Suprostruna for a snowman in the flame of hell

About the book "Amazing numbers of the universe. Traveling for the brink of imagination "

Wanting to show how deep the rabbit nora, a theoretic physicist, the cosmologist of the University of Nottingham and YouTube blogger Antonio Padilla conducts an excursion to the universe, mainly in its extreme states. As accompanying people, he takes some of the most unusual numbers that mathematics have ever known. So, the number of Graham is so large that if you try to imagine it, the head collapses into a black hole (and this is not even a metaphor). Or an extremely small number 10-120, thanks to which the universe known to us can exist longer than one moment and not collapse to the size of the atom. However, is it known? It is possible that we live in a three -dimensional hologram, and the world is actually two -dimensional - there is at least such a hypothesis.

Antonio Padilla. Amazing numbers of the universe. Traveling for the brink of imagination. M.: Mann, Ivanov and Ferber, 2025. Translation from English by E. Ponikarov. Content

Entropy is growing

In the abstract mathematical recording of numbers, monsters can truly excite the GIKs (again-mathematicians). For everyone else, they are like Leonid Andreev for Leo Tolstoy: they scare, but usually no one is scared.

Perhaps this is in vain. So, the number of Graham (how to calculate it, we told in the material dedicated to another book) much more than such huge numbers as Googol, Googolplex and even Googolplexian .

But from the beginning, a few words about two important concepts, which must be sorted out in order to approach this issue. It's about entropy and information.

We briefly mentioned the connection of entropy with heat and energy in the material about the book of physicist Carlo Rovelli (by the way, Antonio Padilla is in some way his opponent, which is later later). Entropy can be described as a measure of irreversible dispersion of energy or its uselessness. Whether we are talking about cars or windmills-they always lose something in the environment, since not all energy is used for useful work.

The constant growth of entropy (sometimes it remains at the same level, but since our universe is very large, in the framework of the general chaotic reality of the physical world it is still increasing) describes the second law of thermodynamics . As entropy increases, more and more energy turns into a useless issuance of heat, therefore, in the global perspective, the future, as Antonio Padilla writes, is: this:

“<...> the postantropic nightmare, covered by paralysis. We are waiting for thermal death, the universe is waiting for us, in which there is no movement, action. ”

There are other versions regarding what the beautiful will be far away, but this is not about that now. If you represent the gas - that is, the extensive space of the void with randomly moving atoms and molecules - in the form of a room, and Brownian pirouettes of particles as flying from corner to corner and sometimes colliding insects, then entropy can be defined as the census of all the micro -condition of the participants in this process.

Imagine the location and movement of each molecule and each atom: where they are and what they are doing at each individual point in time, how exactly each of them rotates, how they interact, at what speed and force they repel from each other. The atoms themselves consist of building blocks, each state of which is also described. It will turn out a breathtaking report in detail.

Entropy is the measure of this hidden detail, as it takes into account all the micro -conditions that support the invariability of the macroscopic properties of the object. You can talk about entropy in any other context where there is a micro -condition of the system, whether it is a car or a human body. At each unit of time at the molecular level, the composition of the fuel in the gas tank changes, like microflora in the human intestine. Such processes of myriad, that is the unimaginable state of state. The number of these micro -conditions only increases over time, which means that entropy always increases and never decreases.

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Kamikadze of calculus

Entropy is closely related to information. Moreover, Padilla takes these two of these concepts closer, considering them the same with some reservations, since they both measure the degree of uncertainty, but differently.

At the same time, the information may have a mass , says Antonio Padilla. The value of this mass depends on the form in which the information is stored. For example, in the smartphone the data is stored by capturing electrons in the memory block, these electrons have slightly higher energy compared to electrons outside the trap, and since they have more energy, their mass is greater (the direct consequence of the E = MC2 Einstein formula - the mass is equivalent to energy). On average, one data bit adds 10–26 milligrams of mass. Therefore, in order to increase the weight of the gadget for the weight of the dust, it is necessary that 10 trillion gigabytes of data is stored in it, which is comparable to the volume of the global data datasmer. In other words, the weight of information in the first approximation may seem completely insignificant. But everything is known in comparison - and it is here that we begin to approach the number of Graham.

What will happen if someone takes on a feat to present it in the full record, that is, will introduce all the information about him into his head? In the human brain ~ 100 billion neurons. If we take into account that each of them can either be excited or not, we get ~ 100 billion bits. These are limit indicators: in reality, the person who would use so many resources for any practical application has not yet been born. Except for our suicide bomber ...

It is not worth trying to repeat this, since all these calculations, of course, are exclusively theoretical - in fact, no head will be able to work with such a breathtaking volume of information. But if you imagine that it can still, accumulating gigabytes behind gigabytes? ..

Since the information has weight, it will ultimately have to pack the mass in one head, more than ten times higher than the ground (the information weighs little, speak?). All these processes will cause in our heroic head to be prohibitive internal pressure and monstrously high temperatures - and it will finally explode.

