String theory relates to psychology

The duel: strings against loops

An icy wind sweeps over the flat farmland near the small town of Golm, which was incorporated into Potsdam last year. Outside of Golm, in the middle of the fields, another world begins. A ghostly world, it would seem. Because there, mysterious superimpositions of pieces of tissue fluctuate, the fibers of which should be everything and between which there should be nothing. Strings vibrate in the highest tones and create objects of which the local population has never heard a word: photinos, gluinos, winos and zinos.

But the world we are familiar with is also a melody of strings. And it gets even stranger: there should be six or seven additional dimensions of space, rolled up - more elegant: compacted - like thin paper; multidimensional branes that flutter like magical sheets in bizarrely shaped Calabi-Yau rooms; Moduli fields and mysterious anti-de-sitter rooms; unstable vacuums, so that our universe could disappear in the blink of an eye, and maybe even more universes than a human can count. These impressions, which would have surprised or disturbed an unsuspecting hiker, are part of the everyday business of a small but industrious group of researchers who - persistently ignoring the rain-lashed days outside - in the airy new building of the Max Planck Institute for Gravitational Physics (Albert -Einstein-Institut, AEI).

The atmosphere is cooperative, but the occasion is competitive. Because as conciliatory as the conference topic sounds - "Strings Meet Loops" - the matter is as tough as it gets. And literally about the whole: the universe and its foundations. Two theoretical approaches, now well developed, are struggling to deepen the foundations of science. The general theory of relativity and the quantum theory are the two undisputed pillars that support the magnificent building of contemporary physics. But they do not get along on small space-time and high energy scales. To reconcile them requires an even bolder theory. And this should - physicists can sometimes be immodest - also unify the fundamental forces of nature and solve the riddles of the Big Bang and the black holes.

String theory and quantum geometry (also called the theory of loop quantum gravity or "loop quantum gravity") are the names of the two opponents. They pursue these goals in different ways and with different results. Hundreds of the most talented physicists worldwide have joined this project - and even developed new mathematical methods for it. Because in the unknown terrain there are no trails, and certainly no royal road. The scientists fight their way through an exotic jungle - with no guarantee that they will not get lost colossally. No one has yet been able to provide solid experimental evidence. But bizarre discoveries have already been made many times - and some splendid fruit has even been found in the process. Nevertheless, string and quantum geometry researchers are not always green.

“There is a certain speechlessness between the two camps that we want to overcome. Because it would do everyone good to sometimes think about the problems from the perspective of others, ”says Hermann Nicolai, Director at the AEI. Promoting this communication and inspecting the respective achievements and weaknesses was the main motivation of the meeting. Abhay Ashtekar, who organized the meeting with Nicolai, agrees and adds: “There are some misunderstandings to be cleared up. And most importantly: we should learn from each other. "

Ashtekar, today a physics professor at Pennsylvania State University and director of the Center for Gravitational Physics and Geometry there, developed quantum geometry together with Lee Smolin, Carlo Rovelli and others (bild der Wissenschaft 12/2003, "Beyond Space and Time" ). According to this, space and time are not fundamental and independent of matter - that is, no background metrics, as physicists say - but are made up of more elementary objects called spin networks or loops. They form a tightly woven fabric with “gaps” in between where there is literally nothing. Also no empty space, because the space emerged from the threads of the network and only appears homogeneous from our blurred, generous viewing angle - similar to how the images on these pages do not turn out to be smooth and coherent, but rather as gridded dot patterns on closer inspection . Forms of excitation of the spin networks - changing states of the lines and nodes - build up the matter and energy in the universe. The forces of nature also “live” on this network. And the time comes, at least one idea, through tiny regroupings in the spin network. This results in the picture of spin foams ("spin foams").

“A spin network represents, as it were, a section through the spin foam, a kind of snapshot,” explains Robert Oeckl from the University of Mexico. “Conversely, the spin foam can be understood as the development of a spin network over time. The smallest parts of the spin foam then correspond to space-time atoms. Accordingly, the time would also be discreet. Of course, the "bars" of time are local - the universe does not run in simultaneous time steps everywhere. ”String theory, on the other hand, is much less radical. Oeckl: “In perturbation-theoretical approaches of quantum gravity, and string theory is one of them, the metric is broken down into a background part, which characterizes the Euclidean space, and a second part, which describes fluctuations in this space. A major deficit is that the cause-and-effect structure is assumed to be static, although in reality it is changed dynamically by gravity. "

Quantum geometry does not have this difficulty - but it has a price: “Imagine if there were neither space nor time in the background and no canvas on which to paint the dynamics of the physical universe. Imagine a play in which the stage takes part in the cast. Imagine a novel in which the book itself is a main character… ”Abhay Ashtekar can strain the imagination of his audience enormously. And he knows how to get to the bottom of things - that means look so deep into the structure of the world that space and time literally dissolve in the glaring spotlight of the theory. "Yes, you can still do physics without sacrificing mathematical accuracy."

