cfgauss

Hah, no kidding about MTW making overblown statements. Although part of that is due to it being written in the 70s when it was still far from clear if how important those kinds of statements were! And sorry if I was being vague earlier, I was trying to keep it simple, plus I've been sick and didn't really feel like being too careful . But the problem is that diffeomorphisms are more than just reparamaterizations since there's an extra pushforward involved. Or you can think about how densities have to properly transform. So there is some subtlety in correctly working with the action here. And the subtlety is exactly where you pull the GR out of of course . In the same way that H=0 is a perfectly good Hamiltonian to do GR with! Anyway, I've done this exercise before so I know it is possible . IIRC, the idea was to start with an infinitesimal transform like x^mu -> x^mu + a^mu(x) which changes the metric (according to normal calculus), eta^{mu nu} -> eta^{mu nu} - (a_mu,nu + a_nu,mu) which breaks invariance, and introduces those derivatives that will cause all your problems (and obviously for global transforms the da terms are zero and you get back normal SR with global infinitesimal transforms we all know and love). [You can also build SUGRA this way too.] I believe you can also look at this in terms of the lie derivative generating your symmetries if that way sounds more fun. The way you fix this ends up introducing some funny combination of other derivatives that look suspiciously like covariant derivatives and curvature tensors and all that stuff! I just checked in MTW and couldn't find it offhand because they're windbags. But I did find a statement in another text that "this is not well known" and a reference to an article, Kibble, "Lorentz Invariance and the Gravitational Field" J. Math. Phys. 2, 212 (1961) Quote: An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the gravitational field is presented. Utiyama's discussion is extended by considering the 10-parameter group of inhomogeneous Lorentz transformations, involving variation of the coordinates as well as the field variables. It is then unnecessary to introduce a priori curvilinear coordinates or a Riemannian metric, and the new field variables introduced as a consequence of the argument include the vierbein components as well as the `local affine connection'. At any rate, the point was that global symmetries lead to local symmetries, which lead to covariant derivatives, which lead to new equations of motion from old equations of motion. Regarding the exact forms of yang-mills theories vs. GR, you're right that they differ, I certainly don't disagree with that. But that's actually not important in terms of their gauge theory structure. The specifics (eg, depending on derivatives of the curvature tensor) are restricted be whatever they are by the larger structure of the symmetries. (It is of course important in their solution structure!) In general, we've got a principle bundle P with structure group G over a manifold M. The gauge group ends up being something like a restricted automorphism group of P (so it can't mix up fibers or anything funny). So a principle bundle P(M,U(1)) is a generalized E&M on a manifold M, and any action it has is restricted by being compatible with all of the structure, such as the allowed automorphisms of P. (Plus some additional structures and details that let us do physics.) Then you can see pretty clearly from here that GR is going to be a little perverse with a structure group of diff(M)! But it's in this sense that GR is a gauge theory like E&M or QCD. And if you really look through the "definitions" of what it means to be a yang-mills theory, this is what you're ultimately lead to. Of course that's a very general construction and pretty clearly you can get lots of very different things out of it! And there are certainly lots of constraints you may want to add to make a specific theory, like E&M besides just saying it's P(M,U(1)). But there are still a number of very nice fairly general statements you can make about these kinds of gauge theories in general that make this construction useful (in addition to providing a recipe for explicitly constructing them when you follow the details!). For example, you can instantly see how totally awesome doing complex E&M to solve 2d problems is with this structure! It's a little more than how your intro classes point out that, "oh, this just happens to satisfy the cauchy-riemann equations!" This is why that coincidence happens! This general structure is also why you can do what that paper above cited. And is also why Ed Witten has put a crazy amount of time into looking at this kind of geometric structure . Quote: Actually it is by no means clear whether the gauge fixing problem is profound or superficial. The traditional hypothesis among general relativists has been that it is profound, and that deeper understanding of the dynamics of spacetime geometry will someday lead to fundamental generalizations of quantum theory. True enough, but it turns out that the GR people's intuition that something funny happens with geometry on small scales is almost exactly the same as what we expect string theory to do to our picture of geometry on small scales! In some ways, both of the arguments are right. The full quantum theory does require knowing short distance physics, which requires knowing about short distance geometry. So from that point of view the gauge fixing problem is "important." On the other hand, in principle, that didn't have to happen. And, in fact, once someone knows the full correct theory, there's nothing stopping them from writing down an intermediate effective theory that integrates out those degrees of freedom which is renormalizable by constructing it from the beginning to have divergences be exactly canceled by knowing the answer in advance. From that point of view, it's not important. Of course, neither of those things are unknown to theorists, but the impression I get in general (even from the QFT/model building people) is that the effective field theory lessons should be taken more seriously than GR's (since you can even see SR as an EFT for GR, classical E&M in matter as an EFT for E&M, etc). Incidentally, you're obviously a physicist; what kind of physicist are you?

