synonymEinstein's Theory of Relativity(Einstein's Theory of Relativity) Generally refers to the theory of relativity (Einstein's basic theory on space-time and gravity)
Theory of relativity (English: Theory of relativity) is a theory about space-time and gravity, which was mainly founded by Einstein.At the beginning of the 20th century, the theory of relativity and quantum mechanics brought revolutionary changes to physics, which together laid the foundation of modern physics.The new space-time concepts such as "simultaneous relativity", "four-dimensional space-time" and "curved space-time" established by the theory of relativity are a leap in human understanding of physical phenomena.The theory limited to inertial reference frame is called special relativity, and the theory extended to general reference frame and including gravitational field is called general relativity[1]。Now relativity has become one of the main theoretical foundations of physics.
The difference between special and general relativity
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Special relativity and general relativity describe different objects.Traditionally, in the early days when Einstein put forward the theory of relativity, people took whether the question under discussion involved a non inertial reference system as a sign of the classification of special and general relativity.With the development of the theory of relativity, this classification method increasingly shows its shortcomings - the reference frame is related to the observer, and it is considered that such a relative physical object cannot reflect the essence of the problem to divide the physical theory.It is generally believed that the difference between the special theory and the general theory of relativity lies in whether the problem discussed involves gravity (curved space-time), that is, the special theory of relativity only involves those problems that have no gravity or can be ignored by gravity, while the general theory of relativity discusses physics when there is gravity.In the language of relativity, the background spacetime of special relativity is flat, that is, four-dimensional ordinary manifold with Min metric, its curvature tensor is zero, also known as Min spacetime;The background spacetime of general relativity is curved, and its curvature tensor is not zero.[2]
The origin of special relativity is different from that of general relativity.If the emergence of the special theory of relativity at the beginning of the twentieth century was due to the inherent contradictions of classical physics, a large number of new experiments and extensive attention, then the proposal of the general theory of relativity is a practice of "theory ahead of experiment" in a sense, largely due to the needs of the development of the theory of relativity itself,It is not from some experimental phenomena that need to be explained urgently, which is rare in the history of physics[1]。In this sense, general relativity is also called the peak of pure rational thinking.[3]
Special relativity
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brief introduction
Main item: Special relativity.Special relativity is limited to discussing physical phenomena in inertial frames.Einstein's 1905 paper "On Electrodynamics of Moving Bodies"[4]Its special theory of relativity is introduced in.
The main contents of special relativity are[1]：
(1) The Lorentz transformation of space-time coordinates between inertial reference frames and its physical significance focus on the space-time view of relativity.
(2) Physical laws can be expressed in the same form in any inertial system, that is, the covariance of physical laws.The covariant requirement is one of the main theoretical guidance for exploring the interaction laws between various fields and particles.
(3) The basic laws of electrodynamics, namely Maxwell equations and Lorentz force formula, are expressed in covariant form, so that electrodynamics becomes an obvious relativistic theory, which can be used to solve the interaction problem of charged particles with arbitrary speed and electromagnetic field.
(4) The basic law of mechanics is generalized to the relativistic mechanics of covariance, from which the relationship between mass, energy and momentum of relativity is obtained.These relationships are the main theoretical basis for the application of atomic energy, and are the main tools to solve the kinematic problems in the movement and transformation process of high-energy particles.
Basic postulates of special relativity
(1) Special relativity principle (special covariance principle): all inertial reference systems are equivalent, that is, the form of physical laws is the same in any inertial reference system.That is to say, no matter through the observation of mechanical phenomena, electromagnetic phenomena or other phenomena, as long as the observer is in the inertial system, the laws seen are the same, and it is impossible to detect any "absolute motion" of the reference system.The principle of relativity has been accurately tested by a large number of experimental facts and is a basic principle of physics.[1]
(2) Principle of constant speed of light: the speed of light in vacuum is constant c in any direction in any inertial frame, and is independent of the movement of the light source.[1]It is precisely because of the experimental nature of light that "the distance traveled by light in 1/299792458 seconds in vacuum" is used in the International System of Units to define the length unit "meter".The principle of light speed invariance is the embodiment of the space-time symmetry of the universe.
