Quantum Graffiti

marcus

the tentative programme schedule for July 11-16 "Strings 05" has been posted.

http://www.fields.utoronto.ca/progra...5/program.html

the titles of many of the talks are listed on this separate page:
http://www.fields.utoronto.ca/progra.../speakers.html

marcus

yesterday a very cautious paper by Martin Bojowald came out
http://www.physicsforums.com/showthr...695#post618695

http://www.physicsforums.com/showpos...&postcount=347

the second link is in case the first one doesnt work.

in a very tentative, "oblique", way he is venturing to suggest that blackhole bottoms may connect to inflations of new branches of the universe.

Bojowald I respect as a careful scientist and he does not seem to be media-phile. he does not do the attentiongetting bold speculations routine.

so this paper is very underplayed, careful almost grudging.

BTW it is already quite risky to do Loop Quantum Cosmology, but what other quantum model cosmology is there where you can actually calculate numbers?
LQC is very close to standard cosmology Friedmann model that almost everybody uses, only quantized. And you can actually calculate stuff that people have hopes of being able to check for---Parampreet Singh is one of the experts on the observational side of LQG, look him up if interested.

anyway LQG is already risky, and LQC which involves simplifying down from the full LQG model is also risky, but at least you can calculate and run computer simulations showing how contraction leads to expansion and how inflation naturally arises.

and now Bojowald and others have begun studying the black hole contraction---but in order to calculate they have to make simplifying assumptions about symmetry. they assume what collapses is nice and round----not shaped like a potato.

who is going to dare to say that black hole looks like it might lead to big bang? I dont mean say that as a "visionary" but say it on the basis of the way the mathematical models fit together. who is going to venture to hint this not on the basis of some mental image but on the basis of how the numbers look.

i remember standing at cliff-edge at Big Sur looking at the Pacific ocean one afternoon in 1961.
one is conscious of the solid ground under one's feet
one does not make any abrupt moves

nightcleaner

A beautiful and disquieting image, Marcus. I am very glad you were careful of your feet. Do you know the bar/restaurant called Nepenthes located near Big Sur? I have a close freind who worked there in the late 60's, and he never seems to tire of recalling the times he spent meditating on the ocean from Nepenthes' deck, hundreds of feet above the surf. But it seems the place is in the hands of developers now, and styles itself a resort. I wonder if the Black Angel still hangs above the gift shop door?

Well, I have been guilty of wild speculations about big bangs beyond black holes before, and I am glad to hear that the polymaths are beginning, with caution, to say it may be possible. The notion seems to me to have a beautiful symmetry. Time and space once again seem to extend themselves beyond the horizons.

Now what about tidal forces and information? I will boldly speculate that tidal forces will not be a barrior to passage of information for the simple reason that the compression is of timespace itself, and objects as we know them are completely dependent on the timespace background. If the background compresses smoothly, so will the objects embedded in it. Therefore there should be some physical conditions which would allow passage of information through the event horizon and then through the "singularity" itself.

Essentially I am speculating that the "singularity" is not a singularity at all, but merely another infinite spacetime, infinitely removed from our point of observation. All lines seem to converge at infinity, but if you translate your point of view to the infinite location, Euclid's fifth postulate still holds. Infinity, like its inverse, the singularity, is permanently shrouded in an event horizon. We are never allowed to look on G-d's naked face. It is for our own protection. If we ever evolved enough to see G-d's face directly, we would no longer exist....not that we would be ripped apart by tidal forces, but that the perfect definition excludes our imperfect existence. G-d naked is solitary, and it seems G-d is not amused by that.

I think G-d is amused when we stand upon the cliff, and pleased when we choose to step back. It is not G-d's fault, when we look down at the surf, full of doubts and fears, but our own.

Be well Marcus, and all.....

Richard

nightcleaner

Oh yeah, about that potato thing. I recall reading in Kip Thorne about some Russian theorists early in the black hole argument (would that have been in the 1960's?) who showed that irregularites ("a mountain") on the surface of a black hole will quickly be reduced to the sphere. Of course this is part of the argument that information passing into a black hole will be lost. In a sense, the irregularities actually are the information.

