Author: Liang Hao
Link:/question/28068598/answer/39871953
Source: Zhihu.
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The hypothesis of reductionism may still be a controversial topic among philosophers, but among most frontline scientists, I think people must have accepted it. As far as we know, our thoughts, our bodies and the operating mechanism of all organic and inorganic substances are considered to be governed by the same set of basic laws; We believe that except for some extreme cases, we have a good understanding of this set of basic laws.
Without thinking, people tend to regard the following proposition as an obvious reductionist inference: if everything follows the same basic laws, then only those scientists who study what is the real foundation are the ones who explore these laws. This actually means that they are nothing more than some astrophysicists, some elementary particle physicists, some logicians and mathematicians. This view, which is also opposed by this paper, is most clearly expressed in a famous remark by Viskorf: [1].
Throughout the development of science in the 20th century, people can see two trends; For lack of a better term, I will call it "extensive research" and "extension research". In short, connotation research explores basic laws, while extension research is devoted to explaining phenomena according to known basic laws. Of course, this distinction is not without ambiguity, but it is clear in most cases. Solid-state physics, plasma physics, and perhaps biology are all epitaxial studies. High-energy physics, as well as a considerable part of nuclear physics, belong to connotative research. Compared with extension research, connotation research is always much less. Once the new basic law is discovered, the research activities of applying it to the phenomenon that has not been explained so far will flock to us. So basic research has two dimensions. The frontier of science is very long, from the latest connotation research to the extensive and rich extension research based on the connotation research in the past few decades.
The influence of this passage may come from the fact that I heard that a leader in the field of materials science recently quoted this passage to urge those who discuss "the basic problems in condensed matter physics" to admit that there are almost no such problems in this field, and condensed matter physics is only an extended science; And extension science, in his view, is not much different from mechanical engineering.
The main mistake of this kind of thinking is that the reductionist's assumption never includes the constructivist's assumption: the ability to reduce everything to simple basic laws does not include the ability to rebuild the whole universe from these laws. In fact, the more properties the elementary particle physicists tell us, the less relevant they are to our understanding of practical problems in other scientific fields, and even less relevant to solving social problems.
Once faced with the double difficulties of scale and complexity, the constructivist hypothesis naturally becomes untenable. The behavior of large and complex elementary particle aggregates cannot be understood by simply inferring the properties of several elementary particles. In fact, at every level of complexity, there will be brand-new attributes; In my opinion, the research to understand these new behaviors is basically the same. So in my opinion, people can arrange science into a roughly linear level according to the following assumptions: the basic entity X of science obeys the law Y of science.
X
Y
Solid state or multibody physics
Elementary particle physics
chemistry
Multi-body physics
molecular biology
chemistry
cytobiology
molecular biology
……
……
psychology
physiology
social science
psychology
However, this hierarchical structure does not mean that scientific X "just applies Y". At every level, new laws, concepts and principles are essential, and their imagination and creativity are no less than the previous level. Psychology is not applied biology, nor is biology applied chemistry.
The field of multi-body physics I am engaged in may be closer to the basic connotation research than other disciplines; In this field, due to the unusual complexity, we have set out to establish a general theory to explain how the change from quantitative change to qualitative change occurs. This theory is the so-called "broken symmetry" theory, which may help to explain that the inverse proposition of reductionism-constructivism-is completely untenable. I will make some basic and incomplete explanations first, and then make some general speculative comments on similar situations and similar phenomena at other levels.
Before that, I want to clarify two possible misunderstandings. First of all, when I say that scale changes cause fundamental changes, I don't mean the well-known concept that phenomena on the new scale may obey fundamentally different basic laws, such as general relativity on the cosmic scale and quantum mechanics on the atomic scale. I think it should be admitted that all ordinary matter obeys electrodynamics and quantum mechanics, and my discussion is mainly limited to ordinary matter (I said before that we should all start from reductionism, which I am convinced of). The second misunderstanding may be that symmetry breaking's concept has been borrowed by elementary particle physicists, but I want to say that particle physicists only use this concept in the sense of analogy, and whether there is symmetry breaking is still a mystery to us.
Let's give an example as simple as possible, that is, ammonia molecules. I also chose it because I have been dealing with it since I was a graduate student. At that time, everyone was familiar with ammonia and used it to calibrate their own theories or instruments, and I was no exception. Chemists will tell you that ammonia molecule is a triangular pyramid composed of negatively charged nitrogen atoms and positively charged hydrogen atoms, so it has an electric dipole moment (μ), and its negative direction points to the top of the pyramid. At that time, I thought it was incredible, because nothing I learned had electric dipole moment. The professor who taught us nuclear physics did prove that no nucleus has electric dipole moment; Since his argument is based on the symmetry of time and space, it should be universally established.
