More Is Different-P. Anderson’s Perspectives On Broken Symmetry And The Nature Of Hierarchical Structure Of Science

More is Different-Brekon Symmetry and the Nature of Hierarchical Structure of Science is a lecture given by Paul Anderson in 1967, and the expanded version was published in 1972.

Anderson has demonstrated his views on the relationships between different fields of nature science-the hierarchical structure of science, and the broke symmetry was presented as a mainline from fundamental laws to the complexity of real phenomenons.
Anderson treat reductionist and constructionist as two totally different hypothesis.
(i) Reductionist Hypothesis: All of the matter are controlled by the same set of fundamental laws.
(ii) Constructionist Hypothesis: We can start from these laws and reconstruct our universe.

The reductionist hypothesis is accepted without question, however, the constructionist breaks down when confronted with the difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires fundamental research in its nature as any other.
Broken symmetry is an appropriate approach to illustrate the difference of the fundamental law between different scale.

Based on symmetry in the particle physics, there should not have a stationary state of a nucleus with electric dipole moment. In fact, as shown in the Figure, ammonia molecule has dipole moment.


Ammonia Molecule

By means of quantum mechanical tunneling, the nitrogen can leak through the triangle of hydrogens to the other side, from the left configuration the the right one in the figure, at a frequency of about 3\times 10^{10} per second. A truly stationary state can only be an equal superposition of the unsymmetrical pyramid and its inverse. That mixture dose not have a dipole moment.

If the molecule is heaver, the frequency will be smaller. When it comes to sugar, it no longer invert itself. But in the progress of synthesize, we will have the same left- and right- handed ones. The symmetry laws are not broken.

In really large systems, quite a different kind of broken symmetry can occur. Anderson gived three inferences form this.
(i)Symmetry is of great importance in physics.
(ii) The internal structure of a piece of matter need not be symmetrical even if the total state of it is.
(iii) The state of a really big system dose not at all have to have the symmetry of the laws which govern it. In fact, it usually has less symmetry.
In the closing, Anderson gave two interesting examples.
(i)Marx said that quantitative differences become qualitative ones.
(ii) -Fitzgerald: The rich are different from us. -Hermingway: Yes, they have more money.
This lecture presented a novel opinion on the laws in different scale, but it seems that there’s nothing new. We do not have a definition on what the fundamental laws is. In a single project, we only focus on a part of the degrees of the subject. All of our research in different fields are based on their experience truths, which may be treated as fundamental laws.

As for the broken symmetry, why the ammonia molecule should has the symmetry in the meaning of time average, why it can not be symmetry at a fixed instant? He use broken symmetry to demonstrate that big system dose not have the symmetry of the laws which govern it, why he didn’t count the asymmetry causes as one of the laws?

It’s surprising that Anderson predicted Josephson effect would play a great role in computers, which already happened. He thought the ordering in time dimension would attract many researchers, but didn’t that happened in the past?

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