Endless space. How many universes are there? Does space have a border

Perhaps the limitations of what we can observe are just artificial; perhaps there is no limit to what is on the other side of the observed.

13.8 billion years ago, the universe began with the Big Bang. Since then it has been expanding and cooling down, so it was yesterday, today and it will be tomorrow. From our point of view, we can observe it at 46 billion light years in all directions, thanks to the speed of light and the expansion of space. Although this is a long distance, it is finite. But this is only part of what the Universe offers us. What's behind this part? Could the universe be infinite?

How could this be proven empirically?

First, what we see tells us more than 46 billion light years.

The further we look in any direction, the further back in time we look. The nearest galaxy, 2.5 million light-years away, appears to us the same as it was 2.5 million years ago, since light takes exactly this time to get into our eyes from the place where it was emitted. We see the most distant galaxies as they were millions, hundreds of millions or even billions of years ago. We see the light of the young universe. So if we look for the light that was emitted 13.8 billion years ago, left by the Big Bang, we find that too: the cosmic microwave background.

His picture of fluctuations is incredibly complex, with different angular scales showing different differences in average temperatures. It also encodes an incredible amount of information about the universe, including an astounding fact: the curvature of space, as far as we can tell, is absolutely flat. If space were positively curved, if we lived on the surface of a four-dimensional sphere, we would see how these distant rays of light converge. If space were curved negatively, as if we were living on a four-dimensional saddle, we would see distant rays of light diverge. But no, rays of light coming from afar continue to move in the original direction, and fluctuations speak of an ideal plane.

The cosmic microwave background and the large-scale structure of the Universe, combined, allow us to conclude that if the Universe is finite and self-contained, it must be at least 250 times larger than what we observe. And since we live in three dimensions, we get (250) 3 as volume, or we multiply space 15 million times. However large this number is, it is not infinite. By the most conservative estimate, the universe should be at least 11 trillion light years in all directions. And that's a lot, but ... of course.

However, there are reasons to believe that it is larger. The Big Bang could mark the beginning of the observable universe as we know it, but it does not mark the birth of time and space as such. Before the Big Bang, the universe was going through a period of cosmic inflation. It was not filled with matter and radiation, and it was not hot. She:

• was filled with energy inherent in space itself;
• expanded in a constant exponential order;
• created new space so quickly that the smallest physical length, the Planck length, stretched to the size of the universe observed today every 10-32 seconds.

It is true that inflation is over in our region of the Universe. But there are several questions to which we do not yet know the answer, which can determine the true size of the universe, as well as whether it is infinite or not.

How big was the region of the universe after inflation, in which our Big Bang was born?

Looking at our universe today, at the uniform afterglow of the Big Bang, and at the plane of the universe, there isn't much we can extract. We can define the highest limit on the energy scale at which inflation has occurred; we can determine how much of the universe has gone through inflation; we can define a lower limit for how long inflation should have continued. But the pocket of the inflationary universe in which our own was born could be much, much larger than the bottom line. It can be hundreds, millions, or googols times larger than we can observe ... or truly infinite. But until we can observe more of the Universe than is currently available to us, we will not get enough information to answer this question.

Is the idea of ​​"eternal inflation" true?

If you believe that inflation should be a quantum field, then at any time during this phase of exponential expansion, there is a chance that inflation will end in a Big Bang, and the likelihood that inflation will continue, creating more and more space. We can easily make these calculations (with a few assumptions) and they will lead to the inevitable conclusion: if you want inflation that produces the Universe we observe, then inflation will always create more space, which continues to expand, compared to regions that have already ended up Large Explosions. And if our observable universe could have emerged as a result of the end of inflation in our region of space about 13.8 billion years ago, there are areas in which inflation continues - creating more and more space and giving birth to Big Bangs - to this day. This idea is called "eternal inflation" and is generally accepted by the theoretical physicist community. And then how big is the entire unobservable universe?

How long did inflation last until its end and the Big Bang?

We can only see the observable universe created at the end of inflation and our Big Bang. We know this inflation should have lasted for at least 10-32 seconds or so, but it could have been longer. But how much longer? For seconds? Years? Billions of years? Or infinitely? Has the universe always been inflationary? Did she have a beginning? Did it arise from a previous state that was eternal? Or perhaps all space and time arose out of "nothing" some time ago? There are many possibilities, but all of them are unverifiable and unprovable to date.

