Usually, to determine the size of an object, its shape and dimensions are known.
For a cuboid, knowing its length, width and height, you can calculate its volume using the formulas of Euclidean geometry. As long as you know its up and down, left and right and front and back distances relative to another stationary reference object of negligible size, you can also use Euclidean geometry. The geometry of a few li is enough.
It is not enough to describe the instantaneous position of a moving object, you also need to know the instantaneous speed and acceleration. From this, the concepts of three-dimensional space coordinate system and one-dimensional time coordinate can be abstracted. The motion properties and laws of objects are closely related to the spatial coordinate system and time coordinate used to measure them. In order to determine the inertial system, L. Newton abstracted the concepts of three-dimensional absolute space and one-digit absolute time. Absolute space satisfies the three-dimensional Euclidean geometry, absolute time passes uniformly, and their nature is independent of any specific objects and their movements in it. The coordinate system in which an object at rest or in uniform linear motion relative to absolute space is the reference object is the inertial system.
In classical mechanics, the space coordinates and time coordinates of any object in different inertial coordinate systems satisfy the Galilean transformation. Under this set of transformations, position and speed are relative; spatial length, time interval, and acceleration of moving objects are absolute or constant. Simultaneity in time measurement is also invariant; whether two events occur simultaneously relative to an inertial reference frame is invariant. Two events that occur at the same time relative to a certain inertial reference system must also be simultaneous relative to other inertial reference systems, which is called the absolute nature of simultaneity. All laws of Newtonian mechanics, including the law of universal gravitation, are invariant under Galilean transformation. This point can be abstracted as the Galilean principle of relativity; the laws of mechanics remain unchanged under the transformation of the inertial reference system. At the same time, invariance is closely related to conservation laws. The time translation invariance of a moving object under the Galilean transformation corresponds to the energy conservation of the object; the space translation and spatial rotation invariance under the Galilean transformation correspond to the momentum conservation and angular momentum conservation of the object.
If absolute space exists, the motion of an object relative to absolute space should be measurable. This is equivalent to requiring that certain mechanical laws of motion should contain absolute velocity. However, scientific laws do not include absolute speed. In other words, the correctness of the scientific laws of the apocalypse does not require the existence of absolute space.
According to this type of transformation, the length of the ruler and the time interval (that is, the speed of the clock) are not constant; the ruler that moves at high speed becomes shorter relative to the ruler that is stationary, and the clock that moves at high speed becomes slower than the clock that is stationary.
Simultaneity is no longer constant (or absolute); two events that occur simultaneously in a certain inertial reference frame do not occur simultaneously in another high-speed moving inertial reference frame.
In the special theory of relativity, the speed of light is an invariant, so the time-space interval (referred to as the space-time interval) is also an invariant; among some inertial systems, in addition to the conservation of energy and momentum corresponding to the invariance of time translation and space translation, There is also time-space translation invariance; therefore, there is an energy-momentum conservation law. According to this conservation law, the mass-energy relationship can be derived. This relationship is extremely basic in atomic physics and nuclear physics.
The principle of special relativity requires that all physical laws have the same form for inertial reference frames. However, incorporating the law of gravity into this requirement is inconsistent 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 reference system, only local inertial systems exist at any space-time point; between local inertial systems at different space-time points, through inertia Forces or gravity are interconnected. The space-time with the existence of inertial force is still a flat four-dimensional Minkowski space-time.
The space-time in which the gravitational field exists is no longer straight, but is a four-dimensional curved space-time, and its geometric properties are described by four-dimensional Riemannian geometry with a sign difference in the metric. The degree of curvature of spacetime is determined by the energy-momentum tensor of matter (objects or fields) in it and its motion, through the gravitational field equation.
In the general theory of relativity, time-space is no longer just a "stage" for the movement of objects or fields. Curved time-space itself is a gravitational field. The properties of time-space that characterize gravity are closely related to the properties of the objects and fields that move in it.
On the one hand, the energy-momentum of the motion of objects and fields serves as the source of the gravitational field, and the strength of the gravitational field is determined through the field equation, that is, the degree of curvature of space and time; on the other hand, the geometric properties of curved space and time also determine the objects and fields that move in it. nature of movement.
For example, as the sun is the source of the gravitational field, its mass causes the space-time where the sun is located to bend, and the degree of curvature represents the strength of the sun's gravitational field. The trajectory of Mercury, which is closest to the sun, is most affected, and starlight passing through the edge of the sun will also be deflected, and so on.
Shortly after the general theory of relativity was proposed, astronomical observations showed that the theoretical calculations of general relativity were consistent with the observational results.
The understanding of space and time has always been closely related to the understanding of the universe. Modern cosmology is based on cosmological principles and Einstein's gravitational field equations.
The principle of cosmology holds that the universe as a whole evolves in time, that is, there is an arrow of time, and it is uniform and isotropic in space.
The spatial position and momentum, time and energy of the system described by quantum mechanics cannot be measured accurately at the same time. They satisfy the uncertainty relationship; classical orbits no longer have precise meaning, etc. There has been a debate on how to understand quantum mechanics and the essence of related measurements. In the end of the world, research on quantum entanglement, quantum teleportation, quantum information, etc. also brings new problems and challenges to important concepts such as causality and locality that are closely related to time and space.
The combination of quantum mechanics and special relativity led to quantum electrodynamics, quantum field theory, electroweak unified model, and the standard model including quantum chromodynamics that describes the strong interaction. Although it has achieved great success, it also brings some challenges. of problems. While profoundly changing some important concepts about time and space, it also brings about some principle issues.
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, perturbation theory calculations of quantum electrodynamics can give results that are in precise agreement with experiments. However, this perturbation expansion is unreasonable. The mechanism of symmetry breaking causes the intermediate boson that transmits the weak interaction to gain mass. However, the vacuum expectation value of the Higgs field and the zero-point energy mentioned above are equivalent to the constant state of the universe in a certain sense, but their values are higher than those of astronomical observations. The cosmological constant is tens to more than a hundred orders of magnitude larger.
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