Abstract

Interaction is a fundamental property of the physical world, occurring between two or more entities. According to our current understanding, fundamental interactions are extremely complex. Even the most straightforward interactions involve multiple-order, up to infinite, increasingly complicated physical processes. Fundamental interactions all meet the requirements of the special relativity theory or the locality principle. Any interaction takes time. But, interaction in quantum mechanics is oversimplified, non-relativistic, and takes no time. If we perceive quantum mechanics from the perspective of fundamental interactions, we find that quantum mechanics does not require an interpretation. We should also comprehend quantum measurement similarly. With interaction in mind, we can intuitively understand quantum measurement, and the annoying discontinuities and probabilities are gone. Furthermore, we will find that quantum entanglement is established through interaction, but the process occurs covertly or simultaneously during the experiment's preparation. Ignoring the coherence-establishing process of the quantum entanglement will lead to an incomprehensible "non-local" view. The non-locality demonstrated in all quantum entanglement experiments comes from the synthetic global outcome of orchestrated interactions between the components. They are all little magic tricks that nature plays, creating the illusion of quantum non-locality.

Ubiquitousness of interaction

Interaction refers to the influence or association between two or more objects. From a physical point of view, there is an interaction between any two objects, or any object interacts with its surrounding objects. Interaction is a fundamental, inextricable, inherent property of any object. Any object must participate in the interaction. It manifests itself on all scales and is the source of all occurrences.

Interactions can be physical, such as the exertion of force or the action of fields; chemical, such as chemical bonds between atoms; or biological, such as the interaction of biological populations. Interactions are crucial to system evolution and change in every domain, producing complex phenomena and behaviors. We often describe interactions in terms of fundamental forces, such as gravity, electromagnetism, weak and strong forces, or fundamental interactions. In the domain of social sciences, interaction can be communication, collaboration, or competition between people, resulting in various social structures and cultural forms. Interactions occur in all aspects of nature and human activities.

Everything in the universe and its evolution, including the movement and evolution of celestial bodies, the ecology and evolution of the biosphere, the development of human society, competition and cooperation between countries, the relationship between people, ..., all kinds of nature and human society at all levels, cultural phenomena, such as seasons, day and night, moon phases, countries, political systems, laws, trade, religion, emotions, are all the result of interaction.

The scientific study of objects is the investigation of their fundamental laws or the rudimentary ways of interaction.

Properties of interaction

widespread, ubiquitous

All substances and states participate in interactions and are the results of interactions. They happen at all scales and levels. Interaction is the fundamental property of everything in the world.

Initialize change, create new phenomena

In addition to participating in changes in the motion state of objects, interaction can also produce new objects, phenomena, and hierarchies, such as nuclear reactions (create new particles), biological evolution (new individuals, species), and fission (increase in number). There will also be new phenomena that only appear when all objects participate, such as global effects, collective effects, resonance, eigenstates, phase changes, etc.

Two people can have various relationships: love, hatred, alliance, hostility, etc. Two countries can trade, alliance, vassalage, war, etc.

That is, emergence occurs in interaction.

Obeys the principle of causality

All interactions satisfy the principle of causality. The possible causes of the current state of causation are complex and arose long ago. For example, people have an innate fear of certain natural phenomena, such as darkness, beasts, and heights. But the cause must precede the effect.

Fundamental interactions

From a physical point of view, all interactions at various levels ultimately boil down to four fundamental interactions: gravity, electromagnetic interaction, weak interaction, and strong interaction. Among them, electromagnetic interaction dominates daily physical phenomena, such as the state of matter, physical and chemical properties, etc.

Complexity and Interweaving of Fundamental Interactions

The fundamental interactions in basic physical theory, or the Standard Model, are very complex. In addition to gravity, the Standard Model holds that any point in space-time contains all elementary particles and fundamental interaction components simultaneously. At different energy scales, the weights of various components, that is, the external physical properties of the point, are different. Specific calculations are implemented through quantum electrodynamics (QED) or quantum chromodynamics (QCD). Even if an elemental particle exists alone, we can not strip its interaction away with the surrounding vacuum. They will be manifested in their external properties, such as the charge size of an electron and the size of the magnetic moment. The complexity and interweaving of fundamental interactions make calculations of any fundamental physical system difficult.

Continuity

At the microscopic scale, fundamental interactions work continuously and can gradually strengthen, weaken, or oscillate, but they will not appear, disappear, or mutate suddenly. Complex, continuous, local interactions can produce long-range or globally ordered patterns, such as eigenstates, dominant modes, or stable correlation patterns like friendship, indifference, etc. The universe is full of electromagnetic radiation, and a system will interact with the background radiation field to find the system's own eigenstate.

