Theoretical physics is obscure to many, but at the same time it is of paramount importance in the study of the world around us. The task of any theoretical physicist is to build a mathematical model, a theory capable of explaining certain processes in nature.
Need
As you know, the physical laws of the macrocosm, that is, the world in which we exist, differ significantly from the laws of nature in the microcosm, within which atoms, molecules and elementary particles live. An example would be a difficult-to-understand principle called carpuscular-wave dualism, according to which micro-objects (electron, proton, and others) can be both particles and waves.
Like us, theoretical physicists want to describe the world in a concise and understandable way, which is the main calling of string theory. With its help, it is possible to explain some physical processes, both at the level of the macrocosm and at the level of the microcosm, which makes it universal, uniting other previously unrelated theories (general relativity and quantum mechanics).
essence
According to string theory, the whole world is built not from particles, as it is believed today, but from infinitely thin objects 10–35 m long, which have the ability to oscillate, which allows us to draw an analogy with strings. With the help of a complex mathematical mechanism, these vibrations can be associated with energy, and hence with mass, in other words, any particle arises as a result of one or another type of vibration of a quantum string.
Problems and features
Like any unconfirmed theory, string theory has a number of problems that indicate that it needs to be improved. These problems include, for example, the following - as a result of calculations, there was mathematically a new type of particles that cannot exist in nature - tachyons, the square of whose mass is less than zero, and the speed of movement exceeds the speed of light.
Another important problem, or rather feature, is the existence of string theory only in 10-dimensional space. Why do we perceive other dimensions? “Scientists have come to the conclusion that at very small scales, these spaces collapse and close on their own, as a result of which we cannot determine them.
Development
There are two types of particles: fermions - particles of matter, and bosons - carriers of interaction. For example, a photon is a boson that carries electromagnetic interaction, a graviton is gravitational, or the same Higgs boson that propagates interaction with the Higgs field. So if string theory took into account only bosons, then superstring theory also took into account fermions, which made it possible to get rid of tachyons.
The final version of the superstring principle developed by Edward Witten is called "m-theory", according to which an 11th dimension must be introduced to unify all the different versions of superstring theory.
On this, perhaps, we can finish. Work on solving problems and improving the existing mathematical model is being diligently carried out by theoretical physicists from around the world. Perhaps soon we will finally be able to understand the structure of the world around us, but looking back at the volume and complexity of the above, it is obvious that the resulting description of the world will not be understandable without a certain knowledge base in the field of physics and mathematics.
superstring theory
Briefly about superstring theory
This theory looks so wild that, quite possibly, it is correct!
Various versions string theories are today seen as the main contenders for the title of a comprehensive universal theory that explains the nature of all things. And this is a kind of Holy Grail of theoretical physicists involved in the theory of elementary particles and cosmology. Universal theory (aka theory of everything) contains only a few equations that combine the totality of human knowledge about the nature of interactions and properties of the fundamental elements of matter from which the Universe is built. Today, string theory has been combined with the concept supersymmetry, resulting in the birth superstring theory, and today this is the maximum that has been achieved in terms of unifying the theory of all four main interactions (forces acting in nature). The theory of supersymmetry itself has already been built on the basis of a priori modern concept, according to which any remote (field) interaction is due to the exchange of particles-carriers of interaction of the corresponding kind between interacting particles (Standard Model). For clarity, interacting particles can be considered the "bricks" of the universe, and carrier particles - cement.
Within the framework of the standard model, quarks act as building blocks, and interaction carriers are gauge bosons, which these quarks exchange with each other. The theory of supersymmetry goes even further and states that the quarks and leptons themselves are not fundamental: they all consist of even heavier and experimentally undiscovered structures (bricks) of matter, held together by an even stronger “cement” of superenergetic particles-carriers of interactions than quarks in hadrons and bosons. Naturally, in laboratory conditions, none of the predictions of the theory of supersymmetry has been verified so far, however, the hypothetical hidden components of the material world already have names - for example, seelectron(supersymmetric partner of an electron), squark etc. The existence of these particles, however, is unambiguously predicted by theories of this kind.
The picture of the Universe offered by these theories, however, is quite easy to visualize. On scales of the order of 10–35 m, that is, 20 orders of magnitude smaller than the diameter of the same proton, which includes three bound quarks, the structure of matter differs from what we are accustomed to even at the level of elementary particles. At such small distances (and at such high interaction energies that it is unthinkable) matter turns into a series of field standing waves, similar topics that are excited in the strings of musical instruments. Like a guitar string, in such a string, in addition to the fundamental tone, many overtones or harmonics. Each harmonic has its own energy state. According to principle of relativity(Theory of Relativity), energy and mass are equivalent, which means that the higher the frequency of the harmonic wave vibration of a string, the higher its energy, and the higher the mass of the observed particle.
However, if a standing wave in a guitar string is visualized quite simply, the standing waves proposed by superstring theory are difficult to visualize - the fact is that superstrings vibrate in a space that has 11 dimensions. We are accustomed to a four-dimensional space, which contains three spatial and one temporal dimensions (left-right, up-down, forward-backward, past-future). In the space of superstrings, things are much more complicated (see inset). Theoretical physicists get around the slippery problem of "extra" spatial dimensions by arguing that they are "hidden" (or, scientific language in other words, "compactify") and therefore are not observed at ordinary energies.
More recently, string theory has been further developed in the form theory of multidimensional membranes- in fact, these are the same strings, but flat. As one of its authors casually joked, membranes differ from strings in much the same way that noodles differ from vermicelli.
That, perhaps, is all that can be briefly told about one of the theories, not without reason claiming today the title of the universal theory of the Great Unification of all force interactions. Alas, this theory is not without sin. First of all, it has not yet been brought to a rigorous mathematical form due to the insufficiency of the mathematical apparatus for bringing it into strict internal correspondence. It has been 20 years since this theory was born, and no one has been able to consistently harmonize some of its aspects and versions with others. Even more unpleasant is the fact that none of the theorists who propose the theory of strings (and, especially, superstrings) has so far offered a single experiment on which these theories could be tested in the laboratory. Alas, I am afraid that until they do this, all their work will remain a bizarre game of fantasy and an exercise in comprehending esoteric knowledge outside the mainstream of natural science.
Introduction to superstrings
translation by Sergey Pavlyuchenko
String theory is one of the most exciting and profound theories in modern theoretical physics. Unfortunately, this is still a rather difficult thing to understand, which can only be understood from the standpoint of quantum field theory. Knowledge of mathematics such as group theory, differential geometry, etc. will not hurt understanding. Thus, for the majority, it remains a "thing in itself."
This introduction is intended as a "readable" short introduction to the basic concepts of string theory for those who are interested. Unfortunately, we will have to pay with rigor and completeness for the availability of the exposition. We hope it will give you answers to the simplest questions about string theory, and you will feel the beauty of this area of science.
String theory is a dynamically developing field of knowledge to this day; every day brings something new about her. So far, we do not know exactly whether the string theory describes our Universe and to what extent. But she may well describe it, as can be seen from this review.
The original version is at http://www.sukidog.com/jpierre/strings/index.html .
Why exactly string theory?
Although the Standard Model describes most of the phenomena that we can observe using modern accelerators, still many questions regarding Nature remain unanswered. The goal of modern theoretical physics is precisely to unify the descriptions of the universe. Historically, this path is quite successful. For example, Einstein's Special Theory of Relativity combined electricity and magnetism into an electromagnetic force. The 1979 Nobel Prize-winning work of Glashow, Weinberg, and Salam shows that the electromagnetic and weak forces can be combined into the electroweak. Further, there is every reason to believe that all the forces within the Standard Model eventually come together. If we begin to compare the strong and electroweak interactions, then we will have to go into regions of ever higher energies until they become equal in strength in the region of GeV. Gravity will join at energies of the order of .
The goal of string theory is precisely to explain the sign " ? " in the diagram above.
The characteristic energy scale for quantum gravity is called Planck mass and is expressed in terms of Planck's constant, the speed of light, and the gravitational constant as follows:
It can be assumed that, in its final form, string theory will provide answers to the following questions:
- What is the origin of the 4 forces of Nature known to us?
- Why are the masses and charges of particles exactly the way they are?
- Why do we live in a space with 4 spatial dimensions?
- What is the nature of space-time and gravity?
Fundamentals of string theory
We are accustomed to think of elementary particles (such as an electron) as point 0-dimensional objects. Somewhat more general is the notion fundamental strings as 1-dimensional objects. They are infinitely thin, and their length is of the order of . But this is simply negligible compared to the lengths we usually deal with, so we can assume that they are almost point-like. But as we shall see, their string nature is quite important.Strings are open and closed. As they move through space-time, they cover a surface called world sheet.
These strings have certain vibrational modes that determine the quantum numbers inherent in the particle, such as mass, spin, etc. The basic idea is that each mode carries a set of quantum numbers corresponding to a certain type of particle. This is the final unification - all particles can be described through one object - a string!
As an example, consider a closed string that looks like this:
Such a string corresponds to the massless graviton with spin 2 - to a particle carrying gravitational interaction. By the way, this is one of the features of string theory - it naturally and inevitably includes gravity as one of the fundamental interactions.
Strings interact by dividing and merging. For example, the annihilation of two closed strings into one closed string looks like this:
Note that the worldsheet surface is a smooth surface. One more "good" property of string theory follows from this - it does not contain a series of divergences inherent in quantum field theory with point particles. Feynman diagram for the same process
contains a topological singularity at the interaction point.