Originally Posted By: Student of Trinity What is "the SR action"? There are Lorentz invariant actions for various fields other than gravity, but the metric itself has no action of its own in SR. Insofar as mere terminology matters, the normal definition is that SR means flat spacetime. What's more than just terminology, though, is the fact that to get GR you need to do more than just relax the assumption that the metric is flat. You also need to add the Einstein-Hilbert action, which isn't there at all in SR. [...] GR can be considered a gauge theory, but it is not like other gauge theories because the gauge field for Lorentz transformations is the Christoffel symbol, but in GR it's important that this is derived from a metric, for which no analog exists in other theories. This brings us back to the Einstein-Hilbert action: it's an action that can't be generalized to other gauge theories, because it needs the metric. It's not the only possible or even the only reasonable action, for a Lorentz group gauge theory (the Kretschmann scalar would be fine, for instance). it's just the one that correctly describes gravity. The SR action is just the usual point-particle action in SR. What else would it be? From the algebraic point of view, the metric just is the map between tangent and dual spaces. There's nothing special about it. But the point is that the SR point particle action is a special case of the Einstein-Hilbert action! And exactly how you get the GR action is to take the SR one and make it locally lorentz invariant. Every word I've said is in MTW if you don't believe me . And--repeat after me--there's nothing special about the metric! It's just that the other-than-gravity-gauge-theories have an INTERNAL metric instead of the spacetime one. But that's okay because the spacetime one was really internal anyway, it's just that we have a convenient description of the things we can easily measure that puts it into a more "concrete" framework. Although working with lie algebras in one theory and manifolds in another does not make this manifest by any means! If you'd like a more careful description of why GR is exactly the same kind of gauge theory as all the others, I invite you to check out "differential geometry, gauge theories, and gravity" by Gockeler and Schucker, or any of the other hundreds on the same topic (that's just the one that comes to me off the top of my head). But you can't argue about this, it's actually the whole point of the modern mathematical construction of gauge theories . It's actually part of what makes symmetries like (local) SUSY not totally nuts, since naively that's some crazy internal/external symmetry. Quote: Classical Kaluza-Klein simply is not quantum field theory by any stretch. You can get mass quantization by compactifying the fifth dimension, but this does nothing to make the gauge fields into operators. Quantizing Kaluza-Klein has all the same trouble as quantizing GR: no-one knows how to fix the gauge without reference to some background metric, and if you try to proceed by perturbing around some given metric, the theory is manifestly non-renormalizable. Classical KK theories give you classical yang-mills theories. There's nothing wrong with the classical versions of the theories. In fact, a lot of effort was put into looking at classical QCD in the 70s and 80s to help understand why it works like it does. And the trouble in quantizing GR is not actually that. That's only a superficial problem (in other words, if you fixed the gauge fixing problem it would still be nonrenormalizable). The real problem runs much deeper than that and has to do with what an effective theory is (c.f., four fermi theory). There seems to be a lot of confusion about what the problem with quantizing GR is in some of the literature (why is another story ) but the background is not it. Most of the confusion comes from the LQG people, and let me assure you, that they do not know anything about gravity or QFTs! It's harder to find a source for a good detailed explanation of this, but Zee's field theory text talks about it in some detail. You can find some good discussions in some of the literature from about the 80s, since people were still looking into things like canonical QG then. But I do not know any sources off the top of my head.

