Gravity is not at all the “Law of Universal Gravitation.” The meaning of the word gravity
Orff. gravity, -I Lopatin's spelling dictionary
I decided, to the best of my ability, to dwell on lighting in more detail. scientific heritage Academician Nikolai Viktorovich Levashov, because I see that his works today are not yet in demand as they should be in a society of truly free and reasonable people. People are still do not understand the value and importance of his books and articles, because they do not realize the degree of deception in which we have been living for the last couple of centuries; do not understand that information about nature, which we consider familiar and therefore true, is 100% false; and they were deliberately imposed on us in order to hide the truth and prevent us from developing in the right direction...
Law of Gravity
Why do we need to deal with this gravity? Isn't there something else we know about her? Come on! We already know a lot about gravity! For example, Wikipedia kindly tells us that « Gravity (attraction, worldwide, gravity) (from Latin gravitas - “gravity”) - the universal fundamental interaction between all material bodies. In the approximation of low speeds and weak gravitational interaction, it is described by Newton’s theory of gravity, in the general case it is described by Einstein’s general theory of relativity...” Those. simply put, this Internet chatter says that gravity is the interaction between all material bodies, and even more simply put - mutual attraction material bodies to each other.
We owe the appearance of such an opinion to Comrade. Isaac Newton, who is credited with the discovery in 1687 "The Law of Universal Gravitation", according to which all bodies are supposedly attracted to each other in proportion to their masses and inversely proportional to the square of the distance between them. The good news is that Comrade. Isaac Newton is described in Pedia as a highly educated scientist, unlike Comrade. , who is credited with the discovery electricity…
It is interesting to look at the dimension of the “Force of Attraction” or “Force of Gravity”, which follows from Comrade. Isaac Newton, having the following form: F=m 1 *m 2 /r 2
The numerator is the product of the masses of two bodies. This gives the dimension “kilograms squared” - kg 2. The denominator is “distance” squared, i.e. meters squared - m 2. But strength is not measured in strange kg 2 / m 2, and in no less strange kg*m/s 2! It turns out to be an inconsistency. To remove it, “scientists” came up with a coefficient, the so-called. "gravitational constant" G , equal to approximately 6.67545×10 −11 m³/(kg s²). If we now multiply everything, we get the correct dimension of “Gravity” in kg*m/s 2, and this abracadabra is called in physics "newton", i.e. force in today's physics is measured in "".
I wonder what physical meaning has a coefficient G , for something reducing the result in 600 billions of times? None! “Scientists” called it the “coefficient of proportionality.” And they introduced it for adjustment dimensions and results to suit the most desirable! This is the kind of science we have today... It should be noted that, in order to confuse scientists and hide contradictions, measurement systems in physics were changed several times - the so-called. "systems of units". Here are the names of some of them, which replaced each other as the need arose to create new camouflages: MTS, MKGSS, SGS, SI...
It would be interesting to ask comrade. Isaac: a how did he guess that there is a natural process of attracting bodies to each other? How did he guess, that the “Force of attraction” is proportional precisely to the product of the masses of two bodies, and not to their sum or difference? How did he so successfully comprehend that this Force is inversely proportional to the square of the distance between bodies, and not to the cube, doubling or fractional power? Where at comrade such inexplicable guesses appeared 350 years ago? After all, he did not conduct any experiments in this area! And, if you believe the traditional version of history, in those days even the rulers were not yet completely straight, but here is such an inexplicable, simply fantastic insight! Where?
Yes out of nowhere! Comrade Isaac had no idea about anything like that and didn’t investigate anything like that and didn't open. Why? Because in reality the physical process " attraction tel" to each other does not exist, and, accordingly, there is no Law that would describe this process (this will be convincingly proven below)! In reality, Comrade Newton in our inarticulate, simply attributed the discovery of the law of “Universal Gravitation”, simultaneously awarding him the title of “one of the creators of classical physics”; in the same way as at one time they attributed to comrade. Bene Franklin, which had 2 classes education. In “Medieval Europe” this was not the case: there was great tension not only with the sciences, but simply with life...
But, fortunately for us, at the end of the last century, the Russian scientist Nikolai Levashov wrote several books in which he gave the “alphabet and grammar” undistorted knowledge; returned to earthlings the previously destroyed scientific paradigm, with the help of which easily explained almost all “unsolvable” mysteries of earthly nature; explained the basics of the structure of the Universe; showed under what conditions on all planets on which necessary and sufficient conditions appear, Life- living matter. Explained what kind of matter can be considered living, and what physical meaning natural process called life" He further explained when and under what conditions “living matter” acquires Intelligence, i.e. realizes its existence - becomes intelligent. Nikolay Viktorovich Levashov conveyed a lot to people in his books and films undistorted knowledge. Among other things, he explained what "gravity", where it comes from, how it works, what its actual physical meaning is. Most of all about this is written in books and. Now let’s look at the “Law of Universal Gravitation”...
The “law of universal gravitation” is a fiction!
Why do I so boldly and confidently criticize physics, the “discovery” of Comrade. Isaac Newton and the “great” “Law of Universal Gravitation” itself? Yes, because this “Law” is a fiction! Deception! Fiction! A scam on a global scale to take earthly science to a dead end! The same scam with the same goals as the notorious “Theory of Relativity” by Comrade. Einstein.
Proof? If you please, here they are: very precise, strict and convincing. They were superbly described by the author O.Kh. Derevensky in his wonderful article. Due to the fact that the article is quite lengthy, I will give here a very brief version of some evidence of the falsity of the “Law of Universal Gravitation”, and citizens interested in the details will read the rest themselves.
1. In our Solar system Only planets and the Moon, a satellite of the Earth, have gravity. The satellites of the other planets, and there are more than six dozen of them, do not have gravity! This information is completely open, but not advertised by the “scientific” people, because it is inexplicable from the point of view of their “science”. Those. b O Most of the objects in our solar system do not have gravity - they do not attract each other! And this completely refutes the “Law of Universal Gravitation”.
2. Henry Cavendish's experience the attraction of massive ingots to each other is considered irrefutable evidence of the presence of attraction between bodies. However, despite its simplicity, this experience has not been openly reproduced anywhere. Apparently, because it does not give the effect that some people once announced. Those. Today, with the possibility of strict verification, experience does not show any attraction between bodies!
3. Launch of an artificial satellite into orbit around an asteroid. Mid February 2000 Americans sent a space probe NEAR close enough to the asteroid Eros, leveled the speed and began to wait for the probe to be captured by the gravity of Eros, i.e. when the satellite is gently attracted by the asteroid's gravity.
But for some reason the first date didn’t go well. The second and subsequent attempts to surrender to Eros had exactly the same effect: Eros did not want to attract the American probe NEAR, and without additional engine support, the probe did not stay near Eros . This cosmic date ended in nothing. Those. no attraction between probe and ground 805 kg and an asteroid weighing more than 6 trillion tons could not be found.
Here we cannot fail to note the inexplicable tenacity of the Americans from NASA, because the Russian scientist Nikolay Levashov, living at that time in the USA, which he then considered a completely normal country, wrote, translated into English and published in 1994 year, his famous book, in which he explained “on the fingers” everything that specialists from NASA needed to know in order for their probe NEAR did not hang around as a useless piece of iron in space, but brought at least some benefit to society. But, apparently, exorbitant conceit played its trick on the “scientists” there.
4. Next try decided to repeat the erotic experiment with an asteroid Japanese. They chose an asteroid called Itokawa, and sent it on May 9 2003 year, a probe called (“Falcon”) was added to it. In September 2005 year, the probe approached the asteroid at a distance of 20 km.