The head was soaking off? Let's imagine that the accumulation of information for some wonderful reason will continue after the explosion of the cranial box. Having reached a threshold of 10 billion trillions of trillion trillion trillion gigabytes (for comparison: a large adron collider gives out 10 million gigabytes for a whole year), there will be a black hole in the place of the head (as always occurs when they try to squeeze too much into too small space). By cosmological standards, it will be a black hole of modest sizes, since the average radius of the human head is about 11 cm. But it will already be a very solid “hard drive”, because even the idea of ​​using black data storage was expressed .

But next to the number of Graham, all this is a zilch - before it is still like Chinese Easter.

You can continue to accumulate the data and be filled in their knowledge more and more, like that of Stalin's universe from the sentimental novel “Blue Blue”, which has filled the whole universe. Night or later nature itself will begin to resist the sooner or later, forcing the universe to go into a large compression . In other words, in order to fix all the information about the number of Graham, our universe is not enough. You need more.

And we have them.

So the small fragment of the number of Graham might look. If you look closely, you can see that the gray ripples are numbers

At least, theoretically, the continuation of this story can still be thought of, using the hypothesis of the multi-verse , that is, about the coexistence of many different universes with different laws of physics. Then, perhaps, sooner or later somewhere and once for the number of Graham there will still be a place.

But there are numbers for which in this reality there is not even an intuitively clear way to realize that they are at all. For example, this is the Tree (3) - it is even more than the number of Graham. In order to deal with him, you will have to survive at least the time of the return of Poincare , necessary for the complete rebooting of the Universe. After each such On/OFF, an accurate return of the entire universe will be realized, up to the location of individual atoms in each star and planet, in each insect in the room and in each copy of the “blue fat” , destroyed by activists of the HOA . There will be a lot of such restarts. But even then the goal will not be achieved. The laws and settings of our Universe will simply not allow us to approach Tree (3).

By the way, about the settings-the monsters also managed to reach them. But this is already good news for us.

Shameless constants

Now we will talk about monstrously small number - 10–120 . However, there is nothing to be scared here, but there is something to be surprised. Previously, we talked about the subtle setting of the universe , thanks to which there is a visible and invisible world. Here, without abysses, it is necessary to immediately declare that in fact, our universe, like us, should not be. The subtle setting of fundamental physical constants (the speed of light, the charge of the electron, gravitational constant, etc.) is so thin that the probability that the constants will have the value that in reality is approximately the same as if you throw a coin and it falls out for 156 times in a row. In numerical terms, it is equal to 10–47 or:

0, 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 01.

Moreover, the emptiness itself has colossal energy. This vacuum energy (the energy of the zero point) arises from quantum fluctuations-constantly born and disappearing virtual particles (like explosive caramel in the mouth or diving and diving back into the sea of ​​dolphins), which permeate the entire space-time and are its integral part. According to calculations, in each sector of space the size of a tea cup should be nearly one hundred thousand trillions of trillions of the Joule of Energy. This is enough to evaporate all the oceans of the Earth. Only in one cup.

With such a colossal amount of energy, the Universe, obeying Einstein’s laws (again recall about E = MC2), should be literally crushed and crumpled under the weight of nothing - void. And since the energy of the vacuum is omnipresent, the world should have an insignificant length - it could not reach the size of the atom.

But in reality, everything is somewhat differently since each of us managed to notice. The true value of the density of the energy of the vacuum is 10–120 of the one that should be according to calculations. If you write down this number as a decimal shot, it looks like this:

0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001.

One tea cup of vacuum will not evaporate not only the ocean, but also a puddle, and even a drop. At least 10,000 cups of energy are needed only in order to crush Mimarid , the smallest insect in the world (from 0.14 to 4 mm).

"Light card" of the Platonic cave

One of the most fascinating ideas for the physics of the turn of the XX-XXI centuries is a hypothesis of a holographic universe . It is about the fact that gravity and three spatial dimensions in a sense of illusion. We allegedly live in the holographic world, being locked within the boundaries of the space that we usually perceive. We are like a tortured two -dimensional cockroaches, studying a three -dimensional world, but with the difference that the world is actually two -dimensional. However, this is just a hypothesis. But she is gaining more and more popularity among scientists.

“The holographic principle is the most important idea that has arisen in physics over the past thirty years. She led to a breakthrough in our understanding of the strength of gravity, resolving the information paradox of the black hole and a deep understanding of the nature of quantum gravity. <...> Moreover, she challenged our perception of reality, our idea of ​​the space surrounding us. She prompted us to wonder if it really exists, or is it just an illusion . ”

Scientists Gerard Joft (Nobel Laureate) from the Netherlands and physicist Lenny Sasskind from Stanford in the early 1990s formulated this idea as follows: if black holes are at the top of the entropy “food chain” (as we described above in the exploded head) and if the maximum entropy is determined by the area is determined by the area The surface of the border of the black hole, it could be assumed that all the information is stored on this border. In other words, a certain volume of three -dimensional space is completely encoded on the border of this volume - on a two -dimensional surface. It is as if the contents of the parcel could be found on its packaging.

