In general, in order to determine the size of an object, it is necessary to know its shape and dimensions. Pen % fun % Pavilion www.biquge.info

In the case of a cuboid, its length, width, and height can be calculated using the formulas of Euclidean geometry, and it is sufficient to know its up-and-down, left-right, and anterior-backward distances relative to another stationary reference of negligible size.

It is not enough to describe the instantaneous position of a moving object, it is also necessary to know the instantaneous velocity and acceleration. From this, the concepts of three-dimensional spatial coordinate system and one-dimensional time coordinates can be abstracted. The nature and law of the motion of an object are closely related to what kind of spatial coordinate system and time coordinates are used to measure it. To determine the inertial frame, L. Newton abstracted the notion of three-dimensional absolute space and one-digit absolute time. Absolute space satisfies three-dimensional Euclidean geometry, absolute time passes evenly, and their nature is independent of any concrete object in it and its motion. The coordinate system in which an object moving in a stationary or uniform linear motion relative to absolute space is the reference object, which is the inertial frame.

In classical mechanics, the Galilean transform satisfies between the spatial and temporal coordinate quantities of any object for different inertial coordinate systems. Under this set of transformations, position and velocity are relative; The length of space, the interval of time, the acceleration of a moving object are absolute or constant. Simultaneity is also constant in time measurement; Whether or not two events occur at the same time relative to an inertial frame of reference is constant. Two events that occur at the same time relative to a certain inertial frame of reference, and two events that occur at the same time relative to a certain inertial frame of reference, must also be simultaneous relative to other inertial frames of reference, which is called the absoluteness of simultaneity. All the laws of Newtonian mechanics, including the law of gravitation, are unchanged in form under Galilean transformations. This can be abstracted to Galileo's principle of relativity; The laws of mechanics remain unchanged under the transformation of the inertial frame of reference. At the same time, invariance is closely related to the law of conservation. The invariance of the time translation of a moving object under the Galilean transformation, which corresponds to the conservation of energy of that object; The spatial translation and spatial rotation invariance under the Galilean transform correspond to the conservation of momentum and angular momentum of the object.

If there is absolute space, the motion of the object with respect to the absolute space should be measurable. This is equivalent to requiring that certain laws of mechanical motion include absolute velocity. However, there is no absolute speed in the laws of science. In other words, the correctness of the laws of eschatological science does not require that there must be an absolute space.

According to such transformations, neither the length of the ruler nor the interval of time (i.e., the speed of the bell) are constant; A ruler moving at high speed becomes shorter relative to a ruler at rest, and a clock moving at high speed slows down with respect to a bell that is stationary.

Simultaneity is no longer immutable (or absolute); Two simultaneous events in one inertial frame of reference do not occur simultaneously in another inertial frame of reference moving at high speed.

In special relativity, the speed of light is invariant, and so is the time-space interval (space-time interval for short). Between some inertial frames, in addition to the conservation of energy and momentum corresponding to the time translation and space translation invariance, there is also a time-space translation invariance; Thus, there is a law of conservation of energy-momentum. According to this conservation law, the mass-energy relation can be derived. This relationship is extremely fundamental in atomic physics and nuclear physics.

The principle of special relativity requires that all physical laws have the same form for an inertial frame of reference. However, the inclusion of the law of gravity in this requirement is not consistent with observational facts.

According to the general theory of relativity, if the inertial force or gravitational interaction between objects is taken into account, there is no large-scale inertial frame of reference, and only local inertial frames exist at any point in space-time; Local inertial frames at different points in space-time are connected to each other by inertial force or gravitational force. The space-time where inertial forces exist is still a straight, four-dimensional Minkowski space-time.

The space-time in which there is a gravitational field, no longer straight, is a four-dimensional curved space-time, and its geometric properties are described by the four-dimensional Riemannian geometry with the sign difference of the gauge. The degree of curvature of space-time is determined by the energy-momentum tensor of matter (object or field) and its motion in it, determined by the gravitational field equation.

In general relativity, time-space is no longer just a "stage" for the motion of objects or fields, and bending time-space is itself a gravitational field. The temporal-spatial properties that characterize gravity are closely related to the properties of the objects and fields in which they are moving.

On the one hand, the energy-momentum of the motion of the object and the field is used as the source of the gravitational field, and the strength of the gravitational field is determined by the field equation, and the degree of curvature of time and space is determined. On the other hand, the geometric nature of curved space-time also determines the nature of the motion of the objects and fields in which it moves.

For example, as the source of the gravitational field, the mass of the sun causes the space-time in which the sun is located to bend, and the degree of bending indicates the strength of the sun's gravitational field. The trajectory of Mercury, which is closest to the Sun, is most affected, and the starlight passing by the Sun's edge is also deflected, and so on.

Soon after the general theory of relativity was proposed, astronomical observations showed that the theoretical calculations of the general theory of relativity were consistent with the observations.

The understanding of space and time has always been closely related to the understanding of the universe. Modern cosmology is based on the principles of cosmology and Einstein's equations of gravitational fields.

The cosmological principle holds that the universe as a whole is evolutionary in time, that is, there are arrows of time, and it is uniformly isotropic in space.

The spatial position and momentum, time, and energy of the system described by quantum mechanics cannot be accurately measured at the same time, they satisfy the uncertainty relation; Classical orbitals no longer have precise meanings, etc., and there has been a debate about how to understand quantum mechanics and the essence of measurement. In the last days, the research on quantum entanglement, quantum teleportation, quantum information, etc., has also brought new problems and challenges to important concepts such as causality and locality, which are closely related to time and space.

The combination of quantum mechanics and special relativity has led to quantum electrodynamics, quantum field theory, electroweak unified models, and the standard model, including quantum chromodynamics, which describes strong interactions, although they have been very successful, but they have also brought some challenging problems. While profoundly changing some important concepts of time-space, it also brings some questions of principle.

For example, the vacuum is not empty, there is zero point energy and vacuum fluctuations, which greatly changes the understanding of vacuum in physics.

On this basis, the perturbation theory calculations of quantum electrodynamics can give results that are in precise agreement with the experiment, but the perturbation expansion is unreasonable. However, the vacuum expectation value of the Heggs field and the zero-point energy mentioned above are equivalent to the cosmic Changshu in a certain sense, but their values are tens to more than 100 orders of magnitude larger than the cosmological constants of astronomical observations. (To be continued.) )