
#1
Sep1903, 09:34 AM

Astronomy
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PF Gold
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Really should call it "Big Bounce" instead of Big Bang.
Yesterday another paper was posted at the Los Alamos arxiv about getting rid of the Big Bang glitch by quantizing General Relativity. Martin Bojowald started this line of research but more people are getting into it, the new paper is by a guy at Hamilton College and someone in the Czech Republic http://arxiv.org/abs/grqc/0309035 "Isotropic Loop Quantum Cosmology with Matter II: the Lorentzian Constraint" Franz Hinterleitner (Masaryk University, Brno) and Seth Major (Hamilton College) The essential thing here is that (by failing at certain points) classical theories sometimes predict their own replacement by quantized versions. GR does this by breaking down at the time zero singularity (BB) and failing to compute. There are historical parallelsin 1900 Planck came up with a theory of thermal radiation (the first quantum theory of anything) that cured a "singularity" in the classical theory of how hot objects radiatethe classical unquantized theory suffered from infinities, failing to compute sensible answers at either very short or very long wavelengths. Not too long after that Bohr came up with a quantum theory of the hydrogen atom which cured another classical glitchthe unquantized theory predicted absurd results at a certain point and he fixed the bug. Sometimes by having glitches, a classical theory will show it needs to be quantized, and quantizing it sometimes fixes the bugs. The Big Bang is a glitch in GR. Quantizing GR in a minimal way (not adding new structure besides what is necessary to quantize the basic equations of GR) gets rid of the trouble at time zero (and also predicts inflation without having to add any new particle or field, just from a quantum geometrical effect of ordinary matter) So there are a bunch of papers cropping up about this and more people getting into it. Here are some names in no particular order of people who (since Bojowald started it) have published about loop quantum cosmology getting rid of the big bang singularity and/or deriving inflation as a result of loopquantizing GR Ashtekar Lewandowski Bojowald Smolin Stephon Alexander (SLAC) Golam Hossain (Chennai, India) Gambini Pullin Seth Major Franz Hinterleitner doubtless I've missed some Hossain's paper was mainly about getting inflation by loopquantizing GR, but incidentally gets rid of BB singularity. 



#2
Sep2703, 10:27 AM

P: 3,715

Marcus, I've been wondering about something. If both LQG and MTheory postulate a "Big Bounce" (as you call it), then is it possible to unify both theories?




#3
Sep2703, 11:15 AM

Astronomy
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I can only comment at level of inconclusive detail LQC does not "postulate" a bounce it is the result of calculating a wave function evolving across the classical singularity the math is pretty simple: all standard cosmology is based on two short diff eqns called Friedmann eqn, if you (loop) quantize them you get again a comparatively simple difference equation model and it does a bounce (changing from contraction to expansion) right at the point where the classical Einstein/Friedmann model blew up The people who worked it outMartin Bojowald, Abhay Ashtekar, et alcall it a bounce (I did not hear them say "Big Bounce" actually, but they do say bounce). It is not my choice of term. There is an incredible difference between LQG and other approaches which it will help to understand. LQG is extremely conservativebare bones quantization of GR with no additional structure beyond what is required by quantizationno "creative" elementsno "branes" and no "extra dimensions" and "ToE"stuff. It is the bare minimum and people have been trying to quantize GR for several generations (since before 1950) and there'v been technical obstacles and they'v finally gotten over some of the obstacles and it's beginning to work. There is a small set of versions of LQG and they are all beginning to predict numbers that will allow them to be tested and some will be rejected and modifiedthe cycle of prediction and experimental test will help the development. The bounce in cosmology is a robust result in the sense that it is predicted by any versionLQC is a simplification of LQG so whatever version of the full theory boils down to very similar versions of cosmology all with the same qualitative behavior. It is very hard to compare this rather concrete, limited nutsandbolts result of doing a standard ("canonical" they call it) quantization job on 1915 GR with "Mtheory" which seems a total oppositehighly unconservative, nonpredictive, proliferated into a huge variety of versions none of which corresponds to reality in any obvious way. Different animal(s) I'd say. How are you on the key concept of background independence? The 1915 General Relativity theory is fully background independentinvariant under diffeomorphisms (smooth transformations of the manifold). It is an awfully important feature of GR that many people fail to recognize. LQG preserves the background independence featureit is also a background independent theory, like GR itself. This is why it is so hard to compare LQG to stringy theories. Or to draw any solid connections. The connections tend to be spurious, specious ones "this contains that" when it doesnt really contain it except in some superficial way. to understand the basic theoretical layout you need to assimilate the background issue. unfortunately. seems to be a major hurdle for a lot of people 



#4
Sep2903, 10:42 AM

P: 3,715

Big Bang Bandwagon
[QUOTE]Originally posted by marcus
that is something which interested young people like yourself will have to determineperhaps other PF posters have ideas I can only comment at level of inconclusive detail LQC does not "postulate" a bounce it is the result of calculating a wave function evolving across the classical singularity the math is pretty simple: all standard cosmology is based on two short diff eqns called Friedmann eqn, if you (loop) quantize them you get again a comparatively simple difference equation model and it does a bounce (changing from contraction to expansion) right at the point where the classical Einstein/Friedmann model blew up The people who worked it outMartin Bojowald, Abhay Ashtekar, et alcall it a bounce (I did not hear them say "Big Bounce" actually, but they do say bounce). It is not my choice of term. There is an incredible difference between LQG and other approaches which it will help to understand. LQG is extremely conservativebare bones quantization of GR with no additional structure beyond what is required by quantizationno "creative" elementsno "branes" and no "extra dimensions" and "ToE"stuff. It is the bare minimum and people have been trying to quantize GR for several generations (since before 1950) and there'v been technical obstacles and they'v finally gotten over some of the obstacles and it's beginning to work. [quote] One point on that though: If it is just barebones quantization of GR, then there could really be no unification between it and MTheory, but rather an assimilation of it into MTheory, if that's even possible (there is the backgrounddepency issue, which seems to be a big hurdle, but I've had difficulty seeing why (I don't completely understand what is meant by "background indepence")). Perhaps you could help me out on that? 