Taking into account the experience of the “dumb Americans,” the smart Japanese equipped their probe with several engines and an autonomous short-range navigation system with laser rangefinders, so that it could approach the asteroid and move around it automatically, without the participation of ground operators. “The first number of this program turned out to be a comedy stunt with the landing of a small research robot on the surface of an asteroid. The probe descended to the calculated height and carefully dropped the robot, which was supposed to slowly and smoothly fall to the surface. But... he didn’t fall. Slow and smooth he was carried away somewhere far from the asteroid. There he disappeared without a trace... The next number of the program turned out to be, again, a comedic trick with a short-term landing of a probe on the surface “to take a soil sample.” It became comedic because, to ensure the best performance of laser rangefinders, a reflective marker ball was dropped onto the surface of the asteroid. There were no engines on this ball either and... in short, the ball was not in the right place... So whether the Japanese "Falcon" landed on Itokawa, and what he did on it if he sat down, is unknown to science..." Conclusion: the Japanese miracle Hayabusa did not was able to discover no attraction between probe ground 510 kg and an asteroid mass 35 000 tons
Separately, I would like to note that a comprehensive explanation of the nature of gravity by the Russian scientist Nikolay Levashov gave in his book, which he first published in 2002 year - almost a year and a half before the launch of the Japanese Falcon. And, despite this, the Japanese “scientists” followed exactly in the footsteps of their American colleagues and carefully repeated all their mistakes, including landing. This is such an interesting continuity of “scientific thinking”...
5. Where do tides come from? A very interesting phenomenon described in the literature, to put it mildly, is not entirely correct. “...There are textbooks on physics, where it is written what they should be - in accordance with the “law of universal gravitation”. There are also tutorials on oceanography, where it is written what they are, the tides, In fact.
If the law of universal gravitation is in effect here, and ocean water is attracted, among other things, to the Sun and the Moon, then the “physical” and “oceanographic” patterns of tides should coincide. So do they match or not? It turns out that to say that they do not coincide is to say nothing. Because the “physical” and “oceanographic” pictures have no relation to each other at all nothing in common... The actual picture of tidal phenomena differs so greatly from the theoretical one - both qualitatively and quantitatively - that on the basis of such a theory it is impossible to pre-calculate tides impossible. Yes, no one is trying to do this. Not crazy after all. This is how they do it: for each port or other point that is of interest, the dynamics of the ocean level are modeled by the sum of oscillations with amplitudes and phases that are found purely empirically. And then they extrapolate this amount of fluctuations forward - and you get pre-calculations. The captains of the ships are happy - well, okay!..” This all means that our earthly tides are too don't obey"The law of universal gravitation."
What is gravity really?
The real nature of gravity was clearly described for the first time in modern history by academician Nikolai Levashov in a fundamental scientific work. So that the reader can better understand what is written regarding gravity, I will give a small preliminary explanation.
The space around us is not empty. It is completely filled with many different matters, which Academician N.V. Levashov named "prime matters". Previously, scientists called all this riot of matter "ether" and even received convincing evidence of its existence (the famous experiments of Dayton Miller, described in the article by Nikolai Levashov “The Theory of the Universe and Objective Reality”). Modern “scientists” have gone much further and now they "ether" called "dark matter". Colossal progress! Some matters in the “ether” interact with each other to one degree or another, some do not. And some primary matter begins to interact with each other, falling into changed external conditions in certain space curvatures (inhomogeneities).
Space curvatures appear as a result of various explosions, including “supernova explosions.” « When a supernova explodes, fluctuations in the dimensionality of space arise, similar to the waves that appear on the surface of water after throwing a stone. The masses of matter ejected during the explosion fill these inhomogeneities in the dimension of space around the star. From these masses of matter, planets (and) begin to form..."
Those. planets are not formed from space debris, as modern “scientists” for some reason claim, but are synthesized from the matter of stars and other primary matters, which begin to interact with each other in suitable inhomogeneities of space and form the so-called. "hybrid matter". It is from these “hybrid matters” that planets and everything else in our space are formed. our planet, just like the other planets, is not just a “piece of stone”, but a very complex system consisting of several spheres nested one inside the other (see). The densest sphere is called the “physically dense level” - this is what we see, the so-called. physical world. Second in terms of density, a slightly larger sphere is the so-called “etheric material level” of the planet. Third sphere – “astral material level”. Fourth sphere is the “first mental level” of the planet. Fifth sphere is the “second mental level” of the planet. AND sixth sphere is the “third mental level” of the planet.
Our planet should be considered only as the totality of these six spheres– six material levels of the planet, nested one within the other. Only in this case can you get a complete understanding of the structure and properties of the planet and the processes occurring in nature. The fact that we are not yet able to observe the processes occurring outside the physically dense sphere of our planet does not indicate that “there is nothing there,” but only that at present our senses are not adapted by nature for these purposes. And one more thing: our Universe, our planet Earth and everything else in our Universe is formed from seven various types of primordial matter merged into six hybrid matters. And this is neither a divine nor a unique phenomenon. This is simply the qualitative structure of our Universe, determined by the properties of the heterogeneity in which it was formed.
Let's continue: planets are formed by the merging of the corresponding primary matter in areas of inhomogeneity in space that have properties and qualities suitable for this. But these, as well as all other areas of space, contain a huge number of primordial matter(free forms of matter) of various types that do not interact or interact very weakly with hybrid matter. Finding themselves in an area of heterogeneity, many of these primary matters are affected by this heterogeneity and rush to its center, in accordance with the gradient (difference) of space. And, if a planet has already formed in the center of this heterogeneity, then the primary matter, moving towards the center of the heterogeneity (and the center of the planet), creates directional flow, which creates the so-called. gravitational field. And, accordingly, under gravity You and I need to understand the impact of the directed flow of primary matter on everything in its path. That is, simply put, gravity is pressing material objects to the surface of the planet by the flow of primary matter.
Is not it, reality very different from the fictitious law of “mutual attraction”, which supposedly exists everywhere for a reason that no one understands. Reality is much more interesting, much more complex and much simpler, at the same time. Therefore, the physics of real natural processes is much easier to understand than fictitious ones. And the use of real knowledge leads to real discoveries and the effective use of these discoveries, and not to concocted ones.
Antigravity
As an example of today's scientific profanation we can briefly analyze the explanation by “scientists” of the fact that “rays of light are bent near large masses,” and therefore we can see what is hidden from us by stars and planets.
Indeed, we can observe objects in Space that are hidden from us by other objects, but this phenomenon has nothing to do with the masses of objects, because the phenomenon of the “universal” does not exist, i.e. no stars, no planets NOT attract no rays to themselves and do not bend their trajectory! Why then do they “bend”? There is a very simple and convincing answer to this question: rays are not bent! They're just do not spread in a straight line, as we are accustomed to understand, but in accordance with shape of space. If we consider a ray passing near a large cosmic body, then we must keep in mind that the ray bends around this body because it is forced to follow the curvature of space, like a road of the appropriate shape. And there is simply no other way for the beam. The beam cannot help but bend around this body, because the space in this area has such a curved shape... A small addition to what has been said.
Now, returning to antigravity, it becomes clear why Humanity is unable to catch this nasty “anti-gravity” or achieve at least anything of what the clever functionaries of the dream factory show us on TV. We are deliberately forced For more than a hundred years, internal combustion engines or jet engines have been used almost everywhere, although they are very far from perfect in terms of operating principle, design, and efficiency. We are deliberately forced extract using various generators of cyclopean sizes, and then transmit this energy through wires, where b O most of it dissipates in space! We are deliberately forced to live the life of irrational beings, therefore we have no reason to be surprised that we are not succeeding in anything meaningful either in science, or in technology, or in economics, or in medicine, or in organizing a decent life in society.
I will now give you several examples of the creation and use of antigravity (aka levitation) in our lives. But these methods of achieving antigravity were most likely discovered by chance. And in order to consciously create a truly useful device that implements antigravity, you need to know the real nature of the phenomenon of gravity, study it, analyze and understand its whole essence! Only then can we create something sensible, effective and truly useful to society.
The most common device in our country that uses antigravity is balloon and its many variations. If it is filled with warm air or gas that is lighter than the atmospheric gas mixture, the ball will tend to fly up rather than down. This effect has been known to people for a very long time, but still does not have a comprehensive explanation– one that would no longer raise new questions.
A short search on YouTube led to the discovery of a large number of videos showing very real examples of antigravity. I will list some of them here so that you can see that antigravity ( levitation) really exists, but... has not yet been explained by any of the “scientists”, apparently pride does not allow...
Explanatory dictionary of the Russian language. D.N. Ushakov
gravity
gravity, plural no, cf.