However, I wonder if this smoothness is just on the outside surface of the horizon. The inside surface of the BH could be all crinkley, and we would never know, would we? The information may be lost, to us on the outside, but that may not mean it is lost, looking back on it from the inside. What would the event horizon look like from the inside? Ahem. Cosmic Microwave Background Energy.

Richard.

marcus

I've had some nice times at nepenthe's but it is expensive now.

You and Smolin. he has had similar speculations about big bangs beyond black holes.

but Bojowald is special for me because he is NOT visionary. I trust him not jump to conclusions. he still has not, about this thing.
what I like is that I can tell that from where he stands he can see it very clearly but he will not jump at it. his example steadies me.

marcus

Let's take a closer look at the program at this month's Paris conference, mentioned in the earlier post.
http://einstein2005.obspm.fr/indexr.php
http://einstein2005.obspm.fr/programmer.php
The abstracts of some Plenary Session talks are posted. Here is a sample:

Monday July 18
...
11h45 - 12h25: Abhay Ashtekar « Gravity, Geometry and the Quantum »

"General relativity is both sublimely beautiful and incredibly successful. But it is incomplete because it ignores quantum physics. Its satisfactory synthesis with quantum mechanics would constitute the next leap in fundamental physics. In the first part of the talk I will discuss the primary challenges we face and summarize the strategies that have been devised to overcome them. In the second part, I will focus on loop quantum gravity, a background independent approach in which the continuum picture of space-time breaks down. I will discuss a few ramifications of the quantum geometry that replaces it. The goal is to provide a few glimpses of the exciting world-view in which gravity, geometry and the quantum merge."


14h00 - 14h40: Brian Greene « The State of String Theory»

"I will briefly review the motivation for and essential ideas of string theory, and then assess the progress the theory has made in a variety of critical areas."

14h45 - 15h30: Alain Connes « Noncommutative geometry and physics»

[no abstract available yet]

15h30 - 15h45: Coffee Break

15h45 - 16h25: Fay Dowker « Causal sets and discrete spacetime. »

"In 1905 the basic question of whether matter was continuous or discrete was still controversial and it was only decisively settled by the work of J.-B. Perrin who verified the quantitative predictions about Brownian motion made by Einstein and by Smoluchowski, ending any remaining scepticism about the physical reality of atoms and molecules. In 2005 our best theory of spacetime itself is General Relativity, in which spacetime is a continuum. But there is growing circumstantial evidence that spacetime is discrete at the tiny scales at which quantum effects on spacetime can no longer be ignored. Taking that evidence seriously, one approach to "quantum gravity'' proposes a fundamentally discrete substructure for spacetime: a causal set. The only structure carried by a causal set is a microscopic notion of "before'' and "after''. A simple model of particles moving on a causal set background implies that they undergo a Brownian motion in momentum. I will speculate on whether this phenomenon may be able to provide a mechanism for the production of the high energy cosmic rays whose origin remains a mystery. If causal set phenomenology can indeed explain the origin of high energy cosmic rays, then this observational data may turn out to be the Brownian motion of our age, convincing us finally of the atomicity of spacetime itself."

...

Tuesday July 19
....
10h15 - 10h55: Carlo Rovelli «Loop Quantum Gravity »

" I review the main ideas and the main results at the basis of the loop approach to quantum gravity. This is an attempt to construct a fully background-independent quantum field theory, where space and time emerge as quantum excitation of the gravitational field. In other words, it is an attempt to fully merge quantum field theory with the lesson of Einstein's general relativity."

...

