Anthropic constraints on dark matter?
The properties of ordinary matter are strongly constrained by the anthropic principle. In soome cases you can even calculate non trivial things. E.g. the anthropic reasoning was used by Hoyle to prove the existence of an energy level of the carbon-12 nucleus. Dark matter seems to be much less constrained. We know that there must exists a lot of dark matter, and this fact could be an observer selection effect. However, since dark matter is believed to have only very weak interactions with ordinary matter, the exact properties of dark matter particles seem to be irrelevant for observers. Some time ago, I noted that annihilations of strongly interacting dark matter can generate large amounts of internal heat inside planets. This is interesting, because it is thought that 50% of Earth's internal heat is supplied by radioactive decay and 50% comes from cooling of the Earth's core. However, if you calculate back in time, the cooling rate implies that the Earth's core must have been completely molten about a billion years ago. Now, today the inner core is solid (due to the high pressure), and this is essential for generating a magnetic field. Old magnetic rocks show that the magnetic field did exists more than 3 billion years ago. So, the geophysicists have a problem here, and I thought that dark matter could be the answer. If dark matter supplies some of the internal heat, the earth's core would be cooling less fast and that would solve the problem. Anthropically, you could say that without a magnetic field life would have had a difficult time on Earth (because of cosmic and solar radiation) and we may not have been here. You would still need to show that we couldn't have evolved on a larger planet where the heat supplied from dark matter annihilations is not necessary. Unfortunately, this idea does not work. Uranus has a very low inernal heat production, and this strongly constrains the properties of strongly interacting dark matter, making the above scenario impossible. See here 40 minutes from now: http://arxiv.org/abs/astro-ph/0408341
Re: Djinni vs. White Rabbit
On Aug 19, 2004, at 2:00 PM, Hal Finney wrote: It's not clear to me that causality and time are inherent properties of worlds. I include worlds which can be thought of as n-dimensional cells that satisfy some constraints. Among those constraints could be ones which induce the effects we identify as causality and time. For example, a two-dimensional cell where C[i,j] == C[i-1,j] XOR C[i-1,j-1]. This particular definition has the property that C[i,.] depends only on C[i-1,.], which lets us identify i as time, and introduce a notion of causality where conditions at time i depend on conditions at time i-1. But we could just as easily create a cell system where there was no natural definition of time, where C[i,j] depended on i+1, i-1, j+1 and j-1. You could still imaging satisfying this via some constraint satisfaction algorithm. +1 I'll have to think about the CA implications --- what is a "cell" in such a CA, and what is meant by the various "nearness" relationships of such cells? (I'm still processing Wolfram's book, a couple of years after reading it the first time. ;-) I'm just adopting a relatively conventional GR point-of-view here, where time is just another direction, albeit one in which travel is (in most circumstances, depending on the local differential geometry and geometrodynamics) directionally constrained. (I'm ignoring the thermodynamic interpretation of time's arrow, though when you throw 2LT into this particular brew things would seem to get rather interesting. ;-) Now these jinni worlds are ones which mostly have these conditions we identify as time and causality, but which locally, or perhaps rarely, do not satisfy such rules. Seen in this perspective, there is a full range of possibilities, from fully causal worlds, to ones which are 99.999% causal and only .0001% noncausal, to ones which are 50-50, to ones for which no meaningful concept of causality can be defined. We're begging the question re: causality; it was perhaps unfortunate that I chose to use that word, as it's interpretive rather than descriptive in itself. The argument Boulware's making appears to be inherently probabilistic and geometric rather than ontological. That became less clear in my exposition, my bad. I'll have to look at this. It doesn't sound quite right. If probabilities are non-unitary that violates the fundamental rules of QM, But do they? This is, I think, perhaps a very interesting and pertinent question. It certainly appears to throw both the QM formalism as well as its interpretations into disarray, but I think perhaps the result is less than fatal. One can certainly do statistics (and hence QM) with non-unitary probabilities --- the method involves a kind of normalizing transformation between different probabilistic measures. (In fact this very issue was dealt with by one of Gott's grad students; the citation escapes me at the moment, but he found that you could patch things up by simply supplying a kind of local correction coefficient. I.e., while this appears prohibitive on the surface, in fact "fixing it up" isn't all that difficult. The ontological interpretation of the relationships between these patch coefficients, OTOH, is IMHO pretty surreal.) I think you're getting awfully speculative here. This is a criticism, in *this* group in particular? ;-) It's admittedly speculative. It sounds like you