RELATIVISTIC EFFECTS

RELATIVISTIC EFFECTS

Phys. phenomena observed at speeds of bodies (c-c) v, comparable to the speed of light c. These include: Relative. reduction of longitudinal (in the direction of body movement) lengths, relative. time dilation, an increase in the mass of a body with an increase in its energy, etc., considered in the particular (special) relativity of the theory. For quantum. systems of h-c (atoms, at. nuclei, etc.), in which it refers. s-ts occurs with velocities v SPIN-ORBITAL INTERACTION). Relativistic called. also the effects of the general theory of relativity (relative theory of gravitation), for example. the effect of slowing down the flow of time in strong gravity. (see GRAVITY).

Physical Encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

RELATIVISTIC EFFECTS

- physical phenomena observed at the speeds of bodies (particles) v, comparable to the speed of light With. These include: relativistic contraction of longitudinal (in the direction of motion of the body) lengths, relativistic time dilation, an increase in the mass of a body with an increase in its energy, etc., considered in a particular (special) relativity theory. For quantum systems of particles (atoms, atomic nuclei, etc.), in which it refers. the movement of particles occurs at speeds, R. e. give corrections to energy levels, proportional. degrees of relation u/s(see, for example, spin-orbit interaction). Relativistic called. also the effects of the general theory of relativity (relativistic theory of gravity), for example. the effect of slowing down the passage of time in a strong gravitational dance. field (see gravity).. I. Yu. Kobzarev.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1988 .

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Physical phenomena observed at speeds of bodies (particles) comparable to the speed of light, as well as in strong gravitational fields (see Relativity theory, Gravity) ... Big Encyclopedic Dictionary

Physical phenomena observed at speeds of bodies (particles) comparable to the speed of light, as well as in strong gravitational fields (see Relativity theory, Gravity). * * * RELATIVISTIC EFFECTS RELATIVISTIC EFFECTS, physical phenomena,… … encyclopedic Dictionary

Phenomena observed at speeds of bodies (particles) comparable to the speed of light. These include: Lorentz Fitzgerald contraction, relativistic time dilation, an increase in the mass of a body with an increase in its energy, etc., considered in ... ...

Phys. phenomena observed at speeds of bodies (particles) comparable to the speed of light, as well as in strong gravitational forces. fields (see Relativity theory, Gravitation) ... Natural science. encyclopedic Dictionary

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Books

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• Relativistic Physics: Special Theory of Relativity. General Theory of Relativity, Mitskevich N.V. This book is a textbook written on the basis of two courses of lectures - on special and general relativity, which were read by the author, respectively, in ...

Classical physics is of the opinion that any observer, regardless of location, will get the same results in their measurements of time and extent. The principle of relativity states that observers can get different results, and such distortions are called "relativistic effects". When approaching the speed of light, Newtonian physics steps aside.

speed of light

The scientist A. Michelson, who conducted light in 1881, realized that these results would not depend on the speed at which the radiation source was moving. Together with E.V. Morley Michelson in 1887 conducted another experiment, after which it became clear to the whole world: no matter in which direction the measurement is taken, the speed of light is everywhere and always the same. The results of these studies ran counter to the ideas of physics of that time, because if light moves in a certain medium (ether), and the planet moves in the same medium, measurements in different directions cannot be the same.

Later, the French mathematician, physicist and astronomer Jules Henri Poincaré became one of the founders of the theory of relativity. He developed the theory of Lorentz, according to which the existing ether is motionless, therefore, relative to it, it does not depend on the speed of the source. In moving frames of reference, Lorentz transformations are performed, and not Galilean ones (the Galilean transformations accepted until then in Newtonian mechanics). From now on, Galilean transformations have become a special case of Lorentz transformations, when moving to another inertial frame of reference at a low (compared to the speed of light) speed.

Abolition of ether

The relativistic effect of length contraction, also called Lorentz contraction, is that for the observer, objects moving relative to him will have a shorter length.

Albert Einstein made a significant contribution to the theory of relativity. He completely abolished such a term as "ether", which until that time was present in the reasoning and calculations of all physicists, and he transferred all concepts of the properties of space and time to kinematics.

After the publication of Einstein's works, Poincaré not only stopped writing scientific papers on this topic, but also did not mention the name of his colleague in any of his works, except for the only case of reference to the theory of the photoelectric effect. Poincare continued to discuss the properties of the ether, categorically denying any publications of Einstein, although at the same time he treated the greatest scientist with respect and even gave him a brilliant testimonial when the administration of the Higher Polytechnical School in Zurich wanted to invite Einstein to become a professor at the educational institution.

Theory of relativity

Even many of those who are completely at odds with physics and mathematics, at least in general terms, understand what the theory of relativity is, because it is perhaps the most famous of scientific theories. Its postulates destroy ordinary ideas about time and space, and although all schoolchildren study the theory of relativity, it is not enough just to know the formulas to understand it in its entirety.

The effect of time dilation was tested in an experiment with a supersonic aircraft. The exact atomic clocks on board began to fall behind by a fraction of a second after returning. If there are two observers, one of which is standing still, and the second is moving at some speed relative to the first, the time for the observer who is stationary will go faster, and for the moving object, the minute will last a little longer. However, if the moving observer decides to go back and check the time, it will turn out that his watch shows a little less than the first. That is, having traveled a much greater distance on the scale of space, he "lived" less time while moving.

Relativistic effects in life

Many people believe that relativistic effects can only be observed when the speed of light is reached or approaching it, and this is true, but you can observe them not only by accelerating your spaceship. On the pages of the scientific journal Physical Review Letters, you can read about the theoretical work of Swedish scientists. They wrote that relativistic effects are present even in a simple car battery. The process is possible due to the rapid movement of electrons of lead atoms (by the way, they are the cause of most of the voltage in the terminals). This also explains why, despite the similarities between lead and tin, tin-based batteries don't work.