If we "glue" two simplest string interactions together, we get a process in which two closed strings interact through union into an intermediate closed string, which then again splits into two:
This main contribution to the interaction process is called tree approximation. In order to calculate the quantum mechanical amplitudes of processes using perturbation theory, add contributions from quantum processes of higher orders. Perturbation theory gives good results as the contributions get smaller and smaller as we use higher and higher orders. Even if you calculate only the first few diagrams, you can get fairly accurate results. In string theory, higher orders correspond to more holes (or "handles") on the world sheets.
The good thing about this approach is that each order of perturbation theory corresponds to only one diagram (for example, in field theory with point particles, the number of diagrams grows exponentially in higher orders). The bad news is that the exact calculations of diagrams with more than two holes are very difficult due to the complexity of the mathematical apparatus used when working with such surfaces. Perturbation theory is very useful in studying processes with weak coupling, and most of the discoveries in the field of elementary particle physics and string theory are connected with it. However, all this is still far from over. The answers to the deepest questions of the theory can be obtained only after the exact description of this theory has been completed.
D-branes
Strings can have completely arbitrary boundary conditions. For example, a closed string has periodic boundary conditions (the string "goes into itself"). Open strings can have two types of boundary conditions - the conditions Neumann and conditions Dirichlet. In the first case, the end of the string is free to move, however, without taking away momentum. In the second case, the end of the string can move along some manifold. This variety is called D-brane or Dp-brane(when using the second notation, "p" is an integer characterizing the number of spatial dimensions of the manifold). An example is two strings with one or both ends attached to a 2-dimensional D-brane or D2-brane:
D-branes can have a number of spatial dimensions from -1 to the number of spatial dimensions of our spacetime. For example, in the theory of superstrings there are 10 dimensions - 9 spatial and one temporal. Thus, in superstrings, the maximum that can exist is a D9-brane. Note that in this case the ends of the strings are fixed on a manifold that covers all space, so they can move everywhere, so the Neumann condition is actually imposed! In the case of p=-1, all spatial and temporal coordinates are fixed, and such a configuration is called instanton or D-instanton. If p=0, then all spatial coordinates are fixed, and the end of the string can only exist at one single point in space, so D0-branes are often called D-particles. Quite similarly, D1-branes are called D-strings. By the way, the word "brane" itself comes from the word "membrane", which is called 2-dimensional branes, or 2-branes.
In reality, D-branes are dynamic, they can fluctuate and move. For example, they interact gravitationally. In the diagram below, you can see how one closed string (in our case, a graviton) interacts with a D2-brane. Of particular note is the fact that, upon interaction, a closed string becomes open with both ends on the D-brane.
So, string theory is more than just string theory!Additional measurements
Superstrings exist in 10-dimensional space-time, while we live in 4-dimensional. And if superstrings describe our Universe, we need to somehow connect these two spaces. To do this, we will collapse 6 measurements to a very small size. If, in this case, the size of the compact dimension turns out to be of the order of the size of the strings (), then due to the smallness of this dimension, we simply cannot see it directly in any way. Ultimately, we will get our (3 + 1)-dimensional space, in which each point of our 4-dimensional Universe corresponds to a tiny 6-dimensional space. This is shown very schematically in the picture below:
Actually it's quite old idea, which goes back to the work of Kaluza and Klein in the 1920s. The mechanism described above is called Kaluza-Klein theory or compactification. Kaluza's work itself shows that if we take relativity in 5-dimensional spacetime, then wrap one dimension into a circle, we get 4-dimensional spacetime with relativity plus electromagnetism! And this happens due to the fact that electromagnetism is U(1) gauge theory. U(1) is the group of rotations around a point in the plane. The Kaluza-Klein mechanism gives a simple geometric interpretation of this circle - this is the same folded fifth dimension. Although folded measurements are small for direct detection, they can nonetheless have a deep physical meaning. [Completely accidentally leaked to the press, the work of Kaluza and Klein caused a lot of talk about the fifth dimension.]
How can we know if there really are extra dimensions and how can we "feel" them, having accelerators with sufficiently high energies? It is known from quantum mechanics that if the space is periodic, then the momentum is quantized: , while if the space is unbounded, then the range of momentum values is continuous. If the compactification radius (the size of additional dimensions) is reduced, then the range of allowed momentum values will increase. This is how you get the tower of momentum states - the tower of Kaluza Klein.
And if the radius of the circle is taken very large ("we decompactify" the measurement), then the range of possible momentum values will be rather narrow, but will be "almost-continuous". Such a spectrum will be similar to the mass spectrum of the world without compactifications. For example, states that are massless in a larger number of dimensions in a smaller number of dimensions will look exactly like the tower of states described above. Then a "set" of particles with masses equidistant from each other should be observed. True, in order to "see" the most massive particles, accelerators are needed that are much better than those that we currently have.
Strings have another remarkable property - they can "wind" around a compactified dimension, which leads to the appearance revolving mods in the mass spectrum. A closed string can wrap around a compactified dimension an integer number of times. Similarly to the Kaluza-Klein case, they contribute to the momentum as
. The essential difference lies precisely in another connection with the compactification radius . In this case, for small extra dimensions, reversal modes become very easy! 
Now we need to move on to our 4-dimensional space. For this we need a 10-dimensional superstring theory on a 6-dimensional compact manifold. Naturally, in this case, the picture described above becomes more complex. The easiest way is to assume that all these 6 dimensions are 6 circles, so they are all a 6-dimensional torus. Moreover, such a scheme makes it possible to preserve supersymmetry. It is believed that some supersymmetry also exists in our 4-dimensional space at energy scales of the order of 1 TeV (it is at these energies that supersymmetry has recently been sought at modern accelerators). In order to preserve the minimal supersymmetry, N=1 in 4 dimensions, one must compactify on a special 6-manifold called Calabi-Yau manifold.
The properties of Calabi-Yo manifolds can have important applications in low energy physics—to the particles we observe, their masses and quantum numbers, and to the number of particle generations. The problem here is that, generally speaking, there are a huge variety of Calabi-Yo varieties, and we do not know which one to use. In this sense, having in fact one 10-dimensional string theory, we get that a 4-dimensional theory becomes by no means the only possible one, at least at our (still incomplete) level of understanding. The "string people" (scientists working in the field of string theories) are hoping that with a complete nonperturbative string theory (a theory NOT based on the perturbations described a little above), we can explain how the universe went from 10- dimensional physics, which may have taken place during the high-energy period immediately after the Big Bang, to 4-dimensional physics, which we are dealing with now. [In other words, we will find a single Calabi-Yo manifold.] Andrew Strominger showed that Calabi-Yo manifolds can be continuously related to each other by conifold transitions and thus it is possible to move between different Calabi-Yo manifolds by changing the parameters of the theory. But this suggests the possibility that different 4D theories emerging from different Calabi-Yo manifolds are different phases of the same theory.
Duality
The five superstring theories described above turn out to be very different from the point of view of the weakly coupled perturbative theory (the perturbation theory developed above). But in fact, as it turned out in the last few years, they are all connected by various string dualities. Let's call the theory dual if they describe the same physics.The first type of duality that we will discuss here is T-duality. This type of duality connects a theory compactified on a circle of radius , with a theory compactified on a circle of radius . Thus, if in one theory space is folded into a circle of small radius, then in another it will be folded into a circle of large radius, but both of them will describe the same physics! Superstring theories of type IIA and type IIB are connected through T-duality, SO(32) and E8 x E8 heterotic theories are also connected through it.
Another duality that we will consider - S-duality. Simply put, this duality relates the strong coupling limit of one theory to the weak coupling limit of another theory. (Note that the loosely coupled descriptions of the two theories can then be very different.) For example, SO(32) Heterotic string theory and Type I theory are S-dual in 10 dimensions. This means that in the SO(32) strong coupling limit, the Heterotic theory transforms into Type I theory in the weak coupling limit and vice versa. Finding evidence of a duality between the strong and weak limits can be done by comparing the spectra of the light states in each of the patterns and finding that they agree with each other. For example, Type I string theory has a D-string that is heavy when weakly bound and light when strong. This D-string carries the same light fields as the SO(32) Heterotic String worldsheet, so when the Type I theory is very tightly coupled, the D-string becomes very light, and we will simply see that the description becomes as well as through a weakly coupled Heterotic string. Another S-duality in 10 dimensions is the self-duality of IIB strings: the strongly coupled IIB string limit is simply another IIB theory, but loosely coupled. The IIB theory also has a D-string (albeit more supersymmetric than the Type I D-strings, so the physics is different here) that becomes light when strongly coupled, but this D-string is also the other fundamental string of the theory. and Type IIB.
The dualities between the various string theories are evidence that they are all simply different limits of the same theory. Each of the limits has its applicability, and different limits different descriptions intersect. What is this M-theory shown in the picture? Read on!
M-theory
At low energies, M-theory is described by a theory called 11-dimensional supergravity. This theory has a membrane and a five-brane as solitons, but no strings. How can we get the strings we already love here? It is possible to compactify an 11-dimensional M-theory on a circle of small radius to obtain a 10-dimensional theory. Then if our membrane had the topology of a torus, then by folding one of these circles, we get a closed string! In the limit where the radius is very small, we get a Type IIA superstring.