#5
Sep2903, 11:27 AM

P: 683

Another question that pops up is how you go from a universe that expands at an accelerating rate to a contracting universe to allow a bounce in the first place. It would still appear that the universe has a beginning (no singularities though), unless there is some mechanism to stop the expansion and reverse.




#6
Sep2903, 01:42 PM

Astronomy
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PF Gold
P: 22,809

There are more imaginative papers that play around with the idea that "dark energy" could decay and even go negative so that expansion stops accelerating and even reverses and the cosmos contracts. So there is some "cyclic" expansion contraction expansion process. But for me the value AND the limitation of LQC is that it is rather conservative, unimaginative, minimalistit just wants to quantize the standard classical Einstein or Friedmann model with the least amount of extra assumptions and machinery and just see what logically results from doing that there is a real value to both approaches (a wide ranging highly imaginative approach and a conservative kind of grudging cautious one that clings to classical GR and only changes enough to quantize it in the traditional way). Human mental diversity. Sometimes I am very glad to belong to this species with all its different ways of looking at the world. But right now I'm personally most excited by what seems to be coming from the minimalist approach of (canonical) quantizing GR. Want to get to replying to Mentat but will get back to this train of thought with you I hope 



#7
Sep2903, 02:21 PM

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Mentat, frankly your question that I quote here is one of the keenest if not the keenest Ive ever seen on PF and I say this not as a compliment but because it is a relevant fact. It would be very exciting to me if some person (say selfAdjoint) would suddenly appear and answer this really major question which you pose:
"what is it about string theory that implies a backgrounddependent structure?" IIRC in one of Tom Bank's thoughtful overview papers (Critique of pure string theory) he indicates that at one time there was a hope of formulating a stringful theory in a backgroundindep way and in that paper he discounts that hope saying that it probably just isnt going to happen. For what that's worth. we dont have to take Banks as gospel! Anyway, there might be a simple answer to your question! Maybe someone will just walk in and say "well the equations for vibrating strings just need a definite background" or "well you have to start with a fixed space just so you can define the basic objects" or something. Or someone will come in and amaze me with the news that soandso has defined a BI version of some variant of string so it is possible after all! But for now all I feel capable of is just echoing your question, with this quote:  So, let me get this right, "background independence" is basically just the preservation of invariance under diffeomorphisms? So, what is it about string theories that calls for "background dependence"? IOW, what is it about string theory that implies a backgrounddpendent structure? [[here you quote my previous post: This is why it is so hard to compare LQG to stringy theories. Or to draw any solid connections. The connections tend to be spurious, specious ones "this contains that" when it doesnt really contain it except in some superficial way. to understand the basic theoretical layout you need to assimilate the background issue. unfortunately. seems to be a major hurdle for a lot of people]] Yeah, that's what I always hear about, but I have apparently not studied string theory enough to see why it should be "backgrounddependent".  I'll try to reply more adequately later today. Maybe the nittygritty of how equations can be invariant under various kinds of transformations should be discussed Actually it is pretty amazing to me that the Einstein GR equation is invariant under diffeomorphisms because they really can mix points around and deform a manifold almost beyond recognition, intuitively it is a radical sort of invariance or as a mathematician might put it a "strong" form of invariancean extreme thing to demand of theory. Between 1912 and 1915 Einstein had decided not to have it and he waffled (even tho in a race with Hilbert he wasted time waffling) and then in 1915 he went for it. Have to go to lunch but will return to this. Thanks for great question __________________ 



#8
Oct203, 01:44 PM

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#9
Oct203, 02:17 PM

P: 683

The 3 large spatial dimensions are still expanding, and will forever. In the ekpyrotic (or cyclic) model, our universe of infinite volume expands forever, but it is the collapse of an extra dimension that produces the effects of the big bang. LQG doesn't have any extra dimensions to resort to, so some kind of other mechanism would be needed to half the expansion in that area.




#10
Oct203, 02:49 PM

P: 3,715

There is no reason why this must be true, Eh. Of course, it might be, but then MTheory would be disproven [*(] Also, MTheory predicts that the other "wrapped up" dimensions are contracting, as the 3, that we are used to, expand. Thus, the socalled "bounce" effect (in MTheory) is really just the idea that, once space reaches the Plank's size it will no longer be measurable in terms of vibrating strings, and must be measured in terms of wound strings, which would then be expanding. 



#11
Oct303, 01:31 PM

P: 683





#12
Oct403, 10:57 AM

P: 3,715





#13
Oct503, 01:45 PM

P: 683

I don't think the cycle is a required part of M theory. But I would like to know where you read that it is.



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