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Science fiction novels describe entire transport networks connecting star systems and historical eras, so-called portals, time machines. But what is much more surprising is that time machines and tunnels in space are quite seriously, as hypothetically possible, actively discussed not only in articles on theoretical physics, on the pages of reputable scientific publications, but also in the media. There have been many reports about the discovery by scientists of certain hypothetical objects called “wormholes.”
While selecting material for the research and development project on the topic “Black Holes,” we came across the concept of “Wormholes.” This topic we were interested, and we made a comparison between them.
Goal of the work: Comparative analysis of black holes and wormholes.
Tasks: 1. Collect material about black holes and wormholes;
2. Make a detailed analysis of the information received;
3. Compare black holes and wormholes;
4. Create an educational film for students.
Hypothesis: Is travel in space-time possible thanks to wormholes?
Object of study: literature and other resources about wormholes and black holes.
Subject of study: versions about the existence of wormholes.
Methods: study of literature; use of Internet resources.
Practical significance This work is to use the collected material for educational purposes in physics lessons and in extracurricular activities in this subject.
The presented work used materials from scientific articles, periodicals, and Internet resources.
Chapter 1. Historical background
In 1935, physicists Albert Einstein and Nathan Rosen, using the general theory of relativity, suggested that special “bridges” across space-time exist in the Universe. These paths, called Einstein-Rosen bridges (or wormholes), connect two completely different points in space-time by theoretically creating a curvature in space that shortens the journey from one point to another.
Theoretically, a wormhole consists of two entrances and a neck (that is, that same tunnel). The entrances to wormholes have a spheroidal shape, and the neck can represent either a straight segment of space or a spiral one.
For a long time this work did not arouse much interest among astrophysicists. But in the 90s of the 20th century, interest in such objects began to return. First of all, the return of interest was associated with the discovery of dark energy in cosmology.
The English-language term that has been adopted for “wormholes” since the 90s has become “wormhole,” but the American astrophysicists Mizner and Wheeler were the first to propose this term back in 1957. “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 took part in the voting. As a result of this vote, the term “wormhole” won.
In physics, the concept of wormholes dates back to 1916, just a year after Einstein published his great work‒ general theory of relativity. Physicist Karl Schwarzschild, who then served in Kaiser's army, found an exact solution to Einstein's equations for the case of an isolated point star. Far from a star, its gravitational field is very similar to that of an ordinary star; Einstein even used Schwarzschild's solution to calculate the deviation of the trajectory of light around a star. Schwarzschild's result had an immediate and very powerful effect on all branches of astronomy, and today it still remains one of the most famous solutions of Einstein's equations. Several generations of physicists have used the gravitational field of this hypothetical point star as an approximation for the field around a real star with a finite diameter. But if we take this point solution seriously, then at its center we suddenly discover a monstrous point object that has amazed and shocked physicists for almost a century - a black hole.
Chapter 2. Wormhole and black hole
2.1. Mole Hole
A wormhole is a supposed feature of space-time, which at every moment of time is a “tunnel” in space.
The area near the narrowest part of the molehill is called the "throat". There are passable and impassable molehills. The latter are those tunnels that collapse (destroy) too quickly for an observer or signal to travel from one entrance to another.
The answer lies in the fact that, according to Einstein's theory of gravity - the general theory of relativity (GTR), the four-dimensional space-time in which we live is curved, and the familiar gravity is a manifestation of such curvature. Matter “bends”, bends the space around itself, and the denser it is, the stronger the curvature.
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.
Wormholes through which light and other matter can pass in both directions are called traversable wormholes. There are also impassable wormholes. 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 the infinite density of matter, which tears apart and destroys any other matter falling into 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). 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.
Features of wormholes are the following characteristics:
The wormhole must connect two non-curved areas 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.
A wormhole can connect either two different Universes, or the same Universe in different parts. In the latter case, the distance through the wormhole may be shorter than the distance between the entrances measured from the outside.
The concepts of time and distance in curved space-time cease to exist absolute values, i.e. as we subconsciously have always been accustomed to consider them.
A study of wormhole models shows that exotic matter is required for their stable existence within the framework of Einstein's theory of relativity. Sometimes such matter is also called phantom matter. For the stable existence of a wormhole, any small amount of phantom matter is sufficient - say, only 1 milligram (or maybe even less). In this case, the rest of the matter supporting the wormhole must satisfy the condition: the sum of the energy density and pressure is equal to zero. And there is nothing unusual in this: even the most ordinary electric or magnetic field satisfies this condition. This is exactly what is needed for the existence of a wormhole with an arbitrarily small addition of phantom matter.
2.2. Black hole
A black hole is a region in space-time. The gravitational attraction is so strong that even objects moving at the speed of light, including quanta of light itself, cannot leave it. The boundary of this area is called the event horizon.