I soon understood that this argument is actually correct (more accurately, it is not incorrect), because his statement is cautious: any system in a steady state (that is, a system that does not change with time) has no electric dipole moment. If the initial state of ammonia molecules is the asymmetric state mentioned above, it will not stay in that state for a long time. Because of quantum tunneling effect, nitrogen atoms will escape to the other side of the triangular plane of hydrogen atoms, thus turning the pyramid upside down; In fact, it happened very quickly. This is called "upside down" and its frequency is. The real steady state can only be the equal overlapping addition of asymmetric pyramid and its inversion. This superposition state has no electric dipole moment (I want to remind readers that this is a highly simplified statement, please refer to the textbook for details).
I won't give proof here, but the conclusion is that if the state of a system is stable, its symmetry must be the same as the law governing it. The reason is simple: in quantum mechanics, there is always a path from one state to another unless symmetry prohibits it. Therefore, if we start from any asymmetric state, the system will jump to other States; Only by superimposing all possible asymmetric states in a symmetrical way can a steady state be obtained. In the case of ammonia molecules, the symmetry involved is parity-the equivalence of left-handed and right-handed (the specific parity destruction discovered by elementary particle experimental physicists is irrelevant: those effects are too weak to affect ordinary matter).
Seeing that ammonia molecules have no electric dipole moment and satisfy our theorem, let's look at other situations, especially those larger and larger systems, to see if their states are always related to symmetry. There are similar pyramidal molecules composed of heavier atoms. PH3 of phosphine is twice as heavy as ammonia, but its frequency is only110 of ammonia. No measurable level of conversion was observed in the molecule PF3 of phosphorus tribromide, in which the hydrogen atom was replaced by a heavier fluorine atom, although in theory, this conversion would occur within an appropriate time interval.
Next, we can look at more complex molecules, such as sugar molecules composed of about 40 atoms. For such molecules, we no longer expect them to be reversed. Every sugar produced by living things has the same spiral direction, but neither quantum tunneling effect nor thermal disturbance at room temperature can reverse it. Here, we must forget the possibility of inversion and put aside the symmetry of parity: the law of symmetry has not been abolished, but has been broken.
On the other hand, if we chemically synthesize sugar molecules near the thermal equilibrium state, we will find that on average, there are as many left-handed molecules as right-handed molecules. Generally speaking, the law of symmetry will never be broken if the complexity does not exceed the free molecular aggregate. We need living matter to produce actual asymmetry in the life world.
In a very large but still lifeless atomic assembly, another kind of symmetry destruction will occur, resulting in net dipole moment or net optical rotation intensity, or both. Many crystals have a net dipole moment (pyroelectricity) in each basic unit cell. In some crystals, this dipole moment can be reversed by a magnetic field (ferroelectricity). This asymmetry is the spontaneous effect of the crystal seeking the lowest energy state. Of course, the states of reverse dipole moment also exist and have the same energy according to symmetry, but the system is so large that there is no thermal effect or quantum mechanical effect that it can change from one state to another in a limited time (relative to the age of the universe).
At least three inferences can be drawn here. First of all, symmetry is extremely important in physics. Symmetry means having different perspectives, so that the system is the same from any perspective. It is a bit exaggerated to say that physics studies symmetry, but it is not so excessive. Newton may have demonstrated the power of symmetry for the first time. He may have asked himself this question: What if the matter around us and the matter in the sky obey the same law? In other words, what if space and matter are homogeneous and isotropic?
The second inference is that even if the general state of matter is symmetrical, its internal structure is not necessarily symmetrical. I advise you to start from the basic laws of quantum mechanics and predict the inversion of ammonia and its easily observed properties, instead of deriving it step by step from its asymmetric pyramid structure, even though no "state" has that structure. Interestingly, it was not until 20 years ago [2] that nuclear physicists no longer regarded the nucleus as a symmetrical ball without any features, and realized that it could be in the shape of a football or a dish, although it had no dipole moment. This has observable consequences in the nuclear reaction and excited state spectra of nuclear physics research, although it is much more difficult to directly prove it than to observe the inversion of ammonia molecules. In my opinion, whether it is called connotation research or not, it is basically the same as many basic things that people say. But this does not require any new knowledge of basic laws, and it is extremely difficult to try to deduce them step by step. It was just an inspiration based on daily intuition, which straightened everything out at once.
