In the world of quantum mechanics, every experiment, we can only see one side of the particle, not both sides of it at the same time. This principle is the basic principle. No matter how perfect our experiment is, we cannot see both sides of the particles at the same time.
The entire quantum mechanics was established, from Planck discovering quantum, to Bohr using quantum in atom and molecules, and finally to Heisenberg and Schrödinger to establish the final form of quantum mechanics.
Bonn found the true physical meaning of waves in wave dynamics , which is the probability that particles appear somewhere.
As the leader of the Copenhagen school, Bohr first found an explanation of quantum mechanics, that is, particles and waves are the two sides of the truth, just like the two sides of a coin. Bohr said that when you care about particles, you see particles; when you care about waves, you see waves. Next, let’s take a look at the Copenhagen School’s explanation of quantum mechanics or Heisenberg’s theory, that is, uncertainty principle .
In this class, we want to expand on the intuitive physical image that talks about the principle of uncertainty.
To understand this intuitive physical image, we need to first explain that wave dynamics is the best framework for explaining the principle of uncertainty. At the same time, here we will also explain the more general form of wave dynamics.


Probability of electrons appearing
When talking about the wave dynamics of De Broglie's waves and Schrödinger, we often use electrons as examples, and now we still take electrons as examples. In wave dynamics, a wave is a complex number distributed spatially. Since it is a plural number, how did its probability explanation come from? Bonn said that taking this complex number an absolute value and then a square is the probability that the particle appears at a point in space.
Quantum mechanics has developed to the point where people also found that waves distributed in space can also be understood as waves distributed in velocity. Of course, these two waves can change from one another. According to Bonn's theory, if the wave distributed on the velocity is taken as the absolute value and squared, the probability of the particle at this velocity is obtained.
That is to say, particles are uncertain in both space and velocity, and we can only talk about probability. This is the mathematical form of quantum mechanics. So, what is its physical explanation?
Heisenberg said that quantum mechanics tells us that there is no way for us to measure the position and velocity of electrons at the same time. Heisenberg's conclusion is still true today. Physicists cannot realize the idea of measuring the position and speed of electrons at the same time if they want to break their heads. Einstein was not satisfied with the probability explanation of waves proposed by Bonn, and had designed experiments to measure the position and velocity of particles at the same time. We will talk about this experiment later.
So, how to measure the position of electrons? For example, when we use a computer, the conventional way of luminous computer monitors is to tap electrons onto the fluorescent screen. When the electrons are tapped onto the fluorescent screen, bright spots will appear on the fluorescent screen. The imaging principle of traditional TVs is the same. The electrons released by the tube located behind the TV hit the fluorescent screen, emitting colorful light. Through the bright spots, we know the location of the electrons. Therefore, tapping electrons onto a fluorescent screen is a way to measure the position of the electron, but this method cannot measure the speed of the electron.
So, how to measure the velocity of electrons or other elementary particles? Physicists have many ways, one of which is the use of energy measuring devices. An energy measuring device is an instrument that can measure the energy of a certain particle. It is common physics common sense to measure the energy of a particle. We learned in high school that the energy of an object is related to its speed. The simplest relationship is what Newtonian mechanics says, the square correlation between energy and velocity. Double the speed of an object and its energy doubles in square form.For example, if the speed of an electron is twice that of another electron, then the energy of this electron is 4 times that of another electron. Therefore, using an energy meter to measure the energy of the electron, and then the speed of the electron can be determined. However, no energy meter can have the function of a fluorescent screen, because the fluorescent screen is used to measure the position of electrons, while the energy meter is used to measure the speed of electrons. Therefore, the energy meter has no way to accurately measure the position of electrons, and it is even completely impossible to measure the position of electrons. Conversely, fluorescent screens can be used to measure the position of electrons, but there is no way to measure the speed of electrons.