Fancy Metals

The speed of rotation of electrons in atoms is rather low, so the theory of relativity simply does not work, but there are some exceptions. If you move further and further along the periodic table, it becomes clear that there are quite a few elements heavier than lead in it. A large mass of nuclei is balanced by increasing the speed of electrons, and it can even approach the speed of light.

If we consider this aspect from the side of the theory of relativity, it becomes clear that electrons in this case must have a huge mass. This is the only way to preserve the angular momentum, but the orbital will shrink along the radius, and this is indeed observed in heavy metal atoms, but the orbitals of "slow" electrons do not change. This relativistic effect is observed in the atoms of some metals in s-orbitals, which have a regular, spherically symmetric shape. It is believed that it is as a result of the theory of relativity that mercury has a liquid state of aggregation at room temperature.

space travel

Objects in space are huge distances from each other, and even when moving at the speed of light, it will take a very long time to overcome them. For example, to reach Alpha Centauri, the nearest star to us, a spacecraft with the speed of light will take four years, and to reach our neighboring galaxy, the Large Magellanic Cloud, it will take 160,000 years.

About magnetism

Among other things, modern physicists are increasingly discussing the magnetic field as a relativistic effect. According to this interpretation, the magnetic field is not an independent physical material entity, it is not even one of the manifestations of the electromagnetic field. The magnetic field from the point of view of the theory of relativity is just a process that occurs in space around point charges due to the transfer of an electric field.

Adherents of this theory believe that if C (the speed of light in vacuum) were infinite, then the propagation of interactions in speed would also be unlimited, and as a result, no manifestations of magnetism could arise.

Many of you will say that to see relativistic effects you have to reach the speed of light. But we will say that you do not need to get into a spacecraft to accelerate it to light speed and verify this. You can take the well-known scientific journal Physical Review Letters, in which Swedish scientists described their theoretical work on relativistic effects in our everyday life. They can be observed even in a conventional car battery. This process occurs due to the fast moving electrons in the lead atoms, which are the cause of 80% of the voltage in the battery terminal connections. This explains why tin-acid batteries can't work the way lead-acid batteries do, and tin and lead are similar.

Under normal conditions, electrons can revolve around atoms at a speed much lower than the speed of light, so relativistic effects are simply ignored. But there are also exceptions. In Mendeleev's list, you can find many heavier elements than lead. To ensure the balance of a large mass of nuclei, electrons must move at a speed close to the speed of light.

If this aspect is considered through the prism of the theory of relativity, then the electrons must have a huge mass. Such a statement contributes to the conservation of angular momentum and the radii of the orbits of the electrons should shrink, which does not happen with slower electrons. Such contraction can be observed in the spherically symmetric s orbitals of some heavy elements. Such evidence reveals the yellow color of gold, and the metal - mercury has a liquid state at room temperature.

At the moment, there are several theoretical works that are based on the study of the structural features of lead in order to identify relativistic effects. Until recently, the impact of fast moving elements was considered as the electrochemical properties of the heavy elements of the periodic table.

As we said at the beginning of the article, the results of the research were published in the scientific journal Physical Review Letters. Where it says that a group of scientists from Sweden (Uppsala University) began to study the behavior of a simple form of lead, namely, the study concerns the processes occurring in a conventional car battery. As you know, batteries have been produced for more than 150 years and their design has not changed until recently. It is based on cells that consist of a pair of lead plates and lead dioxide that are immersed in sulfuric acid. As a result of a chemical reaction, the formation of lead sulfate occurs, which leads to the formation of a potential difference of 2.1. And in real life, such battery models exist. When calculating such a battery, Swedish scientists used one of the basic laws of physics. To determine the potential difference at the terminals of one battery cell, scientists calculated the energy difference between the electronic reagents and products. Separately, the acid component was calculated. As a result of mathematical calculations, they were able to establish that the voltage in each cell is 1.7 V, and a conventional car battery should produce 10-12 V, which indicates the presence of relativistic effects.

In conclusion, the scientists argue that lead works the same as tin, which has the same number of electrons in the far s- and p-orbits. Yet tin has 50 protons, and lead is gifted with 82. Therefore, it follows that the relativistic contraction is smaller in s-orbitals. Therefore, scientists had to conclude in favor of the low profitability of tin-acid batteries, which have a low voltage at the terminals. Previously, this fact was of a qualitative nature, but now there is a quantitative confirmation.

Relativistic effects

This section does not provide a complete explanation of the theory of relativity. In everyday life, we do not realize the significance of the theory of relativity. However, this theory affects many processes, among which the correct functioning of the GPS system. This influence will be briefly explained below.

As we know, time is one of the main factors in GPS navigation and should be 20-30 nanoseconds to be accurate. Therefore, it is necessary to take into account the speed of the satellites (approximately 12000 km / h)

Anyone who has ever dealt with the theory of relativity knows that time passes more slowly at high speeds. For satellites that move at a speed of 3874 m/s, the clock runs slower than for the earth. This relativistic time results in an inaccuracy in time of about 7.2 microseconds per day (1 microsecond = 10-6 seconds). The theory of relativity also says that time goes slower the stronger the gravitational field. For an observer on the earth's surface, the satellite's clock will run faster (because the satellite is 20,000 km higher and is subject to less gravitational forces than the observer). And this is the second reason for this effect, which is six times stronger than the inaccuracy that was mentioned a little earlier.

In general, it seems that the clocks on the satellites are running a little faster. The time deviation for an observer on Earth would be 38 milliseconds per day and would cause a total error of 10 km per day. To avoid this error, there is no need to constantly make adjustments. The clock frequency on the satellites has been set to 10.229999995453 Mhz instead of 10.23 Mhz, but the data is used as if it had a standard frequency of 10.23 MHz. This trick solved the problem of the relativistic effect once and for all.

