Space and time

Connotation and relationship between space and time

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Space and Time, Philosophy On, space and time The dependency relationship of is expressing the evolution order of things.

Time and space are absolute concepts and basic attributes of existence. However, the measured value is relative to the reference system.

The connotation of "time" is endless forever; The extension is the measured value of each time sequence or each limited time period.

The connotation of "space" is infinite forever, and the extension is the measurement value of the relative position or size of each limited part of space.

Because in Special relativity Medium, light speed It is a common ruler for measuring time and space, and the changes of time and space show a dependency law on this common ruler, that is, follow Lorentz transformation 。 Therefore, the measured values of time and space are relative to the specific inertia Systematic, such as simultaneity, which is not absolute in measurement, relative to a Frame of reference Two events that occur at the same time may not occur at the same time relative to another reference system; The length and time period are not absolute in measurement. The moving ruler is shorter than the stationary ruler, and the moving clock is slower than the stationary clock. In special relativity, the speed of light is an absolute quantity. For any inertial reference frame light speed Are constant c.

Chinese name: Space and time
Foreign name: Time and space

Meaning: quality Existence performance of
Space-time quality relation: Quality generates emptiness, emptiness generates time, and time generates everything
Issues involved: All human knowledge and survival knowledge

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Basic relationship

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Point 1 Connotation

Time, space and quality are three absolute concepts that are independent and interrelated in connotation. Time axiom, space point axiom, and mass total axiom express their independence, while space-time relation axiom and mass space relation axiom express their interrelation. Space time relation and mass space relation indicate that U=U (T) and M=M (U), namely Space experienced by time and Space is filled with quality That is to say, "Space and time follow the quality". Quality is the primary element among the three elements. Without quality, there is no space, and without space, there is no time. If the poetic description of Laozi's Tao Te Ching is adopted, there are: The protoplasm generates emptiness, emptiness generates time, and time generates everything 。

Point 2 Measurement relationship

The extension of spatiotemporal quality involves its numerical measurement, which is relative to the reference frame and can only be approximate. Measuring the value of spatiotemporal quality is a problem to be solved scientifically. Before Einstein, they were measured separately under the virtual static reference frame, which specified their respective independence; Einstein added the common ruler measurement method under the actual motion reference frame, and specified their interrelation.

The interdependent relationship between time and space establishes the evolutionary order of things. If the absolute constant speed of light c is taken as the co ruler in measurement, this order can be expressed quantitatively by the following Einstein's special relativity formula:

T=γ (t-vr/c ^ 2), dynamic time T, static time t, the clock slows down under relative motion;

R=γ (r-vt), dynamic distance R, static distance r, and the ruler becomes shorter under relative motion;

M=γm， Dynamic mass M, static mass m, mass becomes larger under relative motion.

Where γ=1/√ (1-v ^ 2/c ^ 2)

It is human wisdom to measure various variables with absolute constants to obtain the functional relationship between variables; It is the great wisdom of the universe to use an infinite space-time quality ruler to measure the events that last forever and the objects that occupy space and have boundaries to create everything. If human beings can understand something from it, they will be able to walk out of the "relative" maze and enter the "absolute" holy land.

Three axioms of the universe

In Universal Philosophy, all human concepts can be defined directly or deductively by the following three axioms.

Table O, three axioms of the universe
axiom	Sorting I	Division II
Time T	Endless: t ∈ (- ∞,+∞)	Forever: △ t ＞ 0
Space U	Unbounded: r ∈ [0,+∞)	Forever: r=ct
Quality M	Infinite: m ∈ (0,+∞)	Always: d ρ _ η≠ d ρ _0

1、 The axiom of time: time is endless. Expression: T ={ t∈(-∞,+ ∞)}∩{△t ＞ 0}。

The time axiom is divided into two parts: time division and time division.

1. Time classification: t ∈ (- ∞,+∞) is "endless", which means "time has no beginning and end".

One of the natures of time is that there are infinite moments and different moments. T is the time, and its measured value is a real number.

2. Time division: △ t>0 means "forever", which means "the increment of time is always positive".

One way continuation of time period is the second nature of time. △ t is the time period, and its measured value is a real number greater than 0.