Friday 22 July

...
15h45 - 16h45: Gerard t'Hooft « Conclusion Talk »

[no abstract available yet]

----------------------------------------------

BTW here is a picture of Fay Dowker. Interesting that both her mother and father were physicists, born c. 1966 undergrad major math, married to physicist Jerome Gauntlett---physics seems to run in the family---has two children.
http://www.stp.dias.ie/events/2004/c...ayDowker-1.jpg

Fay Dowker is one of the featured (Plenary Session) speakers not only at Einstein2005 this month in Paris but also at Loops05 this October in Potsdam.

marcus

dammit nobody has remarked on how beautiful Fay Dowker is!

do I have to paste this in as an attachment?

selfAdjoint

Yeah, she's beautiful! How old are her kids? Are they headed for physics careers too? Wouldn't three generations be a record unmatched since the Bernoullis?

marcus

I agree that three generations would be highly commendable
but we have to wait and see because her kids are only 3 years old and 7 years old

marcus

this lady does not stop
http://arxiv.org/abs/hep-th/0507012

it's her fourth paper this year

selfAdjoint

From the abstract:
I hope this analytical work doesn't fall into the Motl trap of being accused of bad physics for ignoring acausal paths in the path integral. The CDT papers proper avoid that criticism because those paths do not exist even in theory in their model, causality is prior to their whole scheme. But it seems this new analytical work is back to ordinary spacetime.

marcus

good point about how they avoid that trouble.
in this case they manage to retain a causally layered model (continuing to avoid that type of vulnerability) by severely restraining the jitter in the topology. In the Loll-Westra model the wormholes exist only for an "infinitesimal" period of time. They barely exist---unable to register at macroscopic scale---and yet they seem to change the effective cosmological constant.

this is what I find hard to understand. Loll-Westra hardly change the CDT model, if at all. I can hardly believe that these microscopic infinitesimally-brief topology changes are actually taking place. (they seem to 'undo' themselves before any clock has had a chance to tick).
and yet.
and yet.
even though I dont see them really existing they seem to affect the Hamiltonian! so that where there used to be a Lambda (cosm. const) term there is now a effective Lambda, somewhat smaller.

BTW in 2D the newton G is dimensionless. and spacetime volume is an area. and "density of microscopic wormholes in spacetime" being a number per unit spacetime volume has the same dimension as curvature----namely reciprocal area.

so "density of wormholes" has the same dimension as the cosm. const. Lambda.

they find that as (the 2D version of) newton G increases there get to be more wormholes, so that the "density of wormholes" is growing almost linear proportional to G!

and as G is increasing and "density of wormholes" is growing, the effective cosm. const. Lambda is tailing off----see their Fig. 4.

The Catalan numbers get into the analysis. and some Laguerre polynomials.

all in all a bit remarkable. this is how it was in 1998. In 1998 Loll and Ambjorn tested a 2D model, with a 'causal' assumption, and found it worked. But it took roughly 5 years to get it up from 2D to 3D to 4D.

now Loll and Westra have something remarkable working at 2D. but it is not obvious how to picture these infinitesimal very brief wormholes (compatible with the causal restriction of CDT) in the 3D case.

Well, it is Westra's thesis, so I hope it does not take 5 years!

http://arxiv.org/abs/hep-th/0507012
Taming the Cosmological Constant...

marcus

I use these links to check activity in CDT and to see what new authors are getting into this line of research. There has been some growth in the number of papers written per year

Using this kind of keyword search, I try to edit out anything they bring up by mistake. Like Lee Smolin's 2003 survey mentions dynamical triangulations but is not really ABOUT that, so I dont count it.

http://arxiv.org/find/grp_physics/1/...0/1/0/2003/0/1

http://arxiv.org/find/grp_physics/1/...0/1/0/2004/0/1

Last 12 months:
http://arxiv.org/find/grp_physics/1/...0/1/0/past/0/1

here are the authors who have recent CDT articles

Jan Ambjorn
Mohammad Ansari
Bianca Dittrich
Jerzy Jurkiewicz
Tomasz Konopka
Renate Loll
Fotini Markopoulou
Johan Noldus (postdoc with Loll at Utrecht)
Lee Smolin
Willem Westra
Stefan Zohren


this is probably not a complete list. it does not include all of Loll's graduate students at Utrecht,
http://www.phys.uu.nl/~loll/Web/students/students.html
and people like Arundhati Dasgupta who have written CDT papers but they were before 2003. but this is some of the people.

marcus

there is a German physics newsmagazine called P.U.Z.
Physik Unserer Zeit------Physics of Our Time. I think it could be a German version of "Physics Today".
and there is this physicist Claus Kiefer at Uni Köln.
and in January 2005 there was a one-page general audience article by Kiefer about CDT, in particular about the paper "Emergence of a 4D World" by Ambjorn Jurkiewicz Loll that appeared in fall 2004 in Physical Review Letters.