But there is another relativistic effect that is not taken into account when determining the position using the GPS system. This is the so-called Sagnak effect and it is caused by the fact that the observer on the surface of the Earth is also constantly moving at a speed of 500 m/s (speed at the equator) due to the fact that the planet is rotating. But the influence of this effect is small and its correction is difficult to calculate, because depends on the direction of travel. Therefore, this effect is taken into account only in special cases.

GPS system errors are shown in the following table. Particular values ​​are not constant values, but are subject to differences. All numbers are approximate values.

In general, this causes an error of ± 15 meters. When the SA special error was active, the error range reached ± 100 meters. Adjustments to systems such as WAAS and EGNOS, which mainly reduce the influence of the ionospheric effect, as well as the influence of satellite orbit and satellite clock errors, which will reduce the error to ± 3 - 5 meters.

global navigation systemconsists of a network of 24 satellites in approximately 12-hour orbits, each of which has an atomic clock on board. The orbital radius of the satellites is approximately equal to four Earth radii (26,600 km). The orbits are nearly circular, with a typical eccentricity less than 1%. The inclination of the orbit to the Earth's equator is usually 55 degrees. The satellites have orbital velocities of about 3.9 km/s in a coordinate system originating at the center of the Earth and not rotating relative to distant stars. Estimated satellite orbits lie in six equally spaced planes. There are four satellites in each plane, and the angular distance between the satellites in each plane is approximately 90 degrees. The orbital periods of the satellites are approximately 11 hours and 58 minutes, so that the projection of the satellite's trajectory onto the Earth's surface is repeated day after day, because the Earth makes one revolution relative to the stars every 23 hours and 56 minutes. (Four extra minutes are required for a point on Earth to return to a position directly below the Sun because the Sun moves about one degree per day relative to the stars.)

The onboard atomic clock is accurate to approximately 1 nanosecond (ns) in time, and approximately 1 ns/day in rate. Since the speed of light is approximately one foot (1 foot = 30.48 cm) per nanosecond, the system is able to locate objects on Earth or in the near-Earth environment with amazing accuracy. For example, if the satellite clock is fully synchronized with the terrestrial atomic clock and we know the time that the signal is sent from the satellite, then the time delay required for that signal to reach the terrestrial receiver immediately indicates the distance (with a potential accuracy of approximately one foot) between the ground receiver and the satellite. By using four satellites to triangulate and determine time corrections, an unknown receiver position can be determined with comparatively high accuracy.

2. What relativistic effects can be seen with the help of satellite system atomic clocks GPS?

General relativity (GR) predicts that clocks in a stronger gravitational field run at a slower pace. Special Relativity (STR) predicts that moving clocks seem to run slower than stationary clocks. Remarkably, these two effects cancel each other out for clocks located at sea level somewhere on Earth. So, if we use a hypothetical clock at the north or south pole of the Earth as a reference, then the clock at the earth's equator runs slower due to the relative speed due to the rotation of the Earth, but faster due to the greater distance from the center of mass of the Earth due to the oblateness of the Earth. Because the speed of the Earth's rotation determines its shape, these two effects are not independent, which is why they do not fully cancel each other out. However, in the general case, compensation does not occur. Clocks at any altitude above sea level run faster than clocks at sea level; and the clock on a moving rocket runs slower than a stationary clock.

General Relativity predicts for GPS satellites that atomic clocks at the orbital heights of GPS satellites run faster by about 45900 ns/day because they are in a weaker gravitational field than atomic clocks on the earth's surface. Special Relativity (STR) predicts that atomic clocks moving at the orbital speed of GPS satellites are slower by about 7200 ns/day than stationary clocks on the ground. In order not to have clocks with such large rate differences, the satellite clock is adjusted to such a rate before launch to compensate for these predicted effects. In practice, this is achieved simply by changing the international definition of the number of periods in atomic transitions that make up a one-second interval. Therefore, we first observe the rate of the clock with the entered rate offset before starting. We then observe the rate of the clock after it is launched into orbit and compare its rate with the predictions of the theory of relativity, as a combined effect of general relativity and relativity. If the predictions are correct, then we should see that the clock again runs at almost the same rate as the clock on earth, despite using the modified definition for the duration of one second.

We note that this comparison of the clock rate after the start is independent of the frame of reference in question or the observer in question. Since the projection of the trajectory onto the earth's surface is repeated day after day, the distance from the satellite to the earth's surface remains essentially the same. But any difference in rate between satellite clocks and clocks on the ground continues to increase the difference between their readings with each passing day. Therefore, no misunderstanding can arise due to the placement of satellite clocks at some distance from ground clocks when we compare their time readings. One need only wait long enough and the difference in time readings due to the clock rate discrepancy will eventually exceed any conceivable error or ambiguity in such comparisons.

3. Does it confirm GPS changes the rate of the clock, predicted by general relativity and relativity?

Information from the most accurate GPS receivers is collected continuously at two frequencies with a one and a half second interval from all GPS satellites at five US Air Force tracking stations distributed around the Earth. A deep discussion of these data and their analysis is not possible in this article. These data show that the rate of the onboard atomic clocks does indeed match the rate of the ground clocks to a predicted degree that is slightly off par, because the orbit actually achieved does not always exactly match the planned one. The accuracy of this comparison is mainly limited by the fact that atomic clocks change their frequency on a small, semi-random scale (on the order of 1 ns/day) at unpredictable times, for reasons that are not fully understood. As a consequence, the long-term accuracy of these clocks is worse than their short-term accuracy.

Therefore, we can state with confidence that the predictions of the theory of relativity are confirmed with high accuracy over time periods equal to many days. In the terrestrial solution to the data problem, usually once a day, new corrections are determined for the time intervals and for the rate of each clock. These corrections differ by a few nanoseconds for time intervals and by a few nanoseconds per day for the clock rate from similar corrections for other days in the same week. Over longer periods of time, unpredictable clock errors increase with the square of time, so comparisons with predictions become more and more uncertain unless these empirical corrections are used. But within each day, clock corrections remain stable within about 1 nanosecond for time span and 1 nanosecond per day for tempo. the course of the clock.