2、 Space axiom: space is unbounded forever. Expression: U={r ∈ (0,+∞)} ∨ {r=ct}.

Space axiom is divided into two parts: point axiom and space-time relation axiom.

1. Point sorting: r ∈ (0,+∞) is "unbounded", which means "any point in the space is in the middle".

It is the nature of space to have unlimited points, different points and equal rights. Here the point P=(r, θ, φ) [spherical coordinate], r is the distance from the point P to the origin of the spherical coordinate system, and its measured value is a non negative real number, θ∈ [0, π], φ ∈ [0,2 π].

2. Space time relation sorting: r=ct means "forever", which means "space always appears at the current time".

It is the basic relationship between space and time that any space point must appear at the current time. Here c is light speed Constant. Because according to Special relativity In Four-dimensional space-time The concept, spatiotemporal interval ct-r=0 is an invariant, that is, there is no interval between time and space, so r=ct means that point P is the point where light immediately arrives, that is, "space always appears at the current time".

3、 Axiom of quality: quality is infinite. Expression: M={m ∈ (0,+∞)} ∨ {(d ρ) _ η≠ (d ρ) _0}.

The axiom of quality can be divided into two parts: the general axiom and the qualitative spatial axiom.

1. Overall classification: m ∈ (0,+∞) is "infinite", which means "the total mass of the universe is infinite".

Infinite total mass is the nature of quality. Here m is the static mass.

2. The separation of the mass space relationship: (d ρ) _ η≠ (d ρ) _0 is "forever", which means "never evenly fills the space".

"Every part of the universe is full of mass, and there is no pure space without mass, but the density of each point is different", which is the basic relationship between mass and space. (d ρ) _0 is the density of any specified space point, (d ρ) _ η is the density of any other space point, (d ρ) _ η≠ (d ρ) _0 means that the micro density of each point is not equal, that is, "the quality distribution space is never uniform". Here density ρ=m/u, micro density d ρ=dm/du, where dm is an infinitesimal prime element; Du is an infinitesimal empty element, where u is the domain product, including the product of points, lines, surfaces, and bodies; η is a positive integer. "Quality cloth space is never even" quantum mechanics Expressed as“ Uncertainty principle ”Note 1. famous Brownian motion Note 2 is caused by "the quality distribution space is never uniform".

In order to remember it, we use poems to express it:

Three Axioms of the Universe

The increment is always positive, and the time is not always. The space exists now, and the dots can be centered.

The mass is infinite and uneven is full of emptiness. Time and space follow the quality, and the principle of birth and death is the same.

Definition of time, space and quality

Time, space and mass are collectively referred to as the three elements of the universe, namely time, space and mass.

Definition formula of three elements of the universe
concept	connotation	Extension, n is a positive integer	inference
time	T={t∈(-∞,+∞)}∩{△t＞0}	T=∑(t∪→△t)_n=∑t_n∪∑→△t_n	t=∫dt
space	U={r∈[0,+∞)}∩{r=ct}	U=∑(→r∪u)_n=∑→r_n∪∑u_n	u=∫du
quality	M={m∈(0,+∞)}∩{(dρ)_η≠(dρ)_0}	M=∑m_n=∑(ρu)_n	m=∫dm

The definitions of these three elements summarize the connotation and extension of the definitions of time, space and quality in all human disciplines. The connotations in the definitions of time, space and quality are respectively the time axiom, space axiom and quality axiom, and the extensions are deduced from the nature of their respective connotations: Because of the "three nothingness", every part of space-time quality is finite and measurable, but the number of parts can be infinite. The connotation expresses that the quality ruler of space and time is infinite, and the extension expresses that time can be divided into any time to segment and measure the length of each segment, space can be divided into any area and measure the size and quality of each area and measure the number of values of each part. According to the definition of spatiotemporal quality, it can be deduced that the spatiotemporal quality is composed of its prime elements.

The first time

Connotation T={t ∈ (- ∞,+∞)} ∨ {△ t ＞ 0}; Extension T=∑ (t →→△ t) _n=∑t_n →∑→△ t_n.

That is, connotation is endless forever; The extension is the measured value of each time sequence or each limited time period.