Theoretically, the possibility of the existence of such regions of space-time follows from some exact solutions of Einstein's equations. The first was obtained by Karl Schwarzschild in 1915. The exact inventor of the term is unknown, but the designation was popularized by John Archibald Wheeler and first publicly used in the popular lecture "Our Universe: Known and Unknown." Previously, such astrophysical objects were called “collapsed stars” or “collapsars,” as well as “frozen stars.”
There are four scenarios for the formation of black holes:
two realistic ones:
gravitational collapse (compression) of a sufficiently massive star;
collapse of the central part of the galaxy or protogalactic gas;
and two hypotheticals:
the formation of black holes immediately after the Big Bang (primary black holes);
the occurrence of high energy nuclear reactions.
The conditions under which the final state of stellar evolution is a black hole have not been studied well enough, since this requires knowledge of the behavior and states of matter at extremely high densities that are inaccessible to experimental study.
The collision of black holes with other stars, as well as the collision of neutron stars, causing the formation black hole, leads to powerful gravitational radiation, which is expected to be detectable in the coming years using gravitational telescopes. Currently, there are reports of observations of collisions in the X-ray range.
On August 25, 2011, a message appeared that for the first time in the history of science, a group of Japanese and American specialists was able in March 2011 to record the moment of the death of a star, which is absorbed by a black hole.
Black hole researchers distinguish between primordial black holes and quantum ones. Primordial black holes currently have the status of a hypothesis. If at the initial moments of the life of the Universe there were sufficient deviations from the uniformity of the gravitational field and matter density, then black holes could form from them through collapse. Moreover, their mass is not limited from below, as in a stellar collapse - their mass could probably be quite small. The discovery of primordial black holes is of particular interest due to the possibility of studying the phenomenon of black hole evaporation. As a result of nuclear reactions, stable microscopic black holes, so-called quantum black holes, can arise. For a mathematical description of such objects, a quantum theory of gravity is needed.
Conclusion
If a wormhole is impassable, then outwardly it is almost impossible to distinguish it from a black hole. Today, the theory of physics of wormholes and black holes is a purely theoretical science. Wormholes are topological features of space-time described within the framework of special relativity by Einstein in 1935.
The general theory of relativity mathematically proves the possibility of the existence of wormholes, but so far none of them have been discovered by humans. The difficulty in detecting it is that the supposed huge mass of wormholes and gravitational effects simply absorb the light and prevent it from being reflected.
After analyzing all the information found, we learned how wormholes differ from black holes and came to the conclusion that the world of space is still very little studied, and humanity is on the verge of new discoveries and opportunities.
Based on the research done, an educational film “Wormholes and Black Holes” was created, which is used in astronomy lessons.
List of sources and literature used
Bronnikov, K. Bridge between worlds / K. Bronnikov [Electronic resource] // Around the world. 2004. May. - Access mode // http://www.vokrugsveta.ru/vs/article/355/ (09/18/2017).
Wikipedia. Free encyclopedia [Electronic resource]. - Access mode // https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%BE%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_% D0%BD%D0%BE%D1%80%D0%B0 (09/30/2017);
https://ru.wikipedia.org/wiki/%D0%A7%D1%91%D1%80%D0%BD%D0%B0%D1%8F_%D0%B4%D1%8B%D1%80%D0 %B0 (09/30/2017).
Zima, K. “Wormhole” - the corridor of time / K. Zima // Vesti.ru [Electronic resource]. - Access mode // http://www.vesti.ru/doc.html?id=628114 (09.20.2017).
Wormholes and Black Holes [Electronic resource]. - Access mode // http://ru.itera.wikia.com/wiki/%D0%9A%D1%80%D0%BE%D1%82%D0%BE%D0%B2%D1%8B%D0% B5_%D0%BD%D0%BE%D1%80%D1%8B_%D0%B8_%D0%A7%D0%B5%D1%80%D0%BD%D1%8B%D0%B5_%D0%B4% D1%8B%D1%80%D1%8B (09/30/2017).
Mole holes. Popular science with Anna Urmantseva [Electronic resource]. - Access mode // http://www.youtube.com/watch?v=BPA87TDsQ0A (09/25/2017).
Wormholes of space. [Electronic resource]. - Access mode // http://www.youtube.com/watch?v=-HEBhWny2EU (09/25/2017).
Lebedev, V. Man in a wormhole (review) / V. Lebedev // Swan. Independent almanac. [Electronic resource]. - Access mode // http://lebed.com/2016/art6871.htm (09.30.2017).
Through the wormhole, Is there an end to the universe. [Electronic resource]. - Access mode // https://donetskua.io.ua/v(09.25.2017).