The origin of special relativity
Physical laws need to be expressed in a certain reference system.Before the special theory of relativity was put forward, people believed that time and space were independent and absolute.This concept of absolute space-time has been established since Galileo's time. Newton's classical mechanics and laws of motion were founded on the basis of the absolute space-time concept.At low speed, this view is in good agreement with the experimental observation, but at high speed, the contradiction between the absolute space-time view and the objective reality will appear.
In the middle and late 19th century, people summed up the basic law of electromagnetic field from long-term practice, namely Maxwell's equations, and thus concluded that the speed of electromagnetic wave propagation in vacuum is c.Based on the concept of absolute space-time, electromagnetic waves can only propagate at a speed of c in a special reference system, so Maxwell's equations can only be valid for that special reference system.If so, then the relativity principle of all inertial reference frames in classical mechanics will no longer hold true in electromagnetic phenomena.Therefore, the motion relative to the special reference system is called absolute motion.Since all waves known by human beings at that time, such as water waves and sound waves, were propagation phenomena of mechanical vibration in a certain medium, people believed that electromagnetic waves also spread in a certain elastic medium full of space, which was called ether.People regard the reference system which is relatively static in the ether as this special reference system.Finding the ether and determining the movement of the earth relative to the ether became an important subject of physics at the end of the 19th century.At that time, scientific experiments had been able to accurately measure the speed of light, and the results of many experiments had not found any effect of absolute motion, which forced people to accept the fact that the speed of light in vacuum is equal to c relative to any inertial system.This contradicts the old Galilean concept of time and space[1]。At the same time, the ether became one of the "two dark clouds" above the physics building in 1900, which Lord Kelvin said.
In addition to electromagnetic phenomena, human practical activities at the end of the 19th century have begun to penetrate into the microscopic field of matter, and discovered electrons, X-ray diffraction and natural radioactivity. Many new phenomena and laws discovered by people have shaken many basic concepts of classical physics.In this period, physics is facing great changes, and it is against this background that the theory of relativity, which reflects the new concept of space and time, was put forward.Therefore, the theory of relativity is an inevitable product of the development of production level and science and technology to a certain stage[1]。
Before Einstein, people paid extensive attention to the problem that Maxwell's equations were not covariant under the Galileo transformation. Some people (such as Poincare and Lorenz) noticed that Einstein's special theory of relativity was based on experiments (such as the Michelson Morley interferometer experiment), and others deduced mathematical expressions similar to Einstein's (such as Lorenz transformation),But only Einstein combined these factors with the space-time view of classical physics and proposed the special relativity, which greatly changed our space-time view.In this regard, special relativity is revolutionary.[3]
Introduction to Theory
Special relativity abstracts the concept of event from the movement of matter.The event occurred at a certain place at a certain time.The movement of matter can be seen as the development process of a series of events.So four coordinates (x, y, z, t) are used to represent an event in the inertial system S.Use another set of coordinates (x ', y', z ', t') to represent an event in another inertial system S'.From this, we can define a physical quantity called interval, that is, the distance between two four-dimensional coordinates in a four-dimensional coordinate system.The interval between two events in two inertial systems is the same, which is called interval invariance. Interval is a basic concept of relativistic space-time view, which unifies the distance between time and space.
The space-time coordinate transformation of relativity is called Lorentz transformation.If the velocity of inertial system S' relative to inertial system S is v, and the direction of motion of S' relative to S system is x, the transformation of space-time coordinates of S system to S' system can be expressed as:
Thus, the velocity Lorentz transformation formula from S system to S' system is:
The concept of light cone was born from the space-time view of relativity, on which the causal relationship of events can be discussed.The event points whose interval between two events is equal to zero form a cone in the four-dimensional coordinate system, which is called the light cone.These intervals are called light like intervals.
3D light cone
If the two events can be linked by the interaction below the speed of light, the square of the interval is greater than 0, and these event points are located in the light cone in the four-dimensional coordinate system.These intervals are called quasi time intervals, and there is an absolute causal relationship between events in the light cone.For example, if you communicate through radio waves, it must be the sender who influences the receiver's actions.