Ashtekar keeps coming back to Albert Einstein, whose heir he has assumed and whose general theory of relativity needs to be expanded. “In the context of classical physics, Einstein taught us how to weave the gravitational fields into the fabric of space-time itself. In his theory there is no background spacetime, no stage that cannot be influenced, no spectators in cosmic dance. With its gravity, matter tells space-time how to bend and, conversely, space-time tells matter how to move. But classical physics is incomplete. It ignores the quantum world. Can we connect Einstein's geometric world with quantum physics without stealing its soul? Can we realize Einstein's vision on a quantum level? "

In the 1970s, almost every theoretical physicist would have answered this question in the negative. But now there are better reasons to find a workable theory of quantum gravity.

"Every great and deep problem has its own solution", Amitabha Sen quoted the Nobel Prize in Physics Niels Bohr - and in 1981, as a student at the University of Chicago, introduced a new mathematical description into physics, with the help of which Ashtekar Einstein's General Theory of Relativity knew how to express in a new, equivalent language. That was the basis for the development of quantum geometry.

“Here the space is not continuous, but rather resembles atoms,” says Lee Smolin from the Perimeter Institute in Waterloo, Canada. This discrete structure can be characterized by the Planck length (10-33 centimeters). “The smallest possible volume is roughly a cubic Planck length, 10-99 cubic centimeters. So the theory predicts around 1099 volume atoms in each cubic centimeter. This quantum volume is so tiny that there are more space quanta in one cubic centimeter than there are cubic centimeters in the observable universe (1085). ”The space atoms are constituted by the spin network. Smolin: "If we could draw a detailed picture of the quantum state of our universe, it would be a huge spin network with an unimaginable complexity and around 10184 connection points."

Hermann Nicolai is of course only partially impressed by quantum geometry. Beyond the mathematical formalism, it is completely unclear whether this theory can really save all the essential physical features of Einstein’s theory into quantum theory. Too many aspects in the mathematical formalism have not yet been clarified. In addition, quantum geometry primarily only wants to describe gravity. The theory of matter is added by hand, as it were, but not explained from deeper principles. "String theory is a lot more ambitious here because it not only describes gravity correctly, but also wants to explain the origin of matter," explains Nicolai. “Whereby the fundamental contradiction is that string theory says: In principle, it is not possible without matter interactions to make the theory of quantum gravity free from contradictions. And the representatives of quantum geometry say: No, we are simply trying to convert Einstein's theory of relativity into a consistent quantum theory of gravity. ”Nicolai, who, in his own words, worked“ on both sides of the fence ”, is not satisfied with this situation. “This contradiction has to be resolved at some point.” And he doesn't hold back with his preferences: “Personally, I tend more towards the string side. There has to be a reason why matter exists in the world. "

String theory understands elementary particles as forms of excitation of tiny oscillating threads and, in contrast to quantum geometry, can describe all four natural forces uniformly. Your disadvantage: It can only be formulated in nine or ten spatial dimensions. (Strictly speaking, there are five different ten-dimensional string theories and one eleven-dimensional supergravity theory. All of them have proven to be closely related and are now only understood as marginal areas of a comprehensive, as yet largely unknown super theory, which the string theorist Edward Witten of the Institute of Advanced Study in Princeton M. -Theory.)

In view of its abstractness and exoticism, it is surprising how much resonance string theory has had. Last year, the higher-dimensional Calabi-Yau rooms even made it into the "New Yorker", where Woody Allen humoured them in a humorous portrayal of an office affair. In the academic world, too, the string theorist community is likely to be at least ten times as strong as that of quantum geometricians.

“This is because string theory uses the standard methods of quantum field theory, which of course require a background metric. Quantum geometry, on the other hand, is new and different from everything else. It takes a lot of time to develop a new intuition, ”says Jerzy Lewandowski from the University of Warsaw, who at the Albert Einstein Institute emphasized a different kind of unification in quantum geometry:“ All forces 'live' in the same way in spin Network and are also described in the same way in quantum geometry - even if they are not unified, as in string theory. "

Ashtekar suspects another, sociological reason for the numerical predominance of string theorists: There are simply many more particle physicists than relativity researchers. "String theory began as a natural continuation of the perturbation calculations of quantum field theory, which has had such great success in other areas." And one could speculate that quite a few particle physicists have not had much to do in recent years because the standard model of matter has been brilliantly confirmed and new energy areas can only be opened up with the accelerators of the next few years, they inevitably had to look for a new, more spectacular field of research.

