From: <<>> (Steuard Jensen) Subject: Re: Need your ideas... Date: 1999/01/26 Message-ID: Sender: news@midway.uchicago.edu (News Administrator) References: <785f4g$66q$2@camel25.mindspring.com> Newsgroups: rec.arts.books.tolkien In article , Tony <<>> wrote: >Michael wrote: It's always been perfectly obvious to me that Eru originally ^^^^^^^^^^^^^^ That was me, actually. Steuard Jensen != Michael Martinez. >created the universe (that is, Arda) as the flat Minkowski space of Special >Relativity, and then took the opportunity of the rebellion of Numenor to >upgrade to a curved space-time metric as described by General Relativity. [snipping the rest of my technobabble] [Ed.: replacing it for posterity, with proper quote depth] > > The "straight path" taken by the Elves into the West is in fact > > just a quaint statement that the Eldar built their ships with > > advanced drive systems which negated the curvature-inducing > > effects of gravity. >Tony replied: Minkowski considered space and time, which were formerly >thought to be independent, to be coupled together in a four-dimensional >'space-time continuum'. This concept provided a framework for all later >mathematical work in relativity. These ideas were used by Albert Einstein in >developing the general theory of relativity. (Not to be rude, but would I have made the "jokes" I did above if I didn't have some inkling of all this?) >Could you elaborate on the relationship between Arda and the flat Minkowski >space? Certainly. First and foremost, of course, I must thank Michael and Graham for correcting me: Arda is (naturally) only a part of Eru's created universe as a whole. As first created, Arda was a (generally) flat disk in the midst of a relatively homogeneous scattering of "fixed stars". Naturally, for this simplistic arrangement of the universe, no complicated geometry was required, and so Eru instantiated the World by embedding it in Minkowski space. Incidentally, this explains the difference between the experience of the Valar when viewing the Music before creation and after entering Arda itself. In the first case, they were able to view the entire manifold of space-time "at once", as their experience was not bound to its timelike paths. However, upon entering Ea, the Valar were constrained to live on timelike worldlines (geodesics) _within_ Ea, a condition which Tolkien quaintly stated as follows: "But this condition Iluvatar made... that their power should thenceforward be contained and bounded in the World, to be within it for ever, until it is complete..." Note that Tolkien has told us here that the manifold of Ea (as created) was free from singularities, and (this will be important later) that the Valar were supposed to remain in some bounded spatial region. Of course, during this period in its history, gravitational effects were not even Newtonian in character; in fact, g was a flat 10m/s^2 throughout space (although the stars were not subject to it, and rotated on a fixed sphere according to conservation of angular momentum). Amazingly enough, despite the apparent contradiction between this effect and Minkowski structure, the situation remained tenable until Melkor really got going. After the destruction of the Trees, the Valar needed to suspend the Sun and Moon in the sky, but of course didn't want to attach massive rocket boosters to them to keep them moving properly: they wanted a self-sustaining system. Well, Eru came to the rescue, shifting from a static gravitational force to Newtonian gravitation (F = GmM/r^2), which naturally allowed closed orbits for the Sun and Moon. However, this began to erode the delicate balance between classical and relativistic aspects of Ea. When the Valar finally cast Morgoth out of the World, they had to terminate his worldline, something which Eru had initially forbidden (as observed above). To do this, they actually pooled their power and created a singularity in the sense of a minor black hole, picturesquely referred to in Tolkien as "the Door(s) of Night". However, the creation of a singularity was completely at odds with Minkowski structure; Iluvatar managed to create a temporary stabalization for the situation, but needed a more permanant solution. (As a side note, Tolkien struggled with the question of cosmic censorship: did Morgoth actually reach the singularity and leave Ea, or was he trapped at the inner (Cauchy) horizon of the black hole indefinitely, in a position from which (as a supernatural being) he might eventually engineer an escape and return to bring about the end of the world? Tolkien had versions of the Mythology in which Morgoth did and did not return.) Not much later, of course, the Numenorians rebelled and invaded Valimar. Unfortunately, when they arrived, the Valar were busy consulting with Eru on the rapidly deteriorating structure of Ea in the neighborhood of Arda, and really didn't have time to deal with the attacking fleet. Moreover, because of their great concern about the instabilities, they had brought the Elves behind the walls of the Pelori for their protection (calling it a "festival" so as to avoid excessive concern and panic). Eru, of course, was aware that to regain stability in the world, he would need to introduce a metric structure on spacetime that would allow singularities and yet maintain the orbits of the Sun and Moon, and that General Relativity was the best candidate for the job. The transition had to be immediate, as otherwise the Minkowski spacetime structure would decay on its own (and on an entirely global scale). Unfortunately, he also knew that the strain of the new force balance would cause the foundations of Arda to shatter unless its shape was changed to be consistent with the new structure. When the Valar suddenly called on him to deal with the invading Numenorians, he realized what had to be done, despite all of the suffering it would cause. What followed is, in hindsight, obvious: Iluvatar imposed a more general Lorentzian metric on the World, and in fact imposed the Einstein equations to ensure consistency, so that future modifications would not be necessary. At the same moment, he reshaped Arda from its disklike structure to an actual sphere, doing so with such care that only a small region would need to be demolished in the reshaping. Although it filled him with sorrow, he chose a region near Numenor because of its great rebellion that seemingly could not be stopped in any other way. As I said before, the "straight path" taken by the Elves to reach Aman was no more or less than an old Minkowski geodesic. The Valar provided the Elves with the technology to build gravitic ships which would negate the effects of mass-induced curvature, and thereby allow them to reach Valimar just as they had in the past. I hope that answers your question. I've always been amazed how few people in these groups really understand the Akalabeth in its full detail, so hopefully this summary will contribute to the general level of education here. Steuard "Don't Even Get Me Started On Supersymmetry" Jensen