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Penrose's argument that q.g. can't remove the Big Bang singularity

by bcrowell
Tags: argument, bang, penrose, remove, singularity
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bcrowell
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Nov5-12, 01:54 PM
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I came across this argument in the book The Nature of Space and Time, which is based on a series of lectures given by Hawking and Penrose. Although it relates to Penrose's Weyl curvature hypothesis (WCH), it does not depend on it, and that, to me, makes it a lot more interesting, since I wouldn't bet a six-pack on the validity of the WCH.

As a preliminary, Penrose observes that (in my possibly inaccurate paraphrase):

(1) The Big Bang was not a generic state. A generic Big Bang state would have had a large Weyl curvature, but the universe we see looks nothing like the one that would have resulted from such an initial state. Our Big Bang appears to have had a small or even vanishing Weyl curvature.

(2) The evolution of our universe has led to a state with nonvanishing Weyl curvature. (At black hole singularities, we even have diverging Weyl curvature.)

At the end of his first lecture, someone in the audience asks whether he thinks quantum gravity removes singularities. He says:

I don't think it can be quite like that. If it were like that, the big bang would have resulted from a previously collapsing phase. We must ask how that previous phase could have had such a low entropy. This picture would sacrifice the best chance we have of explaining the second law. Moreover, the singularities of the collapsing and expanding universes would have to be somehow joined together, but they seem to have very different geometries. A true theory of quantum gravity should replace our present concept of spacetime at a singularity. It should give a clear-cut way of talking about what we call a singularity in classical theory. It shouldn't be simply a nonsingular spacetime, but something drastically different.
What do folks here think of this? It seems pretty compelling to me, and yet the practitioners of loop quantum cosmology seem to be very convinced at this point that they're on the right track with models in which the big bang singularity is removed.

Presumably he has his cosmic cyclic cosmology (CCC) model in mind here (this was in 1996). Although CCC no longer looks viable, that doesn't resolve the issue he raises, which seems pretty model-independent.

The possibility that occurs to me is that the big bang singularity is removed by quantum effects, the entropy of the universe was minimized at the big bang, and there is time-reversal symmetry, so that the thermodynamic arrow of time was reversed in the universe before the big bang. Thermodynamically, the big bang would then look like an extremely unlikely thermal fluctuation, but presumably whoever set the boundary conditions of the universe got to choose to make it that way.
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Finbar
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Nov5-12, 03:07 PM
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You seem to suggest the existence of a creator?

Thermodynamics isn't time symmetric so you can't have the universe as a thermal state the decreases in entropy before the big bang started. The ccc models I guess are some kind of loop hole in the 2nd law like mapping states of high entropy to states of low entropy. I'm not sure how much sense that makes though.
bcrowell
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Nov5-12, 04:46 PM
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Quote Quote by Finbar View Post
Thermodynamics isn't time symmetric so you can't have the universe as a thermal state the decreases in entropy before the big bang started.
I think this depends on where you think the thermodynamic arrow of time comes from. If you think it comes from the fact that the big bang was a low-entropy state, then in a crunch-bang scenario, I think it's perfectly natural to imagine that the thermodynamic arrow of time flipped at the big bang.

But if that isn't the option one picks, then what counterargument is there to Penrose's?

Finbar
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Nov5-12, 06:10 PM
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Penrose's argument that q.g. can't remove the Big Bang singularity

The second law of thermodynamics has an explanation from statistical physics. I can't understand how you could explain this flip? To create some state before the big bang that created the special low entropy state at the big bang would require some fine tuned pre-big bang state. It can't begin from a generic 'crunch'.

I don't think there is a couter argument to Penrose's argument. Something drastic has to happen to space-time at the big bang.
bcrowell
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Nov5-12, 07:16 PM
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Quote Quote by Finbar View Post
The second law of thermodynamics has an explanation from statistical physics.
Well, not really. It has an explanation from (1) statistical physics plus (2) the assumption that the universe used to be in a low-entropy state. You can't do it without ingredient #2.

