The universe is a wormhole. Wormholes: what is it - a myth, a gateway to other worlds or a mathematical abstraction? What are wormholes?

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This text represents the third version of my book about wormholes and. I tried to make it understandable for the widest possible range of readers. Understanding the material does not require the reader to special education, the most general ideas from the course will be quite enough high school and cognitive curiosity. The text does not contain formulas and does not contain complex concepts. To make things easier to understand, I have tried to use explanatory illustrations where possible. This version has been supplemented with new sections and illustrations. Corrections, clarifications and clarifications were also made to the text. If any section of the book seems boring or incomprehensible to the reader, then it can be skipped while reading without much damage to understanding.

What is commonly called a “Wormhole” in astrophysics

IN recent years in means mass media There have been many reports about the discovery by scientists of certain hypothetical objects called “wormholes.” Moreover, there are even ridiculous reports of observational detection of such objects. I even read in the tabloids about the practical use of certain “wormholes”. Unfortunately, most of these reports are very far from the truth; moreover, even the concept of such “wormholes” often has nothing in common with what is commonly called “wormholes” in astrophysics.

All this prompted me to write a popular (and at the same time reliable) presentation of the theory of “wormholes” in astrophysics. But first things first.

First a little history:

The science-based theory of wormholes originated in astrophysics back in 1935 with the pioneering work of Einstein and Rosen. But in that pioneering work, the “wormhole” was called by the authors a “bridge” between various parts Universe ( English term"bridge"). For a long time this work did not arouse much interest among astrophysicists.

But in the 90s of the last century, interest in such objects began to return. First of all, the return of interest was associated with a discovery in cosmology, but I will tell you why and what the connection is a little later.

The English-language term that has taken root for “wormholes” since the 90s has become “wormhole,” but the first to propose this term back in 1957 were American astrophysicists Mizner and Wheeler (this is the same Wheeler who is considered the “father” of American hydrogen bomb). “wormhole” is translated into Russian as “worm hole.” Many Russian-speaking astrophysicists did not like this term, and in 2004 it was decided to hold a vote on various proposed terms for such objects. Among the suggested terms were: “wormhole”, “wormhole”, “wormhole”, “bridge”, “wormhole”, “tunnel”, etc. Russian-speaking astrophysicists who have scientific publications on this topic (including me) took part in the voting. As a result of this vote, the term “wormhole” won, and henceforth I will write this term without quotes.

1. So what is commonly called a wormhole?

In astrophysics, wormholes have a clear mathematical definition, but here (due to its complexity) I will not give it, and for the unprepared reader I will try to give a definition in simple words.

You can give different definitions wormholes, but common to all definitions is the property that a wormhole must connect two non-curved regions of space. The junction is called a wormhole, and its central section is called the neck of the wormhole. The space near the neck of the wormhole is quite strongly curved. The concepts of “uncurved” or “curved” require detailed explanation here. But I will not explain this now, and I ask the reader to be patient until the next section, in which I will explain the essence of these concepts.

A wormhole can connect either two different universes, or the same universe in different parts. IN the latter case the distance through the wormhole (between its entrances) may be shorter than the distance between the entrances measured from the outside (although this is not at all necessary).

Further, I will use the word “universe” (with a small letter) - part of space-time, which is limited by the entrances to wormholes and black holes, and the word “Universe” (with a small letter) capital letters) I will call all space-time, unlimited by anything.

Strictly speaking, the concepts of time and distance in curved space-time cease to be absolute values, i.e. as we subconsciously have always been accustomed to consider them. But I attach full importance to these concepts physical meaning: we are talking about proper time, measured by an observer who is freely moving (without rocket or any other engines) at almost the speed of light (theorists usually call him an ultra-relativistic observer).

Obviously, it is practically impossible to create such an observer technically, but acting in the spirit of Einstein, we can imagine a thought experiment in which the observer saddles a photon (or other ultra-relativistic particle) and moves on it along the shortest trajectory (like Baron Munchausen on a nucleus).

Here it is worth recalling that the photon moves along the shortest path by definition, such a path is called general theory relativity zero geodetic line. In ordinary uncurved space, two points can be connected by only one zero geodesic line. In the case of a wormhole connecting entrances in the same universe, there can be at least two such paths for a photon (and both are shortest, but unequal), and one of these paths passes through the wormhole, and the other does not.

Well, it seems like I gave a simplified definition for a wormhole in simple in human words(without using mathematics). However, it is worth mentioning that wormholes through which light and other matter can pass in both directions are called traversable wormholes (from now on I will simply call them wormholes). Based on the word “passable,” the question arises: are there impassable wormholes? Yes, I have. These are objects that externally (at each of the inputs) are like a black hole, but inside such a black hole there is no singularity (singularity in physics is called infinite density matter that tears apart and destroys any other matter that enters it). Moreover, the property of singularity is mandatory for ordinary black holes. And the black hole itself is determined by the presence of a surface (sphere), from under which even light cannot escape. This surface is called the black hole horizon (or event horizon).

Thus, matter can get inside an impenetrable wormhole, but cannot leave it (very similar to the property of a black hole). Moreover, there may also be semi-passable wormholes, in which matter or light can only pass through the wormhole in one direction, but cannot pass in the other.

2. Curvature tunnel? Curvature of what?

At first glance, creating a wormhole tunnel out of curved space seems quite attractive. But when you think about it, you begin to come to absurd conclusions.
If you are in this tunnel, what walls can prevent you from escaping from it in the transverse direction?

And what are these walls made of?

Really empty space can prevent us from going through them?
Or is it not empty?

In order to understand this (I don’t even suggest imagining it), let’s consider space that is not curved by gravity. Let the reader consider that this is an ordinary space with which he is always accustomed to deal and in which he lives. In what follows I will call such a space flat.

Figure 1. (original drawing by the author)
Schematic representation of the curvature of two-dimensional space. The numbers indicate successive stages of transition: from the stage of uncurved space (1) to the stage of a two-dimensional wormhole (7).

