This article is from WeChat official account:Return to Pu (ID: fanpu2019)< span class="text-remarks">, author: Cao Zexian (Institute of Physics, Chinese Academy of Sciences), original title: “Cultural Man Schrödinger (Part 2)丨Sages Say Eight Ways”, head picture from: Visual China
“Schrödinger, the Cultural Man” takes you to appreciate the style of Schrödinger, one of the greatest physicists of the 20th century. The full text is divided into the first and second articles. The first part mainly briefly described Schrödinger’s life; he saved Weyl’s new world geometry theory through quantization conditions; and how the most famous quantum mechanics wave equation was vacated. The second part talks about the original meaning of “Schrödinger’s Cat”; Schrödinger’s thinking on life issues as a physicist; and his worldview and philosophy as a cultural scholar.
Schrodinger’s cat
Schrödinger’s name is still tied to cats in the shops. There are discourses on Schrödinger’s cats in popular texts and professional papers. It is vivid and colorful, and there is no lack of added oil and vinegar. This is a model for the vulgarization of science.
Schrödinger’s connection with cats originated from his 1935 article entitled “The State of Quantum Mechanics”. In the fifth section “Sind die Variablen wirklich verwaschen(has the variable really become fuzzy)?” Schrödinger introduced a cat as one of the characters As an example to illustrate his views on quantum mechanics.
This is a long article with a sober critique of the inner logic of quantum mechanics. I thought it was a landmark article in the history of quantum mechanics. Unfortunately, Schrodinger planted a dragon seed, but was given by others. It’s embarrassing to hatch a super fleas like “Schrodinger’s Cat”.
In 1935, there were Schrödinger equations (1926), Pauli equations (1927), Dirac equation(1928), after the von Neumann measurement theory (1930), quantum mechanics generally It is already mature.
After achieving an astonishing series of achievements in quantum mechanics, Schrödinger, in fact, there was also Einstein at about the same time. It is only natural that quantum mechanics should be deeply reviewed.
The first step of quantum mechanics is to use the quantization conditions of momentum and position to achieve energy quantization.(Explanation). The Dirac quantization condition [x, p]=iħ is related to the Poisson bracket of classical mechanics, and mathematically related to Fourier analysis, which can be understood as binding two physical quantities in a special conjugate way.
Correspondingly, Heisenberg noticed the uncertainty of the mechanical quantity resulting therefrom in 1927, and in 1929 Robertson gave the form of ΔxΔp≥ħ/2. It must be pointed out that the greater than sign in this relationship comes from the omission of another positive quantity, and the value of that term is sometimes dominant. The uplift and abuse of Heisenberg’s uncertainty principle stems from Ignorance of the source of thought (refer to my book “Physics Remarks” Volume 2).
To describe quantum mechanics as a revolution relative to classical mechanics is pure ignorance. The founder of quantum mechanics who understands physics like Schrödinger will naturally not have such a confused understanding. In quantum mechanics, the classical concept of state is discarded, and at most half of its complete set of variables are carefully selected to be given a certain value. The role of models in quantum physics cannot be as decisive as in classical physics.
Schrodinger pointed out, “Classical models play the role of Proteus in quantum mechanics[1] Each of its determinants can become an object of interest due to the situation, and acquire a certain kind of reality-this for a while, and that for a while, but the transient state at most allows its complete set of variables to obtain a clear image.” .
Furthermore, according to von Neumann’s measurement theory, a single measured value of a physical quantity in a system in a superposition state corresponds to an eigenvalue(determined and clear), its eigenvalues appear randomly after multiple measurements, but the distribution is determined by the wave function of the state, that is, the protagonist ψ-function of the Schrodinger equation Decided.
However, Schrödinger himself thinks that the ψ-function is Gedankending(imaginary existence), Denkbehelf(Hands and aids to help thinking), the expected label (Katalog der Erwartung), don’t take it So much responsibility. Use the ψ-function as a tool to express the ambiguity of all variables in a clear image(Verwaschenheit, refers to the uncertainty required by quantum mechanics), It is impossible to a certain extent.
If the blur described by the ψ-function is confined to the atomic level, the electron cloud outside the nucleus is a fuzzy image brought by the ψ-function. However, when this kind of fuzzy and uncertainty is applied to touchable and visible things, the label of “superimposed and fuzzy” (refers to uncertainty ) is wrong. This will bring ridiculous understanding.
