# Frank Wilczek’s Concept of ‘Upward Inhertiance’

Yesterday, I happened upon an article entitled Why are there Analogies Between Condensed Matter and Particle Theory (pdf!) by Frank Wilczek. In it, he suggests an alternative view to the one espoused by Laughlin and Pines in their Theory of Everything paper. The views expressed in More is Different by P.W. Anderson, which is the most influential paper of the three, lie somewhere in between. The article by Wilczek is noteworthy because of the idea that he calls “upwardly heritable principles”.

He first addresses the issue of why ideas in condensed matter and particle physics bear such a resemblance (i.e. why the macroscopic reflects the microscopic). Here, he highlights examples of cross-fertilization between these two areas of physics to illustrate how it is not only ideas from particle physics that have influenced condensed matter but also vice versa.

The ones I found the most interesting were: 1) Einstein’s application of the Planck spectrum to obtain the specific heat of crystals following Planck’s original work (particle physics $\rightarrow$ condensed matter) and (2) Dirac’s interpretation of negative energy particles as similar to that of  the particle-hole spectrum of the Fermi Sea (condensed matter $\rightarrow$ particle physics).

While Wilczek does hint at the notion that the cross-fertilization is perhaps an accident, he chooses to believe that a fundamental principle belies these connections. He recognizes that precisely because there is no logical necessity for ideas to bridge the two realms, that such a relationship exists is suggestive of a deep reason for its occurrence. He speculates that the reason behind all this is “the upwardly heritable principles of locality and symmetry, together with the quasimaterial nature of apparently empty space”.

I like this paper because its views seem natural, are much less radical than that of Laughlin and Pines’, and because Wilczek suggests a path forward to understanding why such a cross-fertilization might occur. Moreover, the article hints that even though Anderson’s view of “new principles at each scale” may be true, the fact that it is possible to apply principles (e.g. broken symmetry) from higher up the scale (i.e. condensed matter) to lower on the scale (i.e. particle physics) is suggestive of a lingering connection between the two scales.

Just a quick (perhaps too quick) summary of the respective viewpoints:

1)   Wilczek $\rightarrow$ Deep connection between microscopic and macroscopic.

2)   Anderson $\rightarrow$ Different scales yield new physical principles, but still a connection between different scales.

3)   Laughlin and Pines $\rightarrow$ Microscopic cannot, even in principle, explain phenomena on a macroscopic scale (such as the Josephson quantum).

In writing this post, I know that I have not presented the ideas in the three articles thoroughly, so let me link again Anderson’s article here (pdf!), Wilczek’s here (pdf!) and Laughlin’s and Pines’ here (pdf!) for your convenience.

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### 4 responses to “Frank Wilczek’s Concept of ‘Upward Inhertiance’”

1. D. Koffers

Another example from the less well populated “condensed matter –> particle physics” category:
Yoichuro Nambu, using ideas from the BCS theory of superconductivity to gain insight in particle physics.
See PRL 122 (1961) 345.

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