The principles of oto. General Relativity Is it Consistent? Does it match physical reality?

It was said about this theory that only three people in the world understand it, and when mathematicians tried to express in numbers what follows from it, the author himself - Albert Einstein - joked that now he had ceased to understand it.

Special and general relativity are inseparable parts of the doctrine on which modern scientific views on the structure of the world are built.

"Year of Miracles"

In 1905, Annalen der Physik (Annals of Physics), a leading German scientific publication, published one after another four articles by 26-year-old Albert Einstein, who worked as a 3rd class examiner - a petty clerk - of the Federal Office for Patenting Inventions in Bern. He had collaborated with the magazine before, but the publication of so many papers in one year was an extraordinary event. It became even more outstanding when the value of the ideas contained in each of them became clear.

In the first of the articles, thoughts were expressed about the quantum nature of light, and the processes of absorption and release of electromagnetic radiation were considered. On this basis, the photoelectric effect was first explained - the emission of electrons by matter, knocked out by photons of light, formulas were proposed for calculating the amount of energy released in this case. It is for the theoretical development of the photoelectric effect, which became the beginning of quantum mechanics, and not for the postulates of the theory of relativity, Einstein will be awarded the Nobel Prize in Physics in 1922.

In another article, the foundation was laid for applied areas of physical statistics based on the study of the Brownian motion of the smallest particles suspended in a liquid. Einstein proposed methods for searching for patterns of fluctuations - random and random deviations of physical quantities from their most probable values.

And finally, in the articles “On the electrodynamics of moving bodies” and “Does the inertia of a body depend on the energy content in it?” contained the germs of what will be designated in the history of physics as Albert Einstein's theory of relativity, or rather its first part - SRT - the special theory of relativity.

Sources and predecessors

At the end of the 19th century, it seemed to many physicists that most of the global problems of the universe had been resolved, the main discoveries had been made, and humanity would only have to use the accumulated knowledge to powerfully accelerate technological progress. Only some theoretical inconsistencies spoiled the harmonic picture of the Universe filled with ether and living according to immutable Newtonian laws.

Harmony was spoiled by Maxwell's theoretical research. His equations, which described the interactions of electromagnetic fields, contradicted the generally accepted laws of classical mechanics. This concerned the measurement of the speed of light in dynamic reference systems, when Galileo's principle of relativity ceased to work - the mathematical model of the interaction of such systems when moving at light speed led to the disappearance of electromagnetic waves.

In addition, the ether, which was supposed to reconcile the simultaneous existence of particles and waves, macro and microcosm, did not yield to detection. The experiment, which was carried out in 1887 by Albert Michelson and Edward Morley, was aimed at detecting the “ethereal wind”, which inevitably had to be recorded by a unique device - an interferometer. The experiment lasted a whole year - the time of the complete revolution of the Earth around the Sun. The planet had to move against the ether flow for half a year, the ether had to “blow into the sails” of the Earth for half a year, but the result was zero: no displacement of light waves under the influence of the ether was found, which cast doubt on the very existence of the ether.

Lorentz and Poincaré

Physicists have tried to find an explanation for the results of experiments to detect the ether. Hendrik Lorentz (1853-1928) proposed his mathematical model. It brought back to life the ethereal filling of space, but only under a very conditional and artificial assumption that when moving through the ether, objects can contract in the direction of movement. This model was finalized by the great Henri Poincaré (1854-1912).

In the works of these two scientists, for the first time, concepts appeared that in many respects constituted the main postulates of the theory of relativity, and this does not allow Einstein's accusations of plagiarism to subside. These include the conditionality of the concept of simultaneity, the hypothesis of the constancy of the speed of light. Poincaré admitted that at high speeds Newton's laws of mechanics require reworking, he made a conclusion about the relativity of motion, but in application to the ethereal theory.

Special Relativity - SRT

Problems of a correct description of electromagnetic processes became the motivation for choosing a topic for theoretical developments, and Einstein's articles published in 1905 contained an interpretation of a particular case - uniform and rectilinear motion. By 1915, the general theory of relativity was formed, which explained the interactions and gravitational interactions, but the first was the theory, called the special one.

Einstein's special theory of relativity can be summarized in two basic postulates. The first extends the effect of Galileo's principle of relativity to all physical phenomena, and not just to mechanical processes. In a more general form, it says: All physical laws are the same for all inertial (moving uniformly rectilinearly or at rest) frames of reference.

The second statement, which contains the special theory of relativity: the speed of propagation of light in vacuum for all inertial frames of reference is the same. Further, a more global conclusion is made: the speed of light is the maximum value of the transmission rate of interactions in nature.

In the mathematical calculations of SRT, the formula E=mc² is given, which has appeared in physical publications before, but it was thanks to Einstein that it became the most famous and popular in the history of science. The conclusion about the equivalence of mass and energy is the most revolutionary formula of the theory of relativity. The concept that any object with mass contains a huge amount of energy became the basis for developments in the use of nuclear energy and, above all, led to the appearance of the atomic bomb.