(t →→△ t) _n represents any finite part of time, that is, each part is finite but the number of parts can be infinite. In the formula, t_n represents the value at the nth time, and △ t_n represents the length value of the nth time period. → △ t_n refers to the nth period, where → △ t=△ t → l=(t1-t) → l, where → l is the unit vector, indicating that the time has only the direction of increase, that is, the only direction of the period, where t1 is the value of the later time or the present time, and t is the value of the previous time or the past time.

A. Deduction of time extension:

A.  t ∈ (- ∞,+∞) [There are infinite times, but different notches] ∨ t_n ∈ (- ∞,+∞) [t_n means that you can select any coordinate system and any number of time values to compare their order].

B. ∨ t ∈ (- ∞,+∞) ∨ △ t ＞ 0 [There are infinite moments, different notches and unidirectional duration of time periods] ∨ △ t_n ＞ 0, that is, there is → △ t_n [→ △ t_n means that n multiple unidirectional time periods with finite length can be arbitrarily selected to compare their length].

The connotation expresses that the ruler of time is endless, and the extension expresses that time can be measured by any division or segment.

B. Deduction of time inference:

Time is multiplied by time element into: t=curl dt.

Where time element dt=t1-t → 0, and the previous time t of dt is the limit value of dt.

It is proved that ∨ △ t ＞ 0 [any selected period is greater than 0] ∨ △ t=t1 － t → 0=dt [△ t can be infinitesimal], ∨ t=∨ dt.

Because of the above characteristics of time, we can use different units to measure the value of time and period. as physics stay International System of Units (SI) Basic unit The second (s) is defined as: cesium -133 Atomic ground state The two supers of fine Radiative nine , one hundred and ninety-two , six hundred and thirty-one , seven hundred and seventy Duration of cycles; Astronomical Almanac time The second (s) is defined as: 1/31, 556, 925.9747 of the length of the positive regression year at 12:00 on January 0, 1900; Often used in life millisecond ms、 branch min、 hour h、 Day (day) d and other time units.

Because of the above characteristics of time, it is possible for us to study all the knowledge of the laws of changes in various parts of the universe.

Because of the above characteristics of time, everything in the universe can come into being, change and die!

Point 2 Space

Connotation U={r ∈ (0,+∞)} ∨ {r=ct}; Epitaxy U=∑ (→ r ∨ u) _n=∑→ r_n ∨∑ u_n

That is, the connotation is unbounded forever, and the extension is the measured value of the relative position or size of each limited part of space.

(→ r ∨ u) _n represents any finite part of a space, that is, each part is finite but the number of parts can be infinite. In the formula, r_n represents the coordinate value of the nth point, and u_n represents the domain product of the nth finite point group size.

A. Deduction of space extension:

A. ∨ r ∈ (0,+∞) [There are infinite points, but the points are different and equal] ∨ r_n ≥ 0 [r_n means that the coordinate system can be arbitrarily selected and more than n point values can be selected to compare the relative orientation of their positions].

B. ∨ r_n ≥ 0 [Any point can be selected] ∨ u_n ＞ 0 [u_n means that the connected points can be combined into a finite point group area, and more than n point groups can be selected randomly to compare their sizes]

The connotation expresses that the ruler of space is unbounded forever, and the extension expresses that space can be arbitrarily divided into regions and measure the size of each region.

B. Deduction of spatial inference:

The space is composed of empty elements: u=curl du.

It can be proved that there is an empty element du if ∨ u_n ＞ 0 [any selected region can be infinitesimal], ∨ u=∨ du.

Because of the above characteristics of space, we can measure the relative position of empty points and the specific size of the airspace in different units. For example, in physics, the basic unit of length measurement, meter (m), is defined as: light travels 1/299, 792, 458 seconds in vacuum Kilometers (km), decimeter (dm), centimeter (cm), millimeter (mm), micrometer (μ m), nanometer (nm), etc. Another example is Li and Zhang in China, inches and yards in Britain, sea and knots in aviation and navigation, etc. Different units can also be used when calculating area and volume.

