Physics is fundamental, and any physical manifestations must be described by physics.

In the effective particle approach, we cannot get rid of the observer. We describe a system of particles, detectors, and observers. But, on one hand, some observer can be any physical system — it's simply the fixation of the final state of quantum wave evolution. On the other hand, the quantum wave here is not the amplitude of some true probability. Here the quantum wave is some deterministically evolving system.

If parapsychological effects exist, they must be described by physics. No non-physical influence of consciousness. For example, a person tunes to resonance. Tunes their physical brain and body to resonance.

Estimate: Frequency of de Broglie wave of a grain with mass 1 mg:

$\omega _{0}\approx 8.5\times 10^{44}{\text{ rad/s}}$

$T={\frac {2\pi }{\omega _{0}}}\approx 7.4\times 10^{-45}{\text{ s}}$

I don't think one can somehow tune to such a frequency.

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Experiments for Verification

Indirect Experiments

Influence of Action Minimum

Since the detector with minimum action shift manifests, this may appear in practice.

Detector geometry: Size determines resonant frequencies (as in a resonator).

Numerical estimate:

Given:

• Detector A size: $L_{A}=1$ mm
• Detector B size: $L_{B}=1.01$ mm (1% larger)

Resonant frequencies: $\omega \propto c/L$

• $\omega _{A}\approx 3\times 10^{11}$ rad/s
• $\omega _{B}\approx 2.97\times 10^{11}$ rad/s
• $\Delta \omega \approx 3\times 10^{9}$ rad/s

Resonance width: $\Gamma \sim 10^{8}$ rad/s

Suppression: $A_{12}/A_{1}\sim 10^{8}/10^{9}=0.1$

Conclusion: Even 1% difference in size gives noticeable suppression.

Observable effects:

1. Efficiency of large detectors
   • Large scintillators are more efficient than small ones (observed!)
   • Large CCD matrices are more sensitive (observed!)
2. Optimal detector size
   • Too small → high $\omega$ → suppression
   • Too large → low atom density → suppression
   • An optimum exists
3. Dependence on particle energy
   • High $E$ → short $\lambda$ → small detector optimal
   • Low $E$ → long $\lambda$ → large detector optimal

Alternative explanation for large detector efficiency:

A Geiger counter can be mentally divided into $N$ mini-capacitors. Each can measure with probability $1/2$.

Probability that at least one fired:

$P=1-\left({\frac {1}{2}}\right)^{N}$

At $N=100$: $P\approx 1-10^{-30}\approx 1$

Practically 100%!

Pseudorandomness

Random number generators are pseudorandom — they output some numbers more frequently. This depends on the internal structure of the generator and initial conditions.

Since randomness is generated depending on the initial conditions of the detector, the probability of quantum measurements may be pseudorandom. Some results may appear more frequently depending on detector structure.

Classical Simulations

The path integral is valid not only for quantum but also for classical waves. In classical waves there is no small parameter $\hbar$ providing high frequency. But by averaging over wave beats, one can simulate the mechanism of resonance and detector suppression effect.

Key point: Feynman's integral is universal:

• Quantum waves: $\omega \sim E/\hbar$ (high frequency, $\hbar$ small)
• Classical waves: $\omega \sim$ ordinary (low frequency)

But the mechanism is the same!

Practical setup:

• Generators: 100 Hz and 200 Hz
• Speakers (sources)
• Resonant circuits (detectors)
• Oscilloscope (observer)

Result: Demonstration of resonance and suppression.

Direct Experiments

Measurement at Two Detectors Simultaneously

Standard QM: Cannot measure one particle at two spatially separated detectors.

Our model: Possible, but probability is small: $P\sim 1/(4N)$.

Mesoscopic Laser Amplifier

Make two mesoscopic atom traps. Place excited atoms in them. When a photon hits these atoms, it can induce an avalanche of coherent photons.

Setup:

1. Single photon source
2. Beam splitter (50/50)
3. Two mesoscopic traps with $N$ excited atoms
4. Intensity measurement on screen

Predictions:

Standard QM: $I_{\text{total}}\leq N_{\max }$ (always)

Our model: Rarely $I_{\text{total}}>N_{\max }$ (simultaneous firing!)