Effects of special relativity

Several consequences follow from SRT, which are called relativistic (relativity English - relativity) effects. Time dilation is one of the most striking. Its essence is that in a moving frame of reference time passes more slowly. Calculations show that on a spacecraft that made a hypothetical flight to the star system Alpha Centauri and back at a speed of 0.95 c (c is the speed of light), 7.3 years will pass, and on Earth - 12 years. Such examples are often given when explaining the theory of relativity for dummies, as well as the related twin paradox.

Another effect is the reduction of linear dimensions, that is, from the point of view of the observer, objects moving relative to him at a speed close to c will have smaller linear dimensions in the direction of motion than their own length. This effect predicted by relativistic physics is called the Lorentz contraction.

According to the laws of relativistic kinematics, the mass of a moving object is greater than the rest mass. This effect becomes especially significant in the development of instruments for the study of elementary particles - it is difficult to imagine the operation of the LHC (Large Hadron Collider) without taking it into account.

space-time

One of the most important components of SRT is a graphical representation of relativistic kinematics, a special concept of a single space-time, which was proposed by the German mathematician Hermann Minkowski, who at one time was a teacher of mathematics to a student of Albert Einstein.

The essence of the Minkowski model lies in a completely new approach to determining the position of interacting objects. The special theory of relativity of time pays special attention. Time becomes not just the fourth coordinate of the classical three-dimensional coordinate system, time is not an absolute value, but an inseparable characteristic of space, which takes the form of a space-time continuum, graphically expressed as a cone, in which all interactions take place.

Such a space in the theory of relativity, with its development to a more general character, was later subjected to further curvature, which made such a model suitable for describing gravitational interactions as well.

Further development of the theory

SRT did not immediately find understanding among physicists, but gradually it became the main tool for describing the world, especially the world of elementary particles, which became the main subject of study of physical science. But the task of supplementing SRT with an explanation of the gravitational forces was very relevant, and Einstein did not stop working, honing the principles of the general theory of relativity - GR. The mathematical processing of these principles took quite a long time - about 11 years, and specialists from the fields of exact sciences adjacent to physics took part in it.

Thus, the leading mathematician of that time, David Hilbert (1862-1943), who became one of the co-authors of the equations of the gravitational field, made a huge contribution. They were the last stone in the construction of a beautiful building, which received the name - the general theory of relativity, or GR.

General relativity - GR

The modern theory of the gravitational field, the theory of the "space-time" structure, the geometry of "space-time", the law of physical interactions in non-inertial frames of reference - all these are the various names that Albert Einstein's general theory of relativity is endowed with.

The theory of universal gravitation, which for a long time determined the views of physical science on gravity, on the interactions of objects and fields of various sizes. Paradoxically, but its main drawback was the intangibility, illusory, mathematical nature of its essence. There was a void between the stars and planets, the attraction between celestial bodies was explained by the long-range action of certain forces, and instantaneous ones. Albert Einstein's general theory of relativity filled gravity with physical content, presented it as a direct contact of various material objects.

The geometry of gravity

The main idea with which Einstein explained gravitational interactions is very simple. He declares the physical expression of the forces of gravity to be space-time, endowed with quite tangible features - metrics and deformations, which are influenced by the mass of the object around which such curvatures are formed. At one time, Einstein was even credited with calls to return to the theory of the universe the concept of ether, as an elastic material medium that fills space. He also explained that it was difficult for him to call a substance that has many qualities that can be described as a vacuum.

Thus, gravity is a manifestation of the geometric properties of four-dimensional space-time, which was designated in SRT as non-curved, but in more general cases it is endowed with curvature that determines the movement of material objects, which are given the same acceleration in accordance with the principle of equivalence declared by Einstein.

This fundamental principle of the theory of relativity explains many of the “bottlenecks” of the Newtonian theory of universal gravitation: the curvature of light observed when it passes near massive space objects during some astronomical phenomena and the same acceleration of the fall of bodies noted by the ancients, regardless of their mass.

Modeling the curvature of space

A common example that explains the general theory of relativity for dummies is the representation of space-time in the form of a trampoline - an elastic thin membrane on which objects (most often balls) are laid out, imitating interacting objects. Heavy balls bend the membrane, forming a funnel around them. A smaller ball launched across the surface moves in full accordance with the laws of gravity, gradually rolling into the depressions formed by more massive objects.

But this example is rather arbitrary. The real space-time is multidimensional, its curvature also does not look so elementary, but the principle of the formation of gravitational interaction and the essence of the theory of relativity become clear. In any case, a hypothesis that would more logically and coherently explain the theory of gravity does not yet exist.

Proofs of Truth

General relativity quickly came to be seen as a powerful foundation upon which modern physics could be built. The theory of relativity from the very beginning struck with its harmony and harmony, and not only specialists, and soon after its appearance began to be confirmed by observations.

The closest point to the Sun - the perihelion - of Mercury's orbit is gradually shifting relative to the orbits of other planets in the solar system, which was discovered back in the middle of the 19th century. Such a movement - precession - did not find a reasonable explanation within the framework of Newton's theory of universal gravitation, but was calculated with accuracy on the basis of the general theory of relativity.

The solar eclipse that occurred in 1919 provided an opportunity for yet another proof of general relativity. Arthur Eddington, who jokingly called himself the second person out of three who understand the basics of the theory of relativity, confirmed the deviations predicted by Einstein during the passage of photons of light near the star: at the time of the eclipse, a shift in the apparent position of some stars became noticeable.