Because of the above characteristics of space, we can decompose space into different parts and study the relationship between them, resulting in geometry, algebra and logic. This is discussed in detail in the following third chapter on geometry, algebra and logic.

Point 3 Quality

Connotation M={m ∈ (0,+∞)} ∨ {d ρ _ η≠ d ρ _0}; Extension M=∑ m_n=∑ (ρ u) _n

That is, the connotation is infinite forever, and the extension is a measurement of how much content is filled in the space of each limited part.

M_n represents the static mass value of the n-th finite part of the mass, that is, the static mass of each part is finite, but the number of parts can be infinite.

A. Deduction of mass extension:

∨ m ∈ (0,+∞) [The total mass is infinite] ∨ m_n ＞ 0 [m_n means that n finite parts can be selected arbitrarily to compare their number].

The connotation expresses that the ruler of mass is infinite and eternal, and the extension expresses that the mass can be arbitrarily divided and the number of values of each part can be measured.

B. Deduction of quality inference:

The mass is multiplied by the prime element: m=∨ dm

It is proved that the prime element dm exists if ∨ m_n ＞ 0 [any part can be infinitesimal], ∨ m=∨ dm.

Because of the above characteristics of mass, we can measure the mass of a specific object in different units. Such as physics International System of Units In Basic unit Kg (Kg): the quality of pure water at 4 ℃, Chinese jin, British pound, etc.

Because of the above characteristics of mass, we can find molecules and atoms through chemical research, and find protons, neutrons, electrons, quarks and other microscopic particles through particle physics research. This is discussed in detail in the third chapter on chemistry and particle physics below.

Because the mass never evenly fills the space, and the distribution state is changing at any time, when the mass changes the distribution state of the space, a measurable phenomenon called inertia or universal gravitation in physics occurs. This is discussed in detail in the following chapter on Newtonian mechanics and quantum mechanics in the third chapter.

From the respective inferences of the above three elements, we can see that the time element value dt, the empty element value du, and the prime element value dm are all infinitesimal variables, so we can only approximate the specific measured values of time (time, period), space (point location, distance, area, volume), and mass (static mass, dynamic mass), which has been quantum mechanics On“ Uncertainty principle Experienced and measured.

Brief definition of the three elements of the universe
concept	Connotation 1	Connotation 2	extension
time	Time has no beginning and end	The increment of time is always positive	The measured value of the time sequence or the length of each limited period
space	Center at any point in space	Space is always present at the current moment	The measured value of the relative position or size of each limited part of the space
quality	The total mass of the universe is infinite	Never evenly fill the space	Measurement value of how much content is filled in each limited space

theoretical explanation

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Galileo Relativity has broken Newton Of Absolute space Concept. Principle of relativity in mechanics (Galilean relativity) requires that the motion law of objects must not contain absolute velocity, that is, absolute velocity cannot be measured, which denies the existence of Newton's absolute space.

Newton was very worried about the nonexistence of absolute space, because it was inconsistent with his concept of absolute God. In fact, even if the nonexistence of absolute space was implied in his laws, Newton would refuse to accept it. Because of this irrational belief, Newton was severely criticized by many people, most famously Berkeley He is a philosopher who believes that all material entities, space and time are illusory.

Aristotle Both Newton and Newton believed in absolute time and believed that people could accurately measure the time interval between two events. Time and space are completely independent.

relativity It changed the concept of space and time, and denied absolute space and absolute time. gravitation The function of Empty time Become bent instead of classical mechanics Infinitely extended Euclidean geometry Absolute space and infinitely extended Minkowski space^[1] 。 General relativity reveals the existence of space time objects and points out that the nature of space time is related to the motion of objects.

Einstein A revolutionary idea was put forward, that is, unlike other kinds of forces, gravity distorts space time due to its mass and energy distribution, resulting in the fact that the space time structure is not flat. The new understanding of space time is Cosmology Revolution.