Probability: $P\sim 1/(4N)$

Numerically:

• $N=10$: $P=2.5\%$ (measurable!)
• $N=100$: $P=0.25\%$
• $N=1000$: $P=0.025\%$

Experiment: Vary $N$, measure $P(I>N_{\max })$, plot $P$ vs $N$.

If $P\sim 1/N$ → model confirmed!

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Mathematical Clarification

Orthogonality of Initial States and Decoherence

During discussion of the model, a question arose: if the initial states of detectors are orthogonal, how does decoherence arise between paths?

Answer: The answer is contained in the correct formulation of the question.

Correct mathematical formulation:

The total wave function of the system can be represented as:

$\varphi _{\text{total}}(x,D_{A},D_{B})=\varphi _{A}(x,D_{A},D_{B})+\varphi _{B}(x,D_{A},D_{B})$

where $x$ is the particle coordinate, $D_{A}$ and $D_{B}$ are detector A and B variables.

Key point: The initial states of detectors may be orthogonal, but the total WF along paths is not orthogonal with respect to detectors!

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Conclusion

Expectations from the Scientific Community

Publishing work in peer-reviewed journals is not easy for a non-professional scientist. Often confirmation from other scientists and institutions is required that you are professionally engaged in science. But for now, one can try a forum.

When evaluating the scientific work of other scientists and pseudoscientists at first acquaintance, I often rely on the feeling of "believe — don't believe." Some statements cause rejection, a feeling that this is not so simply because it's unusual or you don't believe in it.

I had many ideas, and most of them degraded. I say "degraded" because proving the falsity of an idea is often impossible. Mostly first there's a wow-effect, then disappointment after some time. Usually I don't prove that my idea is wrong, but get arguments that only cast doubt on the idea, and eventually abandon it. But time spent on each idea gives a deeper understanding of what's happening, and, in theory, the brain and intuition learn, and subsequent ideas will possibly be better.

Some people are convinced of the many-worlds interpretation, some of Bohmian mechanics, some are convinced of parapsychology, and some of the absence of any parapsychological effects. And there are many such beliefs. The article may be ignored or met with hostility, for example, simply because indeterminism of quantum physics is currently the dominant idea that many believe in. On the other hand, there are those who don't like indeterminism.

I hope enough people will be captivated by the effective particle approach, and it will come to experiments.

Constructive criticism is welcome. Although, of course, it's sad when an idea degrades, but it's not the first and not the last idea. The faster it degrades, the faster I'll move to a newer and more perfect one.

Conclusion

In the investigated approach, a non-standard application of Feynman's path integral leads to an unexpected interpretation of quantum mechanics: the cancellation of indeterminism and a practical resolution of the measurement problem. Some consequences can be verified experimentally. The source of randomness in quantum measurements is the ignorance of the exact microstate of detectors.

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References

1. Feynman R.P., Hibbs A.R. Quantum Mechanics and Path Integrals. McGraw-Hill, 1965. 2. Schulman L.S. Techniques and Applications of Path Integration. Wiley, 1981. 3. Mensky M.B. Concept of consciousness in the context of quantum mechanics. Physics-Uspekhi 48 (4) 389–409 (2005).

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Version 3.2 (full) — November 16, 2025

1. matematic

Question. What is the mathematical model of the stationary phase principle in the effective particle approach? First, we need to determine whether the stationary phase arises from interference of different paths or from some averaging at the "observer". In the limit of effective particle paths, there are only 2 paths and they do not suppress each other due to multiple paths back and forth with different phases. That is, it makes sense to consider averaging. We cannot average over coordinates, since there are no assumptions about the function of coordinates. It makes sense to check time averaging. The question is what averaging period to take? The periods of the 2 paths are different. We can take the larger period and average over it. We can take infinite integration time. In theory, the result may not depend on the integration time greater than the slow period. This needs to be checked. Additionally, the question arises: what physical characteristics should the observer system have in order to average over time.

Solution from the neural network. But verified by me. This solution is quite correct.