The experiment to detect clock slowdown or gravitational redshift was proposed by Einstein himself, among other proofs of general relativity. Only after many years was it possible to prepare the necessary experimental equipment and conduct this experiment. The gravitational frequency shift of radiation from the emitter and receiver, spaced apart in height, turned out to be within the limits predicted by general relativity, and Harvard physicists Robert Pound and Glen Rebka, who conducted this experiment, further only increased the accuracy of measurements, and the formula of the theory of relativity again turned out to be correct.

Einstein's theory of relativity is always present in the substantiation of the most significant space exploration projects. Briefly, we can say that it has become an engineering tool for specialists, in particular those involved in satellite navigation systems - GPS, GLONASS, etc. It is impossible to calculate the coordinates of an object with the required accuracy, even in a relatively small space, without taking into account the slowdowns of signals predicted by general relativity. Especially if we are talking about objects spaced apart by cosmic distances, where the error in navigation can be huge.

Creator of the theory of relativity

Albert Einstein was still a young man when he published the foundations of the theory of relativity. Subsequently, its shortcomings and inconsistencies became clear to him. In particular, the most important problem of GR was the impossibility of its growing into quantum mechanics, since the description of gravitational interactions uses principles that are radically different from each other. In quantum mechanics, the interaction of objects in a single space-time is considered, and according to Einstein, this space itself forms gravity.

Writing the "formula of everything that exists" - a unified field theory that would eliminate the contradictions of general relativity and quantum physics, was Einstein's goal for many years, he worked on this theory until the last hour, but did not achieve success. The problems of general relativity have become a stimulus for many theorists in the search for more perfect models of the world. This is how string theories, loop quantum gravity and many others appeared.

The personality of the author of general relativity left a mark in history comparable to the importance for science of the theory of relativity itself. She does not leave indifferent so far. Einstein himself wondered why so much attention was paid to him and his work by people who had nothing to do with physics. Thanks to his personal qualities, famous wit, active political position and even expressive appearance, Einstein became the most famous physicist on Earth, the hero of many books, films and computer games.

The end of his life is described dramatically by many: he was lonely, considered himself responsible for the appearance of the most terrible weapon that became a threat to all life on the planet, his unified field theory remained an unrealistic dream, but Einstein’s words, spoken shortly before his death, can be considered the best result. that he fulfilled his task on Earth. It's hard to argue with this.

General theory of relativity(GR) is a geometric theory of gravity published by Albert Einstein in 1915-1916. Within the framework of this theory, which is a further development of the special theory of relativity, it is postulated that gravitational effects are caused not by the force interaction of bodies and fields located in space-time, but by the deformation of space-time itself, which is associated, in particular, with the presence of mass-energy. Thus, in general relativity, as in other metric theories, gravity is not a force interaction. General relativity differs from other metric theories of gravity by using Einstein's equations to relate the curvature of spacetime to the matter present in space.

General relativity is currently the most successful gravitational theory, well supported by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported observing the deflection of light near the Sun during a total eclipse, which confirmed the predictions of general relativity.

Since then, many other observations and experiments have confirmed a significant number of the theory's predictions, including gravitational time dilation, gravitational redshift, signal delay in a gravitational field, and, so far only indirectly, gravitational radiation. In addition, numerous observations are interpreted as confirmation of one of the most mysterious and exotic predictions of the general theory of relativity - the existence of black holes.

Despite the overwhelming success of general relativity, there is discomfort in the scientific community that it cannot be reformulated as the classical limit of quantum theory due to the appearance of irremovable mathematical divergences when considering black holes and space-time singularities in general. A number of alternative theories have been proposed to address this problem. Current experimental evidence indicates that any type of deviation from general relativity should be very small, if it exists at all.

Basic principles of general relativity

Newton's theory of gravity is based on the concept of gravity, which is a long-range force: it acts instantly at any distance. This instantaneous nature of the action is incompatible with the field paradigm of modern physics and, in particular, with the special theory of relativity created in 1905 by Einstein, inspired by the work of Poincaré and Lorentz. In Einstein's theory, no information can travel faster than the speed of light in a vacuum.

Mathematically, Newton's gravitational force is derived from the potential energy of a body in a gravitational field. The gravitational potential corresponding to this potential energy obeys the Poisson equation, which is not invariant under Lorentz transformations. The reason for the non-invariance is that the energy in the special theory of relativity is not a scalar quantity, but goes into the time component of the 4-vector. The vector theory of gravity turns out to be similar to Maxwell's theory of the electromagnetic field and leads to negative energy of gravitational waves, which is associated with the nature of the interaction: like charges (masses) in gravity are attracted, and not repelled, as in electromagnetism. Thus, Newton's theory of gravity is incompatible with the fundamental principle of the special theory of relativity - the invariance of the laws of nature in any inertial frame of reference, and the direct vector generalization of Newton's theory, first proposed by Poincaré in 1905 in his work "On the Dynamics of the Electron", leads to physically unsatisfactory results. .

Einstein began searching for a theory of gravity that would be compatible with the principle of the invariance of the laws of nature with respect to any frame of reference. The result of this search was the general theory of relativity, based on the principle of identity of gravitational and inertial mass.