Schrodinger uses a model constructed by the atomic nucleus alpha-decay event plus the touchable and visible event such as the detection of alpha particles to explain his thoughts. This is the classic argument that led to Schrödinger’s cat. :
“It is also possible to construct a funny situation. Combine a cat with the following underworld machine (make sure that the cat does not come into direct contact with it) Closed in a steel box: “There is a small amount of radioactive material in a Geiger counting management, as little as an hour, perhaps an atomic decay event may occur, or nothing happens; if an atomic decay event occurs, the counting tube is triggered, and then A small hammer is triggered by a relay device, and the small hammer breaks a glass bubble containing hydrocyanic acid.
Imagine that the system is left unused for an hour. If no atomic decay occurs during this time, the cat can be said to be alive. The first time an atom decaysPoison the cat to death. The ψ-function of the entire system will be described in this way, in which the states of live cats and dead cats (please allow me to say that) are mixed or superimposed with equal weight. ’
The typical feature of this type of situation is that an uncertainty initially limited to the atomic domain is transformed into a thick line uncertainty that can be determined by direct observation. This prevents us from simply and naively treating ambiguous models as realistic images. It’s not that the (model) contains any unclear or contradictory content, it’s just that the blurred photo is the same as the foggy photo due to shaking or poor focus difference between. “
This paragraph of historical significance is not long. In order to avoid misunderstandings caused by the inaccuracy of my translation, I might as well record the following for readers’ reference:
Man kann auch ganz burleske Fälle konstruieren. Eine Katze wird in eine Stahlkammer gesperrt, zusammen mit folgender Höllenmaschine (die man gegen den direkten Zugriff dermus Katze sichten Zugriff dermus Katze) :
in einem Geigerschen Zählrohr befindet sich eine winzige Menge radioaktiver Substanz, so wenig, dass im Lauf einer Stunde vielleicht eines von den Atomen zerfällt, ebenso wahrscheinlich aber auch keines;
geschieht es, so spricht das Zählrohr an nnd betätigt über ein Relais ein Hämmerchen, das ein Kö1bchen mit Blausäure zertrümmert. Hat man dieses ganze System eine Stunde lang sich selbst überlassen, so wird man sich sagen, dab die Katze noch lebt, wenn inzwischen kein Atom zerfallen ist.
Der erste Atomzerfall würde sie vergiftet haben. Die ψ-Funktion des ganzen Systems würde das so zum Ausdruck bringen, dass in ihr die lebende und die tote Katze ( svv) zu gleichen Teilen gemischt oder verschmiert sind.
Das Typische an diesen Fällen ist, dass eine ursprünglich auf den Atombereich beschränkte Unbestimmtheit sich in grobsinnliche Unbestimmtheit umsetzt, die sich dann durch direkte Beobacht ent.
Das hindert uns, in so naiver Weise ein, verwaschenes “Modell” als Abbild der Wirklichkeit gelten zu lassen. An sich enthielte es nichts Unklares oder Widerspruchsvolles.
Es ist ein Unterschied zwischen einer verwackelten oder unscharf eingestellten Photographie und einer Aufnahme von Wolken nnd Nebelschwaden.
The gist of this article by Schrödinger is to discuss the incompleteness of quantum mechanics. The phrase “that’s just the difference between a blurred photo and a cloud photo obtained due to jitter or poor focus” is a metaphor for the difference between the uncertainty of quantum mechanics and the uncertainty in the classical sense. It is indeed The stroke of magic is also what we should pay attention to when we understand quantum mechanics.
Unfortunately, some people who did quantum mechanics research and consumed quantum mechanics only saw the cat in that model but ignored Schrödinger’s thoughts. Schrödinger’s cat later had an image that was dead and alive. You don’t know if it deserves to die or live if you don’t look at it. It has become a gimmick that quantum mechanics can’t get rid of.
This understanding is completely different from Schrödinger’s original intention. Schrödinger, a veteran scholar with a solid foundation in classical mechanics, has been portrayed as an inconspicuous image by many people who have a slight interest in quantum mechanics, which is really wrong. “Schrodinger’s Cat” is the love of unscrupulous scholars, and it is even regarded as a philosophical question.
What is life from a physical perspective?
Schrödinger’s acclaimed and ground-breaking achievement is reflected in his book “What is Life”, which was a collection of lectures he gave at Trinity College Dublin in 1943. The title of the book What is life?—The physical aspect of living cell, the subtitle can be translated as “Physical View of Living Cells” or “Living Cells from a Physical Perspective”, It can be imagined that this is a theoretical physicist Thinking of the source of the structure of life purely from a physical point of view.