Attraction; the inherent property of two material bodies to attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them (physical). Earth's gravity (the force that attracts objects to the center of the earth).
to someone or something. Attraction, desire (book). Attraction to science. Attraction to music.
to someone or something. The need for connection with someone, dependence on someone. or unity with someone. (book). Economic gravity of the outskirts towards the center.
Explanatory dictionary of the Russian language. S.I.Ozhegov, N.Yu.Shvedova.
gravity
The property of all bodies to attract each other is attraction (special). Terrestrial t. Newton's law of universal gravitation.
trans., to someone or something. Attraction, desire for someone, need for something. T. to technology. To feel emotional about someone.
New explanatory and word-formative dictionary of the Russian language, T. F. Efremova.
gravity
The inherent property of two bodies attracting each other depending on their mass and the distance between them; attraction.
Attraction, desire for someone, something.
The need for connection with someone or something.
decomposition The painful influence of someone or something.
Encyclopedic Dictionary, 1998
gravity
GRAVITY (gravity, gravitational interaction) is a universal interaction between any types of physical matter (ordinary matter, any physical fields). If this interaction is relatively weak and the bodies move slowly compared to the speed of light in a vacuum c, then Newton’s law of universal gravitation is valid. In the case of strong fields and velocities comparable to c, it is necessary to use the general theory of relativity (GTR) created by A. Einstein, which is a generalization of Newton’s theory of gravity based on the special relativity theory. General relativity is based on the principle of equivalence of the local indistinguishability of gravitational forces and inertial forces arising during acceleration of the reference system. This principle is manifested in the fact that in a given gravitational field, bodies of any mass and physical nature move the same way under the same initial conditions. Einstein's theory describes gravitation as the effect of physical matter on the geometric properties of space-time (a.p.); in turn, these properties influence the movement of matter and other physical processes. In such a curved p.v. the movement of bodies “by inertia” (that is, in the absence of external forces other than gravitational ones) occurs along geodesic lines, similar to straight lines in uncurved space, but these lines are already curved. In a strong gravitational field, the geometry of ordinary three-dimensional space turns out to be non-Euclidean, and time flows more slowly than outside the field. Einstein's theory predicts a final rate of change in the gravitational field equal to the speed of light in a vacuum (this change is transferred in the form of gravitational waves), the possibility of the emergence of black holes, etc. Experiments confirm the effects of general relativity.
Gravity
gravity, gravitational interaction, universal interaction between any types of matter. If this interaction is relatively weak and the bodies move slowly (compared to the speed of light), then Newton’s law of universal gravitation is valid. In the general case, temperature is described by the general theory of relativity created by A. Einstein. This theory describes T. as the influence of matter on the properties of space and time; in turn, these properties of space-time affect the movement of bodies and other physical processes. Thus, the modern theory of electricity differs sharply from the theory of other types of interaction - electromagnetic, strong and weak. Newton's theory of gravity The first statements about T. as a universal property of bodies date back to antiquity. Thus, Plutarch wrote: “The moon would fall to the Earth like a stone, as soon as the power of its flight was destroyed.” In the 16th and 17th centuries. In Europe, attempts to prove the existence of mutual gravitation of bodies were revived. The founder of theoretical astronomy, J. Kepler, said that “gravity is the mutual desire of all bodies.” The Italian physicist G. Borelli tried to use T. to explain the movement of Jupiter’s satellites around the planet. However, scientific proof of the existence of universal technology and the mathematical formulation of the law describing it became possible only on the basis of the laws of mechanics discovered by I. Newton. The final formulation of the law of universal theory was made by Newton in his main work, “The Mathematical Principles of Natural Philosophy,” published in 1687. Newton's law of gravitation states that any two material particles with masses mA and mB are attracted towards each other with a force F directly proportional to the product of the masses and inversely proportional to the square of the distance r between them: ═(
(material particles here mean any bodies, provided that their linear dimensions are much less than the distance between them; see Material point). The proportionality coefficient G is called Newton's constant of gravity, or gravitational constant. The numerical value of G was first determined by the English physicist G. Cavendish (1798), who measured the forces of attraction between two balls in the laboratory. According to modern data, G = (6.673 ╠ 0.003)×10-8cm3/g×sec2.
It should be emphasized that the very form of the law of T. (1) (proportionality of force to masses and inverse proportionality to the square of the distance) has been tested with much greater accuracy than the accuracy of determining the coefficient G. According to law (1), the force of T. depends only on the position of the particles at a given moment in time, that is, gravitational interaction propagates instantly. Another important feature of Newton’s law of gravitation is the fact that the force T with which a given body A attracts another body B is proportional to the mass of body B. But since the acceleration that body B receives, according to the second law of mechanics, is inversely proportional to its mass, then the acceleration experienced by body B under the influence of the attraction of body A does not depend on the mass of body B. This acceleration is called the acceleration of gravity. (The implications of this fact are discussed in more detail below.)
In order to calculate the force acting on a given particle from many other particles (or from a continuous distribution of matter in a certain region of space), it is necessary to vectorially add the forces acting on the part of each particle (integrate in the case of a continuous distribution of matter). Thus, in Newton's theory of T. the principle of superposition is valid. Newton theoretically proved that the force of gravity between two balls of finite sizes with a spherically symmetric distribution of matter is also expressed by formula (1), where mA and mB ≈ the total masses of the balls, and r ≈ the distance between their centers.
With an arbitrary distribution of matter, the force of gravity acting at a given point on a test particle can be expressed as the product of the mass of this particle and the vector g, called the field strength of the force at a given point. The greater the magnitude (module) of the vector g, the stronger the field T.
From Newton’s law it follows that the field T is a potential field, that is, its intensity g can be expressed as the gradient of some scalar quantity j, called the gravitational potential:
g = ≈grad j. (
Thus, the field potential T of a particle of mass m can be written as:
If an arbitrary distribution of the density of matter in space is given, r = r(r), then potential theory makes it possible to calculate the gravitational potential j of this distribution, and therefore the strength of the gravitational field g throughout space. The potential j is defined as the Poisson solution of the equation.
where D ≈ Laplace operator.
The gravitational potential of any body or system of bodies can be written as the sum of the potentials of the particles composing the body or system (superposition principle), that is, as an integral of expressions (3):
Integration is carried out over the entire mass of the body (or system of bodies), r ≈ the distance of the mass element dm from the point at which the potential is calculated. Expression (4a) is a solution to Poisson equation (4). The potential of an isolated body or system of bodies is determined, generally speaking, ambiguously. For example, an arbitrary constant can be added to the potential. If we require that the potential be equal to zero far from the body or system, at infinity, then the potential is determined by solving the Poisson equation uniquely in the form (4a).
Newton's theory of theory and Newtonian mechanics were the greatest achievements of natural science. They make it possible to describe with great accuracy a wide range of phenomena, including the movement of natural and artificial bodies in the Solar System, movements in other systems of celestial bodies: in double stars, in star clusters, in galaxies. Based on Newton's theory of gravity, the existence of the previously unknown planet Neptune and the satellite Sirius was predicted, and many other predictions were made, which were later brilliantly confirmed. In modern astronomy, Newton's law of gravitation is the foundation on the basis of which the movements and structure of celestial bodies, their evolution are calculated, and the masses of celestial bodies are determined. Accurate determination of the Earth's gravitational field makes it possible to determine the distribution of masses under its surface (gravimetric exploration) and, therefore, directly solve important applied problems. However, in some cases, when the fields of radiation become strong enough, and the speed of movement of bodies in these fields is not small compared to the speed of light, radiation can no longer be described by Newton’s law.
The need to generalize Newton's law of gravitation Newton's theory assumes instantaneous propagation of light and therefore cannot be reconciled with the special theory of relativity (see Relativity theory), which states that no interaction can propagate at a speed exceeding the speed of light in a vacuum. It is not difficult to find conditions that limit the applicability of Newton's theory of T. Since this theory is not consistent with the special theory of relativity, it cannot be used in cases where gravitational fields are so strong that they accelerate bodies moving in them to a speed on the order of the speed of light c. The speed to which a body freely falling from infinity (it is assumed that there it had a negligible speed) accelerates to a certain point is equal in order of magnitude to the square root of the modulus of the gravitational potential j at this point (at infinity j is considered equal to zero). Thus, Newton's theory can only be applied if
|j|<< c2. (
In the T fields of ordinary celestial bodies, this condition is satisfied: for example, on the surface of the Sun |j|/c2» 4×10-6, and on the surface of white dwarfs ≈ about 10-3.
