In his article "More is different", Anderson said that new laws of physics "emerge" at each physical level and new properties appear [1]; Wheeler, when claiming that "law without law" and "order comes out of disorder", argued that chaotic phenomena " generate" different laws of physics [2][3]. What they mean is that the laws, parameters, and constants of the upper level of physics appear to be independent of the laws of physics of the lower level. Is this really the case? Are we ignoring the conditions that form the physical hierarchy, thus leading to this illusion?
Let's suppose a model. The conditions for the formation of new levels are at least two: i. Existence of low-level things A,B ...... , the existence of interaction modes a, b,...... ; two, the existence of a sufficient number of low-level things, NxA, MxB....... Then when they are brought together, there are many possible combinations, e.g., (AA), (AAA), (AAA)', ...... , (AB), (BA), (AAB)', (BAB), ........ Then it escalates to [(AA)(AA)], [(AB)(ABA)], ....... What this actually leads to is a change in the structure of things and a corresponding change in the way they interact. The result of the "change" is the appearance of new physical phenomena, new forces, and so on.
Physics is an exact match for math, so let's use math as an example of this phenomenon. Suppose we have a number of strings (threads) that can be regarded as underlying things, then, when a string is curled into a circle, L=2πR, the law of the relationship between the length of the string and its radius, and the irrational constant π appear; when two strings are in cascade, L=l1+l2, the law that the total length of the string is equal to the sum of the individual string lengths (Principle of superposition) appears; and, when three strings form a right triangle, the law of Pythagoras, c2=a2+b2, the law of sums of interior angles of triangles ∠A + ∠B + ∠C = 180° , and the irrational constant √2 appear ...... ; and the transcendental number e appears when the string length L grows in a fixed proportion (continuous compound interest)[4]‡ ...... ; when the string vibrates, sine waves (sinωt) appear; when two strings are orthogonal, i appears ...... ; and when more kinds of vibrating strings are superimposed under specific conditions, more phenomena appear *.......
All these "qualitative changes" do not seem to be caused by "quantitative changes", but more by the need to change the structure. As mathematical theorems emerge, so must the laws of physics, and it is impossible for physics to transcend mathematics. Therefore, as long as there is a change of structure in physics, i.e. the possibility of symmetry breaking [5]**, new "symmetries", new "laws", new "forces", new "constants", new "parameters" are almost inevitable.
Can we try to attribute all physical phenomena to emergence under hierarchical structural conditions? For example, the fine structure constant‡‡and the Pauli exclusion principle emerge because of the formation of atomic structure; the "nuclear force" emerges because of the combination of protons and neutrons; The "strong interaction force" and "weak interaction force" appeared because of the structure of protons and neutrons. We should pay attention to the causal relationship here. Without structure, there would be no new phenomena; it is the more fundamental interactions that form structure, not these new "phenomena".
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Notes
* e.g. Blackbody radiation law, Bose statistics, Fermi statistics, etc.
** Should there be "spontaneous symmetry breaking"? Any change in symmetry should have a cause and a condition.
‡ What does it mean in physics if e will appear everywhere and the individual mathematical constants appear so simply? They must likewise appear at the most fundamental level of physics.
‡‡ https://www.researchgate.net/post/NO33_What_Does_the_Dimensionless_Nature_of_the_Fine-Structure_Constant_Mean
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2024-07-27 补充
In addition to the structure and statistics generated by the interactions that result in new laws of physics, the expression of the different orders of differentials and integrals of such generating processes is another important way of making the laws of physics emerge.
Typical examples of such expressions can be seen @ Ingo D. Mane: “On the Origin and Unification of Electromagnetism, Gravitation, and Quantum Mechanics“:
Preprint On the Origin and Unification of Electromagnetism, Gravitati...
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Referencs
[1] Anderson, P. W. (1972). More Is Different: broken symmetry and the nature of the hierarchical structure of science.
. Science, 177(4047), 393-396. https://doi.org/doi:10.1126/science.177.4047.393
[2] Wheeler, J. A. (1983). ‘‘On recognizing ‘law without law,’’’Oersted Medal Response at the joint APS–AAPT Meeting, New York, 25 January 1983. American Journal of Physics, 51(5), 398-404.
[3] Wheeler, J. A. (2018). Information, physics, quantum: The search for links. Feynman and computation, 309-336.
[4] Reichert, S. (2019). e is everywhere. Nature Physics, 15(9), 982-982. https://doi.org/10.1038/s41567-019-0655-9;
https://www.nature.com/articles/s41567-019-0655-9
[5] Nambu, Y. (2009). Nobel Lecture: Spontaneous symmetry breaking in particle physics: A case of cross fertilization. Reviews of Modern Physics, 81(3), 1015.