Initial clock rate errors immediately after launch would give the best indication of the absolute accuracy of relativity predictions because they would be the least affected by accumulated random clock rate errors over time. Unfortunately, this has not yet been studied. But if the errors were significantly larger than the velocity dispersion among 24 satellites GPS , which does not exceed 200 ns/day under normal circumstances, it would be noticed even without studying. So we can state that the effect of changing the clock speed predicted by GR is confirmed to be no worse than ± 200 / 45900 or approximately 0.7%, and the effect predicted by SRT is confirmed to be within ± 200 / 7200 or approximately 3%. . This is a very underestimate. In a real study, most of this maximum variance of 200 ns/day is almost certainly attributable to differences between planned and achieved orbits, and relativity predictions will be confirmed with much better accuracy.

Also found are 12-hour variations (orbital period) in the speed of the clock due to small deviations in the orbital altitude and speed of the satellites, caused by the small eccentricity of their orbits. They are observed with the expected magnitude for each satellite's own orbit GPS . For example, if the orbit is eccentric equal to 0.01, the amplitude of this 12 hour change is 23 ns. Changes due to altitude change and speed change, although not separate from each other, are both clearly represented because the observed amplitude is equal to the sum of the two predicted amplitudes.

4. Is the speed of light constant?

Other studies using GPS information have set much more stringent limits than we will impose here. But our goal here is not to set the most stringent limit on possible changes in the speed of light, but rather to determine what the maximum possible change can be that can remain consistent with the data. The GPS system works by sending atomic clock signals from orbital heights to the earth. This takes about 0.08 seconds from our human perspective, but that's a very long time (though equivalent) of 80,000,000 ns in terms of atomic clocks. Because of this accuracy, the system has shown that the speed of radio signals (or "light speed") is the same from all satellites to all ground stations at all times and in all directions within ±12 meters per second (m/s). The same numerical value for the speed of light works equally well for any season of the year.

Technical Note: Measuring the one-way speed of light requires two hours, one at each end of the path. If the distance between the clocks is known, then by dividing the distance by the time interval between the transmission and reception of the signal, we get the one-way speed of the signal. But the measurement of the time interval requires preliminary clock synchronization. If the Einsteinian method of clock synchronization is used, then the measured speed must be the speed of light according to the Einsteinian definition of synchronization (which assumes that the speed of light is the same in all inertial frames of reference). If some other non-equivalent timing method is used, then the measured signal speed will not the speed of light. It is clear that the measured signal speed and the synchronization method are intimately related.

Our result here simply indicates that the measured velocity does not change as a function of the time of day or the direction of the satellite in orbit when the time clock corrections are held constant for one day. As far as seasonal variations are concerned, all satellite clocks are adjusted to keep close to the US Naval Observatory's primary clock to prevent excessive error accumulation from random rate changes over long time periods. So we can't make direct comparisons between different seasons, but just note that the same value for the speed of light works equally well in any season.

5. What is a "GPS watch"?

The atomic cesium clock works by counting the number of cycles of the cesium atom transition rate, which is about 10 billion times per second, at a very steady rate provided by nature. The exact number of such periods was originally calibrated by astronomers, and is now accepted by international convention as the definition of one atomic second.

GPS atomic clocks in orbit run at a pace that is significantly different from that of clocks on Earth, if they are allowed to, and this complicates the use of the system. So the period counter of the cesium transition frequency (or the corresponding phenomenon in the case of using a rubidium atomic clock) is adjusted on Earth before launch so that, after being placed into orbit, the clock ticks whole seconds at the same average rate as clocks on Earth. Therefore, it seems that the GPS clock before being launched on Earth is running slower than the clock on the ground, but after being launched into orbit at the appropriate altitude, it runs at the same speed as the clock on Earth.

We will refer to watches that have been pre-set in this way as "GPS watches". This will help us when discussing the effects of SRT like the twin paradox. Watch GPS pre-adjusted to account for relativistic speed changes so that they continue to run at the same rate as ground clocks even when moving at high relative speeds. So the clock GPS, which available to the traveler twin, can be used to determine the local time in the Earth's reference frame at any point in the flight - this is a great advantage for resolving paradoxes.

6. Is acceleration essential for solving the "twin paradox"?

If the roaming twin has on board its spaceship a conventional clock and clock GPS , then he can observe the effects predicted by SRT without needing any acceleration in the usual twin paradox. This is because cyclotron experiments have shown that even an acceleration of 10 19 g (g = acceleration of free fall on the surface of the earth) does not affect the speed of the clock. Essentially, only the speed affects the speed of the clock, not the acceleration.

Suppose a traveling twin is born at the time when its spacecraft passes the Earth and its two onboard clocks synchronize with the clocks on Earth. Regular onboard clocks are slower than onboard clocks. GPS , because their rate differs by a factor of gamma, which is predicted by SRT to slow down all clocks moving at a relative speed v [gamma = 1/sqrt(1-v 2/c2 ]). But wherever the moving twin hits, as long as its velocity relative to the Earth's frame of reference does not change, the readings of its GPS clock will be the same as those of any clock synchronized with the Earth clock and at rest in the Earth's frame of reference, which it flies by on its way. And his ordinary clock will have indications for the time since the passage of the Earth, smaller by a factor of gamma. Its biological processes (including aging), which occur at a rate corresponding to the rate of normal clocks, are also slowed down by a factor of gamma.

Since this rate difference exists at every moment of the flight, from the very first moment, it is not surprising if the traveling twin completes the entire round trip without changing speed and returns to Earth. After completing the flight, he will check what he observed at each stage of the flight: the pace of his normal clock was slower and his biological age was younger in gamma times than those for its counterparts from the Earth reference system at each point of its flight, including the moment of its completion. The same would be true if he did not return to Earth, but simply continued to fly forward. He would be younger than him peers on any planet he encounters who claim to have been born at the same time that our traveler was born (that is, when he flew past the Earth) according to their point of view from the Earth's frame of reference.

