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What's Wrong With The Second Law?
Interesting discussion about the Second Law of Thermodynamics, aka
entropy always increases. They are suggesting that entropy increases in both directions of time, one in our universe, and one in our universe's twin anti-universe. The only dependence is the direction of time. I think that this is basically right. Yousuf Khan What's Wrong With The Second Law? http://www.science20.com/hammock_phy...cond_law-81855 |
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What's Wrong With The Second Law?
On Aug 20, 1:32*pm, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka entropy always increases. They are suggesting that entropy increases in both directions of time, one in our universe, and one in our universe's twin anti-universe. The only dependence is the direction of time. I think that this is basically right. * * * * Yousuf Khan What's Wrong With The Second Law? It is statistical. There is only order of one kind or another. This was Albert Einstein stance of predetermined Order in time. http://www.science20.com/hammock_phy...cond_law-81855 |
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What's Wrong With The Second Law?
On Aug 20, 4:32*pm, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka entropy always increases. They are suggesting that entropy increases in both directions of time, one in our universe, and one in our universe's twin anti-universe. The only dependence is the direction of time. I think that this is basically right. * * * * Yousuf Khan What's Wrong With The Second Law?http://www.science20.com/hammock_phy...cond_law-81855 Oh no! Another empty nut. — NoEinstein — |
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Ruminations on entropy, the Big Bang, and CDT (was What's WrongWith The Second Law?)
On 20/08/2011 4:32 PM, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka entropy always increases. They are suggesting that entropy increases in both directions of time, one in our universe, and one in our universe's twin anti-universe. The only dependence is the direction of time. I think that this is basically right. Yousuf Khan What's Wrong With The Second Law? http://www.science20.com/hammock_phy...cond_law-81855 Isn't everyone missing the obvious? GR requires that any large chunk of space with matter, such as our observable universe, is unstable -- to exactly balance it with a cosmological constant is like balancing a pencil on its tip. So, the volume will be contracting in one direction in time and expanding in the other. In the contracting direction, Penrose singularity theorems apply and there's some sort of crunch, black hole, or other thing there the mass disappears into. Now, throw quantum gravity into the mix, and, specifically, the Bekenstein Bound. Follow the volume in the contracting time direction and it will end up crunched into regions with arbitrarily small surface areas, at least until more QG effects become important down near the Planck scale. So, the information content of the volume must be quite tiny in this contracted part of its history; that is: 1. The volume's time history includes a region in which it is crunched into a small, dense region near the Planck scale. 2. Its entropy at this time is bounded above by a very small number. Apply statistical mechanics to the time evolution from this small, dense region to the original point of its history, and you expect increasing entropy. Apply ordinary and statistical mechanics farther in the same direction in time and it expands more, at least for a while, and its entropy further increases, at least for a while. (Eventually either it recollapses or goes into thermodynamic heat death.) Within this volume and throughout that portion of its history, its thermodynamic arrow of time points in the same direction as the direction in which it is expanding. So, to an observer in this volume, 1. There is a big bang in the past. 2. The big bang had low entropy. We can *predict from first principles* of GR and our first stabs at quantum gravity that we should find ourselves in an expanding universe with a low-entropy big bang somewhere in our past -- and this bit of explanatory power is one more sign that the bits of QG we have so far, such as the holographic information bound, are meaningful. I'd even go so far as to say that the fact of a low-entropy bang a few billion years ago is good solid Bayesian evidence that black holes evaporate and even that space-time is discrete on the smallest scales. Further, I'd say that it points away from string theory and LQG and towards causal dynamical triangulation as a solid QG contender, simply because CDT predicts that at small length scales space exhibits fractal dimension asymptotic to 2, which fits a holographic bound where the information content of space is limited proportional to its surface area and not its volume. String theory, by contrast, calls for dimension to increase at small scales, and LQG for it to stay 3 all the way down. Another reason for interest in CDT is that it may hold the greatest promise of not having unmanageable infinities from gravity's self-interaction. String theory calls for gravity to strengthen abruptly at small scales, making it potentially able to reach parity with the three quantum field theory forces in strength, but exacerbating the problem of its self-interaction producing divergent behavior and singularities under extreme conditions or down at Planckian length and time scales. Problems even stock GR has in black holes and at the Big Bang. LQG can "fuzz" the singularities into smears and round off their pointy tips with a Planck-sized blur brush of quantum uncertainty but can't get rid of its absurd strength at tiny length scales. CDT, by reducing instead of increasing dimension, can. Famously, and as described in Kip Thorne's _Black_Holes_and_Time_Warps:_Einstein's_Outrageous _Legacy_, crushing a cylindrical bundle of magnetic field lines can't give you a black hole; the field self-repulsion will always be stronger than the gravity in its energy. The same proved true for any crushing in only two dimensions of a long, thing object extended in the third. Cosmic strings have a conical singularity but no infinite-curvature nonsense on their axis (and a real string isn't infinitely thin, but proton-wide for quantum