Czech physicist Petr Hořava on string theory and the quest to unify general relativity and quantum mechanics

Petr Hořava, photo: Jiří Němec

Petr Hořava is a Czech prize-winning physicist specialising in string theory who teaches that as well as quantum field theory at the University of California, Berkley. Hořava is a member of the theory group at Lawrence Berkeley National Laboratory and was awarded the Czech Republic’s Neuron Prize for his contribution to theoretical physics in 2015.

Petr Hořava,  photo: Jiří Němec
He is in the Czech Republic currently and I was lucky to be able to meet the professor to ask what set string theory apart and how it could help unlock some of the secrets of the universe. Before we got to that, however, something a little more basic: how he discusses his job when meeting people on social occasions, say, a party.

"I usually say I am a scientist and sometimes get a blank stare but then I say that it is about trying to figure out the fundamental laws of the universe and then their eyes light up and they want to know what the open questions are and where it is leading. Why are we living in a universe whose expansion is accelerating. And of course there are a lot of areas we don't have a lot of good answers. But the questions are exciting for people at cocktail parties, not that I go to a lot of those!"

It is true though that it is something that interests a lot of people and these are questions that have been popularized by TV shows and movies and especially in popular science books. To my mind A Brief History of Time was one of the first, but there have been many more by experts and physicists since, from John Gribbin to Brian Greene...

"I would venture that there could even be more because of the many exciting and fascinating stories and discoveries. There is a lot of incredible work going on even as we speak."

One of the things that is central in every introduction in such books is that there are two major areas which dominate modern physics: general relativity and quantum mechanics, which, however, are not compatible. Is it the hope of string theory to bring them together?

"Absolutely. That is certainly one of the main aims, although it didn't start that way. Historically, it was invented for a completely different reason, and for that reason the discovery of string theory is sometimes compared to the discovery of penicillin, it was discovered by accident, looking for something else. What it turned out be was a mathematically consistent framework which those two apparently very different and distinct pictures of the universe can be unified in one consistent picture. That doesn't mean it is the correct theory of the universe, but it is the really only self-consistent mathematical framework that is available to us at the moment."

"Even though general relativity as a theory of gravity is probably considered the most beautiful physics theory ever proposed, it also suggests its natural demise."

So there is hope.

"There is hope and we believe that the universe is self-consistent and the fact that the two great pillars of modern physics, general relativity describing gravity on the one hand and quantum mechanics describing all the elementary particles and all their interactions on the other, should be consistent with each other. Before string theory it was not clear whether the two would be unifiable but that was probably more a lack of our imagination than an inconsistency of the universe."

I suppose that put scientists in an uncomfortable position to have to consider that one of the theories was wrong, that Einstein might be wrong.

"Actually, ironically the history was quite different. Historically, the scientists who were dealing with cosmology and the larger universe and gravitational forces were quite a different group of people from those who were studying the microscopic laws of partial physics and even material science. Those communities were quite separate and they didn't even realize how apparently incompatible their points of view were until people started asking how would these different frameworks fit together. That question wasn't really appreciated until the 1970s or '80s of the previous century. So, it has really been a quest, an active quest, for the unification of those two paradigms over the past 30 or 40 years at best."

When we look at the four fundamental forces of nature: gravity, weak and strong nuclear force, electromagnetism. Gravity seems to be the odd-man out...

"Absolutely."'s the only one we experience on a daily basis, whether we realize it or not...

"Yes exactly. It is the first one you experience as a small child. The other three are somewhat mysterious before you encounter things like electromagnetism which is a fairly elementary force but it takes some power of abstract thinking to appreciate. But gravity is something we experience all the time from the first moments of childhood. Yet, in some ways it is the most mysterious of the forces. the other three can be unified within a fancy extension of quantum mechanics called quantum field theory, which deals with systems of many particles but gravity seems to be somewhat resistant to that. And outside of string theory there is no other elementary known mechanism for how to bring gravity into the equation. The other three interactions can be unified in a relatively straight forward way in a mathematically consistent framework which stays within the boundaries of quantum mechanics. As you said, it is gravity that is really the odd man out."

Illustrative photo: archive of ESO,  CC BY 3.0
It is string theory that tries to bring gravity into the picture...

"Absolutely. And it also suggests some very natural ways of even unifying the other three interactions, although there you can also use more conventional means within quantum mechanics. String theory suggests very natural options but of course we don't know until they are proven in experiments, where we can reach high enough energies that we can probe whether any of these unified theories are actually realized in Nature. But there are several different options, several different mechanisms and string theory prefers some of them over others. In that sense it can even serve as a selection principle."

I understand that solving how the four forces of nature relate to each other could have enormous applications when you read that when the universe was just a few hundredths of a second old, it was incredibly hot and that at the moment the forces were much more closely unified...

"Sure. The regime where the forces 'talked to each other much more' came to the forefront in the early universe and we certainly know, based in observational data in cosmology, that there was in the universe in that time period that the energy was high enough to probe this mysterious regime of unification of all forces. As for applications, as with any fundamental quest for the basic laws of nature, real application which would be appreciable by society are many dozens, if not hundreds of years down the line. Much like other discoveries.