It is clear that acceleration or its absence has nothing to do with the observed results. If there is an acceleration, then it simply allows for a more convenient comparison of the clock readings after returning to the starting point. But since the traveler can never return to the same point in space-time simply by returning to the same point in space, the comparison results after a round-trip flight are no different from those made somewhere along the flight path..The traveler always assumes that his own aging is slower than in any other frame of reference with relative motion.

Then why does the traveler have no right to say that he remained at rest and the Earth moved? The traveler is certainly moving relative to the Earth's frame of reference and therefore his clock is certainly running slower and he is aging more slowly in the estimation of any person from the Earth's frame of reference. However, if a traveler makes the same assessment, the result will depend on which watch he considers the best timekeeper - whether his regular watch or his GPS watch. If he takes the readings of the GPS clock as representing earth time, his conclusions will always agree with those of observers from the earth's frame of reference. If he instead uses the results of the exchange of light signals to infer the passage of time in distant places, he will come to the conclusion that the twin-the stay-at-home ages less than he does due to their relative movement. But in the event that any acceleration is applied to his spaceship, the traveler will come to the conclusion about the jump at the age of a stay-at-home twin who can be either forward or backward in time, depending on which direction the traveler is accelerating. At the end of any round trip after any number of such accelerations, the traveler twin and the stay-at-home twin will always agree on whose age should be greater..

7. Does the behavior of the GPS clock confirm Einstein's SRT?

To answer this, we must make a distinction between Einstein's SRT and Lorentz's theory of relativity (LRT). And Lorentz in 1904,and Einstein in 1905 took as their basis the principle of relativity, discussed by Poincaré in 1899, which clearly originated some years earlier in the 19th century. Lorentz also popularized the famous transformations that bear his name, later used by Einstein. However, Lorentz's theory of relativity assumed the existence of an ether (a privileged frame of reference) and universal time. Einstein abandoned the need for them. But it is important to understand that none of the 11 independent experiments confirmed the validity of SRT experimentally more than LRT - according to At least not in favor of Einstein.

Table 1. Independent experiments on special relativity

Experiment	Description	Year
Bradley	Discovery of the aberration of light
Fresnel	Light is dragged along by the local environment
Airy	Aberration does not depend on the local environment
Michelson-Morley	The speed of light does not depend on the orbital motion of the Earth
De Sitter	The speed of light does not depend on the speed of the source
Sagnac	The speed of light depends on the angular velocity of rotation
Kennedy-Thorndike	Movement affects the measured time
Ives-Stilwell	Ions radiate at frequencies that depend on their motion
Frisch-Smith	The radioactive decay of mesons slows down as they move
Havele Keating	The rate of atomic clocks depends on the rotation of the Earth
GPS system	Clocks in all reference systems are continuously synchronized

Some of the experiments on various aspects of SRT (see Table 1) have produced results consistent with both SRT and LTO. But the Sagnac experiment in 1913, Michelson's experiment following Michelson-Gale's confirmation of the Sagnac effect for the rotating Earth in 1925 (not an independent experiment, and therefore not listed in Table 1), and Ives' experiment in 1941, they all declared at the time when they published their results, that their experiments contradicted Einstein's special relativity because they implied a privileged frame of reference. In hindsight, this can be explained by the fact that most experiments contain some aspect that makes them easier to interpret in a privileged frame compatible with LTO. In current discussions of LTO, the preferred frame of reference is not universal, but rather coincides with the local gravitational field. Still, it cannot be said that none of these experiments can be explained from the point of view of SRT.

For example, Fresnel showed that light is partially dragged along by the local medium, suggesting some dependence on the frame of reference. Airy found that the aberration did not change for a telescope filled with water, and therefore it did not occur in the telescope tube. This fact suggests that it must originate somewhere else. In the Michelson-Morley experiment, the speed of the earth was expected to have an effect on the speed of light because it had an effect on the aberration. But that did not happen. If these experimenters had realized that the ether was not a single entity, but changed by the local gravitational field, they would not have been surprised. Their understanding could be helped by the realization that the Moon, in the Earth's gravitational field, does not experience aberration in the way that distant stars do, but only to a much lesser extent, only due to its low speed in the Earth's gravitational field.

Another clue came in 1913 from De Sitter collaborating with Phipps, both of whom reminded us that the components of binary stars with high relative velocities nevertheless have the same stellar aberration. This meant that the relative speed between the light source and the observer did not affect stellar aberration. On the contrary, the relative velocity between the local and remote gravitational fields determined the aberration. In the same year Sagnac showed non-zero results for the Michelson-Morley experiment performed on a rotating platform. In its simplest interpretation, this demonstrated that speeds relative to the local gravity field are added to or subtracted from the speed of light in the experiment as the fringes move. The Michelson-Gale experiment in 1925 confirmed that Sagnac's result is also valid for the case when the entire earth's surface is a rotating platform.

When Ives and Stilwell showed in 1941 that the frequencies emitted by ions depended on their motion, Ives thought he had settled the matter once and for all and that only relative velocity mattered. After all, ions emitted at a specific frequency, no matter what frame of reference they were observed from. He was not dissuaded by the arguments to show that SRT could also explain this phenomenon, because it seemed clear that nature still needed a privileged reference system, the movement relative to which determines the ion frequencies. Otherwise, how would the ions know at what frequency to radiate? There are answers to Ives' dilemma, but they are not simple enough.