If the space distance of two events exceeds the distance of light wave propagation in time t, the square of the interval is less than 0. These event points are located outside the light cone in the four-dimensional coordinate system, and are called quasi space intervals.Events outside the light cone cannot be connected in any way, and there is no causal relationship between them.Space like intervals can lead to simultaneous relativity, that is to say, clocks aligned at different locations in one reference system are inaccurate when observed in another reference system.
Special relativity also leads to the clock slow effect, that is, two events successively occur at the same place in a reference system S, and the two events are observed in another moving reference system S' that moves at a speed v relative to the reference system S.The interval between two events in the static reference system S is the time difference:
, called Gu Shi.In the motion reference system S', two events will be observed in different places, and a time difference will also be observed
。You can get:
, so
That is, the natural process on the moving object in the laboratory reference system is slower than the same process on the stationary object.The faster the object moves, the slower its internal processes are observed.
There is also the scaling effect. Let the rest length of the object be
, then the length of the object moving parallel to this direction at the speed v is
So the length of the moving object is shortened.Clock slowing effect and motion scaling effect are the basic attributes of space-time, and have nothing to do with the internal structure of objects and clocks.
Lorentz transformation can be regarded as rotation in four-dimensional coordinate system.This four-dimensional space includes the three-dimensional coordinate axes x, y, z, and the fourth imaginary coordinate: ict.So the four-dimensional space of relativity is a complex four-dimensional space.The four-dimensional form of Lorentz transformation is:
The special Lorentz transformation matrix along the x-axis is:
The four-dimensional speed is:
The component of four-dimensional velocity is
:, the transformation relationship of four-dimensional velocity is:
For electromagnetic waves, the four-dimensional wave vector is:
Lorentz transformation of vector is:
These physical quantities are also called four-dimensional covariates, and the calculation method meets Einstein's summation formula.The relativity principle can be easily expressed in four-dimensional form.If each term of an equation is a covariate of the same kind, under the transformation of the reference system, each term is transformed in the same way, and the result keeps the equation unchanged.For example, the form of an equation is:
, where
and
They are four-dimensional vectors. Under the transformation of reference system, there are:
The main law of electrodynamics is Maxwell's equations, which meet the principle of covariance required by relativity.Under the framework of relativity, the four-dimensional current density is defined as:
, four-dimensional potential vector:
, and electromagnetic field:
The covariant form of Maxwell's equations can be obtained as follows:
，
, where the tensor transformation relationship between reference systems is:
。Therefore, among the four interactions in nature, the electromagnetic interaction can be fully included in the scope of special relativity, and the non quantized relativistic mechanics can correctly describe the movement of charged particles under certain conditions.
Relativistic mechanics modifies Newton's mechanics under the classical space-time view. On this basis, a static object has a static mass
, corresponding to static energy
This relationship is called the mass energy relationship.The momentum and energy of an object form a four-dimensional vector:
。Energy of moving objects:
, momentum of moving objects, mass of moving objects
, mass of moving object
An important relation about the energy, momentum and mass of the object can be obtained:
。One of the most important corollaries of relativity is to reveal the existence of static energy.It points out that there is still movement inside the stationary particles, and particles with a certain mass have a certain amount of internal motion energy.Conversely, particles with certain internal motion energy will show a certain inertia mass.qualityThe energy relationship has been well confirmed by a large number of experiments in nuclear and particle physics, and is the main theoretical basis for human beings to use atomic energy.[1]
experimental verification
Michelson Morley measured the difference of light speed in different directions in 1887.He designed an interferometer, called Michelson Morley interferometer, to test the existence of the ether.The result is that Michelson's experiment negates the existence of the ether, indicating that the speed of light does not depend on the reference frame of the observer, nor on the movement of the light source relative to the observer.