mechanical reasons anyway). And so forth. Gravity in two dimensions thus cannot apparently produce black holes or other singularities. Penrose's theorems apply in three-space and higher but fail in the plane. And CDT says at small scales that's what space approximates. So, CDT may be uniquely well suited to get rid of the singularities, and also the infinities plaguing attempts to quantize gravity, and it gives a natural geometrical explanation for the Bekenstein bound's dependence on area rather than volume. In fact, there's something even more interesting. The Bekenstein bound can be calculated by observing that it takes energy to hold information bound, and putting more than a certain amount of information in a small enough volume will involve enough energy to put that volume within its own Swarzchild radius. So it becomes a black hole and the standard formula for black hole entropy applies. The argument thus extends that formula to be an upper bound on entropy in any volume of space. Here's the kicker: what distinguishes these volumes is their mass; the entropy reaches a maximum when the mass does, at the mass of a black hole of the same size. This suggests that mass itself is tied to the available and used degrees of freedom in the volume at some deep quantum-gravitational level. The CDT structure bushes out to become more three-dimensional at larger scales -- perhaps something in the amount of this bushing-out is the underlying thing beneath both mass and information? If so, the limit prevents the CDT structure getting "too thick" in some sense, and indeed can make a region collapse back to length scales that force it to two dimensions. At those length scales no-hair predicts no degrees of freedom survive except for mass, charge, and angular momentum. Or, perhaps, CDT makes the interior of the hole a genuine hologram, really existing only as dynamics on the horizon. That the electrostatics near a hole can be regarded as taking place with the horizon as a charged, conducting surface instead of vacuum is a strong hint that this may be the case; likewise, the way a forming or accreting hole "sheds its hair" may also mean it sheds, rather than hangs onto, the information that falls in, with anything that remains being imprinted onto the horizon rather than going deeper inside. If that's the case, though, in one respect it's disappointing: all the science fiction dreams of wormholes and other exotica hiding behind those event horizons go away. Though what of naked singularities? Or will CDT turn out to include strong cosmic censorship, rather than "just" fuzzing the singularities out a bit but preserving such exotica as Kerr wormholes and closed timelike curves? Note: the "causal" in CDT means the individual CDT graphs can't contain CTCs, but I don't think it's clear that this necessarily rules out CTCs in the *quantum superposition* that will exist; you can take limits of sequences of manifolds of a fixed topology, so pairwise homotopic, and get a limit manifold that isn't homotopic to them, e.g. a series of increasingly bent, open-ended finite-length cylinder-surfaces whose limit is a torus. CTCs reemerging in the "quantum limit" from individually-CTC-free graphs likewise cannot be ruled out point blank, on topological grounds, without a deeper analysis. And even absent CTCs, other forms of time travel could exist, such as closed curves in the entropic arrow of time that might allow an observer to experience time travel without anything acausal in the underlying physics! At first, "entropy increases along entropic arrows" appears to rule that out, but we could have a middling-entropy region become high entropy, but with a small volume pumped to low entropy (an ordinary air conditioned room is an example of that), and this volume's entropy gradually increases the other way in time, to a point in the past where it joins the middling-entropy region. The cycle, in general, must "centrifugally spin off" heat into its surroundings as it spins, but it can exist in principle. Boundary conditions that produce multiple low-entropy-constrained regions like the Big Bang might create cosmic-string-like defects in the entropy field that produce entropy-CTCs, in a manner analogous to how multiple bubble nucleations in electroweak symmetry breaking are thought to have produced defects in the Higgs field consisting of ordinary cosmic strings wrapped in curves on which the Higgs phase increases continuously around the loop. In particular, if inflation involves multiple inflationary bubble nucleations, each of which starts out with a very low internal entropy due to the tiny Bekenstein limit on the information content in the tiny initial volume of the bubble, then bubble collisions could theoretically result in entropic CTCs even in the total absence of CTCs in the underlying spacetime topology. Picture a ring of nucleated bubbles that collide while still fairly small, then further expand, leaving a ring-shaped region of generally low entropy surrounded by higher entropy; objects traveling around the ring can shed entropy into surrounding higher-entropy regions as long as such objects can exist at all, which requires only that the ring end up "standing on edge" in time -- which a CDT-based inflationary scenario will probably make possible. The underlying spacetime's time direction goes the same way along both halves of the ring, forming no directed cycle, so no spacetime CTCs, but with low entropy all around the ring something at the end of it could find its entropic arrow of time reversed. In spacetime, a version with increasing entropy goes forward to the future apex of the ring on one side of it, and another with decreasing entropy goes forward to the same apex on the other side, where they, say, collide and annihilate as matter and antimatter, whereas that object's entropic arrow of time has it go up one side of the ring, turn, and go down the other. On a smaller scale, the right kind of thermodynamic setup in a lab might permit creating (at cost in heat generated) a zone in which the entropic arrow of time is reversed, and possibly the use of such a zone as a time machine of sorts, independently of what the truth about quantum gravity turns out to be. (Likely, the zone, and a larger region into which it sheds heat, will have to be shielded from quantum observation, for reasons