Quote Quote by Finbar View Post
I can't understand how you could explain this flip? To create some state before the big bang that created the special low entropy state at the big bang would require some fine tuned pre-big bang state. It can't begin from a generic 'crunch'.
Fine-tuning is required no matter what. We observe that the big bang had low entropy compared to a maximum-entropy big bang. This is a ridiculous amount of fine-tuning, and it's simply an observed fact.

Quote Quote by Finbar View Post
I don't think there is a couter argument to Penrose's argument. Something drastic has to happen to space-time at the big bang.
...in which case loop quantum cosmology is trivially wrong and not worth pursuing? Seems unlikely that its practitioners would never have considered this issue.
friend
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Nov5-12, 09:49 PM
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Quote Quote by bcrowell View Post
Well, not really. It has an explanation from (1) statistical physics plus (2) the assumption that the universe used to be in a low-entropy state. You can't do it without ingredient #2.
How can you tell the difference between the early universe being in a low entropy state or being in complete thermal equilibrium? I mean, if everything then was the same everywhere, isn't that the definition of thermal equilibrium?

Maybe complete thermal equilibrium of the entire universe is acutally equivalent to everything being in one state that can degenerate, and that's how you can go from one cycle of the universe to the next.
bcrowell
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Nov5-12, 10:11 PM
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Quote Quote by friend View Post
How can you tell the difference between the early universe being in a low entropy state or being in complete thermal equilibrium? I mean, if everything then was the same everywhere, isn't that the definition of thermal equilibrium?
We have a FAQ about this: http://www.physicsforums.com/showthread.php?t=509650
Finbar
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Nov6-12, 06:08 AM
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Quote Quote by bcrowell View Post
Well, not really. It has an explanation from (1) statistical physics plus (2) the assumption that the universe used to be in a low-entropy state. You can't do it without ingredient #2.


Fine-tuning is required no matter what. We observe that the big bang had low entropy compared to a maximum-entropy big bang. This is a ridiculous amount of fine-tuning, and it's simply an observed fact.


...in which case loop quantum cosmology is trivially wrong and not worth pursuing? Seems unlikely that its practitioners would never have considered this issue.
I agree. But reversing the 2nd law and requiring fine tuning seems worse than simply the fine tuning.

Nothing is trivial here. LQC works with much symmetry, it's just a toy model.Toy models can be useful but they're not reality.
bcrowell
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Nov6-12, 09:36 AM
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Quote Quote by Finbar View Post
But reversing the 2nd law and requiring fine tuning seems worse than simply the fine tuning.
But then that doesn't address the point of my original post, which is that this seems to invalidate loop quantum cosmology.
bcrowell
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Nov6-12, 03:01 PM
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Possibly relevant:

http://arxiv.org/abs/arXiv:0812.3544
http://physics.stackexchange.com/que...the-big-bounce
Haelfix
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Nov6-12, 07:08 PM
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No one has solved the reason for the low entropy initial conditions of cosmology. The problem exists for almost every single proposal. Loop or other.

Taken at face value, it rules out almost all of cosmology.
TrickyDicky
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Nov7-12, 05:07 AM
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Quote Quote by Haelfix View Post
No one has solved the reason for the low entropy initial conditions of cosmology. The problem exists for almost every single proposal. Loop or other.

Taken at face value, it rules out almost all of cosmology.
Good point.
Don't wanna sound sarcastic, but if GR had no problem not following strictly the previously "sacred" first law of thermodynamics, what prevents it from not strictly following the second too?
I always considered both laws of thermodynamics in the same pack, but that seemed to be just me, last time I argued this here I was told that they are independent of each other and the second one was more important than the first if one was to choose wich one should be disobeyed by a theory like GR. I can't say I'm totally convinced of that, though.
marcus
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Nov7-12, 12:22 PM
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Quote Quote by Haelfix View Post
No one has solved the reason for the low entropy initial conditions of cosmology. The problem exists for almost every single proposal. Loop or other.

