In a Quanta magazine article, Dutch physicist and mathematician Robbert Dijkgraaf uses the spatial metaphor of "landscape" to explain the revolutionary importance of string theory to understanding the universe.
The main dilemma of quantum physics
Imagine that Alice and Bob are asked to cook dinner. Alice loves Chinese food, Bob loves Italian. Each of them picks their favorite recipe, purchases from a local store, and follows the instructions clearly. But when they take the food out of the oven, both are quite surprised. Both dishes turn out to be exactly the same. One can only imagine the existential questions Alice and Bob are asking. How can different ingredients make the same dishes? What does it even mean to cook Chinese or Italian food? Or did they approach the cooking process so wrongly?
This is an illustration of the central dilemma of quantum physicists. They found many examples of how two completely different concepts can describe the same physical system. In the case of physics, instead of meat and sauces, particles and forces act as ingredients, recipes are interaction formulas, and the cooking process is a discretization procedure that puts the probability of physical phenomena in accordance with formulas. Just like Alice and Bob, scientists are amazed at how different recipes lead to the same results.
Did nature have the ability to choose its fundamental laws? Albert Einstein, as far as we know, believed in a sense that there was only one way, based on a few basic principles, to build an elegant, functioning universe. From his point of view, if we investigate the essence of physics at a sufficiently deep level, then we come to the conclusion that there is only one and only possible way of interaction of all the gears of the universal clockwork - matter, radiation, forces, space and time.
String theory as a "theory of everything"
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The current standard model of particle physics is an inert mechanism made up of a meager set of ingredients. But, despite the seeming uniqueness, our Universe is only one of the countless possible worlds. We do not have the slightest idea why this particular configuration of particles and the forces acting on them is the basis of our world order.
Why are there six "flavors" of quarks, three "generations" of neutrinos, and one Higgs particle? In addition, nineteen fundamental physical constants (such as the mass and charge of an electron) are included in the standard model. The values of these "free parameters", it would seem, do not carry any deep meaning. On the one hand, particle physics is an example of elegance. On the other hand, it's just a beautiful theory.
If our world is just one of many, then what are we to do with alternative worlds? The current point of view is the absolute opposite of Einstein's idea of a unique universe. Modern physicists cover a huge space of probabilities and try to understand the logic of its interconnections. From gold prospectors, they have evolved into geographers and geologists, mapping the landscape and studying in detail the forces that shaped it.
A milestone in this process was the birth of string theory. At the moment she is the only candidate for the title of "theory of everything". The good news is that there are no free parameters in string theory. There is no question of which string theory describes our universe, because it is unique. The absence of any additional functions leads to radical consequences. All numbers in nature must be determined by physics itself. These are not "constants of nature", but simply variables obtained from equations (sometimes, though incredibly complex).
Bad news, gentlemen. The solution space for string theory is vast and complex. This is normal for physics. Traditionally, fundamental laws are distinguished, based on mathematical equations and on solutions of these equations. Usually, there are several laws and an infinite number of solutions. Let's take Newton's laws. They're crisp and elegant, but they describe an incredibly wide range of phenomena, from a falling apple to a lunar orbit. Knowing the initial state of the system, these laws can be used to describe its state at the next moment. We do not expect or demand a universal solution that would describe everything.
Ecumenical landscape
In string theory, some of the elements that are commonly viewed as laws are actually solutions. They are determined by the shape and size of the hidden extra dimensions. The space of all these solutions is often referred to as the "landscape", but this is too lightly said. Even the most impressive mountain landscapes pale against the vastness of this space. And although its geography has not yet been fully studied, it is safe to say that its continents are huge.
One of the more sophisticated assumptions in theory is that everything is possibly interconnected. If we shake the universe well, we could move from one hypothetical world to another, changing what we are used to considering the immutable laws of nature, and getting a new combination of elementary particles that make up our reality.
But how do we explore the vast landscape of physical models of the universe, which could easily have hundreds of dimensions? Think of it as a largely undeveloped stretch of wilderness, much of it hidden under thick layers of irresistible complexity. Livable places can only be found at the very borders. Here life is simple and free. Here are the basic models that we perfectly understand. They are not very important in describing the real world, but serve as a convenient starting point for exploring the immediate vicinity.
A good example is quantum electrodynamics (QED), a theory that describes the interactions between matter and light. This model has one parameter, called the “fine structure constant,” which expresses the strength of the interaction between two electrons. Numerically, it is close to 1/137. In QED, all processes can be considered as arising from elementary interactions. For example, the repulsion of two electrons can be thought of as an exchange of photons. Quantum electrodynamics proposes to consider all possible ways in which two electrons can exchange photons.
In practice, this means that physicists are faced with the need to calculate infinite sums of great complexity. But the theory also offers a way out: each additional exchange of photons adds a condition in which the fine structure constant is raised to the next power. Since the number of these exchanges is relatively small, the additional conditions do not have much impact. They can be neglected by bringing them closer to the "real" value. We will find these loosely coupled theories at the outposts of the landscape. Here the forces are weak, and it makes sense to talk about the list of ingredients - elementary particles - and the recipe for their interaction. But if we leave our habitable places and delve into uncharted wilderness, each additional condition will become more and more important. Now we no longer distinguish between individual particles. They dissolveturning into a tangled web of energy, like the ingredients of a pie in the oven.
However, not all is lost. Sometimes another outpost is seen at the end of the path. In other words, another well-controlled model, this time consisting of a completely different set of particles and forces. In such cases, there are two alternative recipes for the same underlying physics, as with Alice and Bob's dinners. These conjugate descriptions are called dual models, and the connection between them is called duality. These opposites can be seen as a grand generalization of the famous wave-particle dualism discovered by Heisenberg. In the case of Alice and Bob, it takes the form of a conversion between Chinese and Italian recipes.
Everything is interconnected
Why is it all so exciting from a physics standpoint? First of all, the assumption that many (if not all) models are part of one huge interconnected space is one of the most surprising findings of modern quantum physics. This is a change in perspective worthy of being called a "paradigm shift." Instead of an archipelago of scattered islands, we explore one vast continent.
In a sense, by studying one model deeply enough, we will be able to understand them all. We can explore the relationship of these models by focusing on the general outline of their structure. It is important to note that this phenomenon is highly dependent on whether string theory is consistent with the real world. This property is inherent in quantum physics, which is immutable regardless of what the "theory of everything" turns out to be.
More dramatic is the conclusion that all traditional theories of fundamental physics must go to the dustbin of history. Particles, fields, forces, symmetries - all these are nothing more than artifacts of a free life at the outposts of an endless landscape of unthinkable complexity. It seems incredible, or at least extremely limited, to view physics in terms of the elementary building blocks.
Perhaps there is a fundamentally new structure that unites the fundamental laws of nature and ignores all the concepts we are used to. The mathematical subtleties and elegance of string theory is a tempting motivation to accept this point of view. But let's be honest. Very few modern ideas about what will take the place of particles and fields are "crazy enough to be true," as Niels Bohr put it.