But how do we know that M-theory on a circle will produce a Type IIA superstring and not IIB or heterotic superstrings? The answer to this question can be obtained after a thorough analysis of the massless fields that we obtain as a result of the compactification of 11-dimensional supergravity on a circle. Another simple test might be to find that the D-brane from M-theory is unique to IIA theory. Recall that the IIA theory contains D0, D2, D4, D6, D8-branes, and an NS five-brane. The following table summarizes all of the above:
D6 and D8-branes are omitted here. The D6-brane can be interpreted as a "Kaluza-Klein monopole", which is a special solution to 11-dimensional supergravity when compactified to a circle. The D8-brane does not have a clear interpretation in terms of M-theory, and this is still an open question.
Another way to obtain a consistent 10-dimensional theory of u is the compactification of the M-theory of u into a small segment. This means that we assume that one of the dimensions (11th) has a finite length. In this case, the ends of the segment define the boundaries of 9 spatial dimensions. At these boundaries it is possible to construct an open membrane. Since the intersection of the membrane with the boundary is a string, it can be seen that the (9+1)-dimensional "world volume" (worldvolume) can contain strings "protruding" from the membrane. After all this, in order to avoid anomalies, it is necessary that each of the boundaries carry an E8 gauge group. Therefore, if we make the space between the boundaries very small, we get a 10-dimensional theory with strings and an E8 x E8 gauge group. And this is the E8 x E8 heterotic string!
Thus, considering different conditions and different dualities between string theories, we will come to the conclusion that the basis of all this is one theory - M-theory. At the same time, five superstring theories and 11-dimensional supergravity are its classical limits. Initially, we tried to obtain the corresponding quantum theories by "expanding" the classical limits using perturbative theory (perturbation theory). However, the perturbative theory has its limits of applicability, so by studying the nonperturbative aspects of these theories, using dualities, supersymmetry, etc. we come to the conclusion that they are all united by one single quantum theory. This uniqueness is very attractive, so work on the construction of a complete quantum M-theory is in progress. full swing.
Black holes
The classical description of gravity - the General Theory of Relativity (GR) - contains solutions called "black holes" (BHs). There are quite a few types of black holes, but they all show similar general properties. The event horizon is a surface in spacetime that, in simple terms, separates the region inside a black hole from the region outside it. The gravitational attraction of black holes is so strong that nothing, even light, having penetrated below the horizon, can escape back. Thus, classical black holes can only be described using parameters such as mass, charge, and angular momentum.
(explanation of the Penrose diagram a)Black holes are good laboratories for studying string theories, since the effects of quantum gravity are important even for fairly large black holes. Black holes are not really "black" because they radiate! Using semi-classical arguments, Stephen Hawking showed that black holes radiate thermal radiation from their horizon. Since string theory is, among other things, also a theory of quantum gravity, it is able to consistently describe black holes. And then there are black holes that satisfy the equation of motion for strings. These equations are similar to those from GR, but they have some additional fields that came there from the strings. In superstring theories, there are special solutions of the BH type, which are also supersymmetric in themselves.
One of the most dramatic results in string theory was the derivation of a formula for bekenstein-hawking entropy A black hole derived from considering the microscopic string states that form a black hole. Bekenstein noted that black holes obey the "area law", dM = K dA, where "A" is the area of the horizon and "K" is a constant of proportionality. Since the total mass of a black hole is its rest energy, the situation is very similar to thermodynamics: dE = T dS, which was shown by Bekenstein. Hawking later showed in a semiclassical approximation that the temperature of a black hole is T = 4k, where "k" is a constant called "surface gravity". Thus, the entropy of the black hole can be rewritten as . Moreover, Strominger and Vafa recently showed that this formula for entropy can be obtained microscopically (up to a factor of 1/4) using the degeneracy of the quantum states of strings and D-branes corresponding to certain supersymmetric BHs in string theory ii. By the way, D-branes give a description at small distances as in the case of a weak connection. For example, the BHs considered by Strominger and Vafa are described by 5-branes, 1-branes, and open strings "living" on a 1-brane, all folded into a 5-dimensional torus, effectively giving a 1-dimensional object, the black hole.
In this case, Hawking radiation can be described within the framework of the same structure, but if open strings can "travel" in both directions. Open strings interact with each other and radiation is emitted in the form of closed strings.
Precise calculations show that for the same types of black holes, string theory gives the same predictions as semiclassical supergravity, including a non-trivial frequency-dependent correction called the "grayness parameter" ( greybody factor).
Quantum gravity discovered on Earth?
<< Вчера Tomorrow >> 
Explanation: Are there separate portions of gravity? The theory known as quantum mechanics describes the laws that govern the universe at small distances, while Einstein's general theory of relativity explains the nature of gravity and the universe at large scales. Until now, no theory has been created that can combine them. Research recently done in France may have shown that gravity is a quantum field. It is claimed that Earth's gravitational field showed its quantum nature. In an experiment carried out by Valery Nezvizhevsky and colleagues at , it was shown that supercold neutrons moving in a gravitational field are detected only at discrete heights. Scientists around the world are awaiting independent confirmation of these results. The figure shows, in false colors, the surface that can form during the evolution of a one-dimensional string. Describing elementary particles as tiny strings, many physicists are working towards a truly quantum theory of gravity. (Ed. note: The experiments of French and Russian physicists described in this note, published in nature, 415 , 297 (2002) have nothing to do with quantum gravity. Their explanation(both given by the authors of the experiments, as well as published in New Scientist and Physicsweb.org) completely different.
Experimenters seek new forces predicted by superstring theories
Researchers at the University of Colorado at Boulder have managed to perform the most sensitive experiment to date, evaluating the gravitational interaction between masses separated by only twice the thickness of a human hair, but they did not observe any of the predicted new forces.The results obtained make it possible to exclude some variants of superstring theory, in which the corresponding parameter of the action of new forces from "folded" measurements is in the range from 0.1 to 0.01 mm.
In string theory or superstrings, string theory, considered the most promising approach to the long-awaited grand unification - a single description of all known forces and matter, it is assumed that everything in the universe is made up of tiny loops of vibrating strings. According to various versions of superstring theory, there must be at least six or seven additional spatial dimensions in addition to the three that are available to us, and theorists believe that these extra dimensions are folded into small spaces. This "compactification" gives rise to what are called modules fields, which describe the size and shape of the folded dimensions at each point in space-time.
The moduli regions have effects comparable in strength to ordinary gravity, and according to recent predictions, they can be detected already at distances of the order of 0.1 mm. The limit of sensitivity achieved in previous experiments made it possible to test the force of attraction between two masses separated by only 0.2 mm, so the question remained open. However, it remains open to this day.
"If these forces really exist, then we now know that they should manifest themselves at smaller distances than we tested," explains the head of the laboratory, Professor John Price of the University of Colorado (John Price). "However, these results in themselves do not refute the theory ii. It is only necessary to keep in mind that the effect will have to be sought at shorter distances and use settings with higher sensitivity. " In addition, the researchers claim that such experiments in and of themselves are not intended to confirm or disprove the theory of superstrings. “The ideas we are testing are just some of the possible string-inspired scenarios, not accurate predictions of the theory itself,” John Price told Space.com. “There is no way yet for string theory to make accurate predictions of this kind , and I would say that no one knows if string theory will ever be able to do that." However, experiments at shorter distances may still "add more patches to the quilt of physics", and it is therefore very important to continue this kind of research, because "something new and 'very fundamental' may be discovered".
The experimental setup of researchers from the University of Colorado, called a high-frequency resonator (high-frequency resonator), consisted of two thin tungsten plates (20 mm long and 0.3 mm thick). One of these records was made to oscillate at a frequency of 1000 Hz. The movements of the second plate, caused by the impact of the first, were measured by very sensitive electronics. We are talking about forces measured in femtonewtons (10–15 N), or about one millionth of the weight of a grain of sand. The force of gravity acting at such small distances turned out to be quite traditional, described by Newton's well-known law.
Professor Price proposes to continue experiments to try to measure forces at even shorter distances. To take the next step, Colorado experimenters remove the gold-plated sapphire screen between the tungsten strips that blocked electromagnetic forces, and replace it with thinner beryllium-copper foil, allowing the masses to move closer together. They also plan to cool the experimental setup to reduce interference from thermal fluctuations.
Regardless of the fate of superstring theory, the ideas of extra dimensions, introduced almost a hundred years ago (at that time many physicists laughed at them), are becoming extremely popular due to the crisis of standard physical models that are unable to explain new observations. Among the most egregious facts is the accelerated expansion of the Universe, which has many confirmations. A mysterious new force, so far called dark energy, is pushing our cosmos apart, acting like some kind of anti-gravity. No one knows what physical phenomenon underlies this. What cosmologists do know is that while gravity holds galaxies together at a "local" level, mysterious forces push them apart. about larger scale.
Dark energy can be explained by interactions between dimensions, those that we see and those that are still hidden from us, some theorists believe. At the annual meeting of the AAAS (American Association for the Advancement of Science) held in Denver earlier this month, the most respected cosmologists and physicists expressed cautious optimism about this.
"There is a vague hope that the new approach will solve the whole set of problems at once," says physicist Sean Carroll, an assistant professor at the University of Chicago.
All these problems are inevitably grouped around gravity, the force of which was calculated by Newton more than three centuries ago. Gravity was the first of the fundamental forces to be described mathematically, but it is still the most poorly understood. Quantum mechanics, developed in the 20s of the last century, describes well the behavior of objects at the atomic level, but is not very friendly with gravity. The fact is that although gravity acts at large distances, it is still very weak compared to the other three fundamental forces (electromagnetic, strong and weak interactions that dominate the microcosm). Understanding gravity at the quantum level is expected to link quantum mechanics to a full description of other forces.