The basic reason why this result is difficult to deduce is instructive for our further discussion. If the nucleus is small enough, there is no way to define its shape strictly: three, four or 10 particles that revolve around each other cannot define a rotating "dish" or "football". Such behavior can only be strictly defined when the core is regarded as a multi-body system, which is usually called limit. We say to ourselves that a macroscopic object of that shape will have such a rotation and vibration excitation spectrum, which is completely different from the spectrum of a featureless system in essence. When we see such a spectrum-even if the resolution is not very good, the spectrum is not very complete-we have to admit that the nuclear is not a macroscopic object after all; It's just close to macro behavior. Starting from the basic law and computer, we will have to do two impossible things to get the core behavior: solve the infinite multi-body problem and then apply the result to the finite system.
The third inference is that the state of a truly large-scale system does not need to have the symmetry of the laws governing the system at all; In fact, it usually has low symmetry. The outstanding example is crystal: crystal is constructed by atoms and space according to the law of complete homogeneity of space, but it unexpectedly shows a new and wonderful symmetry. Generally, the symmetry of large-scale systems is lower than that implied by the structure behind them, and crystals are no exception: although crystals are symmetrical, their symmetry is far lower than that of complete spatial uniformity.
Maybe the crystal example is too simple. As early as the middle of19th century, the regularity of crystals can be deduced semi-empirically, without any complicated reasoning. But sometimes, for example, in the case of superconductivity, the new symmetry-the so-called broken symmetry, because the original symmetry is no longer obvious-may be completely unexpected and hard to imagine. In the case of superconductivity, it took physicists 30 years to have all the necessary basic laws and finally explain them.
Superconducting phenomenon is the most prominent example of symmetry breaking, an ordinary macroscopic object, but it is by no means the only example. Many substances, such as antiferromagnets, ferroelectrics, liquid crystals, etc., obey a fairly common concept and rule, and many many many-body theorists put them under the general heading of symmetry breaking. I don't want to continue discussing history. See the notes for references. [3]
The most basic idea is that for large-scale (that is, our own macro-scale) systems, at the so-called limit, substances will undergo a violent and mathematically strange "phase transition", and then not only the microscopic symmetry will be destroyed, but even the microscopic motion equation will be destroyed to a certain extent. The traces left by symmetry only show some characteristic behaviors, such as long-wave vibration, and the familiar example in this respect is sound wave; Or the strange macroscopic conduction phenomenon of superconductors; Or very similar, lattice and the rigidity of most solids. Of course, the system can't really violate-not break-the symmetry of space-time, but because all parts of the system find it more beneficial to maintain a certain relationship between them from the perspective of energy, symmetry only allows the object as a whole to deal with external forces.
This leads to the concept of "rigidity". This concept can also be used to describe superconductivity and superfluidity, although they seem to be "fluid" behaviors (regarding superconductivity, London [F. London] has long recognized this [4]). In fact, if there is a gaseous intelligent creature living in the hydrogen atom cloud on Jupiter or somewhere in the center of the Milky Way, the properties of ordinary crystals will be more confusing than the behavior of superfluid helium.
I don't want to give you the impression that everything has been solved. For example, I think there are still fascinating principle problems in glass or amorphous phase, where more complex behavior patterns may be revealed. Nevertheless, we now understand symmetry breaking's role in the properties of inert macroscopic objects at least in principle. It can be seen that the whole is not only greater than the sum of parts, but also different from the sum of parts.
As a logical extension of the above question, the next question is naturally whether it is possible to completely destroy the basic symmetry of space-time, and if so, whether there will be a new phenomenon that is essentially different from the "simple" phase transition (that is, condensed into a state with lower symmetry)?
We have ruled out the obvious asymmetry of liquid, gas and glass (in fact, they are much more symmetrical than people think). In my opinion, the next step is to check the regular but informative system. On the one hand, it is regular in space, so that we can "read" it; On the other hand, its adjacent "cells" contain different elements. The obvious example is DNA；; In daily life, a line of words or a film has the same structure. This "information-bearing crystallinity" seems to be crucial to life. It is not clear whether the development of life needs further symmetry breaking.
