SOMA Crystal
SOMA News 19 Dec 2012

The Heisenberg relations to SOMA

According to history Mr. Piet Hein had his idea for the SOMA puzzle in 1936, while attending a lecture about quantum physics, given by Mr. Werner Heisenberg.
We may raise questions to this "birth" and on my web pages about SOMA I seek to gather as much relevant information about SOMA as possible, and present it in these Newsletters.

The question however is, "How do we find this information".
One way is that 'you' the readers of these pages, send e-mails to me at <> this is a great way ;o)

Another way is that I sometimes just browse around on the web, and this time i stumbled upon some historic documents.

First I found the article:

“Heisenberg’s lattice world: The 1930 theory sketch”
Written by Mr. Helge Kragh and Mr. Bruno Carazza

I hurried to copy the article, and wrote a mail to Mr. Kragh asking permission to present this article on the SOMA website.
He responded within the same day, granting his permission for which I am thankfull.

Document reference: Heisenbergs lattice world 1930.pdf
Chapter "VI" on page 602 seem to be the central part for SOMA.
B. Carazza, H. Kragh: Heisenberg's lattice world: The 1930 theory sketch, American Journal of Physics 63 (Issue 7) pp. 595-605 (1995).

The same day I continued my browsing of the web, and found something else.

"Lattice Gauge Theory and the Origin of Mass"
written by Andreas S Kronfeld

This article describe a range of interesting theories.
As it turns out, Heisenberg worked briefly on an approach to quantum electrodynamics with a fundamental shortest length. The idea was to define the electric and magnetic fields (and another field for the electron) only on the sites of a 3d lattice. This idea might be connected to Soma.
Heisenberg wrote a letter to Bohr (which is translated in the article) and he talked about it at a conference in Copenhagen, Easter 1930 (also mentioned in the article).
Later Heisenberg abandoned the idea. But perhaps it was this work and not the uncertainty principle, that inspired Piet Hein. Important is that the timing do predate the patent of SOMA.
In the document appendix on page 18-19, Andreas touch on the subject of “Heisenberg’s Gitterwelt and Hein’s Soma”. This information could be interesting for SOMA players, relating to the historic development of the SOMA puzzle.

Actually I had contact with Andreas Kronfeld already in may 2012 as he was writing his article, but then I forgot about it, until today.
Of course, I immediately wrote to Andreas and again the same day received a mail giving me permission to post his paper. (A special thank you to Andreas for this permission)

Document reference: Lattice Gauge Theory and the Origin of Mass.pdf
A slight warning is appropriate, this is mathematically heavy stuff - but take a peak anyway, and especially at page 18-19

Andreas S. Kronfeld's Home Page is located at:
Document details at "The physics arXiv":

Prof. Dr. G. Muenster of "Institut fuer Theoretische Physik" (a friend of Andreas Kronfeld), commented to me that.:
- - Indeed Piet Hein once claimed that he got the idea of the Soma cube during a lecture by Heisenberg. as it is mentioned by e.g.
Martin Gardner in "Mathematical Games" Scientific American, 1958, and
Martin Gardner in "The Second Scientific American Book of Mathematical Puzzles & Diversions". New York: Simon and Schuster, 1961.

Whether this was a lecture about Heisenberg's "lattice world" from 1930, or a general lecture about field quantisation, where the canonical commutation relations are introduced via discretised space, is unknow to me. I guess it was a general lecture in 1933.

Heisenberg's "lattice world" is from 1930, and he talked about it in Copenhagen already in 1930.
As described in the text at the top, in the "The 1930 theory sketch"

Document reference: Gardner on SOMA.pdf
Document details:
The article was originally printed in 1961 by Martin Gardner in: "The 2'nd SCIENTIFIC AMERICAN book of Mathematical Puzzles & Diversions"
SOMA is mentioned at page: 65 through 77
The article is linked here with permissions.

Written by Helge Kragh <>
Written by Andreas S Kronfeld <>
Comments by G. Muenster <>
Edited by Thorleif Bundgaard <>

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