Talking about the topic of life outside of his profession, Schrödinger’s excuse is, “We have inherited from our forefathers the keen longing for unified, all-embracing knowledge(we have inherited from our forefathers the keen longing for unified, all-embracing knowledge(we have inherited from our forefathers the keen longing for unified, all-embracing knowledge(we Inherited from our ancestors the desire for unified and comprehensive knowledge)“. He believes that scholars should pay attention to the universal aspect of things(full picture), you can try to synthesize knowledge.
The main purpose of these lectures is to explain some basic ideas that hover between biology and physics, and answer “How can the events in space and time which take place within the spatial boundary of a living organism be accounted” for by physics and chemistry(How to use physics and chemistry to explain the spatiotemporal events that occur in the space confined by the living organism)” .
Although there is still nothing he can do, Schrödinger believes that the process of life follows the laws of physics. From his relatively simple, clear and humble science (comparatively simple and clear and humble science) departure can contribute to the understanding of life.
Schrodinger relied on his keen eyes as a theoretical physicist to realize that the key to understanding life lies in the arrangement of atoms. The arrangements of the atoms in the most vital parts of an organism and the interplay of these arrangements differ in a fundamental way from all those arrangements of atoms which physicists and chemists have hitherto made the object of their experimental and theoretical research(The arrangement of atoms in the most vital part of the body and their mutual cooperation are fundamental to the arrangement of atoms in the experimental and theoretical research objects of physicists and chemists. Difference), and the difference in this “statistical structure”(the difference in”statistical structure”) is so small that only physicists who have been instilled with the idea that “the laws of physics and chemistry are statistical” can notice.
Schrödinger pointed out that life must be something that happens above a large number of atoms. Schrodinger asked, why are atoms so small? This is because the life that recognizes the existence of atoms must be the product of a large number of atoms, and atoms must appear small in comparison.
In other words, the “small and big” relationship between atoms and life is actually a “one and many” relationship! The knowledge of statistical mechanics tells us that a system composed of a large number of atoms can avoid the response to the influence of a single atom. If the senses respond to all the effects on the atomic level, Heavens, what would life be like! Is there a fart function?
Schrodinger further thought that perception can only be an orderly thing applied to orderly things(Orderly things act on orderly things) , Because the definite behaviors produced in life and even the thoughts shown on the human level must be something orderly. The sensory process must follow the physical laws based on atomic statistics(physical laws, which rest on atomic statistics). The physical laws that play a role in the process of life must be statistical.
At that time, chromosomes were recognized by biologists as genetic material. Schrödinger praised chromosomes for code and execution of rules, or the combination of designer plans and craftsmanship.(They are law-code and executive power -or, to use another simile, they are architect’s plan and builder’s craft in one).
Schrodinger pointed out, “…the most essential part of a living cell-the chromosome fibre may suitablybe called an aperiodic crystal……Yet, compared with the aperiodic crystal, they(periodic crystal)are rather plain and dull (The most critical component of living cells, namely chromosome pulling filaments, may be more called quasi-periodic crystals… Compared with quasi-periodic crystals, they (periodic Crystal) too boring”).
In quasi-periodic crystals, “every atom, and every group of atoms, plays an individual role, not entirely equivalent to that of many others(Every atom, every group of atoms, plays a unique role that is not equivalent to the others) “.
“……which(aperiodic crystal)shows no dull repetition, but an elaborate, coherent, meaningful design……which, in my opinion, is the material carrier of life(It (quasi-periodic crystal) has no monotonous repetition , But with an exquisite, related, and meaningful design…In my opinion, it is the material carrier of life)“.
Schrodinger confidently declared, “We believe a gene -or perhaps the whole chromosome fibre -to be an aperiodic solid Silk is a quasi-periodic solid) “, pointing out the possible structure of the material carrier of life, and it is a completely new concept. It was first proposed by a theoretical physicist with botanist origins such as Schrödinger. I think this is very logical.
Schrödinger’s discussion of quasi-periodic crystals in 1943 was purely hypothetical. However, by 1984, the greatness of Schrödinger’s thought was verified. In 1984, the five (ten) sub-rotational symmetry excluded by the crystal translational symmetry in the electron diffraction pattern of Al-Mn alloy It was discovered for the first time in, that an ordered solid with a quasi-periodic structure had a concrete realization and was named quasicrystal (quasicrystal). Since then, ordered solids with eight and twelve rotational symmetry have been discovered one after another, which has set off an upsurge in the study of quasicrystals.