In particular, scientists could not determine for a long time whether Newton's law (the inverse proportionality of force to the square of distance) is valid at very small distances, in the so-called quantum world. Newton developed his theory for astronomical distances, such as the interactions of the Sun with the planets, but now it turns out that he is valid in the microcosm as well.
"What's happening right now in particle physics, gravitational physics and cosmology is very reminiscent of the time when quantum mechanics began to unify," says Maria Spiropulu, researcher at the University of Chicago, organizer of the AAAS workshop on extra-dimensional physics (physics of extra dimensions).
For the first time it was possible to measure the speed of gravity
Russian physicist Sergei Kopeikin, who works at the University of Missouri at Columbia, and American Edward Fomalont from the National Radio Astronomy Observatory in Charlottesville, Virginia, said that for the first time they were able to measure the speed of gravity with acceptable accuracy. Their experiment confirms the opinion of most physicists: the speed of gravity is equal to the speed of light. This idea underlies modern theories, including Einstein's General Theory of Relativity, but so far no one has been able to measure this quantity directly in an experiment. The study was released Tuesday at the 201st meeting of the American Astronomical Society in Seattle. The results were previously submitted for publication in a scientific journal, but were criticized by some experts. Kopeikin himself considers the criticism unfounded.
Newton's theory of gravity assumes that the force of gravity is transmitted instantaneously, but Einstein suggested that gravity travels at the speed of light. This postulate became one of the foundations of his Theory of Relativity in 1915.
The equality of the speed of gravity and the speed of light means that if the Sun suddenly disappeared from the center solar system, the Earth would remain in its orbit for about 8.3 minutes more - the time it takes for light to travel from the Sun to the Earth. After those few minutes, the Earth, feeling free from the Sun's gravity, would leave its orbit and fly away into space in a straight line.
How can you measure the "speed of gravity"? One way to solve this problem is to try to detect gravitational waves - small "ripples" in the space-time continuum, which diverge from any accelerated masses. Various installations for capturing gravitational waves have already been built in many, but not one of them has so far been able to register such an effect due to its exceptional weakness.
Kopeikin went the other way. He rewrote the equations of General Relativity in such a way as to express the gravitational field of a moving body in terms of its mass, velocity, and velocity of gravity. It was decided to use Jupiter as a massive body. A rather rare case presented itself in September 2002, when Jupiter passed in front of a quasar (such events occur about once every 10 years), which emits intense radio waves. Kopeikin and Fomalont combined the results of observations from a dozen radio telescopes in different parts the globe, from Hawaii to Germany (using both the 25-meter radio telescopes of the National Radio Astronomy Observatory and the 100-meter German instrument at Effelsberg) to measure the smallest apparent change in the position of a quasar caused by the bending of radio waves from this source in Jupiter's gravitational field. By investigating the nature of the impact of Jupiter's gravitational field on passing radio waves, knowing its mass and speed, one can calculate the speed of gravity.
The joint work of terrestrial radio telescopes has made it possible to achieve an accuracy 100 times greater than is achievable using the Hubble Space Telescope. The displacements measured in the experiment were very tiny - changes in the position of the quasar (the angular distance between it and the reference quasar was measured) were within 50 millionths of an arc second. The equivalent of such measurements could be the size of a silver dollar on the Moon or the thickness of a human hair from a distance of 250 miles, astronomers say (Western sources, apparently, did not think to pay attention to the meaning of the Russian surname of one of the authors of the studies, otherwise they would not be comparing sizes with a dollar, but with our monetary unit ...).
The result obtained: gravity is transmitted from 0.95 of the speed of light, the possible error of the experiment is plus or minus 0.25. "We now know that the speed of gravity is probably equal to the speed of light," said Fomalont. "And we can safely rule out any result that is twice that value."
Steven Carlip, professor of physics at the University of California, says the experiment is a "good demonstration" of Einstein's principle. He says that the experiment was preceded by measurements of the deflection of light by the Sun, but they were much less accurate. Moreover, new measurements of the gravitational velocity in the very near future will have to clarify this value as well. Many gravitational wave interferometers have been put into operation in recent months, one of them should finally detect gravitational waves directly and thus measure their speed - an important fundamental constant of our Universe.
However, it should be noted that the experiment itself is not an unambiguous confirmation of Einstein's theory of gravity. With the same success, it can be considered a confirmation of existing alternative theories. For example, Academician Logunov's (RTG) relativistic theory of gravity, which became known to the general public about ten years ago, does not diverge from general relativity in this respect. There are also gravitational waves in RTG, although, as is known, there are no black holes. And another "refutation" of Newton's theory of gravity is of no particular value. Nevertheless, the result is important in terms of "closing" some variants of modern theories and supporting others - it is associated with cosmological theories of multiple universes and the so-called string or superstring theory, but it is too early to draw final conclusions, the researchers say. In the newest so-called unified M-theory, which is the development of superstring theory, in addition to "strings" ("strings" - strings), new multidimensional objects - branes (brane) have appeared. Superstring theories inherently include gravity because their calculations invariably predict the existence of the graviton, a weightless hypothetical particle with spin 2. It is assumed that there are additional spatial dimensions, only "rolled up". And gravity could act "shortcut" through these extra dimensions, seemingly traveling faster than the speed of light, but without violating the equations of general relativity.
Two relativistic physicists present their views on the universe,
AT Scientific American these lectures were published with abbreviations, the corresponding places in the text are marked with dots
its evolution and the role of quantum theoryIntroduction
In 1994, Stephen Hawking and Roger Penrose gave a series of public lectures on general relativity at the Isaac Newton Institute of Mathematical Sciences at the University of Cambridge. Our journal presents to you excerpts from these lectures published this year by Princeton University Press titled "The Nature of Space and Time", which allow you to compare the views of these two scientists. Although they both belong to the same school of physics (Penrose assisted Hawking's doctoral dissertation at Cambridge), their views on the role of quantum mechanics in the evolution of the universe are very different from each other. In particular, Hawking and Penrose have different ideas about what happens to the information stored in a black hole and why the beginning of the universe is different from its end.
One of Hawking's major discoveries, made in 1973, was the prediction that, due to quantum effects, black holes could emit particles. As a result of such a process, the black hole evaporates, and ultimately it is possible that nothing of its original mass will remain. But during their formation, black holes absorb a lot of particles falling on it with different types, properties and configurations. Although quantum theory requires that such information be stored, the details of what happens to it next remain a topic of heated debate. Hawking and Penrose both believe that, during radiation, a black hole loses the information that it contained in itself. But Hawking insists that this loss is irreplaceable, while Penrose argues that it is balanced by spontaneous measurements of quantum states that feed information back into the black hole.
Both scientists agree that a future theory of quantum gravity is needed to describe nature. But their views differ on some aspects of this theory. Penrose believes that even if the fundamental interactions of elementary particles are symmetrical with respect to time reversal, then quantum gravity must break such a symmetry. The temporal asymmetry should then explain why the universe was so homogeneous at the beginning (as shown by the microwave background radiation produced by the big bang), while at the end the universe must be heterogeneous.
Penrose tries to include such asymmetry in his Weyl curvature hypothesis. Space-time, according to Albert Einstein, is curved by the presence of matter. But spacetime can also have some inherent deformation, referred to as the Weyl curvature. Gravitational waves and black holes, for example, allow spacetime to curve even in areas that are empty. In the early universe, the Weyl curvature was probably zero, but in the fading universe, as Penrose argues, a large number of black holes will lead to an increase in the Weyl curvature. This will be the difference between the beginning and the end of the universe.
Hawking agrees that the big bang and the final collapse ("Big crunch") will be different, but he does not consider time asymmetry to be a law of nature. The main reason for this difference, he thinks, is the way in which the development of the universe is programmed. He postulates a kind of democracy, stating that there cannot be a single spatial point in the universe; and therefore, the universe cannot have a boundary. It is this no-boundary proposal that Hawking claims explains the homogeneity of the microwave background radiation.
The views of both physicists on the interpretation of quantum mechanics are also radically different. Hawking believes that the only purpose of AI theory is to make predictions that are consistent with experimental data. Penrose, on the other hand, believes that a simple comparison of predictions with experiments is not enough to explain reality. He points out that a quantum theory requiring a superposition of wave functions is a concept that can lead to absurdities. These scientists thus take the well-known discussion between Einstein and Bohr about the bizarre consequences of quantum theory to a new level.
Stephen Hawking on quantum black holes:
The quantum theory of black holes... seems to lead to a new level of unpredictability in physics beyond the usual quantum mechanical uncertainty. This is because black holes seem to have internal entropy and lose information from our region of the universe. I must say that these claims are highly controversial: many scientists working in the field of quantum gravity, including almost all those who came to it from particle physics, instinctively reject the idea that information about the state of a quantum system can be lost. However, this view has not led to much success in explaining how information can leave a black hole. Ultimately, I believe that they will be forced to accept my suggestion that information is irretrievably lost, just as they were forced to accept that black holes radiate, which goes against all their preconceptions...