Quantum theory The development of Time concept More fundamental questions were raised. Quantum theory holds that the judgment result of what state a system may exist in the past depends on the choice made in the current measurement. Therefore, unless the past state of a system has been recorded, it cannot be considered that the history of the system exists in the past time independently of the current choice. This relationship between the present and the past is very different from the concept of causal order, which is implied in the concept of time Causal sequence It requires that the existence of the past does not depend on the present. Quantum theory also shows that at 10 －33 Cm, 10 －43 In such a small space-time scale as seconds, the concept of "before" and "after" describing the sequence of events will lose its meaning. Therefore, it may not always be appropriate to use time to describe the sequence of events. Space and time are thing Between order , but not necessarily the most basic order, it may be an approximation of the more basic order^[1] 。

Basic concepts

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Space and time It refers to an order between things. Space is used to describe objects Configuration ； Time is used to describe the order 。 Spatial and temporal physical property It is mainly manifested through their various connections with the movement of objects.

In physics, the understanding of space and time can be divided into three stages: classical mechanics stage, special relativity stage and general relativity stage.

In classical mechanics, the spatial and temporal nature It is considered to be independent of any object and motion, and there are absolute space and absolute time. Newton in《 Mathematical Principles of Natural Philosophy 》"Absolute space, in its nature, has nothing to do with any external situation. It has always remained similar and unchanged.", "Absolute and pure mathematical time, in its nature, flows evenly and has nothing to do with any external situation.". On the other hand, the motion properties and laws of objects are closely related to the space and time used to measure them. Relative to absolute space static Or movement, is the absolute static or movement. Only in absolute space Reference system , or take others as absolute Uniform motion The object of is the reference system, Law of inertia Was established. That is, an object that is not affected by external forces will either remain stationary or move at a constant speed. This special kind of reference system is called Inertial reference frame （ Inertial frame ）。

The space and time quantities of any two different inertial frames meet Galileo transformation 。 Under this transformation, the position and speed are relative, that is, their values are different with respect to different reference systems; the length and time interval are absolute, that is, their values are constant with respect to different reference systems, and their simultaneity is absolute. Two events that occur simultaneously in an inertial system must also occur simultaneously in other inertial systems. In addition, Newtonian mechanical laws remain unchanged under Galileo transformation, which is consistent with Galileo's principle of relativity Requirements.

That's it Principle of relativity , which constitutes the starting point of the doubt about Newton's concept of absolute space. If there is absolute space, the motion of the object relative to this absolute space should be measurable. This is equivalent to requiring that some laws of motion contain Absolute speed 。 However, the principle of relativity requires that there must be no absolute speed in the motion law of objects, that is, the absolute speed cannot be measured in principle. G. Leibniz, G. Berkeley, E. Mach and others have successively raised valuable objections to the concept of absolute space and time, pointing out that there is no evidence to show the existence of Newton's absolute space.

Einstein Promote the above Principle of relativity The relativity principle of special relativity is proposed, that is, not only the mechanical laws in different inertial frames have the same form, but also other physical laws should be the same. In special relativity, space and time in different inertial frames comply with Lorentz transformation 。 According to this transformation, Simultaneity It is no longer absolute. Two events occur simultaneously relative to a certain reference system, and may not occur simultaneously relative to another reference system. In the special theory of relativity, length and time interval also become relative quantities, the moving ruler is shorter than the stationary ruler, and the moving clock is slower than the stationary clock, light speed In special relativity, it is an absolute quantity, and the speed of light is C^[1] 。

Space and time are common descriptions particle Two of the movements Basic physical quantity , which International System of Units (SI) Dimension: length L (m), symbol m; Time T (seconds), symbol s. To describe the motion, it is necessary to accurately point out the particle in the reference system（ Coordinate system ）Time and location of occurrence in. Physics has established the change law of particles in four-dimensional space-time (one-dimensional time+three-dimensional space).

Newton's view of time and space

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Newton's absolute space and absolute time. Generally, in order to determine the size of an object, its shape and size should be known. about Box , know its length, width and height, and use Euclidean geometry Its volume can be calculated by the formula of. In order to determine the position of an object of negligible size, it is necessary to know that it is still relative to another object of negligible size object of reference It is also sufficient to use Euclidean geometry for the distance between up and down, left and right, and front and back. To describe a moving object, the instantaneous position is not enough, but the instantaneous speed and acceleration need to be known. Thus, it can be abstracted that three-dimensional space Coordinate system And one dimension Time coordinate The concept of. The motion properties and laws of objects are closely related to the space coordinate system and time coordinate used for measurement. be relative to Inertial reference frame (inertial system), Law of inertia Was established. In order to determine the inertial frame, Newton abstracted the concepts of three-dimensional absolute space and one-dimensional absolute time. Absolute space satisfies three-dimensional Euclidean geometry, and absolute time passes evenly. Their nature is independent of any specific object and its movement in it. Static or relative to absolute space Uniform linear motion The object of is the coordinate system of the reference object, which is the inertial system.