Black hole [Electronic resource]. - Access mode // http://ru-wiki.org/wiki/%D0%A7%D1%91%D1%80%D0%BD%D0%B0%D1%8F_%D0%B4%D1%8B% D1%80%D0%B0 (09/30/2017).
Black holes. Universe [Electronic resource]. - Access mode // https://my.mail.ru/bk/lotos5656/video/_myvideo/25.html (09/25/2017).
What is a wormhole? Reading [Electronic resource]. - Access mode // http://hi-news.ru/research-development/chtivo-chto-takoe-krotovaya-nora.html (09/18/2017).
Shatsky, A. Wormholes: what is it - a myth, a gateway to other worlds or a mathematical abstraction? [Electronic resource]. - Access mode // http://www.znanie-sila.su/?issue=zsrf/issue_121.html&r=1 (09/18/2017).
Encyclopedia for children. T. 8. Astronomy [Text] / Chapter. ed. M. Aksyonova; method. ed. V. Volodin, A. Eliovich. - M.: Avanta, 2004. S. 412-413, 430-431, 619-620.
- Sergey Vladilenovich, what is a wormhole?
There is no very strict definition. Such definitions are needed when you are proving some theorems, but there are almost no strict theorems, so they are mainly limited to figurative concepts and pictures. Imagine that we took a ball out of our three-dimensional space in one room and took out exactly the same ball in another room, and glued the resulting boundaries of these holes together. Thus, when in one room we step inside this former ball, which has become a hole, we will emerge in another room - from the hole that formed in the place of another ball. If our space were not three-dimensional, but two-dimensional, it would look like a sheet of paper to which a pen is glued. The three-dimensional analogue and its development in time is called a wormhole.
- How do they study wormholes in general?
This is a purely theoretical activity. No one has ever seen wormholes, and, in general, there is no certainty that they even exist. They began to study wormholes, starting from the question: are there mechanisms in nature that would guarantee us that such burrows cannot exist in nature? These mechanisms were not found, so we can assume that wormholes are a real phenomenon.
- Is it possible, in principle, to see a wormhole?
Of course. If in a locked room a person suddenly crawls out of nowhere, then you are observing a wormhole. Wormholes as an object of study were invented and promoted by the American theoretical physicist John Wheeler, who with their help wanted to explain, neither more nor less, electric charges. Let me explain. Describing a free electric field from the point of view of theoretical physics is not a very difficult task. But describing an electric charge from the same point of view is very difficult. An electric charge appears in this sense as a very mysterious thing: some kind of substance, separate from the field, of unknown origin, and it is not clear how to handle it in classical physics. Wheeler's idea was as follows. Let's say we have a microscopic wormhole, which is penetrated by lines of force - these lines enter it at one end, and exit from the other. An outside observer who does not know that these two ends are connected by lines of force will perceive such an object as a simple sphere in space, will examine the field around it, and it will look like the field of a point charge. Only the observer will think that this is some kind of mysterious substance that has a charge, etc., and all because he does not know that in fact it is a wormhole. Of course, this is a very elegant idea, and many have tried to develop it, but they have not made much progress, because electrons are, after all, quantum objects, and, naturally, no one knows how to describe wormholes at the quantum level. But if we assume that the hypothesis is true, then wormholes are more than an everyday phenomenon; everything related to electricity will ultimately depend on them.
Exotic matter - classical concept physics, describing any (usually hypothetical) substance that violates one or more classical conditions, or does not consist of known baryons. Such substances may have qualities such as negative energy density or be repelled rather than attracted due to gravity. Exotic matter is used in some theories, for example, in the theory about the structure of wormholes. Most well-known representative exotic matter is a vacuum in a region with negative pressure produced by the Casimir effect.
- What types of wormholes are there?
From the point of view of theoretical travel, there are passable and impassable wormholes. Impassable are those through which the passage is destroyed, and this happens so quickly that no object simply has time to cross from one end to the other. Of course, the most interesting to study is the second type of wormholes - passable ones. There is even a beautiful theory that says: what we used to think of as supermassive black holes in the centers of galaxies are actually the mouths of wormholes. This theory is almost undeveloped and, naturally, has not yet found any confirmation; it exists, rather, as a kind of idea. Its essence is that outside the wormhole you only see that in the center of the galaxy there is a certain spherically symmetrical object, but what it is - a wormhole or a black hole - you cannot say, since you are outside this object.
In fact, they can be distinguished by only one parameter - mass. If the mass turns out to be negative, then this is probably a wormhole, but if the mass is positive, then additional information is needed, because a black hole can also turn out to be a wormhole. Negative mass in general is one of the central moments of the whole story with wormholes. Because in order to be passable, a wormhole must be filled with what is called an exotic substance - a substance in which, at least in places, at some points, the energy density is negative. At the classical level, no one has ever seen such a substance, but we know for sure that in principle it can exist. Quantum effects that lead to the emergence of such a substance have been recorded. This is a fairly well-known phenomenon and it is called the Casimir effect. It was officially registered. And it is connected precisely with the existence of negative energy density, which is very inspiring.
