There are no laws of physics, only landscape

Original author: Robbert Dijkgraaf
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Scientists are looking for a single description of reality. But modern physics allows us to describe it in a variety of ways, many of which are equivalent to each other, and are connected through a vast landscape of mathematical possibilities.

Suppose we asked Alice and Bob to cook a meal. Alice likes Chinese food, Bob - Italian. Each of them chose their favorite recipe, purchased at a local store specializing in the right products, and carefully followed the instructions. But when they got their dishes out of the oven, they were very surprised. It turned out that both dishes are identical. One can imagine what existential questions Alice and Bob will ask. How can different ingredients make the same dish? What does cooking Chinese or Italian dish mean? Is there a fatal flaw in their approach to cooking?

It is precisely this perplexity that is experienced by specialists in quantum physics. They found many examples of two completely different descriptions of the same physical system. Only in the case of physics, the ingredients are not meat and sauce, but particles and forces; recipes are mathematical formulas coding interactions; and cooking is a quantization procedure that turns equations into probabilities of physical phenomena. And, like Alice and Bob, physicists are perplexed about how different recipes led to one outcome.

Can nature choose its fundamental laws? Albert Einstein, as you know, believed that there was a unique way to build a consistent, working version of the Universe based on basic principles. From the point of view of Einstein, if we get deep enough into the essence of physics, there will be only one way in which all components - matter, radiation, forces, space, time - will be connected with each other, so that reality works, similar to Like gears, springs, dials and pulleys of a mechanical watch, they uniquely combine and count time.

Current Standard ModelParticle physics is in fact a carefully fitted mechanism with a small amount of ingredients. And, nevertheless, instead of remaining unique, the Universe is one of an infinite number of possible worlds. We have absolutely no idea why exactly such a set of particles and forces lies at the basis of the structure of nature. Why are there six flavors of quarks, three generations of neutrinos and one Higgs particle ? Moreover, the Standard Model lists 19 nature constants — such values ​​as electron mass and charge — that must be measured experimentally. The values ​​of these " free parameters“seems to have no deep meaning. On the one hand, particle physics is a miracle of elegance; on the other, the story of what it is, because it is.

If our world is one of many, what to do with alternatives? The current point of view can be seen as the opposite of Einstein’s dream of a unique cosmos. Modern physicists are taking a huge space of opportunities and trying to understand its common logic and interconnectedness. From gold prospectors they turned into geographers and geologists, marking out the details of the landscape and studying the forming it.

To change the situation and change the perspective helped string theory. At the moment, it is the only viable candidate for a theory of nature capable of describing all particles and interactions, including gravity, while obeying the strict logical rules of quantum mechanics and the theory of relativity. The good news is that there are no free parameters in string theory. She has no adjustment knobs to play with. It does not make sense to ask which string theory describes our Universe, since it is only one. The absence of additional features leads to radical consequences. All numbers of nature must be determined by physics itself. There are no "natural constants", only variables fixed by equations (it is possible that they are extremely complex).

And that leads us to bad news. The solution space of string theory is huge and complex. In physics, it happens. We traditionally distinguish between the fundamental laws given by mathematical equations and their solutions. Usually there are only a few laws and an infinite number of solutions. Take Newton's laws. They are strict and elegant, but they describe a huge number of phenomena, from a falling apple to the moon's orbit. If you know the initial conditions of a particular system, the capabilities of these laws allow you to solve equations and predict what happens next. We do not expect or require unique solutions that describe everything.

In string theory, certain features of physics that we would normally consider the laws of nature — for example, certain particles or interactions — are in fact solutions. They are determined by the shape and size of the hidden extra dimensions. The space of all decisions is often called the “landscape”, but this is a monstrous understatement. Even the most fascinating mountainous terrain will seem nonsense compared to the immensity of this space. And although we understand its geography very poorly, we know that there are continents of huge dimensions on it. One of his most seductive features is that everything is probably connected with everything — that is, any two models are connected in a continuous way. If you shake the universe hard enough, we must be able to move from one possible world to another, changing

But how can we explore the vast landscape of the physical models of the Universe, in which there may be hundreds of dimensions? It is useful to imagine the landscape as undeveloped wildlife, most of which is hidden under thick layers of impassable complexity. And only at its very edges can we find habitable places. On these outposts, life is simple and pleasant. Here we find completely understandable to us basic models. They are of little help in describing the real world, but serve as convenient starting points for exploring the surrounding area.

A good example is QED, quantum electrodynamics , which describes the interaction between matter and light. In this model, there is one parameter, the fine structure constantα, measuring the strength of the interaction of two electrons. In absolute terms, it is close to 1/137. In QED, all processes can be viewed as a consequence of elementary interactions. QED offers us to consider all possible ways that two electrons can exchange a photon, which in practice would require physicists to find an extremely complex and infinite sum. But the theory gives us a workaround: each subsequent exchange of a photon adds a member in which α is present, raised to an additional power. Since this number is rather small, members with a large number of exchanges make little contribution. They can be neglected, roughly evaluating the "real" value.

We regard these loosely coupled theories as outposts of the landscape. Here the power of interactions is small, and it makes sense to talk about the shopping list, consisting of elementary particles, and the recipe for calculating their interactions. But if we leave the closest entourage and go to the wild, communications will become larger, and each additional member will become more important. And now we can no longer distinguish individual particles. They dissolve into a tangled net of energies, like the ingredients of a cake in a hot oven.

Not all, however, is lost. Sometimes the path through a dark thicket ends at a different outpost. That is, on another well-controlled model, assembled from a completely different set of particles and interactions. In this case, they become two alternative recipes for the same underlying physics, like the dishes of Alice and Bob. These complementary descriptions are called dual models, and their relationship is dualism. We can consider these dualisms in the form of a great generalization of the famous wave-particle duality , discovered by Heisenberg. In the case of Alice and Bob, it takes the form of a transition between Chinese and Italian recipes.

Why is it so interesting for physics? Firstly, the conclusion that many, if not all, models are part of a huge interconnected space is among the most amazing results of modern quantum physics. This is a change of perspective, worthy of the term " paradigm shift". She says that instead of exploring an archipelago from individual islands, we discovered one massive continent. In a sense, by studying quite deeply one model, we can study them all. We can study how these models are related, will reveal to us what is common in their structures. It is important to emphasize that this phenomenon for the most part does not depend on the question of whether the string theory describes the real world or not. This is an internal property of quantum physics that will not go away no matter what the future of the theory of everything.

A more radical conclusion is that we will have to get rid of all the traditional descriptions of fundamental physics. Particles, fields, interactions, symmetries are all artifacts of simple existence at the outposts of this vast landscape of impregnable complexity. Apparently, the approach to physics in terms of elementary building blocks is incorrect, or at least very limited. Perhaps there is a radically new platform that unites the fundamental laws of nature, ignoring all familiar concepts. The mathematical entanglement and coherence of string theory strongly motivates such a point of view. But I must say honestly. Very few of today's ideas about replacing particles and fields turn out to be “too crazy to be true,” to quote Niels Bohr.. Like Alice and Bob, physics is ready to throw away old recipes and embrace modern fusion cuisine .

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