According to our best observations, we know that the universe is much, much larger than the part we are fortunate enough to observe. Outside of what we see, there is much more of the Universe, with the same laws of physics, with the same structures (stars, galaxies, clusters, filaments, voids, etc.) and with the same chances for the development of complex life. There should also be finite sizes of "bubbles" in which inflation ends, and a gigantic number of such bubbles enclosed in a gigantic space-time that swells in the process of inflation. But there is a limit to any large numbers, they are not infinite. And only if inflation has not continued for an infinitely long time, the universe must be finite.

The problem with all this is that we only know how to access the information available in our observable universe: to that 46 billion light-years in all directions. The answer to the biggest question of all, whether the universe is finite or infinite, may be encoded in the universe itself, but we are too tied hand to know. Unfortunately, the physics we have doesn't give us any other options.

In everyday life, a person most often has to deal with finite quantities. Therefore, it can be very difficult to visualize an unlimited infinity. This concept is shrouded in a halo of mystery and unusualness, mixed with awe for the Universe, the boundaries of which are almost impossible to define.

The spatial infinity of the world belongs to the most complex and controversial scientific problems. Ancient philosophers and astronomers tried to solve this question by means of the simplest logical constructions. To do this, it was enough to admit that it was possible to reach the supposed edge of the universe. But if at this moment you stretch your hand, then the border moves back a certain distance. This operation can be repeated countless times, which proves the infinity of the universe.

The infinity of the universe is hard to imagine, but no less difficult than a limited world might look like. Even those who are not very advanced in the study of cosmology, in this case, a natural question arises: what is beyond the boundary of the Universe? However, such reasoning, built on common sense and everyday experience, cannot serve as a solid basis for rigorous scientific conclusions.

Modern concepts of the infinity of the universe

Modern scientists, exploring multiple cosmological paradoxes, have come to the conclusion that the existence of a finite universe, in principle, contradicts the laws of physics. The world outside the planet Earth, apparently, has no boundaries either in space or in time. In this sense, infinity assumes that neither the amount of matter contained in the Universe, nor its geometric dimensions can be expressed even by the largest number ("Evolution of the Universe", ID Novikov, 1983).

Even if we take into account the hypothesis that the Universe was formed about 14 billion years ago as a result of the so-called Big Bang, this may well mean only that in those extremely distant times the world went through another stage of natural transformation. In general, the infinite Universe has never appeared during the initial push or inexplicable development of some intangible object. The assumption of an infinite universe puts an end to the hypothesis of the Divine creation of the world.

In 2014, American astronomers published the results of the most recent studies that support the hypothesis of the existence of an infinite and flat universe. With high precision, scientists have measured the distance between galaxies located at a distance of several billion light-years from each other. It turned out that these colossal space star clusters are located in circles with a constant radius. The cosmological model built by the researchers indirectly proves that the Universe is infinite both in space and in time.

When studying the Universe and its structure, the question often arises of whether it has an end or is it infinite. The concept of infinity is one of the most interesting in science, as it relates to the field of the mysterious and unusual. Indeed, it is impossible to imagine infinity, because this concept has no clarity, but it is not at all an invented mathematical construction, but is used in science to solve many problems.

Astronomers and physicists are most interested in studying infinity, since they have to deal with the space of the Universe and the geometry of the surrounding world. The study of the infinity of the Universe and space began in ancient times. Great philosophers offered simple and seemingly irrefutable reasoning that, at first glance, did not contradict logic.

So, Lucretius Carus in the poem "On the Nature of Things" wrote: "There is no end on either side of the Universe, for otherwise it would certainly have an edge." It was easier for many scientists of that time to imagine that the Universe has no end and stretches indefinitely in all directions than the fact that it has certain boundaries, because then they would have to look for an answer to the question of what lies beyond these boundaries.

However, the reasoning of Lucretius and his supporters relied, first of all, on logic and the usual ideas about earthly space, and in the modern world it is considered unreasonable to rely on this when studying the problem of infinity on the scale of the Universe. In this case, one should study the real properties of the world and draw conclusions on their basis.

