Einstein and Mayer

In all of these statements the emphasis is on unified fields and not on cosmology. As a matter of fact, the equivalence of the projective unified model to five-dimensional spaces in general, and to that of Einstein and Mayer in particular, was first demonstrated by Veblen himself (Monograph Chapter Vlll). The crucial observation is that this equivalence mapping is done in the tangent space, without implying the equivalence of the Einstein-Mayer five-dimensional construct with four-dimensional projective space-time. The five-dimensional spaces are not projective, but affine spaces. 

Independent of our investigation Einstein and Mayer (Bibl. 1930,3) have published a "unified field theory", which led to essentially the same results as ours (compare Chap. VIII). Furthermore there recently appeared several works by J.A. Schouten and D. von Dantzig (Bibl. 1931, 7 1932, 3, 4, 8, 9 1933, 1) in which the projective relativity theory was treated in different forms. It is remarkable that - in a mathematical sense - all these theories seem to converge together. One can therefore hope to find a final solution of the unification problem in this way. We say more about the limits of this solution in chap. VII. 

Einstein and Mayer (Bibl. 1931, 3) always use these general coordinate systems. In their work the mapping (21) plays a sinificant role that we hope to clarify in the following. Einstein and Mayer used the notation li instead... 

Einstein and Mayer defined the left-hand side of (37) as the "absolute derivative" of Thereby the equations (39) are introduced by geometrical assumptions. The displacement properties of the associated five-dimensional space can then be derived from (37) and (39). The resulting geometrical structure corresponds of course with what we gave above. The field equations also have the same meaning as ours. 

The equations (39) can also be replaced by others. Einstein and Mayer proposed, for instance, in later work, the equations... 

In contrast to mechanics, electromagnetic field theory, or relativity, where the names of Newton, Maxwell, and Einstein stand out uniquely, the foundations of thermodynamics originated from the thinking of over half a dozen individuals Carnot, Mayer, Joule, Helmholtz, Rankine, Kelvin, and Clausius [1]. Each person provided cmcial steps that led to the grand synthesis of the two classic laws of thermodynamics. 

The first iteration of FSCE theory predicted the potential sequencing of up to 2000 bases in less than 1 h under perfect (diffusion-limited) conditions using a drag-tag with an a between 100 and 200. The initial theory, however, assumed that /u.(M) and the diffusion coefficient D M) eould be related using the Nernst-Einstein equation, which it turns out is not a valid assumption under free-solution electrophoresis conditions. This assumption caused Mayer to overestimate the potential performance of DNA sequencing by FSCE. Eurther development of the theory with a eorreetion for this error led to the following equation that estimates the maximum number of bases that ean be sequenced by a drag-tag with a specified a-value ... 

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