Originally Posted By: Celtic Minstrel Originally Posted By: cfgauss Yes, but chaos without perfect measurements is nondetermanistic. That's not what nondeterminism means. Chaos is deterministic because, with perfect measurements, you can predict the outcome exactly. It's exactly what nondeterminism means. It means you can't determine exactly what happens. It doesn't really have an exact formal definition, and I think that's part of the confusion. But the idea is that distributions assigned to measurements are always delta functions in a limiting sense. But this doesn't happen for the example I gave. Specifically, you have a function f:R^2->R^2 such that f(a) = p is well-defined for all a and p in R^2, but, if I = D_r(a) a disc centered at a with radius r, f(I) = R^2 for ALL r>0 in R. Then, if you have non-exact measurements you can simplistically characterize your measurements as being some distribution on D_r(a). That is, I measure something like "distance = |a| +/- r". If f represents a physical system, say, the x-y coordinates of a chaotic pendulum at time t0 as a function of initial x-y positions. Then what does this mean? I measure at time 0 the coordinates a=(x0, y0), with an uncertainty r, so I'm certain to whatever confidence interval I like the actual value lies inside of D_r(a). I take f(a) to find my most likely value for the pendulum later. Now, I'd like to calculate the probability distribution associated with it to find out how likely the value is f(a) given my initial accuracy. So I find f(D_r(a)). But that's all of R^2! Since my distribution must be normalized to 1, that tells me the probability that at time t0 my coordinates are f(a) is zero! [Edit: it's 0 because you've smeared the finite area disc to the whole of R^2] In other words, this system is so chaotic, that any measurement you make at time 0 is completely uncorrelated to any other measurement you make at any other time! Surely the most extreme example of nondeterministic that you can get! Of course, real systems aren't quite as bad, but they can be nearly as bad. Often, the best you can hope for is some kind of exponential suppression in your correlation between initial and "late time" states. This is something that's possible to investigate numerically with, e.g., a pendulum on a spring and a computer, to see exactly how bad this effect is in realistic cases. Though you have to be careful the chaos doesn't ruin your numerics of course! And again, this has something to do with entropy. If you ever take a grad-level stat mech class (or a good undergrad one, but I don't know that such a thing exists; in fact I have doubts that good grad ones exist too ) you'll show how entropy comes about classically by arguments like I have, but in phase space instead of configuration space (ie, entirely classically!). So in an idealized case, this example is deterministic. But if you know less than everything about the system, it's completely nondeterministic! Contrast this all with a simple mechanical system (eg, a point moving in a potential) where you can just easily plug an analytical solution into the error propagation formula to calculate not only finite but sensible probabilities. In that case, by making your errors arbitrarily small, you can make your late-time measurements as accurate as you like---the definition of deterministic!

Originally Posted By: Sporefrog This thread is amazingly incomprehensible. I love it, keep it up I didn't study string theory so everyone could understand me . But if you want clarification on anything I'll be happy to try to explain, if it's possible to do without several weeks' worth of lectures.

Originally Posted By: Celtic Minstrel Chaos is deterministic because if you put a specific specific set of numbers in, you'll always get the same result. Yes, but chaos without perfect measurements is nondetermanistic. If you make a measurement, you are inherently talking about a probability distribution that, under your chaotic system, evolves in time into some crazy looking distribution that may even in principle do something as perverse as allow every possible value with equal probability for late-time measurements. You can loosely think of this by thinking about what happens to the 1-sigma neighborhood around the point under the map. Non-chaotic maps (essentially by definition) map that one sigma neighborhood to "reasonable neighborhoods" which typically preserve a sensible notion of evolution of error bounds. You can also think of chaos as having something to do with entropy by thinking along these lines, but that's more of a technical discussion than I feel like going into! Originally Posted By: Student of Trinity Einstein's Kaluza-Klein theories were classical; he made no contributions to quantum field theory. Extra dimensions are a detail in string theory, not the main idea. Well, so's E&M, and exactly the idea of KK theories was to combine the classical versions of all of the gauge theories known at the time. Once you have that, it is, in principle, an easy matter to quantize them by imposing commutation relations. And in fact, the excitement behind KK theories was partly due to the extra unexpected fields they created that could be identified with particles. The hope was the force-carrying fields would all be from the geometry, and matter fields would be in the spew of moduli fields that came out. Einstein and the other people working on them were certainly aware of field theory's development at the time, and were incredibly clever to see that you could actually get almost the same thing with KK theories. Their only mistake was hoping that the cannonical commutation relations could also come out of geometry, which is a bit too simple to hope for (but by no means unreasonable to guess is true). And that's why (aside from anomaly cancellation, etc) that extra dimensions are very much the main idea in string theory! Them, and their structure is what makes it possible for the theory to have any hope of reproducing a sensible particle spectrum at all! (You can try to have 4d strings, but as we learned in the 60s and 70s those fail hilariously to reproduce anything that looks realistic.) Quote: Any curved space is still locally flat. This is a subtle point, but here's how I explain it. I once found a snippet from a Flat Earther publication that proudly claimed a negative empirical test of earth's curvature. Yeah... but... they were doing it wrong... that's not really an argument for anything at all . Quote: This is a big distinction, so it's really not true that GR is just localized SR. It is in fact not only true, it is exactly true! It is a simple (and fun!) exercise to prove that, writing the SR action, and making lorentz transforms local instantly gives you GR. That is, local lorentz transforms are diffeomorphisms. A more fun, but less simple, exercise to do is to carefully work out all the differential geometry details as you do this and watch where all the exciting stuff appears out of nowhere! (AFAIK no text does this carefully, it's something you've got to do yourself.) Now, to be sure, it would be a huge pain to analyze any extreme case of GR in only SR correctly, but you definitely could do it. The same algebra magic you do in the action to write the covarinat derivatives to turn SR into GR is how you'd compare SR frames in the right GR way. But you would just look at it as a local "linearization" from an SR point of view. This is actually exactly why you can trivially do uniform acceleration in SR even though you "shouldn't" be able to do it. Everything about curvature, or other GR ideas are hidden inside this apparent "linearization," but it's still there, just as how uniform acceleration in SR works even though that should need curvature to do properly. A problem for the industrious reader: how is the covariant derivative above related to the ones in qfts and gauge theories? (Harder, but more exciting, problem: write every gauge theory (including GR) so they all look identical!)

