For two particle systems, the application of quantum mechanics and a change of variable allow the separation of the problem into "one concerning only the centre of mass of the system, and another which describes the behavior of a particle of mass mu under a potential V(r)." (Alistair I. M. Rae, Quantum Mechanics, John Wiley and Sons, New York, 1981, p. 189.)
If you have a small machine shop with two lathes, two mills, two surface grinders, two cylindrical grinders, and two of every other machine tool needed, and duplicate tooling, than taken as a system of 2v machine tools, the system is capable of self-replication. (The foundry is a separate thing. It can go in the middle.) A equiangularly spaced array of such machine tools at appropriate radii has a center of mass at the origin and is amenable to quantum mechanical analysis. It is a muliparticle system. The state of the system is entirely dependent on the positions of the component parts. The ground state is all machines ready to produce. Everything in its place. Simple deviations from the ground state can be expressed merely as the new location of the center of mass of the system, relative to the origin.
This does not contradict the findings of Wigner in "On the impossibility of self-replication" in "The Logic of Personal Knowledge" because the machinist, an agent not included in Wigner's analysis of structures growing in a nutrient "sea", is self-replicating (alive).
I assert that a properly trained machinist inherently knows how to operate such an array to self-replicate, given time, because the machinist is a living, self-replicating being, but special training in the theory of self-replication may help. It may take generations to acheive it if it is done one machine part at a time, but a theoretical solution might be achieved in one machinist's lifetime, and a computer calculation might be a matrix operation that would complete in seconds. Once stated, the theoretical basis can be taught, in context, to students at the appropriate level of instruction in mere minutes.
And this is what we need to take with us to Mars or the Moon. I believe that the quantum mechanical theory of such an array can be put on paper in a useful way.
Now, the question is, who will be the first to do it, and who will get to go to Mars to operate the machines that build our next colony?
I suggest that this should be me, and that you all might be able to help. I know that I am capable of understanding quantum mechanics, I have the time and sources of funding, and I don't know any other machinists who can understand quantum mechanics.
Physics has long been divided into the experimental and theoretical specializations. With a sound grounding in the experimental specialization, I think it is reasonable to extend my understanding to include more theory. There aren't a lot of people with an appetite for such diversity. Many say you have to be young to make your mark in physics. Well, I was reborn when my first lover died. I think that's enough of a start. I've recovered a remarkable sense of fitness since then. An appetite for adventure. I'm four years "old" now.
Goncz's Postulate is : "You Need Two of Everything"
To self-reproduce, that is. Not long ago, some years, I purchased two drill presses, two cross vises, two collet indexers, and two lathe chucks at my own expense and built two four axis milling machines capable of self-reproduction.
I can do this again and again. When I sold the one, arbitrarily numbered serial
00001, to Larry Ritchey on 24 OCT 1997, I should have reinvested the amount charged, which was double the cost of the components, into building another pair. That was a serious error.I'm just having a little trouble writing a proposal to do this. I have to convince my funding source that I am capable of continuing my education, developing this original theory, implementing such an array, and operating it
*on Mars*.Any questions?
Doug Goncz I love: Dona, Jeff, Kim, Mom, Neelix, Tasha, and Teri, alphabetically. I drive: A double-step Thunderbolt with 657% range. I fight terrorism by: Using less gasoline.