The principle of equality of gravitational and inertial masses

In classical Newtonian mechanics, there are two concepts of mass: the first refers to Newton's second law, and the second to the law of universal gravitation. The first mass - inertial (or inertial) - is the ratio of the non-gravitational force acting on the body to its acceleration. The second mass - gravitational (or, as it is sometimes called, heavy) - determines the force of attraction of the body by other bodies and its own force of attraction. Generally speaking, these two masses are measured, as can be seen from the description, in different experiments, so they do not have to be proportional to each other at all. Their strict proportionality allows us to speak of a single body mass in both non-gravitational and gravitational interactions. By a suitable choice of units, these masses can be made equal to each other. The principle itself was put forward by Isaac Newton, and the equality of masses was verified by him experimentally with a relative accuracy of 10?3. At the end of the 19th century, Eötvös conducted more subtle experiments, bringing the accuracy of the verification of the principle to 10?9. During the 20th century, experimental techniques made it possible to confirm the equality of the masses with a relative accuracy of 10x12-10x13 (Braginsky, Dicke, etc.). Sometimes the principle of equality of gravitational and inertial masses is called the weak principle of equivalence. Albert Einstein put it at the basis of the general theory of relativity.

The principle of movement along geodesic lines

If the gravitational mass is exactly equal to the inertial mass, then in the expression for the acceleration of a body on which only gravitational forces act, both masses cancel. Therefore, the acceleration of the body, and hence its trajectory, does not depend on the mass and internal structure of the body. If all bodies at the same point in space receive the same acceleration, then this acceleration can be associated not with the properties of the bodies, but with the properties of the space itself at this point.

Thus, the description of the gravitational interaction between bodies can be reduced to a description of the space-time in which the bodies move. It is natural to assume, as Einstein did, that bodies move by inertia, that is, in such a way that their acceleration in their own reference frame is zero. The trajectories of the bodies will then be geodesic lines, the theory of which was developed by mathematicians back in the 19th century.

The geodesic lines themselves can be found by specifying in space-time an analogue of the distance between two events, traditionally called an interval or a world function. The interval in three-dimensional space and one-dimensional time (in other words, in four-dimensional space-time) is given by 10 independent components of the metric tensor. These 10 numbers form the space metric. It defines the "distance" between two infinitely close points of space-time in different directions. Geodesic lines corresponding to the world lines of physical bodies whose speed is less than the speed of light turn out to be the lines of the greatest proper time, that is, the time measured by a clock rigidly fastened to a body following this trajectory. Modern experiments confirm the motion of bodies along geodesic lines with the same accuracy as the equality of gravitational and inertial masses.

Curvature of space-time

If two bodies are launched from two close points parallel to each other, then in the gravitational field they will gradually either approach or move away from each other. This effect is called the deviation of geodesic lines. A similar effect can be observed directly if two balls are launched parallel to each other over a rubber membrane, on which a massive object is placed in the center. The balls will disperse: the one that was closer to the object pushing through the membrane will tend to the center more strongly than the more distant ball. This discrepancy (deviation) is due to the curvature of the membrane. Similarly, in space-time, the deviation of geodesics (the divergence of the trajectories of bodies) is associated with its curvature. The curvature of space-time is uniquely determined by its metric - the metric tensor. The difference between the general theory of relativity and alternative theories of gravity is determined in most cases precisely in the way of connection between matter (bodies and fields of a non-gravitational nature that create a gravitational field) and the metric properties of space-time.

Space-time GR and the strong equivalence principle

It is often incorrectly considered that the basis of the general theory of relativity is the principle of equivalence of the gravitational and inertial fields, which can be formulated as follows:
A sufficiently small local physical system located in a gravitational field is indistinguishable in behavior from the same system located in an accelerated (relative to the inertial reference frame) reference frame, immersed in the flat space-time of special relativity.

Sometimes the same principle is postulated as "local validity of special relativity" or called the "strong equivalence principle".

Historically, this principle really played a big role in the development of the general theory of relativity and was used by Einstein in its development. However, in the most final form of the theory, in fact, it is not contained, since the space-time both in the accelerated and in the initial frame of reference in the special theory of relativity is uncurved - flat, and in the general theory of relativity it is curved by any body, and precisely its curvature causes the gravitational attraction of bodies.

It is important to note that the main difference between the space-time of the general theory of relativity and the space-time of the special theory of relativity is its curvature, which is expressed by a tensor quantity - the curvature tensor. In the space-time of special relativity, this tensor is identically equal to zero and the space-time is flat.

For this reason, the name "general relativity" is not entirely correct. This theory is only one of a number of theories of gravity currently being considered by physicists, while the special theory of relativity (more precisely, its principle of space-time metricity) is generally accepted by the scientific community and forms the cornerstone of the basis of modern physics. It should, however, be noted that none of the other developed theories of gravity, except general relativity, has stood the test of time and experiment.

Main Consequences of General Relativity

According to the correspondence principle, in weak gravitational fields, the predictions of general relativity coincide with the results of applying Newton's law of universal gravitation with small corrections that increase as the field strength increases.