“Never in the history of physics has there been such a comprehensive collective intellectual effort,” says Nicolai of the string theorists. Compared to that, apart from a lot of top-class mathematics, the results are admittedly meager. "The situation just shows that nature is still a tad more sophisticated than we can be."

Brian Greene, author of the bestseller “The Elegant Universe”, said something similar in a recent interview: “We don't yet know which idea will come out at the summit. When we have it, it will shine like a beacon and light up the whole building of physics. "

For other scientists, this is still pure wishful thinking, especially since string theory, despite all the intellectual effort, has so far not acquired merits through physical applications and verifiable predictions - but could apparently even come to terms with very different data. "All string theories have at least one of the following features that contradict our observations: no dark energy in space, no symmetry breaking of forces, the existence of so-called massless scalar fields," says Lee Smolin, for example.

“What is the quality of a theory that can be reconciled with everything, including the opposite of everything?” Carlo Rovelli from the University of Marseille has a bright quantum geometry student contradict a string theory professor. “Our arguments must relate to the world we experience and not to a world made of paper.” This sentence is already in the book “Four dialogues about two main systems of the world” (1632) by Galileo Galilei, which Rovelli calls himself A model for an equally fictional, but all the more peppery “Dialogue on Quantum Gravity” (2003). In it, the student and the professor continue the Galilean exchange of blows in a new guise.

Rovelli gleefully dissects the weak points and unfulfilled promises of string theory. “The history of science is rich in beautiful ideas that later turned out to be wrong. Admiration for mathematics shouldn't blind us. Despite the tremendous intellectual powers of string theorists, years go by and the theory still fails to provide physics. All main problems are open, and the connection to reality is getting weaker and weaker. "

Nicolai wouldn't judge that harshly. “I also see a certain danger here. In particular, I don't believe that string theory can survive another 20 years without a definitive and experimentally verifiable prediction. ”But quantum geometry also has this problem. "The quantization of areas and volumes on the Planck scale will be even less demonstrable than the supersymmetrical particles required by string models in accelerator experiments."

"Either all matter consists of strings, or the string theory is wrong," says Leonard Susskind. “That's one of the most exciting things about the theory. String theory can either be a theory of everything or it is a theory of nothing. ”The physics professor at Stanford University in California is one of the fathers of string theory, although he is not a slave to it. “The final evaluation of string theory will be based on the ability to explain the facts of nature, not on its own intrinsic beauty and consistency. String theory is in its fourth decade, but so far it has not provided a detailed model of the elementary particles or a convincing explanation of cosmological observations. "

Last year, Susskind gave his colleagues all sorts of unpleasant lectures. So there were long faces when pretty much everything that has rank and name in cosmology met in Davis, California, to celebrate the new measurements from the early days of the universe (Bild der Wissenschaft 8/2003, "The First Light" ). Susskind shocked his audience with a number that worried even researchers, for whom large numbers are part of everyday work. String theory would predict or require 10,100 or even 10,200 different vacuums - at least. In other words, string theory has astronomically many physical solutions, and each could correspond to a universe with its own natural laws and constants.If the physicists are lucky, there will be a solution among them that corresponds to our universe. But even that is not certain.

“The problem is not the poverty of wealth, but the opposite: String theory contains too many possibilities,” Susskind sums up. “For most physicists, the ideal physical theory is one that is unique and perfect, so that it determines everything that can be determined and that cannot be logically otherwise. In other words, it is not just a theory of everything, but the only theory of everything. For the orthodox string theorist, the goal is to discover the one true, consistent version of the theory and to show that the solution yields the well-known laws of nature - like the Standard Model of Matter. "

Instead, the string theorists have encountered an enormous landscape, which they with a wink of the eye call “stringency”, an immensely complex space of possibilities. “To mix up the metaphors: It's a fantastic haystack that contains innumerable straws and only one needle. Even worse: The theory gives us no indication of how the right solution can be selected from these options. "

After all, the stringency receives support from the cosmologists, who also assume a large number of different universes within the framework of the model of so-called eternal inflation (Bild der Wissenschaft 12/2001, "Classic Model"). Susskind: "The enormous number of possibilities of vacuum solutions, which is the curse of particle physicists, could be exactly what the doctor prescribes for cosmology."