Richard Keating was surprised in 1972 that two atomic clocks traveling in opposite directions around the Earth, when compared with a third clock that remained in place, showed a deceleration that depended rather on their absolute velocity through space—the vector sum of the Earth's rotation rate and the velocity aircraft than on the relative clock speeds. But he quickly realized that astronomers always use the earth frame for local phenomena, and the solar center frame for phenomena on other planetary systems, and got the results,which were consistent with the predictions of the theory of relativity. Unfamiliar with LTO, he did not question the interpretation at any deeper level.

Table 2. Independent experiments on special relativity

Experiment	Type of	Interaction note
Bradley	Aberration	moon exception
Fresnel	Fresnel's fascination	The existence of the ether
Airy	The existence of the ether	Water in the telescope is ignored
Michelson-Morley	No universal ether	"Carried away" ether?
De Sitter	The speed of light does not depend on the source	Aberration from double stars
Sagnac	The speed of light depends on rotation	Local gravity field, not rotating
Kennedy-Thorndike	The clock is slowing down	Motion relative to the local gravitational field
Ives-Stilwell	Ions slow down	Same
Frisch-Smith	Mesons live longer	Same
Havele Keating	The clock depends on the rotation	The preferred frame of reference is shown
GPS system	Universal Synchronization	Privileged System = Local Gravity

Table 2 summarizes what various experiments have to say about the preferred frame of reference. These experiments confirm the principle of relativity originally formulated in terms of the existence of the ether with high accuracy. However, the question of the need for a privileged frame of reference in nature, in truth, has not yet been settled. Of course, the experts have not yet agreed on its resolution. But those who have compared LRT and SRT with experiments seem to be most convinced that LRT more easily explains the behavior of nature.

8. How is the "twin paradox" resolved in LTO and SRT?

In LTO, the answer is simple: first the terrestrial frame of reference, and then the dominant local gravitational field in general, constitutes the preferred frame of reference. So the fast moving traveler always returns younger, and there is no true equality of points of view for him and for other frames of reference.

In SRT, the answer is not so simple; but still there is an explanation. The equality of frames of reference required by SRT, when Einstein assumed that all inertial frames of reference are equivalent, introduces a second factor of influence on "time" in nature, which is not reflected only in the speed of the clock. We could call this factor "jump time" and we can discuss it now. A time jump is the difference in time for any distant event from the point of view of observers (even instantly coincident ones) in different inertial frames of reference.

For example, we can state that if here and now we have the date 9/1998, then "now" on Alpha Centauri is the same date - 9/1998. But an observer who is here and now, but moving at a sufficiently high relative speed (say, equal to 99% of the speed of light; gamma = 7) can consider that “now” on Alpha Centauri is another date - 9/1994 (implying that he only one month ago, according to Earth time, he took off from there, and then there was the date 8/1994). Or he could think that “now” on Alpha Centauri is another date - 9/2002 (implying that he will fly there in one month of Earth time, and find that there will be a date of 10/2002). These differences of opinion as to what time it is at distant points are illustrations of the effects of "jumps" in time, which appear to occur only in Einstein's SRT to keep their predictions independent of frames of reference.

So, if a traveler flies past the Earth at time 8/1994 at a speed of 0.99 * C, the effect of the “jump” in time begins to grow. Seven months later, according to his usual clock, the traveler reaches Alpha Certauri. His own GPS clock shows four years of elapsed time, and indeed the inhabitants of Alpha Centauri, who think they are time-synchronized with Earth, agree that the twin's arrival date is 9/1998. But the traveler twin is convinced by Einstein's Special Relativity that only one month of Earth time has passed since he passed Earth and marked the time as 8/1994. Traveler Twin after reaching Alpha Centauri claims to be "now" on Earth 9/1994. The inhabitants of Alpha Centauri claim that "now" on Earth is 9/1998. The difference is the “jump” of time predicted by SRT.

If a traveling twin flies around Alpha Centauri at a speed of 0.99 * C, then when he heads towards Earth, his opinion changes and he believes that "now" on Earth is the date 9/2002. And when he again heads from the Earth, for him on Earth again the same date - 9/1994. Earth time "now" according to SRT changes continuously due to these effects of time jumps necessary to maintain the mutuality of frames of reference. The inhabitants of Earth - even those who died in 1998 - do not notice their repeated passages into the future and past of the moving twin, with their attendant deaths and resurrections.

So, when the traveling twin finally returns to Earth, he will indeed find that the date of his return to Earth is 10/2002, exactly according to his GPS watch. He believes that this happened because two months of slow-moving Earth time passed during his own 14-month (according to his usual clock) flight, plus 8 years of "time jump" when the traveler changed frames of reference. There is no logical or mathematical inconsistency in such a resolution, which is why SRT remains a viable theory today.

We may, of course, question whether this mathematical theory preserves the validity of the principle of causality or not. For those of us who answer yes, LTO is unnecessary, and crude, because it depends on a privileged frame of reference. For those of us who answer no, LTO is the best description of nature, requiring the sacrifice of symmetry (“covariance”) in order to preserve causation.

9. What physical consequences arise from the differences between LTO and SRT?

In SRT, speed causes changes in time and space themselves, not just in clocks and rulers. The rest mass remains the same, but the resistance to increasing acceleration increases indefinitely as the speed approaches the speed of light. There is no absolute time or space in the universe. The time at distant points depends on which frame of reference the observer is in. All frames of reference are equivalent.

In LTO, speed relative to the preferred frame of reference (the local gravitational field) causes the clock to slow down and the rulers to shorten. The forces of an electromagnetic nature become less and less effective as the speed of movement relative to the preferred frame of reference increases, and approaches zero as the speed approaches the speed of light. There are natural, physical reasons why this should be so. The frame of reference of the local gravitational field acts as a privileged frame of reference. Universal time and simultaneity of distant events exist.

The single most important difference is that, in SRT, nothing can travel faster than the speed of light in the forward time direction. In LTO, forces of an electromagnetic nature and clocks would stop working at speeds equal to or faster than the speed of light. But there is no problem in principle to achieve any speed in the forward direction of time, using forces such as gravitational forces, which remain effective at high speeds.