In addition, Newtonian theory is inapplicable to calculating the motion of particles even in a weak field, satisfying condition (5), if particles flying near massive bodies already had a speed comparable to the speed of light far from these bodies. In particular, Newton's theory is not applicable for calculating the trajectory of light in a T field. Finally, Newton's theory is not applicable when calculating an alternating T field created by moving bodies (for example, double stars) at distances r > l = сt, where t ≈ characteristic time of motion in system (for example, the orbital period in a binary star system). Indeed, according to Newtonian theory, the T. field at any distance from the system is determined by formula (4a), that is, the position of the masses at the same moment in time at which the field is determined. This means that when bodies move in the system, changes in the gravitational field associated with the movement of bodies are instantly transmitted to any distance r. But, according to the special theory of relativity, a change in the field that occurs during time t cannot propagate at a speed greater than c.
A generalization of the theory of theory on the basis of the special theory of relativity was made by A. Einstein in 1915–16. The new theory was called by its creator the general theory of relativity.
Equivalence principle The most important feature of the thermal field, known in Newton’s theory and used by Einstein as the basis for his new theory, is that thermal influences different bodies in exactly the same way, imparting to them the same accelerations regardless of their mass, chemical composition, and other properties. Thus, on the surface of the Earth, all bodies fall under the influence of its field T. with the same acceleration ≈ the acceleration of free fall. This fact was established empirically by G. Galileo and can be formulated as the principle of strict proportionality of the gravitational, or heavy, mass mT, which determines the interaction of the body with the T field and is included in the law (1), and the inertial mass mI, which determines the resistance of the body to the acting force on it and included in Newton’s second law of mechanics (see Newton’s laws of mechanics). Indeed, the equation of motion of a body in the T field is written as:
mIA = F = mTg, (
where a ≈ acceleration acquired by a body under the influence of gravitational field strength g. If mI is proportional to mT and the proportionality coefficient is the same for any bodies, then you can choose the units of measurement so that this coefficient becomes equal to one, mI = mT; then they cancel out in equation (6), and the acceleration a does not depend on mass and is equal to the strength g of the field T., a = g, in accordance with Galileo’s law. (For modern experimental confirmation of this fundamental fact, see below.)
Thus, bodies of different masses and natures move in a given field T. in exactly the same way if their initial velocities were the same. This fact shows a deep analogy between the movement of bodies in the field of T. and the movement of bodies in the absence of T., but relative to the accelerated frame of reference. Thus, in the absence of temperature, bodies of different masses move by inertia rectilinearly and uniformly. If you observe these bodies, for example, from the cabin of a spaceship, which is moving outside the T. fields with constant acceleration due to the operation of the engine, then, naturally, in relation to the cabin, all bodies will move with constant acceleration, equal in magnitude and opposite in direction to the acceleration ship. The motion of the bodies will be the same as falling with the same acceleration in a constant uniform field T. The inertial forces acting in a spaceship flying with an acceleration equal to the acceleration of free fall on the surface of the Earth are indistinguishable from the gravitational forces acting in the true field T. in the ship standing on the surface of the Earth. Consequently, the inertial forces in the accelerated reference frame (associated with the spacecraft) are equivalent to the gravitational field. This fact is expressed by Einstein's principle of equivalence. According to this principle, it is possible to carry out the reverse procedure of the simulation of the T field described above by an accelerated reference system, namely, it is possible to “destroy” the true gravitational field at a given point by introducing a reference system moving with the acceleration of free fall. Indeed, it is well known that in the cabin of a spacecraft moving freely (with the engines switched off) around the Earth in its gravitational field, a state of weightlessness occurs—no gravitational forces appear. Einstein suggested that not only mechanical motion, but in general all physical processes in the true field of T., on the one hand, and in an accelerated system in the absence of T., on the other hand, proceed according to the same laws. This principle is called the “strong equivalence principle” in contrast to the “weak equivalence principle”, which relates only to the laws of mechanics.
The main idea of Einstein's theory of gravity
The reference system considered above (a spacecraft with a running engine), moving with constant acceleration in the absence of a gravitational field, simulates only a uniform gravitational field, identical in magnitude and direction throughout space. But the T fields created by individual bodies are not like that. In order to simulate, for example, the spherical field of the Earth's T, we need accelerated systems with different directions of acceleration at different points. Observers in different systems, having established a connection with each other, will discover that they are moving accelerated relative to each other, and thereby establish the absence of a true T field. Thus, the true T field is not reduced simply to the introduction of an accelerated reference frame in ordinary space, or, more precisely, in the space-time of special relativity. However, Einstein showed that if, based on the equivalence principle, we require that the true gravitational field be equivalent to local reference frames appropriately accelerated at each point, then in any finite region space-time will turn out to be curved ≈ non-Euclidean. This means that in three-dimensional space the geometry, generally speaking, will be non-Euclidean (the sum of the angles of a triangle is not equal to p, the ratio of the circumference to the radius is not equal to 2p, etc.), and time will flow differently at different points. Thus, according to Einstein’s theory of gravity, the true gravitational field is nothing more than a manifestation of the curvature (difference between geometry and Euclidean geometry) of four-dimensional space-time.
It should be emphasized that the creation of Einstein's theory of gravity became possible only after the discovery of non-Euclidean geometry by the Russian mathematician N. I. Lobachevsky, the Hungarian mathematician J. Bolyai, and the German mathematicians K. Gauss and B. Riemann.
In the absence of temperature, the inertial motion of a body in the space-time of the special theory of relativity is depicted by a straight line, or, in mathematical language, an extremal (geodesic) line. Einstein’s idea, based on the principle of equivalence and forming the basis of the theory of geodesics, is that in the field of geodesics all bodies move along geodesic lines in space-time, which, however, is curved, and, therefore, geodesics are no longer straight .
The masses that create the T field bend space-time. Bodies that move in curved space-time, in this case, move along the same geodesic lines, regardless of the mass or composition of the body. The observer perceives this movement as movement along curved trajectories in three-dimensional space with variable speed. But from the very beginning, Einstein’s theory laid down that the curvature of the trajectory, the law of change in speed ≈ these are the properties of space-time, the properties of geodesic lines in this space-time, and therefore, the acceleration of any different bodies should be the same and, therefore, the ratio of heavy mass to inertial [on which the acceleration of a body in a given field T depends, see formula (6)] is the same for all bodies, and these masses are indistinguishable. Thus, the T field, according to Einstein, is a deviation of the properties of space-time from the properties of the flat (not curved) manifold of the special theory of relativity.
The second important idea underlying Einstein’s theory is the assertion that temperature, that is, the curvature of space-time, is determined not only by the mass of the substance composing the body, but also by all types of energy present in the system. This idea was a generalization to the case of T. theory of the principle of equivalence of mass (m) and energy (E) of the special theory of relativity, expressed by the formula E = mс2. According to this idea, T. depends not only on the distribution of masses in space, but also on their movement, on the pressure and tension present in bodies, on the electromagnetic field and all other physical fields.
Finally, Einstein's theory of gravity generalizes the conclusion of the special theory of relativity about the finite speed of propagation of all types of interaction. According to Einstein, changes in the gravitational field propagate in a vacuum with a speed c.
Einstein's equations of gravity
In the special theory of relativity in an inertial frame of reference, the square of the four-dimensional “distance” in space-time (interval ds) between two infinitely close events is written as:
ds2= (cdt)2- dx2- dy2- dz2 (
where t ≈ time, x, y, z ≈ rectangular Cartesian (spatial) coordinates. This coordinate system is called Galilean. Expression (7) has a form similar to the expression for the squared distance in Euclidean three-dimensional space in Cartesian coordinates (up to the number of dimensions and signs in front of the squares of differentials on the right side). Such space-time is called flat, Euclidean, or, more precisely, pseudo-Euclidean, emphasizing the special nature of time: in expression (7) there is a “+” sign before (cdt)2, in contrast to the “≈” signs before the squared differentials of spatial coordinates. Thus, the special theory of relativity is a theory of physical processes in flat space-time (Minkowski space-time; see Minkowski space).