Forces and interactions

In classical physics, we are more accustomed to the concepts of force and potential field.

The potential field describes the relationship between the force exerted on an object and its position. The gradient of a potential field (i.e., the spatial derivative of the potential field) gives the magnitude and direction of the force acting on an object.

For example, for a scalar potential field V(x, y, z), the relationship between the force F(x, y, z) experienced by an object in the field and the potential field can be described by the following formula:

F(x, y, z) = -∇V(x, y, z),

where ∇ is the gradient operator, the vector derivative operator of space. The above equation shows that the force is the negative gradient of the potential field. In other words, the gradient of a scalar potential field gives the magnitude and direction of the force that the field exerts on an object.

The potential field is a global description of the force field or the force on the object.

The descriptions of force and potential fields are equivalent. Force manifests the potential field acting on an object at a specific location, and the potential field is the force exerted on objects in all spaces.

Force only causes changes in the dynamic state of the object and does not produce anything new. It may also not produce dynamic state changes, such as internal force, surface tension, etc.

For example, force causes an object to accelerate, decelerate, or deform, but it does not change it into something else or create something new. Even if a new phenomenon finally emerges at other scales, it can be described microscopically by simple forces or dynamics. For example, water molecules collide and attract each other to produce water droplets. However, these dynamic changes cannot create a new entity, such as in radiation. Radiation makes a new particle or a photon.

But fundamental interactions can produce new entities or phenomena, including global or large-scale modes, such as resonance (finding the eigenstate of the system), or elementary particles that do not exist in the original system, such as the photons mentioned above.

According to fundamental physical theory, in addition to gravity, the source of all forces is interaction, that is, the other three fundamental interactions: strong, weak, and electromagnetic. In laboratory experiments or daily life, the forces we talk about, in addition to gravity and inertia forces, basically come from electromagnetic interactions, such as friction, air resistance, pressure, tension, surface tension, etc. Any change in the electromagnetic field manifests as electromagnetic waves, that is, light. Our everyday environment is full of electromagnetic waves of various frequencies.

Interactions are fundamental. Microscopic particles, forces, and potential fields are appearances of fundamental interactions on a larger scale and are an approximation due to the lack of microscopic details.

Treatment of Interactions in Quantum Mechanics

We rarely use the concept of force in quantum mechanics, or although there is, such as pairing, nuclear force, etc., it only appears as part of the potential field in the Hamiltonian.

Although the concept of force is uncommon in quantum mechanics, the force applied on a quantum, <F>, can still be calculated through the corresponding operators.

The concept of the potential field in quantum mechanics is the same as that in classical physics, and it is also global, whether it is the expression of a potential function or a Hamiltonian. It appears in the Schrödinger equation, otherwise written as the Hamiltonian.

As mentioned in the previous section, the interaction is more fundamental and microscopic, and the description of force and potential field is only an approximation. Therefore, in the most important equation of quantum mechanics - the Schrödinger equation - the fundamental interaction has been approximated, so it describes the approximate and global properties of the microscopic system. We have also explained that the Schrödinger equation is an abstract wave equation. The properties of the system are manifested in the global potential function and boundary conditions.

Without any constraints and an external potential field, the solution to the Schrödinger equation is a complex plane wave in all frequencies. Considering the superposition of waves, we can say that any wave satisfies the Schrödinger equation in free space because any wave can be decomposed into a superposition of plane waves of different frequencies.

All fundamental interactions have to meet the requirements of the special theory of relativity. However, the Schrödinger equation is non-relativistic. It implicitly assumes that the interaction propagates at infinite speed. We have demonstrated before that the consequence of this assumption is that coherent feedback of waves is not limited by time and completes instantaneously. The establishment of the dominant state (eigenstate) does not take time. When the system state changes, the establishment of different advantageous state systems also occurs instantaneously. The intermediate process is missing; the system changes instantaneously from the initial to the final state. This is the origin of the instantaneous "collapse" of the quantum wave function in the Copenhagen measurement concept. Even for the Hamiltonian explicitly changes with time, the general treatment is to use the adiabatic approximation, that is, to solve the ideal Schrödinger equation with fixed potential fields and boundary conditions at each moment.

The transformation of complex, local interactions into an ideal, simple global potential is the fundamental principle of quantum mechanics in dealing with interactions.

For example, we introduce some basic quantum mechanics methods in studying atomic nuclei structure.

Quantum mechanical methods in Nuclear Shell Model

The nucleus of an atom is composed of protons and neutrons, collectively called nucleons. Protons and neutrons are not elementary particles; each has its own structure. Nucleons attract each other, a bit like molecules in a liquid. In the early days of nuclear theory, the atomic nucleus was treated as a droplet called the nuclear droplet model. The droplet model can be used to understand properties such as nuclear mass, binding energy, and fission.