For the observation of binary star movement, the binary star moves around its center of mass. If the speed of light depends on the speed of the light source, the light emitted by one star moving towards the earth in the binary star system will spread faster than the other star. Therefore, the orbit of the binary star movement observed on the earth will be distorted. In fact, this situation has not been observed, indicating that the speed of light emitted by the two stars is the same.This also proves that the speed of light does not depend on the movement of the light source[1]。
Modern experiments continue to verify the basic fact that the speed of light is constant.People use the π moving at high speedzeroMesons act as light sources.πzeroThe meson is an unstable particle produced by the collision between high-energy protons. It is 0.87 × 10-16The second will decay into two photons.In Alvager's experiment, πzeroThe meson moves at the speed of 0.9975c, and it is measured experimentally along πzeroThe photon velocity emitted in the direction of meson motion is (2.9977+-0.004) 10eightm/s,Consistent with the speed of light measured with a stationary light source[5]。In conclusion, so far, all experiments have pointed out that the speed of light does not depend on the reference frame of the observer, nor on the movement of the light source. It is a basic law of nature..
In addition, a large number of experiments have verified various effects derived from relativity.For example, the transverse Doppler effect experiment verifies the clock slow effect of relativistic motion[6]。In high-energy physics, the measurement of the lifetime of high-speed particles confirms the clock slow effect.For example, we can observe the average life of pions in the process of motion, and the average life of muons in high-speed motion.The experimental observation results are consistent with the calculated values of the clock slow effect formula[7-8]。The global flight experiment with an atomic clock confirmed the total effect of the clock slowdown under the combined action of special relativity and general relativity[9]。
General relativity
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brief introduction
In order to solve the experimental and theoretical difficulties of Newton's theory of gravity, in 1915, Einstein established his theory of gravity on the basis of the principle of equivalence and the principle of general relativity, and regarded this theory as a generalization of the special theory of relativity, so it was called general relativity, but the general theory of relativity was not completely equivalent to the theory of gravity.
General relativity can be seen as the development of both special relativity and the law of universal gravitation.This is a theory about space, time and gravity.Einstein proposed the principle of equivalence and speculated that gravity might be a geometric effect.He also introduced Riemannian geometry into his research, and was the first to obtain the basic equation of general relativity - Einstein field equation.It points out that the universal gravitation is different from the general force, but the performance of space-time bending, which is a geometric effect.The whole content of general relativity can be summarized as: "Matter tells space-time how to bend, and space-time tells matter how to move.[10]
Basic public design
(1) Equivalence principle: the dynamic effects of inertial force field and gravitational field are locally indiscernible[10]。However, under the existing theoretical framework of general relativity, the equivalence principle can be deduced from other assumptions.Specifically, if there is a viewer (G) in space-time, a local inertial reference system can be established in a field of its world line. The principle of general relativity requires that the Christophel symbols in this system be zero on the world line of viewer G.Therefore, modern relativists often think that it should not be included in the basic hypothesis of general relativity. Synge, one of the more representative ones, thinks that the equivalence principle has played a role as a bridge with the past classical physics in the early days of the establishment of relativity, and it can be called "the midwife of general relativity",And "bury the newborn baby after the birth of general relativity with dignity".
(2) General relativity principle (general covariance principle): all reference systems are equal, in other words, objective and real physical laws should remain unchanged under any coordinate transformation.Geometric description means that any space-time quantity appearing in physical laws should be the metric of the space-time or the physical quantity derived from it.The principle of general relativity points out that a correct physical law must consider the influence of gravitational field, which cancels the superiority of inertial system.[10]
(3) Einstein field equation: it specifically expresses the influence of matter (energy tensor) in space-time on space-time geometry (function of curvature tensor), and the requirements for corresponding energy tensor (its gradient is zero) include the content of the equation of motion of matter.
The Origin of General Relativity
In essence, all physical problems involve the question of which space-time concept to adopt.In classical physics before the twentieth century, people used Newton's absolute view of time and space.The proposition of relativity has changed this space-time view, which leads people to rewrite the formula of classical physics according to the requirements of relativity, so that it has the Lorentz covariance required by relativity instead of the Galilean covariance.In the three major fields of classical theoretical physics, electrodynamics itself is Lorentz covariant, without rewriting;Statistical mechanics has certain particularity, but this particularity does not bring many principled difficulties that need to be solved urgently;Most of the classical mechanics can be successfully rewritten into the form of relativity, so that it can be used to better describe objects in high-speed motion, but only Newton's theory of gravity can not be rewritten under the framework of special relativity, which directly led Einstein to expand his special relativity and get the general relativity.