Let's take as a beginning some point “O” in this space and draw a circle around it - see figure No. 1 in Figure 1. Let both this point and this circle lie on some plane in our flat space. As we all know very well from school course mathematics, the ratio of the length of this circle to the radius is equal to 2π, where the number π = 3.1415926535….. Moreover: the ratio of the change in the circumference to the corresponding change in the radius will also be equal to 2π (hereinafter, for brevity, we will simply say RATIO).

Now let’s place some body with mass M at our point “O”. If we believe Einstein’s theory and experiments (which were repeatedly carried out both on Earth and in the solar system), then the space-time around the body will be curved and the above-mentioned RATIO will be less than 2π. Moreover, the less more mass M – see figures No. 2 – 4 in Figure 1. This is the curvature of space! But not only space is curved, time is also curved, and it is more correct to say that all space-time is curved, because in the theory of relativity, one cannot exist without the other - there is no clear boundary between them.

In what direction is it bent? – you ask.
Down (under the plane) or vice versa - up?

The correct answer is that the curvature will be the same for any plane drawn through the point “O”, and the direction has nothing to do with it. Self geometric property space changes so that the ratio of the circumference to the radius also changes! Some scientists believe that the curvature of space occurs in the direction of a new (fourth) dimension. But the theory of relativity itself does not need additional dimension, it requires three spatial and one temporal dimensions. Usually the time dimension is assigned an index of zero, and space-time is designated as 3+1.
How severe will this curvature be?

For a circle that is our equator, the relative decrease in RATIO will be 10-9, i.e. for the Earth (length of the equator)/(radius of the Earth) ≈ 2π (1 – 10-9)!!! This is such an insignificant addition. But for a circle, which is the equator, this decrease is already about 10-5, and although this is also very small, modern instruments easily measure this value.

But there are more exotic objects in space than just planets and stars. For example pulsars, which are neutron stars(consist of neutrons). The gravity on the surface of pulsars is monstrous, and their average matter density is about 1014 g/cm3 - incredibly heavy matter! For pulsars, the decrease in this RATIO is already about 0.1!

But for black holes and wormholes the decrease in this RATIO reaches unity, i.e. the ATTITUDE itself reaches zero! This means that when moving towards the center, the circumference does not change near the horizon or neck. The area of ​​the sphere around black holes or wormholes also does not change. Strictly speaking, for such objects the usual definition of length is no longer suitable, but this does not change the essence. Moreover, for a spherically symmetrical wormhole the situation does not depend on the direction from which we move towards the center.

How can you imagine this?

If we consider a wormhole, this means that we have reached a sphere of minimum area Smin=4π rmin2 with throat radius rmin. This sphere of minimal area is called the neck of the wormhole. With further movement in the same direction, we find that the area of ​​the sphere begins to increase - this means that we have passed the neck, moved into another space and are moving away from the center.

What happens if the dimensions of the falling body exceed the dimensions of the neck?

To answer this question, let's turn to a two-dimensional analogy - see Figure 2.

Let's assume that the body is a two-dimensional figure (a design cut out of paper or other material), and this design slides along a surface that is a funnel (like the one we have in a bathtub when water flows into it). Moreover, our drawing slides in the direction of the neck of the funnel so that it is pressed against the surface of the funnel with its entire surface. It is obvious that as the pattern approaches the neck, the curvature of the funnel surface increases, and the surface of the pattern begins to deform in accordance with the shape of the funnel in this place drawing. Our drawing (even though it is paper), just like any physical body, has elastic properties that prevent its deformation.

At the same time, the drawing material has physical impact on the material from which the funnel is made. We can say that both the funnel and the drawing exert elastic forces on each other.

1. The drawing is deformed so much that it slips through the funnel, and in this case it may collapse (tear).
2. The pattern and the funnel are not deformed enough for the pattern to slip through (for this it is necessary that the pattern has enough large sizes and strength). Then the drawing will get stuck in the funnel and block its neck for other bodies.
3. The drawing (more precisely, the material of the drawing) will destroy (tear) the material of the funnel, i.e. such a two-dimensional wormhole will be destroyed.
4. The drawing will slip past the neck of the funnel (possibly touching it with its edge). But this will only happen if you haven’t focused your design accurately enough on the direction of the neckline.

The same four options are also possible for the fall of three-dimensional physical bodies into three-dimensional wormholes. This is how illusory, using toy models as an example, I tried to describe a wormhole in the form of a tunnel without walls.

In the case of a three-dimensional wormhole (in our space), the elastic forces of the funnel material, discussed in the previous section, are replaced by gravitational tidal forces - these are the same forces that cause ebbs and flows on Earth under the influence of and.

In wormholes and black holes, tidal forces can reach monstrous levels. They are capable of tearing apart and destroying any objects or matter, and near the singularity these forces generally become infinite! However, we can assume a wormhole model in which tidal forces are limited and, thus, it is possible for our robot (or even a person) to pass through such a wormhole without harming it.

Tidal forces, according to Kip Thorne's classification, are of three types:

1. Tidal tension-compression forces
2. Tidal forces of shear deformation
3. Tidal forces of torsional deformation

Figure 3. (Figure taken from Kip Thorne's report - Nobel laureate in physics 2017) On the left is an illustration of the action of tidal tension-compression forces. On the right is an illustration of the action of tidal torsion-shear forces.

Although the last 2 types can be reduced to one - see Figure 3.

4.Einstein's general theory of relativity

In this section, I will talk about wormholes within the framework of the general theory of relativity created by Einstein. I will discuss the differences from wormholes in other theories of gravity in a subsequent section.

Why did I start my consideration with Einstein’s theory?

To date, Einstein's theory of relativity is the simplest and most beautiful of the unrefuted theories of gravity: not a single experiment to date has disproved it. The results of all experiments are in perfect agreement with it for 100 years!!! At the same time, the theory of relativity is mathematically very complex.

Why such a complex theory?

Because all other consistent theories turn out to be even more complicated...

Figure 4. (figure taken from A.D. Linde’s book “Inflationary Cosmology”)
On the left is a model of a chaotic inflationary multi-element Universe without wormholes, on the right is the same, but with wormholes.

Today, the “chaotic inflation” model is the basis modern cosmology. This model works within the framework of Einstein's theory and assumes the existence (except ours) infinite number other universes arising after “ big bang”, forming during the “explosion” the so-called “space-time foam”. The first moments during and after this “explosion” are the basis of the “chaotic inflation” model.