However, atomic nuclei are exceptionally stable when the number of protons and neutrons is some specific number. These numbers are called the magic numbers of the nucleus. The existence of magic numbers indicates that atomic nuclei have structures, just like atoms. The energy level structure of atoms can be well solved by solving the central electrostatic potential field of the Schrödinger equation, at least for hydrogen atoms. However, the nucleus does not have a core. Nucleons are equal. The nucleus is a many-body system.

The nuclear shell model (NSM) is the model that best explains the structure of the nuclear shell. The shell model is a mean-field theory of independent particles, similar to the shell model of atoms. In NSM, protons and neutrons are independent systems with their own structures. In other words, in NSM, neutrons and protons are independent. Of course, this is contradictory to the interaction between nucleons. Neutrons must interact with protons; otherwise, there should be a nucleus composed of neutrons or protons alone. However, there is no such nucleus (except hydrogen). Moreover, the structure of four nucleons (helium 4 nuclei, or alpha particles) composed of two neutrons and two protons is very stable. Heavy, relatively stable nuclei, such as thorium, uranium, and other heavy elements, often undergo alpha decay when they decay; that is, they emit one alpha particle at a time instead of dropping out neutrons or protons one by one.

The interaction between nucleons is called nuclear force. It is very complex. There are nonlinear terms and multi-body terms (if more than two objects are interacting, in addition to the interaction between the two objects, there are additional interactions. The effect is not just the superposition of two-body interactions). By fitting deuterons and nucleon scattering experiments of various energies, the potential energy distribution of nucleons and nucleons can be obtained, including Paris potential, AV18 potential, etc. There are many terms for the expression of each nucleon potential. From a microscopic perspective, nucleons also have a structure composed of different quark components. The nuclear force is only the effective interaction of more elementary particles, such as quarks and gluons, and is not fundamental.

But NSM is an independent particle mean-field model whose image is that each nucleon moves independently in a potential field. Such an oversimplified model can give the magic number of the nucleus, the nuclear excitation spectrum, the rotational properties of the nucleus, and so on. But it cannot deal with problems such as nuclear decay.

NSM is a pure quantum mechanical model similar to the atomic model. It is widely used and has won the Nobel Prize in Physics.

Judging from the structure of the nucleon and the nature of the nuclear force, it is evident that the nucleon should only have strong interactions with its neighboring nucleons, at least mainly because the strong interaction is much stronger than the electromagnetic interaction. That is, the primary interaction of nucleons should be local and with neighborhood. But in NSM, each nucleon moves in a global potential field. Their orbital properties, etc., are solved by the corresponding Schrödinger equation.

The example of the NSM illustrates that the quantum mechanical system is a simplified and global description of a complex physical system. The same goes for the atomic shell model. We can use quantum mechanics to calculate hydrogen atoms accurately, but it is challenging to do the same for the next more complicated atom, helium.

Measurement

I wrote an essay discussing quantum mechanical measurement. Here are some amendments:

From the perspective of quantum field theory and fundamental interaction, all simple physical systems are complex, nonlinear, and involve many-body interactions. The system must interact with itself or evolve, causing it to change to a specific state, such as the lowest overall energy state, eigenstate (dominant state), etc.

The measurement of microscopic systems generally implies that the device dramatically influences the object and will form a new global dominant state. The state we measure is not necessarily the state without the influence of the measuring device.

Quantum Entanglement

If we carefully analyze all quantum entanglement experiments from the interaction perspective, we will find that quantum entanglement is easy to understand. I have covered the topic in previous articles. Here are a few more points to emphasize:

Interaction is more fundamental and is the reason behind all physical phenomena.

Interactions produce new dominant states. The new dominant state is the natural emergence of a new system.

Interactions occur at all times at the speed of light. For microphysical or macrophysical experiments that meet the conditions for sufficient interaction, the measurement device will thoroughly interact with the system to form new dominant states (eigenstates), such as the resonance of the diamond color center and the dominant state of photon polarization.

The interaction process between the measurement device and the system can be described by the concept of virtual photons in quantum field theory or understood from the interaction between the classic background radiation wave and the system.

The interpretation of Bell's experiment in the literature so far ignores the fundamental and ubiquitous nature of the interaction and the fact that we cannot block the interaction between the background electromagnetic waves and the system.

I call quantum entanglement a magic trick because the new dominant state (coherence) will naturally establish when the experimentalists set up the system, just like a magician secretly changes the arrangement of props during a performance, and the audience fails to notice.