In Minkowski space-time it is not necessary to use Cartesian coordinates, in which the interval is written in the form (7). You can enter any curvilinear coordinates. Then the square of the interval ds2 will be expressed in terms of these new coordinates in the general quadratic form:
ds2 = gikdx idx k (
(i, k = 0, 1, 2, 3), where x 1, x 2, x 3 ≈ arbitrary space coordinates, x0 = ct ≈ time coordinate (hereinafter, summation is performed over twice occurring indices). From a physical point of view, the transition to arbitrary coordinates means a transition from an inertial reference system to a system, generally speaking, moving with acceleration (and in the general case, different at different points), deforming and rotating, and the use of non-Cartesian spatial coordinates in this system. Despite the apparent complexity of using such systems, in practice they sometimes turn out to be convenient. But in the special theory of relativity you can always use the Galilean system, in which the interval is written especially simply. [In this case, in formula (8) gik = 0 for i ¹ k, g00 = 1, gii = ≈1 for i = 1, 2, 3.]
In general relativity, spacetime is not flat, but curved. In curved space-time (in finite, not small, regions) it is no longer possible to introduce Cartesian coordinates, and the use of curvilinear coordinates becomes inevitable. In the finite regions of such a curved space-time, ds2 is written in curvilinear coordinates in the general form (8). Knowing gik as a function of four coordinates, one can determine all the geometric properties of space-time. The gik quantities are said to define the space-time metric, and the set of all giks is called the metric tensor. Using gik, the rate of time flow at different points of the reference system and the distance between points in three-dimensional space are calculated. Thus, the formula for calculating an infinitesimal time interval dt from a clock at rest in the reference frame has the form:
In the presence of a T field, the value of g00 is different at different points, therefore, the rate of time flow depends on the T field. It turns out that the stronger the field, the slower time flows compared to the passage of time for an observer outside the field.
The mathematical apparatus that studies non-Euclidean geometry (see Riemannian geometry) in arbitrary coordinates is tensor calculus. The general theory of relativity uses the apparatus of tensor calculus; its laws are written in arbitrary curvilinear coordinates (this means, in particular, written in arbitrary reference systems), as they say, in covariant form.
The main task of the theory of T. is the determination of the gravitational field, which corresponds in Einstein’s theory to the determination of the geometry of space-time. This last problem boils down to finding the metric tensor gik.
Einstein's gravitational equations connect the gik values with quantities characterizing the matter that creates the field: density, momentum fluxes, etc. These equations are written as:
Here Rik ≈ the so-called Ricci tensor, expressed through gik, ═its first and second derivatives with respect to coordinates; R = Rik g ik (values g ik are determined from the equations gikg km = , where ═≈ Kronecker symbol); Tik ≈ the so-called energy-momentum tensor of matter, the components of which are expressed through density, momentum fluxes and other quantities characterizing matter and its movement (physical matter means ordinary matter, electromagnetic field, and all other physical fields).
Soon after the creation of the general theory of relativity, Einstein showed (1917) that it was possible to change equations (9) while maintaining the basic principles of the new theory. This change consists of adding to the right side of equations (9) the so-called “cosmological term”: Lgik. The constant L, called the “cosmological constant,” has the dimension cm-2. The purpose of this complication of the theory was Einstein's attempt to construct a model of the Universe that does not change over time (see Cosmology). The cosmological term can be considered as a quantity describing the energy density and pressure (or tension) of the vacuum. However, soon (in the 20s) the Soviet mathematician A. A. Friedman showed that Einstein’s equations without the L-term lead to an evolving model of the Universe, and the American astronomer E. Hubble discovered (1929) the law of the so-called red shift for galaxies, which was interpreted as confirmation of the evolutionary model of the Universe. Einstein's idea of a static Universe turned out to be incorrect, and although equations with an L term also allow nonstationary solutions for the model of the Universe, the need for an L term was no longer necessary. After this, Einstein came to the conclusion that introducing an L term into the T equations was not necessary (that is, that L = 0). Not all physicists agree with this conclusion of Einstein. But it should be emphasized that so far there are no serious observational, experimental or theoretical grounds to consider L to be nonzero. In any case, if L ¹ 0, then, according to astrophysical observations, its absolute value is extremely small: |L|< 10-55см-2. Он может играть роль только в космологии и практически совершенно не сказывается во всех др. задачах теории Т. Везде в дальнейшем будет положено L = 0.
Externally, equations (9) are similar to equation (4) for the Newtonian potential. In both cases, on the left are the quantities that characterize the field, and on the right are the quantities that characterize the matter that creates the field. However, equations (9) have a number of significant features. Equation (4) is linear and therefore satisfies the superposition principle. It allows one to calculate the gravitational potential j for any distribution of arbitrarily moving masses. Newton's field T. does not depend on the movement of masses, therefore equation (4) itself does not directly determine their movement. The movement of masses is determined from Newton's second law of mechanics (6). The situation is different in Einstein's theory. Equations (9) are not linear and do not satisfy the superposition principle. In Einstein's theory, it is impossible to arbitrarily define the right-hand side of the equations (Tik), which depends on the motion of matter, and then calculate the gravitational field gik. Solving Einstein's equations leads to a joint determination of both the motion of matter creating the field and to the calculation of the field itself. It is important that the equations of the T field also contain the equations of mass motion in the T field. From a physical point of view, this corresponds to the fact that in Einstein’s theory, matter creates a curvature of space-time, and this curvature, in turn, affects the movement matter that creates curvature. Of course, to solve Einstein's equations it is necessary to know the characteristics of matter that do not depend on gravitational forces. So, for example, in the case of an ideal gas, you need to know the equation of state of matter ≈ the relationship between pressure and density.
In the case of weak gravitational fields, the space-time metric differs little from the Euclidean one and Einstein’s equations approximately transform into equations (4) and (6) of Newton’s theory (if motions are considered that are slow compared to the speed of light, and the distances from the field source are much less than l = сt, where t ≈ characteristic time of change in the position of bodies in the field source). In this case, we can limit ourselves to calculating small corrections to Newton’s equations. The effects corresponding to these corrections make it possible to experimentally test Einstein's theory (see below). The effects of Einstein's theory are especially significant in strong gravitational fields.
Some conclusions of Einstein's theory of gravity
A number of conclusions of Einstein’s theory are qualitatively different from the conclusions of Newton’s theory of T. The most important of them are related to the emergence of “black holes”, singularities of space-time (places where formally, according to the theory, the existence of particles and fields in the usual form known to us ends) and the existence gravitational waves.
Black holes. According to Einstein's theory, the second cosmic velocity in a spherical field T. in vacuum is expressed by the same formula as in Newton's theory:
Consequently, if a body of mass m is compressed to linear dimensions less than the value r = 2 Gm/c2, called the gravitational radius, then the field of T becomes so strong that even light cannot escape from it to infinity, to a distant observer; this would require speeds greater than light. Such objects are called black holes. An external observer will never receive any information from the region inside the sphere of radius r = 2Gm/s2. When a rotating body is compressed, the T field, according to Einstein’s theory, differs from the field of a non-rotating body, but the conclusion about the formation of a black hole remains valid.
In an area smaller than the gravitational radius, no forces can keep the body from further compression. The compression process is called gravitational collapse. At the same time, the field T increases and the curvature of space-time increases. It has been proven that as a result of gravitational collapse, a singularity of space-time inevitably arises, apparently associated with the emergence of its infinite curvature. (On the limited applicability of Einstein's theory in such conditions, see the next section.) Theoretical astrophysics predicts the emergence of black holes at the end of the evolution of massive stars (see Relativistic astrophysics); It is possible that black holes and other origins exist in the Universe. Black holes appear to have been discovered within some binary star systems.