The fact that gravity is attractive means that there is a tendency in the universe for matter to pull together in one place, a tendency for objects like stars and galaxies to form. Further contraction of these objects may be held back for some time by thermal pressure, in the case of stars, or by rotation and internal motions, in the case of galaxies. However, eventually the heat or angular momentum will be carried away and the object will begin to contract again. If the mass is less than about one and a half solar masses, the contraction can be stopped by the pressure of the degenerate gas of electrons or neutrons. The object stabilizes to become a white dwarf or a neutron star, respectively. However, if the mass is greater than this limit, then there is nothing to stop the steady contraction. As soon as the contraction of an object approaches a certain critical size, the gravitational field on its surface will be so strong that the light cones will be tilted inward.... We can see that even outgoing light rays are bent towards each other, so they approach rather than diverge. This means that there is some closed surface....
Thus, there must be a region of space-time from which it is impossible to escape to an infinite distance. This area is called a black hole. Its boundary is called the event horizon, it is a surface formed by light rays that cannot escape to infinity....
A large amount of information is lost when the space body collapses to form a black hole. A collapsing object is described by a very large number of parameters. Its state is determined by the types of matter and the multipole moments of the distribution of their masses. Despite this, the emerging black hole is completely independent of the type of matter and quickly loses all multipole moments except for the first two: monopole, which is the mass, and dipole, which is the angular momentum.
This loss of information did not really matter in the classical theory. We can say that all information about the collapsing object is inside the black hole. For an observer outside the black hole, it would be very difficult to determine what a collapsing object looks like. However, in classical theory it was still possible in principle. The observer would never actually lose sight of the collapsing object. Instead, it would seem to him that the object slows down in its contraction and becomes more and more dimmer as it approaches the event horizon. This observer could still see what the collapsing object was made of and how mass was distributed in it.
However, from the point of view of quantum theory, everything changes completely. During the collapse, the object would emit only a limited number of photons before crossing the event horizon. These photons would be absolutely not enough to give us all the information about the collapsing object. This means that in quantum theory there is no way in which an external observer could determine the state of such an object. One might think that it doesn't matter too much, because the information would still be inside the black hole, even if it couldn't be measured from the outside. But this is precisely the case where the second effect of the quantum theory of black holes manifests itself....
Quantum theory makes black holes radiate and lose mass. And apparently they eventually disappear completely - along with the information inside them. I want to make an argument that this information is indeed lost and not returned in any form. As I will show later, with this loss of information, a higher level of uncertainty enters physics than the usual uncertainty associated with quantum theory. Unfortunately, unlike the Heisenberg uncertainty relation, this new level of uncertainty will be rather difficult to confirm experimentally in the case of black holes.
Roger Penrose on quantum theory and spacetime:
Quantum theory, special relativity, general relativity and quantum field theory are the greatest physical theories of the 20th century. These theories are not independent of each other: general relativity was built on top of special relativity, and quantum field theory has special relativity and quantum theory as its foundation.
It has been commonly said that quantum field theory is the most accurate of all the physical theories that have ever existed, giving an accuracy of up to 11 decimal places. However, I would like to point out that general relativity has now been tested to within 14 decimal places (and this accuracy is apparently only limited by the accuracy of clocks running on Earth). I mean the binary pulsar Hulse-Taylor PSR 1913+16, a pair of neutron stars rotating relative to each other, one of which is a pulsar. General relativity predicts that such an orbit slowly contracts (and its period decreases) because energy is lost due to the emission of gravitational waves. This process has indeed been recorded experimentally, and the full description of its motion observed for 20 years ... is in agreement with the general theory of relativity (which includes Newton's theory) with the remarkable accuracy noted above. The researchers of this star system have rightfully received Nobel Prizes for your work. Quantum theorists have always argued, referring to the accuracy of their theory, that general relativity should take its cue from it, but I think now that quantum field theory should take its cue.
Although these four theories have achieved great success, they are not free from problems.... The general theory of relativity predicts the existence of space-time singularities. There is a "measurement problem" in quantum theory, which I will describe later. It may turn out that the solution to the problems of these theories lies in the recognition of the fact that they are incomplete theories. For example, many people anticipate that quantum field theory could somehow "smear" the singularities of general relativity....
And now I would like to say a few words about the loss of information in black holes, which I believe is relevant to the last statement. I agree with almost everything Stephen has said about this. But while Steven regards the loss of information in black holes as a new uncertainty in physics, a higher level than quantum mechanical uncertainty, I see it as just an "additional" uncertainty.... It is possible that a small amount of information is lost in the black hole's evaporation time... but this effect will be much smaller than the loss of information during the collapse (for which I accept any reasonable picture of the black hole's final disappearance).
As a thought experiment, consider a closed system in a large box and consider the motion of matter inside the box in phase space. In regions of phase space corresponding to black hole locations, the trajectories describing the physical evolution of the system will converge, and the phase volumes filled by these trajectories will shrink. This occurs as a result of the loss of information at the black hole singularity. This reduction is in direct conflict with the law of classical mechanics known as Liouville's theorem, which states that the phase volumes carried by phase trajectories remain constant... Thus, the space-time of a black hole violates the conservation of such volumes. However, in my picture, this loss of phase space volume is balanced by a process of spontaneous quantum measurements that results in information recovery and an increase in phase space volume. As I understand it, this happens because the uncertainty associated with the loss of information in black holes is, as it were, "additional" to quantum mechanical uncertainty: each of them is only one side of the same coin ....
Now let's consider the thought experiment with Schrödinger's cat. It describes the unenviable position of a cat in a box, in which an emitted photon falls on a semitransparent mirror, and the transmitted part of its wave function is recorded by a sensor. If the sensor detects a photon, then the gun goes off, killing the cat. If the sensor does not detect a photon, then the cat remains alive and well. (I know Steven disapproves of mistreatment of cats, even in thought experiments!) The wave function of such a system is a superposition of these two possibilities... But why are we only able to perceive the macroscopic alternatives "cat dead" and "cat alive"? rather than macroscopic superpositions of such states? ...
I suppose that with the involvement of the general theory of relativity, the use of superpositions of alternative space-time geometries faces serious difficulties. It is possible that the superposition of two different geometries is unstable and breaks down into one of these two alternatives. Such geometries could be, for example, the space and time of a living or dead cat. To refer to this collapse of the superposition into one of the alternative states, I use the term objective reduction, which I like because it has a nice acronym (OR). What does the Planck length of 10-33 centimeters have to do with this? This length is a natural criterion for determining whether the geometries are indeed different worlds. The Planck scale also determines the time scale at which the reduction into various alternatives takes place.
Hawking on quantum cosmology:
I end this lecture by discussing a point on which Roger and I have different views - the arrow of time. There is a very clear distinction between the forward and reverse directions of time in our part of the universe. It is enough to scroll back any movie to see this difference. Instead of cups falling off the table and shattering into small pieces, we would see these pieces come back together and bounce back onto the table. Isn't real life like something like that?.
The local laws of physical fields satisfy the requirement of symmetry in time, or to be more precise, CPT invariance (Charge-Parity-Time - Charge-Parity-Time). Thus, the observed difference between past and future comes from the boundary conditions of the universe. Consider a model in which a spatially closed universe expands to its maximum size, after which it collapses again. As Roger emphasized, the universe will be very different at the end points of this story. At its beginning, the universe, as we now think, will be fairly smooth and regular. However, when it starts to collapse again, we expect it to be extremely erratic and irregular. Since there are many more disordered configurations than ordered ones, this means that the initial conditions must be chosen extremely precisely.
As a result, the boundary conditions must be different at these instants of time. Roger's suggestion is that the Weyl tensor should only vanish at one of the ends of time. The Weyl tensor is that part of the curvature of space-time that is not determined by the local distribution of matter through the Einstein equations. This curvature is extremely small in an ordered early stage, and very large in a collapsing universe. Thus, this proposal would allow us to distinguish both ends of time from each other and explain the existence of the arrow of time.
I think that Roger's proposal is Weyl's in two senses of the word. First, it is not CPT-invariant. Roger sees this property as a virtue, but I feel that symmetries should not be abandoned without good enough reason. Second, if the Weyl tensor had been exactly zero at the early stage of the universe, then it would have remained homogeneous and isotropic throughout the subsequent time. The Weyl Hypothesis of Roger cannot explain either the fluctuations in the microwave background or the perturbations caused by galaxies and bodies like ourselves.
Despite all this, I think Roger pointed out a very important difference between these two time limits. But the fact that the smallness of the Weyl tensor in one of the boundaries should not be accepted by us ad hoc, but should be derived from the more fundamental principle of "no boundaries" ....
How can two time limits be different? Why should perturbations be small in one of them, but not in the other? The reason for this is that the field equations have two possible complex solutions.... Obviously, one solution corresponds to one time boundary and the other to the other.... At one end of time, the universe was very smooth and the Weyl tensor is small . However, it certainly could not be equal to zero, since this leads to a violation of the uncertainty relation. Instead, small fluctuations should take place, which can later turn into galaxies and bodies, like ourselves. In contrast to the beginning, the end universe should be very irregular and chaotic, and the Weyl tensor should be very large. This would explain why there is an arrow of time and why cups fall off the table and break much more readily than they recover and jump back up.
Penrose on quantum cosmology:
From what I understand in Steven's concept, I conclude that our disagreements on this issue(Weyl curvature hypotheses) are extremely large... For the initial singularity, the Weyl curvature is approximately zero.... Steven argued that small quantum fluctuations must take place in the initial state, and therefore the zero Weyl curvature hypothesis a is classical and unacceptable. But I think there is some freedom as to the precise formulation of this hypothesis. Small perturbations are certainly acceptable from my point of view in quantum mode. We only need to significantly limit these fluctuations around zero ....