The Casimir effect is an effect consisting in the mutual attraction of conducting uncharged bodies under the influence of quantum fluctuations in a vacuum. Most often we are talking about two parallel uncharged mirror surfaces placed at a close distance, but the Casimir effect also exists in more complex geometries. The reason for the effect is energy fluctuations in the physical vacuum due to the constant birth and disappearance of virtual particles in it. The effect was predicted by Dutch physicist Hendrik Casimir in 1948 and later confirmed experimentally.
In general, in quantum science, negative energy density is a fairly common thing, which is associated, for example, with Hawking evaporation. If such a density exists, we can ask the following question: how large is the mass of the black hole (the parameter of the gravitational field it creates)? There is a solution to this problem that applies to black holes - that is, objects with positive mass, and there is a solution that applies to negative mass. If there is a lot of exotic matter in the wormhole, then the mass of this object outside will be negative. Therefore, one of the main types of “observations” of wormholes is tracking objects that can be assumed to have negative mass. And if we find such an object, then with a fairly high degree of probability we can say that this is a wormhole.
Wormholes are also divided into intra-world and inter-world. If we destroy the tunnel between the two mouths of the second type of hole, we will be able to see two completely unrelated universes. Such a wormhole is called interworldly. But if we do the same thing and see that everything is fine - we remain in the same Universe - then we have an intra-world wormhole in front of us. These two types of wormholes have a lot in common, but there are also important differences. The fact is that an intraworld wormhole, if it exists, tends to turn into a time machine. Actually, it was against the backdrop of this assumption that the latest surge of interest in wormholes arose.
Artist's impression of a wormhole
©depositphotos.com
In the case of an intraworld wormhole, there are two different ways to look at your neighbor: directly through the tunnel or in a roundabout way. If you begin to move one mouth of a wormhole relative to the other, then, in accordance with the well-known twin paradox, the second person, returning from a trip, will turn out to be younger than the remaining one. On the other hand, when you look through the tunnel, you are both sitting in motionless laboratories from your point of view, nothing happens to you, your clocks are synchronized. Thus, you have the theoretical possibility of diving into this tunnel and emerging at a moment that, from the point of view of an external observer, precedes the moment when you dived. A delay brought to the appropriate degree will give rise to the possibility of such a circular journey through space-time, when you return to your original place of departure and shake the hand of your previous incarnation.
The twin paradox is a thought experiment that attempts to “prove” the inconsistency of the special theory of relativity. According to STR, from the point of view of “stationary” observers, all processes in moving objects slow down. On the other hand, the principle of relativity declares the equality of inertial reference systems. Based on this, a reasoning is built that leads to an apparent contradiction. For clarity, the story of two twin brothers is considered. One of them (the traveler) goes on a space flight, and the second (the homebody) remains on Earth. Most often, the “paradox” is formulated as follows:
From the couch potato's point of view, the moving traveler's clock is in slow motion, so when he returns, it must lag behind the couch potato's clock. On the other hand, the Earth was moving relative to the traveler, so the couch potato’s clock must fall behind. In fact, the brothers have equal rights, therefore, after returning, their watches should show the same time. However, according to SRT, the traveler's watch will be lagging behind. In this violation of the apparent symmetry of the brothers, a contradiction is seen.
- What is the fundamental difference between a wormhole and a black hole?
First of all, it must be said that there are two types of black holes - those that were formed as a result of the collapse of stars, and those that existed initially, arose along with the emergence of the Universe itself. These two are fundamental different types black holes. At one time there was such a concept as a “white hole,” but now it is rarely used. A white hole is the same black hole, but evolving backward in time. Matter just flies into a black hole, but can never escape from there. On the contrary, matter only flies out of a white hole, but it is in no way possible to get into it. In fact, this is a very natural thing if we remember that the General Theory of Relativity is symmetric in time, which means that if there are black holes, white ones must also exist. Their totality represents a wormhole.
A black hole as imagined by an artist
©VICTOR HABBICK VISIONS/SPL/Getty
- What is known about the internal structure of wormholes?
So far, models in this sense are only being built. On the one hand, we know that the appearance of this exotic matter may have been discovered even experimentally, but a lot of questions still remain. The only model of a wormhole known to me that is more or less consistent with reality is the model of an initially evaporating (since the origin of the Universe) wormhole. Due to this evaporation, such a hole remains passable for a long time.
- What exactly are you working on?