Gravitational waves. Einstein's theory predicts that bodies moving with variable acceleration will emit gravitational waves. Gravitational waves are alternating fields of tidal gravitational forces propagating at the speed of light. Such a wave, falling, for example, on test particles located perpendicular to the direction of its propagation, causes periodic changes in the distance between the particles. However, even in the case of giant systems of celestial bodies, the radiation of gravitational waves and the energy carried away by them are negligible. Thus, the radiation power due to the movement of the planets of the Solar System is about 1011 erg/sec, which is 1022 times less than the light radiation from the Sun. Gravitational waves interact just as weakly with ordinary matter. This explains that gravitational waves have not yet been discovered experimentally.
Quantum effects. Limitations on the applicability of Einstein's theory of gravity
Einstein's theory is not a quantum theory. In this respect it is similar to classical Maxwellian electrodynamics. However, the most general reasoning shows that the gravitational field must obey quantum laws in the same way as the electromagnetic field. Otherwise, contradictions would arise with the uncertainty principle for electrons, photons, etc. The application of quantum theory to gravity shows that gravitational waves can be considered as a flow of quanta - “gravitons”, which are as real as electromagnetic field quanta - photons. Gravitons are neutral particles with zero rest mass and spin equal to 2 (in units of Planck's constant).
In the vast majority of conceivable processes in the Universe and in laboratory conditions, the quantum effects of gravity are extremely weak, and Einstein's non-quantum theory can be used. However, quantum effects should become very significant near singularities of the T. field, where the curvature of space-time is very large. The theory of dimensions indicates that quantum effects in gravity become decisive when the radius of curvature of space-time (the distance at which significant deviations from Euclidean geometry appear: the smaller this radius, the greater the curvature) becomes equal to the value rpl=. The distance rpl is called the Planck length; it is negligible: rpl = 10-33 cm. Under such conditions, Einstein's theory of gravity is not applicable.
══Singular states arise during gravitational collapse; there was a singularity in the past in the expanding Universe (see Cosmology). A consistent quantum theory of quantum theory applicable to singular states does not yet exist.
Quantum effects lead to the birth of particles in the T field of black holes. For black holes that arise from stars and have a mass comparable to the Sun, these effects are negligible. However, they may be important for low-mass black holes (less than 1015 g), which in principle could arise in the early stages of the expansion of the Universe (see “Black hole”).
Experimental testing of Einstein's theory
Einstein's theory of gravity is based on the principle of equivalence. Its verification with the greatest possible accuracy is the most important experimental task. According to the principle of equivalence, all bodies, regardless of their composition and mass, all types of matter must fall in the T field with the same acceleration. The validity of this statement, as already mentioned, was first established by Galileo. The Hungarian physicist L. Eotvos, using torsion balances, proved the validity of the equivalence principle with an accuracy of 10-8; The American physicist R. Dicke and his colleagues brought the accuracy to 10-10, and the Soviet physicist V.B. Braginsky and his colleagues to ≈ 10-12.
Dr. a test of the equivalence principle is the conclusion that the frequency n of light changes as it propagates in a gravitational field. The theory predicts (see Redshift) a change in the frequency Dn when propagating between points with a gravitational potential difference j1 ≈ j2:
Experiments in the laboratory have confirmed this formula to an accuracy of at least 1% (see Mössbauer effect).
In addition to these experiments to test the fundamentals of the theory, there are a number of experimental tests of its conclusions. The theory predicts the bending of a light beam when passing near a heavy mass. A similar deviation follows from Newton’s theory of T., but Einstein’s theory predicts a twice as large effect. Numerous observations of this effect during the passage of light from stars near the Sun (during total solar eclipses) confirmed the prediction of Einstein's theory (a deviation of 1.75▓▓ at the edge of the solar disk) with an accuracy of about 20%. Much greater accuracy has been achieved using modern technology for observing extraterrestrial point radio sources. By this method, the prediction of the theory was confirmed with an accuracy (as of 1974) of no less than 6%.
Dr. An effect closely related to the previous one is the longer time of light propagation in the T field than is given by formulas without taking into account the effects of Einstein’s theory. For a beam passing close to the Sun, this additional delay is about 2×10-4 sec. The experiments were carried out using radar of the planets Mercury and Venus during their passage behind the disk of the Sun, as well as by relaying radar signals by spacecraft. The theory's predictions have been confirmed (as of 1974) with an accuracy of 2%.
Finally, another effect is the slow additional (not explained by gravitational disturbances from other planets in the Solar System) rotation of the elliptical orbits of planets moving around the Sun, predicted by Einstein’s theory. This effect is greatest for the orbit of Mercury ≈ 43▓▓ per century. This prediction has been confirmed experimentally, according to modern data, with an accuracy of up to 1%.
Thus, all available experimental data confirm the correctness of both the provisions underlying Einstein’s theory of gravity and its observational predictions.
It should be emphasized that experiments testify against attempts to construct other theories of T., different from Einstein's theory.
In conclusion, we note that indirect confirmation of Einstein’s theory of gravity is the observed expansion of the Universe, theoretically predicted on the basis of the general theory of relativity by the Soviet mathematician A. A. Friedman in the mid-20s. of our century.
Lit.: Einstein A., Collection. scientific works, vol. 1≈4, M., 1965≈67; Landau L., Lifshitz E., Field Theory, 6th ed., M., 1973; Fok V.A., Theory of space, time and gravity, 2nd ed., M., 1961; Zeldovich Ya. B., Novikov I. D., Theory of gravitation and evolution of stars, M., 1971; Brumberg V. A., Relativistic celestial mechanics, M., 1972; Braginsky V.B., Rudenko V.N., Relativistic gravitational experiments, “Uspekhi Fizicheskikh Nauk”, 1970, v. 100, v. 3, p. 395.
I. D. Novikov.
Wikipedia
Examples of the use of the word gravity in literature.
Fingers barely straightening in the unexpected pressure on his body gravity, Ewing unfastened his seat belts and saw on the viewing screen small carts roaring across the field of the cosmodrome in the direction of his ship.
World Gravity in the Antiworld there is no, instead there is Universal Repulsion, and therefore everyone has to constantly cling to whatever they have to.
In this case, Disraeli undoubtedly reflected the actual historical process of constant mutual gravity the English bourgeoisie and the English aristocracy, who more than once came to a class compromise when their privileges were threatened by popular indignation.
Water burst out with a slight ringing sound from hundreds of tiny holes, flew up and fell back, obeying the inexorable law gravity and spinning endlessly in a blue whirlpool.
Sneezy was too consumed by the tearless longing for the distant core, and Oniko was too intimidated by the powerful gravity Earth to react to anything.
Among the weaker, disappointment was already noticeably growing; for others, the idea of the pointlessness of further stay in the army was more clearly ripening; gravity go home.
Gravity a skeptic to a believer is as normal as the existence of the law of complementarity of colors.
And here is the result - a race of giant astronauts crystallized, who could no longer live in a strong field gravity home planet without special devices.
Galynin's music is intense in thought, obvious gravity The epic, picturesque nature of the statement is shaded with rich humor and soft, restrained lyrics.
Maximum power gravity always falls on the surface of the geoid, which is why the contact is always located close to sea level.
Underground were power plants, hydroponic gardens, life support devices, processing machines, generators gravity- equipment necessary to maintain the activities of the Callisto station.
The giants looked with horror at the gravimeter, which showed how monstrously growing gravity.
Both of us were obviously thinking about the same thing, listening intently to the alarming song of the gravimeter, a wonderful device that senses fields gravity at a greater distance from the astrolet.
In addition to all our troubles due to exhaustion, we suffered from dementia, which manifested itself in loss of memory, slowness of thought and movement, gravity to stationary postures, especially in men.
It ossified into gravitational shoals, rotted into stellar swamps, festered with black holes, pulsated with instability gravity, addressed in the region of anisotropic space.
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Reissner - Nordström · Kerr ·
Kerr - Newman ·
Gödel · Kasner ·
Friedman - Lemaitre - Robertson - Walker
Approximate solutions:
Post-Newtonian formalism · Covariant perturbation theory ·
Numerical relativity
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| Einstein · Minkowski · Schwarzschild · Lemaitre · Eddington · Friedman · Fock · Kerr · Chandrasekhar · Penrose Hawking and others… |
Gravity (attraction, universal gravity, gravity) (from lat. gravitas- “gravity”) is the universal fundamental interaction between all material bodies. In the approximation of low speeds and weak gravitational interaction, it is described by Newton's theory of gravity, in the general case it is described by Einstein's general theory of relativity. Gravity is the weakest of the four types of fundamental interactions. In the quantum limit, gravitational interaction must be described by a quantum theory of gravity, which has not yet been developed.