It is possible that the James-Hartley-Hawking principle of "no boundaries" is a good candidate for describing the structure of the initial state. However, it seems to me that something else is needed to explain the final state. In particular, a theory explaining the structure of singularities would have to include violation of CPT and other symmetries in order to be compatible with the Weyl curvature hypothesis. Such time symmetry breaking could be quite small; and could be implicitly contained in a new theory that goes beyond quantum mechanics.
Hawking on physical reality:
These lectures made the difference between Roger and me very clear. He is a Platonist and I am a positivist. He is seriously concerned that Schrödinger's cat is in a quantum state in which he is half alive and half dead. He foresees this inconsistency with reality. But those things don't bother me. I do not demand that the theory be consistent with reality, because I do not know what reality is. Reality is not a quality that you can test with litmus paper. All I care about is that the theory predicts the results of measurements. Quantum theory does this very well....
Roger feels that... the collapse of the wave function introduces CPT symmetry breaking into physics. He sees such disruptions in at least two areas of physics: cosmology and black holes. I agree that we can use time asymmetry when asking questions about observations. But I completely reject the idea that there are some physical processes leading to the reduction of the wave function, or that this has anything to do with quantum gravity or consciousness. This is all related to magic and magicians and, but not to science.
Penrose on physical reality:
Quantum mechanics has only existed for 75 years. This is not very much, especially when compared, for example, with Newton's theory of gravity. Therefore, I would not be surprised if quantum mechanics is modified for very large objects.
At the start of this debate, Stephen suggested that he was a positivist and that I was a Platonist. I am glad that he is a positivist, but regarding myself I can say that I am rather a realist. Also, if you compare this debate with the famous Bohr-Einstein debate, some 70 years ago, I think Steven is playing Bohr and I am Einstein! For Einstein, it was necessary that there should be something similar to the real world, described not necessarily by a wave function, while Bohr emphasized that the wave function does not describe the real world, but only the knowledge necessary to predict the results of an experiment.
It is now believed that Bohr's arguments proved to be more weighty, and that Einstein (according to his biography written by Abraham Pais) could have been fishing since 1925. Indeed, he did not make much of a contribution to quantum mechanics, although his insightful criticism was very useful for the latter. I believe that the reason for this was that some important components were missing from the quantum theory. One such component was the radiation from black holes discovered by Stephen 50 years later. The leakage of information associated with the radiation of a black hole is the phenomenon that will possibly raise quantum theory to a new level.
Stephen Hawking believes that the final theory of the universe may not exist
Delivered by renowned physicist Stephen Hawking of England to several audiences at the Massachusetts Institute of Technology (MIT), a television lecture described the ongoing search by scientists for a complete theory of the universe. Finally, the author of the scientific bestsellers A Brief History of Time and The Theory of Everything, a professor of mathematics at the University of Cambridge, suggested that, "perhaps [such a theory ] is not possible".
“Some people will be very disappointed to learn that there is no definitive theory,” Hawking said. “I also belonged to this camp, but now I have changed my mind. We will always deal with the challenge of new scientific discoveries. Without this, civilization will stagnate.” . The search can be continued for a very long time."
The TV show, during which there were some technical difficulties with the image and sound, was also broadcast over the Internet. It was organized by the Cambridge-MIT Institute (CMI) - a three-year strategic alliance between the University of Cambridge in England and the Massachusetts Institute of Technology.
Hawking essentially summarized the history of particle physics, focusing on the key figures and theories in the field, from Aristotle to Stephen Weinberg (Nobel laureate born in 1933).
Maxwell's and Dirac's equations, for example, "govern almost all physics and all chemistry and biology," Hawking reasoned. "Thus, knowing these equations, we could, in principle, predict human behavior, although I cannot claim that I myself had in this case a great success," he concluded to the laughter of the audience.
The human brain contains too many particles to solve all the equations needed to predict someone's behavior. We will only ever in the foreseeable future learn to predict the behavior of the nematode worm.
All theories developed so far to explain the universe "are either inconsistent or incomplete," Hawking said. And he suggested, due to what circumstances it is impossible in principle to develop one complete theory of the Universe. He based his reasoning on the work of Kurt Gödel, the Czech mathematician, author of the famous theorem, according to which, within any area of mathematics, certain propositions can neither be proven nor disproven.
Ecology of knowledge: The most a big problem theoretical physicists - how to combine all fundamental interactions (gravitational, electromagnetic, weak and strong) into a single theory. Superstring theory just claims to be the Theory of Everything
Counting from three to ten
The biggest problem for theoretical physicists is how to combine all fundamental interactions (gravitational, electromagnetic, weak and strong) into a single theory. Superstring theory just claims to be the Theory of Everything.
But it turned out that the most convenient number of dimensions needed for this theory to work is as many as ten (nine of which are spatial, and one is temporal)! If there are more or less dimensions, mathematical equations give irrational results that go to infinity - a singularity.
The next stage in the development of superstring theory - M-theory - has already counted eleven dimensions. And another version of it - F-theory - all twelve. And it's not a complication at all. F-theory describes 12-dimensional space with simpler equations than M-theory describes 11-dimensional space.
Of course, theoretical physics is called theoretical for a reason. All her achievements so far exist only on paper. So, to explain why we can only move in three-dimensional space, scientists started talking about how the unfortunate other dimensions had to shrink into compact spheres at the quantum level. To be precise, not into spheres, but into Calabi-Yau spaces. These are such three-dimensional figures, inside of which there is its own world with its own dimension. A two-dimensional projection of similar manifolds looks something like this:
More than 470 million such figurines are known. Which of them corresponds to our reality, in this moment is calculated. It is not easy to be a theoretical physicist.
Yes, it does seem a bit far-fetched. But perhaps this explains why the quantum world is so different from what we perceive.
Period, period, comma
Start over. Zero dimension is a point. She has no size. There is nowhere to move, no coordinates are needed to indicate the location in such a dimension.
Let's put a second point next to the first one and draw a line through them. Here is the first dimension. A one-dimensional object has a size - length, but no width or depth. Movement within the framework of one-dimensional space is very limited, because the obstacle that has arisen on the way cannot be bypassed. To determine the location on this segment, you need only one coordinate.
Let's put a point next to the segment. To fit both of these objects, we need already a two-dimensional space that has length and width, that is, area, but without depth, that is, volume. The location of any point on this field is determined by two coordinates.
The third dimension arises when we add a third coordinate axis to this system. It is very easy for us, the inhabitants of the three-dimensional universe, to imagine this.
Let's try to imagine how the inhabitants of two-dimensional space see the world. For example, here are these two people:
Each of them will see his friend like this:
And with this layout:
Our heroes will see each other like this:
It is the change in point of view that allows our heroes to judge each other as two-dimensional objects, rather than one-dimensional segments.
And now let's imagine that a certain three-dimensional object moves in the third dimension, which crosses this two-dimensional world. For an outside observer, this movement will be expressed in a change in two-dimensional projections of the object on a plane, like broccoli in an MRI machine:
But for the inhabitant of our Flatland, such a picture is incomprehensible! He can't even imagine her. For him, each of the two-dimensional projections will be seen as a one-dimensional segment with a mysteriously variable length, appearing in an unpredictable place and also unpredictably disappearing. Attempts to calculate the length and place of occurrence of such objects using the laws of physics of two-dimensional space are doomed to failure.
We, the inhabitants of the three-dimensional world, see everything in two dimensions. Only the movement of an object in space allows us to feel its volume. We will also see any multidimensional object as two-dimensional, but it will change in an amazing way depending on our relative position or time with it.
From this point of view, it is interesting to think, for example, about gravity. Everyone has probably seen pictures like this:
It is customary to depict how gravity bends space-time. Curves... where? Exactly not in any of the dimensions familiar to us. And what about quantum tunneling, that is, the ability of a particle to disappear in one place and appear in a completely different one, moreover, behind an obstacle through which, in our realities, it could not penetrate without making a hole in it? What about black holes? But what if all these and other mysteries of modern science are explained by the fact that the geometry of space is not at all the same as we are accustomed to perceive it?
The clock is ticking
Time adds one more coordinate to our Universe. In order for the party to take place, you need to know not only in which bar it will take place, but also exact time this event.
Based on our perception, time is not so much a straight line as a ray. That is, it has a starting point, and the movement is carried out only in one direction - from the past to the future. And only the present is real. Neither the past nor the future exist, just as breakfasts and dinners do not exist from the point of view of an office clerk at lunchtime.
But the theory of relativity does not agree with this. From her point of view, time is a valuable dimension. All events that have existed, exist and will continue to exist are equally real, as real as a sea beach is, no matter where exactly the dreams of the sound of the surf took us by surprise. Our perception is just something like a searchlight that illuminates a certain segment on the time line. Humanity in its fourth dimension looks something like this:
But we see only a projection, a slice of this dimension at each individual moment of time. Yes, yes, like broccoli in an MRI machine.
Until now, all theories have worked with a large number of spatial dimensions, and time has always been the only one. But why does space allow multiple dimensions for space, but only one time? Until scientists can answer this question, the hypothesis of two or more time spaces will seem very attractive to all philosophers and science fiction writers. Yes, and physicists, what is already there. For example, the American astrophysicist Itzhak Bars sees the root of all troubles with the Theory of Everything as the second time dimension, which has been overlooked. As a mental exercise, let's try to imagine a world with two times.