"If you look at the research into the discovery of the laws of electromagnetism, first there was a quest for just finding the truth: a mathematical description of all the phenomena that we were observing. We are very much at that stage right now with the unification of gravity with other interactions and looking for the answers to the basic puzzles: how do things work, how do they consistently work together and have the consequences that we have already observed, without asking how the answers to these questions will influence our everyday life.

"The influence of phenomena like electromagnetism are now obvious and we use a lot of technology today, developed over hundreds of years since the backs laws of nature in that area were discovered. With gravity and quantum gravity I think we are at that early stage where applications will definitely come but only once we understand how the laws work and now it is just a quest for finding the truth."

The kind of inverse of that is that after all this kind of achievement is reached, the rest of us can forget or never learn how it was achieved altogether and just enjoy the benefits...

"Sure. It is a very interesting and rather ironic fact that as much as the general public is interested in discoveries and the nature of the universe, the mathematical details of how things actually work, the formulation of how string theory works, for example, then I am afraid it is inaccessible to most people. That doesn't mean that it lessens the importance that discoveries or understanding of fundamental laws can have for your everyday life. I don't understand how my cell phone works but that doesn't stop me from using it on a daily basis and considering it an important advance. And with other areas of physics it is very much like that."

How does string theory affect relativity and quantum mechanics to make them compatible?

"String theory allows us to modify gravity in Einstein's approach without modifying the laws of quantum mechanics."

"That is an interesting question because a priori before you have any theory of how to bring them together, you don't know which side has to be modified, perhaps both have to be modified... There have been attempts in history to modify the laws of quantum mechanics and attempts to modify the laws of gravity. What happens in string theory, and I think there is an important lesson in this, is that it does not modify the laws of quantum mechanics one bit. It takes quantum mechanics as is, as it was formulated almost one hundred years ago. The lesson there is maybe that the laws of quantum mechanics are very, very difficult, if not impossible, to modify.

"On the other hand, string theory very naturally modifies and improves and enhances the laws of general relativity and gravity. It modifies Einstein's theory in a way some people suspected would have to happen. Even though general relativity as a theory of gravity is probably considered the most beautiful physics theory that we have ever proposed as a civilization, it also suggests its natural demise and its natural limitations because it has a certain energy scale built in. Once the curvatures of space-time and the energies become large enough compared to this natural, fundamental scale of gravity theory asks for its own modification. That is exactly what string theory in principle provides. It allows us to modify gravity in Einstein's approach in a very predictable and calculable way but without modifying the laws of quantum mechanics."

One of the consequences of string theory, which also captures the popular imagination, is the necessity - mathematically - for more dimensions. I have read, under various approaches that there can be 26-dimensional space-time, 10 for superstring, and 11 for string theory...

"That's right."

How should we imagine these dimensions? They are too tiny to observe...

"Exactly. The most likely scenario is that if string theory is realized in the universe, well let's take one step back: if you think about how complex phenomena in the universe are, how many different fundamental elementary particles exist, how many complicated interactions there are, we probe all of that in colliders. Then there is cosmology and that too has very complicated features and laws... All of that complexity, if you are curious where it comes from, can be explained by string theory, by the fact that we don't live in a simple 3 plus 1 dimensional universe but that all these dimensions are required for mathematical self-consistency.

"The extra dimensions curl up into some small compact objects, some small compact manifold which itself can have a lot of geometric features. The geometrical complexity of extra dimensional space-time can be directly responsible for the complexity of the spectrum of elementary particles.

Photo: Public Domain
"The different ways in which a string can wrap around all these non-trivial geometric features of the extra dimensions can explain why we see so many different elementary particles, for example. Earlier on, we mentioned some of the three Grand Unifying Theories of the three non-gravitational interactions, they themselves are quite complex theories and there is a certain order of complexity in these theories. if you compare that to the complexity that is required to the geometrical complexity of string theory compactified in three plus one dimensions on these tiny extra-geometric objects, surprisingly enough, the order of complexity is about the same. Which suggests that there is potentially a string theory explanation for why our world is as complex as it is, as opposed to being much simpler or much, much more complicated. It all has to with the fact that you six or seven extra dimensions in string theory or M-theory, available to you, and the geometrical complexity of six or seven dimensional spaces explains the complexity of the elementary particle spectrum."

Is another way of saying it, is that it is a kind of architecture? Or is that a stretch?

"It sounds like that. The architecture of the universe explains what can populate the universe, who can inhabit this architectural structure, explains why we have electrons and quarks and neutrinos, in principle. The problem is, I shouldn't try and oversell string theory... It provides the conceptual framework but the problem is - and again this is a theory that seems about right in complexity proportionately to what we observe in particle accelerators in particle physics, it appears about the right 'size' to explain the universe - unfortunately the problem is that string theory at the moment at least and at our level of understanding, has just way too many solutions. It is a unique theory, but it suggests ways too many optional universes.

"The question is, do we live in one such a particular universe and why this one and not one of a zillion others. Or is it possible that all of these possible solutions are somehow simultaneously realized and we don't live in just a single universe but some kind of very complicated multi-verse where all of these options are somehow true in one corner or another of this multiverse structure."