Gravitational attraction
The law of universal gravitation is one of the applications of the inverse square law, which is also found in the study of radiation (see, for example, Light Pressure), and is a direct consequence of the quadratic increase in the area of the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to area of the entire sphere.
The gravitational field, like the gravity field, is potential. This means that you can introduce the potential energy of gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed loop. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy and, when studying the motion of bodies in a gravitational field, often significantly simplifies the solution. Within the framework of Newtonian mechanics, gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential depends only on the position of the body at a given moment in time.
Large space objects - planets, stars and galaxies have enormous mass and, therefore, create significant gravitational fields.
Gravity is the weakest interaction. However, since it acts at all distances and all masses are positive, it is nevertheless a very important force in the Universe. In particular, the electromagnetic interaction between bodies on a cosmic scale is small, since the total electric charge of these bodies is zero (matter as a whole is electrically neutral).
Also, gravity, unlike other interactions, is universal in its effect on all matter and energy. No objects have been discovered that have no gravitational interaction at all.
Due to its global nature, gravity is responsible for such large-scale effects as the structure of galaxies, black holes and the expansion of the Universe, and for elementary astronomical phenomena - the orbits of planets, and for simple attraction to the surface of the Earth and the fall of bodies.
Gravity was the first interaction described by mathematical theory. Aristotle (IV century BC) believed that objects with different masses fall at different speeds. Only much later (1589) Galileo Galilei experimentally determined that this is not so - if air resistance is eliminated, all bodies accelerate equally. Isaac Newton's law of universal gravitation (1687) described the general behavior of gravity well. In 1915, Albert Einstein created the General Theory of Relativity, which more accurately describes gravity in terms of the geometry of spacetime.
Celestial mechanics and some of its tasks
The simplest problem of celestial mechanics is the gravitational interaction of two point or spherical bodies in empty space. This problem within the framework of classical mechanics is solved analytically in a closed form; the result of its solution is often formulated in the form of Kepler's three laws.
As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability does not allow us to accurately predict the motion of planets on scales exceeding a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the Solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the complex structure of the rings of Saturn.
Despite attempts to accurately describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.
Strong gravitational fields
In strong gravitational fields, as well as when moving in a gravitational field at relativistic speeds, the effects of the general theory of relativity (GTR) begin to appear:
- changing the geometry of space-time;
- as a consequence, the deviation of the law of gravity from Newtonian;
- and in extreme cases - the emergence of black holes;
- delay of potentials associated with the finite speed of propagation of gravitational disturbances;
- as a consequence, the appearance of gravitational waves;
- nonlinearity effects: gravity tends to interact with itself, so the principle of superposition in strong fields no longer holds.
Gravitational radiation
One of the important predictions of General Relativity is gravitational radiation, the presence of which was confirmed by direct observations in 2015. However, before there was strong indirect evidence in favor of its existence, namely: energy losses in close binary systems containing compact gravitating objects (such as neutron stars or black holes), in particular, in the famous system PSR B1913+16 (Hals pulsar - Taylor) - are in good agreement with the general relativity model, in which this energy is carried away precisely by gravitational radiation.
Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which significantly complicates its detection. Gravity power n-field source is proportional texvc not found; See math/README for setup help.): (v/c)^(2n + 2), if the multipole is of electric type, and Unable to parse expression (Executable file texvc not found; See math/README for setup help.): (v/c)^(2n + 4)- if the multipole is of magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:
texvc not found; See math/README for help with setting up.): L = \frac(1)(5)\frac(G)(c^5)\left\langle \frac(d^3 Q_(ij))(dt^ 3) \frac(d^3 Q^(ij))(dt^3)\right\rangle,
Where Unable to parse expression (Executable file texvc not found; See math/README - help with setup.): Q_(ij)- quadrupole moment tensor of the mass distribution of the radiating system. Constant Unable to parse expression (Executable file texvc not found; See math/README for help with setup.): \frac(G)(c^5) = 2.76 \times 10^(-53)(1/W) allows us to estimate the order of magnitude of the radiation power.
Subtle effects of gravity
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Measuring the curvature of space in Earth's orbit (artist's drawing)
In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which under terrestrial conditions are very weak and therefore their detection and experimental verification are very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, we can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's robotic Gravity Probe B conducted an unprecedented precision experiment to measure these effects near Earth. Processing of the obtained data was carried out until May 2011 and confirmed the existence and magnitude of the effects of geodetic precession and drag of inertial reference systems, although with an accuracy somewhat less than originally assumed.
After intensive work to analyze and extract measurement noise, the final results of the mission were announced at a press conference on NASA-TV on May 4, 2011, and published in Physical Review Letters. The measured value of geodetic precession was −6601.8±18.3 milliseconds arcs per year, and the entrainment effect - −37.2±7.2 milliseconds arcs per year (compare with theoretical values of −6606.1 mas/year and −39.2 mas/year).
Classical theories of gravity
See also: Theories of gravityDue to the fact that quantum effects of gravity are extremely small even under the most extreme and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the vast majority of cases one can limit oneself to the classical description of gravitational interaction.
There is a modern canonical classical theory of gravity - the general theory of relativity, and many clarifying hypotheses and theories of varying degrees of development, competing with each other. All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, most well-developed or known theories of gravity.
General theory of relativity
In the standard approach of the general theory of relativity (GTR), gravity is initially considered not as a force interaction, but as a manifestation of the curvature of space-time. Thus, in general relativity, gravity is interpreted as a geometric effect, and space-time is considered within the framework of non-Euclidean Riemannian (more precisely pseudo-Riemannian) geometry. The gravitational field (a generalization of the Newtonian gravitational potential), sometimes also called the gravitational field, in general relativity is identified with the tensor metric field - the metric of four-dimensional space-time, and the strength of the gravitational field - with the affine connectivity of space-time determined by the metric.
The standard task of general relativity is to determine the components of the metric tensor, which together define the geometric properties of space-time, from the known distribution of energy-momentum sources in the four-dimensional coordinate system under consideration. In turn, knowledge of the metric allows one to calculate the motion of test particles, which is equivalent to knowledge of the properties of the gravitational field in a given system. Due to the tensor nature of the general relativity equations, as well as the standard fundamental justification for its formulation, it is believed that gravity is also of a tensor nature. One consequence is that gravitational radiation must be at least quadrupole order.
It is known that in general relativity there are difficulties due to the non-invariance of the energy of the gravitational field, since this energy is not described by a tensor and can be theoretically determined in different ways. In classical general relativity, the problem of describing the spin-orbit interaction also arises (since the spin of an extended object also does not have an unambiguous definition). It is believed that there are certain problems with the unambiguity of the results and the justification of consistency (the problem of gravitational singularities).
However, general relativity has been confirmed experimentally until very recently (2012). In addition, many alternative approaches to Einstein's, but standard for modern physics, approaches to the formulation of the theory of gravity lead to a result coinciding with general relativity in the low-energy approximation, which is the only one now accessible to experimental verification.
Einstein-Cartan theory
A similar division of equations into two classes also occurs in the RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and Minkowski space. Thanks to the presence of a dimensionless parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments. Moreover, as the parameter tends to infinity, the predictions of the theory become closer and closer to general relativity, so it is impossible to refute the Jordan-Brans-Dicke theory by any experiment confirming the general theory of relativity.
Quantum theory of gravity
Despite more than half a century of attempts, gravity is the only fundamental interaction for which a generally accepted consistent quantum theory has not yet been constructed. At low energies, in the spirit of quantum field theory, the gravitational interaction can be thought of as an exchange of gravitons—spin 2 gauge bosons. However, the resulting theory is non-renormalizable, and is therefore considered unsatisfactory.
In recent decades, three promising approaches to solving the problem of quantizing gravity have been developed: string theory, loop quantum gravity, and causal dynamic triangulation[[K:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]][[K:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]] [ ] .