At these moments, primary space-time tunnels (relict wormholes) may appear, which probably persist after inflation. Further, these relict wormholes connect various regions of our and other universes - see Figure 4. This model was proposed by our compatriot Andrei Linde, who is now a professor at Stanford University. This model opens unique opportunity research of the multi-element Universe and the discovery of a new type of objects - entrances to wormholes.

What conditions are necessary for the existence of wormholes?

A study of wormhole models shows that exotic matter is required for their stable existence within the framework of the theory of relativity. Sometimes such matter is also called phantom matter.

Why is such matter needed?

As I wrote above, strong gravity is needed for the existence of curved space. In Einstein's theory of relativity, gravity and curved space-time exist inextricably from each other. Without enough concentrated matter, curved space straightens and the energy of this process is radiated to infinity in the form of gravitational waves.
But strong gravity alone is not enough for the stable existence of a wormhole - this way you can only get a black hole and (as a consequence) an event horizon.

In order to prevent the formation of a black hole's event horizon, phantom matter is needed. Usually, exotic or phantom matter means a violation of energy conditions by such matter. It's already mathematical concept, but don’t be alarmed – I will describe it without mathematics. As is known from the school physics course, every physical solid there are elastic forces that resist the deformation of this body (I wrote about this in the previous section). In more general case arbitrary matter (liquid, gas, etc.) speak about the intrinsic pressure of matter, or more precisely about the dependence of this pressure on the density of matter.

Physicists call this relationship the equation of state of matter.
So, in order for the energy conditions of matter to be violated, it is necessary that the sum of pressure and energy density be negative (energy density is mass density multiplied by the speed of light squared).

What does it mean?

Well, firstly, if we consider positive mass, then the pressure of such phantom matter should be negative. And secondly, the modulus of the pressure of phantom matter should be large enough to give a negative value when added to the energy density.

There is an even more exotic version of phantom matter: when we immediately consider negative mass density and then pressure does not play a fundamental role, but more on that later.

And even more surprising is the fact that in the theory of relativity the density of matter (energy) depends on the frame of reference in which we consider them. For phantom matter, this leads to the fact that there is always a reference frame (moving relative to the laboratory frame almost at the speed of light) in which the density of phantom matter becomes negative. For this reason, there is no fundamental difference for phantom matter: whether its density is positive or negative.

Does such matter even exist?

And now it’s time to remember the discovery of dark energy in cosmology (do not confuse it with the concept of “dark matter” - this is a completely different substance). Dark energy was discovered in the 90s of the last century, and it was needed to explain the observed accelerated expansion of the universe. Yes, yes - the universe is not just expanding, but expanding with acceleration.

7. How wormholes could have formed in the Universe

All metric theories of gravity (and Einstein's theory among them) affirm the principle of topology conservation. This means that if a wormhole has one topology, then over time it will not be able to have another. This also means that if a space does not have the topology of a torus, then objects with the topology of a torus will not be able to appear in the same space.

Therefore, ringholes (wormholes with a torus topology) cannot appear in an expanding Universe and cannot disappear! Those. if during the “big bang” the topology was disrupted (the process of the “big bang” may not be described by a metric theory - for example, Einstein’s theory), then in the first moments of the explosion, in the “space-time foam” (I wrote about it above - ringholes, which can then turn into impassable wormholes with the same torus topology, but they will no longer be able to disappear completely - that’s why they are called relict wormholes.

But wormholes with the topology of a sphere in Einstein’s theory can appear and disappear (though in strictly topological language this will not be the same topology of a sphere as for wormholes connecting different universes, but I won’t go deeper into these mathematical jungles here) . I can again illustrate how the formation of wormholes with the topology of a sphere can occur using the example of a two-dimensional analogy - see figures No. 5 - 7 in Figure 1. Such two-dimensional wormholes can “inflate” like a child’s rubber ball at any point in a flat rubber “universe.” . Moreover, in the process of such “inflation” the topology is not violated anywhere - there are no breaks anywhere. IN three-dimensional space(three-dimensional sphere) everything happens by analogy - just as I described above.

8. Is it possible to make a time machine from a wormhole?

Among literary works You can find many different novels about a time machine. Unfortunately, most of them are myths that have nothing to do with what is commonly called the TIME MACHINE in physics. So in physics, a time machine is usually called closed world lines material bodies. By world line we mean the trajectory of a body drawn not in space, but in space-time!

Moreover, the length of these lines must have macroscopic dimensions. The last requirement is due to the fact that quantum physics(in the microworld) closed world lines of particles are business as usual. But quantum world this is a completely different matter. In it, for example, there is a quantum tunnel effect, which allows a microparticle to pass through a potential barrier (through an opaque wall). Remember the hero Ivanushka (played by Alexander Abdulov) in the movie Sorcerers, where he walked through the wall? A fairy tale, of course, but from a purely scientific point of view, a large macroscopic body also has the possibility of passing through a wall (quantum tunneling).

But if we calculate this probability, it turns out to be so small that the required number of attempts (which is equal to one divided by this tiny probability) required for successful quantum tunneling there is almost infinity. More specifically, the number of such attempts must exceed the number of all elementary particles in the Universe!

This is roughly the same situation with the attempt to create a time machine from a quantum loop - almost unbelievable.

But we will still return to the issue of creating a time machine using a wormhole. For this (as I already said) we need closed world lines. Such lines, by the way, exist inside rotating black holes. By the way, they exist in some models of the rotating Universe (Godel’s solution).

But in order for such lines to appear inside wormholes, it is necessary mandatory implementation two conditions:

Firstly, the wormhole must be a ringhole, i.e. connect different areas of the same universe.

And secondly, this wormhole must rotate quite quickly (in the right direction).

The phrase “fast enough” here means that the speed of matter moving in it should be close to the speed of light.

That's all? – you ask, will we be able to travel to the past and back? Physicists today cannot answer this question mathematically correctly. The fact is that the mathematical model that needs to be calculated is so complex that it is simply impossible to construct an analytical solution. Moreover: today there is not a single analytical solution for ringholes - there are only approximate numerical calculations made on computers.