The research on quasicrystals has not only brought new understanding of solids in three-dimensional physical space, but also gained a lot of new knowledge about the geometry of stacking problems in any dimensional space. The author even gained some in this field. Small research results. In 2011, Shechtman (Dan Shechtman, 1941-) won the Nobel Prize in Chemistry for research on quasicrystals.
Schrodinger mentioned negative entropy (negative entropy) in this book, which makes it difficult for the author to understand. This kind of low-level basic conceptual mistakes, supposedly he shouldn’t have made them. Entropy is an extended physical quantity, not negative. The change in entropy may be negative. In fact, it can be seen that the article is talking about the entropy change of the process.
I am a cultural scholar
Schrodinger is a great thinker of the 20th century, from the perspective of both a scientist and a cultural scholar. Schrödinger’s works other than academic papers are as influential as “What is Life” and are composed of lectures, as well as “Nature and the Greeks”( 1948), “Science and Humanities” (1950), “Thinking and Matter” (1958), “My World View” (1961) These pamphlets, because of their ideas Rich, elegant and highly praised.
Penrose’s words were deeply influenced by it: “I find a remarkable work, of a similar force and elegance concerned with the nature of reality and with the ways in which reality has been humanly perceived since antiquity.” The philosophy of quantum mechanics and Einstein’s are both classified as “objective”. This implication is understood by anyone who understands it.
About the seventh century BC, the Greeks began to describe the universe, which was the beginning of European thought. At this time, the Greeks no longer believed in the power of divinity behind things, but sought a “knowledge” explanation-the universe can be known. The Greek spirit has always been the life background of European culture, and the formation of modern Western culture is based on the premise of reviving the tradition of Greek classical literature and rational philosophy.
European primary and secondary schools generally have Greek and Latin courses, and European cultural people regard the Greek spirit as the source of their spirit. Hegel believes that as long as Greece is mentioned, educated Europeans have a “sense of home.”
From this perspective, it is not surprising that theoretical physicists and philosophers like Schrödinger have carefully investigated the relationship between nature and Greeks, science and humanities. According to Schrödinger, science is “thinking about the world in the Greek way(Think about the world the Greek way)“.
In the 1940s, physics experienced a relatively peaceful period after experiencing the hustle and bustle caused by the establishment of relativity and quantum mechanics. The development of science brought progress to human society and also contributed to the development of science. The concept itself brings crises, one of which is that the previous habit of separating the person as the subject of knowledge from the object to be known became unreasonable after the birth of quantum mechanics.
Schrodinger sought an answer from ancient Greek philosophy. He believes that the current conflict between science and metaphysics did not exist in the ancient Greek era. Back to ancient Greece, you can investigate how knowledge happened at that time with modern viewpoints and knowledge, and you can obtain some directly from the insights of the ancient Greeks. Inspired. In the process of combing through the history of ancient Greek philosophy, we can learn what factors led them to obtain such views in that era.
Go back to the starting point of the ancient thinkers, to be able to see clearly where our current problems are, at least to be able to see where the later thinking biases came from, to find the source of vices; to gain freedom of thought and weaken the past The historical process of science imposes constraints on us. By returning to ancient Greece, we discovered that some scientific categories that currently restrict our thinking are not natural and logical, but man-made and historical, so it is possible to change them.
In the series of lectures on “Nature and the Greeks”, Schrödinger discussed the competition between rationality and sensibility, and reviewed many of the Ionian, Pythagoras, Efes, and Stoic schools. The thoughts and achievements of the Greek sages, discuss their significance to current science.
Schrodinger finally confirmed the two legacy of ancient Greek natural philosophy. One is that the world is an intelligible concept, and the other is a vision of the world that excludes the subject of the observer. This latter point hinders contemporary science. Answers to metaphysical questions encountered.
The famous philosophical three consecutive questions, namely, who I am, where I come from, and where I go.(Who I am, whence I came and wither I go) , in 1925, Schrödinger, who was 39 years old, had not yet become famous, asked himself in his notes, which was particularly inspirational. This philosophical triple-question has appeared many times in “Nature and the Greeks” in different ways of expression.
Several lectures in “Science and Humanities” involve more scienceContent, such as the concept of continuity, the concept of form, the conflict between quantization and continuity, some expedient understandings in wave dynamics, and so on. What impressed the author was an example that Schrödinger gave to illustrate the meaning of the form (shape, form; Gestalt in German). Schrödinger said that when he was a child, there was a dog-shaped iron paperweight on his father’s desk. He liked it very much. After his father died, the iron paperweight belonged to him, so this iron puppy has a memorial significance.