Taken at face value, it rules out almost all of cosmology.
Quote Quote by TrickyDicky View Post
Good point.
Don't wanna sound sarcastic, but if GR had no problem not following strictly the previously "sacred" first law of thermodynamics, what prevents it from not strictly following the second too?
I always considered both laws of thermodynamics in the same pack, but that seemed to be just me, last time I argued this here I was told that they are independent of each other and the second one was more important than the first if one was to choose which one should be disobeyed by a theory like GR. I can't say I'm totally convinced of that, though.
Compliments, both, on several good points. Penrose argues against LQC bounce, but the essence of the bounce is that gravity becomes repellent due to quantum corrections at near-Planck density--that's why there is a bounce.

If gravity becomes repellent, what happens to BH entropy? If the collapsing universe, prior to bounce, consists mainly of black holes, and its entropy is predominantly BH entropy, then how does one define the global entropy as gravity becomes increasingly repellent going into the bounce?

There seem to be problems with the definition of entropy underlying the 2nd law, when one tries to apply it in this context.
Naty1
#14
Nov7-12, 05:35 PM
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..does quantum gravity remove singularities..

We are, alas, unlikely to resolve the question here.
Well, I know I won't be!!!



Marcus:
[QUOTE][Penrose argues against LQC bounce, but the essence of the bounce is that gravity becomes repellent due to quantum corrections at near-Planck density--that's why there is a bounce./QUOTE]

I agree that's conventional wisdom, but when a 'correction' starts a universe, color me 'suspicious'.

Presumably he has his cosmic cyclic cosmology (CCC) model in mind here
yes....there is a lecture online by Penrose, which I can't find that was referenced in another thread in these forums, in which Penrose describes the transition from a high entropy end to a low entropy start of another universe....lots of his neat transparancies with overlays....


Here are some related references I saved from other discussions in these forums.....no, they don't give a definitive answer.


from Roger Penrose THE ROAD TO REALITY....PG 766

Let us now think of a universe evolving so that an initially uniform distribution of material [with some density fluctuations] gradually clumps gravitionally, so that eventually parts of it collapse into black holes. The initial uniformity corresponds to a mainly Ricci-curvature [matter] distribution, but as more and more material collects gravitationally, we get increasing amounts of Weyl curvature....The Weyl curvature finally diverges to infinity as the black-hole singularities are reached. If we think of the material as having been originally spewed out from the Big Bang in an almost completely uniform way, then we start with a Weyle curvature that is....[essentially] zero. Indeed, a feature of the FLRW models is that the Weyl curvature vanishes completely. ...For a universe to start out closely FLRW we we expect the Weyl curvature to be extremely small, as compared with the Ricci curvature, the latter actually diverging at the Big Bang. This picture strongly suggests what the geometrical difference is between the initial Big Bang singularity- of exceedingly low entropy- and the generic black hole singularities, of very high entropy.




BEFORE THE BIG BANG:
AN OUTRAGEOUS NEW PERSPECTIVE AND ITS IMPLICATIONS FOR
PARTICLE PHYSICS
Roger Penrose
Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, U.K.

. It may be seen that, with time symmetrical
dynamical laws, the mere smallness of the
early universe does not provide a restriction on its degrees
of freedom. For we may contemplate a universe model in
the final stages of collapse. It must do something, in
accordance with its dynamical laws, and we expect it to
collapse to some sort of complicated space-time
singularity, a singularity encompassing as many degrees
of freedom as were already present in its earlier nonsingular
collapsing phase. Time-reversing this situation,
we see that an initial singular state could also contain as
many degrees of freedom as such a collapsing one. But in
our actual universe, almost all of those degrees of
freedom were somehow not activated.
from
http://arxiv.org/PS_cache/arxiv/pdf/...009.1136v1.pdf

The BKL picture was originally developed as an attempt to understand the cosmology of the very early Universe near an initial spacelike singularity. Near such a singularity, light rays are typically very strongly focused by the gravitational field, leading to the collapse of light cones and the shrinking of particle horizons. This “asymptotic silence” [43] is the key ingredient in the ultralocal behavior of the equations of motion, from which the rest of the BKL results follow.
Small-scale quantum gravity has no such spacelike singularity, so if a similar mechanism
is at work, something else must account for the focusing of null geodesics. An obvious candidate is “spacetime foam,” small-scale quantum fluctuations of geometry. Seeing whether such an explanation can work is very difficult;.......

and a 2009 perspective from Steve Carlip that may offer interesting possibilities:


The Small Scale Structure of Spacetime
http://arxiv.org/PS_cache/arxiv/pdf/...009.1136v1.pdf


Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional.