The first predicted and verified experimental consequences of general relativity were three classical effects, listed below in chronological order of their first verification:
1. Additional shift of the perihelion of Mercury's orbit compared to the predictions of Newtonian mechanics.
2. Deviation of a light beam in the gravitational field of the Sun.
3. Gravitational redshift, or time dilation in a gravitational field.

There are a number of other effects that can be experimentally verified. Among them, we can mention the deviation and delay (Shapiro effect) of electromagnetic waves in the gravitational field of the Sun and Jupiter, the Lense-Thirring effect (precession of a gyroscope near a rotating body), astrophysical evidence for the existence of black holes, evidence for the emission of gravitational waves by close systems of binary stars and the expansion of the Universe.

So far, reliable experimental evidence refuting general relativity has not been found. The deviations of the measured values of the effects from those predicted by general relativity do not exceed 0.1% (for the above three classical phenomena). Despite this, due to various reasons, theorists have developed at least 30 alternative theories of gravity, and some of them make it possible to obtain results arbitrarily close to general relativity for the corresponding values of the parameters included in the theory.

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The special theory of relativity was developed at the beginning of the 20th century by the efforts of G. A. Lorentz, A. Poincaré and A. Einstein.

Einstein's postulates

SRT is completely derived at the physical level of rigor from two postulates (assumptions):

Einstein's principle of relativity is valid, an extension of Galileo's principle of relativity.

The speed of light does not depend on the speed of the source in all inertial frames of reference.

Experimental verification of the SRT postulates is to a certain extent hampered by problems of a philosophical nature: the possibility of writing the equations of any theory in an invariant form, regardless of its physical content, and the complexity of interpreting the concepts of "length", "time" and "inertial frame of reference" in conditions of relativistic effects.

Essence of SRT

The consequences of the postulates of SRT are the Lorentz transformations, which replace the Galilean transformations for non-relativistic, “classical” motion. These transformations link the coordinates and times of the same events observed from different inertial frames of reference.

It is they who describe such famous effects as slowing down the passage of time and shortening the length of fast-moving bodies, the existence of a limiting speed of a body (which is the speed of light), the relativity of the concept of simultaneity (two events occur simultaneously according to clocks in one frame of reference, but at different points in time according to hours in another reference system).

The special theory of relativity has received numerous experimental confirmations and is undoubtedly the correct theory in its field of applicability. The special theory of relativity ceases to work on the scale of the entire Universe, as well as in cases of strong gravitational fields, where it is replaced by a more general theory - the general theory of relativity. The special theory of relativity is also applicable in the microcosm, its synthesis with quantum mechanics is quantum field theory.

Comments

Just as in the case of quantum mechanics, many predictions of the theory of relativity are counterintuitive, seem incredible and impossible. This, however, does not mean that the theory of relativity is wrong. In reality, how we see (or want to see) the world around us and how it actually is can be very different. For more than a century, scientists around the world have been trying to refute SRT. None of these attempts could find the slightest flaw in the theory. The fact that the theory is mathematically correct is evidenced by the strict mathematical form and clarity of all formulations. The fact that SRT really describes our world is evidenced by a huge experimental experience. Many consequences of this theory are used in practice. It is obvious that all attempts to "refute SRT" are doomed to failure because the theory itself is based on Galileo's three postulates (which are somewhat expanded), on the basis of which Newtonian mechanics is built, as well as on an additional postulate of the constancy of the speed of light in all frames of reference. All four do not raise any doubt within the maximum accuracy of modern measurements: better than 10 - 12, and in some aspects - up to 10 - 15. Moreover, the accuracy of their verification is so high that the constancy of the speed of light is put at the basis of the definition of the meter - units of length, as a result of which the speed of light becomes a constant automatically if measurements are carried out in accordance with metrological requirements.

SRT describes non-gravitational physical phenomena with very high accuracy. But this does not exclude the possibility of its clarification and addition. For example, the general theory of relativity is a refinement of SRT that takes into account gravitational phenomena. The development of quantum theory is still ongoing, and many physicists believe that the future complete theory will answer all questions that have a physical meaning, and will give both SRT in combination with quantum field theory and general relativity within the limits. Most likely, SRT will face the same fate as Newton's mechanics - the limits of its applicability will be accurately outlined. At the same time, such a maximally general theory is still a very distant prospect, and not all scientists believe that its construction is even possible.

General theory of relativity

General relativity is currently (2007) the most successful gravitational theory, well confirmed by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported observing the deflection of light near the Sun during a total eclipse, which confirmed the predictions of general relativity. In addition, numerous observations are interpreted as confirming one of the most mysterious and exotic predictions of general relativity - the existence of black holes.

The principle of equality of gravitational and inertial masses

The principle of movement along geodesic lines

Modern experiments confirm the motion of bodies along geodesic lines with the same accuracy as the equality of gravitational and inertial masses.

Curvature of space-time

Main Consequences of General Relativity

The first predicted and verified experimental consequences of general relativity were three classical effects, listed below in chronological order of their first verification:

An additional shift in the perihelion of Mercury's orbit compared to the predictions of Newtonian mechanics.
Deflection of a light beam in the gravitational field of the Sun.
Gravitational redshift, or time dilation in a gravitational field.