In classical mechanics, any object has different Inertial coordinate system The space coordinate quantity and time coordinate quantity of Galileo transformation 。 In this group of transformations, the position and speed are relative Of; The space length, time interval and acceleration of moving objects are absolute or constant. The simultaneity in time measurement is also constant: whether two events relative to an inertial system occur simultaneously is constant. The simultaneous occurrence of two events relative to one inertial system must be simultaneous relative to other inertial systems, which is called simultaneous Absoluteness 。 All laws of Newtonian mechanics, including Law of universal gravitation Its form is invariant under Galileo transformation. This can be abstracted as Galileo's principle of relativity : Mechanical laws in inertial frame Transformation The following form remains unchanged. At the same time, invariance is closely related to conservation law. The time translation invariance of a moving object under Galileo transformation corresponds to the Conservation of energy ； The invariance of space translation and space rotation under Galileo transformation corresponds to the Momentum conservation and Conservation of angular momentum 。

Newton's laws of mechanics and their invariance under the Galileo transformation led to the suspicion of Newton's concept of absolute space. If there is absolute space, the motion of objects relative to absolute space should be measurable. This is equivalent to the requirement that some mechanical laws of motion should contain absolute velocity. However, there is no absolute velocity in Newton's law of mechanics. In other words, the correctness of Newton's laws of mechanics does not require the existence of absolute space. After Newton put forward the concept of absolute space, some people successively raised objections to this concept. In fact, there is no strong evidence that absolute space exists. However, with Newtonian mechanics and Law of universal gravitation Newton's concept of absolute space and absolute time has also been playing a leading role in the field of natural science and philosophy.

However, it is impossible to establish a simple cosmic image in the Newtonian system. A simple cosmic image is: in an infinite absolute space and infinite absolute time, an infinite number of stars or galaxies are generally stationary, with an average of luminosity Roughly uniform. However, this simple picture of the universe is unstable under the action of gravity, and even the simple question of why the night sky is dark cannot be answered.

nineteenth century maxwell Summarize electromagnetics Basic laws of—— Maxwell's equations The speed of light appears in the equations C 。 Then I found out electromagnetic wave 。 The physics world, dominated by Newton's absolute space and absolute time concept, naturally believes that absolute space is full of light ether, Maxwell equation It is only valid in an inertial system that is static relative to absolute space, and electromagnetic waves are optical etheric wave 。 The inevitable corollary of this concept is that Maxwell's equation only holds approximately in the system of the earth's motion relative to absolute space. Electromagnetic or optical experiments should be able to measure the earth's relative Drift velocity 。 However, all such experiments have negative results. This shows that ignoring the non inertial motion of the earth effect Maxwell equation is still valid, and there is no ether drift. In this way, Newton's concept of absolute space and light ether was challenged^[2] 。

Relativistic space-time

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At the beginning of the 20th century, Einstein put forward the special theory of relativity, which expanded Galileo's principle of relativity , not only requires that the mechanical laws have the same form in different inertial reference frames (inertial frames), but also requires that other physical laws have the same form in different inertial frames. Einstein also assumed that the one-way speed of light in different inertial reference frames C Is unchanged. Accordingly, the Spatial coordinates and Time coordinate No longer obeys Galileo transformation, but obeys non-homogeneous Lorentz transformation 。 According to such transformations, ruler The length and time interval (that is, the speed of a clock) are not constant: the ruler moving at high speed is shorter than the ruler at rest, and the clock moving at high speed is slower than the clock at rest. Simultaneity is no longer constant (or absolute): for two events that occur simultaneously in one inertial system, they do not occur simultaneously in another high-speed inertial system. In special relativity, the speed of light is an invariant, so the time space interval (abbreviated as Spatiotemporal interval ）It is also an invariant; In addition to the sum of energy conservation corresponding to the invariance of time translation and space translation Momentum conservation In addition, there is time space translation invariance; Therefore, there is a conservation law of energy momentum. According to this conservation law, Einstein's mass energy relation can be derived. This relationship is very basic in atomic physics and nuclear physics.