I didnt yet find this online in English. Does anyone have a link?

there is a horrible scarcity of (semi)POPULAR writing about CDT. In English there is almost nothing written about CDT for general audience, at least not online.

so I am contemplating translating this page of semipopular German science writing.

first let's see if I can just paste in the German text
-----------quote Kiefer from january P.U.Z.-----
QUANTENGRAVITATION: Die vierdimensionale Welt
Die klassische Raumzeit besitzt vier makroskopische Dimensionen. In einer zukünftigen Theorie der Quantengravitation ist damit zu rechnen, dass auch die Dimension zu einer dynamischen Variable wird, für die nur ein Erwartungswert angegeben werden kann. Unabhängig davon muss sich aus Konsistenzgründen im semiklassischen Limes immer die Zahl vier ergeben. Dass dem tatsächlich so zu sein scheint, konnten Jan Ambjørn (Kopenhagen), Jerzy Jurkiewicz (Krakau) und Renate Loll (Utrecht) kürzlich im Rahmen des Pfadintegralzugangs zeigen [1].

Eines der grundlegendsten offenen Probleme der modernen Physik ist die konsistente Vereinigung von Quanten- und Gravitationstheorie. Die Hauptschwierigkeit besteht hierbei darin,dass die Allgemeine Relativitätstheorie keine fest vorgegebene Hintergrund-Raumzeit kennt,sondern eine dynamische Geometrie. Bei den anderen Wechselwirkungen,beispielsweise der Elektrodynamik,quantisiert man aufeiner Raumzeit,bei der Allgemeinen Relativitätstheorie quantisiert man die Raumzeit selbst.

Den ehrgeizigsten Versuch,zu einer Quantengravitation zu gelangen,bietet die Stringtheorie,die davon ausgeht,dass dieses Ziel nur im Rahmen einer Vereinigung aller Wechselwirkungen zu erreichen ist. Andere Zugänge versuchen,Einsteins Theorie direkt zu quantisieren. Hierzu gehören Quantengeometrodynamik und Schleifendynamik. Ambjørn und Kollegen wählten einen Zugang über das Feynmansche Pfadintegral.

In der Quantenmechanik summiert man im Pfadintegral über alle möglichen Pfade für ein Teilchen zwischen zwei Orten und Zeiten. Die meisten Pfade sind stetig,aber nirgends differenzierbar. Das Ergebnis ist eine Übergangsamplitude,welche die Schrödinger-Gleichung erfüllt. In der Gravitationstheorie ist hingegen über alle möglichen vierdimensionalen Geometrien („Raumzeiten“) zu summieren,die zwischen zwei dreidimensionale Geometrien („Räume“) passen.

Formal leicht möglich ist eine so genannte Sattelpunktsnäherung,bei der sich im semiklassischen Grenzfall als dominierende Raumzeit eine solche ergibt,die den klassischen Einsteinschen Feldgleichungen genügt. Für eine saubere Berechnung jenseits dieser Näherung muss die Summe über alle Geometrien aber zunächst definiert werden. Diese Regularisierung geschieht durch Diskretisierung und anschließenden Kontinuumslimes.Als Vorbild dienen die Gittereichtheorien für starke und elektroschwache Wechselwirkung. Dort ist allerdings die Geometrie festgelegt,die bei der Gravitation dynamisch ist.


Bisher hatte man das Pfadintegral zumeist im euklidischen Bereich betrachtet,wo nur über vierdimensionale Räume integriert wird und nicht über Raumzeiten. Dieser Zugang wurde vor allem durch Stephen Hawking populär.Allerdings ergeben sich dort Probleme unter anderem im Zusammenhang mit der Dimension. Man betrachtet den Erwartungswert für die effektive HausdorffDimension H. Dieser wird durch die Beziehung V(r) ~ <r>^H definiert, wobei V(r) das Volumen einer Kugel mit Radius
r darstellt. Für einen dreidimensionalen Raum sollte sich also gerade H= 3 ergeben.