General relativity is already applied to all frames of reference (and not just to those moving at a constant speed relative to each other) and looks mathematically much more complicated than special (which explains the gap of eleven years between their publication). It includes as a special case the special theory of relativity (and hence Newton's laws). At the same time, the general theory of relativity goes much further than all its predecessors. In particular, it gives a new interpretation of gravity.

The general theory of relativity makes the world four-dimensional: time is added to three spatial dimensions. All four dimensions are inseparable, so we are no longer talking about the spatial distance between two objects, as is the case in the three-dimensional world, but about the space-time intervals between events that unite their distance from each other - both in time and in space . That is, space and time are considered as a four-dimensional space-time continuum or, simply, space-time. On this continuum, observers moving relative to each other may even disagree about whether two events happened at the same time—or one preceded the other. Fortunately for our poor mind, it does not come to a violation of causal relationships - that is, the existence of coordinate systems in which two events do not occur simultaneously and in a different sequence, even the general theory of relativity does not allow.

Classical physics considered gravity as an ordinary force among many natural forces (electrical, magnetic, etc.). Gravity was prescribed "long-range action" (penetration "through the void") and an amazing ability to give equal acceleration to bodies of different masses.

Newton's law of universal gravitation tells us that between any two bodies in the universe there is a force of mutual attraction. From this point of view, the Earth revolves around the Sun, since there are forces of mutual attraction between them.

General relativity, however, forces us to look at this phenomenon differently. According to this theory, gravity is a consequence of the deformation ("curvature") of the elastic fabric of space-time under the influence of mass (in this case, the heavier the body, for example the Sun, the more space-time "bends" under it and, accordingly, the stronger its gravitational field). Imagine a tightly stretched canvas (a kind of trampoline), on which a massive ball is placed. The canvas deforms under the weight of the ball, and a funnel-shaped depression forms around it. According to the general theory of relativity, the Earth revolves around the Sun like a small ball rolled around the cone of a funnel formed as a result of "punching" space-time by a heavy ball - the Sun. And what seems to us the force of gravity, in fact, is, in fact, a purely external manifestation of the curvature of space-time, and not at all a force in the Newtonian sense. To date, a better explanation of the nature of gravity than the general theory of relativity gives us has not been found.

First, the equality of accelerations of free fall for bodies of different masses is discussed (the fact that a massive key and a light match equally quickly fall from the table to the floor). As Einstein noted, this unique property makes gravity very similar to inertia.

In fact, the key and the match behave as if they were moving in weightlessness by inertia, and the floor of the room was moving towards them with acceleration. Having reached the key and the match, the floor would experience their impact, and then pressure, because. the inertia of the key and the match would have affected the further acceleration of the floor.

This pressure (astronauts say - "overload") is called the force of inertia. A similar force is always applied to bodies in accelerated frames of reference.

If the rocket flies with an acceleration equal to the free fall acceleration on the earth's surface (9.81 m/s), then the inertia force will play the role of the weight of the key and the match. Their "artificial" gravity will be exactly the same as the natural one on the surface of the Earth. This means that the acceleration of the reference frame is a phenomenon quite similar to gravity.

On the contrary, in a free-falling elevator, natural gravity is eliminated by the accelerated movement of the cabin reference system "chasing" the key and the match. Of course, classical physics does not see in these examples the true emergence and disappearance of gravity. Gravity is only simulated or compensated by acceleration. But in general relativity, the similarity between inertia and gravity is recognized to be much deeper.

Einstein put forward the local principle of the equivalence of inertia and gravity, stating that on sufficiently small scales of distances and durations, one phenomenon cannot be distinguished from another by any experiment. Thus, general relativity has changed the scientific understanding of the world even more profoundly. The first law of Newtonian dynamics has lost its universality - it turned out that the movement by inertia can be curvilinear and accelerated. The need for the concept of a heavy mass has disappeared. The geometry of the Universe has changed: instead of direct Euclidean space and uniform time, a curved space-time, a curved world, has appeared. The history of science has never known such a sharp restructuring of views on the physical fundamental principles of the universe.

Testing general relativity is difficult because, under normal laboratory conditions, its results are almost identical to those predicted by Newton's law of universal gravitation. Nevertheless, several important experiments were carried out, and their results allow us to consider the theory confirmed. In addition, general relativity helps explain the phenomena we observe in space, one example is a beam of light passing near the sun. Both Newtonian mechanics and general relativity recognize that it must deviate towards the Sun (fall). However, general relativity predicts twice the beam shift. Observations during solar eclipses proved the correctness of Einstein's prediction. Another example. The planet Mercury closest to the Sun has minor deviations from a stationary orbit, inexplicable from the point of view of classical Newtonian mechanics. But just such an orbit is given by the calculation by the GR formulas. The slowing down of time in a strong gravitational field explains the decrease in the frequency of light oscillations in the radiation of white dwarfs - stars of very high density. And in recent years, this effect has been registered in laboratory conditions. Finally, the role of general relativity in modern cosmology, the science of the structure and history of the entire universe, is very important. Many proofs of Einstein's theory of gravitation have also been found in this field of knowledge. In fact, the results predicted by general relativity differ noticeably from the results predicted by Newton's laws only in the presence of superstrong gravitational fields. This means that a full test of the general theory of relativity requires either ultra-precise measurements of very massive objects, or black holes, to which none of our usual intuitive ideas are applicable. So the development of new experimental methods for testing the theory of relativity remains one of the most important tasks of experimental physics.