Three main relativistic phenomena, their mechanisms and relationships

Earlier we found out that truly elementary particles do not consist of any separate parts, but can be described as closed curvilinear displacement currents in vacuum (ether). Since curvilinear current (and current, like speed, is a vector quantity because it has a direction) is a current accelerated, then the curvilinear current is the current variable(in the same way as the movement along a curvilinear trajectory uniform in modulus of speed is accelerated). Any alternating current (including bias current) causes induction phenomena. In other words, around the variable (and, accordingly, around curvilinear) current arises electric field of induction E. This is the so-called "electrostatic" field around charged particles. And the "charge" of the particle q is just a man-made way to numerically evaluate some parameters of this field. In fact, the charge is reduced to divE. This is the mechanism of origin of elementary charges. Why, under certain conditions, curvilinear closed displacement currents in the ether can stably exist, we described earlier: this is the result of the simultaneous action of "magnetic" and "inductive" forces between microscopic sections of such currents. It follows from this description that the particle is "inside" a vortex of polarized ether rotating at the speed of light. Outside, it looks like a centrally symmetrical constant electric field. It is an inherent result of the internal arrangement of particles. Thus, the particle consists of conditionally internal areas of curvilinear currents and outdoor areas of the electric field of induction generated by these currents. In this picture, the field outside the particle is generated not by a mysterious inexplicable "charge", but simply by displacement currents, the same ones that make up light and electromagnetic waves in general. Now it is easy to understand how a charged particle can be born from "electrically neutral" electromagnetic waves (the circular motion of the particle's current can be decomposed into two harmonic projections, sine and cosine, i.e. into two "photons"). At the same time, the field of the particle is not some kind of "application" to the particle, but it is its inevitable and integral part. And since the field of a particle does not end anywhere in the Universe, then, consequently, any particle occupies the entire Universe.

Now, since we have described the particle as a system of closed curvilinear currents, and it has the characteristic size of this current region, let's ask ourselves what happens if the particle starts moving relative to the local ether? Due to the fact that the speed of light is the limiting speed of movement of perturbations in the ether, and the polarized ether “inside” the particle moves at the speed of light (this is a necessary condition for the stability of the particle), then in order to remain a closed current when the particle moves as a whole, internal currents are forced change your shape. Well, in fact, imagine a circular motion of a point at the speed of light along a certain circle. Now move this circle itself forward with some speed. In this case, the point must be spinning at the speed of light, and even move forward at some speed. But then its total speed at some moments should exceed the speed of light, and this is impossible! What is the way out of such a point? Of course, move no longer in a circle, but along some other curve. Only then can it spin and move forward at the same time. The same thing happens with the currents inside the particle - their trajectories change, "flatten" across the motion. This is the only way to maintain the balance of forces inside the particle. But if the currents change their curvature, and the curvature of the currents is the reason for the appearance of the electric field of the particle, then, consequently, the electric field of the particle must inevitably change. So this is a well-known fact, called "relativistic distortion of the field"! So we discovered the key "relativistic effect" - the distortion of the particle shape (called "relativistic length contraction") and the inevitable distortion of the electric field outside the particle (called "relativistic field distortion") associated with it. This means that Lorentz was right in seeing the "Lorentz contraction of lengths" at the basis of relativistic phenomena, although he had no idea about the structure of elementary particles. But since the elementary particle itself has "flattened", since its field has "flattened" as well, it means that all systems of particles will "flatten" as well, since they are supported by electric forces. Flatten atoms, molecules and macroscopic objects themselves. So, in a sense, we can say that in the direction of movement "all lengths will be reduced." This would be seen by a motionless observer, if he possessed magical "instantaneous vision." But the material observer, moving along with the objects of study, "shrank" itself. All his length standards have shrunk and, therefore, he will not notice anything. For him, a stick a meter long will remain a meter long, since length is just a number showing how many times a certain material standard of length fits in a stick. And it shrunk exactly the same as the stick itself. Here is the well-known formula for the Lorentz contraction of length:

Wonderful! So, the key relativistic phenomenon, to all appearances, is precisely the "length contraction" effect. And the reason for it is the finiteness of the speed of propagation of electromagnetic disturbances in the world's dielectric medium. That is why Einstein's abstract postulate about the constancy of the speed of light in any frame of reference, in itself inexplicable, led to the creation of a completely working (that is, giving coincidence with experience) theory of SRT. And the point is not in speculative "reference systems", but in real physical mechanisms of phenomena inside the smallest "bricks" of matter - elementary particles. If so, then "relativistic mass growth" and "relativistic time dilation" should follow directly from the contraction of lengths. So what's stopping us from checking it out?

We have revealed the physical mechanism of the phenomenon of inertia, gravitation and, accordingly, the physical essence of mass. Inertia is the result of self-induction of elementary charges during their acceleration in the world environment. The result of the electrodynamic interaction of a particle and a medium during their mutual acceleration. Gravity is the same phenomenon of inertia, but it is no longer caused by the motion of the test body relative to the medium, but by the accelerated motion of the medium itself, caused by the source of gravity. Let's take the formula of electrodynamic mass:

Now let us substitute instead of the radius of the particle r 0 (the "length" of the particle) its Lorentz-reduced radius and get:

We see that the "relativistic mass growth" completely conditioned"relativistic length contraction". An attentive reader will say: but this is only a transverse mass, but what about the longitudinal one? And there is no "longitudinal" mass! The thing is that when a particle is accelerated in a linear accelerator, not one phenomenon (an increase in mass) occurs, but two as many as an increase in mass and a "relativistic distortion of the field." The accelerating field of the accelerator weakens from the point of view of the particle. And vice versa, the field of the particle itself (and, hence, its "charge") weakens from the point of view of the accelerator. Moreover, it weakens by a factor of gamma square. How does an accelerator accelerate a particle? That's right, the field. And why does he "hook" her? For the "charge", i.e. for her own field. Whichever of them weakens by a gamma-square time, the result will be the same - it will fall by a gamma-square time the strength of their interaction. As a result, the inertia of the particle (mass) increases by a factor of gamma, and the force of interaction between the particle and the accelerator weakens by a factor of gamma square. How many times will it decrease acceleration such a particle in such a (linear) accelerator? (a=F/m). That's right, the gamma cube times. This is what is observed in the experiment. To the credit of modern scientists, it should be noted that they themselves suspected what we have just found out and have long ceased to use the terms "longitudinal" and "transverse" mass. Well, thank God!