Die Hausdorff-Dimension ist aus der Theorie der Fraktale bekannt, allerdings als klassische Größe und nicht als Erwartungswert. Da in der Quantengravitation kein Hintergrund existiert,ist H a priori ungleich der Dimension d der Bausteine, über die im Pfadintegral summiert wird. Merkwürdigerweise ergibt sich für das euklidische Pfadintegral der Wert H= 2 für d> 2.

Wegen dieses und anderer Probleme schlagen die oben erwähnten Autoren den alternativen Weg der „Lorentzschen dynamischen Triangulationen“ ein. Hier summiert man tatsächlich über Raumzeiten statt Räumen,was physikalisch vernünftiger erscheint [2]. Die Diskretisierung erfolgt durch Wahl von Tetraedern zur festen (diskretisierten) Zeit,die mit dem nächsten sowie vorangehenden Zeitschritt durch vierdimensionale Simplizes verknüpft sind. Simplizes repräsentieren also die (diskretisierte) Raumzeit. Abbildung 1 zeigt eine typische Konfiguration,die in dem gezeigten Beispiel aus 91100 Simplizes besteht. Die Summe über alle Konfigurationen im Pfadintegral erfolgt durch Monte-Carlo-Simulation.

Die Autoren betrachten den Mittelwert des räumlichen Abstandes zwischen zwei Punkten im räumlichen Volumen und finden für die oben definierte Hausdorff-Dimension den Wert H= 3,10 ±0,15. Dies ist
eine gute Evidenz für die Dreidimensionalität des Raumes (und somit für die Vierdimensionalität der Raumzeit). Hieraus folgt freilich noch nicht, dass es auf kleinsten Skalen tatsächlich einen glatten dreidimensionalen Raum gibt. Doch immerhin liefert dieses Ergebnis einen Hinweis auf die Existenz einer Kontinuumstheorie. Interessant ist noch,dass diese Methode nur bei einer positiven Kosmologischen Konstante funktioniert -- in Einklang mit Beobachtungen. Der numerische Wert wird allerdings nicht festgelegt. Die sich so ergebende dynamisch erzeugte Quantengeometrie kann dann als Hintergrund für die Quantenfluktuationen anderer Freiheitsgrade angesetzt werden.

[1] J. Ambjørn, J. Jurkiewicz, R. Loll, Phys. Rev. Lett. 22000044, 93, 131301.
[2] R. Loll, in: Quantum Gravity (D. Giulini, C. Kiefer, C. Lämmerzahl Hrsg.), SpringerVerlag, Heidelberg 2003. Claus Kiefer, Köln

ABB. 1 SIMULATION: Typische Konfiguration („Raumzeit“), wie sie in einer MonteCarlo-Simulation erscheint. Nach oben sind die Zeitschritte (hier insgesamt 40) aufgetragen, die beiden anderen Achsen sind Raumdimensionen (aus [1]).

marcus

the German text by Kiefer can be found here
http://www3.interscience.wiley.com/c...60245/ABSTRACT
this is the HTML abstract, which has a link to the PDF file.

the Kiefer article can also be found by scanning the table of contents of the January issue of Physik Unserer Zeit
http://www3.interscience.wiley.com/c...ssue/109860236

and also it is at Loll website
http://www.phys.uu.nl/~loll/Web/press/press.html

Because we have a shortage of general audience description of CDT in English, I translated the short Kiefer article:

--------transl. from Claus Kiefer january P.U.Z.-----

QUANTUM GRAVITY: The four-dimensional world

Classical spacetime has four macroscopic dimension. In a future theory of quantum gravity one must take into account that even dimensionality will be a dynamical variable, for which only an expectation value can be provided. For reasons of consistency the number four must arise independently in the the semiclassical limit. Jan Ambjørn (Kopenhagen), Jerzy Jurkiewicz (Krakau) and Renate Loll (Utrecht) were able to show that in the path-integral framework it actually works out that way.[1]
--------------------------------

One of the most fundamental open problems in modern physics is the consistent unification of the quantum and gravitation theory. The chief difficulty consists in the fact that General Relativity knows no fixed prior-given background spacetime, but rather a dynamic geometry.
One quantizes other interactions, for example electrodynamics, ON a given spacetime, but with General Relativity one must quantize the very spacetime itself.