My personal opinion is that even if we manage to get a closed world line, then it will be destroyed by matter (which will move along this loop) even before the loop closes. Those. a time machine is impossible, otherwise we could go back in time and, for example, kill our grandmother there even before her children were born - obvious contradiction in logic. Those. It is possible to obtain only time loops that cannot influence our past. For the same logical reason, we will not be able to look into the future while remaining in the present. We can only be transported entirely into the future, and it will be impossible to return from it if we have already entered it. Otherwise, the cause-and-effect relationship between events will be broken (and in my opinion this is impossible).

9.wormholes and perpetual motion machine

Actually, the wormholes themselves direct relationship they don’t have access to a perpetual motion machine, but with the help of phantom matter (which is necessary for the stationary existence of a wormhole), in principle, it is possible to create a so-called perpetual motion machine of the third kind.

I will remind you one of amazing properties phantom matter (see above): there is always a frame of reference (moving relative to the laboratory frame almost at the speed of light) in which the density of phantom matter becomes negative. Let's imagine a body with negative mass (made of phantom matter). According to the law universal gravity this body will be attracted to an ordinary body with positive mass. On the other hand, an ordinary body will have to repel from a body with negative mass. If the absolute masses of these bodies are the same, then the bodies will “chase” each other to infinity.

The principle of operation is based (purely theoretically) on this effect. perpetual motion machine third kind. However, the possibility of extracting energy (for the needs national economy) from this principle has not been rigorously proven to date either mathematically or physically (although such attempts have been made several times).
Moreover, scientists did not and do not believe in the possibility of creating a perpetual motion machine, and this is the main argument against the existence of phantom matter and against wormholes... Personally, I also do not believe in the possibility of creating a perpetual motion machine, but I admit the possibility of the existence of certain types of phantom matter in nature.

10. The connection between wormholes and black holes

As I wrote above, the first relic wormholes that could have formed in the Universe after the “big bang” could ultimately turn out to be impassable. Those. passage through them is impossible. In mathematical terms, this means that a “trapping horizon” appears at the wormhole, sometimes also called a space-like visibility horizon. Even light cannot escape from under the trapped horizon, and even less so can other matter.

You may ask: “What, horizons are different?” Yes, there are several types of horizons in theories of gravity, and when they say that a black hole has a horizon, they usually mean an event horizon.

I will say more: a wormhole must also have a horizon, this horizon is called the visibility horizon, and there are also several types of such horizons. But I won't go into that here.

Thus, if a wormhole is impassable, then outwardly it is almost impossible to distinguish it from a black hole. The only sign of such a wormhole can only be a monopole magnetic field (although the wormhole may not have it at all).

The phrase “exclusive field” means that the field comes straight out of the wormhole in one direction, i.e. the field either comes out of the wormhole on all sides (like the needles of a hedgehog), or enters it from all sides - see Figure 6.

A black hole has a monopoly magnetic field prohibited by the so-called theorem “On the absence of hair in a black hole.”

For an electric monopole field, this property usually means that inside the surface under which the field enters (or leaves) there is electric charge. But magnetic charges not found in nature, so if a field at one of the entrances enters a wormhole, then it must leave it at the other entrance of the wormhole (or vice versa). Thus, it is possible to implement an interesting concept in theoretical physics, this concept is called “charge without charge”.

This means that a magnetic wormhole at each of its inputs will look like a magnetic charge, but the charges of the inputs are opposite (+ and -) and therefore the total charge of the wormhole inputs equal to zero. In fact, there shouldn't be any magnetic charges, it's just that the external magnetic field behaves as if there are - see Figure 6.

Passable wormholes have their own characteristic features, by which you can distinguish them from black holes, and I will write about this in the next section.
If a wormhole is impassable, then using phantom matter it can be made passable. Namely, if we “water” an impassable wormhole with phantom matter from one of its entrances, then it will become passable from the opposite entrance, and vice versa. True, the question arises and remains: how can a traveler (who wants to go through an impassable wormhole) inform his assistant at the entrance of the wormhole opposite him (closed from him by the horizon) that he (the traveler) is already near his entrance and it’s time to start “watering” ” the opposite entrance with phantom matter, so that the wormhole becomes semi-passable in the direction desired by the traveler.

Thus, in order for an impassable wormhole to become completely passable, it must be “watered” with phantom matter from both of its entrances simultaneously. Moreover, there should be phantom matter sufficient quantity Which one exactly is not a simple question; the answer can only be given by an accurate numerical calculation for a specific model (such models have already been calculated previously in scientific publications). In astrophysics there was even an expression that phantom matter is so terrible that it even dissolves black holes in itself! To be fair, it should be said that a black hole, having dissolved, does not necessarily form a wormhole.

Ordinary matter in sufficient quantities, on the contrary, “locks” the wormhole, i.e. makes it impassable. Thus, we can say that in this sense, the interconversion of black holes and wormholes is possible.

11.Black and white holes as a type of wormhole

I assume that until now the reader has been under the impression that black holes are objects from which nothing can ever come out (including even light). This is not an entirely true statement.

The fact is that in almost all black holes, the singularity repels matter (and light) when it flies too close to it (already below the horizon of the black hole). The only exception to this phenomenon could be the so-called Schwarzschild black holes, i.e. those that do not rotate and have no electrical charge. But for the formation of such a Schwarzschild black hole, the matter that forms it requires such initial conditions, whose measure is zero on the set of all possible initial conditions!

In other words, when any black hole is formed, it will definitely have rotation (even if very small) and there will definitely be an electric charge (even if it’s elementary), i.e. the black hole will not be Schwarzschild. In what follows I will call such black holes real. Real black holes have their own classification: Kerr (for a rotating black hole), Reisner-Nordström (for a charged black hole) and Kerr-Newman (for a rotating and charged black hole).

What happens to a particle that is pushed away by a singularity inside a real black hole?

The particle will no longer be able to fly back - this would contradict the laws of physics in a black hole, because the particle has already fallen under the event horizon. But it turns out that the topology inside black holes turns out to be non-trivial (complex). This leads to the fact that after falling under the horizon of a black hole, all matter, particles, and light are thrown out by the singularity into another universe.