I am engaged in purely theoretical activities, what can be generally called the causal structure of space-time is the classical Theory of Relativity, sometimes semi-classical (quantum theory does not yet exist, as is known).
In classical non-relativistic theory one can come up with fairly convincing evidence that time travel cannot exist, but in general relativity there is no such evidence. And Einstein, when he was just developing his theory, realized this. He wondered if there was some way to rule out this possibility. Then he failed to cope with this task, as he himself later said. And although Einstein created a language to study this question, the task remained academic. There was a surge of interest in it in the late 1940s, when Gödel proposed a cosmological model containing such closed curves. But since Gödel always proposed something exotic, it was treated with interest, but without serious scientific consequences. And then, somewhere at the end of the last century, thanks mainly to science fiction - for example, the film “Contact” with Jodie Foster - interest in the topic of time travel using wormholes was revived again. The author of the novel on which the film script is written is the very famous astronomer and popularizer of science Carl Sagan. He took the matter very seriously and asked his friend, also a very famous relativist, Kip Thorne, to see if everything described in the film was possible from a scientific point of view. And he published a semi-popular article in a magazine for American physics teachers, “Wormholes as a Tool for Studying the General Theory of Relativity,” where he considered the possibility of time travel through wormholes. And I must say that at that time the idea of traveling through black holes was popular in science fiction. But he understood that a black hole is an absolutely impassable object - travel through them is impossible, so he considered wormholes as a possibility of time travel. Although this was known before, for some reason people perceived his conclusions as a completely fresh idea and rushed to investigate it. Moreover, the emphasis was on the presumption that a time machine cannot exist, but they decided to find out why. And quite quickly the understanding came that there were no obvious objections to the existence of such a machine. Since then, larger-scale research has begun and theories have begun to emerge. In general, I have been doing this ever since.
Contact is a 1997 science fiction film. Director: Robert Zemeckis. Main plot: Ellie Arroway (Judy Foster) has devoted her entire life to science, she becomes a participant in a project to search for extraterrestrial intelligence. All attempts to search for extraterrestrial signals are fruitless, and the future of her project is in jeopardy. Ellie despairs of finding support, but unexpectedly receives help from the eccentric billionaire Hadden. And here is the result - Ellie picks up the signal. Decoding the signal shows that it contains a description technical device. Its purpose is unclear, but inside there is space for one person.
After creating and launching the device, Ellie goes on a journey through the wormhole system and is transported, probably to a planet in another star system. Waking up there, on the seashore, she meets a representative of another civilization, who chose the image of her late father. Looking around, the heroine realizes that this area has been recreated by an alien intelligence in her mind in the image of a drawing she drew as a child. The alien tells her that the device makes it possible to organize a system of interstellar communication routes, and the Earth henceforth becomes a member of the community of civilizations of the Universe.
Ellie returns to Earth. From the point of view of outside observers, nothing happened to her after the launch of the installation, and her body did not leave our planet. Ellie finds herself in a paradoxical situation. Being a scientist, from the point of view of strict science, she cannot confirm her words in any way. Another circumstance also becomes clear: the video camera attached to Ellie during the trip did not record anything, but the duration of the empty recording was not a few seconds, but 18 hours...
- Is it possible to “make” a wormhole?
There is a strict scientific result about this. This is due to the fact that there are no exact results on the study of mole holes. There is a theorem that was proven a long time ago, and it says this. There is such a thing as global hyperbolicity. In this case, it doesn’t matter at all what it means, but the point is that for now and since space is globally hyperbolic, it is impossible to create a wormhole - it can exist in nature, but you won’t be able to make it yourself. If you manage to disrupt global hyperbolicity, then perhaps you will be able to create a wormhole. But the fact is that this violation in itself is such an exotic thing, so poorly studied and poorly understood, that the by-product in the form of the birth of a wormhole is already a relatively small thing compared to the very fact that you managed to violate global hyperbolicity. There is a very famous thing at work here called the “principle of strict cosmic censorship,” which says that space is always globally hyperbolic. But this, in principle, is nothing more than a wish. There is no evidence of the correctness of this principle, there is simply a certain internal confidence inherent in many people that space-time must be globally hyperbolic. If this is the case, it is impossible to create a wormhole - you need to look for an existing one. Meanwhile, severe doubts about the correctness of the principle of cosmic censorship were expressed by the author himself, Roger Penrose, but that’s another story.
- So, creating a wormhole requires some serious energy expenditure?
