From junior high school, to high school, to university, to graduate school, I studied physics for ten years, "it can be described as ten years of life and death, without thinking, unforgettable." (Children should not imitate and use ancient poems)
After reading so many books and taking so many classes, I found that physics is still so interesting and so tossing and turning.
Physics is the study of sound, light, heat, force, and electricity, and it helps us explain a wide variety of phenomena in life, from the fall of apples to the movement of planets; From the melting of ice, to the boiling of water.
These physical laws, which are summarized and extracted from the reality of life, in turn guide and change our lives. From rockets to astronautics, to the bits and pieces of life, whether you like it or not, physics has been soaked in our lives.
杠杆原則
"Give me a fulcrum, and I will be able to pry the earth", Archimedes' sentence is familiar to everyone, which contains the principle of leverage.
It may sound unfamiliar, but it's widely used. When we cut paper with scissors, pick up vegetables with chopsticks, and weigh with scales, we are all using levers.
The leverage balance conditions are:
That is, power * power arm = resistance * resistance arm.
From the formula, we can see that it takes distance to save effort, it takes effort to save distance, and it is impossible to save both effort and distance. (Did you learn something from this?)
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To take advantage of the convenience that leverage brings, the key is to find a fulcrum.
According to the lever balance condition, the lever can also be divided into equal arm lever, labor-saving lever and labor-saving lever.
In some places where distance savings are required, laborious levers, such as oars, are naturally required. Have you noticed that this is also a lever?
图源：wikipedia
Here, the power arm is smaller than the resistance arm, and the force exerted by the hand on the pulp is greater than the resistance of the water to the pulp, but as long as the hand moves a small distance, the pulp can move a large distance in the water. Laborious levers are exerted in exchange for distance.
As we get older, we discover that the product of the force and the arm is actually something called a moment.
The principle of lever equilibrium is that the resultant moment is zero.
The rotation of the top, the balance of the bike, are all related to the moment. About the principle of bicycle balancing,
In the course of 1935960 hours, we have cracked the mystery of bicycle balance and given a detailed introduction.
Symmetry and conserved quantities
Another interesting thing in physics is symmetry.
We have a tradition of symmetry for beauty, and nature also likes symmetrical structures. On a macro level, many architectural and man-made things show a certain symmetry; Microscopically, the atomic structure and crystal structure also exhibit some kind of translational or rotational symmetry.
Symmetry plays a pivotal role in the study of physics.
Physicists' favorite thing is symmetry, because symmetry reduces the complexity of the system and simplifies the laws of physics, so that it looks more beautiful, such as a spherical chicken.
Source: Zhihu
Symmetry often corresponds to a certain conserved quantity.
For example, translational symmetry in space corresponds to the conservation of momentum; The rotational symmetry of space corresponds to the conservation of angular momentum; Time-translational symmetry corresponds to the conservation of energy. These conservation relations can be derived from the Rashell quantity, so I won't go into too much detail here.
However, nature is not always symmetrical, and when the system no longer exhibits some kind of symmetry, we call it symmetry breaking. Symmetry breaks often lead to novel physical phenomena.
Electricity and magnetism
Electromagnetic phenomena have a long history. Around 600 B.C., the Greek Thales discovered that rubbed amber can attract small objects such as feathers; In the Eastern Han Dynasty, there was a record of "Sinan" on the mainland.
图源：wikipedia
In electromagnetism, "field" is a very important concept.
In the previous study of mechanics, we came into contact with the interaction forces between objects that exist between objects in direct contact. For example, when pushing a wooden box by hand, the force is applied to the box through the direct contact between the hand and the wooden box. When we study friction, we also pointed out that friction occurs when there is pressure between two objects with rough contact surfaces and there is a tendency to move relative to each other.
However, electric force (the force of interaction between electric charges), magnetic force (such as the attraction of a magnet to a block of iron), and gravitational force work in different ways. These forces can occur between objects that are separated by a certain distance and do not need to be in contact with each other.
This is not to say that these forces are "acting at a distance", but rather by the corresponding "fields". Wherever there is an electric charge, an electric field is excited in the space around it, and the electric field has a force on any other charge in it, which is the electric field force; The magnetic field is similar, the poles or electric currents excite a magnetic field in the space around them, and any current or pole in the magnetic field will exert a force. So the electric field force and the magnetic force are actually a kind of "close-up" action.
图源：wikipedia
Electricity and magnetism are not independent of each other, but are interconnected as a whole. Although electricity and magnetism developed independently of each other for a long time, some important discoveries led to the association of electricity and magnetism.
In 1731, an English merchant discovered that after the thunderbolt, one of his boxes of knives and forks turned out to be magnetic; In 1752, Franklin discovered that the discharge of a Leyden bottle could magnetize a sewing needle; In 1820, in a lecture, Oster placed the wire in a north-south direction, and after the electricity was applied, he found that the compass was deflected, and discovered the magnetic effect of electric current; In 1831, Faraday discovered the phenomenon of electromagnetic induction.