In the universe where all this flies out, there is a white hole - it is from it that matter (particles, light) flies out. But all the miracles don’t end there... The fact is that in the same place in space where there is this white hole (in another universe) there is also a black hole.

Matter that falls into that black hole (in another universe) experiences a similar process and flies out into the next universe. And so on... Moreover, movement from one universe to another is always possible only in one direction: from the past to the future (in space-time). This direction is associated with the cause-and-effect relationship between events in any space-time. In force common sense and logical scientists assume that the cause-and-effect relationship should never be broken.

The reader may have a logical question: will there necessarily be a white hole in our universe - where there is already a black hole, and from where matter from the previous universe could fly out to us? For experts in the topology of black holes, this is a difficult question and the answer to it is “not always.” But, in principle, such a situation may well exist (when a black hole in our universe is also a white hole from another - previous universe). Unfortunately, we cannot yet answer the question - which situation is more likely (whether a black hole in our universe is at the same time a white hole from the previous universe or not).

So these are the objects - black and white holes They also have another name: “dynamic wormholes.” They are called dynamic because they always have a region under the horizon of the black hole (this region is called the T-region) in which it is impossible to create a rigid frame of reference, and in which all particles or matter would be at rest. In the T-region, matter isn't just moving all the time; it's moving at varying speeds all the time.

But between the singularity and the T-region in real black holes there is always still a space with an ordinary region, this region is called the R-region. In particular, space outside a black hole also has the properties of an R-region. So, the repulsion of matter from the singularity occurs precisely in the internal R-region.

Figure 7. (the author took the Carter-Penrose diagram for the Reisner-Nordström black hole as the basis for the figure) The figure on the left schematically depicts a space with a non-trivial (complex) topology black and white hole Reisner-Nordström (Carter-Penrose diagram). On the right is the passage of a particle through this black-and-white hole: outside the black circle is the outer R-region, between the green and black circles is the T-region, below the green circle is the inner R-region and the singularity.

For these reasons, it is impossible to calculate and construct a single trajectory of a particle crossing a black-and-white hole in both universes at once. For such a construction, it is necessary to divide the desired trajectory into two sections and “sew” these sections together in the internal R-region (only there it is possible to do this) - see Figure 7.

As I've written before, tidal forces can tear matter apart before it reaches another universe. Moreover, inside a black-and-white hole, the maximum tidal forces are achieved at the point of minimum radius (in the inner R-region). The closer a real black hole is in its properties to a Schwarzschild one, the greater these forces will be at their maximum, and the less chance matter has to overcome the black-and-white hole without destruction.

These properties of real black holes are determined by the measure of their rotation (this is their angular momentum, divided by the square of their mass) and a measure of their charge (this is their charge divided by their mass). Each of these properties (these measures) cannot be greater than one for real black holes. Therefore, the more any of these measures increases to unity, the less tidal forces will be in such a black hole at their maximum, and the more more chances for matter (or for a person) to overcome such a black and white hole without destruction. Moreover, no matter how paradoxical it sounds, the heavier the real black hole is, the less tidal forces will be at its maximum!

This happens because tidal forces are not just gravitational forces, but a gradient of gravitational force (i.e., the rate of change of gravitational force). Therefore, the larger the black hole, the slower the gravitational forces change in it (despite the fact that the gravitational forces themselves can be enormous). Therefore, the gravitational gradient (i.e. tidal forces) will be smaller in larger black holes.

For example, for a black hole with a mass of several million solar masses (at the center of our galaxy there is a black hole with a mass of ≈ 4.3 million solar masses), the tidal forces on its horizon are small enough for a person to fly there and, at the same time, nothing I wouldn’t have felt it the moment it passed the horizon. And in the Universe there are also much heavier black holes - with a mass of several billion solar masses (as, for example, in the quasar M87) ... I will explain that quasars are the active (brightly glowing) nuclei of distant galaxies.

Since, as I wrote, matter or light can still fly from one universe to another through a black-and-white hole without destruction, such objects can rightfully be called another type of wormhole without phantom matter. Moreover, the existence of this particular type of dynamic wormholes in the Universe can be considered practically proven!

Original video by the author (from his publication), illustrating the free, radial fall of a dust sphere into a black and white hole (all dust particles on the sphere glow monochrome green). The radius of the Cauchy horizon of this black-and-white Reissner-Nordström hole is 2 times less than radius outer horizon. The observer also falls freely and radially (following this sphere), but from a slightly greater distance.

In this case, initially green photons from dust particles of the sphere reach the observer with red (and then violet) gravitational displacement. If the observer remained motionless relative to the black-and-white hole, then after the sphere crossed the visibility horizon, the red shift of photons for the observer would become infinite and he would no longer be able to observe this dust sphere. But thanks free fall observer, he can see the sphere all the time (if we do not take into account the strong red shift of photons) - incl. and the moments when the sphere crosses both horizons, and while the observer himself crosses these horizons, and even after the sphere passes through the neck of this dynamic wormhole (black-and-white hole) - and the exit of dust particles into another universe.

Below is a radius scale for the observer (marked with a yellow mark), the point of the dust shell closest to the observer (marked with a green mark), the point of the dust shell that is furthest away from the observer from which photons come to the observer (marked with a thin white mark), as well as the location of the horizon black hole(red mark), Cauchy horizon (blue mark) and throat point (purple mark).

12.Multiverse

The concept of the Multiverse is usually identified with the non-trivial topology of the space surrounding us. Moreover, in contrast to the concept of “multiverse” in quantum physics, they mean quite large scale spaces where quantum effects can be completely neglected. What is a non-trivial topology? I'll explain this at simple examples. Let's imagine two objects molded from plasticine: an ordinary cup with a handle and a saucer for this cup.

Without tearing the plasticine and without gluing the surfaces, but only by plastic deformation of the plasticine, a saucer can be turned into a ball, but it is in no way possible to turn into a cup or a donut. For a cup it’s the other way around: because of its handle, the cup cannot be turned into a saucer or into a ball, but it can be turned into a donut. These general properties saucers and balls correspond to their general topology - the topology of a sphere, and the general properties of a cup and a donut - the topology of a torus.