If we continue to discuss symmetry breaking in life, I think there is at least one phenomenon that can be confirmed and is universal or quite universal, and that is the ordering of time dimensions (regularity or periodicity). In many theories about life process, regular time pulse plays an important role, such as development theory, growth and growth limit theory, memory theory and so on. In an organism, the regularity of time is easy to observe. It played at least two roles. First of all, the methods of extracting energy from the environment to maintain a continuous quasi-stable process mostly require devices with time periodicity, such as oscillators and generators, and life processes are no exception. Secondly, the regularity in time is a means to process information, which is similar to the regularity in space of load information. Spoken English is an example; It can also be noted that all computers use time pulses. The theory mentioned above also implies a third function: using the phase relationship of time pulses to process and control the growth and development of cells and organisms. [5]
In a sense, structure-functional structure in the teleological sense, not just the morphological structure of crystals-must be regarded as a step to break the symmetry level, which may be between crystallinity and information string.
Based on layer-by-layer speculation, I think the next step may be hierarchical or specialized functions, or both. To some extent, we must stop talking about reducing symmetry and start calling it increasing complexity. Therefore, with the increase of complexity, we will follow the scientific hierarchy. I believe that at every level, we will encounter fascinating and very basic problems, that is, combining less complicated parts into a more complicated system, and understanding the essentially new behavior that comes from it.
The way of complexity in many-body theory and chemistry can't be compared with the way of complexity in cultural theory and biology unless you generally say that the relationship between a system and its parts is a one-way channel. Synthesis is almost impossible; On the other hand, the analysis is not only possible, but also fruitful in all aspects: if the symmetry of breaking in superconductivity is not understood, B.D. Josephson may not find the effect named after him (another name for Josephson effect is "macroscopic quantum interference phenomenon": the interference effect between electrons in superconductors or macroscopic wave functions of helium atoms in superfluid helium. These phenomena greatly expand the accuracy of electromagnetic measurement, and it can be expected that it will play an important role in future computers in its various possible applications, and may eventually bring some major technical achievements in this decade [6]. Another fruitful example is that genetics has been reduced to biochemistry and biophysics, which has rewritten the face of biology as a whole, which will bring immeasurable and significant consequences. Therefore, the view advocated in a recent article [7] that we should all "cultivate our own valleys instead of trying to build roads across mountains between different disciplines" is wrong. In fact, we should realize that such a road, especially the shortcut of adjacent disciplines, cannot be viewed from the perspective of only one discipline.
The arrogance of particle physicists and their connotative research may be our reliance (the discoverer of positrons said that "the rest is chemistry"), but we must get rid of the arrogance of some molecular biologists who try to completely restore human tissues or functions to chemistry, from common colds and various mental diseases to religious instinct. There are obviously more organizational levels between human behavior and DNA than between DNA and quantum electrodynamics, and each level needs a brand-new conceptual framework.
At the end of the article, I use two examples from economics to illustrate the point I want to convey. Marx said that quantitative change will lead to qualitative change; However, a dialogue in Paris in the 1920s summed this up more clearly:
Fitzgerald: The rich are not like us.
Hemingway: Yes, they have more money.
[1] Weiss Kopf, in Brookhaven. Laboratory. Public library. 888t360 ( 1965)。 See also nuovo cimento suppl.ser14,465 (1966); Phy。 Today is 20th (5th) and 23rd (1967).
[2] A. Bohr and B. R. Martzen, Kgl. Daniel Vidensk. Selsk Mat Fys。 Medd。 27, 16 ( 1953).
[3] symmetry breaking and phase transition: L.D. Landau, Phys.Z. SowjetUnion11,26,542 (1937). Breaking symmetry and collective movement, general discussion: J. Goldstone, A. Salam, S. Weinberg, Phys. Rev.127,965 (1962); P.W. Anderson, Concepts in Solids (Benjamin, new york, 1963), pp. 175- 182; Joseph's doctoral thesis at Trinity College, Cambridge University (1962). Symposium: antiferromagnetism, P.W. Anderson, phys Rev.86,694 (1952); Superconductivity,-,same as above110827 (1958); Ibid. 1 12,1900 (1958); Y. Nambu, ibid.,117,648 (1960).
[4] F. London, superfluids (Wiley, new york, 1950), vol. 1.
[5] Cohen, J. Theor Biology. 3 1, 10 1 ( 197 1).
[6] American J. Clark. J. Phys.38， 1075( 1969)； P. W. Anderson, Phys. Today 23 (No.1 1), 23 (1970).
[7] A.B. Pippard, Harmony between Physics and Reality (Cambridge University Press, London, 1972).