In Reiner's hypothesis, the electron is no longer a concrete and fixed particle, because one cannot detect its position and momentum at the same time, it is actually a particle that can appear in a range, and the probability of its occurrence at any point in this range is not 100%, and through the mathematical analysis of this model, a probability function can be obtained, and this probability function, Reiner calls it the wave function.

At the same time, the description of the electron should no longer be described as a separate particle, but should be explained in terms of the wave function, and the electron becomes an electron cloud.

For example, in the orbital spectral analysis of the outer electron energy level of the atom, although according to the past experiments of the masters, several obvious electron spectral lines on the corresponding orbits can be seen, but outside of this spectral line, there are some more slender spectral lines distributed around, in the past, people have always believed that this is due to the perturbation of experimental errors, which is an abnormal phenomenon.

But according to the theory of the probability distribution of the electron cloud, this is the real correct phenomenon.

The wave function of the electron cloud is distributed according to probability, and the probability of its central position is relatively high, while the edge is low, so the spectral lines that the mages originally thought reflected the orbit of the electron were actually composed of many spectral lines, and the slender spectral lines at the edge were the spectral lines where the electron might appear.

However, this does not mean that the electron is really an ethereal cloud, Reiner thought that the electron does exist objectively, but in the microscopic realm, it presents such a state of probability distribution under observation, while on the macroscopic level, humans and other objects do not have quantum phenomena.

At least not yet.

The quill beside Reiner recorded his thoughts, and there were pages of text descriptions and arguments alone.

Eventually, Reiner came up with a series of conjectures and assumptions.

The first idea is that the quantum state of a microscopic quantum system can be described in terms of a wave function, which represents all the information that an observer can obtain about the system.

The second is that the description of a quantum system is probabilistic, and the probability of an event is the square of the absolute value of the wave function.

The third is Ian Gray's uncertainty principle, also known as the uncertainty principle, which is that in a quantum system, the position and momentum of a particle cannot be determined at the same time.

The fourth point is the known conclusion, that is, matter has wave-particle duality, and its wavelength follows the description of Ian Gray's formula, and at the same time, in an experiment, it can show the particle characteristics of matter, or wave characteristics, but not the particle characteristics and wave characteristics of matter, in other words, matter can only show one of the characteristics of waves and particles in the same experimental observation.

The fifth and final point is that in a large-scale macroscopic system, the quantum representation of objects should be similar to that in classical magical systems, i.e., macroscopic objects do not exhibit obvious quantum characteristics.

At the same time, there is another important concept in Reiner's view, and that is the collapse of the wave function.

To put it simply, a microscopic particle follows the probability distribution of the wave function, but when observed, its wave function will collapse to a fixed value, which can be understood as the behavior of observing the wave function leads to the collapse of the wave function.

The state of the particle is like a coin being tossed, before it hits the ground, it may be heads or tails, determined by the probability distribution, and even after falling into the hand and being covered, people still can't determine whether the coin is heads or tails, until the palm of the hand is opened, people can observe the heads and tails of the coin.

But even without observations, coins do have a pros and cons, rather than always showing a probability distribution as described by the wave function.

To put it simply, the wave function collapse that Reiner refers to is actually a process of probability contraction, in which many possibilities of particles fall to a certain possibility based on observation, but all possibilities are confined to the light cone of the world line, because the speed of light cannot be surpassed.

Once the wave function collapses, then the rest of the probability distribution ceases to exist, and only the observed outcome exists.

It is used to explain the phenomenon found in the large cavity, that is, there is an extremely high concentration of magic power in the original large hole, but usually these magic power exists in a quantum state, showing the characteristics of a wave function, and it cannot cause collapse when observed externally by conventional means, so it can only be concluded that the concentration of magic power is normal.

But once the probe goes deep into it and makes a thorough observation, especially when a mage observes directly through the projection, the wave function collapses, and a large amount of magic turns into a substance, destroying the probe in an instant.

This process occurs in every probing, except that the collapse is more pronounced when the mages are directly observing through the projection, and this can only be detected by the instrument.

Here, Reiner put forward a concept of strong observation and weak observation, compared with the simple use of detection instruments to detect, direct projection observation is strong observation, the disturbance of strong observation to the quantum system is greater than the disturbance of the weak observer to the quantum system, it can be simply believed that some quantum systems have thresholds, only the observation above the threshold will cause collapse, just as energy is discontinuous, even the behavior of observation is discontinuous.

Thinking of this, Reiner realized another problem, because although the strange phenomenon of the big hole can be explained according to this theory, it is a macroscopic phenomenon after all, and the quantum theory should not appear in the macroscopic world.

Otherwise, human beings will be probability distributions, which may appear anywhere in the world, and objective reality will be lost.

Reiner was unanswered, and he thought it might be better to leave it to the legendary mages to discuss.

After putting all his thoughts into words, Reiner breathed a sigh of relief, put away all the experimental equipment, and returned to his room, leaving the unstable half-plane.

"You're back."

Phyllis was still lying on the bed, judging from her side, during the time that Reiner was doing the experiment, Phyllis had finished reading the previous one and started to read the new one.

"Hmm."

Reiner nodded, and the parchment beside him began to assemble and expand, turning his experimental conclusions and conjectures into a brief paper.

"Looks like it's going to turn out pretty well?"

Phyllis asked, seeing that Reiner was no longer as solemn as before.

"I can't say that it's good, at least the results of my experiment have been achieved, but whether this conclusion is a good thing for the world is still uncertain."

Reiner shook his head, and outside the window, the big hollow existed silently, silently.