So, the topology of a sphere (saucer and ball) is considered to be trivial, and the more complex topology of a torus (cup and donut) is considered to be non-trivial, although there are others, even more complex types non-trivial topology - not only the topology of the torus. The Universe around us consists of at least three spatial (length, width, height) and one time dimensions, and the concepts of topology are obviously transferred to our world.

Thus, if two different universes with the topology of a sphere are connected by only one wormhole (dumbbell), then the resulting universe will also have a trivial topology of a sphere. But if two different parts of one universe are connected to each other by a wormhole (weight), then such a universe will have a non-trivial torus topology.

If two different universes with the topology of a sphere are connected by two or more wormholes, then the resulting universe will have a non-trivial topology. A system of universes connected by several wormholes will also have a nontrivial topology if there is at least one closed line that cannot be pulled together to one point by any smooth deformation.

For all their attractiveness, wormholes have two significant drawbacks: they are unstable and their existence requires the presence of exotic (or phantom) matter. And if their stability can still be realized artificially, then many scientists simply do not believe in the possibility of the existence of phantom matter. Based on the above, it may seem that without wormholes the existence of the Multiverse is impossible. But it turns out that this is not so: the existence of real black holes is quite sufficient for the existence of the Multiverse.

As I already said, inside all black holes there is a singularity - this is an area in which the density of energy and matter reaches infinite values. In almost all black holes, the singularity repels matter (and light) when it gets too close to it (already below the horizon of the black hole).

The only exception to this phenomenon could be the so-called Schwarzschild black holes, that is, those that do not rotate at all and which have no electrical charge. A Schwarzschild black hole has a trivial topology. But for the formation of such a Schwarzschild black hole, the matter that forms it requires such initial conditions, the measure of which is zero on the set of all possible initial conditions!

In other words, when any black hole is formed, it will definitely have rotation (even if very small) and there will definitely be an electric charge (even if elementary), that is, the black hole will not be Schwarzschild. I call such black holes real.

A Schwarzschild black hole has a singularity inside a central sphere that has an infinitesimal area. A real black hole has a singularity on a ring that lies in the equatorial plane under both horizons of the black hole. It is worth adding here that, unlike the Schwarzschild black hole, a real black hole has not one, but two horizons. And between these horizons mathematical signs space and time change places (although this does not mean that space and time themselves change places, as some scientists believe).

What will happen to a particle that is repelled by a singularity inside a real black hole (already below its inner horizon)? The particle will no longer be able to fly back: this would contradict the laws of physics and causality in a black hole, since the particle has already fallen under the event horizon. This leads to the fact that after falling under the inner horizon of a real black hole, any matter, particles, light are thrown out by the singularity into another universe.

This is because, unlike Schwarzschild black holes, the topology inside real black holes turns out to be non-trivial. Isn't it amazing? Even a slight rotation of a black hole leads to radical change properties of its topology! In the universe where matter then flies out, there is a white hole - everything flies out of it. But all the miracles do not end there... The fact is that in the same place in space where there is this white hole, in another universe, there is also a black hole. Matter that falls into that black hole in another universe undergoes a similar process and flies out into the next universe, and so on.

Moreover, movement from one universe to another is always possible only in one direction - from the past to the future (in space-time). This direction is associated with the cause-and-effect relationship between events in any space-time. By virtue of common sense and logic, scientists assume that the cause-and-effect relationship should never be broken. Such an object is usually called a black-and-white hole (in this sense, a wormhole could be called a white-white hole). This is the Multiverse, which exists due to the existence of real black holes, and the existence of wormholes and phantom matter is not necessary for its existence.

I assume that for most readers it will be difficult to imagine that in the same region of space (within the same sphere having the horizon radius of a black hole) there would be two fundamentally different objects: a black hole and a white hole. But mathematically this can be proven quite strictly.

I invite the reader to imagine a simple model: the entrance (and exit) of a building with a revolving door. This door can only rotate in one direction. Inside the building, the entrance and exit near this door are separated by turnstiles, allowing visitors to pass in only one direction (entry or exit), but outside the building there are no turnstiles. Let's imagine that inside the building these turnstiles divide the entire building into 2 parts: universe No. 1 for exiting the building and universe No. 3 for entering it, and outside the building there is universe No. 2 - the one in which you and I live. Inside the building, the turnstiles also only allow movement in the direction from No. 1 to No. 3. Such simple model well illustrates the effect of a black-and-white hole and explains that outside the building, visitors entering and exiting can collide with each other, but inside the building they cannot due to the unidirectionality of movement (just like particles of matter in the corresponding universes).

In fact, the phenomena that accompany matter during such an ejection into another universe are quite complex processes. The main role in them begins to be played by gravitational tidal forces, which I wrote about above. However, if the matter that gets inside the black hole does not reach the singularity, then the tidal forces acting on it always remain finite and, thus, it turns out to be fundamentally possible for a robot (or even a person) to pass through such a black-and-white hole without harming it. Moreover, the larger and more massive the black hole is, the smaller the tidal forces will be at their maximum...

The reader may have a logical question: will there necessarily be a white hole in our Universe where there is already a black hole, and from where matter from the previous Universe could fly out to us? For experts in black hole topology, this is a difficult question, and the answer is “not always.” But, in principle, such a situation may well exist - when a black hole in our Universe is also a white hole from another, previous universe. Answer the question “Which situation is more likely?” (whether the black hole in our Universe is also a white hole from the previous Universe or not), we, unfortunately, cannot yet.

Of course, today and in the near future it will not be technically possible to send even a robot to a black hole, but some physical effects and the phenomena characteristic of wormholes and black-and-white holes have such unique properties that today observational astronomy came close to their detection and, as a consequence, the discovery of such objects.

13.What a wormhole should look like through a powerful telescope

As I already wrote, if a wormhole is impassable, then distinguishing it from a black hole will be very difficult. But if it is passable, then through it you can observe objects and stars in another universe.