Each dimension exists separately. This is expressed in the fact that if we change the coordinates of an object in one dimension, the coordinates in others can remain unchanged. So, if you move along one time axis that intersects another at a right angle, then at the point of intersection, time around will stop. In practice, it will look something like this:
All Neo had to do was place his one-dimensional time axis perpendicular to the bullets' time axis. A real trifle, agree. In fact, everything is much more complicated.
The exact time in a universe with two time dimensions will be determined by two values. Is it hard to imagine a two-dimensional event? That is, one that is extended simultaneously along two time axes? It is likely that such a world would require time-mapping specialists, just as cartographers map the two-dimensional surface of the globe.
What else distinguishes a two-dimensional space from a one-dimensional one? The ability to bypass an obstacle, for example. This is completely beyond the boundaries of our mind. An inhabitant of a one-dimensional world cannot imagine how it is to turn a corner. And what is this - an angle in time? In addition, in two-dimensional space, you can travel forward, backward, or even diagonally. I have no idea how it is to go diagonally through time. I'm not talking about the fact that time underlies many physical laws, and it is impossible to imagine how the physics of the Universe will change with the advent of another time dimension. But it's so exciting to think about it!
Very large encyclopedia
Other dimensions have not yet been discovered, and exist only in mathematical models. But you can try to imagine them like this.
As we found out earlier, we see a three-dimensional projection of the fourth (temporal) dimension of the Universe. In other words, every moment of the existence of our world is a point (similar to the zero dimension) in the time interval from the Big Bang to the End of the World.
Those of you who have read about time travel know how important the curvature of the space-time continuum is. This is the fifth dimension - it is in it that the four-dimensional space-time “bends” in order to bring two points on this straight line closer together. Without this, the journey between these points would be too long, or even impossible. Roughly speaking, the fifth dimension is similar to the second - it moves the "one-dimensional" line of space-time to the "two-dimensional" plane with all the consequences in the form of the ability to turn the corner.
A little earlier, our especially philosophically minded readers probably thought about the possibility of free will in conditions where the future already exists, but is not yet known. Science answers this question like this: probabilities. The future is not a stick, but a whole broom of possible scenarios. Which of them will come true - we'll find out when we get there.
Each of the probabilities exists as a "one-dimensional" segment on the "plane" of the fifth dimension. What is the fastest way to jump from one segment to another? That's right - bend this plane like a sheet of paper. Where to bend? And again, correctly - in the sixth dimension, which gives the whole complex structure "volume". And thus makes it like three-dimensional space, "finished", a new point.
The seventh dimension is a new straight line, which consists of six-dimensional "points". What is any other point on this line? The whole infinite set of options for the development of events in another universe, formed not as a result of the Big Bang, but in other conditions, and acting according to other laws. That is, the seventh dimension is beads from parallel worlds. The eighth dimension collects these "straight lines" into one "plane". And the ninth can be compared to a book that contains all the "sheets" of the eighth dimension. It is the totality of all histories of all universes with all the laws of physics and all initial conditions. Point again.
Here we hit the limit. To imagine the tenth dimension, we need a straight line. And what could be another point on this straight line, if the ninth dimension already covers everything that can be imagined, and even what cannot be imagined? It turns out that the ninth dimension is not another starting point, but the final one - for our imagination, in any case.
String theory claims that it is in the tenth dimension that strings, the basic particles that make up everything, make their vibrations. If the tenth dimension contains all universes and all possibilities, then strings exist everywhere and all the time. I mean, every string exists in our universe, and every other. At any point in time. Straightaway. Cool, yeah? published
Superstring theory, in popular language, represents the universe as a collection of vibrating filaments of energy - strings. They are the foundation of nature. The hypothesis also describes other elements - branes. All matter in our world is made up of vibrations of strings and branes. A natural consequence of the theory is the description of gravity. That is why scientists believe that it holds the key to unifying gravity with other forces.
The concept is evolving
The unified field theory, superstring theory, is purely mathematical. Like all physical concepts, it is based on equations that can be interpreted in a certain way.
Today, no one knows exactly what the final version of this theory will be. Scientists have a rather vague idea of its general elements, but no one has yet come up with a definitive equation that would cover all superstring theories, and experimentally it has not yet been able to confirm it (although not to disprove it either). Physicists have created simplified versions of the equation, but so far it doesn't quite describe our universe.
Superstring Theory for Beginners
The hypothesis is based on five key ideas.
- Superstring theory predicts that all objects in our world are made up of vibrating filaments and membranes of energy.
- It tries to combine the general theory of relativity (gravity) with quantum physics.
- Superstring theory will unify all the fundamental forces of the universe.
- This hypothesis predicts a new connection, supersymmetry, between two fundamentally various types particles, bosons and fermions.
- The concept describes a number of additional, usually unobservable dimensions of the Universe.
Strings and branes
When the theory arose in the 1970s, the threads of energy in it were considered 1-dimensional objects - strings. The word "one-dimensional" says that the string has only 1 dimension, the length, unlike, for example, a square, which has both a length and a height.
The theory divides these superstrings into two types - closed and open. An open string has ends that do not touch each other, while a closed string is a loop with no open ends. As a result, it was found that these strings, called strings of the first type, are subject to 5 main types of interactions.
Interactions are based on the ability of a string to connect and separate its ends. Since the ends of open strings can combine to form closed strings, it is impossible to construct a superstring theory that does not include looped strings.
This turned out to be important, since closed strings have properties, physicists believe, that could describe gravity. In other words, scientists realized that instead of explaining the particles of matter, superstring theory could describe their behavior and gravity.
Many years later, it was discovered that, in addition to strings, other elements are necessary for the theory. They can be thought of as sheets, or branes. The strings can be attached to one or both sides of them.
quantum gravity
Modern physics has two main scientific laws: general relativity (GR) and quantum. They represent completely different fields of science. Quantum physics studies the smallest natural particles, while general relativity, as a rule, describes nature on the scale of planets, galaxies, and the universe as a whole. The hypotheses that attempt to unify them are called quantum gravity theories. The most promising of them today is the string.
Closed threads correspond to the behavior of gravity. In particular, they have the properties of a graviton, a particle that carries gravity between objects.
Joining Forces
String theory attempts to combine the four forces - electromagnetic, strong and weak nuclear forces, and gravity - into one. In our world, they manifest themselves as four different phenomena, but string theorists believe that in the early Universe, when they were incredibly high levels energy, all these forces are described by strings interacting with each other.
supersymmetry
All particles in the universe can be divided into two types: bosons and fermions. String theory predicts that there is a relationship between the two called supersymmetry. In supersymmetry, for every boson there must be a fermion, and for every fermion, a boson. Unfortunately, the existence of such particles has not been experimentally confirmed.
Supersymmetry is a mathematical relationship between elements of physical equations. It was discovered in another area of physics, and its application led to the renaming of supersymmetric string theory (or superstring theory, in popular parlance) in the mid-1970s.
One advantage of supersymmetry is that it greatly simplifies the equations by allowing some variables to be eliminated. Without supersymmetry, the equations lead to physical contradictions such as infinite values and imaginary
Since scientists have not observed the particles predicted by supersymmetry, it is still a hypothesis. Many physicists believe that the reason for this is the need for a significant amount of energy, which is related to mass by the famous Einstein equation E = mc 2 . These particles could have existed in the early universe, but as it cooled and energy expanded after the Big Bang, these particles moved to low energy levels.
In other words, the strings that vibrated as high-energy particles lost their energy, which turned them into elements with a lower vibration.
Scientists hope that astronomical observations or experiments with particle accelerators will confirm the theory by revealing some of the higher-energy supersymmetric elements.
Additional measurements
Another mathematical consequence of string theory is that it makes sense in a world with more than three dimensions. There are currently two explanations for this:
- The extra dimensions (six of them) collapsed, or, in the terminology of string theory, compactified to an incredibly small size that will never be perceived.
- We are stuck in a 3D brane, and other dimensions extend beyond it and are inaccessible to us.
An important line of research among theorists is the mathematical modeling of how these additional coordinates might be related to ours. Latest Results predict that scientists will soon be able to detect these additional dimensions (if they exist) in upcoming experiments, as they may be larger than previously expected.
Purpose Understanding
The goal that scientists strive for when exploring superstrings is a "theory of everything", that is, a single physical hypothesis that describes the entire physical reality at a fundamental level. If successful, it could clarify many questions about the structure of our universe.
Explanation of matter and mass
One of the main tasks contemporary research- search for solutions for real particles.
String theory began as a concept describing particles such as hadrons in various higher vibrational states of a string. In most modern formulations, the matter observed in our universe is the result of the vibrations of strings and lowest-energy branes. Vibrations with more generate high-energy particles that currently do not exist in our world.
The mass of these is a manifestation of how strings and branes are wrapped in compactified extra dimensions. For example, in a simplified case where they are folded into a donut shape, called a torus by mathematicians and physicists, a string can wrap this shape in two ways:
- a short loop through the middle of the torus;
- a long loop around the entire outer circumference of the torus.
A short loop will be a light particle, and a large loop will be a heavy one. When strings are wrapped around toroidal compactified dimensions, new elements with different masses are formed.
Superstring theory briefly and clearly, simply and elegantly explains the transition of length into mass. The folded dimensions here are much more complicated than the torus, but in principle they work the same way.
It is even possible, although it is hard to imagine, that the string wraps around the torus in two directions at the same time, resulting in a different particle with a different mass. Branes can also wrap around extra dimensions, creating even more possibilities.