The theory of relativity is a physical theory that considers space-time regularities that are valid for any physical processes. The most general theory of space-time is called the general theory of relativity (GR), or the theory of gravitation. In the private (or special) theory of relativity (SRT), the properties of space-time are studied, which are valid with the accuracy with which the action of gravity can be neglected. (Physical Encyclopedic Dictionary, 1995)

Time and Mass A body contracts along its axis of motion as it approaches the speed of light

Atomic decay The atomic mass of new atoms and the amount of energy of motion formed are equivalent to the mass of the original atom

At the end of the 19th century, the laws of motion and gravity discovered by Newton were widely used for calculations and found more and more experimental evidence. Nothing seemed to herald a revolution in this area. However, the matter was no longer limited only to mechanics: as a result of the experimental activities of many scientists in the field of electricity and magnetism, Maxwell's equations appeared. This is where the problems with the laws of physics began. Maxwell's equations bring together electricity, magnetism and light. It follows from them that the speed of electromagnetic waves, including light waves, does not depend on the movement of the emitter and is equal to about 300 thousand km/s in vacuum. This is in no way consistent with the mechanics of Newton and Galileo. Suppose a balloon flies relative to the Earth at a speed of 100,000 km/s. Let's shoot forward from a light gun with a light bullet, the speed of which is 300 thousand km/s. Then, according to Galileo's formulas, the speeds should simply be added up, which means that the bullet will fly relative to the Earth at a speed of 400 thousand km / s. No constancy of the speed of light is obtained!

Much effort has been made to detect the change in the speed of light as the emitter moves, but none of the ingenious experiments has succeeded. Even the most accurate of them, the Michelson-Morley experiment, gave a negative result. So something is wrong with Maxwell's equations? But they perfectly describe all electrical and magnetic phenomena. And then Henri Poincaré suggested that the point is still not in the equations, but in the principle of relativity: all physical laws, not only mechanical, like Newton's, but also electrical, must be the same in systems moving relative to each other uniformly and rectilinearly . In 1904, the Dane Hendrik Anton Lorentz, specifically for Maxwell's equations, obtained new formulas for recalculating the coordinates of a moving system relative to a stationary one and vice versa. But this helped only partly: it turned out that for Newton's laws one must use some transformations, and for Maxwell's equations others. The question remained open.

Special theory of relativity

The transformations proposed by Lorentz had two important implications. It turned out that during the transition from one system to another, it is necessary to subject not only coordinates, but also time to transformations. And besides, the size of the moving body, calculated according to Lorentz's formulas, changed - it became smaller along the direction of motion! Therefore, speeds exceeding the speed of light lost all physical meaning, since in this case the bodies were compressed to zero dimensions. Many physicists, including Lorentz himself, considered these conclusions just a mathematical incident. Until Einstein took over.

Why is the theory of relativity named after Einstein, if the principle of relativity was formulated by Poincare, the constancy of the speed of light was deduced by Maxwell, and the rules for transforming coordinates were invented by Lorentz? First of all, let's say that everything we have talked about so far concerns only the so-called "special theory of relativity" (SRT). Contrary to popular belief, Einstein's contribution to this theory is by no means limited to a simple generalization of the results. First, he managed to get all the equations based on just two postulates - the principle of relativity and the principle of constancy of the speed of light. And secondly, he understood what amendment should be made to Newton's law so that it does not fall out of the new picture of the world and does not change under Lorentz's transformations. To do this, it was necessary to critically treat two previously unshakable foundations of classical mechanics - the absoluteness of time and the constancy of body mass.

Nothing absolute

In Newtonian mechanics, sidereal time was tacitly identified with absolute time, and in Einstein's theory, each frame of reference corresponds to its own, "local" time, and there are no clocks that would measure time for the entire Universe. But the conclusions about the relativity of time were not enough to eliminate the contradictions between electrodynamics and classical mechanics. This problem was solved when another classical bastion fell - the constancy of mass. Einstein introduced changes to Newton's basic law of the proportionality of force to acceleration and found that mass increases indefinitely when approaching the speed of light. Indeed, after all, it follows from the postulates of SRT that a speed greater than the speed of light has no physical meaning, which means that no force can increase the speed of a body already flying at the speed of light, that is, under these conditions, the force no longer causes acceleration! The greater the speed of the body, the more difficult it is to accelerate it.

And since the coefficient of proportionality is the mass (or inertia), it follows that the mass of the body increases with increasing speed.

It is remarkable that this conclusion was made at a time when there were no obvious contradictions and inconsistencies between the results of experiments and Newton's laws. Under normal conditions, the change in mass is insignificant, and it can be detected experimentally only at very high speeds, close to the speed of light. Even for a satellite flying at a speed of 8 km/s, the correction to the mass will be no more than one two-billionth. But already in 1906, the conclusions of SRT were confirmed in the study of electrons moving at high speeds: in Kaufman's experiments, a change in the mass of these particles was recorded. And on modern accelerators, it will simply not be possible to disperse particles if calculations are carried out in the classical way without taking into account the special theory of relativity.