are suggesting that it would be simpler to suppose that "all universes exist which contain jinn" than "all universes exist". Not precisely; I'm suggesting that "simple" is difficult to measure when speaking about TOEs. There might be some measures of "simple" for which the above is true; there are others, e.g. the Champernowne machine and so forth, for which it is certainly not. But Occam's Razor isn't much help here by itself. That doesn't seem at all plausble to me. My heuristic is that any rule of the form "all universes exist except X" is going to be more complicated than one of the form "all universes exist". On the surface, sure. But consider: the statement "all universes exist" presupposes a definition of universe that it omits. What is meant by "universe" requires an exhaustive definition, and the algorithmic hypotheses make varying assumptions about that definition. My intuition would be that the most parsimonious definition would be the preferable one; but we don't have any metrics for "parsimony" on such definitions. It could be that definitions that statically embed such jinn might be more parsimonious by some measure than other ones; the statically-defined jinn might "ground out" the definition and permit a higher-order / more abstract / terser "universe generation algorithm." (Think Python vs. its own bytecode.) Think of it this way: any formal system has its base axioms. In this context, the "universe generator" is the system in toto; the jinn could form (at least a part of) its axioms. Or, thinking abou
Re: Djinni vs. White Rabbit
I'll have to look more closely at those papers, but I have a couple of quick comments. Jeff Bone, <[EMAIL PROTECTED]>, writes: > Stumbled across an interesting if tangential paper that has something > to say about this. First some terminology: let's call events that are > highly improbable "white rabbits" and universes in which such events > happen frequently (or universes with entirely inscrutable laws of > physics) "white rabbit worlds." I think this is an unfortunate terminology choice, although it is true that we have occasionally used it here. The truth is, there is nothing remarkable about white rabbits. Our world is full of white rabbits. Using the term to refer to worlds which are utterly improbable is confusing. I think we got into it by reference to Alice in Wonderland, where the White Rabbit character walks, talks and wears clothes, but by itself, especially without capitals, the term white rabbit does not connote improbability. I would prefer "flying rabbit" or just "magical". > Let's further adopt the term "djinni" or (to follow Gott's > nomenclature) "jinni" to refer to closed time-like (causally cyclic) > curves, and "jinn worlds" as worlds (n-dimensional "spacetime" slices > of the higher-order spacetime, or rather n-m dimensional phase-space > volumes where n is the total dimensionality of the phase space) that > contain such causal cycles. It's not clear to me that causality and time are inherent properties of worlds. I include worlds which can be thought of as n-dimensional cells that satisfy some constraints. Among those constraints could be ones which induce the effects we identify as causality and time. For example, a two-dimensional cell where C[i,j] == C[i-1,j] XOR C[i-1,j-1]. This particular definition has the property that C[i,.] depends only on C[i-1,.], which lets us identify i as time, and introduce a notion of causality where conditions at time i depend on conditions at time i-1. But we could just as easily create a cell system where there was no natural definition of time, where C[i,j] depended on i+1, i-1, j+1 and j-1. You could still imaging satisfying this via some constraint satisfaction algorithm. Now these jinni worlds are ones which mostly have these conditions we identify as time and causality, but which locally, or perhaps rarely, do not satisfy such rules. Seen in this perspective, there is a full range of possibilities, from fully causal worlds, to ones which are 99.999% causal and only .0001% noncausal, to ones which are 50-50, to ones for which no meaningful concept of causality can be defined. Your perspective seems to be that those worlds which are very, very slightly non-causal are particularly interesting. If all you thought existed were causal worlds, then opening the door to slight non-causality may seem like a big step. But from my perspective, causality is not that significant, it is merely an accidental property of some worlds, so it is no big deal to imagine non-causal universes of varying degrees. [Skipping...] > David G. Boulware of the University of Washington published this paper > in PRD: > > http://arxiv.org/abs/hep-th/9207054 > > ...in which he studies the behavior of quantum fields in spaces with > closed time-like curves. What he finds is that probabilities are not > "conserved", i.e. not unitary, in such spaces. That is, the Feynman > sum-over-histories approach always yields precisely 1 --- except when > space contains one or more jinn. In such cases, there are quantum > events that simply cannot occur. I'll have to look at this. It doesn't sound quite right. If probabilities are non-unitary that violates the fundamental rules of QM, which would suggest that jinns and QM cannot exist, or in other words, that if QM describes our universe, we have no jinns. Now, I do recall some earlier famous papers by Novikov in which he found consistent solutions for closed timelike paths, which were presumably