It's very difficult to say anything here. The trouble is that when your global hyperbolicity is violated, then predictability is also violated - this is practically the same thing. You can somehow geometrically change the space near you, for example, take a bag and put it in another place. But there are certain limits within which you can do this, in particular the limit imposed by predictability. For example, sometimes you can tell what will happen in 2 seconds, and sometimes you can't. The line of what you can or cannot predict lies precisely in global hyperbolicity. If your space-time is globally hyperbolic, you can predict its evolution. If we assume that at some point it violates global hyperbolicity, everything becomes very bad with predictability. Therefore, an amazing thing arises, for example, such that right here and now a wormhole can materialize, through which a lion will jump out. It will be an exotic phenomenon, but it will not violate any laws of physics. On the other hand, you can spend a lot of effort, money and resources to somehow facilitate this process. But the result will still be the same - in both cases you don’t know whether a wormhole will appear or not. In classical physics, we can’t do anything about it - if it wants, it will arise, if it doesn’t want, it won’t arise - but quantum science does not give us any clues on this issue yet.
The principle of “cosmic censorship” was formulated in 1969 by Roger Penrose in the following figurative form: “Nature abhors naked singularity.” It states that space-time singularities appear in places that, like the interiors of black holes, are hidden from observers. This principle has not yet been proven, and there are reasons to doubt its absolute correctness (for example, the collapse of a dust cloud with high angular momentum leads to a “naked singularity”, but it is unknown whether this solution of Einstein’s equations is stable with respect to small perturbations of the initial data).
The Penrose formulation (a strong form of cosmic censorship) assumes that spacetime as a whole is globally hyperbolic.
Later, Stephen Hawking proposed a different formulation (a weak form of cosmic censorship), which assumes only the global hyperbolicity of the “future” component of space-time.
21:11 09/11/2018👁 1 719
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 special education from the reader; the most general ideas from the course will be quite sufficient 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 last years There have been many reports in the media 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 bombs). “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 the definition in simple words.
You can give different definitions to wormholes, but what is 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) to refer to the part of space-time that is limited by the entrances to wormholes and black holes, and the word “Universe” (with a capital letter) will mean all space-time, not anything limited.
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 give these concepts a completely physical meaning: we are talking about proper time, measured by an observer who moves freely (without rocket or any other engines) almost at 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 the zero geodesic line in the general theory of relativity. 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 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 (in physics, a singularity is an infinite density of matter that tears apart and destroys any other matter falling into 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 from a 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?
Can empty space really prevent us from passing 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 the school mathematics course, 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 just say ATTITUDE).
Now let’s place some body with mass M at our point “O”. If you believe Einstein’s theory and experiments (which were repeatedly carried out both on Earth and in solar system), then the space-time around the body will be curved and the above-mentioned RATIO will be less than 2π. Moreover, the larger the mass M, the smaller it is – 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. The very geometric property of 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 an additional dimension; three spatial and one time dimensions are enough for it. 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 that 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 (composed 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 design approaches the neck, the curvature of the surface of the funnel increases, and the surface of the design begins to deform in accordance with the shape of the funnel at a given place in the design. Our drawing (even though it is paper), just like any physical body, has elastic properties that prevent its deformation.
At the same time, the material of the design has a physical effect 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 will slip 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, the pattern needs to be large enough and strong enough). 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 human) 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 of modern cosmology. This model works within the framework of Einstein’s theory and assumes the existence (besides ours) of an infinite number of other universes that arise after the “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 up a unique opportunity to study the multi-element Universe and discover 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. This is already a mathematical concept, but don’t be alarmed - I will describe it without mathematics. As you know from a school physics course, every physical solid body has 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 pressure of phantom matter in modulus 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 the closed world lines of 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 in quantum physics (in the microworld) closed world lines of particles are commonplace. But the quantum world is a completely different matter. In it, for example, there is a quantum tunneling 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 is almost infinity. More specifically, the number of such attempts should 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, two conditions must be met:
Firstly, the wormhole must be a ringhole, i.e. unite different areas the same universe.
And secondly, this wormhole must rotate quickly enough (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 mathematical model, which 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 it is possible to obtain a closed world line, it will be destroyed by matter (which will move along this loop) even before the loop is closed. 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 - an 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
Actually, wormholes themselves have no direct relation to perpetual motion, 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.
Let me remind you of one of the amazing properties of phantom matter (see above): 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. Let's imagine a body with negative mass (made of phantom matter). According to the law of universal gravitation, 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 of a perpetual motion machine of the third kind is based (purely theoretically) on this effect. 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.
The existence of a monopole magnetic field in a black hole is 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 there is an electric charge inside the surface under which the field enters (or leaves). But magnetic charges have not been found in nature, so if a field enters a wormhole at one of the inputs, 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 is 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 characteristics, 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 must be a sufficient amount of phantom matter; what exactly is a difficult question; the answer to it can only be given by an accurate numerical calculation for a specific model (such models have already been calculated earlier 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, its constituent matter 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 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 repelled 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. By virtue of 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 could fly out to us from the previous universe? 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 probable (whether a black hole in our universe is at the same time a white hole from the previous universe or not).