But then it turned out that the inconstancy of the mass allows us to draw an even more fundamental conclusion. With an increase in speed, the mass increases, the energy of motion increases ... Isn't it the same thing? Mathematical calculations confirmed the conjecture about the equivalence of mass and energy, and in 1907 Einstein received his famous formula E = mc2. This is the main conclusion of SRT. Mass and energy are one and the same and are transformed into each other! And if some body (for example, an atom of uranium) suddenly breaks up into two, which in total have a smaller mass, then the rest of the mass passes into the energy of motion. Einstein himself assumed that it would be possible to notice a change in mass only with huge energy releases, since the coefficient c2 in the formula he received is very, very large. But he, too, probably did not expect that these theoretical considerations would lead mankind so far. The creation of the atomic bomb confirmed the validity of the special theory of relativity, only at too high a price.

It would seem that there is no reason to doubt the correctness of the theory. But here it’s time to recall the words of Einstein: “Experience will never say “yes” to a theory, but at best it says “maybe”, for the most part it simply says “no”. The last, most accurate experiment to test one of the SRT postulates, the constancy of the speed of light, was carried out quite recently, in 2001, at the University of Konstanz (Germany). A standing laser wave was placed in a "box" of ultrapure sapphire, cooled to the temperature of liquid helium, and the change in the frequency of light was monitored for half a year. If the speed of light depended on the speed of the laboratory, then the frequency of this wave would change as the Earth moved in orbit. But no changes have been noticed so far.

General theory of relativity

In 1905, when Einstein published his famous work “On the Electrodynamics of Moving Bodies”, dedicated to SRT, he moved on. He was convinced that STO was only part of the journey. The principle of relativity must be valid in any frame of reference, and not only in those that move uniformly and rectilinearly. This conviction of Einstein was not just a guess, it was based on an experimental fact, the observance of the principle of equivalence. Let's explain what it is. The so-called "inertial" mass appears in the laws of motion, which shows how difficult it is for a body to accelerate, and in the laws of gravity - a "heavy" mass that determines the force of attraction between bodies. The principle of equivalence assumes that these masses are exactly equal to each other, but only experience can confirm whether this is actually the case. It follows from the principle of equivalence that all bodies must move in the gravitational field with the same acceleration. Even Galileo checked this circumstance, throwing, according to legend, various bodies from the Leaning Tower of Pisa. Then the measurement accuracy was 1%, Newton brought it to 0.1%, and, according to the latest data from 1995, we can be sure that the equivalence principle is fulfilled with an accuracy of 5 x 10−13.

Taking the principle of equivalence and the principle of relativity as a basis, after ten years of hard work, Einstein created his theory of gravitation, or the general theory of relativity (GR), which to this day never ceases to amaze theorists with its mathematical beauty. Space and time in Einstein's theory of gravitation turned out to be subject to amazing metamorphoses. The gravitational field, which is created around themselves by bodies with mass, bends the surrounding space. Imagine a ball lying on a trampoline. The heavier the ball, the more the trampoline mesh will bend. And time, turned into the fourth dimension, does not stand aside: the greater the gravitational field, the slower time flows.

The first confirmed prediction of general relativity was made by Einstein himself back in 1915. It concerned the motion of Mercury. The perihelion of this planet (that is, the point of its closest approach to the Sun) gradually changes its position. Over a hundred years of observations from the Earth, the displacement was 43.1 arc seconds. Only the general theory of relativity was able to give a stunningly accurate prediction of this value - 43 arc seconds. The next step was to observe the deflection of light rays in the gravitational field of the Sun during the total solar eclipse of 1919. Since then, many such experiments have been carried out, and all of them confirm general relativity - despite the fact that the accuracy is constantly increasing. For example, in 1984 it was 0.3%, and in 1995 it was already less than 0.1%.

With the advent of atomic clocks, it came to time itself. It is enough to place one clock on the top of the mountain, the other at its foot - and you can catch the difference in the course of time! And with the advent of global positioning satellite systems, the theory of relativity finally moved from the category of scientific entertainment to a purely practical area. GPS satellites, for example, fly at an altitude of about 20,000 km at a speed of about 4 km/s. Since they are quite far from the Earth, the clocks on them, according to general relativity, advance by about 45 microseconds (µs) per day, but because they fly at high speed, due to STR, the same clocks lag behind by about 7 µs daily. If these amendments are not taken into account, then the whole system will become useless within a few days! Before being sent into orbit, the atomic clocks on the satellites are adjusted so that they go slower by about 38 microseconds per day. And the fact that, after such an adjustment, my simple GPS receiver correctly shows my coordinates on the vast earth's surface every day, seriously strengthens my confidence in the theory of relativity.

All these successes only inflame the hunters for relativity. Today, every self-respecting university has a laboratory to search for gravitational waves, which, according to Einstein's theory of gravity, should propagate at the speed of light. Haven't been able to find them yet. Another stumbling block is the connection between general relativity and quantum mechanics. Both of them agree perfectly with experiment, but are completely incompatible with each other. Isn't it somewhat reminiscent of classical mechanics and electromagnetism of the late 19th century? Perhaps it is worth waiting for a change.