Ladies & Gentlemen: To conserve on my postings, I would like to consolidate three comments:
The first is an addendum by Dr. Ed Dellian, historian of science regarding the linear vs. quadratic forms of energy in QM. I append them below. Secondly, I note Mark Johnsons remarks: "More deeply, Batesons highlighting of the difference between the way we think and the way nature works is important. How can a concept of information help us to think in tune with nature, rather than against it?" If we accept that the way we think is fundamentally different from the way nature works, how might a concept of information avoid exacerbating the pathologies of human existence? Wouldnt it just turn us into information bible-bashers hawking our ideas in online forums (because universities are no longer interested in them!)? Would new metrics help? Or would that simply create new scarcity in the form of a technocratic elite? Or maybe were barking up the wrong tree. Maybe its not information at all (whatever that is) or maybe its not information. I like not information as the study of the constraints within which our crazy thinking takes place because it continually draws us back to what isn't thought. Mark, I think the greatest contribution IT can make to our view on nature the ability it affords us to consider and even quantify the effects of apophasis (that which does not exist). Recall that information is defined as a double negative, so that the starting point is the *lack* of constraint (an apophasis). Bateson pointed out how almost all of science is positivist in viewpoint, but how often the absence of something is what is most important in affecting results. Information theory allows us to view nature with both eyes open to perceive the fundamental dialectic between order formation and entropic decay. <http://people.clas.ufl.edu/ulan/files/FISPAP.pdf> Thirdly, I quote Soeren: "the concept of experience and meaning does not exist in the vocabulary of the theoretical framework of natural sciences" I would agree with the statement from the aspect of pragmatism surely we will never fully encapsulate all that is associated with subjective human meaning. I would disagree with the statement in the absolute sense, however, because I believe the rudiments of meaning are indeed quantifiable. Take, for example, the correspondences between the protein surfaces of an invasive microbe and an antibody, where a lock-and-key relationship can be described and quantified. To the antibody, this correspondence captures the entire meaning of the microbe to the antibodys existence. <http://people.clas.ufl.edu/ulan/files/FISPAP.pdf> Somewhere along the way from an antibody to the human being our ability to quantify meaning necessarily breaks down, but I dont think that meaning can be proscribed from information theory *absolutely*. Now here are Eds remarks: ******************************** Dear Bob, the subject "linear versus squared concept of energy" is so important that I want to add to my former comments the "story behind the story". As I have already said it began with Leibniz's 1686 short paper "Brevis demonstratio erroris memorabilis Cartesii et aliorum", notably published just one year before Newton's Principia. Leibniz in his paper argued against the "measure of force" of a material body's motion, as it was used by his contemporaries in the context of the Cartesian philosophy of the time, i. e. the measure "matter times velocity", in modern notation mv. This concept, already used by Galileo, was confirmed as the true "quantity of uniform straightline motion" of a body, as soon as in the years 1669-1671 the most famous scientists of the time, John Wallis, Christiaan Huygens, and Christopher Wren, by order of the Royal Society, had independently of each other investigated the case. Based on collision experiments, they all corroborated the truth of the said measure; accordingly it has survived until today under the name of "momentum p". Now, if the quantity of uniform-straightline motion is correctly measured by the product mv, what is the measurable quantity of the "force" that causes such a motion? Modern science denies that there exists such a cause; uniform straightline motion is said to result from the "inertia of matter" alone, which inertia is seen not as some measurable /quantity/, but as an intrinsic /quality/ of matter. However, in the middle of the 17th century scientists indeed measured not only the momentum p = mv of uniform-straightline motion, but also the "force" or "cause" of that motion - and correctly so: Even though some believed in a geometric /proportionality /of cause and effect, while some others took cause and effect as /equivalents/, in both cases the quantity of active motion-generating force was to be measured through the quantity of the generated effect, that is, through the quantity of motion mv. This was the situation when Leibniz published his 1686 paper, in which he argued against the measure mv of force, deducing from the mistaken proportionality of velocity of free fall with space the "squared" measure mv^2, the concept which he called "vis viva". Very quickly Cartesian scientists rejected Leibniz's concept, but only to the effect that a fierce controversy began, which - named the "vis viva controversy" - lasted for more than 60 (!) years, involving efforts of many brights of the time to solve the problem of "the true measure of force". For example, the controversy became part of the Leibniz-Clarke Correspondence