Originally Posted By: Kelandon It was hard to award him a Nobel Prize for GR when GR had so few tested predictions. I mean, the Eddington thing was a big deal a few years after Einstein published, but it wasn't until the 1960's or so that people could do precise enough measurements in the right conditions to test a lot of the other predictions. That's one of the tricky parts of working on fundamental physics, really. Technically, that's true, but GR is actually exactly the same as SR in some sense. Fairly generally, GR is the simplest extension of SR to local reference frames. Mathematically speaking, GR follows from SR just like x=2 follows from x^2=4. But a bit more complicated . Indeed, in that GR bible that was mentioned earlier, it's mentioned that one never actually has to know about GR to do GR. If you really wanted to, you could *always* do SR and get the same answers if you were careful not to mix distant reference frames! (You can only mix frames close together.) So GR and local SR are really exactly the same theory (and you only really test local SR) so every test of SR automatically tests GR! [Edit: this is true in the same sense that Newton's "infinitesimal" calculus ("SR") is the same as modern limit calculus ("GR"), their structure seems very different, but if you're careful all the answers you get are identical, even though infinitesimals can be a huge pain sometimes.] The surprising thing is that local SR came from E&M, and gives you gravity! It's almost like there's a bigger picture here, huh? This, by the way, is part of the reason theorists found it so disturbing that quantum mechanics works fantastically well with SR, but fails with GR. (Although the failing is not as bad as is often reported!) Now-a-days (that is, from the ~'80s on) it's been fairly well understood what's going on.

Originally Posted By: Student of Trinity Exactly how light can get emitted and absorbed by matter was not understood then, so there must have seemed to be plenty of wiggle room in this direction. I was under the impression that most of these arguments could be (and had been) ruled out on fairly general grounds, at least qualitatively? I'm also confused as to why you say "we don't understand equipartition or equilibrium very well." We understand them very well. (Unless you mean the way scientists unfortunately tend to use the word understand as in "we understand it very very well but not completely.") I mean, they certainly are not usually well explained, but that's a whole other story . Originally Posted By: Student of Trinity MTW, also known affectionately as 'the phone book' because it's a three inch thick paperback, has never been considered a fantastically good GR text. It's just that in a sense it's the only GR text, because it's the only one that makes a serious effort at covering all the basic topics in a pedagogical way. I never thought it was too bad. It's only problems are that it's very wordy, and overly qualitative compared to what people want to do with calculations, but in this case that's good, since in order to not go totally nuts and try to invent Lorentz invariance violating gravity, you really need to carefully understand things. People also tend to talk about Einstein not doing much with regards to field theory, or really much else after GR and the foundations of QM, but if you look at the stuff he was publishing about in, say, the '50s, it was stuff like Kaluza-Klein theories. So, basically, he was working on pre-string theory . edit: Oh, also, to clarify on what was said earlier about chaos. Chaos is only deterministic when you have either no measurement errors or small enough scales which are suppressed somehow. Although the latter is technically more "morally" true than literally true. In fact, you can find chaotic maps that will, e.g., map any arbitrarily small neighborhood of the plane to the entire plane. (Although I do not believe any physical system is likely to do this!)