So, such objects - black and white holes - 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 of the Reisner-Nordström black-and-white hole (Carter-Penrose diagram). On the right is shown the passage of a particle through this black- 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 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 spin (this is their angular momentum divided by the square of their mass) and the 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 greater any of these measures is to one, the less tidal forces will be in such a black hole at their maximum, and the greater the chances for matter (or 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 Cauchy horizon radius of this black-and-white Reissner-Nordström hole is 2 times smaller than the radius of the 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 grains of the sphere reach the observer with a red (and then violet) gravitational shift. 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 to the free fall of the 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 sufficiently large spatial scales on which 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 other, even more complex types of non-trivial topology - not only the topology of a 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 electric 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 of 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. Moreover, between these horizons the mathematical signs of space and time change places (although this does not mean at all 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 a radical change in the 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 thanks 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 a simple model well illustrates the action of a black-and-white hole and explains that outside a building, visitors entering and exiting can collide with each other, but inside a building they cannot because of 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 phenomena characteristic of wormholes and black-and-white holes are so unique properties that today observational astronomy has come 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 in the sky, 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
There are many interesting things in outer space that are still incomprehensible to humans. We know the theory about black holes and we even know where they are. However, of greater interest are wormholes, with the help of which movie characters move throughout the Universe in seconds. How do these tunnels work and why is it better for a person not to go into them?
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Movies " Star Trek", "Doctor Who" and the Marvel universe are united by one detail: traveling through space at enormous speed. If today it takes at least seven months to fly to Mars, then in the world of science fiction this can be done in a split second. High-speed travel is carried out using so-called wormholes (wormholes) - this is a hypothetical feature of space-time, which is a “tunnel” in space at each moment in time. To understand the principle of operation of the “hole”, you just have to remember Alice from “Through the Looking Glass”. There, the role of a wormhole was played by a mirror: Alice could instantly find herself in another place just by touching it.
The picture below shows how the tunnel works. In films, this is what happens: characters board a spaceship, quickly fly to the portal and, upon entering it, immediately find themselves in the right place, for example, on the other side of the Universe. Alas, even in theory it works differently.
Photo source: YouTubeGeneral relativity allows for the existence of such tunnels, but so far astronomers have not been able to find one. According to theorists, the first wormholes were less than a meter in size. It can be assumed that with the expansion of the Universe they also increased. But let's get to the main question: even if wormholes exist, why is using them a very bad idea? Astrophysicist Paul Sutter explained what the problem is with wormholes and why it is better for a person not to go there.
Wormhole theory
First, it’s worth finding out how black holes operate. Imagine a ball on a stretched elastic fabric. As it approaches the center, it decreases in size and at the same time becomes denser. The fabric bends more and more under its weight, until finally it becomes so small that it simply closes over it, and the ball disappears from sight. In the black hole itself, the curvature of space-time is infinite - this state of physics is called a singularity. It has neither space nor time in human understanding.
Photo source: Pikabu.ru According to the theory of relativity, nothing can travel faster than light. This means that nothing can get out of this gravitational field once it gets into it. A region of space from which there is no exit is called a black hole. Its boundary is determined by the trajectory of the light rays that were the first to lose the opportunity to escape. It's called the event horizon of a black hole. Example: looking out of the window, we do not see what is beyond the horizon, and a conventional observer cannot understand what is happening inside the boundaries of an invisible dead star.
There are five types of black holes, but we are interested in the stellar-mass black hole. Such objects are formed at the final stage of life celestial body. In general, the death of a star can result in the following things:
1. It will turn into a very dense extinct star, consisting of a series chemical elements, is a white dwarf;
2. A neutron star - has the approximate mass of the Sun and a radius of about 10-20 kilometers, inside it consists of neutrons and other particles, and outside it is enclosed in a thin but hard shell;
3. Into a black hole, the gravitational attraction of which is so strong that it can suck in objects flying at the speed of light.
When a supernova occurs, that is, the “rebirth” of a star, a black hole is formed, which can only be detected due to the radiation emitted. It is she who is capable of generating a wormhole.
If you imagine a black hole as a funnel, then an object falling into it loses its event horizon and falls inside. So where is the wormhole? It is located in exactly the same funnel, attached to the black hole tunnel, where the exits face outward. Scientists believe that the other end of the wormhole is connected to a white hole (the opposite of a black hole, into which nothing can fall).
Why you don't need to go into a wormhole
In white hole theory, not everything is so simple. Firstly, it is not clear how exactly to get into a white hole from a black one. Calculations around wormholes show that they are extremely unstable. Wormholes can evaporate or “spit out” a black hole and trap them again.