Einstein reported on the "Explanation of Mercury's Perihelion Motion Based on General Relativity" at the Prussian Academy of Sciences in 1915, and then officially published the article "Basis of General Relativity" in the seventh issue of the physical yearbook in 1916, giving the original form of general relativity [3].He first noticed the experimental fact called (weak) equivalence principle: gravitational mass and inertial mass are equal.This fact can also be understood as that when there is no force other than gravity, all test objects with small enough mass (that is, the influence of their own mass on the gravitational field can be ignored) move in the same gravitational field in the same way.In this case, it may be considered that gravity is not actually a "force", but a space-time effect, that is, the mass of an object (which should be non-zero energy momentum tensor accurately) can produce the curvature of space-time. The gravity of the gravitational source on the test object is a geometric effect caused by this curvature of space-time.At this time, all test objects will make inertial motion in this curved space-time, and their motion track is the geodesic of the curved space-time, and they all obey the geodesic equation.It was in this way that Einstein got his general theory of relativity.It is worth mentioning that the identity of gravitational mass with inertial mass is a coincidence in Newtonian mechanics and special relativity, and has no significance.But Einstein found the clue of new theory from the common facts for hundreds of years[10]。
Introduction to Theory
Inertial mass comes from Newton's law, which reflects the resistance of objects to acceleration through the measurement definition of force and acceleration.Gravitational mass comes from the law of universal gravitation. Through the measurement of force and distance, it reflects the ability of objects to generate and withstand gravitational fields.
When space has no gravitational field, four-dimensional spacetime is (pseudo) Euclidean, that is, space is straight and has the greatest symmetry.But once there is a gravitational field, the space-time symmetry will be destroyed.
Curved space is a non Euclidean space. According to the curvature of space curvature is greater than, equal to or less than zero, the corresponding geometry is Riemann geometry, Euclidean geometry and Lobachevsky geometry.The straight line in non Euclidean geometry is the shortest distance between two points, also called geodesic or geodesic.In general relativity, gravitational field is transformed into metric field, or gravity disappears.So the geodesic is the movement track or light trace of free particles passing through two points.The geodesic equation of the curved space-time of general relativity is[3]：
Clock slow effect in acceleration case: when a clock accelerates (decelerates) around a closed path and finally returns to its original place, the total time it experiences is less than the time it experiences in the stationary clock in the original place.Therefore, under the framework of general relativity, the synchronization time cannot be calibrated even in the same coordinate system, and the concept of simultaneity cannot be established generally.This led to the famous twin paradox effect.
The field strength of gravitational field can be expressed as the sum of the gradient of scalar gravitational potential and the time rate of change of vector gravitational potential, that is, the potential of gravitational field is divided into scalar potential and vector potential.The expression of gravitational field strength is[10]：
, where
Is scalar potential,
Is the gravitational potential.
The speed of light in the gravitational field is also uniform, equal to c.
The motion law of the gravitational field itself is determined by the gravitational field equation.Gravitational field equation will determine the metric tensor of gravitational field characteristics
, associated with the energy momentum tensor that determines the distribution and motion of matter.Under the approximation of weak gravitational field, it should become the Poisson equation of Newton gravitational field:
At the same time, the gravitational field should be generalized covariant, so the gravitational field is a second-order tensor field equation.The form of Einstein's gravitational field equation is:
。In 1917, Einstein proposed the most common form including the cosmological factor term:
[3]
Einstein put forward the Mach principle on the basis of inertial force: acceleration is relative, and the inertial effect of all objects comes from the gravitational effect of space objects when they are relatively accelerating.However, within the range of experimental accuracy, the correctness of Mach principle cannot be determined.Theoretically, there is a certain contradiction with general relativity, so its authenticity is questionable.But Einstein's creation of general relativity was inspired by Mach's thought, so Mach's principle also has an important position in history.[10]
Experimental verification of general relativity
Classical experiments to verify general relativity include: gravitational redshift of spectral lines, precession of Mercury perihelion, gravitational deflection of light, and delay of radar echo [10].
In 2016, LIGO Scientific Cooperation Organization and Virgo cooperation team used the advanced LIGO detector to detect the gravitational wave signal from the merger of two black holes for the first time, and verified the most important inference of general relativity[11]。
In the experiment of muon lifetime, the twin paradox effect is confirmed in the microscopic field[1]。
Application of relativity
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Relativity is mainly applied in two aspects: high-speed movement (comparable to the speed of light), and strong gravitational field.
