God is an eternal and endless truth that has no value or meaning.Today I want to tell you about the most daring and beautiful hypothesis in modern theoretical physics. Many scientists are extremely skeptical about it, some call it openly schizophrenic delirium, while others find it extremely interesting. Let's embark on a journey that could forever change the way you think about the universe.
Baruch Benedict Spinoza
In search of a "theory of everything"
Since the middle of the 20th century, the most difficult and promising task of theoretical physics has been the search for the so-called "theory of everything", which will combine general relativity and quantum mechanics, thereby providing an accurate explanation of all observed physical phenomena. Numerous string theories, the theory of quantum loop gravity and many others claim to be such a theory. But we will not talk about them. We'll take it a step further.
MIT professor Max Tegmark, in his book Our Mathematical Universe, encourages us to think about the most amazing property of all existing physical theories, which people usually take for granted - all our physical theories are described by mathematics.
From the point of view of empiricism(philosophy of the primacy of matter in relation to the idea) this is not surprising, man invented the language of mathematics, observing the real world. We invented numbers and counting to count objects, we invented geometry to build durable buildings. Over time, our mathematical tools became more complex and distant from everyday needs - we invented differentials, integrals, calculus, group theory, topology. But in the end we always found physical phenomena that were amazingly well described using these very tools.
But let's look at the mathematical nature of physical laws from the point of view of idealism.(philosophy of the primacy of ideas in relation to matter). All mathematical laws live in the space of ideas and do not even depend on the existence of our Universe. Even if nothing existed, twice two would still equal four. The birth of galaxies and stars, planetary movements, chemical reactions and genetic mutations strictly followed mathematical formulas long before humans appeared. We only discovered these laws, but we did not invent them.
So what will happen to the theory of relativity, quantum mechanics or the notorious theory of everything, if we throw out all the verbal husks from them, like the words "quantum", "space", "light". Only formulas will remain there, nothing else. And in this place of reasoning Max Tegmark asks an interesting question: what can be fully described by pure mathematics? And he gives the only reasonable answer to it. Pure mathematics can only describe pure mathematics itself. Thus Tegmark arrives at the most striking possible hypothesis: our entire universe is a mathematical structure.
All out of the bit
Max Tegmark was not the first to come up with this idea. Long before him this idea was put forward by the famous American physicist, scientific advisor Richard Feynman, Hugh Everett and Kip Thorne, as well as the author of the terms "black hole" and "wormhole" John Wheeler .
In his article "it from bit" John Wheeler reflected on the fact that all the properties of elementary particles like mass, charge, spin, color, strangeness and beauty do not have any meaning of their own, but only appear when interacting with other particles.
Thus, all these properties are essentially a bit of information in some mathematical structure. Wheeler wrote:
— , , - — , , , — - — , , , «» «», , . « » , — — ; , , «-»-To give you a better understanding of what John Wheeler meant, I'll give you an example of a picture from Max Tegmark's book about how the relationship between points in space (edges of a cube) can be represented as a matrix of bits:
The vertices of this cube themselves, denoted by an index from 1 up to 8, do not make any sense, but the matrix of relations between them (the edges of the cube) already has some unique properties: for example, rotational symmetry. Our Universe, of course, has orders of magnitude more complex than a cube, but it is based on the same principles. Having understood this, we can move on.
Inflationary model of the Universe and fractals
If we do live in a mathematical model, then in which one?
Let's look at our Universe: it is made up of many clusters of billions of galaxies, galaxies are made up of billions of stars, many stars have several planets, and many planets have a number of satellites. Moreover, according to the hypothesis of eternal inflation , which is an explanation and extension of the inflationary model of the development of the universe, millions of "big bangs" occur every second in space distant from us, generating their own bubbles of the Universes.
But back to our world: all clusters, galaxies, stars and planets, in whatever part of the Universe they are, are very similar to each other, but still unique. What mathematical structure has these properties? This is a fractal.
A fractal is generated by the simplest recurrent formula, but develops into a beautiful cyclical picture, each small piece of which is both unique and similar to the general structure.
Time asymmetry and recursive function evaluation
And just the fractal structure of our Universe opens our eyes to the most important mystery of modern physics - time. Is time only going forward? Is it linear?
Modern physics speaks of the existence of the so-called asymmetry of time or arrows of time. The first arrow of time is psychological: we remember the past, but not the future. This asymmetry is a special case of the more general second arrow of time - the cause and effect. Causes give rise to effects, but not vice versa. On the other hand, this can only be a part of our perception, and in the reverse course of time, we would take causes for effects, and consequences for causes. But there is a third absolutely objective asymmetry of time, also called the second law of thermodynamics - entropy in a closed system always grows with time. That is, with the reverse course of time, it would fall.
How can this be explained? One of the first explanations consistent with the hypothesis of a mathematical universe was given by the German pioneer of computer engineering and the author of the first high-level programming language Konrad Zuse . He suggested that our universe is not a static mathematical model, but is constantly computed by a pure recursive function. The input of such a function receives the result of the calculation of the previous iteration. Each tick of such a function is a Planck time., or, more simply, a moment. This hypothesis explains very well all the arrows of time. The result of calculating such a function depends on its input - the future depends on the past, but not vice versa. Over time, the amount of information in such a system will grow, which means that the entropy will also grow. And most importantly, this hypothesis is in very good agreement with the fractality of our Universe, because a fractal is the result of calculating a recurrent function.
Thus, we can define time in this way: time is the process of calculating a pure recursive function of calculating the development of our Universe.
You can argue that our Universe is non-deterministic and when the Schrödinger wave function collapses, the result of the quantum exit from the superposition is unpredictable. But according to the many-worlds interpretation of quantum mechanics Everettat the moment of the collapse of the wave function, our Universe is simply divided into two parallel realities, in one of which the superposition passes into one state, and into the other into the opposite.
It is also worth considering that this time is not the same as described in Einstein's general theory of relativity. This is absolute time - the ticks of the processor that calculates our Universe.
The matrix and the anthropic principle
But if our entire Universe is a computing machine, then how can we determine that we do not live in the Matrix? On the one hand, this is unprovable and irrefutable. On the other hand, if we live in the Matrix and spin on the computer of some programmer from the real universe, then his universe will also obey the laws of mathematics and may also turn out to be a second-level Matrix that exists in the real world. This series can be continued indefinitely, and in no level of the Matrix there will be an opportunity to prove whether or not there is a real world of a higher level.
In any case, Max Tegmark has a more beautiful explanation of the mathematics of our universe. First, let us ask ourselves a question: why do we live in such a mathematical structure, and not in some other? Tegmark finds the answer to this question inanthropic principle : all consistent mathematical structures exist, but only a few of them can give rise to such a finely tuned universe that allows the existence of neural networks capable of realizing cause-and-effect relationships.
Conclusion
The hypothesis of a mathematical computable universe has interesting implications: the heroes of books, films, stories, and even your fictional friend are as real as you are, since they are just like mathematical structures invented by another mathematical structure within a huge mathematical structure. This makes us think about the very meaning of the word "reality".
For a deeper acquaintance with this topic, I recommend Max Tegmark's book " Our Mathematical Universe " and the Wikipedia article on digital physics .