The most ambitious attempt to arrive at quantum gravity has been on the part of string theory, whose point of departure is the assumption that this goal can only be attained in the context of a unification of all the interactions.

Alternative approaches attempt to directly quantize Einstein's theory. Among these approaches are quantum geometrodynamics and loop dynamics (LQG). Ambjørn and colleagues chose an approach via the Feynmanian path integral

In quantum mechanics the path integral is summed over all possible paths a particle can take from one point to another. Most of the paths are continuous but nowhere differentiable. The result is a transition amplitude, which satisfies the Schrödinger-equation. In quantum gravity, the job is to sum over all possible four-dimensional geometries ("spacetimes") which fit between two three-dimensional geometries ("spaces")

Formally, it's easy to write down a so-called saddle-point approximation which in the semiclassical limiting case is dominated by a spacetime satisfying the Einstein field equations. But to go beyond this approximation to a clean calculation, one must define the sum over all geometries. This regularization occurs by discretizing and a subsequent continuum limit. The lattice theories of strong and electroweak interactions serve as models. There, however, the geometry is fixed ahead of time, while in the case of gravity it is dynamic.

Up till now the path integral has mostly been used in the Euclidean context, where one integrates only over fourdimensional space, rather than spacetime, geometries. This approach was made popular above all by Stephen Hawking. However problems arise there, among other things with the dimension.

Consider the expectation value for the effective Hausdorff dimension H. This is defined by the relation V(r) ~ <r>^H where V(r) is the volume of a ball with radius r. For a three-dimensional space this should come right out H = 3.

The Hausdorff dimension is known from the theory of fractals, however as a classical quantity and not a quantum expectation value. Since in quantum gravity there is no background, H is a priori NOT equal to the dimension d of the building blocks used in the path integral summation. Notably, in the Euclidean path integral the value of H turns out to be 2, even for d >2.

Because of these and other problems, the above-mentioned authors have introduced the alternative way of "Lorentzian dynamical triangulations". Here one actually sums over spacetimes rather than spaces, which seems physically more reasonable [2]. The discretization is accomplished by choosing, at some fixed (discrete) time, spatial tetrahedra which are then joined by four dimensional simplices to like tetrahedra at the next timestep. Thus the simplices represent the (discretized) spacetime. Figure 1 shows a typical configuration which in the example shown here consists of 91,100 simplices. The sum over all configurations in the path integral is performed by Monte-Carlo simulation.

The authors consider the mean value of the spatial separation between two points in a spatial volume and find, for the Hausdorff dimension defined earlier, the value H = 3.10 ±0,15. this is good evidence of the three-dimensionality of space (and thus the four-dimensionality of spacetime). From this it certainly does not yet follow that at the smallest scale there is actually a smooth three-dimensional space.

But nevertheless this result offers a pointer towards the existence of a continuum theory. Moreover it is interesting that this method only works with a postive cosmological constant--in agreement with observations.
The numerical value has however not been determined. The resulting dynamically produced quantum geometry can then serve as a background for the quantum fluctuations of other degrees of freedom.


[1] J. Ambjørn, J. Jurkiewicz, R. Loll, Phys. Rev. Lett. 22000044, 93, 131301.
[2] R. Loll, in: Quantum Gravity (D. Giulini, C. Kiefer, C. Lämmerzahl Hrsg.), SpringerVerlag, Heidelberg 2003. Claus Kiefer, Köln

FIG. 1 SIMULATION: Typical configuration ("spacetime") as it appears in a Monte-Carlo simulation. The time steps (here 40 in all) are upwards, the other two axes are spatial dimensions.[1]

----end quote from the Claus Kiefer article---

selfAdjoint

Marcus you are to be congratulated and you deserve our thanks for translating these articles. If there are no copyright issues in the way it would be nice to collect them into a permanent website for people wishing to getr some non technical info on CDT. (I like it that this article defines the Hausdorf dimension. That's something that a slightly technical public might know and respond to, from all the fractal stuff around).