Figure 9. (original drawing by the author)
The left panel shows a section of the starry sky observed through a circular hole in the same universe (1 million identical, evenly distributed stars). The middle panel shows the starry sky of another universe, viewed through a static wormhole (1 million different images from 210,069 identical and evenly distributed stars in another universe). The right panel shows the starry sky of another universe as seen through a black-and-white hole (1 million different images from 58,892 identical and evenly distributed stars in another universe).

Let's consider the simplest (hypothetical) model of the starry sky: there are quite a lot of identical stars, and all these stars are evenly distributed across the celestial sphere. Then the picture of this sky, observed through a circular hole in the same universe, will be as shown in the left panel of Figure 9. This left panel shows 1 million identical, evenly spaced stars, so the image appears to be an almost uniform circular blob.

If we observe the same starry sky (in another universe) through the neck of a wormhole (from our universe), then the picture of the images of these stars will look approximately as shown in

Astrophysicists are sure: there are tunnels in space through which you can move to other Universes and even to other times. Presumably, they were formed when the Universe was just beginning. When, as scientists say, space “boiled” and curved.

These cosmic “time machines” were given the name “wormholes.” A “hole” differs from a black hole in that you can not only get there, but also return back. The time machine exists. And this is no longer a statement by science fiction writers - four mathematical formulas, which so far prove in theory that you can move both into the future and into the past.

AND computer model. This is roughly what a “time machine” in space should look like: two holes in space and time connected by a corridor.

"IN in this case We are talking about very unusual objects that were discovered in Einstein's theory. According to this theory, in a very strong field, space is curved, and time either twists or slows down, these are fantastic properties,” explains Deputy Director of the Astrospace Center of the Lebedev Physical Institute Igor Novikov.

Such unusual objects scientists called them “wormholes.” This is not a human invention at all; so far only nature is capable of creating a time machine. Today, astrophysicists have only hypothetically proven the existence of “wormholes” in the Universe. It's a matter of practice.

Finding wormholes is one of the main tasks modern astronomy. “They started talking about black holes somewhere in the late 60s, and when they made these reports, it seemed like science fiction. It seemed to everyone that this was absolute fantasy - now it’s on everyone’s lips,” says Anatoly Cherepashchuk, director of the Astronomical Institute of Moscow State University named after Sternberg. - So now “wormholes” are also science fiction, nevertheless the theory predicts that “wormholes” exist. I’m an optimist and I think that the wormholes will also be opened someday.”

"Wormholes" belong to this mysterious phenomenon How " dark energy", which makes up 70 percent of the universe. “Dark energy has now been discovered - it is a vacuum that has negative pressure. And in principle, “wormholes” could be formed from a state of vacuum,” suggests Anatoly Cherepashchuk. One of the habitats of “wormholes” is the centers of galaxies. But the main thing here is not to confuse them with black holes, huge objects that are also located at the center of galaxies.

Their mass is billions of our Suns. Moreover, black holes have the most powerful force attraction. It is so large that even light cannot escape from there, so it is impossible to see them with a regular telescope. The gravitational force of wormholes is also enormous, but if you look inside the wormhole, you can see the light of the past.

“In the center of galaxies, in their cores, there are very compact objects, these are black holes, but it is assumed that some of these black holes are not black holes at all, but entrances to these “wormholes,” says Igor Novikov. Today, more than three hundred black holes have been discovered.

From Earth to the center of our galaxy Milky Way 25 thousand light years. If it turns out that this black hole is a “wormhole”, a corridor for time travel, humanity will have to fly and fly to it.

A wormhole or wormhole, in theory, is an intersection of time and space that significantly reduces the time of long-distance travel throughout the universe. The concept of a “wormhole” was born thanks to the general theory of relativity. Wormholes have not yet been studied and carry a colossal danger in the form of sudden contacts with unexplored matter, high radiation and other unknown collapses.

Wormhole theory

Back in 1935, physicists and Nathan Rosen discovered the theory general relativity, which suggested the existence of “bridges” across space and time. These paths are called “Einstein-Rosen bridges” or wormholes. These bridges connect two different points in time and space, theoretically creating a path that reduces travel time and travel distance.

In theory, it contains two holes, which are then connected. The beginnings of these holes are most likely spherical. They then move into a straight section, although it is possible that this could form a circle, providing the traveler with a longer path than the traditional route.

Einstein's theory of general relativity mathematically suggests the existence of wormholes, but to date none have been discovered by astrophysicists. The only thing that suggests the presence of CN is the negative mass, which can be detected due to the way its gravity affects the light passing by.

Some of the statements of the general theory of relativity allow the existence of wormholes, some of which consist of black holes. True, by its nature a black hole that appears during an explosion dying star, by itself cannot create a wormhole.

Science fiction is replete with stories of travel through wormholes. But the actual reality of such a journey does not yet seem real.

The first problem is the size of the wormholes. Conventional wormholes, according to scientists, have a size of 10-33 centimeters. However, as the Universe expands, it is possible that some of them could stretch to larger sizes.

Another problem for travelers comes from the unexplored stability of the wormhole. The Einstein-Rosen research was simply useless for practical travel. But more recent research has shown that a wormhole containing "exotic matter" could remain open to exploration and remain unchanged for years. long periods time.

Exotic matter that is different from dark matter or antimatter, contains negative energy density, as well as negative pressure.

If the wormhole (wormhole) contains a sufficient amount of exotic matter, be it natural origin or artificially developed material - it could theoretically be used as a way to send information or travelers through space.

Wormholes can not only connect two separate regions of the universe, but they can also connect two different galaxies. Interestingly, some scientists suggest that if one entrance to the KN is moved in a certain learned order, then this may subsequently allow travel to occur. Despite this, British astrophysicist and cosmologist Stephen Hawking argues that using CN for travel is not yet possible.

"A wormhole doesn't actually give you the ability to travel back in time," wrote NASA scientist Eric Christian.

Humanity is exploring the world around us at an unprecedented speed, technology does not stand still, and scientists are exploring with their sharp minds. the world around us. Undoubtedly, space can be considered the most mysterious and little-studied area. This is a world full of mysteries that cannot be understood without resorting to theories and fiction. A world of secrets that go far beyond our understanding.

Space is mysterious. He keeps his secrets carefully, hiding them under the veil of knowledge inaccessible to the human mind. Humanity is still too helpless to conquer Space, like the already conquered world of Biology or Chemistry. All that is currently accessible to man are theories, of which there are countless numbers.