During the Renaissance, Copernicus developed a heliocentric model of the world, according to which the Sun was in the center of the Universe, and the Earth and other planets revolved around it. According to the scientist, the universe was limited by a sphere of fixed stars. He believed that all celestial bodies revolve around the Sun at the same speed, making one revolution per day. Consequently, the greater the distance from the Sun to the celestial body, the greater the speed of revolution of the latter.

Thus, if there are stars located at infinitely large distances from the Sun, then they must have an infinitely high speed, which is impossible. It follows from this that the Universe has an end, that is, it is enclosed in the sphere of stars. To Copernicus's contemporaries, such a proof seemed irrefutable, because then they did not yet know that the Sun is not the center of the Universe, but the center of the Solar system.

The Italian scientist Giordano Bruno was the first to question the conclusions of Copernicus. He was the first to suggest the idea of ​​an infinite universe. In his reasoning, the scientist relied on philosophical views, and not on physical or astronomical research.

Isaac Newton was the first to try to give a natural scientific explanation of the infinity of the Universe and in the laws of mechanics he developed. According to its provisions, if material particles are attracted to each other, then over time they should scatter in boundless space. Therefore, there cannot be an unchanging finite Universe. For a long time it was believed that the answer to the question of the infinity of the Universe was received and is considered final, but the opinion turned out to be erroneous. It has always been believed that to the question of whether the Universe has a boundary, there should be only two answers: "yes" or no. " And only later it turned out that there can be several types of infinity. For example, in mathematics there is an infinity of a series of natural numbers and an infinity of all points located on a line segment.

Different infinities can also exist in geometry. For example, there are such concepts as infinity and unboundedness of space, which are not identical to each other. Unlimited space is that which has no boundaries, but with that it is closed in itself, or of course. An example of such a space is a sphere. The area of ​​a sphere has a finite value, but it is impossible to reach its border, therefore it is considered unlimited. The sphere example serves as an example that space can have a finite volume, but it has no boundaries.

In modern science, no one doubts that the space of the Universe is unlimited, i.e. it is impossible to reach the border of the universe. But the question of its infinity or finiteness is still open. In order to find the answer to it, scientists study the geometry of the world and try to figure out the location of matter in the Universe. With the help of theoretical calculations, the critical density of matter in the Universe is measured. So, it is calculated that 1/100000 of the proton mass falls on 13 cm of space. Based on the theory of relativity, scientists say that world space has an end if the average density of matter in the Universe is greater than the critical one. Conversely, the Universe has an infinite volume if the density of matter in it is below the critical value.

Cosmology, a special branch of astronomy, deals with the origin, evolution and properties of the Universe. It draws on sciences such as physics, mathematics, astronomy, as well as theology and philosophy.

Based on this conclusion, many researchers have created different versions of calculating the average density of matter in the world. Some, based on their calculations, have come to the conclusion that the universe is finite, and have made attempts to calculate its radius. However, such calculations cannot answer the question about the infinity of the Universe and tell about its geometric properties.

General relativity provides a physical criterion on the basis of which one can make guesses about the curvature of space, but the physical value of this curvature can be judged, most likely, only on the basis of observations indicating that the average density of matter in the world is approximately equal to the critical one.

All this speaks in favor of the fact that modern science is not yet ready to give an unambiguous answer to the question of the finiteness and infinity of the Universe and to prefer one of these probabilities.

universe friedman kant creationism

Infinity as a concept is the height of abstraction. In this respect, only the speed of light or a black hole can compete with it. To tame the idea of ​​infinity, mathematicians for centuries have come up with signs, images and stories that reconcile our minds with what is impossible to imagine.

1. The sign of infinity

Perhaps when he came up with the infinity sign, Wallis took as a basis the symbol for the number 1000, written in Roman numerals (CIƆ or CƆ), which the Romans often used to denote countless objects. According to another version, the infinity symbol refers to omega (Ω or ω) - the last letter of the Greek alphabet.

The concept of infinity was proposed long before Wallis came up with a symbol for it. For example, the ancient Greek philosopher Anaximander introduced the concept of "apeiron", which meant a kind of infinite primordial substance.