Special relativity denied the existence of the light ether in the 19th century, and electromagnetic waves are electromagnetic field Self wave 。 So the field becomes material object Different material forms. At the same time, this also denied Newton's absolute space and absolute time, and passed Principle of invariance of light speed Combine one-dimensional time and three-dimensional space Connected, it becomes a four-dimensional time space. H. Minkowski This property was first discovered, so it is called Minkowski spacetime 。 The geometry of four-dimensional Minkowski spacetime is Gauge The invariant group of Euclidean geometry with sign difference is a nonhomogeneous Lorentz group.

Principle of special relativity It is required that all physical laws have the same form for inertial frames. However, put Law of gravity Inclusion of this requirement does not conform to the observed facts. Einstein further proposed General relativity , once again changed the concept of time space in physics.

According to general relativity, if we consider the inertia force or Gravitational interaction , there is no large-scale inertial frame, but only exists at any space-time point Local inertial frame ； Between local inertial frames of different space-time points, through inertial force or gravitation Interconnection. Space time with inertial force is still flat and straight in four dimensions Minkowski spacetime 。 existence gravitational field Of space-time , no longer straight, is a four-dimensional curved spacetime, whose geometric properties are described by four-dimensional Riemannian geometry with signed difference in metric. The curvature of space-time is determined by the energy momentum tensor of matter (object or field) and its motion in it Einstein's gravitational field equation To determine. In general relativity, time space is no longer just a "stage" for the movement of objects or fields, while bending time space itself is a gravitational field. The properties of time space that characterize gravity are closely related to the properties of objects and fields moving in it. On the one hand, as the source of the gravitational field, the energy momentum of the motion of objects and fields passes Field equation Determine the strength of the gravitational field, that is, the curvature of space-time; on the other hand, Curved spacetime The geometric properties of also determine the motion properties of the object and field moving in it. For example, the sun, as the source of the gravitational field, its mass makes the space-time where the sun is located bend, and the degree of bending represents the strength of the solar gravitational field. Closest to the sun Mercury The movement track of is most affected, and the starlight passing the edge of the sun will also deflect, and so on. Soon after the general relativity was proposed, astronomical observations showed that the theoretical calculation of general relativity was consistent with the observation results. However, research in the middle and late 20th century shows that under the conditions that can be realized physically, the time space of general relativity must be unacceptable Singularity 。 stay singularity The time space, that is, the gravitational field, is completely meaningless, which is the manifestation of the theoretical problems of general relativity^[2] 。

The evolution of the universe

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The universe is a evolution As a whole. The understanding of space and time has always been closely related to the understanding of the universe. modern Cosmology with Cosmological principle And Einstein's gravitational field equation. The principle of cosmology holds that the universe, as a whole, evolves in time, that is, it has time arrows and is uniform in space Isotropy Of. In the middle of the 20th century Big Bang Cosmic Model , explained Extragalactic galaxy red shift , predicted Cosmic microwave background radiation For the evolution of the universe, the formation of galaxies, and the abundance Both of them can give explanations that are basically consistent with astronomical observations, and also solve the problem that Newton's system cannot establish a cosmic image. It can be said that the understanding of the universe as a whole of evolution is an important achievement and symbol of natural science's understanding of time and space in the 20th century. However, the singularity mentioned above is at the beginning of the Big Bang or Galactic nucleus or black hole The center of The origin of the universe 、 Galactic evolution Bring new problems^[2] 。

Influence of quantum theory

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The influence of quantum theory on space and time theory. At the beginning of the 20th century, the transformation of physics from classical mechanics to quantum theory also brought about revolutionary changes in the concept of space and time, and also caused embarrassment in the field of physics. quantum mechanics Of the described system spatial location and momentum Time and energy cannot be measured accurately at the same time, and they meet the uncertainty relationship; Classical orbits no longer have precise meaning. How to understand quantum mechanics and the essence of measurement has always been controversial. At the end of the 20th century Quantum Entanglement 、 Quantum invisibility Transmission Quantum information The research of Causality , locality and other important concepts, but also bring new problems and challenges.

