Idag publicerar Physical Review Letters vår nya teori om universums mörka energi. För teoretisk fundamental fysik är PRL den mest prestigefulla tidskriften (Nature och Science kan i sammanhanget jämföras med Hemmets Journal). Artikeln omnämndes i somras av Scientific American i en intervju om den nya krisen inom strängteorin.
I korthet går det ut på att hela vårt universum rider på randen av en bubbla som expanderar i en extra dimension. Det ser ut ungefär så här:
Vårt universums tre rumsdimensioner svarar mot randen av bubblan, medan radien av den växande bubblan är den extra dimensionen. Liknande bilder av vårt universum kan man hitta i den populärvetenskapliga litteraturen men vad vi visar är att det bokstavligt kan vara sant om man har koll på sin strängteori. Av strängteorins nio rumsdimensioner måste fem vara riktigt små och ihoprullade medan fyra hyfsat stora för att det skall fungera. Den fyrdimensionella (eller femdimensionella om man räknar in tiden) rymden är instabil och här och var bildas bubblor som börjar växa. Detta svarar mot ett universum som föds. Det märkliga med modellen är att bubblorna expanderar på ett sådant sätt att den som rider på randen får för sig att det finns en mörk energi. Egentligen handlar det bara om en effekt av den extra dimensionen.
Men hur är det med de underliga dödsstjärneliknande strålarna på bilden? För att allt skall fungera måste den materia som du, jag och stjärnorna består av utgöras av strängar som sträcker sig ut i den extra dimensionen. Deras ändpunkter på bubblan tolkar vi som fundamentala partiklar typ kvarkar och elektroner.
Och varför skall man tro på detta? För att det ser ut att fungera och att andra alternativ inom strängteorin inte längre verkar hålla ihop. Nästa steg blir att kontrollera alla matematiska detaljer och hitta sätt att testa teorin mot observationer…
Our universe rides a dark bubble in an extra dimension
Today, Physical Review Letters publishes our new theory about the dark energy of the universe. For theoretical fundamental physics, PRL is the most prestigious journal (Nature and Science can in this context be compared to The Sun). The article was mentioned this summer by Scientific American in an interview on the new crisis in the string theory.
In short, our universe rides on the boundary of a bubble that expands into an extra dimension. It looks like this:
Our three space dimensions correspond to the boundary of the bubble, while the radius of the growing bubble is the extra dimension. Similar images of our universe can be found in the popular science literature, but what we show is that it can literally be true if you believe in string theory. Of the nine space dimensions of string theory, five must be really small and rolled up while four fairly large for it to work. The four-dimensional space (or five-dimensional if you include time) is unstable and here and there bubbles are formed that begin to grow. This corresponds to the birth of a universe. The marvelous thing about the model is that the bubbles are expanding in such a way that the rider on the bubble observes dark energy. Actually, it’s just an effect of the extra dimension.
But what about the strange death-star-like rays in the picture? For
everything to work, the matter that you, me and the stars consist of must be
strings that extend out in the extra dimension. We interpret their end points
on the bubble as fundamental particles like quarks and electrons.
Why should you believe in this? Because it seems to work and that other
options within string theory no longer seem to hang together. The next step is
to check all mathematical details and find ways to test the theory against
String theory is not in crisis – on the contrary – but string theorists are. The theory refuses to adopt to human preconceptions, and the ruling paradigm since the turn of the millennium is questioned.
After the discovery of dark energy, just over 20 years ago, there was a healthy shift in the attitude to string theory. The hope of developing a unique theory of everything, capable to predict in detail all the properties of the standard model of particle physics, as well as the absence of dark energy, gave way to its exact opposite. Our universe was nothing more than a tiny corner of a gigantic multiverse with wildly varying properties – including the value of the dark energy. In this way, finely tuned aspects of the fundamental laws of nature, apparently necessary for the appearance of stars, planets and life, could easily be explained by the anthropic principle. If the value of the dark energy had been any bigger we would not have been here. There is furthermore no particular reason why it should be much smaller than this. So simple chance, conditioned on the fact that we actually exist, suggests that the most likely value is close to what we actually observe.
There was only one catch, how would you construct all of these solutions within string theory? Luckily, new and powerful tools had been developed during the 1990’s, and they were rapidly put to work. The progress was astounding, and an enormous number of solutions, the string theory landscape, was claimed to exist. An estimate of 10500 became popular, and was used to indicate the vastness of the multiverse. Physics had finally matured in a way that biology had done already in the 19’th century through the discovery of evolution. Neither the living world, nor the universe itself, had to be the result of design or purpose. It was just that the universe (let us call it the multiverse) was so much larger than what we so far had been able to observe (let us call it the universe).
An almost perfect parallel are the conditions on Earth so miraculously habitable to life. Surely, this is in need of an explanation. If the Earth had been the only planet in the universe, you would have had to choose between two options: someone made it so on purpose, or the nature of the Earth is by necessity and built into the mathematical laws. The latter is what the German astronomer Johannes Kepler believed in the beginning of the 17’th century, when he tried to mathematically deduce the distances between the planets of the solar system. But why would math care about life? The way out of the dilemma is the realization that Earth is not alone. The universe is large and there are billions upon billions of possible planets. By pure luck, some of them should have just the right properties and we must live on one of them. This is the essence of an anthropic explanation. String theorists argued that a similar reasoning applies to the laws of particle physics and the dark energy, and when the string theory landscape was discovered it seemed case close.