Definition of space and time
In many versions of superstring theory, the dimensions collapse, making them unobservable on modern level technology development.
It is currently not clear whether string theory can explain the fundamental nature of space and time any more than Einstein did. In it, measurements are the background for the interaction of strings and have no independent real meaning.
Explanations have been offered, not fully developed, regarding the representation of space-time as a derivative of the total sum of all string interactions.
This approach does not meet the ideas of some physicists, which led to criticism of the hypothesis. Competitive theory uses the quantization of space and time as a starting point. Some believe that in the end it will turn out to be just a different approach to the same basic hypothesis.
Gravity quantization
The main achievement of this hypothesis, if it is confirmed, will be the quantum theory of gravity. The current description in general relativity is inconsistent with quantum physics. The latter, by imposing restrictions on the behavior of small particles, leads to contradictions when trying to explore the Universe on an extremely small scale.
Unification of forces
At present, physicists know four fundamental forces: gravity, electromagnetic, weak and strong nuclear interactions. It follows from string theory that all of them were once manifestations of one.
According to this hypothesis, as the early universe cooled after the big bang, this single interaction began to break up into different ones that are active today.
High-energy experiments will someday allow us to discover the unification of these forces, although such experiments are far beyond the current development of technology.
Five options
Since the superstring revolution of 1984, development has progressed at a feverish pace. As a result, instead of one concept, we got five, named types I, IIA, IIB, HO, HE, each of which almost completely described our world, but not completely.
Physicists, sorting through versions of string theory in the hope of finding a universal true formula, created 5 different self-sufficient versions. Some of their properties reflected the physical reality of the world, others did not correspond to reality.
M-theory
At a conference in 1995, physicist Edward Witten proposed a bold solution to the problem of five hypotheses. Based on the newly discovered duality, they all became special cases of a single overarching concept, called Witten's M-theory of superstrings. One of its key concepts was branes (short for membrane), fundamental objects with more than 1 dimension. Although the author did not offer a complete version, which is not yet available, the M-theory of superstrings briefly consists of the following features:
- 11 dimensions (10 spatial plus 1 time dimension);
- dualities that lead to five theories explaining the same physical reality;
- branes are strings with more than 1 dimension.
Consequences
As a result, instead of one, there were 10,500 solutions. For some physicists, this caused a crisis, while others accepted the anthropic principle, which explains the properties of the universe by our presence in it. It remains to be seen when theorists will find another way to orient themselves in superstring theory.
Some interpretations suggest that our world is not the only one. The most radical versions allow the existence of an infinite number of universes, some of which contain exact copies of our own.
Einstein's theory predicts the existence of a coiled space, which is called a wormhole or an Einstein-Rosen bridge. In this case, two distant sites are connected by a short passage. Superstring theory allows not only this, but also the connection of distant points of parallel worlds. It is even possible to transition between universes with different laws of physics. However, it is likely that the quantum theory of gravity will make their existence impossible.
Many physicists believe that the holographic principle, when all the information contained in the volume of space corresponds to the information recorded on its surface, will allow a deeper understanding of the concept of energy threads.
Some believe that superstring theory allows for multiple dimensions of time, which could result in travel through them.
In addition, there is an alternative to the big bang model in the hypothesis, according to which our universe appeared as a result of the collision of two branes and goes through repeated cycles of creation and destruction.
The ultimate fate of the universe has always preoccupied physicists, and the final version of string theory will help determine the density of matter and the cosmological constant. Knowing these values, cosmologists will be able to determine whether the universe will shrink until it explodes, so that everything starts again.
No one knows what it can lead to until it is developed and tested. Einstein, writing down the equation E=mc 2 , did not assume that it would lead to the appearance of nuclear weapons. The creators of quantum physics did not know that it would become the basis for creating a laser and a transistor. And although it is not yet known what such a purely theoretical concept will lead to, history shows that something outstanding will certainly turn out.
You can read more about this hypothesis in Andrew Zimmerman's Superstring Theory for Dummies.
A similar question has already been asked here:
But I will try to tell about it in my corporate style;)
We have a very long conversation, but I hope you will be interested, bro. In general, listen, what is the point here. main idea can be seen already in the name itself: instead of point elementary particles (such as electrons, photons, etc.), this theory offers strings - sort of microscopic vibrating one-dimensional threads of energy that are so small that no modern equipment they cannot be detected (specifically, they are at the Planck length, but this is not the point). Don't say particles consist from strings, they and eat strings, just because of the imperfection of our equipment, we see them as particles. And if our equipment is capable of reaching the Planck length, then we are supposed to find strings there. And just as a violin string vibrates to produce different notes, a quantum string vibrates to produce different particle properties (such as charges or masses). This, in general, is the main idea.
However, it is important to note here that string theory has very big ambitions and it claims nothing less than the status of a "theory of everything" that combines gravity (the theory of relativity) and quantum mechanics (that is, the macrocosm - the world of large objects familiar to us, and the microcosm - the world of elementary particles). Gravity in string theory elegantly appears on its own, and here's why. Initially, string theory was generally perceived only as the theory of the strong nuclear force (the interaction by which protons and neutrons are held together in the nucleus of an atom), no more, since some types of vibrating strings resembled the properties of gluons (carrier particles of the strong force). However, in it, in addition to gluons, there were other varieties of string vibrations, reminiscent of other particles-carriers of some kind of interaction, which had nothing to do with gluons. Having studied the properties of these particles, scientists found that these vibrations exactly coincide with the properties of a hypothetical particle - a graviton - a particle-carrier of gravitational interaction. This is how gravity appeared in string theory.
But here again (what are you going to do!) there is a problem called "quantum fluctuations". Yes, do not be afraid, this term is terrible only in appearance. So, quantum fluctuations are associated with the constant birth and destruction of virtual (those that cannot be seen directly because of their continuous appearance and disappearance) particles. The most indicative process in this sense is annihilation - the collision of a particle and an antiparticle with the formation of a photon (particle of light), which subsequently generates another particle and antiparticle. And gravity is, in essence, what? It is a smoothly curved geometric fabric of space-time. The key word here is smooth. And in the quantum world, because of these very fluctuations, the space is not smooth and smooth, there is such chaos that it is even scary to imagine. As you probably already understand, the smooth geometry of the space of the theory of relativity is completely incompatible with quantum fluctuations. Embarrassment, however, physicists have found a solution, stating that the interaction of strings smooths out these fluctuations. How, you ask? But imagine two closed strings (because there are also open ones, which are a kind of small thread with two open ends; closed strings, respectively, are a kind of loops). These two closed strings are on a collision course and at some point they collide, turning into one larger string. This string still moves for some time, after which it splits into two smaller strings. Now the next step. Let's imagine this whole process in a shot of film: we will see that this process has acquired a certain three-dimensional volume. This volume is called the "world surface". Now let's imagine that you and I are looking at this whole process from different angles: I look straight ahead, and you look at a slight angle. We will see that from your point of view and from mine, the strings will collide in different places, since for you these string loops (let's call them that) will move slightly at an angle, but for me straight. However, it is the same process, the same two strings colliding, the difference is only in two points of view. This means that there is a kind of “smearing” of the interaction of strings: from the position of different observers, they interact in different places. However, despite these different points view, the process is nevertheless one, and the point of interaction is one. Thus, different observers will fix the same place of interaction of two point particles. That's it! Do you understand what's going on? We smoothed out quantum fluctuations and thus combined gravity and quantum mech! Look!
Okay, let's move on. Not tired yet? Well, listen. Now I will talk about what I personally don’t really like about string theory. And this is called "mathematization". Somehow, theorists got too carried away with mathematics ... but the point here is simple: here, how many dimensions of space do you know? That's right, three: length, width and height (time is the fourth dimension). Now, the mathematics of string theory does not fit well with these four dimensions. And five too. And ten. But it gets along well with eleven. And the theorists decided: well, since mathematics requires, let there be eleven dimensions. You see, mathematics requires! Math, not reality! (Exclamation to the side: if I'm wrong, someone will convince me! I want to change my mind!) Well, where, one wonders, have the other seven dimensions gone? To this question, the theory answers us that they are "compactified", folded into microscopic formations at the Planck length (that is, at a scale that we are not able to observe). These formations are called the "Calabi-Yau manifold" (after the names of two prominent physicists).
It is also interesting that string theory brings us to the Multiverse, that is, to the idea of the existence of an infinite number of parallel Universes. The whole point here is that in string theory there are not only strings, but also branes (from the word “membrane”). Branes can be of different dimensions, up to nine. It is assumed that we live on a 3-brane, but there may be others near this brane, and they may periodically collide. And we do not see them because open strings are tightly attached to the brane at both ends. These strings can move along the brane with their ends, but they cannot leave it (unhook). And if string theory is to be believed, then all matter and all of us are made up of particles that look like strings at the Planck length. Therefore, since the open strings cannot leave the brane, then we cannot interact with another brane (read: parallel universe) in any way or somehow see it. The only particle that doesn't really care about this limitation and can do it is the hypothetical graviton, which is a closed string. However, no one has yet been able to detect the graviton. Such a Multiverse is referred to as the "brane multiverse" or "braneworld scenario".
By the way, due to the fact that not only strings, but also branes were found in string theory, theorists began to call it "M-theory", but no one really knows what this "M" means;)
That's it. Such is the story. I hope you enjoyed it bro. If something remains unclear, ask in the comments - I will explain.