As a result, the electric and magnetic fields are unified and collectively known as the "electromagnetic field". In addition, it has been proved that the electromagnetic field can exist independently of charge and current, and that it has the same energy and momentum as the real thing. Field and physical object are just two different forms of physical existence.
Vector and cross-productive
In the study of electromagnetism, due to the interaction of electricity and magnetism, a bunch of left-handedness rules appeared:
The right-hand spiral rule for judging the direction of the magnetic field of the energized wire, the left-hand rule for judging the force of the energized wire in the magnetic field, the left-hand rule for judging the direction of the Lorentz force, and the right-hand rule for judging the direction of the current generated by the conductor cutting the magnetic inductance line.
图源：wikipedia
Xiaobian remembers that these rules were vividly summarized by the teacher as "left force and right electricity". Although I didn't memorize it when I was in school, after so many years, I can't remember it now.
When I was older, I came into contact with the fork vehicle and found that these left and right hand rules could be unified into the fork vehicle.
Point product and cross product are both properties of vectors.
When we were learning about speed, we learned that vectors are quantities that have both size and direction, and are represented by an arrow.
The triangular rule of vectors is used to add and subtract vectors.
Vector addition is to connect the arrows of each vector end to end, and the vector from the tail of the first vector to the head of the last vector is the vector; Vector subtraction is to put two vector tails together, and pointing from the head of the reduced vector to the vector of the reduced vector is the difference between the two vectors.
The two vector points are multiplied to get a scalar, and the scalar has only a magnitude and no direction, which is a number. The scalar is operated on as:
where |a|,|b| is the size of the vector.
The multiplication of two vector crosses still yields one vector,
The size is
The direction is perpendicular to the direction of these two vectors and can be judged with the right hand. The four fingers are bent from the direction of the A vector to the direction of the B vector, and the length of the thumb is the direction of the C vector. Therefore, by swapping the positions of the two vectors before and after the cross, the direction of the result is reversed.
图源：wikipedia
With the concept of fork multiplication, it is possible to express both the left and right hand rules in terms of cross multiplication.
The Lorentz force on the motion of charged particles in a magnetic field is,
The direction should be determined by the left-hand rule, assuming that the direction of the magnetic field is perpendicular to the paper face inward, the particle moves to the right, stretch out the left hand, let the magnetic field pass through the palm, and the four fingers point to the direction of the particle velocity, then the thumb direction is the direction of the Lorentz force.
This is what we have learned before, and now that we have the concept of fork vehicle, it has been transformed into it
Stretching out his right hand, the four fingers bend from the direction of velocity to the direction of the magnetic field, and the direction of the thumb is the direction of the Lorentz force, which is perfectly consistent.
With the concept of cross multiplication, the size calculation and direction judgment of the vector are unified in a formula, although the calculation has not become simpler, but it seems to be a lot more concise, and it is a lot easier to write.
Electromagnetism is broad and profound, and the editors of various vector fork products, point products, integrals, and differentials and various electromagnetic-related concepts are dizzy and happy.
Electron spin
After crossing the mountain of classical mechanics, we finally came to the door of quantum mechanics. The statistical interpretation of the wave function is already a puzzling concept, and the electron has an extra spin.
When I was a child, I only knew that electrons have charge and mass, but when I grew up, I realized that electrons still have spins. Electron spin is a new degree of freedom of the electron discovered after the development of quantum mechanics, it is an intrinsic property of electrons, and there is no classical correspondence, and the magnetic moment corresponding to the spin is the intrinsic magnetic moment.
Uhlenbeck and Goudsmit proposed the concept of electron spin based on the two-line structure of alkali metal spectra and the anomalous Zeeman effect. The electron spin is not a mechanical rotation because under this assumption, the electrons will rotate faster than the speed of light.
The Stern-Gerlach experiment directly confirmed that electrons have spins, and that electron spins can only take two discrete values.
图源：wikipedia
The experiment is actually very simple, a bundle of silver atoms enters the magnetic field, according to classical physics, the result on the observation screen should be as shown in 4, but the actual observation is the result shown in 5, the atomic beam is divided into two, indicating that the magnetic moment of the electron is quantized along the vertical direction, and only two values can be taken. This shows that electrons also have a new intrinsic degree of freedom – spin.
The discovery of electron spin has had a profound impact on the development of quantum information and quantum computing.
From junior high school to university, from classical physics to quantum physics, the knowledge of physics is all-encompassing, explaining the world and changing the world. Despite the difficulties we may encounter in the learning process, the beauty of physics has always attracted us to continue to explore and never stop.
Bibliography:
1. Quantum Mechanics, Zeng Jinyan, Science Press
2. Electromagnetism, Zhao Kaihua, Chen Ximou, Higher Education Press
Editor: Ah Bai