Quote: Originally written by Bryce: Quote: Originally written by kkarski: they don't understand magic itself too well, they are just using certain ready-to-use procedures they were taught. This train of reasoning is faulty. Bolt of venom is no more general or customized than spray acid. The enemies use the same style of cookie cutter magic as your party does, except they read up "Teach yourself Magic in 21 Days" instead of "Magic for Dummies" so it's superficially different. Further, the analogy is not correct in another way. Those entry-level computer programming books are not that different from the textbooks we use in introductory computer science courses, honestly. A computer science class (or a good O'Reilly book) is better, but both will teach you real programming and how to use the language constructs, not just how to hack together something from other people's code. You're right that it would take work to unify the magic systems, of course. The argument is that it would save work in the long run while making the game better now and in the future. I think it'd be more accurate to say the differences are like: Tower of magi mage/priest: physicist You: Engineer most NPCs: do it yourself book / instinct Technically, the physicist can do everything anyone else can, but in practice, they cover a much broader range of topics in beginning training, and a much narrower range in research. So you end up with, eg, the guy researching teleporters in a cave who can't defend himself against much. An engineer has a practical knowledge of a narrow range of things he can use every day. E.g, fire, ice, poison, etc. The NPCs picked up a book that taught them some neat tricks, but they don't always get the bigger picture. So he has one book that tells him how to build a wooden deck, but that doesn't help him if he wants to build stairs. Or, in some cases, the NPCs know it instinctually, like a bird knows how to build a nest. That said, I would still appreciate a much wider variety of magic. Look at all the areas of science we have, there would have to be magical versions of each of those things, and all the applications and methods of those kinds of things. Not to mention there should be lots of different ways of doing the same thing. I much prefer a more exile-like system of magic, over avernum's or geneforge's.

I have to say that I dislike the lack of variety of spells bad guys use against me. More variety makes things more fun. As it is now, if I get stuck in a hard battle because I have low health, or no potions, or whatever, I can always eventually win. If I die, when I reload, I know the enemy will do almost exactly the same thing as it did before because it doesn't have very many options about what it can do. Just adding something in like a small chance of them using an exile-like area of effect spell can significantly change how I have to react to them. Suddenly, I might be forced to move mages out of attack range of bad guys, or scatter people and leave them unprotected. Or, I could summon shades to help attack, and suddenly they're worthless because this *particular* enemy knows repel spirit. Which forces me to have to change my strategy, and not rely on doing the same repetitive things over and over again at each battle. As it is now, a lot of the battles lack any challenge, and you can easily mindlessly follow a recipe to finish things, without using any kind of strategy. And when you do have to use a strategy, it's scripted in, and is something like "attack with fire, because that's the only thing that hurts him." And I think this is unfortunate, because it needn't be that way. Quote: Originally written by Student of Trinity: As I explained once before on this topic, in some thread or other, there is another big difference between PCs and NPCs, which unlike saving and restoring is indeed something within the game world. The PCs gain power rapidly by killing monsters and completing quests. The NPCs don't. My pet peeve is that this bizarre situation is hardly ever explained in RPGs, when in fact it is usually the most remarkable aspect of the story, once you notice it at all, and would surely make an excellent plot thread. This is just the anthropic principle. The less-than-exceptional parties don't end up going very far before they give up or get killed, so we don't make games about them. Your party just happens to have exceptional skills, because without exceptional skills, they could never finish the game.

One of the things I liked about the older games was being able to play almost entirely with the keyboard. I think it would be really nice if you were able to do that again, because I still find myself pressing "l" while playing Avernum 4 and being annoyed that nothing happens! The only other complaints I have about Avernum are the lack of PC graphics. It would be nice if there was a system like in some older games where you could pick combinations of heads/bodies, so you can have more possible characters with fewer total graphics. Also, the "color shifting" the graphics and pretending they're new is totally lame.

I get that 'member profile corrupt" message sometimes, too. It seems to work fine again later on, though. Sometimes I get it when I'm not logged in at all, too...

When he's doing this all in his free time for fun and letting everyone look at it for free, and then doesn't fix problems, it's because he's busy. When we pay for it and he doesn't fix things, it's because he's lazy, and it's bad for buisness, too.

Don't read this if you're religious, but... I like to name my priests Jesus, so I can say things like "Jesus, heal me!" or "they killed Jesus!" (I'm an atheist, what do you expect?) If I have a slith, I like to name him Godzilla, and I often name other people 'Tom Servo' or 'Crow T. Robot' from MST3K!

Why does it have to be backwards compatable? Why not just have something you can add in the begining of the script like: use_format_1; use_format_2; It seems like this might be a nice way to impliment commands that would otherwise break compatability.

I don't think you can have state=-1 on anywhere but the very first node. You have nextstate=-1 when you want to end it, but with just state= they each have to be unique, I think.