One of greatest mysteries Universe - Wormholes.

Wormholes in space

So, a Wormhole (“Bridge”, “Wormhole”) is a feature of the interaction of two fundamental components of the universe - space and time, and in particular - their curvature.

[The concept of “Wormhole” in physics was first introduced by John Wheeler, the author of the theory of “charge without charge”]

The peculiar curvature of these two components allows one to overcome colossal distances without spending a colossal amount of time. To better understand the principle of operation of such a phenomenon, it is worth remembering Alice from Through the Looking Glass. The girl's mirror played the role of the so-called Wormhole: Alice could, just by touching the mirror, instantly find herself in another place (and if we take into account the scale of space, in another universe).

The idea of ​​the existence of wormholes is not just a whimsical invention of science fiction writers. Back in 1935, Albert Einstein co-authored works proving the possibility of so-called “bridges.” Although the Theory of Relativity allows this, astronomers have not yet been able to detect a single Wormhole (another name for a Wormhole).

The main problem of detection is that, by its nature, the Wormhole absorbs absolutely everything, including radiation. And it doesn’t “let out” anything. The only thing that can tell us the location of the “bridge” is gas, which, when it enters the Wormhole, continues to emit X-ray radiation, unlike when it enters the Black Hole. Similar behavior of gas was recently discovered in a certain object Sagittarius A, which leads scientists to believe that there is a Wormhole in its vicinity.

So is travel through Wormholes possible? In fact, there is more fantasy here than reality. Even if we theoretically assume that a Wormhole will be discovered in the near future, modern science would be faced with a lot of problems that it is not yet able to cope with.

The first stone on the path to mastering the Wormhole will be its size. According to theorists, the first burrows were less than a meter in size. And only, relying on the theory of an expanding universe, can we assume that the Wormholes increased along with the universe. This means they are still increasing.

The second problem on the path of science will be the instability of Wormholes. The ability of the “bridge” to collapse, that is, to “slam shut,” negates the possibility of using or even studying it. In fact, the lifespan of a Wormhole can be tenths of a second.

So what will happen if we discard all the “stones” and imagine that a person nevertheless made a passage through the Wormhole. Despite the fiction that talks about the possibility of returning to the past, it is still impossible. Time is irreversible. It moves in only one direction and cannot go back. That is, “seeing yourself young” (as, for example, the hero of the film “Interstellar” did) will not work. This scenario is guarded by the theory of causality, unshakable and fundamental. Transferring “oneself” to the past implies the ability for the hero of the journey to change it (the past). For example, kill yourself, thus preventing yourself from traveling into the past. This means there is no possibility of being in the future, where the hero came from.

Science

The recently released visually arresting film Inresttellar is based on real scientific concepts such as rotating black holes, wormholes and time dilation.

But if you are not familiar with these concepts, you may be a little confused while watching.

In the film, a team of space explorers goes to extragalactic travel through a wormhole. On the other side they find themselves in another solar system with a rotating black hole instead of a star.

They are in a race against space and time to complete their mission. This kind of space travel may seem a little confusing, but it is based on basic principles of physics.

Here are the main ones 5 concepts of physics Things you need to know to understand Interstellar:

Artificial gravity

Most big problem, which we humans face over long periods of time space travel, is weightlessness. We were born on Earth and our body has adapted to certain gravitational conditions, but when we are in space long time, our muscles begin to weaken.

The heroes in the movie Interstellar also face this problem.

To cope with this, scientists are creating artificial gravity in spacecraft. One way to do this is to spin up the spaceship, just like in the movie. Rotation creates centrifugal force, which pushes objects towards the outer walls of the ship. This repulsion is similar to gravity, only in the opposite direction.

This is a form of artificial gravity you experience when you are driving around a small radius curve and feel as if you are being pushed outward, away from the center point of the curve. In a rotating spaceship the walls become the floor for you.

Rotating black hole in space

Astronomers, albeit indirectly, have observed in our Universe rotating black holes. Nobody knows what's at the center of a black hole, but scientists have a name for it -singularity .

Rotating black holes distort the space around them differently than stationary black holes.

This process of distortion is called "entrainment" inertial systems reference" or the Lense-Thirring effect, and it affects how the black hole will look by distorting space, and more importantly the space-time around it. The black hole you see in the movie is quitevery close to the scientific concept.

• The spaceship Endurance is heading towards Gargantua - fictional supermassive black hole 100 million times the mass of the Sun.
• It is 10 billion light years away from Earth and has several planets orbiting it. Gargantua spins at an astonishing 99.8 percent of the speed of light.
• Garagantua's accretion disk contains gas and dust with the temperature of the Sun's surface. The disk supplies the Gargantua planets with light and heat.

The complex appearance of the black hole in the film is due to the fact that the image of the accretion disk is distorted by gravitational lensing. Two arcs appear in the image: one formed above the black hole, and the other below it.

wormhole

The wormhole or wormhole used by the crew in Interstellar is one of the phenomena in the film that whose existence has not been proven. It is hypothetical, but very convenient in the plots of science fiction stories where you need to overcome a large space distance.

Just wormholes are a kind of shortest path through space. Any object with mass creates a hole in space, which means space can be stretched, warped, and even folded.

A wormhole is like a fold in the fabric of space (and time) that connects two very distant regions, which helps space travelers overcome long distance in a short period of time.

The official name for a wormhole is an “Einstein-Rosen bridge,” as it was first proposed by Albert Einstein and his colleague Nathan Rosen in 1935.

• In 2D diagrams, the mouth of a wormhole is shown as a circle. However, if we could see the wormhole, it would look like a sphere.
• On the surface of the sphere, a gravitationally distorted view of space on the other side of the “hole” would be visible.
• The dimensions of the wormhole in the film: 2 km in diameter and the transfer distance is 10 billion light years.

Gravitational time dilation

Gravitational time dilation is real phenomenon observed on Earth. It arises because time is relative. This means that it flows differently for various systems coordinates

When you are in a strong gravitational environment, time moves slower for you compared to people in a weak gravitational environment.