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Home , Initial singularity, Lee Smolin, Planck length

FIRSTHAND KNOWLEDGE GRAVITATIONAL A of Bubbling Loops

overcome this, the most significant plastic film, but textured like terry quantum were developed to- ones being theory and loop cloth. The same also applies to time: tally isolated from each other. Then . it consists of tiny steps whose fur- the two theories slowly converged, assumes that all ther breakdown is neither possible but even today, they are still funda- types of elementary particles, from nor practical. mentally incompatible. Nevertheless, leptons to to , which Why didn’t we ever notice this scientists take both very seriously, make up and neutrons, structure before? Because it is ex- and an increasing number – current- manifest themselves as different tremely fine. The smallest unit, a ly around 300 worldwide – are work- states of excitement of a single type loop, is approximately 10-33 cen- ing on loop theory and similar ap- of object: strings. These strings vi- timeters long. This is called the proaches to quantum gravity. brate like the strings on a guitar Planck , calculated from three GRAVITY NEEDS (hence the name) in a space that has natural constants: the , NO FIXED TIME 10 or 11 dimensions. Planck’s constant and the gravita- does not tional constant. Similarly, a time Along with the Perimeter Institute in need this multidimensionality. It re- quantum is the time a particle trav- Waterloo, Canada and the Institute mains within the 4 familiar dimen- eling at the speed of light would take for Gravitational Physics and Geom- sions of space and time and postu- to move through a space quantum. etry in the US, the Insti- lates that they are not continuous, In other words, the surface of an A4 tute for Gravitational Physics in but consist of quanta (the smallest sheet of paper would be made up of Potsdam is one of the centers for this indivisible units) – the loops. Using 1068 – or 1 followed by 68 zeros – of research. Around 150 loop theoreti- this imagery, it is possible to picture these loops. cians, including all the leaders in the the world as having a web-like For more than 10 years, from 1984 field, met last October at the Loops structure: space is not smooth like a to 1996, string theory and loop 05 conference in Potsdam to share their latest ideas and progress re- ports. They also discussed how the This image, as well as that on the left above, shows an artist’s impression of theory might be put to the test in ex- quantized space. They are snapshots of a dynamic geometry consisting of loops. periments. can be present only where the geometry is activated. Of the four known forces – elec-

IBRARY tromagnetic, weak and strong forces L and gravity – gravity is the least un-

A is the Holy Grail of physicists. Yet, in the search for this theory that unites HOTO P derstood. Unlike the other forces, it

all forces, they are brought up short by the limits of what the human mind can actually grasp. CIENCE resists quantization. Quantization of : S

HOTO the other forces has been described Today, loop quantum gravity is considered a promising candidate for the solution to this problem. P by theories such as quantum electro- THOMAS THIEMANN from the MAX PLANCK INSTITUTE FOR GRAVITATIONAL PHYSICS in dynamics, quantum flavor dynamics and quantum chromodynamics. Each Potsdam is one of its leading proponents worldwide. In the following article he reports on his work. of these theories, summarized in the Standard Model of matter, is subject to physical predictions that ince the beginning of the 20th and particles. Today, we have physi- everything, one that takes into ac- have been measured very precisely HYSICS Scentury, physics has celebrated cal theories that correctly describe count and explains every force and P and confirmed by experiments in some brilliant successes. Not only natural processes over a huge range every particle. The biggest names in accelerators, such as CERN, DESY

has it developed quantum theory of distances – from the diameter of a physics have tried, but none of them RAVITATIONAL and SLAC. There is, therefore, no G

and the theory of relativity, it has al- to the expanse of the visible has yet had any success. Particularly FOR doubt that quantum theory is the so demonstrated their validity in nu- universe. And all of that with mathe- the attempt to reconcile the phe- correct description for these forces. : MPI

merous experiments. Gradually, the- matical formulas that fit on a sheet nomena of the fourth interaction, HOTO So-called interaction mediators – the ories were developed that describe of paper! namely gravity, with quantum theo- P particles that carry the forces – play the electromagnetic force, the nu- However, despite these great feats, ry always comes up against an un- a part in it. clear force and weak interaction, as physics remains essentially a patch- yielding mathematical limit. Today What is so different about gravity well as their connection with fields work. There is still no theory of there are various approaches to that it resists quantization? Does it

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seething mass of tiny loops. Similar taken to its logical limits. This guar- ÖRING HYSICS