This is what Heisenberg calls the physical reality in microscopic world , and it is also an experimental explanation of the principle of uncertainty in quantum mechanics. What is the physical reality of
? For elementary particles, when we can measure their positions, there is no way to measure their velocity; when we can measure their velocity, there is no way to measure their positions. In other words, at the same time, we can only understand one side of the microscopic world, but we cannot see the other side at all.
We know that there is another way to express speed, which physicists call it momentum. In the mechanics theory of Newton , there is a linear relationship between velocity and momentum . When we increase the speed by 2 times, the momentum will also increase by 2 times. It can also be said that when we measure speed, we are measuring momentum accurately.
When talking about the views on the physical world and physical phenomena, we cannot help but talk about another anecdote, which is a real event that happened between Heisenberg and Einstein.
After discovering quantum mechanics, Heisenberg once chatted with Einstein and took a walk with him. Heisenberg said to Einstein: "I finally understand a truth you have taught us, that is, in physics, only the quantities that can be measured can be written into equations and into theory." Einstein smiled at him and said: "Now my idea has changed. Only the quantities that appear in the theory are the quantities that can be measured."
A coin has two sides. We can carefully savor Heisenberg and Einstein's conversation, and although their views vary, they all have their own deep understanding. When talking about physical reality, our theory can only talk about physical reality. However, when we are thinking about physical theory, we are also thinking about physical reality.
Bol is a very humble person. When one of his assistants, Heisenberg, completely abandoned his atomic model, he let go of his body and mind to embrace new quantum mechanics. Similarly, when Bonn proposed the probability explanation of waves, he quickly accepted it. However, he had an unpleasant debate with Heisenberg on the principle of wave-particle duality and uncertainty.
For Bohr, the correct physical explanation of quantum mechanics is wave-particle duality. When you look at it from the perspective of a particle, the appearance it reflects is a particle, and when you look at it from the perspective of a wave, the appearance it expresses is a wave. In Bohr's words, the world has two sides, and either side is incomplete. Therefore, he called his wave-particle duality the principle of complementarity , which means complementing each other.

wave-particle duality
Heisenberg proposed the principle of uncertainty. We used the measurement of electrons as an example to talk about the experimental explanation of the principle of uncertainty, that is, when you measure the position of an electron, you cannot measure its speed, and vice versa. Nowadays, Heisenberg's theory is undoubtedly more correct. However, in that year, Bohr and Heisenberg had a fierce debate, so much so that Bohr tried to convince Heisenberg at his home, but it took several days without success. This conflict led to an insolvent gap between the master and the apprentice for the rest of their lives.
The so-called Copenhagen explanation of quantum mechanics is largely Heisenberg's explanation: the perception of a particle is completely different from the perception of stones and cars in our daily life experience. It is completely elusive.Of course, macroscopic objects, such as stones, actually satisfy quantum mechanics, but because macroscopic objects are too large, we mistakenly think that their position and speed can be measured at the same time.
Finally, we want to talk about Dirac , which has made a great contribution to quantum mechanics.
In September 1925, by chance, Dirac saw Heisenberg's basic paper on quantum mechanics published by Heisenberg in a scientific journal, and saw Heisenberg's uncertain relationship about position and speed. Dirac noticed that although this is a very abstract relationship, the Planck constant appears in it. This is a constant that is not available in Newtonian mechanics. This constant is very small and can be completely negligible. It can even be considered zero. But in the microscopic world, it is no longer zero and becomes very important. It determines the energy level of the atom and also determines the intensity of the spectrum . When seeing this abstract relationship, Dirac thought that although there was a Planck constant in it, this relationship looked very similar to some kind of relationship in Newtonian mechanics. In order to verify the relationship between the two, he ran to the library in the middle of the night, but the library was closed. He had to wait until the next morning. As soon as the library opened, he rushed in and found the classic Newtonian mechanics textbook, and found the Newtonian mechanics formula from the book. As expected, he found that this was indeed true: Heisenberg's formula is very similar to the formula in Newtonian mechanics, only one Planck's constant was missing. It can be seen from this that Dirac has particularly strong mathematical ability.
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-