Not all were as positive, and there were critics. The multiverse was seen as a sign that the string theorists had lost it, and were working on a theory that could not predict anything. The theory was deemed meaningless.
Ironically, it now seems as if the proponents of the stringy multiverse, as well as their critics, were equally wrong. The theory now seems to be much more clever and meticulous, and it is likely that not a single one of all those vacua exhibiting dark energy actually exists. The criticism against the theory turned out to be completely beside the point and, in a sense, not even wrong. The problem was instead that the string theorists themselves had been led astray not appreciating how wonderful string theory actually is.
During the last decade or so, hints have been accumulating that there are no de Sitter vacua in string theory at all. (de Sitter vacuum is a technical term for having a positive cosmological constant – the simplest kind of dark energy). When you are able to perform reliable calculations, you cannot find any, and when you do find a solution, your calculations turn out to rely on unjustified assumptions or good fate.
Together with another string theorist, Thomas van Riet, we wrote a review this spring describing some of the efforts elucidating the properties of the landscape. In the work we have been involved in over the past decade, we have seen one mysterious conspiracy against de Sitter after the other. Despite its richness, the theory always seems to fail in one way or the other to yield de Sitter. In fact, could it be that the string theory landscape is completely barren, and all the de Sitter are out in swampland1 and shown by string theory to be inconsistent?
A turning point that finally caught the attention of people in the field came just recently in a paper by Cumrun Vafa – a leading figure within the field of string theory for decades. In a talk at the conference Strings 2018 on Okinawa, Japan,, at the end of June, he puts forward a conjecture that would rule out the complete string landscape, and put all that we hoped for into the swampland. The battle about the landscape of string theory has begun.
It reminds me be a bit about the Monty Python Dead Parrot sketch:
Adopted to the present context it would run something like this:
Mr. Pheno: I wish to complain about this string landscape what I purchased not 20 years ago from this very boutique.
Owner of string theory shop: Oh yes, the, uh, the one with dS vacua…What’s wrong with it?
Mr. Pheno: I’ll tell you what’s wrong with it, my lad. It’s barren, that’s what’s wrong with it!
Owner: No, no, it’s full of stable dS vacua!.
Mr. Pheno: Look, matey, I know a swampland when I see one, and I’m looking at one right now.
Owner: No no it’s not barren! Remarkable landscape, the de Sitter one, isn’it, ay? Beautiful supersymmetry!
Mr. Pheno: The supersymmetry don’t enter into it. It’s a stone dead swampland.
Mr. Pheno: No, there isn’t, that was you hitting my computer!
Owner: I never!!
Mr. Pheno: Yes, you did!
Owner: I never, never did anything…
Mr. Pheno: Look, I took the liberty of examining that landscape when I got it home, and I discovered the only reason that the de Sitter vacua seemd to be there in the first place was that they had been NAILED there.
Owner: Well, o’course they were nailed there! If I hadn’t nailed that landscape down, your computer would have exploded, VOOM! Feeweeweewee!
These are exciting times. String theory is an extrapolation of quantum field theory and general relativity from which we are starting to learn the rules of the game when constructing a theory of quantum gravity. What we thought would easily work turns out to be much more tricky – and interesting. The string landscape is becoming a swampland, but somewhere there should still be a little island that could harbor our universe. That is a least what string theorists hope.
It is not at all true that string theory cannot be tested. Its first test, which we thought was easy to pass, is to accommodate the accelerated expansion of the universe. At the moment, we do not know how, and if no answer is found string theory does not work. We would have to go back in our tracks and see where it went wrong.
I am an optimist. Finally, the community has a clear goal, an important puzzle, to resolve. There are a few possibilities. Vafa suggests quintessence pointing out that even if the universe is accelerating it may not go on forever. The acceleration might be decreasing, lasting no longer than string theory permits and for us to appear, with a scary and rapid end. Instead of the universe growing old and wary through billions of billions of billions of… years of expansion, it might end in a catastrophic breakdown of the known laws of physics in just some tens of billions of years. Enjoy it while you can.
Another possibility that I find even more intriguing, and have developed together with a number of other string theorists, is that we are living on the edge of bubble expanding into an extra dimension. The positive dark energy is not a property of a stable vacuum, but induced in a subtle way through the interplay between the bubble walls on which we are living and the higher dimensions. In this way you can perhaps find a way around the difficulties and turn the instability that killed the landscape into a virtue. Or maybe the answer is something all together different?
As Vafa puts it in his response to a question during his talk: “You might be right, I’m not saying you are wrong. You might be right, but this might also be right.” It has nothing to do with postmodern relativism, By studying the mathematics of the theory we will find out what it predicts, and by comparing with observations we will learn whether it has anything to do with reality. I, for one, think it has. It is just good old natural science. There is a chance that there will be some exciting progress in the next few years, but it may take some time before we really know. To quote the Swedish author and Nobel Laureate Harry Martinson: “It takes time to know it all. Meanwhile, Nature just carries on.”
1. The swampland refers to laws of nature that cannot be realized in string theory and, therefore, would be inconsistent.↩
2. A popular technique argued to give a positive cosmological constant.↩