of 1715/1716. Samuel Clarke (with Newton in the background) of course rejected Leibniz's "squared" concept, arguing for the "linear" measure mv. In 1728, Clarke published a famous letter on the subject in the "Philosophical Transactions", which I have for the first time translated into German and published with my 1999 German edition of the Leibniz-Clarke Correspondence (Felix Meiner Verlag Hamburg). In 1746, even 22-years-old Immanuel Kant published a book on the "vis-viva" subject. In 1748, there appeared Colin Maclaurin's "Account on Isaac Newton's Philosophical Discoveries", which also dealt with the vis-viva controversy, representing Newton's vote for the "linear" measure mv (proportional to the generating force). But at the middle of the 18th century the controversy seemed to be settled when "analytical mechanics" was conceived in Berlin by Euler and Lagrange, and was based on a "new" concept of "force": the concept "F = ma" (Euler 1750), which from now on provided the basis of the new "analytical" or "classical" mechanics; I call it "Berlin Mechanics", as you know. Unfortunately, the competing concepts mv and mv^2 nevertheless survived somehow, since they both resulted with Leibnizian mathematics from the new concept of "force", mv being the "time integral", mv^2 being the "space integral" of this concept. But the "linear" concept mv from now on meant no longer a "cause" or "force", but only the quantity of effect "momentum p" only, while the "squared" Leibnizian concept took the leading role as a generating cause in "dynamics" (a Leibnizian term, never used by Newton). This happened when the Hamiltonian formalism of mechanics was developed, the H of this mechanics basically just representing Leibniz's "vis viva", now called "energy". After in the middle of the 19th century the Faraday-Maxwell theory had been established, in 1884 John Henry Poynting derived from the Maxwell equations the formula "energy over momentum = c = constant - the "Poynting vector" - . Evidently this derivation brought to light the "linear" concept of "force" again (now called "energy", E), being the proportional cause of uniform-straightline motion, p = mv; E/p = c; but nobody was aware of this revival, because scientists didn't and do not think in historical dimensions. The same revival of the "linear" energy concept happened when in 1900 Max Planck introduced to the public his new "energy" concept E = fh (f = frequency), believing that he had found something that had never been known before. Actually he had found the geometric proportionality between a cause called "energy", and an effect called "momentum" that Poynting had derived. This can be seen by dimensional analysis if one puts E over mv, which results in a constant that bears the dimensions "space over time" - just as Poynting's vector! And, it was and is just the same thing as the "linear" measure of "force" of the 17th century, that is, the force that is proportional to its generated effect "uniform straightline motion": the "impetus" of Galileo, and the "inertial force" (a true force!) of Newton. Albert Einstein as well was clever enough to introduce a concept of "energy" in 1905, which appeared "squared" (E = mc^2) as well as "linear" (E/mc = c, with mc = momentum of light). In 1925, Werner Heisenberg conceived his "matrix mechanics", which again implied the "linear" concept E/p = c. It can also be found behind Heisenberg's "indeterminacy relations" when put together in a quaternate proportion, as I have shown for several times elsewhere. History, however, sometimes repeats itself; and so it happened that the "squared" energy concept had a come-back when Erwin Schrödinger conceived his "wave mechanics" in 1926. His famous equation is basically nothing else but Leibniz's "squared" energy concept, now in the equivalent form E = p^2/2m. And, with Schrödinger there came the unrealistic consequences of this mistaken concept into quantum mechanics (entanglement, non-locality, as already mentioned in my last email). All in all, the historical survey shows that the different concepts of "energy" do not belong to different parts of physics, for example, one to relativity, the other one to "classical" mechanics, or, one to the more precise, the other one to the more approximative. One can also not say that the founders of quantum mechanics were aware of the difference; rather there is evidence that they did not realize it, since Heisenberg and Schrödinger both asserted the equivalence of their actually incompatible formalisms, which incompatibility is rooted in the said incompatible energy concepts. Moreover, none of the established experts in QM so far has realized the mathematically provable fact that the Schrödinger formalism because of its being based on the "squared" Leibnizian concept, should be the source of the known weird aspects of QM. Rather they embrace these appearances and sell them to the uneducated as characteristics of an allegedly unique "enigmatic microphysical reality". This matter has been a main subject of my studies since the 1980ies. I have already published my findings in several papers, some of which can be found on my page www.neutonus-reformatus.com. I remain ready for discussion with everybody who wants to defend quantum mechanics by saving it from the absurd, that is, independently of the current textbook presuppositions and prejudices. All the best, Ed. ********************************** _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