If a spaceship or a person falls into a black hole, he will get stuck there. There will be no way back - from the side of the black hole, for sure, because he will not see the event horizon. But the unfortunate person can try to find a white hole? No, because he does not see boundaries, so he will have to “fall” towards the singularity of a black hole, which may have access to the singularity of a white one. Or maybe not.
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In science fiction wormholes, or wormholes, are a method often used to travel very long distances in space. Could these magical bridges really exist?
As enthusiastic as I am about humanity's future in space, there is one glaring problem. We are soft meat sacs, consisting mainly of water, and those others are so far from us. Even with the most optimistic spaceflight technologies, we can imagine that we will never reach another star in a time equal to the duration of a human life.
Reality tells us that even the stars closest to us are incomprehensibly distant, and it would take an enormous amount of energy or time to make the journey. Reality tells us that we need a spaceship that can somehow fly for hundreds or thousands of years while astronauts are born on it, generation after generation, live their lives and die on the flight to another star.
Science fiction, on the other hand, leads us to methods for building improved engines. Fire up the warp drive and watch the stars flash past, making the journey to Alpha Centauri as fast and enjoyable as cruising on a ship somewhere at sea.
Still from the movie "Interstellar".
Do you know what's even simpler? Worm-hole; a magical tunnel connecting two points of space and time. Just set your destination, wait for the stargate to stabilize and just fly... fly halfway across the galaxy to your destination.
Yes, it's really cool! Someone should have invented these wormholes, ushering in a brave new future of intergalactic travel. What are wormholes, and how soon can I use them? You ask...
A wormhole, also known as an Einstein-Rosen bridge, is a theoretical method of folding space and time so that you can connect two points in space together. Then you could instantly move from one place to another.
We'll use the classic demo from , where you draw a line between two points on a piece of paper, and then fold the paper and insert a pencil into those two points to shorten the path. This works great on paper, but is it real physics?
Albert Einstein, captured in a 1953 photograph. Photographer: Ruth Orkin.
As Einstein taught us, gravity is not a force that attracts matter like magnetism, it is actually the curvature of space-time. The Moon thinks it is simply following a straight line through space, but in reality it is following a curved path created by the Earth's gravity.
And so, according to physicists Einstein and Nathan Rosen, you could spin a ball of spacetime so dense that two points would be in the same physical location. If you could keep the wormhole stable, you could safely separate the two regions of spacetime so that they were still in the same location, but separated by the distance you liked.
We go down the gravity well on one side of the wormhole, and then appear with lightning speed in another place at a distance of millions and billions of light years. While creating wormholes is theoretically possible, they are practically impossible from what we currently understand.
The first big problem is that wormholes are impassable, according to the General Theory of Relativity. So keep this in mind, the physics that predicts these things prohibits their use as a method of transportation. Which is a pretty serious blow to them.
Artistic illustration of a spaceship moving through a wormhole in distant galaxy. Credit: NASA
Secondly, even if a wormhole could be created, it would most likely be unstable, closing instantly after creation. If you tried to go to one end of it, you might just fall through.
Third, if they are traversable and it is possible to keep them stable, once any matter tries to pass through them - even photons of light - it would collapse the wormhole.
There is a glimmer of hope, as physicists still haven't figured out how to combine the theories of gravity and quantum mechanics. This means that the Universe itself may know something about wormholes that we do not yet understand. It is possible that they were created naturally as part of when the spacetime of the entire universe was pulled into a singularity.
Astronomers have proposed looking for wormholes in space by looking at how their gravity distorts the light of the stars behind them. None have shown up yet. One possibility is that wormholes look naturally like the virtual particles we know exist. Only they would be incomprehensibly small, on a Planck scale. You will need a smaller spaceship.
One of the most interesting implications of wormholes is that they could also allow you to travel through time. Here's how it works. First, create a wormhole in the laboratory. Then take one end of it, put a spaceship in it and fly at a significant fraction of the speed of light, so that the effect of time dilation takes effect.
For people on spaceship Only a few years will pass, while hundreds or even thousands of generations of people will change on Earth. Assuming you could keep the wormhole stable, open, and traversable, then traveling through it would be very interesting.
If you walked in one direction, you would not only travel the distance between the wormholes, but you would also move forward in time, and on the way back: back in time.
Some physicists such as Leonard Susskind believe that this would not work because it would violate two fundamental principles of physics: the law of conservation of energy and the Heisenberg energy-time uncertainty principle.
Unfortunately, it seems that wormholes will have to remain in the realm of science fiction for the foreseeable future, perhaps forever. Even if it were possible to create a wormhole, you would need to keep it stable, open, and then figure out how to allow matter to pass into it without collapsing. Still, if you could figure it out, you would do space travel very comfortable.
Title of the article you read "What are wormholes or wormholes?".