D THE LEGO BRICKS to the way electrons incessantly or- antees that either the right theory is P OF LOOP THEORY RAFIK bit the nucleus of an atom, here, the constructed or, in the course of In loop quantum gravity, the basic structure of

geometry of space dances and analysis, it is systematically deter- RAVITATIONAL surges. mined which new structures are re- G turns out to be discrete: the values of ar- FOR eas and volumes can be changed in (naturally tiny) The edges between the crystal sur- quired, rather than having to guess

: MPI steps and there are minimum areas and space vol- . 20, 2005/F.A.Z.-G CT faces are particularly important; like at them. umes below which the space cannot be further di- , O RAPHIC the surfaces themselves, they are la- We assess a philosophy of this na- G vided – in the same way that it is not possible to Such images illustrate the construction of quantized space. On the left, a spin build an object with a Lego set that is smaller than network of polyhedrons, on the right, the development of spins over time. The knots beled with quantum numbers. As the ture, which might look like a highly loops are all linked together, every- intelligent game, based on whether it the smallest Lego brick available. The basic structure in the left-hand image can split open and create a kind of foam structure. ONNTAGSZEITUNG

S of space is a “” of linked knots as shown thing is vastly interconnected – so progresses the description of nature in the illustration. The smallest conceivable volume, a space nonlinear. Nevertheless, the theorists beyond the existing theories – and quantum, contains one knot. Any volume, therefore, consists of a certain number of knots. LLGEMEINE even need to be quantized? The an- tromagnetic fields, the interesting A use only those mathematical tools loop theory does just that. It re- If another knot is added, the space content increases by one characteristic space quantum. swer can be found by carefully con- quantities are electrical and magnetic with which they are already familiar. quires, as I already mentioned, only

sidering Einstein’s theory of relativi- fluxes. For example, magnetic flux RANKFURTER They exploit mathematics to the log- our four dimensions, and it also : F ty. According to this theory, gravity can be shown as an integral over a ical extreme. They also use every- manages to avoid a shortcoming of Quantization of space helps to nucleus would therefore fall into the is not a force in the traditional sense, surface or as a linear integral over the thing that the quantum field theo- the general theory of relativity: ap- avoid such singularities. This exam- nucleus after a short time. The atoms LLUSTRATIONS but is equivalent to geometry. A edge of this surface. This is how the I rists have come up with in the last plying its equations logically gives ple from atomic physics is an ana- would be unstable and we would planet does not orbit a star because image of loops is created – they are century. Even when they put some- rise to bizarre physical situations, logy: according to the classical positively burn up. Quantum theory interaction-carrying particles (gravi- the edges of the flux surfaces. These thing new together, they use new va- known as spacetime singularities. Maxwell theory of electromagne- explains why this does not happen: tons) facilitate an exchange of forces quantities are interesting as they are rieties of familiar constructions. These are the points in space where tism, atoms should not exist at all. the permitted energy levels in the between them; rather, the planet or- invariant (that is, unchanging) in the Accordingly, gravity creates the the curvature, and thus the concen- This is because electrons, which atom are discrete, that is, quantized. bits the star because the star bends face of movement of any kind. space in which everything happens. tration, of matter is infinitely large. move in an orbit, normally emit Experiments also allow this to be the geometry of spacetime. In the In the Maxwell theory, for exam- The theorists also want to bring mat- Black holes are such singularities, as bremsstrahlung, thus losing energy. read from the atomic spectra: there same way a ball in a mini-golf game ple, it is possible to rescale the po- ter into the game. However, as loop is the . Each that circles the atomic are no bremsstrahlung lines because is diverted by a dip and rolls toward tential – in other words, to move the theory creates its own spacetime, the the atom emits none – the classic the lowest point, the dent in space zero point – without any physical particle terminology from quantum singularity disappears. caused by the star influences the changes being visible. The loops are mechanics, which is based on a fixed According to Einstein’s general theory of relativity, gravity is synonymous Quantizing spacetime achieves a planet’s path and makes it circular. invariant in the face of such rescal- spacetime, cannot be used here. The with geometry. A “dent” caused by a star in space, for instance, affects the similar situation. Martin Bojowald path of a planet and shapes it into an orbit. Matter thus curves space. In other words, matter curves space. ing. As quantum gravity theoreti- particle term from other theories can from Pennsylvania State University

cians also deal with loop integrals, nevertheless build on loop theory, as IBRARY in the US has applied my work on A MODEL FROM L these objects of the theory have it is possible to develop a similar the dynamics of loop quantum grav- HOTO

CLASSICAL PHYSICS P commonly been dubbed loops since language for matter and, as it were, ity to a model