Schrodinger believes that its meaning comes from its form rather than its material composition. If the paperweight is melted, it will still be the piece of iron, but the puppy is gone. This vivid example of Schrödinger can easily arouse people’s attention to philosophical speculation about form and content. As far as the author is concerned, I believe that form has a decisive significance in mathematics and theoretical physics.
The author recommends that the three pamphlets of “What is Life”, “Nature and the Greeks” and “Science and Humanities” be put together for study. I also recommend that they be put together with Russell’s “History of Western Philosophy” for detailed study. There must be something. Of course, if you look at Schrödinger’s “My World View” and “What are the laws of nature” together, you will know that there has never been a barrier between science and humanities in this world. The estrangement exists in the obsession of people who are unable to see the world.
In addition, Einstein has a book “My World View” (Mein Weltbild), which is similar to Schrödinger’s “My World View” similar. The masters above the peak often worry about the rationality and consistency of the mountain foundation, and it is interesting to pay attention to where our knowledge comes from and what kind of understanding is the law of nature.
By the way, Schrödinger loved poetry since he was a child and published a collection of poems in 1949. He is said to have told Born that praising his poems makes him more happy than praising his academic papers. In addition to love poems with practical value, the love of nature and a certain sense of metaphysical despair are the two main themes of Schrödinger’s poems.
Schrödinger’s poems, frankly speaking, are not highly evaluated by German-speaking cultural circles. Heisenberg also seems to like to write poetry, and his poetry has never been well received—Dirac wondered how one can do both good physics and good poetry. In my opinion, Schrödinger and Heisenberg’s poems are not flattering. In addition to these two temperaments are not suitable for writing poems, an important reason is that German is not suitable for writing poems.
Excess words
Schrodinger is a pinnacle in the history of modern physics. Understanding Schrödinger’s academic achievements, his life and research process are of enviable significance, if not reference significance, for the self-growth of a scholar and how a country trains scholars. How many conditions are needed for the growth of a scientific giant?
It’s just that I was born with that material. I happened to be born in an educated family. I grew up in a place with cultural heritage. When I was young, I went to a university that could be regarded as a university.(such as the University of Vienna in Austria and the University of Zurich in Switzerland related to Schrodinger), there are several outstanding peers who can strengthen each other as adults (For example, Einstein, Born, Weyl, etc. related to Schrodinger).
As far as physics learning is concerned, learning around people who understand physics or even participate in the creation of physics is probably a very effective path. In fact, the best way of education is nurturing. In a place where there is “University as a good teacher(Erudite as a good teacher)” haunted randomly, such as Mach and Boltzmann At the University of Vienna, which is haunted by people, Erwin, a young physics-loving teenager, will not feel helpless when he encounters setbacks in his studies, and he does not have to worry about being too good.
On the one hand, no matter how good it is, it may not be good. On the other hand, “the wood is beautiful in the forest, the wind will destroy it” is not the German cultural tradition in the Habsburg dynasty, otherwise it is not there. There will be a Vienna circle that will greatly affect human civilization.
How Schrodinger specifically vacated the quantum mechanical wave equation is an interesting topic in the history of physics. The special thing is that Schrödinger’s equation is not derived, but it is not derived in a vacuum. It is necessary to guess, piece together, and construct on the basis of existing knowledge, but also to sublimate it (reflected in Schrödinger’s essay on the principle of least action Rationalize the process of obtaining the equation), and find support for its correctness (the solution to the hydrogen atom problem).
If we only take a look-up perspective on physics, then we can’t talk about anatomy and research, let alone the LordMove to transform and create it. It seems that it is necessary to seriously disenchant physics in our physics education. For true physicists such as Einstein and Schrödinger, the disenchantment of physics does not detract from their image-only great physicists without achievements in physics need to maintain the halo fog of physics.
In 1997, I realized that Professor Friedrich Hund who gave Hong’s specific rules was an uncle from a neighboring village. He definitely had a strong impact on the author’s understanding of physics and physicists, but the strong impact came too late. some. Of course, it is useless for a dead wood like the author to come early. However, excellent young people have been growing on this land. If the elders prepare enlightenment and smiling faces for them, they will be the hope for the future.
(Note: This article is an excerpt from Cao Zexian’s Majestic One, to be published)
Note:
[1] Proteus, a character in Greek mythology, may be Poseidon’s eldest son, here may be that it has many possible forms (capable of assuming many forms ). Schrödinger uses Proteus as a metaphor for micro-reality.
This article is from WeChat official account:Return to Pu (ID: fanpu2019)< span class="text-remarks">, author: Cao Zexian (Institute of Physics, Chinese Academy of Sciences)