unitary. So I will have to look more closely and see how these results compare. > So: jinn defeat white rabbits. If any world-line through the phase > space is cyclic / allowed to self-intersect, the overall phase-space is > constrained, presumably to those set of configurations which are of > higher probability. The very existence of such causal cycles may > indeed be --- meta-paradoxically ;-) --- essential in stabilizing the > overall structure of the phase space. It would seem that these cycles > act as a kind of strange attractor around which probable configurations > (universes) coalesce. I think you're getting awfully speculative here. I don't know where all this is coming from, why you think that jinn would particularly make unlikely events even less likely to occur. [skipping] > So that's all well and good for physics, but what about the more > algorithmic cosmologies? One school of thought regarding the COMP > hypothesis is that it is easier to simulate all possible worlds t
Djinni vs. White Rabbit
At some point in the past various of us have argued about whether the simulation argument and / or the multiple worlds interpretation of quantum mechanics implies an "every possible world" (EPW) interpretation, i.e. one in which highly improbable events, laws of physics, etc. obtain. Stumbled across an interesting if tangential paper that has something to say about this. First some terminology: let's call events that are highly improbable "white rabbits" and universes in which such events happen frequently (or universes with entirely inscrutable laws of physics) "white rabbit worlds." Let's further adopt the term "djinni" or (to follow Gott's nomenclature) "jinni" to refer to closed time-like (causally cyclic) curves, and "jinn worlds" as worlds (n-dimensional "spacetime" slices of the higher-order spacetime, or rather n-m dimensional phase-space volumes where n is the total dimensionality of the phase space) that contain such causal cycles. In order to explain what this means: these are causally consistent chains of events in which there is no ultimate cause, but rather a closed causal chain that traverses both forward and backward along the time dimension. A peculiarity of this idea is that, in such a world, information "appears" without cause. For example a computer employing a closed time-like curve as a register can compute "hard" problems, but when one examines the execution history of the computer through time one finds that it never actually executes the computation! Cf.: http://arxiv.org/pdf/gr-qc/0209061 Anyway, "jinni" are these little closed curves of causality in the presence of time travel that are consistent but defy common sense. David G. Boulware of the University of Washington published this paper in PRD: http://arxiv.org/abs/hep-th/9207054 ...in which he studies the behavior of quantum fields in spaces with closed time-like curves. What he finds is that probabilities are not "conserved", i.e. not unitary, in such spaces. That is, the Feynman sum-over-histories approach always yields precisely 1 --- except when space contains one or more jinn. In such cases, there are quantum events that simply cannot occur. So: jinn defeat white rabbits. If any world-line through the phase space is cyclic / allowed to self-intersect, the overall phase-space is constrained, presumably to those set of configurations which are of higher probability. The very existence of such causal cycles may indeed be --- meta-paradoxically ;-) --- essential in stabilizing the overall structure of the phase space. It would seem that these cycles act as a kind of strange attractor around which probable configurations (universes) coalesce. Speculation: it may be that through studying the impact of such closed time-like curves in various spacetimes that we ultimately reconcile Cramer's transactional interpretation (retarded waves moving forward in time, advance waves reaching back to "handshake" on each quantum event, producing a kind of causal contract) of QM with MWI --- and ultimately COMP. Indeed, each retarded wave-advance wave pair *is* a jinni. Cramer doesn't just embrace jinn in his interpretation --- he bases the whole idea on their existence! (FWIW: this seems to me an embarrassment of riches. Why should *every* quantum event require a jinni, when a few --- acting as strange attractors --- might suffice? Though admittedly the latter leads to the questions which few, and why?) The implication ala Boulware is that if this is a real physical effect, then this provides a kind of global probabilistic censorship that makes the world the predictable place that it is! And --- connectionism --- it's rather ironic that Cramer's transactional hypothesis is based in part on some of Feynman's own speculation, when Feynman probably didn't realize the essential seemingly paradoxical consequences of pairing the histories approach with cyclic causality. So that's all well and good for physics, but what about the more algorithmic cosmologies? One school of thought regarding the COMP hypothesis is that it is easier to simulate all possible worlds than it is to simulate any subset of them. (Cf. previously-discussed Champernowne machine / "everything" algorithm.) But what if the dynamics of the simulation are such that these jinni exist as a priori structural parameters, "roots" if you will of the computation? In such an environment, "every computable universe" is NOT every possible universe. Curiouser and curiouser, jb