And if you go even further, you can imagine a physics in which some spatial dimensions would be superfluous and, moreover, illusory. Since the border covers everything, these dimensions are simply not needed. In this sense, the border is everything .

About the same way, a hologram is created, which is not a static image, but a “light card” of a three -dimensional object. In the hologram, light, optics and physics are combined to encode information of a higher measurement (three -dimensional) on the surface of a lower (two -dimensional).

“The gloss of the hologram is that it allows you to create a code for a three -dimensional image on a two -dimensional plate. Roughly speaking, you can consider the density of light and dark stripes by the image of the depth according to the missing measurement. In other words, a dense dark strip encodes some distance along the perpendicular close to the plate, and the lighter depicts something more distant. <...> You feel three dimensions, not two, because this is how your brain preferred to decode light and dark stripes. He decided to present them as the third spatial dimension and a little gravity. ”

How to create and decodate a hologram (illustration from the book)

And if in connection with this recall Plato’s textbook cave, then the shadows on its walls will be no less real than the objects that discard them. Or we can say differently: these objects are no less illusory than shadows. In the holographic world, we and the world around us are shadows. There is nothing but shadows in it.

Or maybe quantum fields ?

New spaces in the sleeve

Quantum physics gave us a contributive and generally not too comparable picture of the world with everyday experience.

For example, particles in such optics are only vibrations - quantum ripples of quantum fields. If we take the surface of the sea as an analogue of some fundamental field, when ripples appear on the top of such a wave, this will be the equivalent of some particle. Rice in different fields are different particles. Ryab in the electron field gives an electron, in electromagnetic - photon, etc. Here we can still talk about real and virtual particles: there may be real photons, or may virtual (like electrons, quarks, gluons, etc.). A virtual particle is just a kind of outrage of a field caused by other particles and other fields.

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Earlier, we mentioned physicist Carlo Rovelli, an adherent of the theory of loop quantum gravity , which is entrusted with the hope of a possible reconciliation of quantum physics and classical. Opponents of loop theorists are string theorists who believe that the future theory of quantum gravity will be based on string theory. Antonio Padilla also refers to her supporters.

The essence of the theory of strings is that at the fundamental level we are dealing with extended objects of zero thickness, zero width and having only a length. These are constantly fluctuating with an endless number of different methods open/closed loops - strings.

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The theory of strings works only if the space-time has a dimension of 26: one time and 25 spatial measurements (in the theory of supership, this dimension was reduced to 10 dimensions). By the way, in general, there are not one of the theories of strings, there are five of them: such as I, types IIA and IIB and two heterotic string theories (we will not go into the details of each of them now). It combines five different versions of the theory of strings of m-theoria (in it 11 dimensions), where the fundamental objects are brothers (extended two-dimensional or more than the number of measurements of the membrane)-oscillating objects of a higher dimension than a string.

Building levels of matter: 1. Macroscopic level - substance. 2. Molecular level. 3. Atomic level - protons, neutrons and electrons. 4. Subatomic level - electron. 5. Subatomic level - quarks. 6. String level. Source

Where are all these additional measurements if we live in a four -dimensional world with three spatial and one time ? Yes, anywhere - at least in your sleeve. Like a wilting flower, in the theory of superstrod, additional dimensions, as it were, “wither” or turn off.

“They are everywhere - from here to the Andromeda nebula <...> but they are rolled up and inconspicuous - a silent eternal partner living next to our macroscopic world. Measurement is just another direction of movement. When we say that the space has three dimensions, we mean three independent directions of movement: forward and back, left and right, up and down. Six additional measurements of strings theory are just six new directions of movement. Но они свернуты, как крошечные окружности, и вы не сможете продвинуться далеко в этих новых направлениях — вы просто вернетесь туда, откуда начали <...> мы просто слишком велики, чтобы их увидеть. Мы не видим их даже на Большом адронном коллайдере, хотя заглядываем в мир, который в миллиард раз меньше атома. Если дополнительные измерения и существуют, их просто затмевает все, что мы видим в природе. <...> существуют гуголы способов их свернуть».

Все это происходит на умопомрачительно малых планковских масштабах длины порядка 10–32 см: если бы атом был размером с галактику, то струны, составляющие его электроны, кварки и глюоны, были бы размером не больше мухи.

Впрочем, теория струн до сих пор не получила экспериментальных подтверждений: адронный коллайдер так и не обнаружил суперсимметричные частицы в том диапазоне энергий, где их ожидали увидеть. Это разочарование особенно остро чувствуется после открытия бозона Хиггса, одного из важнейших событий в науке XXI века (его масса составляет 0,0000000000000001 от ожидаемой, физики до сих пор — c 2012 года — не нашли этому внятного объяснения).

«Обнаружить такой бозон Хиггса <...> все равно что найти снеговика в пламени ада. Это может случиться, но в реальности не должно происходить», — пишет Антонио Падилья.

Впрочем, мы уже усвоили, что многое в реальности существовать не должно, — как и самой реальности.

Но это все-таки случилось.