Michael Douglas from Rutgers University is also trying to make a virtue out of necessity. At the “Strings Meet Loops” conference he gave a transatlantic lecture via internet video that was very controversial. Douglas also assumes at least 10,100 different string vacuums. (20 years ago 101,500 were even mentioned, which Douglas considers “out of the question”. Whereupon Hermann Nicolai got carried away with the sarcastic comparison with the medieval theologian discussion about the number of angels on a needle point.) But he thinks about it certain selection principles with the help of which the string theorists could fish out of the abundance of possibilities interesting solutions for our world. Douglas is even working on statistical methods to scour the stringency, as it were, for striking terrain formations and to explore the structure of string theory itself more closely.

Scoffers see this as a futile labor of love, as long as it is not clear whether a “realistic” universe is required at all - or whether there are not even an infinite number of vacuums, so that verifiable physics is not even possible.

Susskind has applied the “anthropic principle”: We don't need to wonder why we are living in our universe, because in almost all others there are conditions in which we could not exist - because there are no stars there, for example. Douglas is more cautious: “The valid physical theory must describe what we observe. Whether it can explain why we are watching is another question. Anthropic arguments are interesting, but do not play a central role in fundamental physics. "

A group of physicists led by Shamit Kachru from Stanford University succeeded in reaching into the haystack to find the proverbial needle. With a few tricks they managed to find a string vacuum that has at least some similarity to the vacuum state of our universe. Fernando Quevedo from the University of Cambridge and his colleagues have since tracked down other such “de-sitter spaces” in string theory that are not yet realistic, but at least have a positive cosmological constant, such as that in question for the observed accelerated expansion of space is coming (Bild der Wissenschaft 8/2003, “Phantom energy tears the universe apart”). Of course, if there are so many different vacuums, then there is a risk that our own vacuum only exists temporarily, but is unstable in the long term and breaks down into an energetically lower one. That would be the end of our universe. But Quevedo reassures: "Such transitions take a very long time - usually much longer than our universe already exists."

“We shouldn't be blinded by the awe of the math behind string theory. Despite the tremendous mental power that researchers have put into it, it does not provide physics. All of the main problems remain unsolved. I think it's time to try something different, ”said Rovelli for quantum geometry. “There are only two options: Either we construct the quantum fields from scratch, as in quantum geometry. Or we undo Einstein's discovery and reintroduce a fictional background space as in string theory. Then the theory of relativity is not fundamental. "

Abhay Ashtekar is more conciliatory: “Both groups agree that the final theory should be independent of the background metric and should unite all natural forces. The question is what to start with and what to emphasize in order to keep the program going. "Lee Smolin, who has also worked in string theory, sees it similarly:" For science, it is best to pursue multiple perspectives and when researchers have the opportunity to tackle unsolved problems with different approaches. "Brian Greene also emphasizes the common elements:" Perhaps we will develop the same theory from different perspectives. It is possible that the different routes to quantum gravity meet. It can turn out that the strengths of quantum geometry are our weaknesses and vice versa. "

“Before you can give a final rating, you first have to see how everything fits together in the end. Any solutions can always be presented for individual aspects, ”says Hermann Nicolai and frowns critically. Despite his preferences for string theory, he admits, “The goal is to find a theory that describes all of physics. Einstein already had the dream of putting all of this into a formula that would fit on a piece of paper. That is also the dream of string theory - only it has not yet arrived there. ”Of course, quantum geometry cannot do this either. And whether it can succeed with combined forces also remains open. Nicolai: “I doubt that the two approaches will resolve harmoniously in a single theory, because they are based on diametrically opposed assumptions. But it was precisely the intention of our meeting to highlight the differences and differences of opinion. "

What is certain is that Einstein's dream is not over yet. The great physicist called both sides of his relativistic field equations - geometry on the one hand, matter on the other - as "marble" and "wood". Like Einstein, Ashtekar and his colleagues believe that the world is ultimately built on the stone foundation of geometry and not on the rotten wood of matter. The string theorists, on the other hand, can use their vibrating strings to make both songs sound. It remains to be seen who will strike the last note - or whether a third party is needed in the game.

COMPACT

• The world is woven from tiny threads or nets. That is the assumption of two bold theories that aim to complete Einstein's dream: the unified description of all natural forces and the explanation of space and time. • Now the two leading approaches to a theory of quantum gravity have collided: strings versus loops. Bild der Wissenschaft reports on the dispute on the research front.

Rüdiger Vaas

April 20, 2004

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