String theory
In it, instead of particles and background space-time, strings and their multidimensional analogues - branes appear. For high-dimensional problems, branes are high-dimensional particles, but from the point of view of particles moving inside these branes, they are space-time structures. A variant of string theory is M-theory.
Loop quantum gravity
It attempts to formulate a quantum field theory without reference to the space-time background; according to this theory, space and time consist of discrete parts. These small quantum cells of space are connected to each other in a certain way, so that on small scales of time and length they create a motley, discrete structure of space, and on large scales they smoothly transform into continuous smooth space-time. While many cosmological models can only describe the behavior of the universe from Planck time after the Big Bang, loop quantum gravity can describe the explosion process itself, and even look further back. Loop quantum gravity allows us to describe all particles of the standard model without requiring the introduction of the Higgs boson to explain their masses.
Causal dynamic triangulation
In it, the space-time manifold is constructed from elementary Euclidean simplexes (triangle, tetrahedron, pentachore) of dimensions on the order of Planckian ones, taking into account the principle of causality. The four-dimensionality and pseudo-Euclidean nature of space-time on macroscopic scales are not postulated in it, but are a consequence of the theory.
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Principles
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Classic
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Between all material bodies. In the approximation of low speeds and weak gravitational interaction, it is described by Newton’s theory of gravity, in the general case it is described by Einstein’s general theory of relativity. In the quantum limit, gravitational interaction is supposedly described by a quantum theory of gravity, which has not yet been developed.
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Gravitational attraction
The law of universal gravitation is one of the applications of the inverse square law, which is also found in the study of radiation (see, for example, Light Pressure), and is a direct consequence of the quadratic increase in the area of the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to area of the entire sphere.
The gravitational field, like the field of gravity, is potential. This means that you can introduce the potential energy of gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed loop. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy and, when studying the motion of bodies in a gravitational field, often significantly simplifies the solution. Within the framework of Newtonian mechanics, gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential depends only on the position of the body at a given moment in time.
Large space objects - planets, stars and galaxies have enormous mass and, therefore, create significant gravitational fields.
Gravity is the weakest interaction. However, since it acts at all distances and all masses are positive, it is nevertheless a very important force in the Universe. In particular, the electromagnetic interaction between bodies on a cosmic scale is small, since the total electric charge of these bodies is zero (matter as a whole is electrically neutral).
Also, gravity, unlike other interactions, is universal in its effect on all matter and energy. No objects have been discovered that have no gravitational interaction at all.
Due to its global nature, gravity is responsible for such large-scale effects as the structure of galaxies, black holes and the expansion of the Universe, and for elementary astronomical phenomena - the orbits of planets, and for simple attraction to the surface of the Earth and the fall of bodies.
Gravity was the first interaction described by mathematical theory. Aristotle (IV century BC) believed that objects with different masses fall at different speeds. And only much later (1589) Galileo Galilei experimentally determined that this is not so - if air resistance is eliminated, all bodies accelerate equally. Isaac Newton's law of universal gravitation (1687) described the general behavior of gravity well. In 1915, Albert Einstein created the General Theory of Relativity, which more accurately describes gravity in terms of the geometry of spacetime.
Celestial mechanics and some of its tasks
The simplest problem of celestial mechanics is the gravitational interaction of two point or spherical bodies in empty space. This problem within the framework of classical mechanics is solved analytically in a closed form; the result of its solution is often formulated in the form of Kepler's three laws.
As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability does not allow us to accurately predict the motion of planets on scales exceeding a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the Solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the complex structure of the rings of Saturn.
Despite attempts to accurately describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.
Strong gravitational fields
In strong gravitational fields, as well as when moving in a gravitational field at relativistic speeds, the effects of general relativity (GTR) begin to appear:
- changing the geometry of space-time;
- as a consequence, the deviation of the law of gravity from Newtonian;
- and in extreme cases - the emergence of black holes;
- delay of potentials associated with the finite speed of propagation of gravitational disturbances;
- as a consequence, the appearance of gravitational waves;
- nonlinearity effects: gravity tends to interact with itself, so the principle of superposition in strong fields no longer holds.
Gravitational radiation
One of the important predictions of General Relativity is gravitational radiation, the presence of which was confirmed by direct observations in 2015. However, before there was strong indirect evidence in favor of its existence, namely: energy losses in close binary systems containing compact gravitating objects (such as neutron stars or black holes), in particular, in the famous system PSR B1913+16 (Hals pulsar - Taylor) - are in good agreement with the general relativity model, in which this energy is carried away precisely by gravitational radiation.
Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments; this fact suggests that the gravitational radiation of most natural sources is directional, which significantly complicates its detection. Gravity power n-field source is proportional (v / c) 2 n + 2 (\displaystyle (v/c)^(2n+2)), if the multipole is of electric type, and (v / c) 2 n + 4 (\displaystyle (v/c)^(2n+4))- if the multipole is of magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:
L = 1 5 G c 5 ⟨ d 3 Q i j d t 3 d 3 Q i j d t 3 ⟩ , (\displaystyle L=(\frac (1)(5))(\frac (G)(c^(5)))\ left\langle (\frac (d^(3)Q_(ij))(dt^(3)))(\frac (d^(3)Q^(ij))(dt^(3)))\right \rangle ,)Where Q i j (\displaystyle Q_(ij))- quadrupole moment tensor of the mass distribution of the radiating system. Constant G c 5 = 2.76 × 10 − 53 (\displaystyle (\frac (G)(c^(5)))=2.76\times 10^(-53))(1/W) allows us to estimate the order of magnitude of the radiation power.
Since 1969 (Weber's experiments (English)), attempts are being made to directly detect gravitational radiation. In the USA, Europe and Japan there are currently several operating ground-based detectors (LIGO, VIRGO, TAMA (English), GEO 600), as well as the LISA (Laser Interferometer Space Antenna) space gravitational detector project. A ground-based detector in Russia is being developed at the Dulkyn Scientific Center for Gravitational Wave Research in the Republic of Tatarstan.
Subtle effects of gravity
In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which under terrestrial conditions are very weak and therefore their detection and experimental verification are very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, one can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's robotic Gravity Probe B conducted an unprecedented precision experiment to measure these effects near Earth. Processing of the obtained data was carried out until May 2011 and confirmed the existence and magnitude of the effects of geodetic precession and drag of inertial reference systems, although with an accuracy somewhat less than originally assumed.
After intensive work to analyze and extract measurement noise, the final results of the mission were announced at a press conference on NASA-TV on May 4, 2011, and published in Physical Review Letters. The measured value of geodetic precession was −6601.8±18.3 milliseconds arcs per year, and the entrainment effect - −37.2±7.2 milliseconds arcs per year (compare with theoretical values of −6606.1 mas/year and −39.2 mas/year).
Classical theories of gravity
Due to the fact that quantum effects of gravity are extremely small even under the most extreme and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the vast majority of cases one can limit oneself to the classical description of gravitational interaction.
There is a modern canonical classical theory of gravity - the general theory of relativity, and many clarifying hypotheses and theories of varying degrees of development, competing with each other. All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, most well-developed or known theories of gravity.
General theory of relativity
However, general relativity has been confirmed experimentally until very recently (2012). In addition, many alternative approaches to Einstein's, but standard for modern physics, approaches to the formulation of the theory of gravity lead to a result coinciding with general relativity in the low-energy approximation, which is the only one now accessible to experimental verification.
Einstein-Cartan theory
A similar division of equations into two classes also occurs in the RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and Minkowski space. Thanks to the presence of a dimensionless parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments. Moreover, as the parameter tends to infinity, the predictions of the theory become closer and closer to general relativity, so it is impossible to refute the Jordan-Brans-Dicke theory by any experiment confirming the general theory of relativity.
Quantum theory of gravity
Despite more than half a century of attempts, gravity is the only fundamental interaction for which a generally accepted consistent quantum theory has not yet been constructed. At low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as an exchange of gravitons - spin-2 gauge bosons. However, the resulting theory is non-renormalizable, and is therefore considered unsatisfactory.
In recent decades, several promising approaches to solving the problem of quantization of gravity have been developed: string theory, loop quantum gravity, and others.
String theory
In it, instead of particles and background space-time, strings and their multidimensional analogues appear -