2. Zeno's aporias

One of the most famous aporias of the ancient Greek philosopher Zeno is called "Achilles and the tortoise": the tortoise invites Achilles to race, on the condition that it starts moving a little earlier.

The turtle is confident in its victory, because the moment Achilles reaches the turtle's starting point, it will already crawl a little further, again increasing the distance between them.

Thus, despite the fact that the distance will be reduced, Achilles will never catch up with the turtle. This paradox can be explained in another way. Imagine that you are crossing the room, covering half the remaining distance with each step. First, your stride will be half the total distance, then a quarter, then 1 / 8th, 1 / 16th, etc. Although with each next step you will get closer to the opposite wall of the room, it is impossible to reach the end: you will have to take an infinite number of steps.

3. Pi number

Another example of infinity is π: mathematicians use a special symbol for it because it consists of an infinite number of digits. Most often it is shortened to 3.14 or 3.14159, but no matter how many decimal places there are, it is completely impossible to write down this number.

4. The Infinite Monkey Theorem

This theorem states that if an abstract monkey hits the keys of a typewriter for an infinitely long time, sooner or later it will print Shakespeare's Hamlet. While some see this theorem as a confirmation that anything is possible, mathematicians generally use it as an example of a very low probability event.

5. Fractals

A fractal is an abstract mathematical object used, among other things, to depict phenomena of natural origin. In mathematics, this is a set that has the property of self-similarity: its parts are similar to the whole. Visually, such an object is a figure, where the same motif is repeated in a successively decreasing scale. Therefore, the image of a fractal can be infinitely enlarged: when the scale is increased, all new details appear.

Written down as a mathematical equation, most fractals are non-differentiable functions.

6. Dimensions of infinity

Although infinity has no boundaries, it can be of different sizes. Positive and negative numbers represent two infinite sets of equal size. However, what happens if you add these two sets? You will end up with something twice the size of each of them.

Even numbers can be considered in a similar way: this is also an infinite set, but it is half the size of the set of all positive numbers.

In addition, you can try adding one to infinity and make sure that the number ∞ + 1 will always be greater than ∞.

7. Cosmology and infinity

Cosmologists continue to study the universe and ponder the concept of infinity. Is space infinite? There is still no answer to this question. Even if our physical universe is finite, chances are that it is just one universe out of many!

8. Division by zero

We know from school that division by zero is an arithmetically forbidden technique. The number 1 divided by 0 cannot be determined: any calculator will give an error code. However, according to another theory, 1/0 is a perfectly valid form of infinity.

Regarding the boundaries of space and the infinity of the universe, I will dare to refer to one of my previous answers.

As for the visible part of the universe, it is a little trickier there. Due to the expansion of the universe, the light from those parts of it that fly away from us faster than the speed of light will never reach us. However, the light of those objects that are already beyond this boundary reaches us, still reaches us, however, with a shifted wavelength - one of the manifestations of the Doppler effect. Read more here.

If we now talk about what is beyond the boundaries of the visible part of the universe, then speaking roughly, "now" there is most likely in general the same universe as the part that surrounds us. More precisely, in the terms of the special theory of relativity, if we go to some distant point of the universe at subluminal speed, then, by the time of our arrival, according to our clock, the universe at this point will apparently resemble ours in general terms.

Finally, the same redshift effect, due to which light comes to us with a longer wavelength from the far ends of the visible universe - and therefore, for the most part, is no longer visible to our eye - and allows us to conclude that the universe is expanding. It is due to the expansion that the sky looks dark at night - in an infinite or large finite universe, it should appear almost uniformly light.

The reasons for the expansion of the universe are still not clear, so far the concept of "dark energy" has been introduced in physics, due to which the universe is expanding. Its nature is not yet clear, it is not yet possible to observe its carriers directly - that is why this hypothetical object is called "dark" energy.

Still, it is not entirely accurate, the Hubble sphere is not yet an event horizon, and light from objects that are moving away faster than the speed of light precisely due to the acceleration of the expansion of the universe will ever get inside the Hubble sphere and reach us. With an event horizon (not particles) - it is trickier, we can see light from certain objects and will see it in the future, but we will not see how, for example, those stars will go out (even if they have already extinguished), in general, events are later than a certain date / time.