In this sense, the general theory of the mid-1980s. With many compli- pack it on top of what has previous- CIENCE and discovered that the singularity : S

relativity is much more than a theo- cated mathematical operations, it is ly been said. At the same time, the HOTO predicted by the general theory of P ry of gravity – it also realizes Ein- now possible to construct a dynamic forces develop from this. Photons are relativity as the Big Bang no longer stein’s basic idea of the geometriza- spacetime from these loops. To do described by loops; quarks and elec- figures in loop theory – quite like the tion of physics. For him, gravity is this, they are combined, in the form trons, on the other hand, sit at spe- example of the atom with discrete synonymous with geometry and is of spatial structures, into graphs or – cific points on this structure. energy levels. Although this is not therefore independent of fixed in mathematical terms – into func- proof that there are no singularities LOOPS REQUIRE spacetime. It is this principle of the tions. Each loop is always linked to at all in loop quantum gravity, it can ONLY FOUR DIMENSIONS underlying independence of the gen- all of its neighbors. In this way, an be considered an initial first indica- eral theory of relativity that cannot infinite number of these graphs The loop quantum gravity approach tion. Instead of singularities, there be reconciled with quantum theory. form, to put it simply, a kind of crys- is consciously conservative: it is are values that might become big, Proponents of loop quantum gravity tal. However, this crystal is not rigid, based solely on facts that are sup- but remain finite. Calculating the have implemented this idea logically but honeycombed because, like most ported by experiment; it does not re- largest possible curvature yields a and have quantized, not gravity, but objects in the quantum world, all of quire additional assumptions; and it value of one divided by the square of the geometry of space itself. its tiny elements are constantly analyzes the consequences of the in- the Planck length, or 1066 cm-2. But how can a world be construct- changing. Space thus no longer has terplay of the principles of the gen- What does this mean for the Big ed only from quanta? An analogy the smooth, Euclidian geometry that, eral theory of relativity and quantum Bang? It is not yet fully understood, from classical physics can help us in our experience, describes the visi- theory. Aiming for rigorous mathe- but it might mean that the universe here: in the Maxwell theory of elec- ble world, but rather consists of a matical consistency, the theory is had no initial singularity at all. In

50 M AXP LANCKR ESEARCH 2/2006 2/2006 M AXP LANCKR ESEARCH 51 FIRSTHAND KNOWLEDGE GRAVITATIONAL PHYSICS HYSICS P RAVITATIONAL means that things can indeed re- the person who falls into it. Seen Sapienza University in Rome and G FOR IBRARY L emerge from a . from the outside, the black hole John Ellis from CERN in Geneva cast : MPI HOTO

P A black hole is a strange phenom- looks exactly the same as it did be- doubt on this assumption with some RAPHIC

enon. From the outside, it is possible fore. The person falling is still stuck bold speculations. The trick they G CIENCE

