Principles of computer modeling of physical processes. Part 1

annotation: This work discusses the basic principles of computer modeling of physical processes associated with the interaction of electrons in a vacuum. In this part, special attention is paid to the scientific-conceptual approach, minimization of mathematical calculations and integration of philosophical views in the context of modern fundamental physical pictures of the universe.

Scenario: In a vacuum, at a certain distance from each other, two electrons move towards each other.

Our goal is to simulate this process and its outcomes using computer simulations to reflect real physical phenomena as accurately as possible.

1. Spacetime:

When constructing a computer model to study the interaction of electrons in a vacuum, it is necessary to carefully approach the definition of the boundaries of space-time. Introducing restrictions on space-time can distort the behavior of particles, since such restrictions must have a clear physical justification. In light of the lack of evidence to support the existence of physical boundaries in a vacuum, the model must assume that spacetime is unbounded. This will make it possible to study the interactions of electrons without introducing additional assumptions that are not supported by data.

As part of the theoretical modeling of electron motion in a vacuum, it is necessary to take into account a number of inherent limitations determined by fundamental physical laws. According to the postulates of the special theory of relativity, the speed of any standard particle, including the electron, cannot exceed the speed of light in a vacuum. This represents the upper limit for the speed of particles in our universe.

The Heisenberg uncertainty principle introduces additional restrictions by establishing that precise and simultaneous measurement of the position and momentum of a particle is impossible, which leads to a stochastic description of their behavior in space. The Pauli principle, although applicable primarily to electrons in atoms, implies that two electrons cannot be in the same quantum state, indicating limited spatial states for electrons.

These restrictions, although not the only ones, are one of the key ones when constructing any physically realistic model of electron motion and must be integrated into computer modeling to ensure its scientific correctness and accuracy.

2. Electron mass and dimensions:

The electron, as a fundamental quantum particle, does not have a certain size in the traditional classical sense. Instead, its “size” and position in space are described by a wave function, which is a probability distribution. This function obeys the Schrödinger equation and does not have strict localization, which reflects the uncertainty and fundamental probabilistic nature of quantum objects.

When making a measurement, the electron's wave function “collapses”, which leads to the “selection” of a certain position in space, which can be interpreted as its “classical size”. This phenomenon, known as wave function collapse, is a key aspect of quantum mechanics and demonstrates how quantum systems move from a quantum description to a classical result when interacting with macroscopic measuring devices…

The mass of the electron, although small, contributes to the gravitational interaction with the fabric of space-time, which is described within the framework of the general theory of relativity. When modeling gravitational effects at the microscopic level, it is necessary to take into account the curvature of the spatial geometry near the electron in accordance with the principles of general relativity, even if such curvature is extremely small and usually does not have a noticeable effect on the behavior of the electron.

3. Interactions:

When modeling electron interactions, special attention should be paid to Coulomb repulsion. This fundamental phenomenon, caused by the interaction of like charges, creates an electrostatic barrier that effectively prevents electrons from approaching less than a certain threshold, causing them to “reflect” from each other.

Gravitational interaction on the scale of elementary particles is insignificant, but it is worth taking it into account for the completeness of our model.

Running the model:

In the process of modeling the interaction of two electrons, we imagine how the wave functions of each electron, which describe their probability distribution in space, move towards each other. When close enough, the wave functions interact, but do not “collapse” into each other, since the collapse of the wave function occurs only during measurement, as a result of interaction with a macroscopic measuring device.

Coulomb repulsion between electrons results in the fact that when they try to approach each other, they experience a repulsive force, which changes their trajectories, causing them to move in opposite directions. Gravitational interaction at such scales is extremely weak and is usually not taken into account on the quantum scale, but within the framework of the completeness of the model and for systems with higher mass it can be included.

Thus, in the model we observe changes in the probability distributions of electrons under the influence of Coulomb repulsion, while taking into account gravitational effects. This allows us to predict the possible trajectories of electron motion within the framework of quantum mechanics.

…

Even though our model includes a number of physical processes, it still greatly simplifies the complexity of real-life phenomena in such systems. Obviously due to the extreme smallness of the physical processes taken into account. As an example, consider a situation where in the model electrons move at such a speed that they are able to overcome the Coulomb barrier upon collision. In this case, the model may not provide an accurate prediction of the consequences because it is limited by its initial parameters.

We can try to use artificial neural networks to predict behavior under such extreme conditions, but even advanced algorithms may struggle due to the complexity of the problem, potentially leading to significant errors in the modeling. Physical reality often goes beyond analytical understanding, and we regularly encounter phenomena that were not predicted by existing theories, highlighting the need for the search for a “theory of everything”

Thus, computer modeling of physical processes is a complex task that requires not only deep knowledge in the field of physics, but also a creative approach to solving problems that may arise during the modeling process. It is important to remember that a model is just a simplified representation of reality and cannot fully reproduce all aspects of the physical world. Despite this, modeling is a powerful tool that allows us to better understand and predict the behavior of complex systems.

From the author

This article was created by me as an experiment. In this part I omit some details and nuances that would be important for a rigorous scientific analysis. However, I try to stay within the bounds of modern scientific concepts by presenting information in a somewhat unorthodox manner. If readers are interested, in subsequent sections I plan to outline key physics, mathematics and computational concepts that will help illuminate many aspects of our topic.