Quantum mechanics hidden in a tiny window? So I advise you to close the curtains at night!

With the continuous development of urbanization, high-rise buildings are common today, and residential buildings are getting taller and taller. When we are bored, I believe that many students like me always like to look out the window at the water and high-rise buildings. At this time, I wonder if you have noticed that during the day, the windows of other people's houses are dark inside, but after entering their homes, you find that the lighting in their homes is very good and bright, but it is very dark from the outside. At night, you can clearly see the internal structure of other people's homes through the windows. This made me fall into contemplation: the light intensity during the day is not much different from the light intensity at night (the light intensity of indoor lights during the day is about 100-500 lux, and the light intensity of LED lights at night is 100-300 lux). Why can't I see things in other people's homes during the day?

First of all, we need to explain a concept of light - reflection. Reflection is divided into specular reflection and diffuse reflection. When light hits a smooth surface, it will be reflected in one direction, which is specular reflection. As shown in Figure 1. When light hits an uneven surface, it will be reflected in all directions, which is diffuse reflection, as shown in Figure 2. When light hits an object, it will be reflected, or refracted through the object.

Now everyone must have understood what reflection is, so the next step is to talk about a new physical quantity - black body. As the name implies, if an object can completely absorb electromagnetic waves of various wavelengths without reflection, this object is an absolute black body. As shown in Figure 4.1-1, a very small hole is opened on the wall of the cavity. The electromagnetic waves entering the small hole will be reflected and absorbed many times on the inner surface of the cavity, and ultimately cannot be emitted from the cavity. This cavity with a small hole can be approximated as an absolute black body. Light is also an electromagnetic wave. From this, it is not difficult for us to explain the previous problem. The window is very small, and the room is very large. After the light enters the room from the window, it is reflected a lot, making the room very bright. From the outside, due to the multiple reflections and attenuation of light, very little light is finally reflected from the room. In other words, the room at this time can be regarded as an approximate black body, so we cannot see the indoor environment from the outside. At night, because the light is emitted from inside the room, a lot of light can enter our eyes through the window, so we can see inside other people's homes at night.

Let's discuss the physical quantity of black body. It cannot reflect electromagnetic waves (the light shining into the room during the day cannot go out), but it can radiate electromagnetic waves outward (a lot of light can go out after turning on the lights at night). We call this phenomenon "black body radiation". In the 19th century, due to the needs of metallurgy and stellar temperature measurement, people conducted a lot of research on thermal radiation. At that time, physicists were able to measure the distribution of thermal radiation intensity with wavelength more accurately. Studies have shown that for objects of general materials, the radiation of electromagnetic waves is not only related to temperature, but also to the type of material and surface conditions, while the distribution of the intensity of electromagnetic waves radiated by black body by wavelength is only related to the temperature of the black body. So people began to explore the law of black body radiation. Using spectroscopic technology and equipment such as thermocouples, the distribution of the intensity of electromagnetic waves radiated by black body by wavelength can be measured. As shown in Figure 4.1-2. As can be seen from the figure, as the temperature rises, the radiation intensity of each wavelength increases, and on the other hand, the maximum value of the radiation intensity moves towards the direction of shorter wavelength.

People tried to explain this law. The development of science must find universal laws, so scientists began to explore and calculate this law. According to the knowledge of physics at that time, the vibration of each charged particle produces a changing electromagnetic field, thereby generating electromagnetic radiation. Therefore, scientists used Newton's basic mechanics and electromagnetic principles to derive this theoretical explanation.

In 1896, German physicist Wien and British physicist Rayleigh proposed theoretical formulas for the distribution of radiation intensity by wavelength, respectively. The formulas they proposed can only explain part of the experimental phenomena. Wien's formula is very close to the experiment in the short-wave region, but deviates greatly from the experiment in the long-wave region; Rayleigh's formula is basically consistent with the experiment in the long-wave region, but seriously inconsistent with the experiment in the short-wave region.

When people were at a loss, Planck found a formula that fit the experimental results perfectly, so he combined electromagnetism, mechanics, statistical physics and other disciplines to derive the formula. He boldly assumed that the energy of electromagnetic radiation generated by charged particles is in parts, not continuous, that is, the energy is an integer multiple of a certain minimum energy value €. For example, 1€, 2€... We call this minimum energy value € an energy quantum, and the expression is:

€=hv

Here h is a constant, we call it Planck constant, and v is the vibration frequency of the particle. The value of h is h=6.62607015*10-34J.S

Planck's assumption about the energy of microscopic charged particles is very different from our understanding of energy in the macroscopic world. For example, a spring oscillator pushes a ball away from its equilibrium position and starts vibrating with energy E. The next time we can push it a little further to make it vibrate with a little more energy, for example, 1.2E or 1.3E. We can also push it further to have a greater energy. The energy of a spring oscillator is not necessarily an integer multiple of a certain minimum value. As long as it is within the elastic limit, we can push the ball to any position and its energy can be any value.

It can be seen that the energy value of a macroscopic spring oscillator is continuous. However, Planck's hypothesis holds that the energy of microscopic particles is quantized, or in other words, the energy of microscopic particles is discrete. This is one of the most important differences between the physical laws of the microscopic and macroscopic worlds.

Therefore, Planck's hypothesis in 1900 unveiled for the first time a corner of the veil of physical laws in the microscopic world. From then on, physics entered a new era. Planck himself won the Nobel Prize in Physics in 1918 for this.

Planck's bold hypothesis and proof opened a new era of physics - the era of quantum mechanics. He is also known as the "father of quantum theory". Unexpectedly, through a small window, we can see such a huge world of quantum mechanics! Planck's story also tells us that we should not be limited to the various rules and regulations that have existed before. Only through bold attempts and innovations can we explore the true laws and values. As Planck said: The history of science is not only a series of facts, rules and the mathematical descriptions that follow, it is also a history of concepts. When we enter a new field, we often need new concepts.

Therefore, you can open the windows during the day, and remember to draw the curtains at night. At the same time, I hope we can discover science from the little things in life and have eyes to discover science.