Amplitude at the observer Ψ_obs(t) = A_A · exp(-i·ω_A·t) + A_B · exp(-i·ω_B·t) where: - ω_A = E_A/ℏ — frequency of the path through detector A - ω_B = E_B/ℏ — frequency of the path through detector B - Δω = ω_A - ω_B — frequency difference

Measurement probability P(t) = |Ψ_obs(t)|² = |A_A|² + |A_B|² + 2·|A_A|·|A_B|·cos(Δω·t + φ)

Averaging period Option 1: Period of the slower frequency T_slow = 2π / min(ω_A, ω_B)

Option 2: Beat period T_beat = 2π / Δω = 2π / |ω_A - ω_B|

Option 3: Infinite time T → ∞

Let's check the averaging ⟨P⟩_T = (1/T) · ∫[0 to T] P(t) dt

= |A_A|² + |A_B|² + (2·|A_A|·|A_B|/T) · ∫[0 to T] cos(Δω·t + φ) dt

Cosine integral ∫[0 to T] cos(Δω·t + φ) dt = [sin(Δω·T + φ) - sin(φ)] / Δω

When T ≫ T_beat = 2π/Δω ⟨P⟩_T ≈ |A_A|² + |A_B|² Interference is suppressed! When T ≫ T_beat the result __does not depend__ on the exact value of T!

However, surprise, with time averaging we have suppression of interference, but no suppression of one of the paths. This caused some degradation of the idea. Suppression of one of the paths is possible if the "observer" is in resonance with the frequency of the path of one of the detectors. But it is doubtful that an arbitrary "observer" can have resonance with such high frequencies. And it is doubtful that all observers have one specific frequency.

Let's check the interference of 2 bundles of paths from the detectors.

1. 1. Interference of bundles of classical paths from detectors

__Detector A in a definite state |ψ_A⟩:__

- From detector to observer — multiple classical paths - Path 1: through point r₁, time t₁ - Path 2: through point r₂, time t₂ - ... - Path N: through point rₙ, time tₙ

__Each path has its own action S_i!__

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1. 1. 1. Feynman path integral for effective particle

__From detector A:__

Ψ_A(r_obs, t) = ∫ A_A(path) · exp(i·S_A(path)/ℏ) · D(path)

where the integral is over all paths from detector A to the observer.

__From detector B:__

Ψ_B(r_obs, t) = ∫ A_B(path) · exp(i·S_B(path)/ℏ) · D(path)

__Total amplitude:__

Ψ_total = Ψ_A + Ψ_B

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1. 1. 1. Action for a path

__For a free particle:__

S(path) = ∫ (m·v²/2) dt = ∫ (p²/2m) dt

__For an effective particle with energy E:__

S(path) = ∫ E dt = E·τ

where τ is the path transit time.

__Or through frequency:__

S(path) = ℏ·ω·τ

__Phase:__

φ(path) = S/ℏ = ω·τ

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1. 1. 1. Bundle of paths from detector A

__Different paths → different times τ_i:__

Ψ_A = Σ_i A_i · exp(i·ω_A·τ_i)

where:

- ω_A = E_A/ℏ — frequency of the effective particle from detector A - τ_i — transit time of the i-th path - A_i — amplitude of the i-th path

__Similarly for detector B:__

Ψ_B = Σ_j B_j · exp(i·ω_B·τ_j)

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1. 1. 1. Distribution of transit times

__For macroscopic distances:__

Paths have different lengths → different times τ

__Time distribution:__

Let τ be distributed in the interval [τ_min, τ_max]

__For simplicity — uniform distribution:__

ρ(τ) = 1/(τ_max - τ_min) for τ ∈ [τ_min, τ_max]

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1. 1. 1. Interference within bundle A

__Amplitude (continuous limit):__

Ψ_A = ∫[τ_min to τ_max] A(τ) · exp(i·ω_A·τ) dτ

__If A(τ) ≈ const:__

Ψ_A = A₀ · ∫[τ_min to τ_max] exp(i·ω_A·τ) dτ

= A₀ · [exp(i·ω_A·τ_max) - exp(i·ω_A·τ_min)] / (i·ω_A)