Stephen Hawking and George Ellis prefaced their seminal book, The Large Scale
Structure of Space-Time.......

At much smaller scales, on the other hand, the proper description is far less obvious….Indeed, it is not completely clear that “space” and “time” are even the appropriate categories for such a description….Over the past several years, evidence for another basic feature of small-scale spacetime has been accumulating: it is becoming increasingly plausible that spacetime near the Planck scale is effectively two-dimensional. No single piece of evidence for this behavior is in itself very convincing, and most of the results are fairly new and tentative. But we now have
hints from a number of independent calculations, based on different approaches to quantum gravity, that all point in the same direction.....
all rather mysterious!!
tom.stoer
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Nov7-12, 06:14 PM
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The big difference is that Penrose uses entropy in his reasoning whereas LQC doesn't. Both approaches are incomplete: Penrose has no detailed model at all, LQG is a detailed model but with too many simplifications.
julian
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Nov7-12, 08:06 PM
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"The nature of space and time" is an old book. I think he put similar views forward in "The Emperor's new mind". You know that Penrose has made a bit of a U-turn and now argues that in the thermal death of one universe (in which he presumes there are no non-zero rest mass particles) there is no way of building clocks or reference systems to provide a notion of time intervals or length intervals and so the universe is induistinguishable from zero volume big bang situation (this is the view he puts forward in his new book "Cycles of time"). I have been wondering how he reconciles these seemingly contradictory views. Glad bcrowell brought it up. Would like to understand better.
marcus
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Nov7-12, 08:50 PM
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Quote Quote by tom.stoer View Post
The big difference is that Penrose uses entropy in his reasoning whereas LQC doesn't...
I heard Penrose give this argument in March 2006 to an audience of math and physics people at the MSRI. He was charming and had great slides but the argument was handwaving and not convincing. You cannot use entropy in a rigorous math argument unless you can define it and he was not able to define the global entropy through the course of the LQC bounce. So he used vague suggestive language and did not claim certainty.

It is really interesting to consider how the entropy of a BH could be defined and could evolve when gravity becomes repellent! On the face of it, considered naively, the entropy should change sign:

Suppose we take the Bekenstein-Hawking effective description at face value: S = A/(4GNewton) and the effective value of GNewton goes temporarily negative. Then unless the black hole has dissipated by then it would seem to have negative entropy

This is not how one would argue in reality, just meant to be suggestive. In LHC gravity becomes repellent at extreme density. that is what causes the bounce. So all I can say is that this makes the definition of entropy itself an extremely interesting problem (in the context of LQC models).

In the talk by Penrose I attended he did not address this at all, just waved his hands. So he actually did not make logical contact with LQG. But it was otherwise a delightful and stimulating talk about his new (Conformal Cyclic) Cosmology idea.
Haelfix
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Nov7-12, 10:45 PM
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Negative entropy does not make sense. It is defined (for a microcanonical ensemble) as the logarithm of the number of microstates. You cannot, by definition, have a negative value.

Now, whether entropy is or is not defined in the quantum gravity regime is one question. However if you believe in unitary physics, you do run into a contradiction at some stage from the global point of view. So it is true that there is a problem of principle.

If you take a state in the far past pre bounce (where slices are nice, well behaved and semiclassical), and a state in the far future post bounce (likewise), and derive that the former has higher entropy than the latter, that does violate the second law (and unitarity) regardless of what tricks you want to pull in the middle. Amongst other catastrophes, it implies that you do not have reversible physics.

Now, as I said, these types of stat mech arguments are essentially a problem with all proposals really (eg an infinite finetuning in a boundary conditions or alternatively a discontinuity in the laws of physics).

Interestingly there might be a way out if you believe in observer complementarity in which case inflation might potentially resolve some of the finetuning (b/c crucially the all important volume factor enters (and dissappears) from the picture). See recent papers by Banks et al


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