The combination of quantum mechanics and special relativity Quantum electrodynamics 、 Quantum field theory Electric weak unified model, including Quantum chromodynamics Inside Standard model Although it has achieved great success, it also brings some challenging problems. While profoundly changing some important concepts about time and space, it also brings some principles. as vacuum Not empty, existing Zero point energy And vacuum fluctuations have greatly changed the understanding of vacuum in physics. On this basis, the quantum electrodynamic Perturbation theory The calculation can give a result that is in good agreement with the experiment, but this perturbation expansion is unreasonable. Symmetry breaking The mechanism of Intermediate boson The mass is obtained, however, the vacuum expectation value of the Higgs field and the zero point energy mentioned above are equivalent to Cosmological constant , but its value is higher than that observed in astronomy Cosmological constant It is tens to more than one hundred orders of magnitude larger. Description of quantum chromodynamics quark and Gluon But quarks and gluons are trapped in hadron Inside, no free quarks and gluons have been found, which may be related to the nature of vacuum.

On the other hand, quantum theory predicts that at 10 －33 Cm, 10 －43 Seconds such a small space – time scale The classical concept of space time will no longer apply. To solve this problem, we must establish a theoretical basis Self consistent Of Quantum gravity theory , namely quantum space-time theory. However, how to combine quantum theory with general relativity has not been solved. One possible candidate is superstring theory or M-theory. However, the self consistent superstring theory or M theory in quantum sense can only be realized in one-dimensional time – nine dimensional space or one-dimensional time – ten dimensional space. This has caused some profound problems: how to return to one-dimensional time - three-dimensional space. Why is the real space three-dimensional and time one-dimensional? Maybe the universe is just a piece of high-dimensional space-time (it can be called "membrane"). However, there is obviously more than one way to go from high-dimensional space – time to four-dimensional space – time. Then, can there be other "membrane" universes besides the "membrane" universe? Whether there will be other stages before the big bang. The research and solution of these problems, and dark substance 、 Dark energy , and Cosmological constant And other issues are closely related^[2] 。

Parity violation

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Weak action Left-right symmetry（ Parity ）And so on. The laws of mechanics and electromagnetism are important for Inertial reference frame (Inertial system) The change from left-handed system to right-handed system is invariable, and the reverse sign of time is invariable. These invariable laws, called spatial inversion and temporal inversion, are closely related to the concepts of space and time. At the same time, there are also Symmetry The associated positive and negative charge symmetry. But in Microparticle Of Weak interaction Middle, the spatial inversion is unchanged Time inversion The laws of invariance and inversion invariance of positive and negative charges are no longer tenable. From the middle of the 20th century Li Zhengdao and Yang Zhenning propose Parity nonconservation , and for the beginning of experimental confirmation, physics is gradually recognizing this point. However, it is not clear that the more profound essence What is it?^[2] 。

Dark energy

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Dark energy And the cosmological constant. Since the late 1990s, astronomical observation has made great progress. Determined, invisible dark substance Dark energy, totally different from ordinary energy, accounts for at least 20% and 70% of the total matter and energy in the universe respectively; The cosmological constant is positive, about 10 －52 centimeter －2 。 In this way, cosmic space time is no longer asymptotically flat, but should be asymptotically positive constant curvature spacetime. However, for positive constant curvature spacetime, not only superstring or M theory has difficulties in principle Quantum field theory , quantum mechanics, and even classical mechanics will encounter difficulties. Because, in theory, there is no accepted way to define the physical and mechanical Observable measurement 。 Why the value of the cosmological constant is so small is also a big problem.

At any stage in history, human understanding of space and time is not complete and has no problems, but some problems have not been found for a while. Human's understanding of space and time is constantly raising and solving problems in this way, and constantly deepening in practice^[2] 。

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