Herbert Salzer nsIn chnops-thermodynamics, Herbert E. Salzer (1915-2006) was an American applied mathematician noted for his age 23 (1938) corrections to Einstein's unified field theory equations and more importantly his rather impressive and unique 1957 (age 42) “Toward a Gibbsian Approach to the Problems of Growth and Cancer”, in which he outlines a Gibbsian thermodynamics theory of form development, normal and abnormal, at the cellular level.

Overview
In 1950s, Salzar began reading, in detail, the thermodynamics works Willard Gibbs. In 1957, Salzar published his “Toward a Gibbsian Approach to the Problems of Growth and Cancer”, the abstract of which is as follows:

“Certain sections of Josiah Willard Gibbs's thermodynamics papers might be applicable to biological equilibrium and growth, normal or abnormal. Gibbs added terms⌆ Μ i dm i to the differential of the internal energy dε=tdη−pdΝ, (t=temperature, p=pressure, η=entropy, Ν=volume) where μi=δεδmi is the potential of substance m i , to provide for chemical as well as thermal and mechanical equilibrium. In this article a further generalization is suggested, to include biological equilibrium by adding to de terms of the form GdN, the variable N being the number of cells, where G=δεδN is a “growth potential” that measures exactly the resistance toward spontaneous growth. The function G, like Μ i is intensive in nature (i.e. depends on intensive variables only) except for a conversion factor dMdN, M=⌆m i , affording possible insight into why incipient abnormal growth is often independent of the number of cells. Useful applications might follow from identities between δGδη,δGδv , or δGδmi and δtδN,−δpδN or δμiδN respectively. The following new function is studied, ζ¯=ζ−GN , a natural generalization of the Gibbs free energy function ζ, the possibility of measuring it electrically, and comparison of its role with that of ζ for the possible experimental determination of G. Gibbs's necessary and sufficient conditions for heterogeneous equilibrium of n components in m phases are generalized and also modified to include broader restraining conditions like ∑mi=1δNj(i)⩾o ,j=1,f,n, the > being characteristic of only living cellular phases. Careful appraisal of the term “biological stability” is followed by new criteria for stability, instability, and limits of stability, (neutral equilibrium) in terms of derivatives of G, with possible medical applications. Three different sections of Gibbs's works tend to indicate that, for a biological phase, lower pressure usually increases its stability. The equation p′′−p′=σ(Ir+Ir′) , where σ=surface tension, p′, p′ = pressures, r, r′=radii of curvature, is applied to possible control of tissue growth at interfaces. Methods of altering the equilibrium between three phases A, B, C by varying the interfacial tensions σ AB ,σ BC ,σ AC, using relations like AB <σ AC + BC for stability of the A, B interface, suggest different means for shifting biological equilibrium between normal and abnormal cells through the introduction of new third phases at the interface. Various devices are mentioned for possible control of growth through proper channeling of surface or other equivalent forms of energy.”

Salzer’s article is a bit of a rare gem; since 2014, e.g., it has only been cited by three scholars: Alexander Zotin (1972, 1997), American biomedical engineer Martin Macklin, and his interesting “Free Energy of Cell Differentiation” (Ѻ) (1969) article, and G.W. Swan (“Tumor Growth Models and Cancer Chemotherapy”, 1987). This paucity of citation can be attributed to the following rather humorous yet at the same time fascinating prerequisites Salzer discusses in the opening of his article:

“For a number of years the writer has studied rather thoroughly the life and works of that greatest of all American theoretical scientists, Josiah Willard Gibbs (Wheeler, 1952), with more emphasis upon the first of the two volumes of his collected works, that dealing with thermodynamics and heterogeneous equilibrium. The reader is assumed to be familiar with that part of Gibbs’ work. A number of semi-popular articles (Garrison, 1909 a and b; Donnan, 1924; Miller, 1925) contain convenient summaries and explanations of the more important ideas of Gibbs, sufficient to familiarize the reader with his work and to follow most of this discussion. For a better understanding, the writer advises study of the collected works of Gibbs (first volume only) and the two volume commentary by Donnan and Haas.”

(add discussion)

In 1997, Russian biophysicist Alexander Zotin credited Salzer as one of the early thermodynamic theories of development pioneers as follows: [2]

“All phenomena occurring in nature may be subdivided into two classes: occurring on their own (that is spontaneous processes) and occurring as a result of some forces (action-compelling processes). It is evident that the development of an organism is a "spontaneous process", and we can hardly imagine this process to be the result of some forces outside an organism. We cannot accept the vitalism views of special forces or laws inside organisms, which are not physical but may determine. The phenomenological theory of ontogenesis regards the processes of organism development, growth and aging as a spontaneous process of living system transition from a less probable state to a more probable one, which may be described in terms of thermodynamics. In this respect, it takes over after other thermodynamic theories of development (Bauer, 1935; Salzer, 1957) and especially the theory of Prigogine-Wiame (Prigogine and Wiame, 1946; Prigogine, 1967; Zotin, 1972).”
Salzer-Einstein letters (1938)
Salzer's neice Jacqueline Salzer behind Einstein's two 1938 thank-you letters to Salzer, in regards to corrections to transformation equations in his unified field theory work, which fetched near to $400,000 dollars in a 2013 auction. [3]

Einstein
In 1938, at age 23, Salzer, while working on his master’s degree in mathematics and applied sciences at Columbia University, wrote Einstein to question him about a point regarding his first approximation equation in his relativity theory, after which Salzer received two letters from Einstein in which he thanked Salzer for the correction, stating “therefore your transformation equation is correct, mine wrong”. [3]

Despite prolonged efforts to develop a unified field theory concerning gravitation and electromagnetic fields, Einstein completely abandoned all work on this venture around 1931. After Salzer's letter, Einstein revisited his previously abandoned search for an acceptable set of field equations to justify his approach for a unified theory on distant parallelism. The letters, auctioned in 2013, were evaluated at $400,000 dollars. [4]

Education
Salzer completed his MS in mathematics and applied sciences at Columbia University; after graduate school, he went on to become a mathematician, scientist, and inventor. [3]

Tributes
The following are noted praise and or tributes:

Salzer was one of the few people on the planet who could say that he corrected Albert Einstein’s math—and got the brilliant physicist to admit as much.”
— Gary Buiso (2013), “He Proved Einstein Was Wrong” [3]

References
1. Salzer, Herbert E. (1957). “Toward a Gibbsian Approach to the Problems of Growth and Cancer” (abs) (pg. 1), Acta Biotheoretica, 12(3):135-66.
2. Zotin, Alexeyi A. and Zotin, Alexander I. (1997). “Phenomenological Theory of Ontogenesis” (pdf), International Journal of Developmental Biology, 41:917-21.
3. Buiso, Gary. (2013). “He Proved Einstein Wrong”, New York Post, Oct 19.
4. Jhunjhunwala, Raghunath. (2013). “Albert Einstein’s Letters Set to Fetch $400,000 at Auction” (Ѻ) The Economic times, Oct 20.

External links
Salzer, Herbert E. – WorldCat Identities.
Herbert E. Salzer (publications) – Springer.com.

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