It remains to deal with the "time". Oh, this accursed time, the eternal riddle that torments mankind! So many works, so many theories, so many disputes and conversations around this concept... And meanwhile, this is just a human idea. It is not some kind of physical object, not some kind of material substance, it cannot be put on the table and subjected to an experiment. It's i-de-i! It is in people's heads and nowhere else. It's just a habit of comparing one process with another, more regular one, which we call "hours". Let's think for a moment, does the concept of "time" have any meaning for a stable true elementary particle, for example, an electron? Yes, none! And why? Yes, because he lives forever, unlike us. Even the entire life of the Universe (according to the theory of the Big Bang) for him is an insignificant moment, an indescribably short episode in his eternal existence. Why is that? Why is he eternal? Yes, because nothing changes inside him! Whatever we do with an electron, nothing happens inside it that can be seen from its own system. And when nothing changes, when nothing happens, the concept of "time" completely loses its meaning. Time is for mortals only. As, however, and "space". For space is only the mutual arrangement of objects. And the mutual arrangement can be judged only when something happens, at least something changes. When we can move objects by matching them. And if we can't change anything (we can't even send a ray of light), then "space" loses its meaning. Whatever we do with an electron, neither the processes nor the mutual arrangement of "objects" will change inside it from its own point of view. For him, there is only the eternal and omnipresent "here and now." However, for us, time makes sense and we want to understand how it "slows down" in moving systems? The key word here is "system". Why? Because although the elementary particles themselves are eternal, the systems composed of them no longer exist. For example, an atom. The simplest hydrogen is a proton and an electron. An electron can be in different "orbits", in different states. And not forever, because the absorption or emission of electromagnetic radiation changes its state. And such a change is noticeable not only to us, mortal observers from outside the atom, it is also noticeable "from within" the atom. Those. the atom or atom-like structure (as all complex and unstable "particles" are) is already related to time. Good. Let's deal with the atom, read out, deal with "time" at the lowest level of matter, at which this concept still makes sense. What is "atomic time"? Or how often do they say "atomic clock"? These are precisely the time intervals that we register between different states of the atom, for example, the ground state and the excited state. And how is it defined? A very long time ago, even on the Bohr model of the atom, it was established that all atomic times are related to the so-called "Rydberg constant".

We see that if the electron mass m increases by a factor of gamma (for example, when an atom moves), then the Rydberg constant for such an atom will also increase. And the Rydberg constant is the reciprocal of the wavelength emitted by an atom during energy transitions from the nth level to the mth:

At the same time, the period of the emitted wave is related to the wavelength as:

And finally, expressing the period T in terms of the Rydberg constant, we have:

And since "time" can be expressed (and this is how it is done in modern practice) through the number of periods T of atomic radiation (cesium standards, etc.), we see that when an atom moves, any time interval is reduced due to the relativistic increase in mass, constituting N periods of such radiation, because the period T itself is reduced. It turns out that the time interval measured by a moving atom (modern atomic "clock") will be less than measured by a stationary clock. If some clocks show chronically less time than others, which one is running slower? Of course, those that show less time. Those. this clock is running slowly. This is what is called "relativistic time dilation". Although the concept (and time is just a human concept) cannot "slow down". It remains to be concluded that it is not the concept of "time" that slows down in moving atom-like systems, but the rate of internal processes, a kind of "atomic clock wheels" that simply move more slowly.

Now look, the lengths L have decreased by a factor of gamma, but the clock T has also slowed down by a factor of gamma. If we try to measure the speed of light with = L / T, then it is for us Will not change! That is why the abstract postulate of the invariance of the speed of light in any frame of reference has been so boringly confirmed by experiments for more than 100 years. Because it corresponds to reality, although it does not explain anything. Especially in the "empty" universe of SRT. But in our dielectric Universe, which consists of the world environment, everything is natural and understandable: in any environment there is some specific speed of propagation of electromagnetic disturbances, and for the ether it is equal to the speed of light c. And since everything is ether, including and elementary particles themselves, and electromagnetic waves, and "fields", then all the matter of this world is subject to the same condition - the constancy of the speed of propagation of perturbations. As a result, all "relativistic phenomena" are based on this speed and can be expressed through it. But we are doing this not by means of genius, but speculative guesses, and consistently revealing mechanisms of physical phenomena.

So, let's talk about the chain of basic relativistic phenomena in their interconnection:

Due to the constancy of the speed of propagation of perturbations in the ether and the structure of the particles, they are forced to change their shape when moving (shrink in the direction of movement), this causes a distortion of their electric field and, as a result, a corresponding reduction in the size of any material objects, this automatically leads to an increase in inertia (mass) of both the particles themselves and all material objects, which in turn leads to a slowdown in the rate of internal processes in all composite systems, starting with atoms and atom-like composite particles. The result is the impossibility (from within the moving system) of detecting either a change in size or a change in tempo. Therefore, any measurements of the speed of light inside closed systems will always give the same number, equal to the speed of light in free ether. This most clearly suggests that in the Universe there is nothing but a diversely moving perturbed ether. We, people, single out only a narrow circle of perturbations and their movements, which today we are able to somehow determine and call them waves, fields, particles, atoms, etc.