: S to see someone fall into it, but it is in it, but is not crushed into a point. suggest is “to wait long enough” in HOTO P never possible to observe whether Whether loop theory is correct the experiment – meaning one to ten the person really falls into the center with regard to these statements must billion years! It is not necessary for because that would take infinitely first be proven through experiments. experimental physicists to sit out long – like a star, for example, that “If you have a theoretical structure this time themselves – the universe collapses into itself. Thus, viewed that explains nothing and predicts will do that for them; there are According to loop theory, space is full of tiny loops, analogous to the magnetic flow from the outside, a black hole should nothing, you are no longer doing galaxies from which light takes bil- lines of Maxwell theory. not be called a black hole but rather science,” says Lee Smolin from the lions of years to get to Earth. a frozen star. From the outside, it Perimeter Institute. Gamma ray bursts, which reach us does not look like a dot, but like a With a theory like loop gravity, now and again from distances of result of these measurements is of sphere that can’t get any smaller which deals with Planck scales of around ten billion light years, are enormous significance. If loop theo- than the , 10 -33 centimeters, experimental test- particularly suitable for informing ry is correct, it will have far-reach- which marks the sphere from which ing is difficult because the objects physicists that the different light ing consequences, and physics text- the object could still escape if it were are so tiny. It is not, however, as ab- waves have left the starting line. If books will have to be rewritten. One faster than light – but the special surd as it sounds: if loop theory is these can be broken down with suffi- of the conclusions would be that the theory of relativity forbids this. right, then our conception of space is cient precision, the light they emit world is discrete and not continuous. For an observer on the inside of wrong – it is not a smooth, flawless might reveal a frequency-dependent This is not noticeable in everyday the black hole, however, things look structure, but a crystal on the Planck shift in the transit time. Based on life, but it plays a role in drastic situ- bizarrely different. Someone falling scale that changes constantly. And predictions from loop quantum ations, such as black holes and the into a black hole falls in finite prop- this is where an experiment could gravity, it could indeed be within the Big Bang. er time precisely into the singularity. start out: in our normal world, light measurable range. The situation today is similar to According to the theory of relativity, does not pass undisturbed through a that at the beginning of the last cen- PLANCK TO SUPPLY they wouldn’t have a chance: they crystal, but is scattered widely. As a tury, when nothing was known Loop quantum gravity has provided the first mathematical PROOF OF THE LOOPS basis for calculating back further than the Big Bang. would be crushed to an infinitely result, the speed of light changes in about . However, small dot. The discrepancy between the crystal and the change depends At the Loops 05 conference, Oliver the new theory would not complete- the perceptions that the observer and on the frequency of the light. This Winkler and Stefan Hofmann from ly displace the previous rules, as it other words, the universe has always It works in a very similar way with the intrepid traveler have of a black is reflected in experiments by the the Perimeter Institute put forward finds expression only in extreme cir- existed; it had no beginning. It may, black holes. The whole theory had to hole is the result of the peculiarity of different transit times for photons another idea for experimentally test- cumstances. We still use Newtonian at some point, have been quite small, be reconstructed from scratch be- the concept of simultaneity. This has passing through the crystal. ing loop quantum gravity. They have mechanics today, although it has ac- but before that, it may have also cause many propositions relating to already given rise to a few brain- A similar thing could happen in been addressing the effects quan- tually been overtaken by the theory been just as large as it is today. black holes were based on the as- teasers in the special theory of rela- the quantized spacetime geometry of tized spacetime had on quantum of relativity. G sumption that they collapse into a tivity. loop quantum gravity: the speed of fluctuation when the very young THE INFINITELY LONG FALL point, which is not possible in loop In loop theory, the total matter light in the vacuum would no longer universe was still expanding expo- DR. THOMAS THIEMANN, 38, works at INTO THE BLACK HOLE theory. In physical terms, this is doesn’t collapse into a point, but is be an absolute value, but would vary nentially. Using a highly simplified the Max Planck Institute for Gravita- By no means does the loop theory something completely different. It instead stretched infinitely – also for over time. The more energy the pho- model, Winkler and Hofmann calcu- tional Physics in Potsdam and is one of the pioneers of loop quantum gravity. dispute that there was a Big Bang. At ton has, the more strongly it feels lated that the frequency spectrum of He has been at Pennsylvania State that time, the entire universe was the presence of discrete structures, this must have University, and the packed into a very tiny volume – but the more its propagation is disrupted changed constantly. This would still Perimeter Institute in Canada. There, A TABLE HAS STATES not to zero. From a philosophical – and the more it slows down. be making itself felt today as tem- as well as at Beijing Normal Univer- standpoint, it makes a big difference The hydrogen atom has precisely defined levels of energy. The same can be posited for a However, these transit time differ- perature fluctuations in the cosmic sity, he held a visiting professorship. whether it must be assumed that table surface, for example. According to loop theory, it also has a spectrum. The table can ences, which are a result of the im- background radiation. assume only certain values for its area, not just any random values, because its geometry DR. BRIGITTE RÖTHLEIN has turned her everything had a beginning or is quantized. If the length of the table could be measured precisely to the Planck length, pact of gravity, would be so small As the scale of the effect is around curiosity into a career. She is a physi- whether it was always there. Loop then that would be visible, depending on the table’s eigenstate. If a loop is removed, the (even if they were linear) that they 1 percent, it could be measured with cist and freelance science writer, quantum gravity has now also pro- area of the table would change by certain units of the Planck area (10-66 cm2). This is would be impossible to measure, the Planck satellite planned for writing on everything to do with the vided a mathematical basis that al- analogous to the excitation states of the hydrogen atom. Each has a different energy. even with the greatest accuracy – at launch in 2007. If the model is cor- natural sciences and technology. However, the excitation states of the table are not expressed by energy levels, but by the She is particularly passionate about

lows calculations to back before the least that is what physicists thought rect, this would also present a good RIVATE SOURCE loop variables, or more precisely, their spin quantum numbers. The area of the table also basic research, where (as here) she : P Big Bang. This did not previously has a discrete spectrum because its geometry is excited. for a long time. In 2001, however, opportunity to experimentally test sees herself as an interpreter for what HOTOS

exist with such clarity. Giovanni Amelino-Camelia from La predictions for quantum gravity. The P is often difficult subject matter.

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