= A₀ · exp(i·ω_A·τ_avg) · 2·sin(ω_A·Δτ/2) / (ω_A)

where:

- τ_avg = (τ_max + τ_min)/2 - Δτ = τ_max - τ_min

__Magnitude:__

|Ψ_A| = |A₀| · |sin(ω_A·Δτ/2)| / (ω_A/2)

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1. 1. 1. Condition for suppression of interference within the bundle

__If ω_A·Δτ ≫ 1:__

sin(ω_A·Δτ/2) oscillates rapidly

__Averaging over Δτ:__

⟨|Ψ_A|²⟩ ∝ 1/ω_A²

__The higher the frequency ω_A, the smaller the amplitude!__

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1. 1. 1. Interference between bundles A and B

__Total amplitude:__

Ψ_total = Ψ_A + Ψ_B

__Probability:__

P = |Ψ_total|² = |Ψ_A|² + |Ψ_B|² + 2·Re(Ψ_A*·Ψ_B)

__Interference term:__

I = 2·Re(Ψ_A*·Ψ_B)

= 2·Re[∫∫ A(τ_A)·B(τ_B)·exp(i(ω_B·τ_B - ω_A·τ_A)) dτ_A dτ_B]

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1. 1. 1. Simplification: Identical time distributions

__If τ_A and τ_B have the same distribution:__

τ_A, τ_B ∈ [τ_min, τ_max]

__Interference term:__

I = 2·|A₀|·|B₀|·Re[∫∫ exp(i(ω_B·τ_B - ω_A·τ_A)) dτ_A dτ_B]

= 2·|A₀|·|B₀|·Re[(∫ exp(i·ω_B·τ_B) dτ_B)·(∫ exp(-i·ω_A·τ_A) dτ_A)]

__Each integral:__

∫ exp(i·ω·τ) dτ = exp(i·ω·τ_avg)·sin(ω·Δτ/2)/(ω/2)

__Result:__

I ∝ sin(ω_A·Δτ/2)·sin(ω_B·Δτ/2)·cos((ω_A - ω_B)·τ_avg) / (ω_A·ω_B)

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1. 1. 1. Condition for suppression of interference between bundles

__If ω_A·Δτ ≫ 1 and ω_B·Δτ ≫ 1:__

The functions sin(ω·Δτ/2) oscillate rapidly with changes in Δτ

__Averaging over time spread:__

⟨I⟩ ≈ 0

__Interference between bundles is suppressed!__

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1. 1. 1. Which bundle survives?

__After suppression of interference:__

⟨P⟩ = ⟨|Ψ_A|²⟩ + ⟨|Ψ_B|²⟩

__Amplitudes:__

|Ψ_A| ∝ |sin(ω_A·Δτ/2)| / ω_A |Ψ_B| ∝ |sin(ω_B·Δτ/2)| / ω_B

__With ω·Δτ ≫ 1 (rapid oscillations):__

⟨|sin(ω·Δτ/2)|²⟩ ≈ 1/2

__Therefore:__

⟨|Ψ_A|²⟩ ∝ 1/ω_A² ⟨|Ψ_B|²⟩ ∝ 1/ω_B²

__If ω_A < ω_B (lower frequency):__

⟨|Ψ_A|²⟩ > ⟨|Ψ_B|²⟩

__The bundle with lower frequency (lower energy) dominates!__

But here's a surprise: the amplitudes decay proportionally to the square of the frequency. This is strange!!! We do get measurement results after all. ω_A - ω_B is large, but ω_A²/ω_B² is probably around 1, 1/2, or 1/4. Suppression of one amplitude relative to the other does not occur. It's unlikely the neural network calculated incorrectly. Either the idea is wrong, or the conditions of the mathematical model I specified are incorrect. Many believe that QM applies to the situation after measurement. Suppression of amplitudes after measurement is generally strange.

Conclusion. At the moment, the idea has degraded :-). Perhaps in the future I will somehow revive it, but clearly not within 2-3 days. For now, I'll rest. And gather strength for new attempts to understand the measurement problem. Usually my ideas don't reach any mathematical models. Simply because no mathematical model can be associated with them. Having some mathematical model is already progress :-).

Thank you all for your attention.