Special relativity Relativistic effect can explain the phenomenon of cosmic rays in high energy physics.For example, cosmic rays contain many high-energy muons, which are produced in the atmosphere.But the lifetime of the stationary muon is only 2.197 × 10-6s，Without the relativistic effect, these muons can only fly 660 meters at the speed of light, and cannot cross the atmosphere.In fact, most muons can travel through the atmosphere to the ground.For those who observe muons on the ground, their lifetime has been extended due to the clock slowing effect, while for muons, their observed atmospheric length has been shortened due to the scaling effect.So muons can fly across the atmosphere within their lifetime.
In the radiotherapy department of the hospital, most of them have a particle accelerator to generate high-energy particles to produce isotopes for treatment or imaging purposes.The synthesis of fluorodeoxyglucose is a classic example.Since the speed of particle motion is quite close to the speed of light (0.9c-0.9999c), the relativistic effect must be considered in the design and use of particle accelerators.
The atomic clock on the GPS satellite is very important for accurate positioning.At the same time, these clocks are affected by the time slowing effect (- 7.2 μ s/day) caused by the high-speed movement of the special relativity, and the time speeding effect (+45.9 μ s/day) caused by the weak gravitational field of the general relativity.The net effect of relativity is that those satellite clocks run faster than those on the ground.Therefore, the software of these satellites needs to calculate and offset all relativistic effects to ensure accurate positioning.The algorithm of GPS itself is based on the principle of light speed invariance. If the principle of light speed invariance does not hold, the GPS needs to be replaced with a different algorithm to accurately locate.
The inner electrons of transition metals such as platinum run very fast, and the relativistic effect cannot be ignored.When designing or researching new catalysts, it is necessary to consider the influence of relativity on the energy levels of electronic orbital states.Similarly, relativity can also explain the 6s inert electron pair effect of lead.This effect can explain why some chemical batteries have higher energy density, providing a theoretical basis for designing lighter batteries.Relativity can also explain why mercury is a liquid at room temperature, while other metals are not.
In modern times, general relativity is one of the theoretical bases for the observation of gravitational waves and the study of some high-density celestial bodies.On the other hand, the introduction of general relativity also provides a new tool and perspective for people to re understand some ancient issues such as cosmology, time travel, etc[1]。In addition, the gravitational lens effect derived from general relativity allows astronomers to observe black holes and dark matter that does not emit electromagnetic waves, and estimate the distribution of mass in the universe.
It is worth mentioning that the appearance of the atomic bomb and the famous mass energy relationship (E=mctwo）It doesn't matter much, and Einstein himself affirmed this.The mass energy relationship is only a mathematical tool to explain the power of the atomic bomb, and it is of little significance to the production of the atomic bomb[12]。
The Influence of Relativity on the Development of Physics
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Relativity also directly and indirectly gave birth to the birth of quantum mechanics, and established a new mathematical model for studying the high-speed movement of the micro world.After the establishment of quantum mechanics, Schrodinger, Klein, Gordon and others successively introduced special relativity, established relativistic quantum mechanics, and discovered Klein Gordon equation.Then Dirac established the Dirac equation, and determined the existence of spin, the basic physical quantity.Relativistic quantum mechanics has promoted the establishment of quantum field theory, which is the basis for modern physics to study basic particles.
In 1917, Einstein first used general relativity to model the large-scale structure of the universe, which led to the development of gravity theory and modern cosmology.General relativity has revolutionized human understanding of the universe.General relativity has also brought a unique research mode for theoretical physics, that is, relying on rational thinking supported by philosophy and mathematics to insight into the mysteries of nature.
General relativity promoted the development of geometry and gave birth to the development of unified theory.The unity of strong electromagnetic weak interactions opens a broader field of vision for physics.
In the process of constructing the theory of relativity, Einstein made the symmetry principle deeply rooted in the hearts of the people, making it a decisive concept or principle guiding and shaping theoretical physics.The symmetry principle plus symmetry breaking is also the paradigm of condensed matter physics.[3]