that are too complex to explain in a reasonably short usenet post.) A naturally occurring candidate for a similar locally-time-reversed zone is ... a black hole, though only if the interior is real after all. Inside, there's a local Bekenstein arrow of time directed AWAY from the singularity, so entropy ought to increase outward -- in principle, in a big enough one (the size of the observable universe, say) stars could form with planets, life, and conscious observers. Indeed, one could question if the cosmos we observe is the inside of one, but time-reversed into a white hole from our perspective. If so, a) the universe should turn out to be finite in two directions, with spherical topology, though very large, b) it should be contracting in the third (which ours doesn't seem to be), and c) there'd be an event horizon in our future on which we'd splatter, since our entropic arrow of time would not have anywhere to go there, as all the timelike geodesics would continue into a collapsing region there and not an expanding one. Our matter would continue on but we presumably would not continue on with it, instead annihilating counterparts in the external world that had the misfortune to fall into the hole there from their own temporal perspective. (This of course presumes the Bekenstein bound to hold in the hole interior, which QG will probably insist on if the hole interior exists at all. The usual argument for the bound only applies outside of a black hole, however, and the classical picture of a black hole interior allows entropy to increase without limit, and damn the Bekenstein bound, as the singularity is approached.) If miniature black holes can be produced in the lab, there is a likelihood of enlightenment from studying their evaporation. Such evaporation could give clues as to whether the interiors' entropies decrease inward from the horizon, increase, or sit at the Bekenstein bound all the way in; and the exact nature of the radiation could rule out some models of QG and clarify others in the way that observations of particle collisions clarified the Standard Model through the 60s and 70s. Indeed, more light would be shed on ordinary particle physics, as any particle much lighter than the hole should be among its potential decay products and so we should expect evaporating holes to shed Higgs bosons, dark matter, and any other exotica that might exist such as sterile neutrinos, axions, and so on. At the same time, whether we can even produce them or not at a given energy will give strong clues as to how gravity's strength changes at small length scales: if it increases, some brand of string theory looks likely, but if it weakens further, it points to CDT. If neither, LQG is the best candidate. So, if black holes are easy to produce, it points to strings, and in particular if the LHC makes any string theory becomes a near shoo-in. The most energetic cosmic rays remain unexplained, but it would be interesting if some proved to be primordial black holes, their evaporation slowed by time dilation in much the manner of muon decays in ordinary cosmic ray showers. They hit the atmosphere, slow violently, the time dilation goes away, and bang! Particularly energetic cosmic ray shower. This, if it panned out, would give us evaporating holes to examine even if string theory is false, and the holes' speeds and masses at impact would give us a good idea of how large they were at the Bang. Moreover, the lower cutoff on their masses could tell us the minimum energy to create one -- low means probably strings, exactly the Planck mass means probably LQG, and high means probably CDT, as these predict 4, 4, and 4 dimensions of spacetime at tiny length scales. High energy also forces a phenomenon in CDT to treat space as low-dimensional, which could have implication for the most energetic gamma rays, as the normal structure and polarization of electromagnetic radiation only makes sense in 3-space. In particular, electric and magnetic components can't be orthogonally transverse polarized in only 2 dimensions, if they can even coexist at all, so CDT might mean a cutoff to gamma ray energy, or a modification in the behavior of such rays (particularly wrt polarization) at high energy. This hypothetical cutoff might show up directly in cosmic rays or GRB observations, or indirectly in quantum systems that should be able to emit a very high energy gamma to drop to a ground state, but don't actually do so. In particular, there'd be a maximum mass for a particle-antiparticle pair to annihilate! This mass likely would be the mass above which the pair are two possibly-charged black holes that merge into a neutral hole instead of two particles annihilating -- so, probably the (QG-modified) Planck mass. Put in reverse, all holes of this mass should be extremal, which might in turn suggest that 1) quantum numbers such as color and flavor apply, in principle, to holes, and make them more extremal in a manner analogous to charge; 2) holes can undergo weak decays(!); and 3) some formula exists to compute mass from particle quantum numbers, and gives the (QG-modified) Planck mass only for combinations of statistics that make extremal holes of that mass and lower masses only for combinations that give superextremal holes of those masses. Then the fundamental particles ARE, precisely, all the possible superextremal black holes. If the formula gives higher masses only for combinations that give subextremal holes of those masses, then strong cosmic censorship is (more or less) true, as only tiny particles get to be naked singularities and their large-in-comparison quantum wavelengths fuzz them out completely, whereas otherwise the fundamental particles include some real bigons, such as Kerr rings of various masses and spins, with wavelengths tiny compared to their sizes. Note: the Planck mass should ideally be the point where Swarzchild radius and quantum wavelength cross, both equaling the Planck length. The QG theories that alter dimensionality at small scales would presumably affect this point, both by altering the Swarzchild radius (upward for string theory and downward for CDT) and the wavelength (the discreteness of space would begin to impact on wavelengths near this scale, and for large enough masses would render it physically meaningless). |
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