Supplemental Material
Following is a transcript of an exchange granted by Dr. RN Kiehn, U of Houston
Subject:4D Artifact. (RN KIEHN Quote: "Thermodynamic Irreversability is an Artifact of four dimensions")
| [COX said] | Hi: The above caught my eye. I'm doing a conceptualization of the 7-D Einsteinian Hyperspherical Universe and realize the implications of that statement. I've asked some other mathmeticians to comment, and the silence is deafening! Like most revolutionary ideas, backed by math, the counterintuitve nature of what you say is like a bone in the throat to many people, but that won't eliminate the possible truth implied in your work. ************************** |
| [RMK says] | Yes, you are correct, the implication is startling. The proof is based upon the thermodynamic concept that a process is reversible iff the Heat 1-form admits an integrating factor. The second assumption is that a physical system admits a description in terms of a 1-form of Action, A, (the integrand of Hibert's variational calculus) and that a physical process can be represented by a vector field, V. Then, without a geometric constraint of connection ot metric, the evolution of the physical system is described by the application of the Lie derivative with respect to V on A. The result produces the heat 1-form Q, and by CArtan's magic formula L(V) A = i(V)dA + d(i(V)A) = W + dU = Q Which is the first law. Then a test is made for integability, by the Frobenius theorem:Q^dQ <> 0 implies non-integrable implies irreversible. Either the virtual Work,W or the Heat Q must satisfy dW^dW = dQ^dQ <>0 Such a space has a minimum topological dimension of 4. The result is universal and applies to eletrodynamic or mechical systems which admit a representation in terms of a variational procedure. **** |
| [COX said] | There is a lot of powerful evidence for the "seven sphere". I assume a credited one or two sentence quote from your summary would be OK? |
| [RMK says] | OK |
| [COX said] | Have you done any further work, or do you have any personal comments on the implications of this finding? Was any previous work done which you wish to note? What is your full name, and the complete address of your URL? Warmest regards, Sam Cox |
| [RMK says] | Regards R. M. Kiehn This work was started in 1970 with publication R. M. Kiehn "An Extension of Hamilton's Principle to Include Dissipative Systems" J. Math Phys Vol 15 no 1 (1974) p.9 the next important thermodynamic work was the recognition that topological evolution was the basis of irreversibility. R. M. Kiehn "Retrodictive Determinism" Int. J. of Eng. Sci. 1976 Vol.14, p. 749 All of these things are in the form of pdf files on the website. There are many other articles and pdf files related to his topic on this site. see http://www22.pair.com/csdc/car/carmulti.htm and http://www22.pair.com/csdc/pd2/pd2multi.htm |
